Mathematics College

please help me with these 5 math problems please hurry

Answers

Answer 1

1) A and D are linear equations while B and C are non linear

2) The rule of the equation is given by option C

3) The solution is option C

4) The area is option B

5) The standard form expressions are shown by option C

What is a linear equation?

We know that;

y = x + 3

-2x + y = 1

Then

x - y = -3 ---- (1)

-2x + y = 1 ---- (2)

x = -3 + y --- (3)

Substitute (3) into (2)

-2(-3 + y) + y = 1

6 - 2y + y = 1

6 -y = 1

-y = 1 -6

y = 5

Substitute y = 5 into (1)

x - 5 = -3

x = -3 + 5

x = 2

Thus the solution is (2, 5)

a^2 = 10^2 - 8^2

a = √100 - 64

a = 6

A = 1/2bh

A = 0.5 * 8 * 6

A = 24cm^2

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Related Questions

Compare the three decimals in each column. Circle the decimal that is greatest, and underline the decimal that is least. (4) 13.655 13.565 13.65 .

Answers

13.655 is the greatest.
13.565 is the least.

What is the sum of the polynomials?
17m-12n-1
+ 4-13m-12n

Answers

Answer: 4m-24n+3

Step-by-step explanation:

Expand and collect like terms!

[tex](17m-12n-1) + (4-13m-12n)\\= 17m - 12n - 1 + 4 - 13m - 12n\\=4m-24n+3[/tex]

Hope this helps <3

$500 is deposited in an account with 7%
interest rate, compounded continuously.
What is the balance after 10 years?
7
F = $[?]

Answers

The required balance after 10 years with continuous compounding at a 7% interest rate would be approximately $1007.

To calculate the balance after 10 years with a continuous compounding interest rate of 7%, we can use the formula for continuous compound interest:

[tex]F = P * e^{rt}[/tex]

Where:

F is the future balance or the final amount

P is the principal amount (initial deposit)

e is the base of the natural logarithm (approximately 2.71828)

r is the interest rate (expressed as a decimal)

t is the time in years

In this case, the initial deposit (principal) is $500, the interest rate is 7% (0.07 as a decimal), and the time is 10 years. Plugging these values into the formula, we get:

[tex]F = 500 * e^{0.07 * 10}[/tex]

Using a calculator, we can evaluate e^(0.07 * 10) ≈ 1.96728. Multiplying this by 500 gives us:

[tex]F=500 * 1.96728[/tex]
F = $1007

Therefore, the balance after 10 years with continuous compounding at a 7% interest rate would be approximately $1007.

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If you multiply or divide both sides of an inequality by a negative number you must_______ the inequality sign

Answers

Answer:

reverse or flip

Which of the following can you determine, when you use deduction and start
from a given set of rules and conditions?
OA. None of these
B. What may be false
C. What may be true
D. What must be true
R
SUBMIT

Answers

Answer: D

Step-by-step explanation:

When using deduction and starting from a given set of rules and conditions, you can determine what must be true. Therefore, the correct answer is:

D. What must be true

D because it’s the start so everything you have is true

I need this quickly please

Answers

(a)The arrow will reach a maximum height of 130 feet.

(b) After around 5 seconds, the arrow will strike the ground.

How to determine maximum height and time?

a) The maximum height of the arrow occurs at the vertex of the parabolic pathway. The x-coordinate of the vertex is given by -b/2a, where a=-16 and b=80. So, t= -b/2a = -80/(2x(-16)) = 2.5 seconds. To find the maximum height, plug in t=2.5 into the equation: h(2.5) = -16(2.5)² + 80(2.5) + 50 = 130 feet.

Therefore, the maximum height of the arrow is 130 feet.

b) To find the time it takes for the arrow to reach the ground, find the value of t when h(t)=0 (since the arrow hits the ground when h=0). We can use the quadratic formula to solve for t:

t = (-V₀ ± √(V₀² - 4ah₀)) / 2a

where a=-16, V₀=80, and h₀=50.

t = (-80 ± √(80² - 4x(-16)50)) / 2(-16) = 5 seconds or -1.5625 seconds

Since time can't be negative, the arrow will hit the ground after about 5 seconds.

c) To find the time it takes for the arrow to be 114 feet high, solve for t when h(t) = 114.

