Find the height of the triangle. Round the answer to one decimal place.

Answer:

x=21

Step-by-step explanation:

For simplicity's sake, I started by naming the angles. Please reference the attachment.

For this, we're using parallel lines with one intersecting line (transversal) to give us valuable information about the angles.

First, based on the Corresponding Angles Theorem, corresponding angles, such as A and B, are congruent.

This means that angle B can also be represented by the expression 6x-19.

Furthermore, since angles B and C are on the same line, they must be supplementary, meaning that they add up to 180 degrees.

This said, we can set up an equation to solve for x because B+C=180

6x-19+3x+10=180

Combine Variables

9x+10-19=180

9x-9=180

Add 9 to both sides to isolate x

9x=189

Divide both sides by 9

x=21

This problem could have also been solved with various other theorems such as, but not limited to:

Keep in mind a prerequisite for all of these theorems except the vertical angles theorem are that it must be for a transversal cutting/intersecting 2 parallel lines.

The Alternate Exterior Angles Theorem states that alternate exterior angles are congruent (A and D)

The Alternate Interior Angles Theorem states that alternate interior angles are congruent (C and E)

The Vertical Angles Theorem states the vertical angles- angles across from each other- are congruent (B and D)

The Same Side Exterior Angle Theorem states that same side exterior angles supplementary (A and F)

The Same Side Interior Angle Theorem states that same side interior angles are supplementary (E and B)

Please let me know if you have any questions!

Answer:

answer is 151.3575 dollars.

In a quadrilateral ABCD, the measure of the length of the quadrilateral CD will be 25.98 cm.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The length of AD will be

tan θ = AB/AD

AD = 12/ tan 35

AD = 17.14 cm

Then the value of the BD will be given by the Pythagoras.

BD² = AB² + AD²

BD² = 12² + 17.14²

BD² = 144 + 239.78

BD² = 437.78

BD = 20.92 cm

Then operate the sine rule in triangle BCD, we have

[tex]\dfrac{BD}{\sin C} = \dfrac{CD }{\sin B}\\\\\\\dfrac{20.92}{\sin 52} = \dfrac{CD }{\sin 102}\\\\\\CD = \dfrac{20.92 \times \sin 102}{\sin 52}[/tex]

On further solving, the value of CD will be

CD = 25.98

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Answer:

both technically, but it would be an equation, cause you can use substitute of any number in place of A and B, to find C

Answer:

19.61505096...

Step-by-step explanation:

Area in a circle is pi(ratio)squared

Circumference is pi multiplied by diameter

Ratio is half of diameter

15.7 divided by pi is roughly 5 (4.997465213 to be exact)

Half of 5 is 2.5

pi(2.5)squared is 19.61505096...

The value of David's investment will be at least $415 after a period of 20 years

The formula for calculating the compound interest is expressed as:

A = p(1+r)^t

Given the following parameters

Substitute

415 = 230(1+0.03)^t
415/230 = 1.03^t
1.8043 = 1.03^t
t = ln(1.8043)/ln1.03

t = 20 years

The value of David's investment will be at least $415 after a period of 20 years

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Percy solved the equation by expanding the expression on the left-hand side, and this is incorrect

The equation is given as:

x^2 + 7x + 12 = 12

The first step in solving the equation is to equate the equation to 0.

i.e.

x^2 + 7x + 12 - 12 = 0

This given

x^2 + 7x = 0

From the question, Percy solved the equation by expanding the expression on the left-hand side

Hence, Percy's solution is incorrect

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Answer:

Percy is not correct because he applied the zero product property to a factored expression that was not equal to 0. He should have subtracted 12 from both sides to get x2 + 7x = 0 before factoring. The correct solutions are 0 and -7.

Answer:

Not sure if you still want the answers but here you go

Step-by-step explanation:

Noah's mean: 87

Noah's median: 85.5

Noah's mode: 85

Gabriel's mean: 87.17

Gabriel's median: 86

Gabriel's mode: 86

Answer:

What are Noah’s mean, median, and mode?

✔ 87, 85.5, 85

What are Gabriel’s mean, median, and mode?

✔ 87.17, 86, 86

Step-by-step explanation:

just did it they are correct

Answer:

Step-by-step explanation:

Answer:

you are so good are this so keeping up

Answer:

sum of terms: 55550

Explanation:

[tex]\sf S_n = \dfrac{n}{2} (u_{start}+u_{end}})[/tex]

Here the number of terms:

1100 ÷ 11 = 100

Using the Formula:

[tex]\sf \dfrac{100}{2} (11+1100)[/tex]

[tex]\sf 55550[/tex]

Answer:

[tex]313.3333\%[/tex]

Step-by-step explanation:

Based on given conditions, formulate:

[tex] \frac{310 - 75}{75} [/tex]

Calculate the sum:

[tex] \frac{253}{75} [/tex]

Simplify it:

[tex] \frac{47}{15} [/tex]

Convert that to a decimal:

[tex]3.133333[/tex]

Multiply that:

[tex]3.133333 \times \frac{100}{100} [/tex]

Calculate that:

[tex] \frac{3.133333 \times 100}{100} [/tex]

Convert that:

[tex]313.3333\%[/tex]

Answer:

[tex]x=e^5\approx148.413[/tex]

Step-by-step explanation:

[tex]4\ln x-8=12\\\\4\ln x=20\\\\\ln x = 5\\\\x=e^5[/tex]

Parallel lines are lines which are equidistant to each other long every point on both lines.

