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Problem 5.2
Here are three lines that intersect at
one point.
Determine the values of x, y, and z

Answer:

x = 11.3

Step-by-step explanation:

[tex]cos(61^{o} )=\frac{5.5}{x}[/tex]

[tex]x=\frac{5.5}{cos(61^{o}) } =11.34[/tex]

Rounded to the nearest tenth:

x = 11.3

Hope this helps

Answer:

x ≈ 11.3

Step-by-step explanation:

using the cosine ratio in the right triangle

cos61° = [tex]\frac{DE}{DF}[/tex] = [tex]\frac{5.5}{x}[/tex] ( multiply both sides by x )

x × cos61° = 5.5 ( divide both sides by cos61° )

x = [tex]\frac{5.5}{cos61}[/tex] ≈ 11.3 ( to the nearest tenth )

Answer:

Step-by-step explanation:

A line perpendicular to the given line has a slope that is the negative inverse of the reference line.  

Rewrite the given equation in the format of y=mx+b, where mi is the slope and b is the y-intercept (the value of y when x = 0.

2x + 3y = 4

3y=-2x+4

y = -(2/3)X + (4/3)

The reference slope is -(2/3).  The negative inverse is (3/2), which will be the slope of a perpendicular line.  We can write the new line as:

y = (3/2)x + b

Any value of b will still result in a line that is perpendicular.  But we want a value of b that will shift the line so that it intersects the point (-3,-5).  Simply enter this point in the above equation and solve for b.

y = (3/2)x + b

-5 = (3/2)(-3) + b

-5 = -(9/2) + b

-5 = -4.5 + b

b = - 0.5

The equation of the line that is perpendicular to 2x + 3y = 4 and includes point (-3,-5) is

y = (3/2)x - 0.5

The value of (gof)(4) is 9 if the function f(x) is f(x) = -x³, and function g(x) is g(x) = |1/8x-1| option (B) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = -x³

[tex]\rm g(x) = |\dfrac{1}{8}x-1|[/tex]

Plug x = 4 in the f(x)

f(4) = -4³ = -64

Plug the above value in the g(x)

[tex]\rm g(x) = |\dfrac{1}{8}(-64)-1|[/tex]

g(f(4)) = |-8-1| = |-9| = 9

Thus, the value of (gof)(4) is 9 if the function f(x) is f(x) = -x³, and function g(x) is g(x) = |1/8x-1| option (B) is correct.

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Answer:

  ∠AXB or ∠PXQ or ∠AXQ or ∠PXB or ...

Step-by-step explanation:

A vertical angle is formed from the rays that are opposite the rays that form the original angle.

__

The rays forming angle CXD are rays XC and XD. The ray opposite XC will have end point X, and can be named by either of the two points shown on the ray: A or P. That is, rays XA and XP are opposite ray XC.

Similarly, rays XB and XQ are opposite ray XD.

The vertical angle can be named using either of the first pair of opposite rays with either of the second pair:

  ∠AXB, ∠PXB, ∠AXQ, ∠PXQ

Of course, the ray names can be reversed in the angle names:

  ∠BXA, ∠BXP, ∠QXA, ∠QXP

Altogether, there are 8 ways to name the vertical angle to ∠CXD.

The polynomial function represented by the data is equal to D. f(x) = −x² + 10.

In order to determine the polynomial function represented by the data, we would substitute the value of x (-3) into the given set of functions as follows:

For option A, we have:

f(x) = 6x + 15

f(-3) = 6(-3) + 15

f(-5) = -18 + 15

f(-5) = -3 (False).

For option B, we have:

f(x) = -6x - 45

f(x) = -6(-3) - 45

f(x) = 18 - 45

f(x) = -27 (False).

For option C, we have:

f(x) = x² - 40

f(x) = -3² - 40

f(x) = 9 - 40

f(x) = -31 (False).

For option D, we have:

f(x) = −x² + 10

f(x) = −(-2)² + 10

f(x) = −9 + 10

f(x) = 1 (True).

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Complete Question:

A polynomial function is represented by the data in the table.

x = -5, -4, -3, -2, -1

f(x) = -15, -6, 1, 6, 9

Choose the function represented by the data.

A. f(x) = 6x + 15

B. f(x) = −6x − 45

C. f(x) = x² − 40

D. f(x) = −x² + 10

Answer:

(4,0)

Step-by-step explanation:

The point where the line cuts the x-axis is called the x-intercept.

x-intercept is when y = 0.

So given y = 0,

3x+4(0) = 12

3x =  12

x = 12/3

x = 4

therefore the point is (4,0)

Answer:

in the picture

Step-by-step explanation:

You need 2 points to graph a line.

