(7x-7)
63°
(3x +45)
(9-4)
Find x and y

Answer:

  (b)  22 in

Step-by-step explanation:

You want the perimeter of a rectangle with side lengths 4 inches and 7 inches.

The perimeter of a rectangle is the sum of the lengths of its sides. Your rectangle has two sides that are 4 inches, and two sides that are 7 inches. The perimeter is the sum of these lengths:

  P = 4 in + 4 in + 7 in + 7 in

  P = 22 in

The perimeter of the rectangle is 22 inches.

__

Additional comment

We can save a math operation by recognizing the sum can be arranged to ...

  P = (4 in +7 in) +(4 in +7 in) = 2(4 in +7 in)

This is evaluated using one sum and one product, rather than the three sums we need if we simply add the lengths of the four sides.

This is why the usual formula for the perimeter of a rectangle is ...

  P = 2(L +W)

Answer:

y= -4x

Step-by-step explanation:

it will be more helpful to answer this question if the equations were provided.

Answer:

4 cups of flour is needed and 4/3 cups of sugar

Step-by-step explanation:

Given

2 dozen Muffins; 3 cups of flour and 1 cup of sugar

Required

Determine the cups of flour if 18 muffins is used

First, we have to determine the proportion of the number of muffins used previously and now;

Represent this with p;

\(p = \frac{2\ dozen}{18}\)

\(p = \frac{2 * 12}{18}\)

\(p = \frac{24}{18}\)

\(p = \frac{4}{3}\)

Multiply this to the previous cups of flours and sugars;

Cups of flour = p * previous cups of flour

\(Cups\ of\ flour = \frac{4}{3} * 3\)

\(Cups\ of\ flour = 4\)

Cups of Sugar = p * previous cups of sugar

\(Cups\ of\ sugar= \frac{4}{3} * 1\)

\(Cups\ of\ sugar= \frac{4}{3}\)

Hence, 4 cups of flour is needed and 4/3 cups of sugar

Using the trigonometry relation, the value of sin2x=4√2/9, cos2x=7/9 and tan2x=4√2/7.

In the given question, we have to find the value of sin(2x), cos(2x) and tan(2x).

The given value of six=1/3, x in quadrant first.

We firstly finding the value of cosx.

cosx = √1-(sinx)^2

Now putting the value of sinx

cosx = √1-(1/3)^2

cosx = √1 -1/9

cosx = √(9-1)/9

cosx = √8/9

cosx = 2√2/3

We know that;

sin2x=2sinxcosx

sin2x=2* 1/3 * 2√2/3

sin2x=4√2/9

Now finding the value of cos2x

We know that;

cos2x=1-2(sinx)^2

cos2x=1-2(1/3)^2

cos2x=1 -2/9

cos2x=(9-2)/9

cos2x=7/9

Now finding the value of tan2x

As we know that

tan2x=sin2x/cos2x

tan2x=(4√2/9)/(7/9)

tan2x=4√2/7

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Answer:

a:b

3:7

Step-by-step explanation:

a:b  also means a/b

Taking the equation

7a = 3b

Dividing each side by b

7a/b = 3b/b

7 a/b = 3

Divide each side by 7

a/b = 3/7

The ratio is 3/7

a:b

3:7

Answer:

a:b = 3/7

Step-by-step explanation:

we need to find the ratio a:b which is the same as a/b.

7a=3b

Devide left and right of the = sign by b gives

7a/b = 3 * b/b

7a/b = 3 * 1

7a/b = 3

Multiply left and right of the = sign by 1/7 gives

1/7 * 7a/b = 1/7 * 3

7/7 * a/b = 3/7

1 * a/b = 3/7

a/b = 3/7

Since a/b is the same as a:b, we now have the answer.

a:b = 3/7

Answer:

y=mx + b

Step-by-step explanation:

y= y intercept coordinate

m=slope=x coordinate

b = y intercept

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer:

28/33

Step-by-step explanation:

We first let 0.84 be  x.

Since  x  is recurring in 2 decimal places, we multiply it by 100.

100x=84.84

Next, we subtract them.

100x−x=84.84−0.84

99x=84

Lastly, we divide both sides by 99 to get  x  as a fraction.

x=84/99

=28/33

The number of people who felt that traffic improved in there area will be 1800.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

From the information, 2/5 felt that traffic improved in there area. If 4,500 people were surveyed, the number of people who felt that traffic improved in there area will be:

= 2/5 × 4500

= 1800

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In an area, 2/5 felt that traffic improved in there area. If 4,500 people were surveyed, how many people felt that traffic improved in there area.

Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

Step by step:

Perimeter = Summation of all sides = AB+BC+CD+DA = 2x+2+x+2x+2+x=(6x+4)

⇒6x+4=154

⇒6x=154−4

⇒\(\frac{150}{6x}\)

⇒25=x

The breadth is x=25

The length of the rectangular pool = (2×25+2)=50+2=52m

breadth is 25 and the length is 52

Hope it helps!

\(\blue\star \rm\pink{ Question:}\)

The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?

\( \\ \\ \)

\(\blue\star \rm\pink{ Given :}\)

\( \\ \\ \)

\(\blue\star \rm\pink{ To ~Find :}\)

\( \\ \\ \)

\(\blue\star \rm\pink{Let :}\)

\( \\ \\ \)

We know:-

\( \bigstar \boxed{ \rm perimeter \: of \: rextangle = 2(length +breadth)}\)

So:-

\( \\ \\ \)

\( \dashrightarrow\sf perimeter \: of \: rextangle = 2(length +breadth) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + 2x +x) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + 3x) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 )+ 2(3x) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 4+ 2(3x) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 4+ 6x\)

\( \\ \\ \)

\( \dashrightarrow\sf 154 - 4 =6x\)

\( \\ \\ \)

\( \dashrightarrow\sf 150 =6x\)

\( \\ \\ \)

\( \dashrightarrow\sf 6x = 150\)

\( \\ \\ \)

\( \dashrightarrow\sf x = \dfrac{150}{6} \)

\( \\ \\ \)

\( \dashrightarrow\sf x = \cancel \dfrac{150}{6} \)

\( \\ \\ \)

\( \dashrightarrow\bf x =25\)

\( \\ \\ \)

Let's Verify value of x:-

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + 2x +x) \\ \)

put value of x in equation

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + \{2 \times 25 \} +25) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + 50+25) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2( 2 + 75) \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf 154 = 2(77) \\ \)

\( \\ \\ \)

\( \dashrightarrow\bf 154 =154\)

\( \\ \\ \)

\(\Large \bf\dag LHS = RHS \dag\)

Hence proved

\( \\ \\ \)

Finally Let's find length and breadth of pool:-

\( \\ \\ \)

To find breadth

➙ Breadth = x

➙ Breadth = 25 m

\( \\ \)

To find length

➙ Length = 2 + 2x

➙ Length = 2 + 2(25)

➙ Length = 2 + 50

➙ Length = 52 m

____________________________________☆~

Cheers! all done. :)

Answer:

18m-20

Step-by-step explanation:

4(3m-2)+3(2m-4)=

12m-8+6m-12=

collect like terms

12m+6m-8-12=

18m-20

The expression that is equal to the given Polynomial expression is (x^3-4)(2x+5).

The polynomial expression given is 2x^4+5x^3-8x-20. We have to identify the expression that is equal to this given polynomial expression.

We will factor the given polynomial expression to determine the equivalent expression. We can use factorization by grouping to factor the expression completely and determine the equivalent expression .

Factorization by grouping:

We can group the first two terms 2x^4 and 5x^3 together and factor out x^3 from them. We can also group the last two terms -8x and -20 together and factor out -4 from them.

This gives us;2x^4+5x^3-8x-20= x^3(2x+5)-4(2x+5) =(x^3-4)(2x+5)

Therefore, the expression that is equal to the given polynomial expression is (x^3-4)(2x+5).

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Answer:

1.19 minutes

Step-by-step explanation:

First, subtract the $3 monthly fee:

16.09 - 3

= 13.09

Then, divide this by 11:

13.09/11

= 1.19

So, he was billed for 1.19 minutes

According to the information, we can infer that the area of this polygon is 34 units².

To find the area of the figure we must graph it and divide it into different segments. Then we find the area of all the segments and add them to get the total area.

Rectangle 1

6 * 3 = 18

Rectangle 2

2*4=8

Triangle 1

2 * 4 / 2 = 4

Triangle 2

2 * 4 / 2 = 4

Total Area

18 + 8 + 4 + 4 = 34

Based on the above, we can infer that the total area of the polygon is 34 ² units.

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Answer:

0.674 means that it 674/1000

Step-by-step explanation:

which mean that if the model consist of 1000 squares, you have to shade 674 of the squares.

If the model consist of 100 squares, you have to shade 337 of the squares  ( you get the number after dividing both 674 and 1000 with 2)

The height of the cylinder whose surface area is given would be = 85 yards.

The cylinder is a type of shape that has three sides which consists of two opposite circles that are joined by a curved surface.

To calculate the height of a cylinder, the formula that should be used is given as follows:

Surface area of cylinder = 2πrh + 2πr²

radius = 29 yards

surface area = 20,761.68 square yards

height = ?

That is ;

20,761.68 = 2×3.14× 29×h + 2×3.14× 29×29

20,761.68 =182.12h + 5281.48

182.12h = 20,761.68-5281.48

182.12h = 15480.2

h = 15480.2/182.12

= 85 yards

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Part a: The data points appear to follow an exponential pattern. This is because the balance is increasing at a rate that is proportional to the current balance.

Part b: The equation of the best fit is y = 50(1.06)^x. This can be found using a variety of methods, including graphing the data points and fitting a curve to them, or using a statistical software package.

Part c: When x = 32, y = 50(1.06)^32 = $2,499.82.

Years since 1990, x 0 5 10 15 20 25 30

Balance, y $50 $62.31 $77.65 $96.76 $120.59 $150.27 $187.27 $2,499.82

The equation of the fitted curve is y = 50(1.06)^x.

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Answer:

D. 4 (5 + 16)

Step-by-step explanation:

20 + 64 = 84

To solve this problem we have to simplify each of the expressions in the answer column:

A. = 80

(16 + 60 = 76) giving us

4 + 76 = 80

B. = 25

(5 + 16 = 21)

4 + 21 = 25

C. = 80

(16 + 60 = 76)

4 + 76 = 80

D. = 84

(5 + 16 = 21)

4 x 21 = 84

So The correct option is D. 4 (5 + 16)

Answer:

You need to add the graphs

Step-by-step explanation:

The steps Sergey could use to solve the quadratic equation by completing the square is 5(x2 + 4x) = –7

We should know that in completing the square method both sides of the equation are made perfect squares.

The given equation is 5x²+20x-7=0

Solving this equation by completing the square method we have

5(x²+4x+4)=-7

This means that (x+2)=±√27/5

Simplifying further we have

5(x²+4x)=7

Then expanding to make ²HS a perfect square we have

5(x²+4x+4)=7+20

This means that 5(x²+4x)=-7

Therefore the step he could use is 5(x²+4x)=-7\

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$6500 is invested at the rate of 6% and $500 is invested at the rate of 8%.

What is annual interest rate?

An annual percentage rate is expressed as an interest rate. It calculates what percentage of the principal you'll pay each year by taking things such as monthly payments into account.

Invested amount = $7000

Let x be the invested amount at 6% and y be the invested amount at 8%.

According to the question,:

x+y=7000......(1)

annual interest is $430.

Therefore Interest on x + interest on y = $430

Interest=(invested amount*rate*time)/100

Here Time is 1 year.

(6*x)/100+(8*y)/100=430

This shows, 6x+8y=43000.......(2)

From equation (1), we have:

x=7000-y.........(3)

Substitute the value of x in equation (2),

6(7000-y)+8y=43000

On simplifying, y=500

Put y = 500 in equation (3)

we get x=6500

Therefore $6500 is invested at the rate of 6% and $500 is invested at the rate of 8%.

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Answer:

x=36 and y=60

Step-by-step explanation:

Multiplying the second equation by 4 gives x+0.4y=60.

Subtracting this from the first equation yields 0.6y=36, and thus y=60.

So, x=36.

Answer:

719/721

Step-by-step explanation:

Subtract 2 from 721

Answer:

Take a look at the 'proof' below

Step-by-step explanation:

The graph of the function g(x) is similar to that of the function f(t). The local minimum, local maximum, absolute minimum, maximum etc... of 'x' is always the closest x-intercept of the graph of f(t).

Let's check if this statement is right. The two local minimum(s) of the function f(t) occurs at x = 2, and x = 6. The two local maximum(s) occur at 1/4 and 4. As you can see the maximum / minimum of the function g(x) is always an x-intercept, x = 3, x = 7.

For part (b) the absolute maximum value of the function f(t), is 8. The closest x-intercept is 9, which is our solution.

Step-by-step explanation:

From x=0 to x=1, the function is above the x-axis, so the area is positive.

From x=1 to x=5, the area above the x-axis is greater than the area below the x-axis, so the net area is positive.

From x=5 to x=9, the area above the x-axis is greater than the area below the x-axis, so the net area is positive.

Since the area increases in each interval, the area is a maximum at x=9.

Answer:

False

Step-by-step explanation:

The number on top of the division house is called the numerator.

The quotient is the result of the numerator / denominator.

Answer:

The magnitude of the vector is 9.165 and it's direction is 40.6°

Step-by-step explanation:

A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.

Magnitude of vector v is given by

|v| = √6²+7²

= √36+49

= √84

= 9.165

Direction of vector v is obtained by:

\( \tan( \theta) = \frac{x}{y} \)

\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)

\(\theta = {40.6°}\)

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Point d is at (5, -5), which is five units to the right of the origin on the x-axis and five units below the origin on the y-axis. Similarly, point e is at (7, 3), point f is at (-1, 5), and point G is at (-3, -3).

The given points, d (5, -5), e (7, 3), f (-1, 5), and G (-3, -3) form quadrilateral DEFG. To plot these points, we can first draw the x and y axes on a graph paper.

Then, we can plot each point by locating its x-coordinate on the x-axis and its y-coordinate on the y-axis.

After plotting the points, we can click on the "Graph Quadrilateral" button to see the quadrilateral DEFG. It should be a closed shape with four sides, connecting the four points in the given order.

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Answer:

I think a polynomial... could be wrong though....

Step-by-step explanation: