A rotation is a transformation that turns a figure around a given ______ called the center of rotation
Will give BRANILEST

To solve this math problem, calculate the expression, write a linear equation, and round the result. Include units in your final answer.

To solve this math problem, you need to calculate the given expression, write a linear equation, and round the result to four decimal places. Let's break it down:

Remember to include the appropriate units in your final answer.

Answer:

dssdac

Step-by-step explanation:

Answer:

The average rate of change is:

[tex]\frac{13}{161}[/tex]

Step-by-step explanation:

The rational function given to us is;

[tex]f(x)=\frac{3x+4}{2x+7}[/tex]

[tex]f(0)=\frac{3(0)+4}{2(0)+7}[/tex]

[tex]f(0)=\frac{4}{7}[/tex]

[tex]f(8)=\frac{3(8)+4}{2(8)+7}[/tex]

[tex]f(0)=\frac{28}{23}=1[/tex]

The average rate of change of this function from x=0 to x=8  is the slope of the secant line connecting:

(0,f(0)) and (8,f(8))

Average rate of change =[tex]=\frac{f(8)-f(0)}{8-0}[/tex]

[tex]=\frac{\frac{28}{23}-\frac{4}{7} }{8}[/tex]

[tex]=\frac{13}{161}[/tex]

Answer:

Option a) [tex]h=28\ cm[/tex]

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

Note In this problem the volume is equal to [tex]847\pi\ ml[/tex] instead of [tex]847\ ml[/tex]

so

[tex]847\pi\ ml=847\pi\ cm^{3}[/tex]

[tex]r=5.5\ cm[/tex]

substitute in the formula and solve for h

[tex]847\pi=\pi(5.5)^{2}h[/tex]

simplify

[tex]847=(5.5)^{2}h[/tex]

[tex]h=847/(5.5)^{2}[/tex]

[tex]h=28\ cm[/tex]

Answer:

You can find the point of intersection of the line with the y-axis and the  the point of intersection of the line with the x-axis. See the graph attached.

Step-by-step explanation:

Find the intersection with the y-axis. Substitute [tex]x=0[/tex] into the equation and solve for y:

[tex]y-3=\frac{1}{3}(x+1)\\\\y-3=\frac{1}{3}(0+1)\\\\y-3=\frac{1}{3}(1)\\y=\frac{1}{3}+3\\\\y=\frac{10}{3}[/tex]

[tex]y[/tex]≈3.33

Find the intersection with the x-axis. Substitute [tex]y=0[/tex] into the equation and solve for x:

[tex]y-3=\frac{1}{3}(x+1)[/tex]

[tex]0-3=\frac{1}{3}(x+1)\\(-3)(3)=x+1\\-9-1=x\\x=-10[/tex]

Now, you know that the line passes through the point (0,3.33) and (-10,0). Now you can graph the function. (Observe the graph attached)

ANSWER

[tex]y = 3( \frac{1}{2} )^{2} [/tex]

and

[tex]y = ( {0.25)}^{x} [/tex]

EXPLANATION

The first equation represents an exponential decay because;

[tex]y = 3( \frac{1}{2} )^{2} [/tex]

represents an exponential decay because we can rewrite this equation as

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

The equation;

[tex]y = ( {0.25)}^{x} [/tex]

is also an exponential decay because

this equation can also be written as:

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

All exponentiial functions of the form

[tex]y = a( {b}^{kx} )[/tex]

where k is negative is an exponential decay function.

Answer:

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[tex]x\geq 3 \ and \ x+1 \geq 4[/tex]

The question in this problem is:

The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger. What are the numbers?

