The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism?

a base area of 4y square units and height of 4y2 + 4y + 12 units
a base area of 8y2 square units and height of y2 + 2y + 4 units
a base area of 12y square units and height of 4y2 + 4y + 36 units
a base area of 16y2 square units and height of y2 + y + 3 units

Answer:

B

Step-by-step explanation:

At - infinity, the function will tend to 0 and at +infinity, the function will tend to +infinity. Those are the two extremas of the function and extremas define the range. Range is all positive real number

Answer:

£32.50

Step-by-step explanation:

my first question to the teacher : so, no windows in the living room ?

so, it is a square living room with 5.5 m side length.

but each wall is a rectangle of 2.2 × 5.5 m.

for one wall we have to deduct a door area of 1.8×0.9 m.

so, one wall

2.2 × 5.5 = 12.1 m²

4 walls

4 × 12.1 = 48.4 m²

minus one door area

1.8 × 0.9 = 1.62 m²

48.4 - 1.62 = 46.78 m² total paint area

1 L paint covers 8 m².

so, we need 46.78/8 = 5.85 liters.

she gets the paint in 2 L tins. so, she needs 3 tins (6 L).

each tin costs £13.

and because she buys 3 tins, she gets the third one for half the price (13/2 = £6.50).

so, she has to pay

2×13 + 6.50 = 26 + 6.50 = £32.50

Answer:

Step-by-step explanation:

There are 2 very distinct and important things that we need to know before completing the problem. First is that we are given that the cos of an angle is 1/3 (adjacent/hypotenuse) and it is in the first quadrant. We also need to know that the identity for sin2θ = 2sinθcosθ.

We already know cos θ = 1/3, so we need now find the sin θ. The sin ratio is the side opposite the angle over the hypotenuse, and the side we are missing is the side opposite the angle (we do not need to know the angle; it's irrelevant). Set up a right triangle in the first quadrant and label the base with a 1 (because the base is the side adjacent to the angle), and the hypotenuse with a 3. Find the third side using Pythagorean's Theorem:

[tex]3^2=1^2+y^2[/tex] which simplifies to

[tex]9=1+y^2[/tex] and

[tex]y^2=8[/tex] so

[tex]y=\sqrt{8}=2\sqrt{2}[/tex] so that's the missing side. Now we can easily determine that

[tex]sin\theta=\frac{2\sqrt{2} }{3}[/tex]

Now we have everything we need to fill in the identity for sin2θ:

[tex]2sin\theta cos\theta=2(\frac{2\sqrt{2} }{3})(\frac{1}{3})[/tex] and multiply all of that together to get

[tex]2sin\theta cos\theta=\frac{4\sqrt{2} }{9}[/tex]

Answer:

18225 cm²

Step-by-step explanation:

Divide 540 by 4 to get the length of all sides

540/4 = 135

Square 135 to get the max possible size

135² = 18225

18225 cm²  is the greatest possible area for the quilt.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given

Divide 540 by 4 to obtain the length of all sides

540/4 = 135

Square 135 to acquire the max possible size

135² = 18225

18225 cm²  is the greatest possible area for the quilt.        

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Answer:

total balls = 18 .... 3/x = 1/6

blue = 10 ... 18-(5+3) = 10

p of green = 5/18 = .277

Step-by-step explanation:

Answer:

The angle in decimal form is 167.009°.

Step-by-step explanation:

We know an angle in terms of integer angles, minutes and seconds, whose conversion into decimal degrees is expressed by the following formula:

[tex]\theta = n + \frac{m}{60}+\frac{s}{3600}[/tex] (1)

Donde:

[tex]n[/tex] - Integer angle, in sexagesimal degrees.

[tex]m[/tex] - Minutes.

[tex]s[/tex] - Seconds.

If we know that [tex]n = 167[/tex], [tex]m = 0[/tex] and [tex]s = 31''[/tex], then the angle in decimal form is:

[tex]\theta = 167^{\circ}+\frac{0}{60}^{\circ} + \frac{31}{3600}^{\circ}[/tex]

[tex]\theta = 167.009^{\circ}[/tex]

The angle in decimal form is 167.009°.

Answer:

x=13.6

Step-by-step explanation:

By Pythagoras theorem, 5.5^2+x^2=14.7^2. x^2=14.7^2-5.5^2. x=13.6

Answer:

[tex] \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) [/tex]

Step-by-step explanation:

I assume the question want us to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula and note that it's not an equation therefore θ can never be specified

===========================

so we want to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula the good news is that the number of the function of the given expression is even so there's a way to do so, rewrite the expression in parentheses notation:

[tex] \rm\displaystyle \left( \cos( \theta) + \cos(3 \theta) \right) + \left(\cos(5 \theta) + \cos(7 \theta) \right)[/tex]

recall that,Sum-to-Product Formula of cos function:

[tex] \rm \boxed{\displaystyle \cos( \alpha ) + \cos( \beta ) = 2 \cos \left( \frac{ \alpha + \beta }{2} \right) \cos \left( \frac{ \alpha - \beta }{2} \right) }[/tex]

notice that we have two pair of function with which we can apply the formula thus do so,

[tex] \rm\displaystyle \left( 2\cos \left( \frac{ \theta + 3 \theta}{2} \right)\cos \left( \frac{ \theta - 3 \theta}{2} \right) \right) + \left(2\cos \left( \frac{5 \theta + 7 \theta}{2} \right) \cos \left( \frac{5 \theta - 7 \theta}{2} \right) \right)[/tex]

simplify addition:

[tex] \rm\displaystyle \left( 2\cos \left( \frac{4 \theta}{2} \right)\cos \left( \frac{ - 2\theta }{2} \right) \right) + \left(2\cos \left( \frac{12 \theta }{2} \right) \cos \left( \frac{ - 2 \theta}{2} \right) \right)[/tex]

simplify division:

[tex] \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { - \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { - \theta} \right) \right)[/tex]

By Opposite Angle Identities we acquire:

[tex] \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { \theta} \right) \right)[/tex]

factor out 2cosθ:

[tex] \rm\displaystyle 2 \cos( \theta) (\cos \left( {2 \theta} \right) + \cos \left( {6 \theta } \right) )[/tex]

once again apply Sum-to-Product Formula which yields:

[tex] \rm\displaystyle 2 \cos( \theta) (2\cos \left( {4\theta} \right) \cos \left( {2 \theta } \right) )[/tex]

distribute:

[tex] \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) [/tex]

and we're done!

Answer:

A.15/8

Step-by-step explanation:

the answer is 15/8

Answer:

D.

[tex]{ \tt{ \cos( \theta) = \frac{adjacent}{hypotenuse} }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{ \sqrt{ {15}^{2} + {8}^{2} } } }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{ \sqrt{289} } }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{17} }}[/tex]

Answer:

B

Step-by-step explanation:

Given the three integrals, we want to determine which integrals necessarily have the same value.

We can let the first integral be itself.

For the second integral, we can perform a u-substitution. Let u = x + a. Then:

[tex]\displaystyle du = dx[/tex]

Changing our limits of integration:

[tex]u_1=(0)+a=a \text{ and } u_2 = (b+a)+a = b+2a[/tex]

Thus, the second integral becomes:

[tex]\displaystyle \int_{0}^{b+a}f(x+a)\, dx = \int_a^{b+2a} f(u)\, du[/tex]

For the third integral, we can also perform a u-substitution. Let u = x + c. Then:

[tex]\displaystyle du = dx[/tex]

And changing our limits of integration:

[tex]\displaystyle u_1=(a-c)+c=a \text{ and } u_2=(b-c)+c=b[/tex]

Thus, our third integral becomes:

[tex]\displaystyle \int_{a-c}^{b-c}f(x+c)\, dx = \int_{a}^{b} f(u)\, du[/tex]

Since the only difference between f(x) and f(u) is the variable and both the first and third integral have the same limits of integration, our answer is B.

Answer: Becomes four times

Step-by-step explanation:

Given

Speed is doubled for a moving object

Suppose initial speed is u

Increased speed is 2u

Kinetic Energy is given by

[tex]\Rightarrow K=0.5mu^2[/tex]

When speed is doubled

[tex]\Rightarrow K'=0.5m(2u)^2\\\Rightarrow K'=(0.5mu^2)\times 4\\\Rightarrow K'=4K[/tex]

Kinetic energy becomes four times

Step-by-step explanation:

Hope it is helpful to you

Answer:

Smaller angle = 53.2

Larger angle = 126.8

Step-by-step explanation:

Lets say x is the measure of the supplement. Since we know they're supplementary, we know their angle measure sum will equal 180. We can set up our equation like this [tex]x + (x-73.6) = 180[/tex]. Note: (x - 73.6) is the measure of the smaller angle. By solving, we get 126.8 degrees for the measure of the supplement. If we plug in the value of x into (x-73.6), we get 53.2 degrees as the angle measure of the smaller angle.

Answer:

FG ≈ FL (Both are hypotenuse, supposed to be equal in order to the congruency to become HL)

Answered by GAUTHMATH

Step-by-step explanation:

Increase in dollars

19/100 x 472.000 = $89,670

and the current value house is $472,000 + $89,670 = $561,680

Answer:

44

Step-by-step explanation:

The difference between 15 and 9 is 6. 5 times the sum of 7 and 3 is 50 because 7+3=10 and 10 times 5 is 50. So if you subtract the difference between 15 and 9 from 50 you get 44.

30

Answer:

12÷2/5=12*5/2=30 is a required answer

Answer:

30

Step-by-step explanation:

Given:

The tens digit of a two digit number is 5 greater the units digit.

If you subtract double the reversed number from it, the result is a fourth of the original number.

To find:

The original number.

Solution:

Let n be the two digit number and x be the unit digit. Then tens digit is (x+5) and the original number is:

[tex]n=(x+5)\times 10+x\times 1[/tex]

[tex]n=10x+50+x[/tex]

[tex]n=11x+50[/tex]

Reversed number is:

[tex]x\times 10+(x+5)\times 1=10x+x+5[/tex]

[tex]x\times 10+(x+5)\times 1=11x+5[/tex]

If you subtract double the reversed number from it, the result is a fourth of the original number.

[tex]11x+50-2(11x+5)=\dfrac{1}{4}(11x+50)[/tex]

[tex]11x+50-22x-10=\dfrac{1}{4}(11x+50)[/tex]

[tex]40-11x=\dfrac{1}{4}(11x+50)[/tex]

Multiply both sides by 4.

[tex]160-44x=11x+50[/tex]

[tex]160-50=11x+44x[/tex]

[tex]110=55x[/tex]

Divide both sides by 55.

[tex]\dfrac{110}{55}=x[/tex]

[tex]2=x[/tex]

The unit digit is 2. So, the tens digit is [tex]2+5=7[/tex].

Therefore, the original number is 72.

Given set:- x - 7 > - 2

Solving It:-

x - 7 > - 2

x > -2 + 7 [Here '7' is greater than '-2' So Sign Changes To Positive]

x > 5

So Correct Solution Set Will Be

Option C= {x | x R, x > 5}

Answer:

730.88

Step-by-step explanation:

Area of the entire circle = pi * r^2

r = 16

Area = 3.14 * 16^2

Area = 803.84

1/4 of the circle contains the shaded area. It's area = 1/4 * 803.84

Area of 1/4 circle =

200.96

the area of the triangle

Area = 1/2 AG * G?

AG and G? are equal

Area = 1/2 * 16^2

Area = 128

Area of 1/4 circle - area of the triangle = area of the shaded portion

shaded portion = 200.95 - 128

Shaded Portion = 72.96

So the area of the unshaded part

unshaded = 803.84 - 72.96

Unshaded = 730.88

Answer:

-1

Step-by-step explanation:

are you sure this is the right equation ? it would mean that the more toppings the cheaper the ice cream.

but as it is written, the slope is -1.

the slope of a line is always the factor of the variable in the equation.

it is the ratio of y/x indicating how many units y is changing for a given change of x.

in our example here, if x changes 1 unit to the right (+1), then y changes 1 unit down (-1).

so, -1/+1 = -1

The slope of the function f(t) = 3 - t is -1

"It defines a relation between input and output values."

