Draw a reference triangle and find the trig ratio for the angle (if possible) without a calculator.

Answer:

x>-2

Step-by-step explanation:

3 times five is fifteen, which is larger than 12, so all x needs to be is be bigger negative 2.

Question 10

Lines a and b by the converse of the consecutive interior angles theorem

Question 11

Lines e and f by the converse of the alternate interior angles theorem

Step-by-step explanation:

x + 3y = 1

x = 1 - 3y-(i)

7x + 8y = 11

x= 11-8y/7-(ii)

substituting eqn (i) in eqn (ii)

11-8y/7= 1-3y

11-8y=7-21y

13y=-4

y=-4/13

putting the value of y in eqn (i)

x=1-(-12/13)

x=25/13

Answer:

positive

Step-by-step explanation:

for a line to be perpendicular to another line, the slope must be reciprocaled and if its positive it becomes negative (vice versa)

y = -1/2x+3 = Line A

y = 2x+3 = PERPENDICULAR to Line A

The number of miles that is covered is  1458 miles.

The term gas mileage refers to the distance that have been covered by the car using a given volume of gas. It is common that the unit that is used to measure the volume of the gas is the US gallon.

We have been told that;

420 miles could be covered by the use of 20 gallons

1 mile can be covered by the use of 1 mile  * 20 gallons/ 420 miles

= 0.048 gallons

If 1 mile requires  0.048 gallons

x miles requires 70 gallons

x = 1 mile  * 70 gallons/0.048 gallons

x = 1458 miles

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We have the following:

A.

Let m represent the number of miles per gallon, the inequality would be as follows

B. In two simple inequalities we have this

C.

The sampling distribution of the sample mean approaches a Normal Distribution when the sample size becomes larger.

According to the central limit theorem for samples, if we keep drawing larger .And larger samples and calculating their means, then the sample forms its . Own normal distribution (the sampling distribution). The mean of normal distribution has the same the original distribution and a variance that is equal to the original variance divided by the sample size. The variable p is the number of values whose average is taken together ,and not the number of times we do the experiments.

Thus, for a large random sample, the sample does not resemble the regular curve but for a large random sample it will closely resemble the normal curve.

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The value of a in the equation (3x869)+(19x528)+428(3)(1049)=a is 1359555

From the question, the equation to evaluate is given as

(3x869)+(19x528)+428(3)(1049)=a

Rewrite the above equation to make it legible

So, we have the following equation

(3 x 869) + (19 x 528) + 428(3)(1049) = a

Evaluate the products in the expression

So, we have the following equation

2607 + (19 x 528) + 428(3)(1049) = a

Evaluate the other products in the expression

So, we have

2607 + 10032 + 428(3)(1049) = a

Remove the brackets in the equation

So, we have the following equation

2607 + 10032 + 1346916 = a

Evaluate the sum

1359555 = a

Rewrite as

a = 1359555

Hence, the solution to the equation is 1359555

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The table is a linear function and the equation is y = -3(x - 1) + 4

From the question, we have the pairs to be

From the above representations, we can see that:

As the values of x increase by +2, the values of y constantly increase by -6

This means that the table has a constant rate

By the definition of a linear function, the table represents a linear function

In (a), we have

x = +2

y = -6

The slope is calculated as

Slope = y/x

So, we have

Slope = -6/2

Evaluate

Slope = -3

The equation is then calculated as

Y = Slope * (X - x) + y

Where

(x, y) = (1, 4)

So, we have

y = -3(x - 1) + 4

Hence, the linear function is y = -3(x - 1) + 4

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In the graph you can see two variables: Cost and Number of rooms to clean in house.

You can find the cost when both cleaning companies clean the same number of rooms as the point when the value in the varibles (y-axis and x- axis) are the same in the lines of both companies (the point where the lines cross each other)

Given:

Evelyn sells beauty supplies. She gets 5% commission for selling beauty products.

Required:

To find the commission she receive if she sells $1,648 worth of beauty products.

Explanation:

The commission she receive if she sells $1,648 worth of beauty products is

Final Answer:

$82.4

Answer:

3.525/0.25=14.1

Step-by-step explanation:

Answer: 14.1

Step-by-step explanation:

3.525/0.25 = 14.1

Since "quotient" just means the result of two numbers being divided together. Therefore we would divide the two numbers you just gave.

Answer:

  x = 10°

Step-by-step explanation:

Given the figure with angles 2x, 4x, 5x, and 50° marked, you want to find the value of x.

∠HAC = ∠HCA . . . . base angles of isosceles triangle HAC

2(∠HAC) = 4x . . . . . exterior angle 4x is equal to the sum of the equal remote interior angles HAC and HCA

∠HAC = 2x . . . . . . . divide by 2

∠AED = 180° -2x -2x = 180° -4x . . . . sum of angles in ∆AED is 180°

∠AHC = 180° -4x . . . . angles at H are a linear pair

HC ║ ED . . . . converse of corresponding angles theorem

∠FEG = ∠FCH = 50° . . . . . corresponding angles theorem

5x = 50° . . . . . substitute value of ∠FEG

x = 10° . . . . . divide by 5

Using this value for the marked angles, we get the measures shown in the attachment.

Answer:If t= time sprinting then (50-t)= time recovering

Distance = rate  x time= t(48) + (50-t)18

Step-by-step explanation:just yes

Substitute 80 for C in the formula F = 9/5C +32 to obtain the temperature in fahrenheit.

Thus temperature in

Answer:

8.2 units (nearest tenth)

Step-by-step explanation:

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where (x₁, y₁) and (x₂, y₂) are the two points.

Given points:

Substitute the given points into the distance formula and solve for d:

[tex]\implies d=\sqrt{(4-6)^2+(-1-7)^2}[/tex]

[tex]\implies d=\sqrt{(-2)^2+(-8)^2}[/tex]

[tex]\implies d=\sqrt{4+64}[/tex]

[tex]\implies d=\sqrt{68}[/tex]

[tex]\implies d=8.2 \; \sf (nearest\;tenth)[/tex]

Therefore, the distance between the two given points is 8.2 units to the nearest tenth.

By dividing $180 in the ratio of 2:3:4, we get 40,60 and 80

Solution

2 + 3 + 4 = 9

180 ÷ 9 = 20

Hence, we get the quotient of 20.

20 × 2 = 40

20 × 3 = 60

20 × 4 = 80

Hence, by dividing $180 in the ratio of 2:3:4, we get 40,60 and 80

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The coordinates of point C on AB such that AC is 2/3 the length of AB is (2,0)

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).

To find out how long AC is, we must first find the length of AB.

According to Pythagoras’ theorem,

[tex]a^2 + b^2 = c^2[/tex].

Thus [tex]4^2 + 6^2 = c^2[/tex].

[tex]16 + 36 = c^2[/tex].

The square root of this is;

c = √52.

AB is 7.21 units long.

2/3 of 7.21 is 4.8

The coordinate that fits this is (2,0).

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Answer:

Step-by-step explanation:

round up

√3 = √4

70-√4= 70-2

=68

Answer:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Since line has a slope of -3, equation is y = -3x + c.

Substitute (-3,1) into the equation to find c.

1 = -3(-3) + c

c = -8

Hence, equation of line is y = -3x - 8.

"When creating a graph, it is important to assign the x and y axis."

Assigning the x and y axes is crucial when making a graph because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally. A point or line's separation from the y-axis can be determined using the x-axis. The y-axis displays a point's location on a Cartesian plane in the y (vertical) direction. Additionally, it serves as the origin (zero) point for calculating how far a point is from the x-axis.

A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.

"When creating a graph, it is important to assign the x and y axis."

Because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally, determining the x and y axes is essential when creating a graph. The x-axis can be used to calculate a point or line's distance from the y-axis. A point's position on a Cartesian plane is shown on the y-axis in the y (vertical) direction. It also acts as the origin (zero) point for determining a point's distance from the x-axis.

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Answer:

(-13, - 6)

Step-by-step explanation:

Midpoint =(x₁ + x₂)/2, (y₁ + y₂)/2

(-4,-6) = (9+x)/2, (1+y)/2

9+x= - 4

X= - 13

1+y= - 6

Y= - 7

Ans=

(-13, - 6)

Answer:

0

Step-by-step explanation:

the domain can’t be the same

The measure of the value of ∠j is 10°.

What are a few properties of a triangle considering its angles?
A triangle's outer angle is the sum of its internal angles' two opposite sides.
The sum of two linear angles is supplementary.

Given, the three angles of the triangle are measured as (5x - 3)°,
(4x - 2)° and j°.
Also, the exterior angle of the triangle is (10x - 20)°.
Following the literature established above, considering that a triangle's outer angle is the product of its internal angles' two opposite sides, we have: (5x - 3) + (4x - 2) = 10x - 20 ⇒ 9x - 5 = 10x - 20 ⇒ 10x - 9x = 20 - 5
⇒ x = 15 --(i)
Again, since the sum of two linear angles is supplementary, we have using (i):
j + (10x - 20) = 180 ⇒ j + 150 - 20 = 180 ⇒ j = 10°
Therefore, the measure of the value of ∠j is 10°.

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The two triangles are not similar to each other.

The perimeter of the triangle is the sum of the lengths of all its sides.

The angle of triangle = 62

The two equal angles = [4(x +2)] and (5x - 7)

According to the question,

The Perimeter of triangle are;

[4(x +2)] + (5x - 7) + 62 = 180

4x + 8 + 5x - 7 + 62 = 180

9x + 63 = 180

9x = 117

x = 13

The other triangle is

6x + 62 + 6x + 6 = 180

12x + 68 = 180

12x = 112

x = 9.33

Hence, the two triangles are not similar to each other.

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The measure of angle 2 is 81° because angles 1 and 2 are corresponding angles.

Corresponding angles:

Corresponding angle means the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.

Given,

Two electricity poles are built standing parallel to each other, as shown below. The measure of angle 1 is 81°.

Here we need to find the measure of the angle 2.

We know that,

If the lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet.

And as per the definition of corresponding angles, we know that, if any two lines are said to be parallel if the Corresponding angles so formed are equal.

Then the measure of the angle 2 is 81° because angle 1 and 2 are parallel.

Therefore, those angles are the corresponding angles also.

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Colton has $67,696 in a savings account that earns 2% interest per year. The interest is not compounded. How much interest will he earn in 1 year?​

we know that

2%=2/100=0.02

so

To find out the amount of interest, multiply the total amount by the percentage in decimal form

(67,696)*0.02

The time for the teacup to last is D. m = 3.5 minutes.

An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number of minutes be m.

The amount of time is one minute more than twice the length of time for the teacup ride. This will be:

= (2 × m ) + 1 = 8

2m - 1 = 8

Collect like terms

2m = 8 - 1

2m = 7

Divide

m = 7/2

m = 3.5

The correct option is D.

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Answer:

d) m = 3.5 minutes

Step-by-step explanation:

Now we have to,

→ find the time the teacup ride last.

Forming the equation,

→ 2m + 1 = 8

Then the value of m will be,

→ 2m + 1 = 8

→ 2m = 8 - 1

→ m = 7/2

→ [ m = 3.5 min ]

Hence, ride lasts for 3.5 min.

The volume of a cylinder is given by the following formula:

Where r is the radius and h is the height of the cylinder.

By replacing 8 for r and 6 for h into the above formula, we get:

Then, the volume of the cylinder equals 1205.76 units³