What is the area, in square centimeters, of an 8.5 inch by 11 inch sheet of paper?A) 94 cm2 B) 240 cm2 C) 420 cm2 D) 6.0 × 102 cm2 E) 1.2 × 104 cm2

Answers

Answer 1

The square of the centimeter of the area is calculated by the square of the centimeter. The area of the rectangle is calculated by the formula width x length. So the rectangles area is 94cm  

Squares have only one side that is squared to find the area of the shape. But in rectangle there will be two sides given that width and length of the shape. So to find the area the width and the length of the rectangle is given so the numerical must be multiplied. In the given question the width of the rectangle is 8.5 and the length of the rectangle is 11.

o the area of the rectangle can be found by the formula= w x l

=8.5 x 11

=93.5

approximately can be taken as 94 cm.

A rectangle can is a four sided shape that includes the length, width and height and that opposites sides are equal in the rectangle. The adjacent sides of the rectangle is perpendicular and the angle is right angle that is it is measured as 90 degree. A rectangle can be a parallelogram but parallelogram can not be equal to the rectangle.

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The question has an area because the square because the square has only one side and the area of the square can be found by squaring one side of square. So the actual question should be What is the area, in rectangle centimeters, of an 8.5 inch by 11 inch sheet of paper?


Related Questions

What is the solution of the inequality of -0.4x1.2 >0.8 ?
A. x<-5
B. x<-1
C. x<-0.8
d. x>5
Please answer and give out a step-by-step explanation! Thank you :)

Answers

Answer:

A. x<-5

Step-by-step explanation:

-0.4x - 1.2 > 0.8

-0.4x > 2

x < -5

So, the answer is A. x<-5

the table below shows the summary for weights of 7 people before a diet program and after. the weight lost by each person was also recorded and summarized in the table below. mean standard deviation before 204.71 18.117 after 189.71 18.273 weight loss 15 3.786 find a 95% confidence interval for the true mean weights loss.

Answers

The 95% confidence interval for the true mean weight loss is (11.168, 18.832).

To find the 95% confidence interval for the true mean weight loss, we can use the formula:

CI = x(bar) ± t*(s/√n)

where:

x(bar) = sample mean weight loss

s = sample standard deviation of weight loss

n = sample size

t = t-value from the t-distribution table with (n-1) degrees of freedom and a 95% confidence level

Using the values given in the table, we have:

x(bar) = 15

s = 3.786

n = 7

The t-value for a 95% confidence level with 6 degrees of freedom (n-1) is 2.447.

Substituting these values into the formula, we get:

CI = 15 ± 2.447*(3.786/√7)

CI = 15 ± 3.832

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Choose ALL answers that describe the quadrilateral

Answers

Answer:

All of the above.

Quadrilateral's must have at the maximum 4 equal sides, or the minimum 2 equal sides.

a square has 4 equal sides.

a rectangle has 2 equal side. (that add up to 4 because each side is a pair of 2)

a rhombus can be a quadrlaterial depending on the shape.

a parrellelogram mostly have atleast 2 equal sides.

and a trapezoid mostly has atleast 2 equal sides.

Hope this helps!

A(n) ______ design compares different independent variable levels by using homogeneous groups of experimental units.

Answers

A blocked design compares different independent variable levels by using homogeneous groups of experimental units.

In this type of experimental design, subjects are divided into homogeneous groups, or blocks, based on similar characteristics or traits. These blocks help to control or account for potential confounding variables that may affect the outcome of the experiment.

By grouping subjects into blocks, researchers can reduce the variability within each group and increase the accuracy of the experimental results. This allows for a more precise comparison of the effects of different levels of the independent variable on the dependent variable. Blocked designs are particularly useful when there are natural groupings within the experimental units or when the variability between units is high.

In summary, a blocked design is a powerful experimental tool that can help researchers account for potential confounding factors and reduce variability among experimental units. By doing so, it enables the accurate comparison of different levels of the independent variable, ultimately leading to more reliable and valid results.

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Choose an appropriate scale for the replica so that it will fit on a 8.5-by-11am j

Answers

To ensure that the replica will fit on an 8.5-by-11-inch paper, we need to choose a scale that will result in dimensions that are smaller than or equal to 8.5 inches by 11 inches.