-16t² + 80t + 50 = 114

-16t² + 80t - 64 = 0

Dividing both sides by -16 gives:

t² - 5t + 4 = 0

Factoring gives:

(t-4)(t-1) = 0

So t=4 seconds or t=1 second.

Therefore, the arrow will be 114 feet high at 1 second and 4 seconds after launch.

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Find x,y if (x-1) 8i = 5 + (y² - 1) i

Answers

To solve for x and y, we can equate the real and imaginary parts of the equation.

Given: (x-1) 8i = 5 + (y² - 1) i

Real Part:
(x-1) 8 = 5
x-1 = 5/8
x = 5/8 + 1
x = 13/8

Imaginary Part:
(y² - 1) = 0
y² = 1
y = ±1

Therefore, the solutions are (x,y) = (13/8,1) and (13/8,-1).

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one
baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has
no effect, so the probability of a girl is 0.5. Assume that the groups consist of 45 couples. Complete parts (a) through (c)
below.

Answers

a) The value of the mean is μ = 22.5

The value of the standard deviation is σ = 3.5

b) The Value of 15 girls or fewer is significantly low.

The value of 30 girls or more is significantly high.

c) The result 36 is significantly high because 36 is greater than 30 girls. A result of 36 girls is not necessarily definitive proof of the method's effectiveness.

What is the standard deviation?

The standard deviation is a measure of the amount of variability or dispersion in a set of data values. It is a statistical measure that tells you how much, on average, the values in a dataset deviate from the mean or average value.

According to the given information

a) Since the probability of having a girl for each couple is 0.5, the number of girls each couple will have can be modeled as a binomial distribution with parameters n=1 and p=0.5.

Let X be the random variable denoting the number of girls in 45 couples. Then, X follows a binomial distribution with parameters n=45 and p=0.5.

The mean of a binomial distribution is given by μ = np, so in this case, the mean number of girls in a group of 45 couples is:

μ = np = 45 x 0.5 = 22.5

Therefore, we expect to see around 22-23 girls in a group of 45 couples.

The standard deviation of a binomial distribution is given by σ = √(np(1-p)), so in this case, the standard deviation of the number of girls in a group of 45 couples is:

σ = √(np(1-p)) = √(45 x 0.5 x 0.5) = 3.535

Therefore, we can expect the number of girls in a group of 45 couples to have a standard deviation of around 3.5.

b) In this case, we can assume that the number of girls in a group of 45 couples follows a normal distribution due to the Central Limit Theorem.

Using the standard deviation we found in the previous answer (σ = 3.535), we can calculate the values that separate the results that are significantly high and significantly low.

Significantly high:

Mean + 2σ = 22.5 + 2(3.535) = 29.57

Significantly low:

Mean - 2σ = 22.5 - 2(3.535) = 15.43

c) To determine if the result of 36 girls is significantly high, we need to compare it to the values we calculated in the previous answer.

Mean + 2σ = 22.5 + 2(3.535) = 29.57

Since 36 is greater than 29.57, we can conclude that the result of 36 girls is significantly high.

This suggests that the method of gender selection may be having an effect on the probability of having a girl. However, we cannot conclusively say this without conducting further analysis or testing.

It is also important to note that the result of 36 girls is not necessarily definitive proof of the method's effectiveness.

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The net income of the Apex Company was $110 million in 1995 and has been increasing by $30 million per year since. Over the same period, the net income of its
chief competitor, the Best Corporation, has been growing by $20 million per year, starting with $170 million in 1995. Which company earned more in 2004?
Apex Company
Best Corporation
In what year did/will Apex surpass Best?

Answers

Answer:

Step-by-step explanation:

In 2004, the net income of the Apex Company would be $110 million + ($30 million x 9 years) = $380 million.

The net income of the Best Corporation in 2004 would be $170 million + ($20 million x 9 years) = $350 million.

Therefore, Apex Company earned more in 2004.

