A rectangle with an area of 4/7 m2 is dilated by a factor of 7. What is the area of the dilated rectangle

Answer:

4a + 2b + 1/4 c.

Step-by-step explanation:

1/4(16a+8b+c)

= 1/4 * 16a + 1/4 * 8b + 1/4 * c

= 4a + 2b + 1/4 c.

Final answer:

To apply the distributive property to the expression 1/4(16a+8b+c), we distribute the 1/4 to each term inside the parentheses and simplify the expression.

Explanation:

To apply the distributive property to the expression 1/4(16a+8b+c), we distribute the 1/4 to each term inside the parentheses. This means multiplying 1/4 by 16a, 1/4 by 8b, and 1/4 by c. The distributive property states that a (b + c) = ab + ac. So, the expression becomes:

1/4(16a) + 1/4(8b) + 1/4(c)

Since 1/4 times any number equals the number divided by 4, we can simplify further:

(16a/4) + (8b/4) + (c/4)

Which simplifies to:

4a + 2b + c/4

Answer: 47+B(.85) = A

Step-by-step explanation:

One bagel = $0.85

Sold 47 today

One bagel(.85) = profit

A = profit

B = additional bagels

47+B(.85) = A

Using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.

Line of best fit refers to the "a line through a scatter plot of data points that best expresses relationship between those points". Lines of best fit is used to describe data and predict data where the new data will appear. Examples for lines of best fit is 'Least square method'.

Two variables wherein "change in the value one variable produces a change in the variable other variable then it is called variables are correlated or there is a correlation coefficient".

According to the question,

In order to determine the correlation between two variables on a graph using line of best fit and correlation coefficient.

Correlation coefficient holds only if there is a linear correlation between the variables; that is the relationship between the variables is linear in graph. Variation in 'y' is caused by variation in 'x' on graph . Variation in 'x' is caused by variation 'y' on graph. Variable 'x' and variable 'y' are jointly dependent on graph. This is how we determine the correlation coefficient between two variables on the graph.

Line of best fit suppose (x₁, y₁) (x₂, y₂) ..... (xₙ, yₙ) be 'n' pairs of values on a graph to determine the line of best for this data. Assume 'y = a + b x' as a line of best fit (trend line). Using the principle of least squares we can determine the parameter 'a' and 'b'. It can be shown that 'a' and 'b' are determined by the equation.

n a + b∑ x = ∑y  -->(1)

a ∑x +b ∑x² = ∑x y  --->(2)

These equations are called Normal equation. Therefore, the line of best fit is y=a x+ b where 'a' and 'b x' are given by the equation. This is how we determine the correlation or relationship between two variables on a graph.  

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Answer:

c. amplitude: 1; period: [tex]2\pi[/tex]

Step-by-step explanation:

The given function is [tex]f(t)=- \cos t[/tex]

This function is of the form;

[tex]y=A \cos Bt[/tex]

where [tex]|A|[/tex] is the amplitude.

When we compare [tex]f(t)=- \cos t[/tex] to [tex]y=A \cos Bt[/tex], we have

[tex]A=-1[/tex], therefore the amplitude of the given cosine function is [tex]|-1|=1[/tex]

The period is given by;

[tex]T=\frac{2\pi}{|B|}[/tex]

Since B=1, the period is [tex]T=\frac{2\pi}{|1|}=2\pi[/tex]

Answer:

c. amplitude: [tex]\displaystyle 1;[/tex]period: [tex]\displaystyle 2\pi[/tex]

Explanation:

[tex]\displaystyle f(t) = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1[/tex]

With the above information, you now should have an idea of how to interpret graphs like this.

I am joyous to assist you at any time.

Answer:

neither am i bro no worries

Step-by-step explanation:

no cap

Answer:

Step-by-step explanation:

It's parallel to the side BC, from a known theorem (the segment linking the midpoints of two sides of a triangle is parallel to the third, and its lenght is half of it.

Answer:

16.47 in.

Step-by-step explanation:

Add the lengths of the sides:

3.4 in. + 5.75 in. + 7.32 in. = 16.47 in.

The perimeter of the triangle will be equal to 16.47 in. The correct option is B.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

The perimeter is defined as the sum of all the sides of the figure. The perimeter of the triangle is the sum of all three sides of the triangle.