Choosing an appropriate scale for a replica depends on the size of the original object and the desired size of the replica. To fit a replica on an 8.5-by-11-inch paper, we need to determine the maximum size that the replica can be while still fitting on the paper.

One common method for determining the appropriate scale is to measure the dimensions of the original object and then divide them by the desired size of the replica. For example, if the original object is 20 inches wide and we want to create a replica that is 8 inches wide, the scale would be 20/8, or 2.5.

In order to fit the replica on an 8.5-by-11-inch paper, we need to make sure that the dimensions of the replica are smaller than or equal to 8.5 inches by 11 inches.

We can use the scale factor to determine the maximum dimensions of the replica. For example, if the scale factor is 2.5 and we want the replica to be 8 inches wide, the maximum height of the replica would be 8/2.5, or 3.2 inches.

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Word Problem: The company For The Ocean has already cleared the earth's oceans of 125 million pounds of trash. They are committed to picking up exactly 550 pounds of trash per day. Write an equation to represent total "p" pounds of trash removed as a function of number of "d" days passed.

Answers

The equation to represent total "p" pounds of trash removed as a function of the number of "d" days passed is:

p = 550d + 125,000,000

What is 2^6*2^5 is other exponent?

Answers

Answer:

below

Step-by-step explanation:

Yes, there is another exponent.

When you are multiplying exponents, you add the exponents.

So from the equation 2^6 x 2^5, you can keep the 2 the same, as this is the base:

2^11

and add the exponents (6+5)

To check:

2^6=64

2^5=32

64x32=2048

2^11=2048

So, 2^11 is equivalent to your equation.  Hope this helps ;)

Find the value of x. If a segment looks like a tangent, it is a tangent.

Answers

We got x = 84.50 by using Pythagorean theorem.

What is the Pythagorean theorem in plain English?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.

angle of semicircle is always be 90°.

[tex]115^2 = 78^2 + x^2[/tex]

[tex]13225 = 6084 + x^2[/tex]

[tex]x^2 = 13225- 6084[/tex]

[tex]= 7141[/tex]

[tex]x = \sqrt{7141}[/tex]

[tex]x = 84.50[/tex]

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Evaluate (-25)^1/2
Answers:
a) 625
b)-625
c) not a real number

Answers

Then the answer is C. not a real number

How to evaluate that?

An exponent of 1/2 is equivalent to the square root, so we can write:

√-25

That is the square root of a negative number, so we will get the complex numbers ±i

Then the answer is C.

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Val needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 58-m​-by-58-m square. Val says the area is 1917.48 m. Find the area enclosed by the figure. Use 3.14 for π. What error might Val have​ made?

Answers

The area that is enclosed by the figure which is being observed by Val would be = 3,364m²

How to calculate the area of the given figure?

To calculate the area of the enclosed figure, the area of 2 circles and a square should be calculated and added together.

The area of a circle = πr²

r = 58/2 = 49

area = 3.14×49×49

= 7539.14×2

= 15078.28m

Area of the enclosed region = 58×58 = 3,364m²

Therefore, Val is wrong with the area of he calculated.

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What is 4.5621 rounded to the nearest tenth?

Answers

The answer is: 4.6

Reason?: because 4.56 you round up the 6 because if is not 1-4 it would of been 4.5 but because it’s 5-9 it’s 4.6

a continuous random variable x has a uniform distribution between 5 and 25 (inclusive), then p(x = 15) = 0.05. a. true b. false

Answers

Answer:

Step-by-step explanation:

The probability of a continuous random variable taking any specific value is always zero, so the statement p(x = 15) = 0.05 is false.

assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $3,403 per hour and a standard deviation of $398.what is the operating cost for the lowest 2% of the airplanes?

Answers

Answer:

$2,611.9.

Step-by-step explanation:

To find the operating cost for the lowest 2% of the airplanes, we need to find the corresponding z-score from the standard normal distribution using a z-table.

Using the formula:

z = (x - μ) / σ

where x is the cost we are interested in, μ is the mean cost, and σ is the standard deviation.

For the lowest 2% of airplanes, the z-score can be found by looking up the area to the left of z in the z-table. This area is 0.02.

Looking up 0.02 in the z-table gives a z-score of approximately -2.05.

So we have:

-2.05 = (x - 3403) / 398

Solving for x, we get:

x = -2.05 * 398 + 3403 = $2,611.9

Therefore, the operating cost for the lowest 2% of the airplanes is approximately $2,611.9.

How do you express 0.000 000 000 000 1 in exponential form.

Answers

Answer:

1 x 10^-12

Step-by-step explanation:

....

10^-13 because it moves 13 decimal places left

A. Draw and write the correct answer in each letters. (3 points each)
A={ pink, brown, white, blue}
B={ pink, yellow, red, green}
C={ pink, red, yellow, brown, white, purple}
A. Find AUB
B. Find AnB
C. Find AnBnc
D. Find AUBUC
E. Find (AUB)'
F. Find (ANB)'
G. Venn diagram (Draw

Answers

A. AUB = {pink, brown, white, blue, yellow, red, green, purple}

B. AnB = {pink}

C. AnBnc = {brown, white, blue}

D. AUBUC = {pink, brown, white, blue, yellow, red, green, purple}

E. (AUB)' = {black} (assuming black is the universal set and A and B are not complements of each other)

F. (ANB)' = {brown, white, blue, yellow, red, green, purple}

G. [Please refer to the attached image for the Venn diagram]

What is the mean of this data set?
Please help ASAP giving Brainlyist (I don’t know how to spell it) it is not 24 cm

Answers

The closest option is (b) 23 12/15.

What are mean in statistics?

Mean: The average of a set of values, is calculated by adding up all the values in the set and dividing by the total number of values.

To find the mean (average) of the data set, we need to first find the sum of all the lengths of roses multiplied by their respective frequencies, and then divide by the total number of roses:

(22 x 2) + (23 x 4) + (24 x 5) + (25 x 3) + (26 x 1) = 344

Total number of roses = 2 + 4 + 5 + 3 + 1 = 15

Mean = Sum of all lengths / Total number of roses = 344 / 15 ≈ 22.93 cm

Rounding to the nearest whole number, the mean length of roses in this data set is 23 cm. Therefore, the closest option is (b) 23 12/15.

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WILL MARK AS BRAINLEIST!! ASAP PLEASE!!
Question in picture
I have more questions on my account if u can help me out!!

Answers

For the region above x + 3y = 9 and below x + 9 = y², we have:

a = 18, b = -9, f(x) = (y² - 9)/3, and g(x) = (9 - x)/3.

For single integration: α = -6, β = 3 and h(y) = [(9 - y²)/3 - (y² - 9)].

What is the area bounded by the curves?

To solve this problem, we first need to find the intersection points of the two curves x + 3y = 9 and x + 9 = y². We can do this by solving the system of equations:

x + 3y = 9

x + 9 = y²

Rearranging the first equation, we get:

x = 9 - 3y

Substituting this expression for x into the second equation, we get:

9 - 3y + 9 = y²

Simplifying, we get:

y² - 3y - 18 = 0

Factorizing, we get:

(y - 6)(y + 3) = 0

So the solutions are:

y = 6 or y = -3

Substituting these values of y into the equation x + 3y = 9, we get:

When y = 6, x = -9

When y = -3, x = 18

So the intersection points of the two curves are (-9, 6) and (18, -3).

Now we can find the area between the two curves by splitting it into two regions: the region above the curve x + 3y = 9 and below the curve x + 9 = y², and the region below the curve x + 3y = 9 and above the curve x + 9 = y².

For the region above x + 3y = 9 and below x + 9 = y², we have:

a = 18

b = -9

f(x) = (y² - 9)/3

g(x) = (9 - x)/3

Alternatively, to compute the area between the two curves x + 3y = 9 and x + 9 = y² using a single integral, we need to express the area as a function of y instead of x.

We can rearrange the equations x + 3y = 9 and x + 9 = y² to get:

x = 9 - 3y

x = y² - 9

Setting these two expressions equal to each other, we get:

9 - 3y = y² - 9

Simplifying, we get:

y² + 3y - 18 = 0

Factorizing, we get:

(y + 6)(y - 3) = 0

So the solutions are:

y = -6 or y = 3

Substituting these values of y into the equation x + 3y = 9, we get:

When y = -6, x = 27

When y = 3, x = 0

So the intersection points of the two curves are (27, -6) and (0, 3).

