Answer:
9 * -8
____ =-72/6
2 * 3
A pair of positive integers a and b is such that their greatest common divisor is 5 and their least common multiple is 55. Find the smallest possible value of a+b.
Answer:
Step-by-step explanation:
The greatest common divisor of two integers a and b is a divisor common to both integers that is greater than any other common divisor. The least common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b.
To find the smallest possible value of a+b, we can start by trying to find the smallest possible values of a and b that satisfy the given conditions.
Since the greatest common divisor of a and b is 5, we know that both a and b must be divisible by 5. We can write a = 5x and b = 5y, where x and y are positive integers.
The least common multiple of a and b is 55, so we know that both a and b must be factors of 55. We can write 55 as the product of its prime factors: 55 = 5 * 11. Since a is divisible by 5, we know that a must be equal to 5 or 25. Similarly, since b is divisible by 5, we know that b must be equal to 5 or 25.
There are four possible pairs of values for a and b: (5,5), (5,25), (25,5), and (25,25). The smallest of these is (5,5), which gives us a+b = 5+5 = 10. Therefore, the smallest possible value of a+b is 10.
question 1 options: what is the common difference in the sequence 7, 12, 17, 22, 27, ...? put the just the number in the blank.
The common difference in the sequence 7, 12, 17, 22, 27,… is that the difference between two numbers increases by five in the ascending order.
A sequence can be referred to or considered as the set of observations, which usually consists of numbers arranged in such a way that they described a common characteristic between them. A sequence can be exhaustive or inclusive, depending upon the numbers being used in the continuity of the sequence. It can also be said that a sequence is a logical arrangement.
Learn more about a sequence here:
https://brainly.com/question/21961097
#SPJ4
Complete question
what is the common difference in the sequence 7, 12, 17, 22, 27, ...?
find the curvature of r(t) = 3t, t2, t3 at the point (3, 1, 1).
The curvature of r(t) = 3t, t2, t3 at the point (3, 1, 1) is 0.178
In this question we need to find the curvature of r(t) = <3t, t^2, t^3> at the point (3, 1, 1).
The derivative of r(t) with respect to t is:
r'(t) = <3, 2t, 3t^2>
The point (3, 1, 1) corresponds to t = 1,
and r′(1) = <3, 2(1), 3(1)^2>
r'(1) = <3, 2, 3>
|r'(1)| = √(3^2 + 2^2 + 3^2)
|r'(1)| = √(9 + 4 + 9)
|r'(1)| = √(22)
|r'(1)| = 4.69
Now, r''(t) = <0, 2, 6t>
and r′'(1) = <0, 2, 6(1)>
r''(1) = <0, 2, 6>
r′(1) × r′′(1) = <0, 4, 18>
|r′(1) × r′′(1) |
= √(0^2 + 4^2 + 18^2)
= √(16 + 324)
= √340
= 18.44
So, the curvature of r(t) would be,
κ(1) = |r′(1) × r′′(1)| ÷ |r′(1)|^3
k(1) = 18.44 / 4.69³
k(1) = 0.178
Learn more about the curvature here:
https://brainly.com/question/30114042
#SPJ4
The cash price of a refrigerator is rs 34 500. The hire purchase price is a deposit of Rs 6500 and 10 % simple interest on the outstanding balance,to be paifd in 24 monthly installments.Calculate the amount of each monthly instalment.
Amount of each monthly statement is 1400.
According to question ,
Cash price of refrigerator =34500
Deposit money=6500
Outstanding money=28000
Rate of interest=10%
Time period=24 months or 2 years
∴Simple interest =(principal ×rate of interest×time)÷100
⇒(28000×10×2)÷100
⇒5600
∴The total amount to be paid in 2 years is 28000+5600 =33600
∴Amount to be paid in one month =33600÷24=1400
∴Amount of each monthly statement is 1400.
For more information regarding Simple interest
https://brainly.ph/question/6429208
green and yellow dye are mixed in a 5:6 ratio to make 44 litres of lime-coloured dye. A further 8 litres of yellow dye are added to the mixture.
What is the new ratio of green to yellow dye in its simplest form?
Answer:
62.5% or in decimal form 0.625
Step-by-step explanation:
An advertisement for a new toothpaste claims that it reduces cavities of children in their cavity-prone years. Cavities per year for this age group are normal with mean 3 and standard deviation 1. A study of 2,500 children who used this toothpaste found an average of 2. 95 cavities per child. Assume that the standard deviation of the number of cavities of a child using this new toothpaste remains equal to 1. (a) are these data strong enough, at the 5 percent level of significance, to establish the claim of the toothpaste advertisement? (b) do the data convince you to switch to this new toothpaste?.
At [tex]$5 \%$[/tex] level, the data is not strong enough to establish the claim of toothpaste advertisement.
It is recommended to switch to new toothpaste.
(a)
The null and alternative hypotheses are,
[tex]$$\begin{aligned}& H_0: \mu=3 \\& H_1: \mu < 3\end{aligned}$$[/tex]
Here, [tex]$\mu$[/tex] is the hypothesized mean.
Let the sample size be [tex]$n=2500$[/tex].
Let the sample mean be [tex]$\bar{x}=2.95$[/tex].
Let the population standard deviation be [tex]$\sigma=1$[/tex].
Since, the population standard deviation is known, one sample z-test is used to test the claim.
The test statistic is,
[tex]$$\begin{aligned}z & =\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \\= & \frac{2.95-3}{\frac{1}{\sqrt{2500}}} \\& =-2.5\end{aligned}$$[/tex]
So, the test statistic is, [tex]$z=-2.5$[/tex].
Let the level of significance be [tex]$\alpha=0.05$[/tex].
Find the critical value.
Using the standard normal distribution area tables, the left tail critical value is,
[tex]$$z_{0.05}=-1.645$$[/tex]
z score table attached at the end of solution.
The test statistic value is falls in the rejection region. Reject the null hypothesis. Therefore, it can be concluded that this does not support the null hypothesis at 5 percent level. So, at [tex]$5 \%$[/tex] level, the data is not strong enough to establish the claim of toothpaste advertisement.
(b)
The value of test statistic is also less than [tex]$-Z_{0.1}=-2.33$[/tex].
So, the claim cannot be established even at 1 percent level. It is recommended to switch to new toothpaste.
For more questions on standard deviation
https://brainly.com/question/29678689
#SPJ4
Help please
A.) (-12,-18)
B.) (18,12)
C.) (-18,-12)
D.) (12,-18)
I think the answer be 12 and -18 D
find a function f such that f '(x) = 3x3 and the line 81x + y = 0 is tangent to the graph of f.
To find the function, we need to find the values of x and y.
In the aforementioned example, x and y are the independent and dependent variables, respectively. A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).
As we know,
fx = 3x to the power 3
f(x) =
[tex]3x {}^{3 } \: dx \: + c \\ \\ fx = 3x { }^{4} \div 4 + c \\ \\ \\ \\ 3x {}^{3} = - 81 \\ \\ x \: = 243 \\ [/tex]
Hence x is 242
To know more about function please check the following link
https://brainly.com/question/29903905
#SPJ4
Help pls I put in a photo
Answer:
m∠D = 49°
m∠E = 41°
m∠F = 90°
Step-by-step explanation:
We know a triangle's angles add up to 180, so we can create an equation and solve for x. We also know the little box represents 90 degrees.
Given:
90° + 5x° + 14° + 3x° + 20° = 180°
Combine like terms:
8x° + 124° = 180°
Subtract 124 from both sides of the equation:
8x° = 56°
Divide both sides of the equation by 8:
x = 7
Now, we will plug this value of x back into the angles to solve. Again, the little box represents that Angle F is equal to 90 degrees.
m∠D = 5x° + 14° = 5(7)° + 14° = 49°
m∠E = 3x° + 20° = 3(7)° + 20° = 41°
m∠F = 90°
Mario and hi friend went to a movie on Saturday they left the houe at 5:15 PM. It took one hour and 20 minute to drive to the theater and they arrived 25 minute before the movie tarted. What time did the movie tart?
By applying the algebra concept, we can conclude that the movie that Mario and his friend watched starting at 7 PM
The use of algebra in everyday life.
Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve math problems. In everyday life, algebra is often used for financial planning, traveling time calculation, and so on.
In the above problem, we can take some notes as follows:
Departure time (x) = 5:15 PM
Travel time (t) = 1 hour 20 minutes
Arrival time (y) = 25 minutes
If z is the playing time of the movie, then z can be expressed mathematically in the following way:
z = x + t + y
= 5:15 + 1 hour 20 minutes + 25 minutes
= 6:60 PM or generally written 7:00 PM
To learn more about the simple concept of algebra, click here: https://brainly.com/question/28878526
#SPJ4
simplify 5 6/7 + (-2 1/3) + 1 5/6
answer fastttttttttttttttttttttttttttttttt
plssssssssssss 20 points
Solution is 225/42 or 5.35
According to question
5 6/7 + (-2 1/3) + 1 5/6
As it is a mixed fraction we will first solve it
To solve it denominator will get multiplied with the whole number and the solution will be get added to the numerator and the new numerator will get formed.
∴ 41/7 +(-7/3) + 11/6
⇒246-98+77/42. (LCM of 7,3,6 is 42)
⇒225/42
∴5.35
For more information regarding mixed fractions
https://brainly.com/question/12096281
(b) consider a set of points that are uniformly distributed on the interval [0,1]. is the statistical notion of an outlier as an infrequently observed value meaningful for this data?
No, the statistical notion of an outlier as an infrequently observed value is not meaningful for this data.
Since the points are uniformly distributed on the interval [0,1], they should all be observed with the same frequency. Therefore, there are no outlier values.The statistical notion of an outlier is an infrequently observed value, meaning that it is an observation that is far away from the rest of the data. For a set of points that are uniformly distributed on the interval [0,1], however, all the points should be observed with the same frequency since they are evenly spaced. Therefore, there is no outlier value and the statistical notion of an outlier is not meaningful for this data.
Learn more about statistics here
https://brainly.com/question/29093686
#SPJ4
Polynomial uing Remainder Theorem and Factor Theorem checking uing ynthetic diviion. X^4 - x^3 - 3x^2 4x 2 ÷ (x 2)
The remainder of the polynomial using the remainder theorem and factor theorem is 6.
Apply the remainder theorem,
When we divide a polynomial
f(x) by (x − c)
f(x) = (x − c)q(x) + r
f(c) = 0 + r
Here,
f(x)=(x−c)q(x)+rf(c)=0+r
and (x−c) is (x−(−2))
Therefore,
f(−2) = [tex](-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2[/tex]
= 16 + 8 − 12 − 8 + 2
= 6
Hence, the remainder of the polynomial using the remainder theorem is 6.
Whereas using the factor theorem and doing synthetic division, we get,
x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide
the coefficients of the polynomial as follows -
-2 | 1 -1 -3 4 2
-2 6 -6 4
-----------------------------------------
1 -3 3 -2 6
Hence, we get that 6 is the remainder when ([tex]x^4-x^3-3x^2+4x+2[/tex]) ÷ (x+2), using the factor theorem.
Read more about factor theorem:
brainly.com/question/19030198
#SPJ4
The complete question is -
Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, [tex]x^4-x^3-3x^2+4x+2[/tex] ÷ (x+2)
a local civic theatre has 22 seats in the first row and 21 rows in all. each successive row contains 3 additional seats. how many seats are in the civic theatre
Using the arithmetic progression, If a theatre has 30 rows of seats there are 22 seats in the first row,21 in the second row, 51 in the third row, then the total number of people that the theatre hold is 2400
The total number of rows = 51
Number of seats in the first row = 22
Number of seats in the second row = 21
Number of seats in the third row = 51
Common difference= Second term - first term
= 26-22
= 4
The given sequence is in arithmetic progression
Substitute the values in the equation
= 15[44+29×4]
= 15[44+116]
= 15×160
= 2400
Hence, using the arithmetic progression, if a theatre has 51 rows of seats and there are 22 seats in the first row,21 in the second row, 51 in the third row, then the total number of people that the theatre hold is 2400
Learn more about arithmetic progression here
brainly.com/question/16947807
#SPJ4
Tamba jut received a bonu which increaed hi dipoable income by $860. If Tamba' marginal propenity to conume (mpc) i 0. 75, hi conumption rie by _______
The formula for calculating the change in consumption is MPC x Change in Disposable Income.Thus, Tamba's change in consumption = 0.75 x $860 = $645
The marginal propensity to consume (MPC) is a measure of the proportion of an increase in disposable income that is spent on consumption. In Tamba's case, his MPC is 0.75, which means that for every $1 increase in his disposable income, he will spend 75 cents on consumption. The formula for calculating the change in consumption is MPC x Change in Disposable Income. Therefore, when Tamba's disposable income increased by $860, his consumption increased by 0.75 x $860 = $645.
Learn more about income here
https://brainly.com/question/7619606
#SPJ4
x^2-12x+43 i need some help with this maths question
In order to solve a quadratic equation with one unknown, we need to factor it. If at first glance we can't find easy roots, we do a discrimination.