Given that the three sides of a triangle measure 3.4 inches, 5 inches, and 7.32 inches.

The perimeter of the triangle is calculated as,

P = 3.4 in. + 5.75 in. + 7.32 in.

P = 16.47 in.

Therefore, the perimeter of the triangle will be equal to 16.47 in. The correct option is B.

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Translations, rotations, and reflections are all rigid transformations.

Answer:

Explanation:

To solve log (−5.6x + 1.3) = −1 − x graphycally, you must graph this system of equations on the same coordinate plane:

1) To graph the equation 1 you can use these features of logarithmfunctions:

        log ( -5.6x + 1.3) = 0 ⇒ -5.6x + 1.3 = 1 ⇒x = 0.3/5.6 ≈ 0.054

       x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11

        x            log (-5.6x + 1.3)

        -1           0.8

        -2           1.1

        -3           1.3

2) Graphing the equation 2 is easier because it is a line: y = - 1 - x

3) The solution or solutions of the equations are the intersection points of the two graphs. So, now the graph method just requires that you read the x coordinates of the intersection points. From the least to the greatest, rounded to the nearest tenth, they are:

Answer:

x = -2.1

& .2

Step-by-step explanation:

Answer:

option B

Step-by-step explanation:

Step 1

A + B = C

[tex]A=\left[\begin{array}{ccc}8&-3\\3&y+2\end{array}\right][/tex][tex]+B=\left[\begin{array}{ccc}3x&z+4\\w&1/2y\end{array}\right][/tex]

=

[tex]C=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right][/tex]

Step 2

[tex]\left[\begin{array}{ccc}8+3x&-3+z+4\\3+w&y+2+y/2\end{array}\right][/tex][tex]=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right][/tex]

Step 3

4 equations are form

Equation 1

8 + 3x = x

8 = -2x

x = -4

Equation 2

-3 + z + 4 = 2z

1 + z = 2z

1 = z

z = 1

Equation 3

3 + w = 4

w = 1

Equation 4

y + 2 + y/2 = y

2 + y/2 = 0

4 + y = 0

y = -4

Step 4

[tex]\left[\begin{array}{ccc}3(-4)&1+4\\1&1(-4)/2\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-12&5\\1&-2\end{array}\right][/tex]

Answer:

B

Step-by-step explanation:

I got 100% on EDGE 2020 Unit test

Answer:

Hello cheaters lol jk, Answer is B.  

Step-by-step explanation:

more interest equals more money, if you divide the amount of the house by 6% and do the same for the other by 5, the amount for B is greater.  

The House A is more worth than House B .

Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.

Formula of Compound interest :

[tex]A = P (1+\frac{r}{100} )^{n}[/tex]

Where,

A = Final amount

P = initial principal

r = rate per annum

n = Time in years

According to the question

House A:

Principal = 125260

Rate = 5%

Time in years = 2

Applying Formula of Compound interest for final amount

[tex]A = P (1+\frac{r}{100} )^{n}[/tex]

[tex]A = 125260 (1+\frac{5}{100} )^{2}[/tex]

[tex]A = 125260 (1.05)^{2}[/tex]

A = 138,099.15

House B:

Principal = 120160

Rate = 6%

Time in years = 2

Applying Formula of Compound interest for final amount

[tex]A = P (1+\frac{r}{100} )^{n}[/tex]

[tex]A = 120160 (1+\frac{6}{100} )^{2}[/tex]

[tex]A = 120160(1.06)^{2}[/tex]

A = 135,011.776

Hence , House A is more worth than House B .

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C. If a<0, then the parabola opens down

Answer:

[tex]3,726\ m^{2}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor

Let

z----> the scale factor

x----> corresponding side of the larger trapezoid

y----> corresponding side of the smaller trapezoid

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=64\ m[/tex]

[tex]y=12\ m[/tex]

substitute

[tex]z=\frac{64}{12}[/tex]

step 2

Find the area of the larger trapezoid

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z----> the scale factor

x----> area of the larger trapezoid

y----> area of the smaller trapezoid

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{64}{12}[/tex]

[tex]y=131\ m^{2}[/tex]

substitute

[tex](\frac{64}{12})^{2}=\frac{x}{131}[/tex]

[tex]x=(\frac{4,096}{144})(131)[/tex]

[tex]x=3,726\ m^{2}[/tex]

A function assigns the values. The temperature that will model most accurately predict the time spent cooling will be 300.

