Given that cos(30°) = cos(45°)cos(15°) + sin(45°)sin(15°), it follows that cos(30°) =

Answer: [tex](f\°g)(0)=3[/tex]

Step-by-step explanation:

- For the function g(x) you must find the value of y (output value) when [tex]x=0[/tex]. As you can see in the graph (observe the parabola), when [tex]x=0[/tex] (input value), then:

[tex]y=2[/tex] or [tex]g(0)=2[/tex]

- Now, 2 will be the input value of the function f(x). Then,  you must find the value of y (output value) when [tex]x=2[/tex]. As you can see in the graph of this function, when [tex]x=2[/tex], then:

[tex]y=3[/tex] or [tex]f(2)=3[/tex]

Therefore, you can conclude that:

[tex](f\°g)(0)=3[/tex]

The number in the parenthesis is the X value and they are looking for what the Y value is at that specific X.

So when you look at f(-2), find the Y value where the line crosses.

At X-2, the line crosses Y at -2

At X = 2, the line crosses at Y = 2

At X = 4, the line crosses at Y = 1

The answer is -2,2,1

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ We know that the total amount of distance he has to go is 8/8.

Add 3/8 and 1/8.

3/8+1/8=4/8. He went half of the way already.

Since he needs 8/8 and he already went 4/8, he has 4/8 left, or 1/2 left to go.

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

DOGE

Answer: A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. The formula  A=1/2 bh

Answer: the trainer uses a stimulus, paired with a reward to ge the response they want.

Step-by-step explanation:

Answer:

Step-by-step explanation:

5^2(72-45)/5

25(27)/5

675/5

135

Final answer:

The evaluated expression of 5 to the second power (72 - 45) divided by 5 is 135. This is found by subtracting inside the parentheses, squaring the number 5, multiplying these results, and finally dividing by 5.

Explanation:

Evaluating the Expression

To evaluate the expression 5 to the second power (72 - 45) divided by 5, we follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, we calculate the value within the parentheses:

72 - 45 = 27

Next, we raise 5 to the second power (also known as squaring a number):

52 = 5 × 5 = 25

Now, we multiply this result by the value we found within the parentheses:

25 × 27 = 675

Last, we divide by 5:

675 ÷ 5 = 135

Therefore, the evaluated expression is 135.

3^2 = 9

3^4= 81

9 x 81 = 729

Your answer is 729 . Good luck (:

The correct answer is 8 yd

63cm is smaller than 6 m

63 cm is less than 6 m. A centimeter is a small unit used to measure length. It is equal to one hundredth of a meter. The term "centi" is used in the International System of Units to represent 1/100 of something.

To look at the lengths of 63 cm and 6 m, one need to ensure that both values are in the same unit of measurement. Since 6 m is in meters, we should convert 63 cm to meters before making the comparison.

1 meter is equal to 100 centimeters, so one can convert 63 cm to meters by dividing it by 100:

63 cm = 63/100 m = 0.63 m

So,  both values are in meters, and one can compare them:

0.63 m < 6 m

Therefore,  one can say that 63 cm is less than 6 m.

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Answer:

1/4 or 0.25

Step-by-step explanation:

Isn't latex a devil?

You want to know the probability of a blue marble.

Formula

P(blue) = #Blue / # Total

Givens

#Blue = 333

#Total = 333 + 444 + 555 = 1332

Solution

P(blue) = 333 / 1332      Divide by 111

P(blue) = 3/12

P(blue) = 1/4 or 0.25

Answer:

1/4 or 0.25

Step-by-step explanation:

The exact circumference of a circle with a diameter of 15 inches is 41.72 inches

Check the picture below.

the volume of the prism will simply be the product of the triangular area and its length, it has a length of 8, thus

[tex]\bf \stackrel{\textit{area of a triangle}}{A=\cfrac{1}{2}bh}~~ \begin{cases} b=9\\ h=6 \end{cases}\implies A=\cfrac{1}{2}(9)(6)\implies A=27 \\\\\\ \stackrel{\textit{volume of the triangular prism}}{V=27\cdot 8}\implies V=216[/tex]

Answer:

C. x = -5.6 and x = -1.4

Step-by-step explanation:

The quadratic formula is [tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]. Here a=1, b=7, and c=8.

Substitute and you'll have:

[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-7+/-\sqrt{7^2-4(1)(8)} }{2(1)}=\frac{-7+/-\sqrt{49-32} }{2)}[/tex]

[tex]\frac{-7+/-\sqrt{17} }{2}=\frac{-7+/-4.1 }{2}= -1.4, -5.6[/tex]

Answer:

3 ± i5

Step-by-step explanation:

Here we're given four sets of possible roots of the given polynomial.   Each set consists of two complex quantities and 1 real quantity.