To find the year when Apex surpassed Best, we need to set their net incomes equal and solve for time:

110 + 30t = 170 + 20t

10t = 60

t = 6

Therefore, Apex surpassed Best in the year 1995 + 6 = 2001.

Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?

A. d= 163 + t

B. d= 163/2 × t/2

C. d = 163t

D. d = 81.50t

Answers

Answer:

Step-by-step explanation:

163 money t for time 2 for 2hours

At the beginning of a population study, a city had 300,000 people. Each year since, the population has grown by 2.5%.
Let t be the number of years since start of the study. Let y be the city's population.
Write an exponential function showing the relationship between y and t.

Answers

The population growth can be modeled by an exponential function of the form:

y = ab^t

where y is the population, t is the number of years since the start of the study, a is the initial population, and b is the annual growth rate expressed as a decimal.

In this case, the initial population a is 300,000, and the annual growth rate is 2.5%, or 0.025 as a decimal. Therefore, the exponential function is:

y = 300,000 * (1 + 0.025)^t

Simplifying the expression inside the parentheses, we get:

y = 300,000 * 1.025^t

This is the exponential function that shows the relationship between the city's population y and the number of years t since the start of the study.

Shen bought a desk on sale for $218.40. This price was 72% less than the original price. What was the original price?

Answers

Answer:

780

Step-by-step explanation:

In this example we will call Original Price = y

72%=0.72

218.40=0.72*y

1-0.72=0.28

218.4÷0.28=780

9. In a certain school, of the students had over 80%
in math. If 465 students had 80% or less, how many
had over 80%?

Answers

Answer:

4 students

Step-by-step explanation:

Let's call the total number of students in the school "x". We know that a certain percentage of them had over 80% in math, and the rest (100% - that percentage) had 80% or less.

Let's call the percentage of students who had over 80% "p". Then, we can set up the following equation:

p% of x + (100% - p%) of x = x

We can simplify this to:

p/100 * x + (100 - p)/100 * x = x

Multiplying both sides by 100 to get rid of the denominators, we get:

px + (100 - p)x = 100x

Simplifying further:

px + 100x - px = 100x

100x = 465

x = 465/100 = 4.65 (rounded to two decimal places)

So the total number of students in the school is approximately 4.65. However, we can't have a fraction of a student, so let's round up to the nearest whole number and assume there are 5 students in the school.

Now we can use the information given to find the number of students who had over 80%:

"of the students had over 80% in math"

implies that

p% of x = number of students who had over 80%

So if we plug in the values we have:

p% of 5 = number of students who had over 80%

Simplifying:

0.01p * 5 = number of students who had over 80%

0.05p = number of students who had over 80%

We don't know the value of p, but we can solve for the number of students who had over 80% for different values of p. For example:

If p = 90, then:

0.05(90) = 4.5

So 4.5 students had over 80%. Since we can't have half a student, we can assume that 4 students had over 80%.

Alternatively, we can solve for p using the information given:

"of the students had over 80% in math"

implies that

p% of x = number of students who had over 80%

So:

p% of x = number of students who had over 80%

p% of 5 = number of students who had over 80%

0.01p * 5 = number of students who had over 80%

0.05p = number of students who had over 80%

We know that the number of students who had over 80% is some integer value between 0 and 5, inclusive. We can test different values of p within this range to see if they give us an integer solution:

If p = 90, then:

0.05(90) = 4.5

This is not an integer solution, so p = 90 is not the correct answer.

If p = 80, then:

0.05(80) = 4

This is an integer solution, so p = 80 is the correct answer. Therefore, 4 students had over 80%.

Let's use algebra to solve the problem. Let x be the total number of students in the school. Then, we know that the number of students who had over 80% in math is 0.6x (since 60% is the same as 0.6 as a decimal). We also know that 465 students had 80% or less in math, so the number of students who had over 80% in math is x - 465. Setting these two expressions equal to each other, we get:

0.6x = x - 465

Solving for x, we get:

0.4x = 465

x = 465 / 0.4

x = 1162.5

Since the number of students must be a whole number, we round up to the nearest whole number to get:

x = 1163

Therefore, the number of students who had over 80% in math is:

0.6x = 0.6 * 1163 = 698.