"It is the rate of change of the dependent variable of the function with respect to that of the independent variable."

For given question,

We have been given a function f(t) = 3 - t

We need to find the slope of the function.

[tex]m=\frac{d}{dt}f(t)\\\\ m=\frac{d}{dt}( 3 - t)\\\\m=-1[/tex]

Therefore, the slope of the function f(t) = 3 - t is -1

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Answer:

y=4x-7

Step-by-step explanation:

here,

the equation of straight line in slope intercept form is;

y=mx+c

( m= slope

c= y-intercept )

soo..

the question has asked for slope 4 i.e. m=4

and y- intercept -7 i.e. c= -7

now.

the required equation is

y= 4x-7

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Answer:

[tex]\frac{16}{45}x-\frac{11}{12}[/tex]

Step-by-step explanation:

We are given that an expression

[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)[/tex]

We have to find the equivalent expression.

[tex]\frac{2}{5}(\frac{1}{3}x-\frac{15}{8})-\frac{1}{3}(\frac{1}{2}-\frac{2}{3}x)[/tex]

[tex]\frac{2}{5}\times \frac{1}{3}x-\frac{2}{5}\times \frac{15}{8}-\frac{1}{3}\times \frac{1}{2}-\frac{1}{3}\times (-\frac{2}{3}x)[/tex]

Using the the property

[tex]a\cdot (c-b)=a\cdot c-a\cdot b[/tex]

[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)[/tex]

[tex]=\frac{2}{15}x-\frac{3}{4}-\frac{1}{6}+\frac{2}{9}x[/tex]

[tex]=\frac{6x+10x}{45}+\frac{-9-2}{12}[/tex]

[tex]=\frac{16}{45}x-\frac{11}{12}[/tex]

[tex]\frac{2}{5}(1/3x-15/8)-\frac{1}{3}(1/2-2/3x)=\frac{16}{45}x-\frac{11}{12}[/tex]

Answer:

to add on to what the other dude said its 4

Step-by-step explanation:

Answer: SSS Similarity Theorem (Choice A)

This is because we have three pairs of corresponding sides that form the same ratio, as shown by the given equation PQ/ST = QR/TU = RS/US.

That equation is basically the shorthand version of PQ/ST = QR/TU and QR/TU = RS/US combined together as one.

Answer:

people who ordered a cold drink=

[tex]8+12+5=25[/tex]

people who ordered a large cold drink= 5

[tex]probability= \frac{5}{25}[/tex] [tex]=\frac{1}{5}[/tex]

[tex]=\frac{1}{5} \times100=20~\%[/tex]

[tex]Answer: 20\%[/tex]

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

Hope it helps...

Have a great day!!

The probability that the customer ordered a large given that he or she ordered a cold drink is 5%.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given the order of the first 100 customers in a coffee shop.

Number of customers who ordered a large which is also a cold drink = 5

Total number of customers = 100

Probability = Number of desired outcomes / Total number of outcomes

Substituting,

Probability = 5 / 100 = 0.05 = 5%

Hence the required percent is 5%.

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Answer:

it should be 3

Step-by-step explanation:

I hope this help

The question is incomplete. The complete question is :

A school in Delhi has its own flag, which is rectangular and divided into 4 rows and 6 columns. The word ‘SCHOOL’ is inscribed in the first row, ‘FLAG’ in the fourth row, and a  purple colored rhombus is in the middle, as shown in the given figure.

Based on this picture of the school flag, answer the following questions:  

(a) What fraction of the flag has the purple rhombus?

Solution :

From the figure, the total number of squares in the flag of 4 rows and 6 columns are : 4 x 6 = 24 blocks

The purple colored rhombus is made on the half of the 4 blocks.

i.e. [tex]$\frac{1}{2} \times 4 = 2\ \text{blocks}$[/tex]

Therefore, the fraction of the flag that has the purple rhombus is :

[tex]$=\frac{2}{24}$[/tex]

[tex]$=\frac{1}{12}$[/tex]