What is the measure of angle x?

The equation of line perpendicular to the line 5x + 3y = -21 will be;

⇒ y = 3x/5 + 4

What is Equation of line?

The equation of line with slope m and passes through the point

(x₁, y₁) is;

⇒ y - y₁ = m (x - x₁).

Given that;

The equation of perpendicular line is,

⇒ 5x + 3y = -21

And, The point on the line will be (-5 , 1)

Now,

The product of the slopes of the perpendicular line will be -1.

Slope of the perpendicular line 5x + 3y = -21 is;

5x + 3y = -21

y = - 5x/3 - 21/3

y = -5x/3 - 7

dy/dx = m₁ = -5/3

So, The slope of line which is perpendicular to the line is;

m₁ m₂ = -1

m₂ = -1/m₁

m₂ = 3/5

So, The equation of line perpendicular to the line 5x + 3y = -21 and passes through the point (-5, 1) is;

⇒ y - y₁ = m (x - x₁).

⇒ y - 1 = 3/5 (x - (-5)).

⇒ y - 1 = 3/5 (x + 5)

⇒ 5 (y - 1) = 3 (x + 5)

⇒ 5y - 5 = 3x + 15

⇒ 5y = 3x + 15 + 5

⇒ 5y = 3x + 20

⇒ y = 3x/5 + 4

Thus, The equation of line perpendicular to the line 5x + 3y = -21 will be;

⇒ y = 3x/5 + 4

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Answer:

y = - [tex]\frac{5}{2}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (- 2, 4 )

m = [tex]\frac{4-(-6)}{-2-2}[/tex] = [tex]\frac{4+6}{-4}[/tex] = [tex]\frac{10}{-4}[/tex] = - [tex]\frac{5}{2}[/tex] , then

y = - [tex]\frac{5}{2}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 2, 4 ) , then

4 = 5 + c ⇒ c = 4 - 5 = - 1

y = - [tex]\frac{5}{2}[/tex] x - 1 ← equation of line

Answer: m<F = 134
EF = 18in

Step-by-step explanation:
Since both angles FEG and FGE are equal, we could make out that lines EF and FG are equal measures making an isosceles triangle. Therefore we just add up both 23 to get 46 and subtract it by 180 getting 134

A 28.26

The approximate circumference of a lid that will fit his frying is 28.26.

Circumference of circle

In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.

Formula of circumference if a circle is 2[tex]\pi[/tex]r.

Given that the diameter of the pan is 9 inches.

Radius of pan = 4.5 inches

Therefore circumference of pan = 2 × (22/7) × 4.5

                                                      = 28.28 inches

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In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.

Formula of circumference if a circle is 2r.

Given that the diameter of the pan is 9 inches.

Radius of pan = 4.5 inches

Therefore circumference of pan = 2 × (22/7) × 4.5

= 28.28 inches

Answer:

The number is 9

Explanation:

So, the first thing you have to do is write out the problem. 2x+6x=72

Then, you combine like terms. 8x=72

Then, you have to isolate the variable, so you divide by 8 on both sides. 8x/8=72/8

Then, you have x=9, which is your answer.

Answer:

The number is 9.

Step-by-step explanation:

Framing the expression and solving:

     Let the number be 'x'.

Twice a number = 2x

 6 times the number = 6 *x = 6x

       2x + 6x = 72

Combine the like terms,

              8x = 72

Divide both sides by 8,

                  x = 72 ÷ 8

                  x = 9

[tex]\cfrac{x^2-9}{3x^2+8x-3}\div\cfrac{x-3}{x+2}\implies \cfrac{x^2-9}{3x^2+8x-3}\cdot \cfrac{x+2}{x-3}\implies \cfrac{\stackrel{\textit{diff. of squares}}{x^2-3^2}}{(x+3)(3x-1)}\cdot \cfrac{x+2}{x-3} \\\\\\ \cfrac{~~\begin{matrix} (x-3)(x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} (x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(3x-1)}\cdot \cfrac{x+2}{~~\begin{matrix} x-3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \cfrac{x+2}{3x-1}[/tex]

The code is DHGB.

We are given four puzzles.

1. The equation of the line is : -4x + 2y = 8. The slope of the line is 2. We need to find the parallel line. The slope will be the same. The equation of the parallel line is y = 2x - 5. The code letter is D.

2. The slope of the line is [(3-2)/(0-3)] = -1/3. We need to find the perpendicular line. The slope will be the negative reciprocal. The slope of the perpendicular line is 3. The equation of the perpendicular line is y = 3x - 2. The code letter is H.

3. The slope of the line is [(2-(-2)/(0-(-1)] = 4. We need to find the parallel line. The slope will be the same. The equation of the parallel line is y = 4x - 7. The code letter is G.

4. The equation of the line is : 3x + y = 1. The slope of the line is -3. We need to find the perpendicular line. The slope will be the negative reciprocal. The slope of the perpendicular line is 1/3. The equation of the perpendicular line is y = (1/3)x + 2. The code letter is B.

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Answer:

-8 hours/week

Step-by-step explanation:

Erik = 4 hours/week

Little Brother = 12 hours/week

How many more hours does Eric ride his bike during the week than his little brother?

Erik - Little Brother = (4 hrs/wk - 12 hrs/wk)

Erik rides his bike -8 hours/week more than his little brother.

Answer: |3.7| = 3.7 so the answer will be 3.7

Step-by-step explanation:

Answer:   No, there isn't enough carpet

Explanation:

The room is 20 feet by 15 feet. The floor area is length*width = 20*15 = 300 square feet, which is larger than the 270 sq ft of carpet you have available. Therefore, you don't have enough carpet. The amount needed is 300-270 = 30 sq ft

Answer:

No

Step-by-step explanation:

20 ft*15 ft=300 ft^2

you need to cover 300 ft^2

you only have 270 ft^2

so you can't cover it

Answer:

84 pairs of shoes

Step-by-step explanation:

Since Cici has  pairs of shoes, use this equation to solve for the number of pairs of shoes Aubree has

Answer:

Dude I wish I could help you

A

Step-by-step explanation:

The system of equations that represents the height of the seedling after x weeks is:

y = 6 + 1.5x

y = 8 + 1.4x

Two or more expressions with an equal sign are defined as an equation.

Given that, the tomato seeding is 6 inches tall and growing 1.5 inches per week, and the radish seedling is 8 inches tall and growing 1.4 inches per week.

Let x represent the number of weeks and y represent the total height.

The total height of the tomato seedling after x weeks is:

y = 6 + 1.5x

The total height of the radish seedling after x weeks is:

y = 8 + 1.4x

Hence, the system of equations that represents the height of the seedling after x weeks is:

y = 6 + 1.5x

y = 8 + 1.4x

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Answer:

The conjecture is;

"The quotient of two negative integers is a positive rational number"

Explanation:

Recall that negative divided by negative is equal to positive;

for the given question;

secondly;

Thirdly;

we can observe that all the quotient of two negative integers solved in the three questions above gave a positive rational number.

Therefore, The conjecture is;

"The quotient of two negative integers is a positive rational number"

Answer:

1.25 without the sales tax and tip

Step-by-step explanation:

The coordinates of the circumcenter of the circle is (3,2)

In geometry, a polygon's circumscribed circle, also known as its circumcircle, is a circle that passes through each of the polygon's vertices.

4.The given coordinates are J(6,0) , K(0,0) and L(0,4) .

The coordinates of the circumcenter are (3,2)

5. The given coordinates are J(-6,6) , K(0,0) and L(-4,0) .

The coordinates of circumcenter are (-2,4)

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If a vertical line exists moved across the graph and, at any time, touches the graph at only one point, then the graph exists a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

The vertical line test is a visual approach for assessing whether a curve in the plane accurately depicts the graph of a function by counting the points on the curve where vertical lines cross it. Consequently, any vertical line in the plane can only ever cross the graph of a function once.

Use the vertical line test to define whether or not a graph represents a function. If a vertical line exists moved across the graph and, at any time, touches the graph at only one point, then the graph exists a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

Therefore, the correct answer is option D. No, the graph fails vertical line test.

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The like terms in the expression are 2x and 3x, and the solution is 3x^2 + 5x - 1

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

3x(exponent of 2) + 2x + 3x -1

Rewrite the expression properly

So, we have

3x^2 + 2x + 3x -1

The like terms are the expressions that have the same variables

In this expression, the like terms are 2x and 3x

When evaluated, we have

3x^2 + 5x - 1

Hence, the equivalent expression is 3x^2 + 5x - 1

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The number of groups of 3 and 1/3 in 6 and 1/6 are 37/20.

We can write the given mixed fraction in the form of an improper fraction form.

Mixed fraction

Mixed fractions are those fractions that are formed by combining a whole number with a fraction.