▪︎ if x = 0, y = 0 - 6 => y = -6

1st point: (0, -6)

▪︎if y = 0, 0 = -x - 6 => x = -6

2nd point: (-6, 0)

Answer:

13.) 314.2 in²

15.) 181.5 ft²

Step-by-step explanation:

The area of a circle is found using the equation:

A = πr²

In this equation, "π" represents the number pi (3.14....) and "r" represents the radius (half the diameter).

For 13.), you have been given the radius. Thus, you can substitute it into the equation and solve for "A".

A = πr²

A = π(10)²

A = π x (100)

A = 314.2 in²

For 15.), you have been given the diameter. To find the radius, you need to divide this value by 2. Once you find the radius, you can plug it into the equation and simplify like above.

diameter = 15.2 ft
radius = 7.6 ft

A = πr²

A = π(7.6)²

A = π x (57.76)

A = 181.5 ft²

The data values that are outliers are 4 and 56.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. An outlier distorts the mean and median of the dataset.

In this data, 4 is smaller than the average of the data set and 56 is larger than the average numbers. They are the outliers.

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Answer:

50 cents

Step-by-step explanation:

The question is basically asking what is the unit price

So we simply do :

$3.50 ÷ 7 = $0.50 = 50 cents

Hope this helped and brainliest please

Answer:

$0.50

Step-by-step explanation:

let the cost of one candy bar = X

7 candy bar ---------------$3.50

1 candy bar ---------------- X

crodd multiplying

7×X = 3.50×1

7X = 3.50

dividing bothsides by

7X/7 = 3.50/7

X = 0.50

therefore, one candy bar will cost $0.50

Answer:

2400 words

Step-by-step explanation:

First choose the first letter. You have 5 choices of consonant for this.

Next choose the last letter. You have 4 remaining consonants for this.

Now you have 5 remaining letters which can be placed in any order.

So the answer will be:

5⋅4⋅5!

20⋅120

2400

Answer:

Step-by-step explanation:

16 - 4 = 12

16 + 4 = 20

then 20 ; 2 = 10

Half of 12 is 6, therefore the two numbers 10 - 6 = 4 and 10 + 6 = 16 will have a mean of 10 and a range of 12.

Answer:

πr²h= 1696

⇒r²=1696/3.14×15

⇒r²=36.009

⇒r=√36.009

∴r=6.0008=z

Answer:

A a pair of intersecting lines

Step-by-step explanation:

i got it right on the test bub

Answer: a pair of intersecting lines

Step-by-step explanation: i had many people help me know this is right

Answer:

1.1 x 10¹² mg of sodium

Step-by-step explanation:

(3.4 x 10³ mg)(3.27 x 10⁸) = 1.1 x 10¹² mg

Answer:

You are to write a five paragraph literary essay based on one of the 4 prompts and what you have read and learned in this module. These are your options:

1. How do the events of "The White Umbrella" teach the narrator a lesson about shame and acceptance?

2. What role does creativity play in "The Bat-Poet"?

3. How does the character of Squeaky change over the course of "Raymond's Run"?

4. Discuss the influences of older family members on the protagonists and speakers in the stories and poems of this unit.

You are to write a five paragraph literary essay based on what you have read and learned in this module. Your final submission should meet the following requirements.

• Submit completed pre-writing and outline documents.

• Write an essay that contains an introduction with hook and thesis statement, supporting paragraphs with evidence and at least one quotation, and a conclusion that restates the thesis and reviews main points.

• Use transitions appropriate to the pattern of organization.

• Use vocabulary to create tone and voice.

• Cite primary source (quotation).

• Submit completed revision checklist.

• Vary sentence structure.

• Create sentences with parallel structures.

• Use technology in the writing process.

Step-by-step explanation:

Answer:

175 Kg

Step-by-step explanation:

Convert 385 pounds into kg given the fact that 1 kg = 2.2 pounds.

385 : 2.2 =

175 Kg

----------------

The functions have complex roots from the image are

Functions (b) and (d). This is further explained below.

Generally, Function is simply defined as a connection between two or more variables that may be expressed mathematically.

In conclusion,  Functions with graphs that never touch or cross the x-axis are said to have complicated roots, not real ones.

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The graph state that the initial point is (6.9), and the terminal point is (2,1). The vertex of the parabola is  (3,0). Arrows along the parabola to indicate motion right to left.

Let take x = 4 - t    =t  =  4 - x       as equation  (1)

And y = (t - 1)^2       as equation (2)

Then input equation  (1)  into equation   (2)

y  = ( 4 - x - 1)^2

y = ( 3 - x)^2

y = ( x - 3)^2

So therefore, y = a ( x -3)^2  +  0

It can be written as y  = a(x - h)^2  + k      

Where, a = 1    

The vertex  known to be (h, k)  will be = (3,0).

The starting point is  if t = -2

Therefore, x  = (4 - -2)   = 6      

  y =  (-2 - 1)^2  = (-3)^2    = 9  

So x, y =  (6,9).

Note that if t  = 2

Then x = (4 - 2) =  2      

  y  =  (2 - 1)^2   = 1^2  

=  1    

Therefore, x, y =(2, 1).

Therefore, The graph of the parametric equations  state that the initial point is (6.9), and the terminal point is (2,1). The vertex of the parabola is  (3,0). Arrows along the parabola to indicate motion right to left.

See full question below

What does the graph of the parametric equations x(t)=4−t and y(t)=(t−1)^2, where t is on the interval [−2,2], look like?

The parametric equations graph as a portion of a parabola. The initial point is _____, and the terminal point is _____. The vertex of the parabola is ____. Arrows are drawn along the parabola to indicate motion ____.

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Answer:

volume of the pramind is 90332 ans And like

Answer:

90

Step-by-step explanation:

Answer:

the missing angle or the missing exterior angle is 90

Step-by-step explanation:

180-90=90

The correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9 is,

⇒ - 12 + 20x ≥ - 6x + 9

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The inequality is,

⇒ - 4(3 - 5x) ≥ - 6x + 9

Now, We can simplify as;

⇒ - 4(3 - 5x) ≥ - 6x + 9

⇒ - 12 + 20x ≥ - 6x + 9

⇒ 20x + 6x ≥ 12 + 9

⇒ 26x ≥ 21

⇒ x ≥ 21/26

Thus, The correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9 is,

⇒ - 12 + 20x ≥ - 6x + 9

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The area of the circle grows by a factor of 9, and the actual area is 360

The given parameters are:

Old area = 40

Scale factor = 3

When the circle is dilated, the new area becomes

New area = Old * (Scale factor)^2

Substitute 3 for scale factor

New area = Old * 3^2

Evaluate the exponent

New area = Old * 9

This means that the area of the circle grows by a factor of 9, and the actual area is:

New area = 40 * 9 = 360

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Every term in pattern B is two times the corresponding term in pattern A

The correct option is (B).

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Given:

pattern A uses the rule add five pattern

pattern B uses the rule add 10

if we take example

5x2=10 and comparable to pattern A x2 to get the next number.

Hence, every term in pattern B is two times the corresponding term in pattern A.

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The correct option is (B).

Answer:

8

Step-by-step explanation:

use tangent so opp/adj

9/tan4 which equals 7.7 or 8

The two limiting factors that affect both deciduous forests and grasslands very low rainfall throughout the year ,  a wide range of temperatures throughout the year , Option 1 and 3 are the correct answer.

The places where there is not enough rainfall for the forest to sustain and grow , a layer of grass is spread out , these are called as grasslands.

The two limiting factors that affect both deciduous forests and grasslands is that they both receive very low rainfall throughout the year.

and a wide range of temperatures throughout the year , It can get very warm and simultaneously very cold .

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Answer:

B

Step-by-step explanation:

an arithmetic squeegee is defined by

an = an-1 + d

that means that every term of the sequence is created by adding a constant d (the common difference) to the pervious term.

so, we get the common difference by caucuses the difference of 2 neighboring terms.

e.g.

a1 = 9

a2 = 22

a2 - a1 = 22 - 9 = 13

so, B. 13 is the right answer.

as a quick check if it is truly an arithmetic sequence, we can look, if all the other pairs have the same difference.

yes, they do. the difference is always 13.

The probability that two boys will be selected is 0.3 .

Probability is defined as the study of likelihood of an event.

It has the range of 0 to 1.

Probability is equal to the ratio of possibility of an event to total occurrences

It is given in the question that

There are total 5 children , 3 boys and the 2 girls

Total outcome = 5

The probability of selection of first boy is 3/5

Total outcome = 4

No. of boys left to be selected = 4

The probability of selection of second boy is 2/4

Therefore the probability that two boys will be selected

= (3/5)*(2/4)

= (3/5)*(1/2)

=3/10

= 0.3

the probability that two boys will be selected is 0.3 .

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Answer:It is B i promise!!! i just got it right!

Step-by-step explanation:

Answer: 36°

Step-by-step explanation: 360° ÷ 10 = 36°.

Espero que esto te ayude!!