A line is said to be perpendicular if it crosses another line at exactly 90°. Hence, as depicted in the image attached, TZ is perpendicular to RS.

It is important to note that perpendicular lines always bisect one another and that the slopes of lines that are perpendicular are negative of each other and reciprocals.

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Answer:

an integer is a whole number so adding integers is the same as adding whole numbers

The distance between a and b is 5 units.

An equilateral triangle has three sides that have the same length. The triangle is defined as the plane two-dimensional figure with three sides having the sum of the three angles of 180 degrees.

Since the figure is missing in the question so I have attached the figure of the points on the graph for better understanding.

The given coordinates are as follows:-

a (-3, 2)

b (-6, -2)

c (0, -2)

Use the distance formula,[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] , to find ab.

ab  = √[(−6−(−3))² + (−2−2)²]

ab  = √25

ab  = 5 units

Therefore the distance between A and B is 5 units.

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Step-by-step explanation:

angle G = 81°

angle CFG = 60°

total angle inside CFG = 180

a+81+60=180

a=39°

In DBCF

Total angle is 360

60+39+138+b=360

b=134°

hope its right :)

Answer:

14.

Step-by-step explanation:

Plug 3 in for y:

= 4(3) + 8 - 2(3)

= 12 + 8 - 6

= 14.

Answer:

210

Step-by-step explanation:

divide 150 by 5 to get individual cost, multiply by 7 to get total cost

Answer:

Jimmy is correct

Step-by-step explanation:

The dimensions of the rhombus and square are probably almost the same

Answer:

Jamal will have to borrow 31,800.

Step-by-step explanation:

Total tuition for the full four years = 11,800 + 11,900 + 12,000 + 12,100 = 47,800

Total money from scholarship = 1,500 × 4 = 6,000

Total income received = 2,500 × 4 = 10,000

Total money to borrow = 47,800 - 6,000 - 10,000 = 31,800

Hello!

First we should figure out what 7 x 800 is.

7x800 is 5,600.

Next, start step 1.

7 x 8 is already 56, so you would multiply 1 in the box

(7x8x1)

Second, step 2.

56 x 100 is 5,600, so you would put 100 in the box.

(56x100)

Finally, step 3.

Put your total in the box

(TOTAL: 5,600)

Hope this helps!

Answer:

See below

Step-by-step explanation:

The terms that can be used to best describe the relationship between 60 degree angle and the angle labelled y degree is:

Since vertically opposite angles are equal, y° = 60°.

[tex]\rule[225]{225}{2}[/tex]

Answer:

Vertical angles

Step-by-step explanation:

The 60° angle and the angle marked y° are vertical angles. Vertical angles are equal. They are formed by two lines crossing (intersecting lines) I like to think of them like a pair of scissors, opening and closing! The angles get bigger or smaller together. The angle marked x° and the unmarked angle are another pair of vertical angles.

The best estimate of the profit when 350 pounds of food are produced is $5300

The quadratic regression is given as:

[tex]f(x) = -0.0817x^2 + 102.24x - 20421[/tex]

When 350 pounds are produced, it means that:

x = 350.

So, we have:

f(350) = -0.0817(350)^2 + 102.24(350) - 20421

Evaluate

f(350) = 5354.75

Approximate

f(350) = 5300

Hence, the best estimate is $5300

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Answer:

As the given equation is a linear equation, to graph it, we simply need to calculate two points on the line, plot these points, then draw a straight line through them.

Given equation:

[tex]y=\dfrac{2}{3}x-5[/tex]

Calculating two points on the line:

[tex]\textsf{when }\: x=0 \implies \dfrac{2}{3}(0)-5=-5 \implies (0,-5)[/tex]

[tex]\textsf{when }\: x=6 \implies \dfrac{2}{3}(6)-5=-1 \implies (6,-1)[/tex]

Plot these points and draw a straight line through them (attached).

The cost of each bag of soil is $ 16.25 and the cost of each bag of fertilizer is $ 12.99.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Mr. Ellis has started a vegetable garden.

He bought 15 bags of soil and 3 bags of fertilizer for 282.72.

He realized he did not have enough supplies so he bought another 5 bags of soil and 2 bags of fertilizer for 107.23.

Let the cost of each bag of soil be x and the cost of a bag of fertilizer be y.

Then we have the linear equations,

15x + 3y = 282.72

5x + 2y = 107.23

On solving the equations 1 and 2, we have

x = 16.25 and y = 12.99

The cost of each bag of soil is $ 16.25 and the cost of each bag of fertilizer is $ 12.99.

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Answer:

The speed i total is 750 meters per second

Step-by-step explanation:

9000/12 = 750