The area between the curves can be expressed as the difference between the integrals of the curves' respective functions with respect to y, since the curves are better expressed in terms of y.

The function representing the curve x + 3y = 9 in terms of y is:

x = 9 - 3y

We can rearrange this equation to get:

y = (9 - x)/3

Substituting x = y² - 9, we get:

y = (9 - y² + 9)/3

Simplifying, we get:

y² + 3y - 18 = 0

This is the same equation we obtained before, so we know that the bounds of integration are -6 and 3.

The function representing the curve x + 9 = y² in terms of y is:

x = y² - 9

Substituting this expression into the formula for the area of a region between two curves, we get:

Area = ∫(y=α)^(y=β) [(9 - y²)/3 - (y² - 9)] dy

Where;

α = -6 and β = 3 are the bounds of integration, and

the integrand [(9 - y²)/3 - (y² - 9)] represents the difference between the y-values of the two curves at a given x-value.

Simplifying the integrand, we get:

Area = ∫(y=-6)^(y=3) (18 - 2y²)/3 dy

Integrating, we get:

Area = [(6y - (2/3)y³)/3] |(y=-6)^(y=3)

Plugging in the limits of integration, we get:

Area = [(18 - 216)/3] - [(-36 + 216)/3]

Simplifying, we get:

Area = 66

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True or False : The environmental lapse rate is usually the same as the dry adiabatic rate

Answers

False. The environmental lapse rate, which changes based on various variables like humidity and atmospheric stability, is the real rate at which temperature decreases with increasing altitude in the atmosphere.

The pace at which a parcel of dry air cools as it ascends in the atmosphere, on the other hand, is known as the dry adiabatic rate and is set at around 9.8 degrees Celsius per 1000 meters of ascension.

Although it is not often the same, the environmental lapse rate can occasionally be comparable to the dry adiabatic rate. The environmental lapse rate can differ from the dry adiabatic rate due to things like the presence of moisture or atmospheric instability.

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Question 9(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)

A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.

Which graphical representation would be best for his data?

Stem-and-leaf plot
Histogram
Circle graph
Box plot

Answers

The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. answer is option (a).

What is a histogram?

In a histogram, which is a graphical depiction of the distribution of a set of continuous or discrete data, the height of a bar above the bin on the x-axis represents the frequency or count of the data falling within each bin. On the y-axis of the histogram, the frequency or count of the data points that fall into each bin is displayed.

The most useful visual representation of the teacher's data on the preferred subjects of 100 kids at the school would be a histogram. In a histogram, bars are used to illustrate the frequency distribution of a group of continuous or discrete data points.

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Find the mean of the following data 0,5,30,25,16,18,19,26,0,20,28 A. 0 B. 18 C. 19 D. 17

Answers

The mean of the following data 0,5,30,25,16,18,19,26,0,20,28 is 17.

Hence option D is the correct option.

Mean is the average value of a given set of data. It is calculated by the formula,

Mean =  {Summation of all the values in the data set} / {Number of observations is the data set}

That is, Mean = {Σ all values in the data set} / {number of observations}

The given data set is as follows,

0,5,30,25,16,18,19,26,0,20,28

The number of observations in the data set is 11.

The summation of all the values in the data set is = {0 + 5 + 30 + 25 +
16 + 18 + 19 +26 + 0 + 20 + 28} = 187

Therefore, by applying  the formula of Mean we get

Mean = 187/ 11 = 17

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PLEASE HELP I have no idea how to do this.. our teacher hasnt been here all week.. and I have no clue what this is..

solve for the value of V (9v+3)° 60°​

Answers

The value of v is 13 degrees.

What are supplementary angles?

Supplementary angles are a set of given measure of angles which add up to 180 degrees. Thus producing a measure of the sum of angles on a straight line.

To determine the value of v in the given diagram, we have;

60 + (9v + 3) = 180       (sum of angles on a straight line)

So that;

9v + 3 = 1890 - 60

9v + 3 = 120

9v = 120 - 3

    = 117

v = 117/ 9

  = 13

v = 13^o

The value of v in the question is 13 degrees.

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On Ernest Airlines, baggage cannot weigh more than 40 pounds. Devin packed 21 pounds of clothes and four packages which weighed a total of 7 pounds. Write an inequality for this scenario. Then solve and determine the weight that each package must be less

Answers

Inequality for this scenario

x ≤ 4.75

So, each package must weigh less than or equal to 4.75 pounds in order for Devin to stay within the weight limit of 40 pounds on Ernest Airlines.

HOW TO SOLVE AN INEQUALITY?

Let x be the weight of each package (in pounds).

The inequality for the scenario can be written as:

21 + 4x ≤ 40

This represents the total weight of Devin's clothes (21 pounds) plus the total weight of the four packages (4x pounds) cannot exceed the weight limit of 40 pounds on Ernest Airlines.

To solve for x, we can subtract 21 from both sides of the inequality:

4x ≤ 40 - 21

4x ≤ 19

Finally, we divide both sides by 4 to isolate x:

x ≤ 19 / 4

Let x be the weight of each package (in pounds).

The inequality for the scenario can be written as:

21 + 4x ≤ 40

This represents the total weight of Devin's clothes (21 pounds) plus the total weight of the four packages (4x pounds) cannot exceed the weight limit of 40 pounds on Ernest Airlines.

To solve for x, we can subtract 21 from both sides of the inequality:

4x ≤ 40 - 21

4x ≤ 19

Finally, we divide both sides by 4 to isolate x:

x ≤ 19 / 4

x ≤ 4.75

So, each package must weigh less than or equal to 4.75 pounds in order for Devin to stay within the weight limit of 40 pounds on Ernest Airlines.

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there was no red arc. so please help me on this. its for geometry ​

Answers

Answer:

21. x=70

22. x=15

*Not sure what the red arc is, but I found the value of x for both 21 and 22*

Step-by-step explanation:

Let's start with 21 first.

Line AB is a straight line, meaning the arc length of AB is 180 degrees.  So,

(2x-30)+x=180

let's solve:

3x-30=180

3x=210

x=70

I'm not sure what the red arc is, so I can't help you there.

Next, 22.

All the arcs in a complete circle need to add up to 360 degrees, so:

4x+6x+7x+7x=360

simplify first:

24x=360

let's solve:

x=15

Again, not sure where or what the red arc is, so can't help again.  I hope that the x values help.

The slope at [1,pi/2] from -8x^3/siny

Answers

As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.

what is slope ?

The slope of a line in mathematics serves as a gauge for how steep it is. Between any two locations on the line, it is the proportion of the shift in the vertical motion (y) to the shift in the horizontal position (x). If we take into account two points on a line, (x1, y1) and (x2, y2), we can use the following formula to get the slope of the line: slope equals (y2 - y1)/. (x2 - x1) . Depending on the line's direction, the inclination can be zero, positive, or negative. A line with a positive slope is moving upward from left to right, whereas one with a negative slope is moving downward.

given

Finding the derivative of the given function with respect to x can be our first step. By applying the quotient rule, we get:

F(x) = 8x 3 sin (y)

[tex][(sin(y))(-24x2)] = f'(x) - (-8x^3) (cos(y))(y')] / (sin(y))^2[/tex]

where the derivative of y with respect to x is denoted by y'.

We can change x=1 and y=pi/2 in the equation above since we are interested in the slope at the position [1, pi/2].

Due to the fact that cos(pi/2) = 0 and sin(pi/2) = 1, we can write:

[tex]f'(1) = [(1)(-24) (-24) - (-8)(1)(0)(y')] / (1)^2[/tex]

f'(1) = -24 + 0

f'(1) = -24

As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.

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on aurora ave the distance between thomas st to denny way is 0.2 miles. what is the distance between these two streets on broad st? show your work below and round your answer to the nearest tenth of a mile.

Answers

The distance between Thomas St and Denny Way on Broad St is approximately 0.2 miles (rounded to the nearest tenth of a mile).

To determine the distance between Thomas St and Denny Way on Broad St, we can use the Pythagorean theorem.

Let x be the distance between Thomas St and Denny Way on Broad St. We can draw a right triangle where the hypotenuse is 0.2 miles (the distance between Thomas St and Denny Way on Aurora Ave), and one leg is x (the distance between Thomas St and Denny Way on Broad St). The other leg is the distance between Aurora Ave and Broad St.

Using the Pythagorean theorem, we have:

[tex]0.2^2 = x^2 + d^2[/tex]

where d is the distance between Aurora Ave and Broad St.