First, we determine whether +4 is a root, then whether -4 is a root.  Let's use synthetic division to do that:

     -----------------------

4   /  1   -2    10   136

             4      8    72

    ---------------------------

        1     2    18    208     Since the remainder is not zero, 4 is not a root.

Eliminate the first two possible answer choices, and assume that -4 is a root.

Let's check this out to be certain:

     -----------------------

-4  /  1   -2    10   136

             -4   24  -136

    ---------------------------

        1     -6    34    0

Since the rem. is zero, -4 is a root, and the coefficients of the 2nd-degree quotient are 1, -6 and 34.

In other words, a = 1, b = -6 and c = 34.

Let's apply the quadratic rule to find the roots:

       6 ± √(36 - 4[1][34] )       6 ± √ (-100)

x = ------------------------------ = ----------------------- = 3 ± i5

                     2                                   2

So the correct answer is the last one of the four given possible answers:

3 ± i5

Answer:

[tex]3+5i, 3-5i,-4[/tex]

Step-by-step explanation:

Given is a cubic equation in x as

[tex]x^3-2x^2+10x+136=0[/tex]

We know by remainder theorem if f(a) =0 then x=a is a root

Constant term = 136 has factors as 1,2,4,8, 17, 34

We find that f(a) not 0 for a =1,2.

[tex]f(1) = 144\\f(2) = 156\\f(-1) = 123\\f(-4) = -64-2(16)+10(-4)+136 = 0[/tex]

Hence [tex]x=-4[/tex] is one zero.

We can divide by x+4 to make it as a quadratic equation

[tex]x^3-2x^2+10x+136=(x+4)(x^2-6x+34)[/tex]

Now using quadratic formula we can find other roots

[tex]x^2-6x+34=0[/tex] has roots as

[tex]x=\frac{6+/-\sqrt{36-136} }{2} \\=3+5i, 3-5i[/tex]

Thus roots are

[tex]3+5i, 3-5i,-4[/tex]

Answer:

Sarah is 22

Step-by-step explanation:

64 times 4 =44

44 divided by 2= 22

a.)0.4 is the multiplier

b.)$32 after 1 year, $2.048(or $2.05) after 4 years

c.)V(t) = 80(0.4)t

d.)10 years because it will be below 2 cents

e.) [The graph isn't hard, you just have to plug in the numbers into y=80(0.4)^x]

The multiplier we would use to calculate the DVD players is [tex]80(0.4)^x[/tex].

We get exponential rise when the base of the variable exponent is greater than 1 and exponential decay when base is less than 1.

According to the given question a DVD player loses 60% of its value every year it is a video store.

Also given that the initial value of the DVD player was 80 dollars.

If every years it looses 60% of it's value means it retains it's 40% value and 40% in decimal or fraction can be written as 40/100 = 4/10 = 2/5 = 0.4.

Let us denote the numbers of years by x.

∴ To calculate DVD player value each year after year we'll use [tex]80(0.4)^x[/tex] and it will be an exponential decay as multiplies is less than 1.

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Answer:

0

Step-by-step explanation:

0 is the furthest away from the average.

The number 0 would be your outlier

[tex]\bold{Hey\ there!}[/tex]

[tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

answer: D

explanation:

volume is equal to length * surface area.

surface of a tube base is a circle, so it' surface are can be calculated as:

[tex]\pi \: {r}^{2} [/tex]

where r is a radius

[tex] r \: = \frac{1}{2} diameter[/tex]

so you calculate volume V as:

[tex]v \: = \pi( {r}^{2} ) \times length \: = \pi \times \frac{1}{4} \times {diameter}^{2} \times length[/tex]

[tex]v = 3.14 \times \frac{1}{4} \times 4 \times 4 \times 24 = 301.44[/tex]

so the answer is D

Answer:

$8.25

Step-by-step explanation:

We first need to find the amount of money we give the cashier

20+10 = 30

We give the cashier 30 dollars

Our bill was 21.75

30.00

-21.75

---------------

We need to borrow

2 10.00

-2 1  .75

---------------

We need to borrow

2 9. 10 0

-2 1  .7  5

---------------

We need to borrow

2 9. 9  10

-2 1  .7  5

---------------

  8 .2   5

We will get $8.25 back from the cashier

Answer:

Step-by-step explanation:

I gave total $20+$10= $30

$30-$21.75= $8.25

Answer:

D

Step-by-step explanation:

The Answer is D, first you would multiply A by 2, then divide it by h. You would then subtract b2 giving you D.

The correct option is D

See the image

Answer:   [tex]\bold{x^{\frac{1}{3}}}[/tex]

Step-by-step explanation:

[tex]\sqrt[6]{x^2} =x^{\frac{2}{6}}=x^{\frac{1}{3}}[/tex]

Answer:

[tex]4.4\ hours[/tex]

Step-by-step explanation:

we know  that

using proportion

Ryan

Find how much can clear in one hour

[tex]\frac{100}{7.5}\frac{\%}{hours}=\frac{x}{1}\frac{\%}{hour}\\ \\x=100/7.5\\ \\x=13.33\%[/tex]

Ethan

Find how much can clear in one hour

[tex]\frac{100}{10.5}\frac{\%}{hours}=\frac{x}{1}\frac{\%}{hour}\\ \\x=100/10.5\\ \\x=9.52\%[/tex]

therefore

Ryan +Ethan in one hour can clear--------> [tex]13.33\%+9.52\%=22.85\%[/tex]

by proportion

[tex]\frac{100}{x}\frac{\%}{hours}=\frac{22.85}{1}\frac{\%}{hours}\\ \\x=100/22.85\\ \\x=4.4\ hours[/tex]

Answer:

The pressure is [tex]20\ psi[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

In this problem we have

[tex]V*P=k[/tex]

where

V is the volume of a gas at a constant temperature

P is the pressure

we have

For [tex]V=100\ in^{3}[/tex],[tex]P=25\ psi[/tex]

step 1

Find the value of k

substitute the values of V and P

[tex]100*25=k[/tex]

[tex]k=2,500[/tex]

The equation is equal to  [tex]V*P=2,500[/tex]

step 2

Find the pressure when the volume is 125 cubic inches

For [tex]V=125\ in^{3}[/tex]

substitute in the equation and solve for P

[tex]125*P=2,500[/tex]

[tex]P=2,500/125=20\ psi[/tex]

Answer:

the answer is 3/4

Step-by-step explanation:

Answer:

The correct answer is 3/4

Step-by-step explanation:

1/2+1/4=3/4

The surface area of a rectangular prism is SA = 2wl + 2lh + 2hw

Answer:

There is no prism

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

The pythagorean theorem says that a²+b²=h², therefore h = [tex]\sqrt{a^{2} +b^{2} }[/tex].

Based on Pythagorean theorem, the best solution for h that Paul writes is [tex]h=\sqrt{a^2 + b^2}[/tex]

Pythagorean theorem can be defined as a fundamental mathematical expression in Euclidean geometry that can be used to determine any of the three (3) sides of a right-angled triangle.

Mathematically, Pythagorean's Theorem is given by this formula:

[tex]h^2 = a^2 + b^2[/tex]

Where:

Simplifying further, we have:

[tex]h^2 = a^2 + b^2\\\\h=\sqrt{a^2 + b^2}[/tex]

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The slope is undefined because it is a vertical line

Answer:

Step-by-step explanation:

The vertical line equation has the form x = a (a - any real number).

The vertical line has an undefined slope.

We have x = -4. It's a vertical line. Therefore, the slope is undefined.

Answer:

456.5

Step-by-step explanation:

The area of circle B is 4,500.81 inches².

The first step to take in order to determine the answer is to determine the value of the diameter of circle B.

Area of a circle = πr²

Where :

π = pi = 3.14

R = radius

500 = 3.14r²

r = √(500 / 3.14)

r = 12.62 inches

Diameter = 2 x radius

2 x 12.62 = 25.24 inches

The second step is to determine the diameter of circle B.

Dimeter of circle B = 3 x 25.24 inches = 75.72 inches

Radius of circle B = 75.72 inches / 2 = 37.86 inches

Determine tie area of circle B

Area of circle B = 3.14 x 37.86² = 4,500.81 inches²

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Answer:

The y coordinate of point R is  [tex]-9[/tex]

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M(x,y)=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

In this problem

[tex]R(x2,y2)[/tex]

[tex]Q(-2,-6)=(\frac{-5+x2}{2},\frac{-3+y2}{2})[/tex]

so

[tex]-2=(-5+x2)/2[/tex] --->[tex]x2=-4+5=1[/tex]

[tex]-6=(-3+y2)/2[/tex] --->[tex]y2=-12+3=-9[/tex]

therefore

The y coordinate of point R is  [tex]-9[/tex]