[tex]f(x)=x^2-12x+43[/tex]Δ[tex]f(x)=b^2-4ac=(-12)^2-4(43)[/tex]Δ[tex]=-28[/tex]If this value is less than zero, Δ[tex]< 0,[/tex] we determine that it has no solution belonging to the set of real numbers. We will find a conjugate and two complex roots. ([tex]a+bi[/tex])
Let's use the following formulas to find the roots.
[tex]x_{1}=\frac{-b-\sqrt{D} }{2a}= \frac{12-\sqrt{-28} }{2}=6-\sqrt{7}i[/tex][tex]x_{2}=\frac{-b-\sqrt{D} }{2a}= \frac{12+\sqrt{-28} }{2}=6+\sqrt{7}i[/tex]Complex Solutions:
[tex]6+\sqrt{7}i[/tex][tex]6-\sqrt{7}i[/tex]A random sample of 1012 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1012 adults surveyed, 514 indicated that televisions are a luxury they could do without. Complete parts (a) through (e) below.
(a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without.
enter your response here
(Round to three decimal places as needed.)
Part 2
(b) Verify that the requirements for constructing a confidence interval about p are satisfied.
The sample
▼
is stated to be
can be assumed to be
cannot be assumed to be
is stated to not be
a simple random sample, the value of
▼
n
ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesis
ModifyingAbove p with caret
n ModifyingAbove p with caret
n ModifyingAbove p with caret left parenthesis 1 minus ModifyingAbove p with caret right parenthesis
is
enter your response here, which is
▼
greater than or equal to
less than
10, and the
▼
population proportion
sample proportion
population size
sample size
▼
cannot be assumed to be
can be assumed to be
is stated to not be
is stated to be
less than or equal to 5% of the
▼
population proportion.
sample size.
sample proportion.
population size.
(Round to three decimal places as needed.)
Part 3
(c) Construct and interpret a % confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without. Select the correct choice below and fill in any answer boxes within your choice.
(Type integers or decimals rounded to three decimal places as needed. Use ascending order.)
A.
There is a
enter your response here% probability the proportion of adults in the country who believe that televisions are a luxury they could do without is between
enter your response here and
enter your response here.
B.
We are
enter your response here% confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between
enter your response here and
enter your response here.
Part 4
(d) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely?
It is
▼
possible, but not likely
not possible
likely
that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval
▼
does not contain
contains
enter your response here.
(Type an integer or a decimal. Do not round.)
Part 5
(e) Use the results of part (c) to construct a % confidence interval for the population proportion of adults in the country who believe that televisions are a necessity.
Lower bound:
enter your response here, Upper bound:
enter your response here
(Round to three decimal places as needed.)
Answer: (a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without.
The point estimate for the population proportion is 514 / 1012 = 0.507.
(b) Verify that the requirements for constructing a confidence interval about p are satisfied.
The sample is stated to be a simple random sample.
The value of n * p = 1012 * 0.507 = 514.7796 is greater than or equal to 10.
The value of n * (1 - p) = 1012 * (1 - 0.507) = 497.2204 is greater than or equal to 10.
The population proportion is less than or equal to 5% of the population size.
Therefore, the requirements for constructing a confidence interval are satisfied.
(c) Construct and interpret a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without.
The 95% confidence interval for the population proportion is 0.507 +/- 1.96 * sqrt((0.507 * (1 - 0.507)) / 1012) = 0.507 +/- 0.0245 = (0.4825, 0.5315).
We are 95% confident that the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.4825 and 0.5315.
(d) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely?
It is possible that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval contains 60%. However, it is not likely because the confidence interval is relatively narrow and the point estimate is far from 60%.
(e) Use the results of part (c) to construct a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a necessity.
The 95% confidence interval for the population proportion of adults who believe that televisions are a necessity is 1 - 0.5315 = 0.4685 to 1 - 0.4825 = 0.5175. Therefore, the 95% confidence interval for the population proportion of adults who believe that televisions are a necessity is (0.4685, 0.5175).
Step-by-step explanation:
please help me with this question!! it would be helpful if you drew the rotated shape A on the grid. thank you!! i will vote brainliest to the first person to answer correctly :)
When rotated through 180° anticlockwise or clockwise about the origin, the new position of the above points is.
Rotate shape A [tex]$180^{\circ}$[/tex] about point (1,0) is (-1,0)
How do you rotate a shape about a certain point?
Move each point on a shape the specified number of degrees in a circle centered on the point of rotation to rotate it. Make sure that every new point is located the same amount of time away from the point of rotation as its corresponding original point.
There are 360 degrees in a circle's complete revolution. We discovered that a rotation of 270 degrees is virtually a full circle. We learned that a whole rotation of a circle is divided in half by 180 degrees. 90 degrees, or half of 180, are simple to identify as angles.
To learn more about complete revolution visit:https://brainly.com/question/17773408
#SPJ1
one of two or more numbers that multiply together to form a specific product; a number that divides into another number with no remainder.
one of two or more numbers that multiply together to form a specific product; a number that divides into another number with no remainder is a factor.
What does a factor mean in its simplest form?A component is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, therefore the numbers we are adding are factors of a product because the product is divisible by them.
What types of factors are there?Which of these four main types of factoring are they? The Grouping technique, the Differences in Two Squares, the Total or Difference in Cubes, as well as the Greatest Common Factors (GCF) are the four primary methods of factoring.
Briefing:A factor is a value that completely divides another number. Consequently, the values we are multiplication are factors if multiplying two whole numbers results in a product.
To learn more about factor visit:
https://brainly.com/question/9231261
#SPJ4
15. Robert wants to invest $20,000 in an account
with an annual interest rate of 1.9%. How much
extra will he have after two years if he
compounds continuously, instead of collecting
simple interest monthly? Round answer to the
nearest dollar.
[A] $800
[B] $750
[C] $711
[D] $683
[E] $821
To find the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly, we need to calculate the compound interest on the investment.
The compound interest is calculated by multiplying the principal (the initial amount invested) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 1.9%/12 = 0.158% per month, and there are 12*2 = 24 compounding periods (12 months per year for 2 years).
The compound interest is therefore calculated as follows:
Compound interest = $20,000 * e^(0.158%*24) - $20,000
= $20,000 * e^0.3832 - $20,000
= $20,000 * 1.454 - $20,000
= $4,080 - $20,000
= -$15,920
So the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly is -$15,920. Therefore, the correct answer is [A] $800.
A steep line has a bigger ____________ than a flat line
a steep line line has a bigger absolute greater slope than a flat line
Harry plans to charge $5 for cookies and $10
for cupcakes at the bake sale. He needs to
make a total of $75 to earn a profit. Write an
equation for the number of cookies (x) and
cupcakes (y) that Harry needs to sell at the bake sale.
Answer: 5x + 10y = or > 75
Step-by-step explanation:
make the number of cookies sold = x, and the number of cupcakes sold = y, since we don't know the number.
each cookie is $5 so it is 5 times x, and each cupcake is $10 so it is 10 times y.
add those together, and the sum must equal 75. If you have already learned this, it would be an equal to or greater than sign. if not then just use an equal sign.
Jess has a 4-digit password for her mobile phone.
Each digit can be between 0 and 9 inclusive.
a How many choices are possible for each digit of the code?
b What is the total number of 4-digit passwords that Jess can create?
Jess would like to choose an even number.
The code can start with a zero.
c How many different ways are possible now?
a. The number of choices possible for each digit of the code is of: 10.
b. The total number of 4-digit passwords that Jess can create is of: 10,000.
c. The number of different ways to create even passwords is of: 5,000.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the number of outcomes for each trial, according to the rule presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Each digit can be between 0 and 9 inclusive, hence the number of outcomes possible for each digit of the password is given as follows:
10.
The password is composed of four digits, hence the total number of passwords possible is of:
N = 10 x 10 x 10 x 10 = 10,000.
Considering that Jess would like an even number, there are only five outcomes possible for the last digit (0, 2, 4, 6 or 8), hence the number of outcomes is of:
N = 10 x 10 x 10 x 5 = 5,000.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/15878751
#SPJ1
PLS HELP!!! WILL GIVE BRAINLIEST :)
Answer:
1/ We use the SSS method to prove that triangle CBD = triangle ABD
2/ We use the AA method to prove that <CBD equal < ABD
Step-by-step explanation:
1/ SSS, or side side side method, is the method we use to see if triangles are the same or not, and we know that the sides of both triangles are equal; this proves that both triangles are equal!
2/ AA, or Angle Angle method, is the method we use to see if the angles of triangles are the same or not, and we know that there are marks at <C and <A, these marks prove that both angles are equal! So, <CBD equal <ABD
list the reasons and statement reasons why line AE ≅ A.F
. Thanks!
Add missing statements and reasons.
Statement Reason
7. FC ≅ EC CPCTC8. AE ≅ A.F. Transitive propertyI can’t figure this one out
Answer:
g = 109 degree
h = 71 degree
m = 71 degree
k = 84 degree
Step-by-step explanation:
g= 109 degrees because it is a vertical angle to the 109-degree angle, that is why it is 109 degree
h= 71 degrees because they are supplementary angles which means they add up to 180 degrees. We see that one is 109 degrees, so the other must be 71 degrees.
k = 84 degrees because it is a vertical angle to the 84-degree angle, which is why it is 84 degrees.
m= 71 degrees because m and g must add up to 180 degrees, and we know that g is 109 degrees, so m is 71 degrees!
Swimming Pool On a certain hot summer's day, 240 people used the public swimming pool. The daily prices are $1.50 for children and $2.25 for adults. The receipts for admission totaled $510.75. How many children and how many adults swam at the public pool that day?
Answer:
39 children, 201 adults
Step-by-step explanation:
Let c = number of children
a = number of adults
c + a = 240
1.50c + 2.25a = 510.75
--------------------------------
1.50c + 1.50a = 360
1.50c + 2.25a = 510.75
-------------------------------
.75a = 150.75
a = 201, c = 39
Square ABCD is reflected about side BC. Which of the following statements are true? Select three that apply.
Vertex B is the midpoint of AA'.
Side BC is parallel to AA.
The length of CD is equal to the length of C'D'.
Vertex C and vertex C are located at the same point.
Reflection is a type of rigid transformation in which an object is flipped about a reference point or line to produce the required image. The three statements that apply are:Vertex B is the midpoint of AA'The length of CD is equal to the length of C'D'Vertex C and vertex C are located at the same point
What i Rigid transformation?Rigid transformation is a process in which the size, orientation or position of a given object can be changed by applying some principles. Types of rigid transformation are: reflection, translation, dilation, and rotation.
In the given question, the required statements that apply are:
Vertex B is the midpoint of AA'The length of CD is equal to the length of C'D'Vertex C and vertex C are located at the same point
Learn more about reflection of an object at https://brainly.com/question/6780432
#SPJ1
If 5 log 3 3x=15, what is the value of x?
The value of x for the expression 5log(3x) = 15 is 6.7.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 5log(3x) = 15. The value of x for the expression will be calculated as,
5log(3x) = 15
log(3x) = 15 / 5
log(3x) = 3
3x = e³
x = 20 / 3
x = 6.7
To know more about an expression follow
https://brainly.com/question/24434884
#SPJ1
Plot the piecewise function on the graph.
2x+6,
-5 < x < -2
-2 < x≤2
2
f(x) = { 1,
-3x+10,
What we should do is plot each part of the graph individually.
Step 1: Plot f(x) = 2x + 6 part
We know it starts at x = -5 (noninclusive) and ends at x = -2 (inclusive). Therefore, we can draw a line between the two points (-5, -4) and (-2, 2), with an open point at x = -5 and a closed point at x = -2
Step 2: Plot f(x) = 1 part
We know it starts at x = -2 (noninclusive) and ends at x = 2 (inclusive). Therefore, we can draw a line between the two points (-2, 1) and (2, 1), with an open point at x = -2 and a closed point at x = 2
Step 3: Plot f(x) = -3x + 10 part
We know it starts at x = 2 (noninclusive) and ends at x = 5 (inclusive). Therefore, we can draw a line between the two points (2, 4) and (5, -5), with an open point at x = 2 and a closed point at x = 5
You should end up with a graph that looks like the attached image!
The given function f(x) has been plotted in the graph piecewise with proper endpoints.
How t plot a graph?A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
As per the given piecewise function,
f(x) = [tex]\left \{ {{2x+6 \ \ \ \ -5 < x\leq -2}} \right.[/tex]
f(x) = [tex]\left \{ {{1 \ \ \ \ -2 < x\leq 2}} \right.[/tex]
f(x) = [tex]\left \{ {{-3x+10 \ \ \ \ 2 < x\leq 5}} \right.[/tex]
The function f(x) = 2x + 6 is a linear line with slope 2 and y-intercept 6 shown in red line -5 is excluded while - 2 is included.
The function f(x) = 1 is a constant horizontal line shown in the blue line that -2 excludes while 2 is included.
The function f(x) = -3x + 10 is a linear line with slope -3 and y-intercept 10 shown in the green line 2 is excluded while - 5 is included.
Hence "With the appropriate endpoints, the supplied function f(x) has been piecewise displayed in the graph".
For more information about the graph of a function
brainly.com/question/27757761
#SPJ1