Improper fraction

A fraction with the numerator value greater than the denominator is known as an improper fraction.

Hence, we can write,

3 and 1/3 = 10/3 and,

6 and 1/6 = 37/6

To find the number of groups of 3 and 1/3 in 6 and 1/6, we will divide 6 and 1/6 by 3 and 1/3

Hence, we can write,

(37/6) ÷ (10/3) = (37/6)*(3/10) = 37/20

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If a coin weighing 11.5 grams, has 12 Percentage of Cu content by mass in it, then the exact quantity of Cu in the coin in grams will be 1.38 grams.

As per the question statement, a coin weighing 12 grams, has 12 % of Cu content by mass in it.

We are required to calculate the exact quantity of Cu present in the coin in grams, from the above mentioned data.

To solve this question, we will simply need to calculate 12% of 11.5, and we will obtain our desired answer, that is,

12% of 11.5 = [(12/100) * 11.5] = (0.12 * 11.5) = 1.38 grams.

Hence, a coin weighing 11.5 grams, having 12 Percentage of Cu content by mass, will have 1.38 grams of Cu inside it.

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Answer:

(x+6)/4

Step-by-step explanation:

We are given the following function:

f(x) = 4x-6

It can also be written as:

y = 4x - 6

Finding the inverse:

We have to exchange y with x, and then isolate y. It becomes:

Isolating y:

The inverse function is:

if we covert 4 cm/second into cm/minute we get answer as 240 centimeters per minute.

What is centimeter?

A centimeter is a unit of measurement that is one tenth of a meter or ten millimeters in the metric system. The length of an object is measured in centimeters, which are metric units of measurement. The abbreviation is cm.

We have given,

4 centimeters per second and we have asked to convert it in centimeters per minute.

We know that 1 minute contains 60 seconds.

It tells us that,

x cm/s = 60x cm/minute

4 cm/s = 60(4) cm/minute

4 cm/s = 240 cm/minute

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Complete Question

Convert 4 cm/s to cm/min

this is:

answer: E

Using proportions, the solution to the given rule of three is as follows:

x = 0.61.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three among the proportional amounts, using basic arithmetic operations such as multiplication or division.

The multiplication can be on the line or cross multiplication, depending if the variables are inverse or direct proportional, respectively.

In the context of this problem, the rule of three that represents the relation between the variables is:

1/x = 54/33

Supposing a direct relationship, we apply cross multiplication, hence the solution for x is found as follows:

54x = 33

x = 33/54

x = 0.61.

This problem is incomplete, hence we are going to suppose that we have to solve for x = alpha considering the drawing as a rule of three.

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The values of x and y are: 24° and 58° respectively.

We know that vertically opposite angles are equal, so:

(5x+20) = (6x-4)

5x-6x = -4-20

-x=-24

x=24

hence x=24°

also, angles on a straight line adds up to 180°, so:

5x+20+y-18=180°

using x=24

5(24)+20+y-18=180°

120+20+y-18=180

140+y-18=180

y+122=180

y=180-122

y=58°

Hence the values of x and y are 24° and 58° respectively.

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Answer: 36 5/9

Step-by-step explanation:

The minimum length = 192ft, that Natalie must throw the javelin on her next throw in order to qualify for the final round.

Based on the given conditions,

The length of her javelin throws in the first round must be at least 195 feet.

She has 1 more throw left in the first round.

This list shows the length, in feet, of Natalie's first 7 javelin throws.

= 188, 204, 194, 195, 187, 201, 199

The minimum length is,

= 188 + 204 + 194 + 195 + 187 + 201 + 199

= 1368

Let us assume,

Final length = x

So,

We can write,

( x + 1368 ) / 8 ≥ 195

x + 1368 ≥ 195 * 8

We can multiply the coefficient,

x + 1368 ≥ 1560

x ≥ 1560 - 1368

We can sum or difference the coefficient,

x ≥ 192

This is Inequality function.

Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤ or ≥.

Therefore,

The minimum length = 192ft, that Natalie must throw the javelin on her next throw in order to qualify for the final round.

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So, if in 15 minutes, a person can burn 120 calories. In 1 minute, a person can burn 8 calories.

120 ÷ 15

8

15 | 120

120

0

NOW, how many calories a person burn in 1.5 hours?

60 × 1.5

60

X 1.5

300

60

90.0

15 minutes x 8 calories = 120 calories (GIVEN)

90 minutes × 8 calories

90

x 8

720