Assuming d is negligible, we can solve for x:

[tex]x^2 = 0.2^2 - d^2x^2 = 0.2^2x = sqrt(0.2^2) = 0.2[/tex]

Therefore, the distance between Thomas St and Denny Way on Broad St is approximately 0.2 miles (rounded to the nearest tenth of a mile).

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least common multiple of 43 24 17

Answers

the least common multiple of 43, 24, and 17 is 87,672.To find the least common multiple (LCM) of three numbers, we first need to find their prime factorization.

what is prime factorization ?

Prime factorization is the process of finding the prime numbers that multiply together to give a given composite number. A composite number is any positive integer greater than 1 that is not itself a prime number.

In the given question,

To find the least common multiple (LCM) of three numbers, we first need to find their prime factorization.

Prime factorization of 43: 43 is a prime number, so its prime factorization is simply 43.

Prime factorization of 24: 24 can be factored as 2 × 2 × 2 × 3.

Prime factorization of 17: 17 is a prime number, so its prime factorization is simply 17.

Next, we find the highest power of each prime factor that appears in any of the three factorizations:

The prime factor 2 appears to the third power in the factorization of 24, and to the first power in the factorizations of 43 and 17.

The prime factor 3 appears to the first power in the factorization of 24, and to the zero power in the factorizations of 43 and 17.

The prime factor 17 appears to the first power in the factorization of 17, and to the zero power in the factorizations of 43 and 24.

The prime factor 43 appears to the first power in the factorization of 43, and to the zero power in the factorizations of 24 and 17.

Therefore, the LCM of 43, 24, and 17 is:

2³ × 3¹ × 17¹ × 43¹ = 87,672

Hence, the least common multiple of 43, 24, and 17 is 87,672.

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Simplify. 4 2/5 x 3 = ?

Answers

The answer for that question is 13.2

Answer:

66/5 or 13.2

Step-by-step explanation:

..........

LOOK AT PHOTO
5x+3> 10

Answers

The smallest integer value of x that would be a solution in the inequality would be x = 2.

How to find the smallest integer ?

To find the smallest integer value of x that satisfies the inequality 5x + 3 ≥ 10, first solve the inequality for x:

Subtract 3 from both sides:

5x ≥ 7

Divide by 5:

x ≥ 7/5

The inequality states that x must be greater than or equal to 7/5, which is equal to 1.4. Since we are looking for the smallest integer value, we should round up to the next integer, which is 2. Therefore, the smallest integer value of x that satisfies the inequality is x = 2.

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PLSSSSSSSSSSSSSSSS HELP I WILL MARK YOU BRAINLYEST

Answers

d.) refer to table— 2x+2= y
2x0+2=2
2x1+2=4
2x2+2=6
2x3+2=8

Isaiah is trying to find the height of a radio antenna on the roof of a local building. He stands at a horizontal distance of 20 meters from the building. The angle of elevation from his eyes to the roof ( (point � A ) ) is 32 ∘ ∘ , and the angle of elevation from his eyes to the top of the antenna ( (point � B ) ) is 43 ∘ ∘ . If his eyes are 1.62 meters from the ground, find the height of the antenna ( (the distance from point � A to point � B ) ). Round your answer to the nearest meter if necessary.

Answers

The height of the antenna is approximately 29 meters.

What is the angle of elevation?

The point of rise is a point that is framed between the even line and the view. An angle of elevation is formed when the line of sight extends upward from the horizontal line.

We should refer to the level of the structure as "h" and the level of the receiving wire "x". Two equations can be created with the help of the tangent function:

Since the elevation angle to the roof is 32 degrees,

tan(32) = h/20, and

tan(43) = (h+x)/20

because the elevation angle to the antenna's peak is 43 degrees.

We can solve for "h" in the first equation by multiplying both sides by 20:

h = 20 tan(32)

We can substitute this expression for "h" into the second equation:

tan(43) = (20 tan(32) + x)/20

Now we can solve for "x":

x = 20 tan(43) - 20 tan(32)

We can then add the height of Isaiah's eyes (1.62 meters) to get the total height of the antenna:

height = x + 1.62

Plugging in the values and using a calculator, we get:

height ≈ 28.7 meters

As a result, the antenna stands about 28.7 meters tall. The answer is 29 meters when rounded to the nearest meter.

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