Match the value to the correct image. Not all values will be used.
Find the approximate surface area of each right regular prism.

The exponent expression ∛(56x⁷y⁵) is equivalent to the expression 2x²y∛(7xy²).

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

The expression will be given as

[tex]\sqrt[3]{56x^7y^5}[/tex]

The expression can be written as

[tex]\rightarrow \sqrt[3]{2*2*2*7 \ x^3 \ x^3 \ x \ y^3 \ y^2 }\\\\\rightarrow 2*x*x*y * \sqrt[3]{7xy^2} \\\\\rightarrow 2x^2 y \sqrt[3]{7xy^2 }[/tex]

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Answer:

x=4

Step-by-step explanation:

20x-5x=65-5

15x=60

x=60/15

x=4

Answer:

Step-by-step explanation:

In the question we are given with an equation that is 20x + 5 = 5x + 65 . And we are asked to find the value of x.

Solution :

[tex] \longmapsto \: 20x + 5 = 5x +65[/tex]

Step 1 : Subtracting 5 on both sides :

[tex] \longmapsto \: 20x + \bold{ \cancel{5}} - \bold{ \cancel{5}}= 5x + \bold{65 }- \bold{5}[/tex]

On further calculations, we get :

[tex] \longmapsto \: 20x = 5x + 60[/tex]

Step 2 : Subtracting 60 on both sides :

[tex] \longmapsto \:20x - 60 = 5x + \bold{ \cancel{60}}- \bold{ \cancel{60}}[/tex]

On further calculations, we get :

[tex] \longmapsto \:20x - 60 = 5x[/tex]

Step 3 : Transposing 5x to left hand side and -60 to right hand side :

[tex] \longmapsto \:20x - 5x = 60[/tex]

On further calculations , we get :

[tex] \longmapsto \:15x = 60[/tex]

Step 4 : Divide by 15 on both sides :

[tex] \longmapsto \: \frac{ \cancel{15}x}{ \cancel{15} } = \cancel{ \frac{60}{15} }[/tex]

On further calculations, we get :

[tex] \longmapsto \: \red{ \boxed{x = 4}}[/tex]

Now, we are verifying our answer by substituting value of x in given equation :

Therefore , our answer is correct

Answer:

[tex](x^{3} + 9\, x^{2} + 14\, x - 12)[/tex].

Step-by-step explanation:

Let [tex]p(x)[/tex] denote the polynomial in question.

The question states that dividing [tex]p(x)[/tex] by [tex](x + 3)[/tex] gives the quotient [tex](x^{2} + 6\, x - 4)[/tex] (with no remainder.) In other words:

[tex]\displaystyle \frac{p(x)}{x + 3} = x^{2} + 6\, x - 4[/tex].

Multiply both sides by [tex](x + 3)[/tex] to find an expression for the polynomial in question, [tex]p(x)[/tex]:

[tex]p(x) = (x^{2} + 6\, x - 4)\, (x + 3)[/tex].

Expand this expression to obtain:

[tex]\begin{aligned}p(x) &= (x^{2} + 6\, x - 4) \, (x + 3) \\ &= x\, (x^{2} + 6\, x - 4) \\ & \quad + 3\, (x^{2} + 6\, x - 4) \\ &= x^{3} + 6\, x^{2} - 4\, x \\ &\quad + 3\, x^{2} + 18\, x - 12 \\ &= x^{3} + 9\, x^{2} + 14\, x - 12\end{aligned}[/tex].

Answer:

its 18

Step-by-step explanation:

Answer:

the answer is 18

Step-by-step explanation:

Answer: 2.23 hours

Step-by-step explanation:

dimensions of the room------------------- >16*13

1 in---------------- >0.0833333 foot

3 in----------------- >x

x=3*.0833333=0.25 ft

Let

C-------------- > dimensions of the piece of carpet that Charlotte must purchase

C-------------- > (16+2*0.25)*(13+2*0.25)---------- > (16.50)*(13.50)=222.75 ft²

The answer a the question 1) is 16.50 feet X 13.50 feet

The answer a the question 2) is 222.75 ft²

3. How many hours should it take for the four-person crew to lay the flooring in Charlotte's bedroom?

if two-person carpet crew can lay 50 square feet of carpet---------- > 1 hour

four person carpet crew can lay 100 square feet of carpet---------- > 1 hour

therefore

if  100 ft² carpet----------------------- > 1 hour

222.75 ft² carpet--------------------- > x

x=222.75/100=2.2275 hours=2.23 hours

The answer is 2.23 hours

Answer:

19 cubic centimeters

Step-by-step explanation:

The equation for the volume of a sphere is [tex](4/3)\pi r^3[/tex].

We can setup the equation as [tex]29307 = \frac{4}{3}\pi r^3[/tex].

Now we need to isolate the r^3.  Divide both sides by 4/3 and pi, which leaves [tex]\frac{29307}{(4/3) \pi } =r^3[/tex]

Now we take the cube root of both sides to have a single r on the right side.  This comes out to equal 19 cm^3

Answer:

77

Step-by-step explanation:

A=B x H divide by 2

A= 14 x 11 /2 = 77

The linear function f(x) = ax + b has a constant rate

The conclusion from the each interval is that the function values changes at a constant rate

The linear function is given as:

f(x) = ax + b

The interval is given as:

[-3,3] and [9,15]

Since the function is a linear function, the conclusion from the each interval is that the function values changes at a constant rate

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Answer:

h = 16.5

Step-by-step explanation:

Remark

The formula below really is the Pytharagan formula disguised.

h^2 = hypotenuse (side)^2 - (1/2 side)^2

Givens

side = 19 cm

Solution

h^2 = 19^2 - (1/2*19)^2      Substitute given into formula

h^2 = 361 - (9.5)^2            square 9.5

h^2 = 361 - 90.25             Subtract

h^2 = 270.75                    Take the square root of both sides

√h^2 = √270.75

Answer: h = 16.5

Check the picture below.

we know the LA is 9 and 1/2 or namely 19/2 and the height is 5, so

[tex]\stackrel{slant~height}{\cfrac{19}{2}}~~ = ~~\stackrel{slant~height}{\sqrt{r^2+h^2}}\implies \left( \cfrac{19}{2} \right)^2~~ = ~~r^2+5^2\implies \cfrac{361}{4}~~ = ~~r^2+25 \\\\\\ \cfrac{361}{4} - 25~~ = ~~r^2\implies \cfrac{261}{4}=r^2\implies \sqrt{\cfrac{261}{4}}=r\implies \boxed{\cfrac{3\sqrt{29}}{2}=r} \\\\[-0.35em] ~\dotfill\\\\ LA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}\implies LA=\pi \left( \cfrac{3\sqrt{29}}{2} \right)\cfrac{19}{2}\implies \boxed{LA=\cfrac{57\pi \sqrt{29}}{4}}[/tex]

[tex]~\dotfill\\\\ SA=\pi r\sqrt{r^2+h^2}~~ + ~~\pi r^2\implies SA=LA~~ + ~~\pi r^2 \\\\\\ SA=\cfrac{57\pi \sqrt{29}}{4}~~ + ~~\cfrac{3\pi \sqrt{29}}{2}\implies \boxed{SA=\cfrac{63\pi \sqrt{29}}{4}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill LA\approx 241.1\qquad SA\approx 266.5~\hfill[/tex]

Answer:

12x3-9x

=3-12x9x

=3-21x

=21x-3

Answer:

The answer is 221/2 or 73 ⅔

Step-by-step explanation:

5 ⅔ = (3 × 5 + 2) ÷ 3 = 17/3

Now,

17/3 × 13 = 221/2 = 73 ⅔

Thus, The answer is 221/2 or 73 ⅔

Answer:

Step-by-step explanation:

For the first problem you have:

[tex]sin^2(x)-sin(x)=0[/tex]

Factor out a sin(x) to get:

[tex]sin(x)[2sin(x)-1]=0[/tex]

Individually, set both terms equal to zero:

[tex]sin(x)=0[/tex]

[tex]2sin(x)-1-0[/tex]

The first equation is asking "sine of what angle gives zero?" The sine of 0 will give zero, and so will the sine of pi, and 2pi, etc. Therefore, you can generalize this by saying the solution is pi multiplied by an integer 'n' where 'n' can be from zero to infinity:

[tex]x=n\pi[/tex]

where n = 0, 1, 2, 3, 4, 5, etc..

(make sure you specify that 'n' can equal zero.)

For the second equation, add 1 to both sides to get:

[tex]2sin(x)=1[/tex]

Divide both sides by 2 to get:

[tex]sin(x)=\frac{1}{2}[/tex]

Sine of what gives 1/2? Sine of pi/6 gives 1/2, and so does 5pi/6. Therefore, the two solution here would be pi/6 plus a phase shift of 2pi, and 5pi/6 plus a phase shift of 2pi:

[tex]x=\frac{\pi }{6} +2n\pi[/tex]

[tex]x=\frac{5\pi }{6} +2n\pi[/tex]

The second problem states that:

[tex]cos(u)=\frac{4}{5}[/tex]

Cosine is defined as the adjacent side of a right triangle divided by the hypotenuse of the right triangle:

[tex]cos(u)=adjacent/hypotenuse[/tex]

After drawing a triangle, the adjacent side is 4, and the hypotenuse is 5. But first, lets rewrite sin(2u) using the double angle identity to get:

[tex]sin(2u)=2sin(u)cos(u)[/tex]

But we know the value of cosine of 'u', it is 4/5. Therefore:

[tex]sin(2u)=2sin(u)*\frac{4}{5}[/tex]

[tex]sin(2u)=\frac{8}{5} sin(u)[/tex]

To find the sine of 'u', use the triangle you should have constructed when I defined cosine as the adjacent over the hypoptenuse. Sine is defined as the opposite over the hypotenuse. We have:

[tex]sin(u)=opposite/hypotenuse[/tex]

We have the adjacent, we have the hyppotenuse, and we want the opposite. If we find the opposite side, we can find the sin(2u). Use pythagogrean's theorem to find the opposite:

[tex]adjacent^2+opposite^2=hypotenuse^2[/tex]

[tex]4^2+opposite^2=5^2[/tex]

[tex]opposite^2=25-16[/tex]

[tex]opposite=3[/tex]

Finally, we have that:

[tex]sin(u)=\frac{3}{5}[/tex]

Or:

[tex]sin(2u)=\frac{8}{5}*\frac{3}{5} =24/25[/tex]

Hopefully you could follow along. There is a lot going on here, but since youre in pre-calc, you should be able to follow along as long as you follow my steps.

Answer:

The correct to the question about is simply C. A is ruled out because it doesn't represent refections

Answer:

well its two

Step-by-step explanation:

but A nonlinear system could be representative of two circles that overlap and intersect in two locations, hence two solutions. A nonlinear system could be representative of a parabola and a circle, where the vertex of the parabola meets the circle and the branches also intersect the circle, hence three solutions.

Answer:

64 square in.

Step-by-step explanation:

4*4=16

4*6*1/2*4= 48

16+48= 64

Answer:

64in^2

Step-by-step explanation:

Surface area of pyramid =

[tex] \frac{1}{2}( p \times l) + b[/tex]

plugging the numbers in, 1/2(16*6)+16

SA= 64

Answer:

C. Students in language arts classes.

Step-by-step explanation:

Because out of all of the options, this one seems like it is the best time that they could get the students attention and get an acurate response.

La manguera que necesita Martín para rodear el helado es de 304,48m

Para calcular la longitud de la manguera que necesita Martín para rodear el helado es necesario aplicar la siguiente fórmula matemática:

De acuerdo a lo anterior, la longitud de la manguera que necesita Martín es de 304,48m.

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Answer:75

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

The answer is: 7π6=−π6

π= 3.14 or 22/7

so 7x3.14= 21.98

than divide by 6

Answer:

Below in bold.

Step-by-step explanation:

x^2 + 2x- 11 = 0

x^2 + 2x = 11

x^2 + 2x + 1 = 11 + 1

(x + 1)^2 = 12

x + 1 = ±√ 12

x = -1  ± √12

= -4.464, 2.464 to the nearest thousandth.

Answer:

Part 1: 2.25

Part 2: (5, 11.25)

Step-by-step explanation:

Part 1: 33.75/15= 2.25

Part 2: 5*2.25= 11.25

Answer:

9x²

Step-by-step explanation:

(- 3x)²

= - 3x × - 3x

= - 3 × - 3 × x × x

= 9 × x²

= 9x²

An exponential decay function is flx) = (-3)9, the correct option is D.

Consider the function:

[tex]y = a(1\pm r)^m[/tex]

where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is plus sign, then there is exponential growth happening by r fraction or 100r %

If there is negative sign, then there is exponential decay happening by r fraction or 100r %

We are given that;

f(x) =4

An exponential decay function is a function of the form:

f(x) = ab^x

where a and b are positive constants and b < 1.

The value of b determines how fast the function decreases as x increases. The smaller the value of b, the faster the decay.

To find which option is an exponential decay function, we need to compare their values of b.

Option A has f(x) = 4(1/3)x. This means that b = 4^(1/3), which is approximately 1.587. Since b > 1, this is not an exponential decay function.

Option B has f(x) = 13(7)^x. This means that b = 7, which is greater than 1. This is not an exponential decay function.

Option C has f(x) = (9/5)^x. This means that b = 9/5, which is also greater than 1. This is not an exponential decay function.

Option D has f(x) = (-3)(9)^(-x). This means that b = 9^(-1), which is equal to 1/9. Since b < 1, this is an exponential decay function.

Therefore, by exponential growth and decay the answer will be flx) = (-3)9

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Answer:

10.47 to the nearest hundredth

Step-by-step explanation:

By Pythagoras

c^2 = 2^2 + 4^2 = 20

c = √20

c = 4.47

Perimeter = 2 + 4 + 4.472

The perimeter of the right-angled triangle is 6 + 2√(5) feet.

Pythagoras' Theorem states that the square of the hypotenuse side of a right-angled triangle is equal to the sum of the squares of the other two sides.

Given that a right-angled triangle.

The perpendicular length is 2 feet, the base length is 4 feet.

We need to use the Pythagorean theorem to find the length of the hypotenuse, and then add up the lengths of all three sides to get the perimeter.

In this case, we can use it to find the length of the hypotenuse c:

2² + 4² = c²

4 + 16 = c²

20 = c²

c = √(20) = 2√(5)

Now we can add up the lengths of all three sides to get the perimeter:

Perimeter = a + b + c

Perimeter = 2 + 4 + 2√(5)

Perimeter = 6 + 2√(5) feet

Therefore, the perimeter = 6 + 2√(5) feet

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Answer:

(D) 29.3

Step-by-step explanation:

The answer is all the days added together and then divided by 10.

20+30+40+38+25+22+39+22+26+31=293.

293/10=29.3

Answer:

Given Equation

[tex] \bf \: 25 {x}^{2} - 64[/tex]

we have to factorise the given equation .

We will use the following identity here

Let's factorise it

[tex]\sf \longrightarrow \: 25 {x}^{2} - 64 \\ \\ \\ \sf \longrightarrow \: {5x}^{2} - {8}^{2} \\ \\ \\ \sf \longrightarrow \:(5x + 8)(5x - 8)[/tex]

Therefore,

So, your answer is (5x+8) ( 5x-8)

The expression  [tex]\rm log_{7} 98[/tex]  using the product property is [tex]\rm log_{7} 49 + \rm log_{7} 2[/tex].

A logarithm is the exponentiation inverse function that can be expressed by the exponent or power to which a base must be raised to yield a number.

It is given that [tex]\rm log_{7} 2[/tex] = 0.356

We can write [tex]\rm log_{7} 98[/tex] in terms of  [tex]\rm log_{7} 2[/tex]

[tex]\rm log_{7} 98[/tex] = [tex]\rm log_{7} (49\times 2)[/tex]

In logarithm, the product will change in addition

[tex]\rm log_{7} 98[/tex] = [tex]\rm log_{7} (49\times 2)[/tex]

= [tex]\rm log_{7} 49 + \rm log_{7} 2[/tex]

Hence, the expression  [tex]\rm log_{7} 98[/tex]  using the product property is [tex]\rm log_{7} 49 + \rm log_{7} 2[/tex]

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Answer:

log7 2 + log7 49

log7 49= 2

Step-by-step explanation: