Find the value of the variables in each figure. Explain your reasoning.

Answer:

200

Step-by-step explanation:

20*10=200

500,000

                              OR

five hundred thousand

Using the Pythagorean Theorem and the given values, we can solve for c.

a^2 + b^2 = c^2
12^2 + 16^2 = c^2
144 + 256 = c^2
400 = c^2
√400 = √c^2
c = 20

The line that has a slope of -2 and a y-intercept of -1 is shown in the graph below.

An equation of a line in slope-intercept form that is expressed as y = mx + b, can be graphed if we know the value of the slope (m), and the value of the y-intercept (b).

We are given the following:

To write the equation of the line in slope-intercept form, substitute m = -2 and b = -1 into y = mx + b:

y = -2x - 1

This means that the rise/run of the line, which is the slope, to be graphed would be equal to -2 while the line will intercept the y-axis at point -1, because the y-intercept given is -1.

The line with the stated features are shown in the graph below.

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Answer:

x=10

Step-by-step explanation:

-3+x=7

Add 3 to both sides.

7+3=10

x=10

Answer:

x=10

Step-by-step explanation:

-3+x=7

You have to add 3 to both sides to cancel out the -3

x=10

That leaves you with x=10

There will be 16 teaspoons of salt is needed for the 4 tablespoons of sugar.

Given, In a recipe, for every tablespoons of sugar there are four teaspoons of salt.

If a batch use four tablespoons of sugar then we have to find the number of tablespoons of salt needed.

as, 1 sugar = 4 salt

4 sugar = 4×4 salt

4 sugar = 16 salt

So, the number of tablespoons of salt needed is 16 for the use of 4 tablespoons of sugar.

Hence, there will be 16 teaspoons of salt is needed for the 4 tablespoons of sugar.

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Answer:

Full truck = 18.2 tons

Step-by-step explanation:

FT = ET + 20R. ET (Empty Truck) = 15t

R (refrigerator) = 0.16t

FT = 15t + 3.2t

FT= 18.2t

With the help of the given trendline equation, the length of the flight will be 3,613.34 miles.

So, the length of the flight will be:

Now, calculate for D as follows:

We can write as D = 3,613.34

Therefore, with the help of the given trendline equation, the length of the flight will be 3,613.34 miles.

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If m∠RTG = 5.8° and m∠GTU = 113.6°. Then the measure of the angle ∠RTU will be 119.4°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

Angles RTG and GTU are adjacent angles. If m∠RTG = 5.8° and m∠GTU = 113.6°.

∠RTU = ∠RTG + ∠GTU

∠RTU = 5.8° + 113.6°

∠RTU = 119.4°

The measure of the angle ∠RTU will be 119.4°.

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Answer: D

Step-by-step explanation: Proportional relationship = relationships between two variables where their ratios are equivalent. 6:15 is equivalent with both 8:20 and 10:25. So D is the correct answer.

The point (-2,7) is not lie on the graph of y = -2x +1 .

Given,

In the question:
To check the :

Does the point (-2, 7) lie on the graph of y=-2x+1?

Now, According to the question:

The equation is :

y = -2x + 1

Substitute the values of x = -2 and y = 7 into y = -2x +1

7 = -2(-2) + 1

LHS = 7

RHS = -2(-2) + 1 = 5

Write in the form :

7 = 5

Verify the relationship

False

Determine whether the point is on the line:
(-2, 7) not on the graph.

Hence, The point (-2,7) is not lie on the graph of y = -2x +1 .

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No the two rectangles are not similar as the ratios of the sides are not equal.

Two rectangles are said to be similar if the ratio of the sides of the rectangles are equal.

Now let us consider the given rectangles:

In rectangle ABCD:

AB = 18

AD = 36

In rectangle WXYZ :

WX = 25

XY = 45

Now the ratio of the sides of the rectangle are:

AB/AD = 18 / 36 = 1 / 2

WX/XY = 25 / 45 = 5 / 9

Thus we can see that AB : AD ≠ WX : XY

Hence the rectangles are not similar.

If the ratios of the adjacent sides of two rectangles are equal, then they are similar. A rectangle is a quadrilateral in the Euclidean plane because it has four right angles.

Other definitions include a parallelogram with a right angle or a quadrilateral that is equiangular, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

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The expression that is equivalent is 6(y + 1) and 6y + 6.

The expression that are not equivalent are 3(x + 3) and 3x + 6 and x(x + 4) and x² + 4.