First of all, let's name the first variable [tex]x[/tex] which is the smaller number. Accordingly, the lager number will be [tex]x+1[/tex] given that those numbers are consecutive. On the other hand at most conveys the idea of an inequality, which is:

[tex]\leq \\ which \ means \ less \ than[/tex]

So:

1. The sum of 2 consecutive integers can be written as:

[tex]v+(v+1)[/tex]

2. Nine times the smaller and 5 times the larger can be written as:

[tex]9v-5(v+1)[/tex]

Finally, the whole statement:

The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger:

[tex]x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\ [/tex]

[tex]x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\ \frac{6}{2} \leq \frac{2x}{2} \\ \\ 3 \leq x \\ \\ x\geq 3 \\ \\ and \\ \\ x+1 \geq 4[/tex]

The two numbers are:

[tex]x\geq 3 \ and \ x+1 \geq 4[/tex]

Plot the points ( -4,2.5), (-3,3), (-2,1.5), (-1,2), (0,1), (1,2), (2,3.5), (3,0.5), (4,2.5) then connect them with a line

Answer:

[tex]f(x)=|x+4|+2[/tex]

Step-by-step explanation:

The given absolute value function is

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

This is the base or the parent function.

The transformation [tex]f(x)=|x+b|+c[/tex] will shift the parent function b units to the left and c units up.

From the question, b=4 units and c=2 units.

The new equation is [tex]f(x)=|x+4|+2[/tex]

Answer:  The equation of the new function is [tex]f(x)=|x+4|+2.[/tex]

Step-by-step explanation:  We are given to find the equation of the new function if we apply the following changes to the absolute value parent function f(x)=lxl :

Shift 4 units left   and  Shift 2 units up.

We know that

if we shift the absolute value parent function f(x) = |x| to h units left and k units up, then the new equation will be

[tex]f(x)=|x+h|+k.[/tex]

Therefore, if the function is shifted 4 units left and 2 units up, then the equation of the new function will be

[tex]f(x)=|x+4|+2.[/tex]

Thus, the equation of the new function is [tex]f(x)=|x+4|+2.[/tex]

Answer:

Option: B is the correct answer.      

B)     Decay, y- intercept = 3.4, rate is 34%

Step-by-step explanation:

We are given an exponential equation as follows:

                    [tex]y=3.4(0.66)^x[/tex]

We know that any exponential function of the type:

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

is growth function if: b>1

and is a decay function if 0< b< 1

Hence, here we have: b=0.66<1

Hence, the function is a decay function.

Also, we know that the y-intercept of a function is the point where x=0

Hence, we take x=0

we have:  [tex]y=3.4\times (0.66)^0\\\\\\y=3.4[/tex]

Hence, the y-intercept is:   3.4

Also, the rate of a function is denoted by 'r'

where b=1-r

    ⇒ 0.66=1-r

   ⇒   r=1-0.66

    ⇒ r=0.34

Hence, the rate is: 34%

          option: B is the correct answer.

Answer:

Option 1 and 2 are correct.

Step-by-step explanation:

1. {x:x <-3 or >4}

Here the values of x can be less than -3 or the values of x can be greater than 4. Since 5 is greater than 4 so, 5 is included in the solution

2. {x:x ≥5}

Here the values of x can be greater than or equal to 5. So, 5 is included in the solution.

3. {x:x <5}

Here the values of x can be less than 5. So, 5 is not included in the solution

4. {x:0<x<4}

Here the value of x is greater than 0 but less than 4. So, 5 is not included in the solution

So, Option 1 and 2 are correct.

Answer:

[tex]A=(2x^{2}+9x-18)\ m^{2}[/tex]

Step-by-step explanation:

Let

L-----> the length of the concert hall

W----> the width of the concert hall

we know that

The area of a rectangle ( concert hall) is equal to

[tex]A=LW[/tex]

we have

[tex]L=(x+6)\ m[/tex]

[tex]W=(2x-3)\ m[/tex]

substitute the values

[tex]A=(x+6)(2x-3)\\ \\A=2x^{2} -3x+12x-18\\ \\A=(2x^{2}+9x-18)\ m^{2}[/tex]

The area of the concert hall's floor, in square meters, is represented by the simplified algebraic expression 2x² + 9x - 18, which is derived by multiplying the hall's length (x + 6) by its width (2x - 3) then simplifying the resulting expression.

The area of a rectangle is calculated by multiplying the length by the width. In this case, the length of the concert hall is given as (x + 6) meters and the width as (2x - 3) meters. Therefore, the area of the concert hall's floor, expressed in square meters, is the product of these two expressions.

So, you multiply (x + 6) by (2x - 3) to get the area, which gives you the following expression: 2x² - 3x + 12x - 18. Now, simplify this expression by combining like terms.

The simplified expression for the area of the floor in square meters is then 2x² + 9x - 18.

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Answer:

Kyle purchased 12 pencils

Step-by-step explanation:

p= pencils

1.24p - 5.12 = 20

or, you can do this back wards like this....

20 - 5.12 = 14.88

14.88 / 1.24 = 12

p=12

(sorry for any confusion, this is just how my brain works...)

Kyle bought 12 pencils at $1.24 each. This determination is based on subtracting the amount of change he received from his $20 payment and dividing by the cost per pencil.

Kyle bought x pencils for $1.24 each, paid with a $20 bill, and received $5.12 in change. Therefore, the total amount he spent can be calculated by subtracting the change from the total payment ($20 - $5.12 = $14.88). As he spent this amount on pencils that cost $1.24 each, the number of pencils he bought can be determined by dividing the total spent by the cost per item ($14.88 / $1.24). Therefore, Kyle bought approximately 12 pencils (the exact result is 12.003, but as pencils cannot be fractional, we round down to the nearest whole number).

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Find the x intercepts by setting each x to equal 0:

(4-x)=0

4 -4 = 0

First x intercept = (4,0)

(x+2) = 0

-2 + 2 = 0

Second x intercept = (-2,0)

Now find the Y intercept by setting the x's to 0 and solve for y:

y = (4-0)(0+2)

y = 4*2

y = 8

The Y intercept is (0,8)

Now find the graph the the parabola crosses the x axis at -2 and 4 and also crosses the Y axis at 8.

Graph A is the correct one.

Answer:

Second graph

Step-by-step explanation:

The second graph is the correct one.  Why?  because the y intercept is (0, 3), and also because the base, 1/5, is between 0 and 1, which leads to a decaying exponential graph.

Answer:

-6.912

Step-by-step explanation:

Answer: -6.912

Step-by-step explanation: -6.912 Would Be Your Answer. Have A Great Day!

Answer:

7+24i

Step-by-step explanation:

A math conjugate is formed by changing the sign between two terms in a binomial. For instance, the conjugate of x + y is x - y. We can also say that x + y is a conjugate of x - y. In other words, the two binomials are conjugates of each other.

The conjugate of a complex number is obtained by negating its imaginary part while keeping the real part unchanged. So, for 7 - 24i, the conjugate is 7 + 24i. The real part remains 7, and the imaginary part changes from -24i to +24i.

In the field of mathematics, specifically complex numbers, the conjugate of a complex number is formed by changing the sign of its imaginary part. Given the complex number 7 - 24i, its conjugate is obtained by changing the sign of the imaginary part (-24i) to a positive. So, the conjugate of 7 - 24i is 7 + 24i.

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Answer:

120

Step-by-step explanation:

it is an obtuse angle

The answer is:

The missing angle "x" is equal to 130°.

We need to remember that the sum of all of the angles of any polygon will be all equal to 360°.

So, we are given the following exterior angles:

[tex]140\°\\34\°\\56\°\\[/tex]

Now, if the sum of all the exterior angles is equal to 360°, we can use it to calculate "x", so:

[tex]360\°=140\°+34\°+56\°+x\\\\x=360\°-(140\°+34\°+56\°)=360\°-230\°\\\\x=130\°[/tex]

Hence, the missing angle "x" is equal to 130°.

Have a nice day!

Answer:

59,000 * .02= $1,180 commission plus $300 = $1480

(.15 miles / 1 minute) * (60 minutes / 1 hour) = 9 miles / hour

Answer:

314 cm²

Step-by-step explanation:

It's not the point O, but the circle O, a point has no area.

The area of a circle is given by the formula A = π r²

We don't have r (radius), but we have the diameter, which is double the radius.  So, r = d / 2 = 20 cm / 2 = 10 cm

Now, we can plug r directly into the equation:

A = π r² = π 10² = 100π = 314 cm²

Answer:0.15789474

Step-by-step explanation:

5/2=2.5s+ 3/4=0.75 = 9/4=2.25

add 5/2/2.5 to the other side{like terms because of the letter s} which would=4.75s

now divide that to other side of .75 divided by 4.75 which would equal= 0.15789474

(i think, sorry if its incorrect)

Answer:

The value of s is -0.33

Step-by-step explanation:

Given the equation

[tex]\frac{5}{2s}+\frac{3}{4}=\frac{9}{4s}[/tex]

we have to solve the above equation

[tex]\frac{5}{2s}+\frac{3}{4}=\frac{9}{4s}[/tex]

[tex]\frac{5}{2s}-\frac{9}{4s}=-\frac{3}{4}[/tex]

[tex]\frac{10-9}{4s}=-\frac{3}{4}[/tex]

[tex]\frac{1}{4s}=-\frac{3}{4}[/tex]

[tex]s=-\frac{1}{3}=-0.33[/tex]

The value of s is -0.33

7lb in 12 oz equals blank ounces = 124 ounces

Answer:

[tex]\cos^{-1}(\frac{6.3}{9.8})[/tex]

[tex]\sin^{-1}(\frac{7.5}{9.8})[/tex]

Step-by-step explanation:

Recall the mnemonics SOH-CAH-TOA

The sine ratio is the length of the opposite side expressed over the hypotenuse.

[tex]\sin m\angle ABC=\frac{7.5}{9.8}[/tex]

Take the sine inverse of both sides to get;

[tex]m\angle ABC=\sin^{-1}(\frac{7.5}{9.8})[/tex]

The cosine ratio is the length of the adjacent side expressed over the hypotenuse.

[tex]\cos m\angle ABC=\frac{6.3}{9.8}[/tex]

Take the cosine inverse of both sides to get;

[tex]m\angle ABC=\cos^{-1}(\frac{6.3}{9.8})[/tex]

Answer:

The explicit rule is:

Step-by-step explanation:

The explicit rule is given by:

[tex]a_n=a_1+d(n-1)[/tex]

The given sequence is 25,21,17,13

[tex]a_1=25[/tex]

d=21-25

d=-4

We plug in the values into the formula to get;

[tex]a_n=25+-4(n-1)[/tex]

[tex]a_n=25-4n+4[/tex]

[tex]a_n=29-4n[/tex]

Answer:

B. is your answer because its compounded

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that Leah flips a coin, and then she spins the pointer on a spinner with equal sections of red, green, and blue.

Both flipping a coin and spins the pointer on a spinner is the compound event.

A is not compound since only coin is flipped

B is compound because it contains two events together

C is compound

D is not compound as this is single event.

5280 feet in a mile

3.25 x 5280 = 17160 feet

the answers is 17,160 ft. one mile contains 5280 feet.

Answer:

The answer is C. 119cm³

Step-by-step explanation:

SA= [tex]\pi r^{2} +\pi rl[/tex]

    = 49[tex]\pi +\pi 7(10)[/tex]

    = 49[tex]\pi +20\pi[/tex]

SA= 119[tex]\pi[/tex]

Answer:

The correct answer is option C.   119π cm²

Step-by-step explanation:

Points to remember

Surface area of cone = πrl + πr²

Where r is the base radius and l is the lateral edge

To find the surface area of given cone

Here r = 7 cm and l = 10 cm

Surface area =  πrl + π r² =( π * 7 * 10) + (π *7²)

  = 70 π + 49π

  = 119π cm²

Therefore correct answer is option C.    119π cm²

Since the perimeter of said hexagon is 120√3, we simply multiply this number by 10 and divide it by 2.

1200√3/2 = 600√3

Answer:

d. 40 pounds

Step-by-step explanation:

We know both weights of the astronaut, and we know one of the weight of the rock... we need to find the other weight of the rock (on Earth).

The easiest way to deal with those problems is to use a cross-multiplication.

We'll place on top the weights on Earth and as denominators the weights on Mars:

[tex]\frac{x}{16} = \frac{180}{72}[/tex]

So we isolate x = (16 * 180) / 72 = 2,880 / 72 = 40 pounds.

The rock then weights 40 pounds on Earth.