A function assigns the value of each element of one set to the other specific element of another set.

For the given function [tex]f(t)=349.2 (0.98)^t[/tex], the value of t which will lie within the given function range will be the value function that will model most accurately predict the time spent on cooling. Therefore, let's substitute the values and check,

A.) t = 0

[tex]f(t)=349.2 (0.98)^t\\\\0=349.2 (0.98)^t[/tex]

As the value of t will lie at infinite, therefore, this will not give an accurate prediction of the model.

B.) f(t) = 100

When the value of the function will be 100 then the value of t will be 61.6, therefore, this can not be the most accurate prediction.

C.) f(t) =300

When the value of the function will be 300 then the value of t will be 7.5, therefore, this is the most accurate prediction.

D) f(t) = 400

When the value of the function will be 400 then the value of t will be -6.724, therefore, this can not be the most accurate prediction.

Thus, the temperature that will model most accurately predict the time spent cooling will be 300.

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Answer:

Domain = Range =  All real numbers

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x)=2x+cos x

From the plot, we can see the answer is

Option a.

Domain = Range = (-∞,∞)

Answer: a

Step-by-step explanation:

right on edg

Answer:

3. f(x) = 5^x

4. f(x) = 3 (8)^x

Step-by-step explanation:

3. Which function represents the data 2=>25, 3=>125, 4 =>625

You just have to plug the values of x in the equations provided and see which one fit, you stop testing for a given equation when it doesn't match the data table.

f(x) = x^4 + 9 - NO

for x = 2, 2^4 + 9 = 16 + 9 = 25 YES

for x = 3, 3^4 + 9 = 81 + 9 = 90 NO, should be 125

f(x) = 4^x + 9 - NO

for x = 2, 4^2 + 9 = 16 + 9 = 25 YES

for x = 3, 4^3 + 9 = 64 + 9 = 73  NO, should be 125

f(x) = x^5 - NO

for x = 2, 2^5 = 32 NO, should be 25

f(x) = 5^x YES

for x = 2, 5^2 = 25  YES

for x = 3, 5^3 = 125  YES

for x = 4, 5^4 = 625  YES

4. Which of the options is equivalent to f(x) = 3(2)^(3x)

By property of the powers you can easily break down the 3x exponent into a much simpler way.

[tex](2)^{3x} = (2^{3} )^{x} = 8^{x}[/tex]

From (2)^(3x) we got to 8^x, so the equation can now be written:

f(x) = 3 (8)^x, which is the first choice.

You could easily verify it with x = 2 in each equation.

That is 99 degrees if you have the triangle facing the other way

the measure of angle KJL is [tex]\( 40^\circ \)[/tex].

Given information

[tex]\( m(KP) = 2 \cdot m(IP) \)\\\( m(IVK) = 120^\circ \)[/tex]

Using the fact that the sum of angles in a circle is [tex]\( 360^\circ \)[/tex], we have:

[tex]\[ m(KP) + m(IP) + m(IVK) = 360^\circ \][/tex]

Substituting the given values:

[tex]\[ 2 \cdot m(IP) + m(IP) + 120^\circ = 360^\circ \][/tex]

Solving for [tex]\( m(IP) \)[/tex]:

[tex]\[ 3 \cdot m(IP) = 360^\circ - 120^\circ \]\[ 3 \cdot m(IP) = 240^\circ \]\[ m(IP) = \frac{240^\circ}{3} \]\[ m(IP) = 80^\circ \][/tex]

Finding [tex]\( m(KP) \)[/tex]:

[tex]\[ m(KP) = 2 \cdot m(IP) = 2 \cdot 80^\circ = 160^\circ \][/tex]

Using the angle formed by a tangent and a secant theorem, we can find [tex]\( m(\angle KJL) \)[/tex]:

[tex]\[ m(\angle KJL) = \frac{1}{2} (m(KP) - m(IP)) \][/tex]

Substituting the known values:

[tex]\[ m(\angle KJL) = \frac{1}{2} (160^\circ - 80^\circ) \]\[ m(\angle KJL) = \frac{1}{2} (80^\circ) \]\[ m(\angle KJL) = 40^\circ \][/tex]

Therefore, the measure of angle KJL is [tex]\( 40^\circ \)[/tex].

The complete question is:

given:  [tex]\( m(KP) = 2 \cdot m(IP) \)\\[/tex] and [tex]\( m(IVK) = 120^\circ \)[/tex]

find: m∠KJL.

Answer:

im pretty sure its the first one

Answer with explanation:

When the size of Preimage is greater than size of Image than dilation factor will be less than 1 and greater than zero.

And, when Size of preimage is greater than Size of Image than dilation factor will be greater than 1.

In the given diagram

Size of Preimage > Size of Image

Dilation Factor=0 <Dilation factor <1

Option A: It has a scale factor between zero and one and is a reduction.

answer for this question is (d)3x2-x+6

This is the answer:)

Do what? I can't see a question

repost and let me know once it’s up because I can’t see the picture

Good luck,

:)

Answer:

slope=-1/4

Step-by-step explanation:

point 1: -4,-1

point 2: 0,-2

y1-y2/x1-x2

1/-4

-1/4

Answer:

The measure of angle BCD is [tex]68.5\°[/tex]

Step-by-step explanation:

step 1

Find the value of x

In this problem

[tex]m<ABD+m<BCD+m<EDF=180\°[/tex] -----> is a straight line

substitute the values

[tex](3x+4)+(6x-8)+(7x-20)=180\°[/tex]

[tex](16x-24)=180\°[/tex]

[tex]16x=180\°+24\°[/tex]

[tex]x=12.75\°[/tex]

step 2

Find the measure of angle BCD

[tex]m<BCD+=(6x-8)\°[/tex]

substitute the value of x

[tex]m<BCD+=(6(12.75)-8)=68.5\°[/tex]

Answer:

the person above me is correct

Step-by-step explanation:

by the way its 8 because 24 words divided by 4 weeks is 8.

The unit rate describing Alan's vocabulary acquisition is 6 words per week.

The unit rate that describes the situation where Alan learned 24 new vocabulary words in 4 weeks is 6 words per week.

To find the unit rate, divide the total number of words learned by the total number of weeks. In this case, 24 words / 4 weeks = 6 words per week.

Answer:

[tex]4w^4-7z^4+6w^2z^2[/tex]

Step-by-step explanation:

We can reformat this equation so we can vertically add.

Then, we can just add down.

Since all the degrees and the variables are the same, we only have to worry about the coefficients.

5 - 1 = 4 --> [tex]4w^4[/tex]

-7 + 13 = 6 --> [tex]6w^2z^2[/tex]

-3 - 4 = -7 --> [tex]-7z^4[/tex]

Now let's rewrite this.

[tex]4w^4-7z^4+6w^2z^2[/tex]

The value of ∑n=14[100(−4)n−1] is -5368709100

The sequence is given as:

∑n=14[100(−4)n−1]

The above sequence is a geometric sequence, with the following properties

The sum of n terms of a geometric series is:

[tex]S_n = \frac{a* (r^n - 1)}{r - 1}[/tex]

So, we have:

[tex]S_n = \frac{100* ((-4)^{14} - 1)}{-4 - 1}[/tex]

Evaluate

[tex]S_{14} = -5368709100[/tex]

Hence, the value of ∑n=14[100(−4)n−1] is -5368709100

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The sum [tex]\(\sum_{n=1}^4 [100(-4)^{n-1}]\)[/tex] is [tex]\[\boxed{-5100}\][/tex]

To find the sum [tex]\(\sum_{n=1}^4 [100(-4)^{n-1}]\),[/tex] we will calculate the individual terms of the sequence and then sum them up.

The general term of the sequence is [tex]\(100(-4)^{n-1}\)[/tex]. Let's compute the terms from [tex]\(n = 1\) to \(n = 4\):[/tex]

1. For [tex]\(n = 1\):[/tex]

[tex]\[ 100(-4)^{1-1} = 100(-4)^0 = 100 \cdot 1 = 100 \][/tex]

2. For [tex]\(n = 2\):[/tex]

[tex]\[ 100(-4)^{2-1} = 100(-4)^1 = 100 \cdot (-4) = -400 \][/tex]

3. For [tex]\(n = 3\):[/tex]

[tex]\[ 100(-4)^{3-1} = 100(-4)^2 = 100 \cdot 16 = 1600 \][/tex]

4. For [tex]\(n = 4\):[/tex]

[tex]\[ 100(-4)^{4-1} = 100(-4)^3 = 100 \cdot (-64) = -6400 \][/tex]

Now, let's sum these terms:

[tex]\[100 + (-400) + 1600 + (-6400)\][/tex]

Perform the calculations step-by-step:

1. [tex]\(100 - 400 = -300\)[/tex]

2. [tex]\(-300 + 1600 = 1300\)[/tex]

3. [tex]\(1300 - 6400 = -5100\)[/tex]

4x➕6(503-x)=2296

Distribute the 6 into the parentheses

Let x represent the students

503-x will represent the non-students

4x➕3018➖6x=2296

Then combine like terms

-2x➕3018=2296

Now since you move your constant your sign has to change as well,

-2x=2296➖3018

Then subtract

-2x=-722

Then divide both sides by -2

You are left with x=361

This represents the students

503➖361= 142 which equal the non-students

Therefore your answer is:

361=students

142=non-students

Hope this helps! :3

Answer:

361 students and 503-361=142 non students

Step-by-step explanation:

Let x = number of students. And 503-x = the number of non students. Therefore, 4x+6(503-x)=2296

Answer:

[tex]\$17,500[/tex]

Step-by-step explanation:

Let

x----> that month's sales

y----> October earnings

we know that

[tex]8\%=8/100=0.08[/tex]

[tex]y=0.08x+1,400[/tex] -----> equation A

[tex]y=2,800[/tex] -----> equation B

Equate equation A and equation B and solve for x

[tex]2,800=0.08x+1,400[/tex]

[tex]0.08x=2,800-1,400[/tex]

[tex]x=1,400/0.08[/tex]

[tex]x=\$17,500[/tex]

Final answer:

The salesperson needs to earn an additional $1,400 on top of the base salary to meet the goal, which means they need to sell $17,500 worth of merchandise with an 8% commission rate.

Explanation:

To calculate the amount of merchandise the salesperson must sell to meet the goal of $2,800, we need first to understand how much more money is needed beyond the base salary. The salesperson receives a base salary of $1,400. Since the goal is $2,800, the additional amount needed from commission is $2,800 - $1,400 = $1,400.

With an 8% commission rate, we can set up an equation where the amount of merchandise sold (let's call it x) times the commission rate (0.08) equals the additional amount needed ($1,400). The equation is: 0.08x = $1,400. To find x, divide both sides by 0.08, therefore x = $1,400 / 0.08, which equals $17,500.

So, the salesperson will need to sell $17,500 worth of merchandise to meet the goal of earning $2,800 in October.

Answer:

Okay I might not be right on this one but, I believe you divide 27 and 3. As to the part about simplifying, you might want to give me so details.

Step-by-step explanation:

Answer:

  B) x^2/12 +y^2/16 = 1

Step-by-step explanation:

The distance from focus to covertex is the same as the distance from the center to the vertex: 4. So, the Pythagorean theorem tells you ...

  a^2 + 2^2 = b^2

  a^2 +4 = 4^2 = 16

  a^2 = 16 -4 = 12

So, the standard-form equation ...

  x^2/a^2 +y^2/b^2 = 1

looks like this when the values are filled in:

  x^2/12 +y^2/16 = 1

Answer:

[tex]f(x)=3^x[/tex]

Step-by-step explanation:

Given that the function is represented by the graph below, which  begins in the second quadrant near the x−axis and increases slowly while crossing the ordered pair 0, 1. When the graph enters the first quadrant, it begins to increase quickly throughout the graph

Because it passes through (0,1) it is of the form

[tex]y=a^x[/tex]

Also for negative x large it is very near x axis, So a must be positive then only it increases faster in the I quadrant.  Range is only posiitve real numbers

So the function is

[tex]f(x) =3^x[/tex]

Answer:

Option A

Option C

Step-by-step explanation:

A relationship is defined as a function if and only if each element of the "domain" set is assigned only one element of the "range" set. That is, there is only one output value y assigned to each input value x.

The relation x = 3 is not a function because there are infinite output values y, assigned to the same input element x.

(3, 2), (3, 5) (3, 9) (3,10000)

Then the option A is true

Option C is also true, the equation of the line shown is

[tex]x = 3[/tex]

The rest of the options are false because x = 3 is not a function