- Higher Order Thinking A sporting goods store manager was selling
a kayak set for a certain price. The manager offered the markdowns
shown on the right, making the one-day sale price of the kayak set $328.
Find the original selling price of the kayak set.
KANN &
SET
10%
OFF
TRRAY
EXTRA
30%
OFF

Answers

The original selling price of the kayak set, given the discounts, would be $ 520. 63

How to find the original selling price ?

The kayak is being sold such that a discount was offered of 10 % and then an additional discount was offered for 30 %.

The first step to the original price is:

= 328 / ( 1 - 30 %)

= 328 / 0. 70

= $ 468. 57

Then, the original price, would then account for the original discount of 10 % to become:

= 468. 57 / ( 1 - 10 %)

= 468. 57 / 0. 90

= $ 520. 63

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Numbers in the octal number system are numbered from 0 to 7. Based on the numbering pattern in the decimal number system, list the next 20 octal numbers

Answers

The next 20 octal numbers after 7 are: 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33

How to determine the next 20 octal numbers

In the decimal system, we count from 0 to 9 before moving to the next place value. In the octal system, we count from 0 to 7 before moving to the next place value. Therefore, the next 20 octal numbers after 7 are:

10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33

To understand how this pattern works, consider the decimal number 32. To convert it to octal, we can repeatedly divide it by 8 and record the remainders:

32 ÷ 8 = 4 with remainder 0

4 ÷ 8 = 0 with remainder 4

So the octal representation of 32 is 40. Similarly, we can convert any decimal number to octal by repeatedly dividing by 8 and recording the remainders.

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Write the coordinates for
each given point on the
coordinate plane below.

1. Point A
2. Point B
3. Point C
4. Point D

Answers

Answer:

Point A (-3,3)

Point B about (3,-2.75)

Point C (-4,-4)

Point D (1,0)

Step-by-step explanation:

A baseball player threw a baseball from the top of a stadium 48
feet above the ground, with an upward velocity of 32
feet per second. To find the time, t
, that it took for the ball to land on the ground, Greg solved the equation 0=−16t2+32t+48
. Using Greg's work, which choice is the correct time, t
, that it took for the ball to hit the ground?

0=−16t2+32t+48

0=16(−t2+2t+3)

0=−t2+2t+3

0=(−t+3)(t+1)

Answers

As per the given equation the correct time, t, that it took for the ball to hit the ground is t = 3 seconds.

What is an equation?

An equation is a mathematical statement that expresses the equality between two expressions. Equations typically include variables, which are symbols that represent unknown or varying quantities, and constants, which are known values.

An equation can be written in various forms, depending on the type of equation and the context in which it is used. Some common forms of equations include linear equations, quadratic equations, and polynomial equations.

For example, the equation x + 5 = 10 is a linear equation that has one variable, x. It can be solved by subtracting 5 from both sides of the equation to get x = 5.

A quadratic equation, such as x² + 2x + 1 = 0, has a variable raised to the second power. It can be solved using the quadratic formula or by factoring.

According to the given information

To solve the equation 0=−16t²+32t+48, Greg factored out a common factor of -16 from all three terms to get:

0 = -16(t² - 2t - 3)

Then, he factored the quadratic expression inside the parentheses as:

0 = -16(t - 3)(t + 1)

This gives us two solutions for t: t = 3 and t = -1.

However, we can discard the solution t = -1, since time cannot be negative in this context. Therefore, the correct time, t, that it took for the ball to hit the ground is t = 3 seconds.

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At the beach, Trevor and his sister both built sandcastles and then measured their heights. Trevor's sandcastle was 1/2 of a foot tall and his sister's was 1/5 of a foot tall. How much taller was Trevor's sandcastle than his sister's?

Answers

The height of Trevor's sandcastle is 3/10 foot taller than his sister's.

Given that, Trevor's sandcastle was 1/2 of a foot tall and his sister's was 1/5 of a foot tall.

Difference in the height of sandcastles = 1/2 - 1/5

= 5/10 - 2/10

= (5-2)/10

= 3/10

So, the difference in heights = 3/10 foot

Therefore, the height of Trevor's sandcastle is 3/10 foot taller than his sister's.

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All eleven letters from the word MATHEMATICS are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having the letter C written on it?

Answers

The odds against the paper having the letter C written on it is 10 : 11

What are the odds against the paper having the letter C written on it?

From the question, we have the following parameters that can be used in our computation:

MATHEMATICS

In the above word, we have

Letter C = 1

letters = 11

So, the probability of C is

Probability = 1/11

When converted to odds we have

Odds = Letter - Letter C : Letters

Substitute the known values in the above equation, so, we have the following representation

Odds = 11 - 1 : 11

Evaluate

Odds = 10 : 11

Hence, the odds is 10 : 11

Answers

If the recipe requires 3(1/2) pounds of flour for every (3/4) cups of sugar, then for 1 cup of sugar , Joseph should use 4.67 pounds of flour.

A "Proportion" is defined as a statement that two fractions are equal. It expresses the relationship between two quantities that are in the same ratio.

To solve the problem, we set up a proportion to relate the amount of flour to the amount of sugar:

We know that, recipe requires 3(1/2) pounds of flour for every (3/4) cups of sugar,

Which means,

⇒ (3.5 pounds of flour)/(0.75 cups of sugar) = (x pounds of flour)/(1 cup of sugar),

where x is = amount of flour needed for 1 cup of sugar.

We "cross-multiply" and simplify;

⇒ 3.5 × 1 = 0.75 × "x" pounds of flour,

⇒ 3.5/0.75 = x,

⇒ x ≈ 4.67 pounds of flour,

Therefore, Joseph should use 4.67 pounds of flour for 1 cup of sugar.

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A stack of two hundred eighty cards is placed next to a ruler, and the height of stack is measured to be 7/ 8 inches. How thick is one card?

Answers

In a case whereby stack of two hundred eighty cards is placed next to a ruler, and the height of stack is measured to be 7/ 8 inches the thickness of one card is 1/320 inches

How can the thickness be known?

Based on the provided information, two hundred eighty cards is placed next to a ruler ten we can set up the expression as

( 7/ 8) / 280

7/ 8 * 1/280

1/320

Therefore, based on the given information, this implies that Each card is 1/320 inches

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Find the solution to the systems \frac{m}{5}+\frac{n}{3}=0,\frac{m}{10}-\frac{7n}{6}=4

Answers

The two points on the line are (5, -9/5) and (-5/3, 3).

The other point on the line is (0, -12/7).

What is system of equations?

The equation [tex]\frac{m}{5} +\frac{n}{3} =0[/tex] can be rewritten as:

3m + 5n = 0

When m=5:

3m + 5n = 0

3(5) + 5n = 0

n = -9/5

Simplify the above equation,

When n=3:

3m + 5n = 0

3m + 5(3) = 0

m = -5/3

the two points on the line are (5, -9/5) and (-5/3, 3)

The equation [tex]\frac{m}{10} -\frac{7n}{6} =4[/tex] can be simplified as follows:

m/10 - 7n/6 = 4

m/10 = 7n/6 + 4

m = 70n/6 + 40

m = 35n/3 + 20

When n=0:

m = 35n/3 + 20

m = 20

So, the point on the line is (20, 0).

When m=0:

35n/3 + 20 = 0

35n/3 = -20

n = -12/7

So, the other point on the line is (0, -12/7).

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1. Each person in a random sample of 1.026 adults in the United States was asked the following question "Based on what you know about the Social Security System today, what would you like Congress and the President to do during this next year? The response choice and the percentages selecting them are shown below
Completely overhaul the system 19%
Make some major changes 39%
Make some minor adjustments 30%
Leave the system the way it is now
No opinion 1%

Find a 95% confidence interval for the proportion of all United States adults who would respond "Make some major changes to the question
a. Identify the variables needed to solve the problem.
b. Can a normal distribution be used to approximate this data Justify your evidence. c. Find the standard deviation
d. Calculate the point estimate and margin of error
e. calculate the confidence interval

Answers

Answer:

Step-by-step explanation:

a. Variables needed to solve the problem:

Sample size: n = 1,026

Proportion of the sample that responded "Make some major changes": p = 0.39

Confidence level: 95%

b. To determine if a normal distribution can be used to approximate the data, we need to check if the sample size is large enough to meet the requirements for a normal approximation. The sample size should be at least 10 times larger than the number of successes (np) and 10 times larger than the number of failures (n(1-p)). In this case, we have:

np = 1026 x 0.39 = 399.14

n(1-p) = 1026 x 0.61 = 626.86

Both np and n(1-p) are greater than 10, so we can assume that a normal distribution can be used to approximate the data.

c. The standard deviation of the proportion can be calculated using the following formula:

standard deviation = sqrt(p(1-p) / n)

standard deviation = sqrt(0.39 x 0.61 / 1026) = 0.024

d. The point estimate of the proportion of all United States adults who would respond "Make some major changes" is simply the sample proportion, which is p = 0.39. The margin of error can be calculated using the following formula:

margin of error = z* * standard deviation

where z* is the z-score associated with the 95% confidence level. Using a standard normal distribution table or a calculator, we find that the z-score for a 95% confidence level is approximately 1.96. Therefore:

margin of error = 1.96 * 0.024 = 0.047

e. The confidence interval can be calculated using the following formula:

confidence interval = point estimate ± margin of error

confidence interval = 0.39 ± 0.047

confidence interval = (0.343, 0.437)

Therefore, we are 95% confident that the proportion of all United States adults who would respond "Make some major changes" is between 0.343 and 0.437.

If you know 4 parts (angles and sides) of one triangle are congruent to the
corresponding 4 parts of another triangle, are the triangles congruent? Why?

Answers

Answer: Yes, the triangles are congruent.

Step-by-step explanation:

According to the Side-Angle-Side (SAS) congruence theorem, if two triangles have two pairs of corresponding sides that are congruent and the included angle between those sides is also congruent, then the triangles are congruent.

In this case, we know that four parts (angles and sides) of one triangle are congruent to the corresponding four parts of another triangle. This means that two pairs of corresponding sides are congruent (since corresponding sides are equal) and the included angles between those sides are also congruent (since corresponding angles are equal). Therefore, the triangles satisfy the conditions of the SAS congruence theorem and are congruent.

It's important to note that this applies only to two triangles with exactly the same four congruent parts. If there is even one part that is not congruent between the two triangles, they cannot be proven to be congruent just by these means alone.

Answer:

If you know that 4 parts (angles and sides) of one triangle are congruent to the corresponding 4 parts of another triangle, then the triangles are congruent by the Side-Angle-Side (SAS) Congruence Postulate. This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

The SAS postulate is one of five ways to prove that two triangles are congruent. The other four ways are Angle-Side-Angle (ASA), Side-Side-Side (SSS), Hypotenuse-Leg (HL), and Reflexive Property of Congruence.

Please help me with this math question

Answers

The first three terms of the expression (2 · x + 1 / x)¹² are 4096 · x¹², 24576 · x¹⁰ and 67584 · x⁸, respectively.

How to determine the first three terms of the power of a binomial

In this problem we find the case of a expression of the form (a + b)ⁿ, where any term of the expression can be found by binomial theorem:

[tex](a + b)^{n} = \sum\limits_{k = 0}^{n} \frac {n!}{k! \cdot (n - k)!}\cdot a^{n - k}\cdot b^{k}[/tex]

Where:

a, b - Coefficients of the binomial.n - Power of the binomial. k - Index of the term of the expanded form of the binomial.

If we know that a = 2 · x, b = 1 / x and 12, then the first three terms of the power of the binomial are, respectively:

n = 0

[tex]C_{0} = \frac{12!}{0! \cdot (12 - 0)!}\cdot (2\cdot x)^{12 - 0} \cdot (\frac {1}{x})^{0}[/tex]

C₀ = 4096 · x¹²

n = 1

[tex]C_{1} = \frac{12!}{1! \cdot (12 - 1)!}\cdot (2\cdot x)^{12 - 1} \cdot (\frac {1}{x})^{1}[/tex]

C₁ = 12 · (2048 · x¹¹) · (1 / x)

C₁ = 24576 · x¹⁰

n = 2

[tex]C_{2} = \frac{12!}{2! \cdot (12 - 2)!}\cdot (2\cdot x)^{12 - 2} \cdot (\frac {1}{x})^{2}[/tex]

C₂ = 66 · (1024 · x¹⁰) · ( 1 / x²)

C₂ = 67584 · x⁸

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Find the perimeter and area of a square if the length of its diagonal is 16 mm. Round your answers to the nearest tenth. (Hint: Draw and label the square)

Answers

The solution is : the perimeter and area of a square if the length of its diagonal is 16 mm is, 45.3 mm and 512mm².

Here, we have,

Use the basic 45-45-90 triangle with side length 1 as the building block here. If the length of one side is 1, then the perimeter is 1 + 1 + 1 + 1, or 4, and the length of the diagonal is √2.

We are told that the length of the diagonal of the given square is 16 m.

Determine the length of one side of this square, using an equation of proportions:

16 x

------ = -------

√2 1

Then (√2)x = 16, and x = -----------

√2

The perimeter of the given square (with diagonal 16 mm) is 4 times the side length found above, or:

16 16

4 ---------- = (2)(2) ----------- = (2)(√2)(16) = 32√2 (all measurements in mm)

√2 √2

This perimeter, rounded to the nearest tenth, is 45.3 mm.

so, area of the square is:

(16/√2)² = 512mm².

Hence, The solution is : the perimeter and area of a square if the length of its diagonal is 16 mm is, 45.3 mm and 512mm².

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Determine the function is positive, negative, increasing, or decreasing. Then describe the end behavior of the function.

Answers

The graph is positive and increases as the value of x increases.

What is the behavior of graph of y = √(4x)?

The behavior of the graph of y = √(4x) is determined by substituting some value of x into the function and check the corresponding value of y.

When x = 0, the value of y is calculated as;

y = √(4(0))

y = 0

When x = 1, the value of y is calculated as;

y = √(4(1))

y = 2

When x = 4, the value of y is calculated as;

y = √(4(4))

y = 4

When x = 9, the value of y is calculated as;

y = √(4(9))

y = 6

From the data above, the value of y increases as x increases, although not at equal increment.

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brainliest and 20 point goes to whoever shows work that i can understand

Answers

Answer:

9. 40 = 2πr

r = 20/π inches = 6.4 inches

d = 40/π inches = 12.7 inches

10. 256 = 2πr

r = 128/π feet = 40.7 feet

d = 256/π feet = 81.5 feet

If the length of BE is 3x-11 and the length of CD is 9x - 43, what is the length of CD?

Answers

The value of line CD is 20

How to determine the value

From the diagram shown, we have that;

Line BE = 3x - 11

Line CD = 9x - 43

Note that the length of line BE is half the length of line CD

this is represented as;

2BE = CD

Now, substitute the values

2(3x - 11) = 9x - 43

expand the bracket

6x - 22 = 9x - 43

collect the lie terms

6x - 9x = -43 + 22

-3x = -21

Make 'x' the subject

x = 7

Then, CD = 9(7) - 43 = 20

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What is the length of side c? (Hint: There are 2 angles and 2 sides)

Answers

The length of side c is approximately 4.62 units.

How to solve

Calculating the value of side c can be done by applying the Law of Sines on two angles and two sides.

Initially, determining angle C is necessary:

The corresponding formula for Angle C: 180° - (Angle A + Angle B) evaluates to 90° after substituting in reference values; 60°, and 30° respectively.

Implementing the Law of Sines culminates in this expression:

a/sin(A) = b/sin(B) = c/sin(C)

Replace with known angles and evaluate as follows:

Since the measures are known;

c/sin(C) = a/sin(A).

Subsequently,

by simple algebra c= a * sin(C) / sin(A) leads to desired outcome.

Putting relevant points into the equation above gives:

c = 4 * sin(90°) / sin(60°)

By using sine values from a calculator:

the preceding expression becomes,

c = 4 * 1 / (sqrt(3)/2)

After solving for c:

c = 8 / sqrt(3)

Using square root's rationalization: multiply numerator, and denominator by √3 resulting in

c = (8 * sqrt(3)) / 3

The length of side c is approximately 4.62 units.