The length of a rectangle is (3x - 5) inches, and its width is 2x inches. Find the area of the rectangle.

Answer:

AAS theorem

Step-by-step explanation:

Angle SUT = Angle TVS (given)

Angle SRY = Angle TRV (vertically opposite angles)

SU = TV (given)

So, Triangle SUR is congruent to triangle TVR by AAS theorem.

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Answer:

5=.25, 3=.30, 2=.50

Step-by-step explanation:

5×5=.25

Answer: 25%

Step-by-step explanation: A nickel is worth 5 cents. There are 5 nickels. Multiply 5 by 5. 5 x 5 = 25. You have 25 cents in nickels. There are 100 cents in a dollar, so divide 25 by 100. 25/100 = 0.25. To get the percent, multiply 0.25 by 100. 0.25 x 100 = 25%.

There are 24 bouquets making by Rachel.

What is Factor?

A number which means to break it up into numbers that can be multiplied together to get the original number.

Now, To solve this problem,

Let us first lay out all the factors of each number.

72 : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

So, The greatest number of bouquets that can be made would be equal to the greatest common factor of the two numbers 72 and 48 will 24.

Hence, There are 2 bouquets making by Rachel.

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Rachel can make 24 bouquets with 72 carnations and 48 roses.

To determine the greatest number of bouquets Rachel can make with 72 carnations and 48 roses, we need to find the greatest common divisor (GCD) of 72 and 48. The GCD is the largest number that divides both 72 and 48 without leaving a remainder.

Here are the steps to find the GCD:

Answer:

B. [3,5]

Step-by-step explanation:

The rate of change of a function is the same as the slope between two given points from that same function,

Hence,

all we need to do is use the slope's equation, that is

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

And eval it in every couple of ordered pairs given from the table we obtain the following>

x2 y2 x1 y1  m

0 4 -1 3,5  0,5

1 5 0 4  1

2 7 1 5  2

3 11 2 7  4

4 19 3 11  8

5 35 4 19  16

The rate of change from g(x) is 4 (its slope)

Hence, the interval when the rate of change of f(x) is greater than g(x) is from x=3 to x=5

The domain is the X values.

There are two dots located at x = -4 and x = 9

The answer would be: D -4 < x < 9

The domain of the graphed function is - 4 ≤ x ≤ 9, that is option D. This can be obtained by finding all the x-values.

⇒Domain is all x-values of a function.

From the graph, we can say that the graph start from (-4,-4) to (8,9).

Thus x-values are from -4 to 9.

Since the endpoints are closed circles the points -4 and 9 are included.

∴The required domain is - 4 ≤ x ≤ 9

Hence the domain of the graphed function is - 4 ≤ x ≤ 9, that is option D.

Learn more about graphed functions here:

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Answer:

The number of toys that Kevin can make per hour is equal to [tex]60\frac{c}{m}\ toys[/tex]

Step-by-step explanation:

we know that

Kevin makes c toys in m minutes

Remember that

1 hour=60 minutes

so

Using proportion find out how many toys can be make in 60 minutes (one hour)

Let

x -----> the  number of toys that Kevin can make per hour

so

[tex]\frac{c}{m}=\frac{x}{60}\\ \\x=60\frac{c}{m}\ toys[/tex]

therefore

The number of toys that Kevin can make per hour is equal to [tex]60\frac{c}{m}\ toys[/tex]

first off, let's check what's the slope of that line through those two points anyway

[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-(-2)}{7-5}\implies \cfrac{2+2}{7-5}\implies \cfrac{4}{2}\implies 2[/tex]

now, let's take a peek of what is the slope of that equation then

[tex]\bf -5y+kx=6-4x\implies -5y=6-4x-kx\implies -5y=6-x(4+k) \\\\\\ -5y=-x(4+k)+6\implies -5y=-(4+k)x+6\implies y=\cfrac{-(4+k)x+6}{-5}[/tex]

[tex]\bf y=\cfrac{(4+k)x-6}{5}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{(4+k)}{5}} x-\cfrac{6}{5}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{since both slopes are the same then}}{\cfrac{4+k}{5}=2\implies 4+k=10}\implies \blacktriangleright k=6 \blacktriangleleft[/tex]

Answer:

1/40

Step-by-step explanation:

A bag contains 5 blue, 3 red, and 8 green marbles

You have (5+3+8=16) marbles

P(red 1) = red/total = 3/16

You do not replace it

A bag contains 5 blue, 2 red, and 8 green marbles

You have (5+2+8=15) marbles

P(red 2nd) = red/total = 2/15

P(red 1, red 2) = P (red 1)* P (red 2) = 3/16 * 2/15

                                                         =1/40

Answer:

[tex]\frac{3\pi}{4}[/tex]

(Assuming you want your answer in radians)

If you want the answer in degrees just multiply your answer in radians by [tex]\frac{180^\circ}{\pi}[/tex] giving you:

[tex]\frac{3\pi}{4} \cdot \frac{180^\circ}{\pi}=\frac{3(180)}{4}=135^{\circ}[/tex].

We can do this since [tex]\pi \text{ rad }=180^\circ[/tex] (half the circumference of the unit circle is equivalent to 180 degree rotation).

Step-by-step explanation:

[tex]\cos^{-1}(x)[/tex] is going to output an angle measurement in [tex][0,\pi][/tex].

So we are looking to solve the following equation in that interval:

[tex]\cos(x)=-\frac{\sqrt{2}}{2}[/tex].

This happens in the second quadrant on the given interval.

The solution to the equation is [tex]\frac{3\pi}{4}[/tex].

So we are saying that [tex]\cos(\frac{3\pi}{4})=\frac{-\sqrt{2}}{2}[/tex] implies [tex]\cos^{-1}(\frac{-\sqrt{2}}{2})=\frac{3\pi}{4}[/tex] since [tex]\frac{3\pi}{4} \in [0,\pi][/tex].

Answer is [tex]\frac{3\pi}{4}[/tex].

Answer:

F=0 or (7/3)

Step-by-step explanation:

When F is 0, the equation reads -0(3(0)-7)=0. The outside 0 will multiply by everything and make it equal 0. When F is 7/3, the inside of the parenthesis read 3(7/3)-7. This equals 7-7. It'll end up being (7/3)0, which equals 0.

Answer:

41 units

Step-by-step explanation:

The diagonal forms a right triangle with the sides, so we can use Pythagorean theorem.

c² = a² + b²

d² = 9² + 40²

d = 41

The diagonal is 41 units long.

Answer:

P(10)=0

Step-by-step explanation:

As per factor theorem:

If x-10 is factor of polynomial p(x), then the remainder after division by x-10 should be zero. i.e.  If we synthetic-divide a p(x) by x = 10 and get zero remainder as following

P(10)=0

it is reverse of remainder theorem!

Answer: First and last option

The birds began 1320 miles from the equator.

The birds are flying toward the equator at a rate of 60 mph.

Step-by-step explanation:

Note that the function f(x) is a linear function.

[tex]f (x) = - 60x + 1320[/tex]

If x represents the number of hours and f(x) represents the distance from the equator, then x = 0 means that the first hour has not yet elapsed.

When x = 0 then:

[tex]f (0) = -60 * 0 +1320\\f (0) = 1320[/tex].

This means that the initial distance at which the birds of the equator are located is 1320 miles.

Then when x = 1 then:

[tex]f (x) = -60 * 1 + 1320\\f (x) = -60 +1320[/tex]

When x = 2 then:

[tex]f (x) = -60 * 2 + 1320\\f (x) = -120 +1320[/tex]

As x increases by one unit then the distance of the birds to the equator decreases by 60 miles. This means that birds travel at a speed of 60 miles per hour

Answer:

The birds began 1320 miles from the equator.

The birds are flying toward the equator at a rate of 60 mph.

Step-by-step explanation:

Answer:

[tex]\lim_{x \to 0} x^2-3=-3[/tex]

Step-by-step explanation:

This limit can be written as follows

[tex]\lim_{x \to 0} x^2-3[/tex]

Direct substitution means that we substitute in the value for x to get our limit

[tex]\lim_{x \to 0} x^2-3\\\\0^2-3\\\\-3[/tex]

[tex]\displaystyle\\\lim_{x\to 0}(x^2-3)=0^2-3=-3[/tex]

Answer:

70

Step-by-step explanation:

75-55=20

95-85=10

100-90=10

115-95=20

100-90=10

sum of the differences is 70

Answer:

A: 10

Step-by-step explanation:

Let's add the actual enrollments all together. 55 + 80 + 95 + 100 + 115 + 90 all added together is 535. The predicted enrollments, all added together, is: 75 + 80 + 85 +90 +95 + 100 = 525.

535 - 525 = 10 residuals.

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

See attached reference

Answer:

The values of x are 0 and 4

Step-by-step explanation:

we have

[tex]f(x)=x^{2}-2x-4[/tex] ------> equation A

[tex]g(x)=2x-4[/tex] ----> equation B

To find the values of x when f(x) and g(x) intersect

equate f(x) and g(x)

[tex]f(x)=g(x)[/tex]

[tex]x^{2}-2x-4=2x-4[/tex]

[tex]x^{2}-2x-4-2x+4=0[/tex]

[tex]x^{2}-4x=0[/tex]

Factor x

[tex]x(x-4)=0[/tex]

The solutions are

x=0 and x=4

Final answer:

The functions f(x) = x²- 2x - 4 and g(x) = 2x - 4 intersect at x = 0 and x = 4, found by setting the equations equal to each other and solving for x.

Explanation:

To find the intersection points of the functions f(x) = x2 - 2x - 4 and g(x) = 2x - 4, we need to set the two functions equal to each other and solve for x.

Set f(x) equal to g(x): x ²- 2x - 4 = 2x - 4.

Move all terms to one side to set the equation to zero: x² - 4x = 0.

Factor the quadratic equation: x(x - 4) = 0.

Find the solutions for x by setting each factor equal to zero: x = 0 and x - 4 = 0, which gives us x = 0 and x = 4.

Therefore, the functions f(x) and g(x) intersect at the values x = 0 and x = 4.

Answer:

9.10 km to the nearest hundredth.

Step-by-step explanation:

We have a triangle whose adjacent side is 25 km and angle  20 degrees.

If h is the height we have the equation:

tan 20 = h / 25

h = 25 tan 20

= 9.099 km.

Answer:

B

Step-by-step explanation:

Given

5x + y = 14 ( subtract 5x from both sides )

y = 14 - 5x

Substituting values of x into the right side allows the corresponding value of y to be found.

x = - 1 : y = 14 - 5( - 1) = 14 + 5 = 19

x = 0 : y = 14 - 5(0) = 14 - 0 = 14

x = 1 : y = 14 - 5(1) = 14 - 5 = 9

Hence the corresponding values of x and y are

x    y

- 1   19

0     14

1       9

The equation (x+5)^2 + (y+7)^2=81 is a variation of a circles standard formula (x - h)^2 + (y - k)^2 = r^2

To find the diameter you must first know the radius.

In this question the radius is 9.

9^2 = 81

The diameter is composed of the length of two radii, this means that the equation to find the diameter when the radius is known is (let diameter be D and radius be r): D = 2r

D = 9 * 2

D = 18

The diameter is 18 units

Hope this helped!

~Just a girl in love with Shawn Mendes

As you can see from the image in the picture all the sides of the triangle are equal to each other (25). This means that this is an equilateral triangle.

The definition of an equilateral triangle is:

A triangle that has all sides equal to each other. The angles are also equal to each other. Since it is known that the sum of all the angles of a triangle equals 180, one angle of an equilateral triangle is always 60 degrees ( 180 / 3 = 60).

That means angle B has the measure of 60 degrees

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Construct a square of side length 4 cm

Step-by-step explanation:

* Lets explain how to construct a square polygon with side length 4 cm

- Use your straightedge to draw a horizontal line

- Measure on the horizontal line a segment of 4 cm

- Label its endpoints by A and B (AB = 4 cm)

- Open your compass at a distance greater then half AB (3 cm)

- Put the pin of the compass at point B and draw an arc intersects AB

 at point E and the horizontal line at point F

- Open the compass at a distance greater than the length of the side

 of the square (6 cm) and put its pin on the point E and draw an arc

- Put the pin of the compass on the point F without changing the open

 of the compass and draw another arc

- The two arcs intersect each other at point G

- Join BG and measure 4 cm from point B and label the end point of

 the 4 cm by C

- Open your compass at a distance 4 cm and put the pin on point C

 and draw an arc and put it on point A with the same distance 4 cm

 and draw another arc, the two arc intersect each other at point D

∴ ABCD is a square of side length 4 cm

# Look to the attached figure to more understand

Answer:

Step-by-step explanation:

Step 1 : 27-t*3

Now put the value  t=6

Step 2:

=27-6*3

According to the DMAS rule multiplication wll be solved first.

Step3:

=27-18

Step 4:

=9 ....

Answer:

x = 5

Step-by-step explanation:

the expression is "undefined"  when the denominator is equal to zero

denominator =  25 - x²

Values of x where the equation is "undefined"

0 = 25 - x²

x² = 25

√x² = √25

x = ± 5

Nonnegative value of x where the equation is "undefined"

x = 5

An expression is said to be undefined, if it has 0 as its denominator. For [tex]\frac{5 + x}{25 - x^2}[/tex] to be undefined, x must be 5.

Given that:

[tex]\frac{5 + x}{25 - x^2}[/tex]

For the expression to be undefined, the denominator must equal 0.

i.e.

[tex]25 - x^2 = 0[/tex]

Collect like terms

[tex]-x^2 = 0 - 25[/tex]

[tex]-x^2 = - 25[/tex]

Cancel out negatives

[tex]x^2 = 25[/tex]

Take positive square root

[tex]x = 5[/tex]

This means that when [tex]x = 5[/tex],  [tex]\frac{5 + x}{25 - x^2}[/tex] is undefined.

Read more about undefined expressions at:

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Answer:

8a.

Step-by-step explanation:

32 = 2*2*2*2*2

40 = 2*2*2* 5

Thus the GCF of 32 and 40 is 2*2*2 = 8.

The GCF of a and ab = a.

For this case we must find the GCF of the following expressions:

[tex]32ab ^ 3\\40a ^ 2[/tex]

By definition, the GCF is given by the largest factor that divides both numbers without leaving residue.

We look for the factors of 32 and 40:

32: 1,2,4,8,16

40: 1,2,4,5,8,10,20

Thus, the GCF is 8.

On the other hand, the GCF of [tex]ab ^ 3[/tex]and [tex]a ^ 2[/tex] is a.

Finally, the GFC of the expressions is:

[tex]8a[/tex]

Answer:

[tex]8a[/tex]

Answer:

Two times the difference of a number x and 7 plus 10.

Step-by-step explanation:

We are to write a phrase which matches the following algebraic expression below:

[tex] 2 ( x − 7 ) + 1 0 [/tex]

We can see that there is a bracket with a coefficient outside it so we can express it as:

'Two times the difference of a number x and 7'.

While + 10 can be added to it to complete the phrase:

Two times the difference of a number x and 7 plus 10.

Finding the slope using two points:

The formula for slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =-7\\y_{1} =2\\x_{2} =4\\x_{1} =-3[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{-7 - 2}{4 - (-3)}[/tex]

[tex]\frac{-9}{6}[/tex]

^^^Reduce this fraction

[tex]\frac{-3}{2}[/tex]

^^^This is your slope

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Option A.) 16 m³. The volume of the new pyramid is the volume of the original pyramid times 1/64.

Step-by-step explanation:

step 1

Find the volume of the original pyramid

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base

h is the height of the pyramid

we have

[tex]B=16^{2}=256\ m^{2}[/tex] ----> is the area of a square

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

substitute

[tex]V=\frac{1}{3}(256)(12)[/tex]

[tex]V=1,024\ m^{3}[/tex]

step 2

Find the volume of the new pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z -------> the scale factor

x ------> the volume of the new pyramid

y -----> the volume of the original pyramid

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{1}{4}[/tex]

[tex]y=1,024\ m^{3}[/tex]

substitute and solve for x

[tex](\frac{1}{4})^{3}=\frac{x}{1,024}[/tex]

[tex]x=(1,024)\frac{1}{64}=16\ m^{3}[/tex]

therefore

The volume of the new pyramid is the volume of the original pyramid times 1/64

Answer:

The answer is A

Step-by-step explanation:

part A)

[tex]\bf \begin{array}{|c|cccccc|ll} \cline{1-7} x&8&27&64&125&&x\\ \cline{1-7} y&\stackrel{\sqrt[3]{8}}{2}&\stackrel{\sqrt[3]{27}}{3}&\stackrel{\sqrt[3]{64}}{4}&\stackrel{\sqrt[3]{125}}{5}&&\sqrt[3]{x} \\ \cline{1-7} \end{array}~\hspace{10em}y = \sqrt[3]{x}[/tex]

part B)

f(x) = 10 + 20x

so if you rent the bike for a few hours that is

1 hr.............................10 + 20(1)

2 hrs..........................10 + 20(2)

3 hrs..........................10 + 20(3)

so the cost is really some fixed 10 + 20 bucks per hour, usually the 10 bucks is for some paperwork fee, so you go to the bike shop, and they'd say, ok is 10 bucks to set up a membership and 20 bucks per hour for using it, thereabouts.

f(100) = 10 + 20(100) => f(100) = 2010.

f(100), the cost of renting the bike for 100 hours.

Answer:

True.

Step-by-step explanation:

This is  'less than' so the area below the line is shaded.

It is a dotted line  because the solution does not contain points on the line as the inequality sign is < NOT ≤.

Answer:

First option: True.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Given this inequality:

[tex]y<2x -5[/tex]

We know that the line is:

[tex]y=2x -5[/tex]

Whose slope is 2 and the y-intercept is -5

The symbol "<" provided in the inequalty, indicates that the shaded region must be below the line and the line must be dotted. Therefore, the answer is: TRUE.