Kathy designed a square patio. She made the sides of the patio 15 feet. What is the area of the patio?

Answer:

Step-by-step explanation:

[tex]\dfrac{3}{4}\times\dfrac{1}{2}=\dfrac{3\times1}{4\times2}=\dfrac{3}{8}[/tex]

Answer:

5. 25.4     6. 53.5        7. 107.9

Step-by-step explanation:

since you do not know the height you do the side time the base times the gamma or the angle degrees

Answer:

+1

-1

Step-by-step explanation:

Given equation :

[tex]x^{2} +0x-1[/tex] = 0

[tex]x^{2} -1 = 0\\x^{2} =1\\x=\sqrt{1}[/tex]

x= ±1

x= 1 and x= -1

±1 lies in solution set of real numbers !

Answer:

32[tex]m^{2}/min[/tex]

Step-by-step explanation:

We let the length of the square be l, the diagonal be z and the area be A.

Then by Pythagoras theorem;

[tex]l^{2}+l^{2}=z^{2}\\2l^{2}=z^{2}[/tex]

The are of a square of length l is given as;

[tex]A=l^{2}[/tex]

Combining these two equations yields;

[tex]z^{2}=2A[/tex]

[tex]A=\frac{z^{2} }{2}[/tex]

Next, we have been given;

[tex]\frac{dz}{dt}=8[/tex]

We are required to find;

[tex]\frac{dA}{dt}[/tex] when z = 4

By chain rule;

[tex]\frac{dA}{dt}=\frac{dA}{dz}*\frac{dz}{dt}[/tex]

Differentiating [tex]A=\frac{z^{2} }{2}[/tex] with respect to z yields;

[tex]\frac{dA}{dz}=z[/tex]

Therefore,

[tex]\frac{dA}{dt}=\frac{dA}{dz}*\frac{dz}{dt}[/tex] = 8z

When z is 4m the area of the square will be increasing at a rate of;

8m/min * 4m = 32[tex]m^{2}/min[/tex]

The area of the square is increasing at a rate of 32 m^2/min when the diagonals are each 4 meters long. This is calculated using the relationship between the diagonal and the side length of the square, and applying the concepts of calculus.

The subject of your question is related to Mathematics, specifically in the field of calculus, which deals with rates of change and accumulation. In this scenario, we're looking at how fast the area of a square is increasing given that its diagonals are increasing at a steady rate.

In a square, the diagonal and the side length 's' have a specific relationship, given by the Pythagorean theorem as diagonal = s * sqrt(2). As the diagonal is increasing at 8 m/min, ds/dt = 8/(sqrt(2)) m/min. Now, the area of a square (A) is given by A = s^2. By differentiating this respect to time 't', dA/dt = 2s*(ds/dt). Substituting the given length of the diagonal (4 m), we find s = diagonal/sqrt(2) = 2 sqrt(2) m. Now, substituting s and ds/dt into the equation for dA/dt, we find dA/dt = 2s*(ds/dt) = 2*2sqrt(2)*8/sqrt(2) = 32 m^2/min. So, the area of the square is increasing at the rate of 32 m^2/min when the diagonals are 4 meters each.

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Answer:

The journey took 4 hours.

Step-by-step explanation:

The relationship between distance, speed, and time is expressed in the formula;

[tex]Speed=\frac{Distance}{Time}[/tex]

The car covered 52 km at a speed of 13km/h.

This means that; distance =52km and speed =13km/h

We substitute the given values into the formula to get;

[tex]13=\frac{52}{Time}[/tex]

[tex]Time=\frac{52}{13}[/tex]

This simplifies to:

[tex]Time=4hrs[/tex]

The journey took 4 hours.

The speed is the ratio of distance to time. Then the time taken by the journey is 4 hours.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity.

We know that the speed formula

[tex]\rm Speed = \dfrac{Distance}{Time}[/tex]

Then the time is given as

[tex]\rm Time = \dfrac{Distance}{Speed}[/tex]

A car drives 52 km at a speed of 13km/h.

Then the time taken will be given as

[tex]\rm Time = \dfrac{52}{13} \\\\ Time = 4[/tex]

More about the speed link is given below.

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Answer:

Step-by-step explanation:

The formula of an area of a parallelogram:

[tex]A=ah[/tex]

a - base

h - height

We have

[tex]a=11\dfrac{2}{3}\ cm,\ h=3\dfrac{3}{5}\ cm[/tex]

Convert the mixed numbers to the improper fractions:

[tex]11\dfrac{2}{3}=\dfrac{(11)(3)+2}{3}=\dfrac{35}{3}\\\\3\dfrac{3}{5}=\dfrac{(3)(5)+3}{5}=\dfrac{18}{5}[/tex]

Substitute:

[tex]A=\left(11\dfrac{2}{3}\right)\left(3\dfrac{3}{5}\right)=\left(\dfrac{35\!\!\!\!\!\diagup^7}{3\!\!\!\!\diagup_1}\right)\left(\dfrac{18\!\!\!\!\diagup^6}{5\!\!\!\!\diagup_1}\right)=(7)(6)=42\ cm^2[/tex]

Answer:

1- D   2-A

number one: you multiply all the numbers together...

number two: you add the numbers together and i got A because if you add it all up, it is 42.593 and that is greater than 42.537.

hope dis helps! :p

Answer:

The minimum number of rolls she should buy is 9 rolls

Step-by-step explanation:

* Lets study the information in the problem

- Katie wants to put the crepe paper around the perimeter of the

 ceiling which shaped a square of side length 12 feet

- And also from each corner to the opposite corner

- She needs the length of the 4 sides of the square and the length

 of its 2 diagonals

* Lets find the length of the diagonal of the square

∵ The two adjacent sides of the square formed two legs of a right

   angle triangle and the diagonal joining the endpoints of the legs

  is the hypotenuse of the triangle

- Use Pythagoras theorem to find the length of the diagonal

∴ The length of the diagonal = √(s² + s²) √(2s²) = s√2

∵ The length of the side of the square = 12 feet

∴ The length of the diagonal = 12√2

* Now lets find the length of the crepe papers she needs

∵ She needs the length of the 4 sides of the square and the length

  of its 2 diagonals

∴ The length of crepe papers = 12 + 12 + 12 + 12 + 12√2 + 12√2 = 81.94 feet

∵ Each roll of the crepe papers contain 10 feet

- To find the number of rolls divide the length of the crepe papers by 10

∴ The number of rolls = 81.94 ÷ 10 = 8.194

* She must to buy 9 rolls to have enough crepe papers to decorate

 her ceiling

* V.I.N:

- If she decide to buy 8 rolls, some part of ceiling will not decorate

 because the 8 rolls have 80 feet only and she needs 81.94 feet

ANSWER

[tex] \frac{9}{25} [/tex]

EXPLANATION

The given information is represented on the Venn diagram above, where x represents students who have both cat and dog.

The sum of all the regions should give us 25.

[tex](15 - x) + x + (16 - x) + 3 = 25[/tex]

Group similar terms to obtain;

[tex] - x + x - x = 25 - 15 - 16 - 3[/tex]

Simplify

[tex] - x = - 9[/tex]

[tex]x = 9[/tex]

The probability that a student chosen at random has a cat and a dog is

[tex] = \frac{9}{25} [/tex]

The probability that a student chosen at random has a cat and a dog is; P(cat and dog) = 9/25.

According to the question, the total number of students is; 25.

The information above are drawn in a Venn diagram in the attached image.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

In essence, x = 9

The probability that a student chosen at random has a cat and a dog is therefore;

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Answer:

A

Step-by-step explanation:

the y intercerpt is what is given as (0,5) and the slope is given as -4, so using y=mx+b where m=slope and b=y int, we get y=-4+5

Answer:

A, y = -4x + 5

Step-by-step explanation:

the slope intercept form is y = mx + b with mx being the slope, and y being the y-intercept

we are given the y-intercept (0,5) and the slope -4, so we plug this into slope intercept form

y = -4x + 5

the answer is A

408 ft

Can I have brainliest?

:)

Answer:

Event A = white marble is selected

Event B = blue marble is selected

P(A) = 5/10 = 1/2

p(B) = 5/10 = 1/2

Probability that A and B are independent events is:

P(A∩B) = 1/2 × 1/2

Answer: 1/4

Answer:  C) P(A and B) = 1/2  1/2

12 to 20 is 60 percent

12 is 60% of 20

To find the percent you must divide to two numbers 12 and 20. You then get 0.6 which is 60 percent because 6 is in the tenths place which also determines how many zeros there are.

Answer:

24/25

Step-by-step explanation:

because of sinФ you use the opposite/hypotenuse to get 24/25

The value of sin 74° in the given question is 24 / 25.

The sine of an angle in a right angled triangle is the ratio of side opposite to the angle and the hypotenuse of the triangle.

In the given question:

Side opposite to 74° angle = 24

Hypotenuse of the triangle = 25

sin(74) = Perpendicular / Hypotenuse

sin(74) = 24 / 25

Hence, the value of sin74 is 24/25.

Learn more about trigonometry on:

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Answer:

[tex]\frac{1-cos^2x}{1+cosx}[/tex]

Step-by-step explanation:

We are given the expression

[tex]\frac{sin^2x}{1+cosx}[/tex]

We can use the Pythagorean identity of [tex]sin^2x+cos^2x=1[/tex] when solved for [tex]sin^2x=1-cos^2x[/tex]

Now we can substitute in our identity for [tex]sin^2x[/tex]

[tex]\frac{1-cos^2x}{1+cosx}[/tex]

Answer:

80

Step-by-step explanation:

The total was 125

0.64 of them voted for the winner.

The number who voted for the winner = ratio * total

Votes for the winner = 0.64 * 125

Votes for the winner = 80

Answer:

The answer is D

Step-by-step explanation:

Answer: B. .06%

Step-by-step explanation: In the first column, 0.04% owned a bird and fish. .02% owned a bird, but not a fish. So:

0.04% + 0.02% = 0.06%

Answer:

B, Right by 4 units

Step-by-step explanation:

we want to factor g(x), and the factorization of that would be (x - 4)² as its a perfect square trinomial

when translating on a graph, we determine the translation. the translation of g(x) is a horizontal shift 4 units to the right, as we are subtracting 4. if it was adding 4, we would be shifting to the left 4 units

ANSWER

Right by 4 units

EXPLANATION

The given functions are

[tex]f(x) = {x}^{2} [/tex]

and

[tex]g(x) = {x}^{2} - 8x + 16[/tex]

To obtain how much f(x) is shifted to obtain g(x), we need to rewrite g(x) in vertex form.

Observe that,

[tex]g(x) = {x}^{2} - 8x + ( - 4) ^{2} [/tex]

is a perfect square trinomial.

The vertex form is

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

When f(x) is shifted 4 units to the right, we obtain g(x).

Answer:

the answer is C.  5 cubic in

Step-by-step explanation:

V = LWH

length is 2 (1/2 in)

width is 5 (1/2 in)

height is 4 (1/2 in)

V = (2/2) (5/2) (2)

V = 1 * 5/2 * 2

V = 5 cubic in

The volume of the rectangular prism will be 5 cubic inches. Then the correct option is C.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

The prism below is made of cubes that measure 1/2 of an inch on one side.

The dimension will be

L = 2 x 1/2 = 1 inch

W = 5 x 1/2 = 2.5 inches

H = 4 x 1/2 = 2 inches

Then the volume of the rectangular prism will be

V = 1 x 2.5 x 2

V = 5 cubic inches

Then the correct option is C.

More about the volume of the prism link is given below.

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Dilation means every coordinate of the given original image will be multiplied by the given scale factor.

If the scale factor of a dilation is less than one and greater than zero.

The resulting image will be an enlargement of the original image.

A scale factor is defined as the ratio between the scale of a given new object and an original object,

We have,

The scale factor of a dilation is less than one and greater than zero,

This means,

The scale factor = x

0 < x < 1

We can have,

x = 0.5, 0.6, 0.7

Dilation means every coordinate of the given original image will be multiplied by the given scale factor.

This means,

The image will be an enlargement of the original image.

Thus,

If the scale factor of a dilation is less than one and greater than zero.

The resulting image will be an enlargement of the original image.

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____________________________________________________

Answer:

The Potato has a greater mass.

____________________________________________________

Step-by-step explanation:

In order to see which one of them has the greater mass, we're going to need to figure out how much one of them weigh.

Lets get the key information from the question:

5 potatoes = 1 kilograms (kg)

8 pears = 1,200 grams (g)

With the information above, we can solve the problem.

1 Kilogram = 1000 grams

With that information, we know that 5 potatoes would equal 1000 grams, now we would need to divide 1000 by 5 to get the grams for one potato in order to find the mass of it.

[tex]1000 \div 5=200[/tex]

1 Potato = 200 grams

Now, we would need to divide 1,200 by 8 to find the mass of 1 pear.

[tex]1200 \div 8=150[/tex]

1 Pear = 150 grams

With the information we have now, we would know that the Potato has the greater mass than the pear.

A potato has a greater mass.

____________________________________________________

i think the answer is 8

Answer:

1. 21x⁴+3y-35x² + 41

2. -21x⁴-3y+6x² + x

Step-by-step explanation:

When adding and subtracting polynomials , you can use the distributive property to add or subtract the coefficients of like terms.

1. The polynomial is 21x⁴ + 3y -6x² + 34

To obtain polynomial 29x² -7 , we must subtract some polynomial from it.

Let that polynomial be k.

So, 21x⁴ + 3y -6x² + 34 - k =  29x² -7

k = 21x⁴ + 3y - 6x² +34 - 29x² +7 = 21x⁴ + 3y - 35x² + 41

2. To obtain a first degree polynomial, let that polynomial be x +34

So, 21x⁴ + 3y - 6x² + 34 + K = x + 34

K = x + 34 - 21x⁴ -3y + 6x² - 34

  = -21x⁴ - 3y + 6x² + x

Answer:

the correct answer is the letter X

Step-by-step explanation:

because the shaded sides are between the two larger rectangles

I believe the answer your looking for is “X”

Answer:

2680

Step-by-step explanation:

i just did 6.70 times 400g

Answer:

400 grams (or 0.4 kg) of this cheese would cost £2.68.

Step-by-step explanation:

Let's write and solve an equation of ratios:

 0.4 kg            x

------------- = -------------

  1.0 kg         £6.70

Cross multiplying to solve for x, we get:

0.4(6.70) = x, or

x = £2.68

400 grams (or 0.4 kg) of this cheese would cost £2.68.

Answer:

[tex]80x\geq 750[/tex]

She'll need to save at least 10 months to be able to go buy the computer.

Step-by-step explanation:

Let

x ----> the number of months

we know that

The inequality that represent this situation is equal to

[tex]80x\geq 750[/tex]

solve for x

[tex]x\geq 750/80[/tex]

[tex]x\geq 9.4\ months[/tex]

therefore

The minimum number of months is 10

Answer:

C.2/3x−2

Step-by-step explanation:

The answer is definitely C

Answer:

Diameter = 2*Radius

So, 2*16cm = 32cm

The answer is 32. I hope this helps!

Replace h with 49 ( the given height) and solve for d ( distance).

49 = d^2 - 36d +324

Subtract 49 from both sides:

0 = d^2 - 36d + 275

Factor the polynomial, by finding two numbers when added together equal -36 and when multiplied equal 275.

(d-25)(d-11) = 0

Now solve for d by setting both equations to 0:

d-25 = 0

d = 25

d-11 = 0

d = 11

The two distances would be 11 yards and 25 yards.

Answer: The vertex is 1

Step-by-step explanation:

The vertex is the line that passes through the center of the parabola