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Now, let's check if the expression are equivalent by simplifying it.

3(x + 3) and 3x + 6

3x + 9 and 3x + 6

Therefore, the expressions are not equivalent.

6(y + 1) and  6y + 6

6y + 6 and 6y + 6

They are equivalent expression.

x(x + 4) and x² + 4

x² + 4x and x² + 4

They are not equivalent expression.

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If the total cost to rent 2 chairs and 12 tables is $107 and the total cost to rent 5 chairs and 3 tables is $38, then the costs to rent each chair and table are $2.5 and $8.5 respectively. We can solve this question using elimination and substitution methods.

Elimination and substitution methods are involved in solving this problem. We're going to use the variables x for the cost of a chair and y for the cost of a table. The total cost to to rent 2 chairs and 12 tables is $107, so the equation can be written as 2x + 12y = 107. The total cost to rent 5 chairs and 3 tables is $38, so the equation can be written as 5x + 3y = 38.

To find the value for x, we need to eliminate the variable y first. Start by multiplying each term in the second equation by 4.

5x · 4 + 3y · 4 = 38 · 4

20x + 12y = 152

Then, subtract the terms in the second equation from their counterparts in the first equation.

2x   + 12y = 107

20x + 12y = 152 -

-18x  + 0   = -45

Finally, with a little bit of algebraic manipulation, we've got x = 2.5, hence $2.5 is the cost in to rent a chair.

-18x = -45

x = -45/-18

x = 2.5

What about the cost to rent a table? Well, we can substitute 2.5 for x in either of the equations to get the value for y. For instance, we can pick the equation 2x  + 12y = 107 and substitute x with 2.5 to isolate the variable y, like this:

2(2.5) + 12y = 107

5 + 12y = 107

12y = 107 - 5 = 102

y = 8.5

The value for y turns out to be 8.5. So the cost to rent a table is $8.5.

Your question is incomplete, but it was most probably "A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 12 tables is $107. The total cost to rent 5 chairs and 3 tables is $38. What is the cost to rent each chair and each table?"

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To solve f(1)+h(1) .....

plug in 1 for x in both equations f(x) and h(x):

f(1)=2(1)²+3(1)-4 = 2+3-4 = 1

h(1)= -(1)²+8 = -1+8 = 7

f(1)+h(1) = 1 + 7 = 8

Hope it helps!

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g(x) = 7(x+5) + 1 is the newly transformed function

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Given that: He graphs the function f (x) = 7x + 1 and then transforms the function by horizontally translating it 5 units to the right

To solve this problem, we need to understand the direction of movement. In the cartesian plane or graph, the x-axis is either a movement to the left(negative) or right(positive)

Since the function f (x) = 7x + 1 translates by 5 units to the right. You need to add 5 to x  i.e. 7(x+5) + 1

Therefore, the newly transformed function, g (x) = 7(x+5) + 1

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The inequality to represent the perimeter of the triangle is given by (2n + 3) + (2n + 2) + n ≤ 30

Side a + side b + side c ≤ perimeter of the triangle

(2n + 3) + (2n + 2) + n ≤ 30

2n + 3 + 2n + 2 + n ≤ 30

5n + 5 ≤ 30

substract 5 from both sides

5n ≤ 30 - 5

5n ≤ 25

n ≤ 25/5

n ≤ 5 cm

The largest possible lengths of the sides is:

Side a = (2n + 3)cm

= 2(5) + 3

= 10 + 3

= 13 cm

Side b = (2n + 2) cm

= 2(5) + 2

= 10 + 2

= 12 cm

Side c = n cm

= 5 cm

So therefore, the largest possible length of the triangle is 13 cm

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Answer: It is b

Step-by-step explanation:

Answer: 126.5

Step-by-step explanation:

This is Pythagoras theorem so a² + b² = c²

c² is always the diagonal bit

The soccer field is rectangle and draw the route of the players on and you get the triangle

a = 120

b = 40

c² = a² + b² (square root after)

120² + 40² = 16000

Then square root that to get 126.5

I hoped this helped so please thank and rate :)

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

y = 180 -71 = 109

x = 360 - (81+100+71)

x = 360 -252

x = 108

answer is B

x = 108 and y = 109

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The value of X is 108 and the value of y is 109. The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division.

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

y = 180 -71 = 109

x = 360 - (81+100+71)

x = 360 -252

x = 108

Therefore the value of x and y is x = 108 and y = 109

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For the given expressions the roots with rational exponents are as follow:

a.  27¹/³ = 3

b. 225 ¹/² = 15

c. 49 ³/² = 243

As given in the question,

For the given expressions the roots with rational exponents are as follow:

Solution of each expression is given by:

a. 27¹/³

Prime factors of 27 is equal to 3 × 3 × 3

27¹/³

= ( 3 × 3 × 3 )¹/³

= ( 3³ )¹/³

= 3

b.  225 ¹/²

Prime factors of 225 is equal to 3 × 3× 5× 5

225 ¹/²

= ( 3× 3× 5× 5)¹/²

= ( 15²)¹/²

= 15

c.  49 ³/²

Prime factors of 49 is equal to 7 × 7

49 ³/²

= ( 7 × 7) ³/²

= (7²) ³/²

= 7³

= 343

Therefore, for the given expressions the roots with rational exponents are as follow:

a.  27¹/³ = 3

b. 225 ¹/² = 15

c. 49 ³/² = 243

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The percent of the number is 0.5% when the number is 1/200.

Given that,

We have to find the percent of the number 1/200.

A percentage is a number or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the symbol "%" or just "percent" or "pct."

Take the number.

1/200

Multiply by 100

1/200×100

We get

1/2

In decimal we get

0.5%

Or

Convert the number to decimal.

1/200= 0.005

Multiply 0.005 by 100 to convert to a percentage.

0.005×100

Simplify

0.5%

Therefore, The percent of the number is 0.5% when the number is 1/200.

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Applying the definition of angle bisector, the value of x is: x = 3.

An angle bisector can be defined as a ray or line that divides an angle into two parts that are congruent or equal to each other in measure.

Since TR is the angle bisector that bisects angle ATS, it implies that angle ATS is divided into equal parts.

Given the following:

Measure of angle RTS = (17x - 5)°

Measure of angle ATS = (28x + 8)°

Therefore:

Measure of angle ATS = 2(measure of angle RTS) [definition of angle bisector]

Substitute

28x + 8 = 2(17x - 5)°

28x + 8 = 34x - 10

Combine like terms

28x - 34x = -8 - 10

-6x = -18

Divide both sides by -6

-6x/-6 = -18/-6

x = 3

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The likelihood of their next third child having additional digits of (six fingers on each hand and six toes on each foot) is 1/2.

For the given condition,

Because the father has the dominant feature as well as the mother is now in normal condition, there is a 50% chance that this deformity will be passed down to children.

Thus, the likelihood of their next (third) child having additional digits is 1/2.

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Answer:

(a) $2.40

(b) Chips: 4/7

Drink: 3/7

(c) $9.60

Step-by-step explanation:

Polly buys a drink at a convenience store for $1. 80. She also buys a bag of chips.

(a) The ratio of the cost of the chips to the cost of the water is 4:3. Find the cost of the chips.

chips : water = 4 : 3

chips/water = 4/3

c/1.8 = 4/3

3c = 1.8 × 4

c = 0.6 × 4

c = 2.4

$2.40

(b) Polly has $6 to spend. Work out the total amount she spends on a drink and chips as a fraction of the $6. Give your answer in its lowest terms.

4 + 3 = 7

Chips: 4/7

Drink: 3/7

(c) The $6 is 37. 5% less than the amount Polly had to spend last week. Calculate the amount she had last week.

Last week it was 100%.

This week it is 37.5% less.

100% - 37.5% = 62.5%

This week, it is 62.5% of last week.

Let x = last week's amount.

62.5% of (last week's amount) = $6

62.5% × x = 6

0.625x = 6

Divide both sides by 0.625

x = 6/0.625

x = 9.6

$9.60

Height of cylinder is 5 units

Define Cylinder

               ⇒ V = (π × radius²) × h

We have given,

Slant height of cylinder = √29

Radius is = 2 units

Now, we to have to calculate the height for that we have the formula

h = √l² - r²

where, l = slant height

            r = radius of the circular base

            h = height of the cylinder

Now, for the sake of simplicity

h = √l² - r²

h² =  l² - r²

Now, plug in the values

h² = (√29)² - 2²

h² = 29 - 4

h² = 25

h = 5

Hence, the height of cylinder is 5 units

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Answer:

mary=x

andrew=8

jim=2*8=16

together=4*mary

total=8+16=24

24/4=x

x=6

Step-by-step explanation: