The point at which three or more lines intersect is the point of _____ concurrency. concurrency. tangency. equality. parallelism.

Answers

Answer 1

The point at which three or more lines intersect is the point of concurrency.

What is the point where three line intersect?

The point were three lines meet or intersect is a point of concurrency.

In other words, a point of concurrency is where three or more lines intersect in one place.

This point of concurrency is a single point shared by three or more lines.

Perpendicular bisectors, and altitudes are concurrent in every triangle.

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Answer 2

Answer:

concurrency

Step-by-step explanation:

Look above for more


Related Questions

WHAT IS THE VALUE OF X ?
NEED THIS ANSWER QUICK!!

Answers

Answer:

8.5

Step-by-step explanation:

24x = 17 ×12

24×= 204

divide each side to get your awnser.

EGG DROP The physics class is holding an egg drop competition. The formula h= −16t2+h0 can be used to approximate the number of seconds, t, it will take for the eggs to reach height, h, from an initial height of h0 in feet.

Find the time it takes an egg to reach the ground if it is dropped from an initial height of 40 feet. Round to the nearest hundredth, if necessary.

Answers

By solving a quadratic equation we will see that the egg will hit the ground after 1.58 seconds.

How long will take the egg to reach the ground?

Here we know that the initial height of the egg is 40ft, so the equation for the height will be:

[tex]h(t) = -16*t^2 + 40[/tex]

The egg will hit the ground when h(t) = 0, so we need to solve the quadratic equation:

[tex]h(t) = -16*t^2 + 40 = 0\\\\16t^2 = 40\\\\t^2 = 40/16\\\\t = \sqrt{40/16} = 1.58[/tex]

This means that the egg will hit the ground after 1.58 seconds.

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22. Which is an expression for the area
of ABC?

Answers

Answer:

C

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] product of 2 sides × sin ( angle between the 2 sides )

We are only given 1 side (AC) so require to find AB or BC using the Sine rule

the third angle B = 180° - (48 + 67)° = 180° - 115° = 65°

using the Sine rule to find AB

[tex]\frac{AB}{sin67}[/tex] = [tex]\frac{15}{sin65}[/tex] ( cross- multiply )

AB × sin65° = 15 × sin67° ( divide both sides by sin65° )

AB = [tex]\frac{15sin67}{sin65}[/tex]

Now

A = [tex]\frac{1}{2}[/tex] × AB × AC sin48°

   = [tex]\frac{1}{2}[/tex] × [tex]\frac{15sin67}{sin65}[/tex] × 15sin48°

  = [tex]\frac{15sin67}{2sin65}[/tex] × 15sin48° → C

A bus company operates services to and from the East, North,South and West regions of the country. A recent report from the Operations Manager contains the following summary of their operations. "The total number of passenger journeys made on our services was 430,000. Of these, 124,000 were to and from the North, 61,000 to and from the South, and 80,000 to and from the East. Passengers used bus passes to pay for 158,000 of the total number of journeys: 43,000 on northern services, 51,000 on western services, and 35,000 on eastern services. Passengers who did not use a bus pass paid for their journeys in cash", Construct a two-way tabulation with rows for the country regions and columns for the method of payment. Work out the figures that are not quoted in the summary by using the information provided.

Answers

To find the number going to and from West is 165,000.

The number of bus passes from Southern services is 29,000.

The two-way tabulation

East------------------- 80,000

North------------------- 124,000

South------------------- 61,000

West-------------------- 165,000

Total--------------------------- 430,000

To find the number going to and from West:

80,000 + 124,000 + 61,000 + x = 430,000

265,000 + x = 430,000

x = 430,000 - 265,000

x= 165,000.

Table for the method of paymentBus Passes  

       

Northern services-------------------- 43,000

Western services-------------------- 51,000

Eastern services---------------------- 35, 000

Southern services---------------------- 29,000

Total----------------------------------------------158,000

Let x be the unknown variable,

43,000 + 51,000 + 35,000 + x = 158,000

129,000 + x = 158,000

x= 158,000 - 129, 000

x= 29,0000

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Which combined inequality has the same solution set shown in the graph?



Number line ranging from negative sixteen to zero with a line beginning with a close point at negative twelve and continuing to the left without end, and a second line beginning with a closed point at negative five and continuing to the right without end.


a ≤ –12 or a > 5


a ≤ –12 or a > –5


–a ≤ –12 or a > –5


–a ≤ –12 or a < –5

Answers

Step-by-step explanation:

there is a problem here. based on your textual description none of the 4 answer possibilities are right.

you said, one line starts with a closed (filled) point at -12 and going to the left (without end). a closed point means the point is included.

so, everything -12 and smaller.

that is a <= -12

the other line starts with a closed (filled) point at -5 and goes to the right without end.

this is a >= -5

so, if your textual description is right, you need an answer option

a <= -12 or a >= -5

FYI

the answer options with -a <= -12 don't make much sense, because that simply means a >= 12. and you don't have any line starting at plus 12 and going to the right.

A function, h(x), is defined as shown.
-X - 4, X ≤ 0
4
h(x) =
글 x-3,0 < x≤ 3
2/x-2₁
-X2, X2 4
Which graph represents h(x)?

Answers

From the below graph option B is correct.

What is graph function?

The graph of a function f is the set of all points in the plane of the form (x, f(x)).

It is also define as the graph of f to be the graph of the equation y = f(x).

Given,

Three different function for h(x)

[tex]\frac{1}{4}x -4 , x \leq 0\\ \\\frac{1}{3} x -3, 0 < x \leq 3\\\\\frac{1}{2} , x\geq 4[/tex]

From the above function,

x ≤ 0, the slope of the graph of h(x) is  [tex]\frac{1}{4}[/tex]

0 < x ≤ 3, the slope of the graph of h(x) is  [tex]\frac{1}{3}[/tex]

x ≥ 4, the slope of the graph of h(x) is  [tex]\frac{1}{2}[/tex]

As we progress from left to right,

The slope of h(x) increases  and the slope of the graph becomes steeper.

Therefore,

The graph starts at (4,0) and goes to the right.

Graph is missing in this question, So you might be referring to the one attached.

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Answer:it’s option 2

Step-by-step explanation:

If y varies directly as as x and y=12 when x=4, find y when x=12

Answers

Answer:

y=48

Step-by-step explanation:

Chad created a table that shows the ratio of his sports game cards.

Chad’s Cards
Card Type
Outfield
Infield
Catcher
Pitchers
Quantity
3
4
1
2

Next, Chad created the graph below showing possible ratios for Pitchers cards to Infield cards in his deck. Which of the following statements are true?

On a coordinate plane, a graph titled Chad's Cards has Damage on the x-axis and Defense on the y-axis. Points (1, 2), (2, 4), (3, 6), and (4, 8) are plotted.
Chad should not have included the values (1, 2) and (3, 6) because that would mean he only had half a Catcher card.
Chad should not have included the values (1, 2) and (3, 6) because the ratio would be different for these points.
Chad should have changed the axes for the Infield and Pitchers cards so it was the same order as the table.
Chad needs to switch the order of each (x, y) value to show the decreasing values of the Pitchers cards.

Answers

The true statement for Chad graph is that:

On a coordinate plane, a graph titled Chad's Cards has Damage on the x-axis and Defense on the y-axis. Points (1, 2), (2, 4), (3, 6), and (4, 8) are plotted.

What is a coordinate plane?

A  coordinate plane is known to be a kind of  two-dimensional plane that is often created by two number lines of intersection.

Note that there is the horizontal number line known as  the x-axis and the  vertical number line also called the y-axis.

Looking at the question (Image attached), for every two offense, there is 4 defense.

So we can say that the proportion of  offense to defense is 1:2

Therefore, the correct  value or the graph is (1, 2), (2, 4), (3, 6), and (4, 8) as it doubles itself.

The true statement for Chad graph is that:

On a coordinate plane, a graph titled Chad's Cards has Damage on the x-axis and Defense on the y-axis. Points (1, 2), (2, 4), (3, 6), and (4, 8) are plotted.

Therefore, option A is correct.

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Answer: A

Step-by-step explanation: I did the test and got it right

One positive number is 5 times another number. The difference between the two numbers is 1432, find the
numbers.

Answers

Answer:

358 , 1790

Step-by-step explanation:

PLease help me solve this

Answers

Answer: 729

Step-by-step explanation:

[tex]\frac{1}{3^{-2} * 3^{-4} * (-1)^{2} }[/tex]

3^-2 = 1/9

3^-4 = 1/81

(-1)^2 = 1

1/(1/9 * 1/81 * 1)

1/ 1/729 = 729

need help on how to use percent box
20% of 25

Answers

20% of 25 is 5.
20% as a decimal is 0.2
Your going to times 0.2 and 25 which gives you the answer which is 5

Two corresponding sides of two similar triangles are 3 cm and 5 cm. The area of the first triangle is 12 cm. What is the area of the second triangle?

Answers

Since the are of the first triangle is 12 cm², the area of the second triangle is 33.33 cm².

To answer the question, we need to know what similar triangles are

What are similar triangles?

Similar triangles are triangles in which the ratio of their corresponding sides is constant.

Given that the corresponding sides of the two similar triangles are 3 cm and 5 cm respectively. Also, the area of the first triangle is 12 cm². We need to find the area of the second triangle.

Area of second triangle

Since the triangles are similar, we have that

(side of second triangle/side of first triangle)² = Area of second triangle/Area of first triangle

Area of second triangle = (side of second triangle/side of first triangle)² × Area of first triangle

= (5 cm/3 cm)² × 12 cm²

= 25/9 × 12 cm²

= 25/3 × 4 cm²

= 100 cm²/3

= 33.33 cm²

So, the area of the second triangle is 33.33 cm².

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Salazar assigns the same number of homework questions each school day. The ratio table below shows the total number of homework questions assigned after a certain number of school days.




After 16 days, how many total homework questions have been assigned?
A:60
B:80
C:95
D:115

Answers

Answer:

B

Step-by-step explanation:

First, we have to find the rate of change for this problem. To do this, we subtract any two numbers of days and the coordinating two total questions. Let's just use the first two rows. 8-4=4, and 40-20=20. For every 4 days, he answers 20 questions. We can further simplify this by dividing both sides by 4. 4/4=1, and 20/4=5. For every 1 day, he answers 5 questions. Now, to find 16 days, we just multiply both sides by 16. 16*1=16 and 16*5=80. For every 16 days, he answers 80 questions. 80 is our answer.

Hope this helps!

Question 4 of 21
What is the value of f(4) in the function below?
f(x) = 1/2 • 2x

Answers

Answer:

same rin tayo ganyan rin akin ang hirap

Step-by-step explanation:

good evening po

1/2 x 2(4)
=1/2 x 8
=4
Answer is 4

Mark transferred songs from his computer onto his portable music player. He transferred songs in minutes. How many songs did he transfer per minute?

Answers

Answer:

Need more info

Step-by-step explanation:

You're working with rates. It's relatively straight forward. Take miles per hour for instance. If you travel 60 miles in one hour, you're rate of speed is 60 miles per hour.

You haven't given any data in this example but the idea is the same. Let's say he transferred 10 songs in 5 minutes. That's means his rate is 10 songs per 5 minutes. You can change that to a fraction so it's easier to understand:

[tex]\frac{10 songs}{5minutes}[/tex]

Now just reduce the fraction and it becomes

[tex]\frac{2 songs}{1 minute}[/tex]

Also known as 2 songs per minute

Identify the exponent and the base in the following term [tex]8^{4}[/tex] then simplify.

base =


exponent =


The simplified result is =

Answers

Base = 8

Exponent = 4

Simplified Result = 4096

If you found this useful, please mark it as the BRAINLIEST.

XD

Base = 8

Exponent = 4


The simplified answer = 4,096

hi people ~

can you give me eassy on WORLD AGAINST CHILD LABOUR I need 80 word I already write this but I want 80 word more please give me your own choice on WORLD AGAINST CHILD LABOUR thnks ​

Answers

♨ANSWER♥

Child labor is a service rendered by children in any field during their childhood. This is done due to lack of resources for subsistence, irresponsibility of the parents or lack of resources by the owner to increase their returns on low investment.

This does not matter with the cause of child labor as all the reasons force children to live life without childhood. Childhood is the greatest and happiest period of everyone’s life, during which one learns about the basic strategy of life from parents, loved ones and nature. Child labor interferes with the proper growth and development of children in all aspects, mentally, physically, socially and intellectually.

...hope this helps...

_♡_mashi_♡_

In a class of students, the following data table summarizes the gender of the students and whether they have an A in the class. What is the probability that a student is a
female given that they have an A?

Answers

The probability that a student is a female given that they have an A is; 2/7

How to find the probability?

From the given table, we see that;

Number of males that got A = 4

Number of males that did not get A = 8

Number of females that got A = 6

Number of females that did not get A = 3

The probability that a student is a female given that they have an A is;

P(Female|A) = 6/(4 + 8 + 6 + 3)

P(Female|A) = 6/21 = 2/7

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Which data set could be represented by the box plot shown below?

Answers

It’s B i believe others are not correct I think

Answer:

  B

Step-by-step explanation:

A box and whisker plot is a graphical representation of the 5-number summary of a data set. It shows the minimum, maximum, median, and the values of the 1st and 3rd quartiles. Here, you're asked to identify the data set having the same 5-number summary as that shown in the plot.

__

extremes

The minimum of the data set is shown by the end of the left "whisker." The plot shows a minimum value of 41. Choice C has a minimum of 40, so is not the data set we're looking for.

The maximum of the data set is shown by the end of the right whisker. The plot shows a maximum of 50, matching all of the answer choices shown.

median

The median of the data set is shown by the vertical line in the middle of the box. Here, the median of the data set is indicated as 44. This will be the middle value, or the average of the two middle values of the set of data.

These sets of data have 10 values, an even number, so the median is the average of the middle two.

Choices A and B have a middle pair of 43 and 45, which means their median is (43+45)/2 = 44. Choice D has a middle pair of 43 and 47, so a median of (43+47)/2 = 45. Choice D is not the data set we're looking for.

quartiles

The 1st and 3rd quartiles of the data set are shown by the left and right ends of the box, respectively. They are indicated as being 43 and 48.

The median divides the data set into two parts. It is not considered to be a member of either part. The 1st quartile is the median of the lower (left) part. The 3rd quartile is the median of the upper (right) part.

Here, each part has 5 data values, so the quartile values are 3rd from the ends of the data set. In choice A, they are 43 and 49, not a match to the given plot. In choice B, they are 43 and 48, matching the values in the given box plot.

The data set in choice B could be represented by the box plot shown.

What is the symbolic representation for this argument?
If a polygon has exactly three sides, then it is a triangle.
Jeri drew a polygon with exactly three sides.
Therefore, Jeri drew a triangle.

Answers

The symbolic representation for this argument is that Jeri drew a polygon with exactly three sides.

What is a polygon?

A polygon is a plane figure with at least three straight sides and angles, typically five or more.

In this case, the symbolic representation for this argument is that Jeri drew a polygon with exactly three sides.

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Answer:d

Step-by-step explanation:

I don’t know but I got it right:)

A face of a solid is
any one of the flat surfaces of a prism or a pyramid.
a pattern of two-dimensional shapes that can be folded to form a solid figure.
a solid figure with a base that is a polygon and sides that are triangles that meet at the top.
the total area of the surface of a solid figure.

Answers

A face of solid is given by

any one of the flat surfaces of a prism or a pyramid. a pattern of two-dimensional shapes that can be folded to form a solid figure.

What is faces?

" Faces are defined as the flat surfaces of any object enclosed by its edges or sides . It is always 2-dimensional."

According to the question,

A face of a solid,

any one of the flat surfaces of a prism or a pyramid : Any one of the  flat surfaces prism and pyramid represents two dimensional shape.

It is a correct answer.

a pattern of two-dimensional shapes that can be folded to form a solid figure : Represents two dimensional and face of a solid is two dimensional .

It is a correct answer.

polygon and sides that are triangles that meet at the top: represents three dimensional shape.

It is not a correct answer.

the total area of the surface of a solid figure: represents three dimensional shape.

It is not a correct answer.

Hence, a face of solid is given by

any one of the flat surfaces of a prism or a pyramid. a pattern of two-dimensional shapes that can be folded to form a solid figure.

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Answer:

the second one

Step-by-step explanation:

Which set of rectangular coordinates describes the same location as the
polar coordinates (3-√2.37)?
4

Answers

The rectangular coordinates will be (2.999, -0.1239)

What are different Coordinate System ?

The Cartesian Coordinate system is not sufficient to locate points in a plane , therefore some other systems like polar coordinates , spherical coordinates , cylindrical coordinate systems are used.

Polar coordinates are given in the question and we need to determine rectangular coordinates for the same.

The equations used to convert from polar coordinates to rectangular coordinates.

x=rcosθ

y=rsinθ

z=z

For the polar coordinates

(3-√2.37)

r = 3

[tex]\rm \theta \\[/tex] = -√2.37

x = 3cos (-√2.37)

x = 3 *0.999

x =2.999

y = 3 sin.(-√2.37)

y = 3*(-0.0413)

y = -0.1239

Therefore the rectangular coordinates will be (2.999, -0.1239)

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2/
For all values of x,
f(x)=2x-3
and
a) Find fg(x).
Simplify and give your answer in the form ax² + b
b) Find gf(x).
Simplify and give your answer in the form ax² + bx + c
g(x) = x² + 1

Answers

Answer:

2/

For all values of x,

f(x)=2x-3

and

a) Find fg(x).

Simplify and give your answer in the form ax² + b

b) Find gf(x).

Simplify and give your answer in the form ax² + bx + c

g(x) = x² + 1

Step-by-step explanation:

i needs help please ​

Answers

Answer:

Angle of Elevation

If a person is looking up at an object, the angle of elevation is the angle between the horizontal line of sight and the object.  Angle of elevation problems can be solved by using trigonometry as the problem can be modeled as a right triangle.

The MIB agent is on the ground looking up at the alien at the top of the CN tower, and we need to find the angle he should shoot his laser gun.  Therefore, we need to find the angle of elevation.

Diagram attached, where [tex]x[/tex] is the angle of elevation.

To find the angle of elevation, use the tan trig ratio:

[tex]\tan(x)=\sf \dfrac{O}{A}[/tex]

where:

[tex]x[/tex] is the angleO is the side opposite the angleA is the side adjacent the angle

Given:

O = 553.3 mA = 67 m

Substituting the given values into the formula and solving for x:

[tex]\implies \tan(x)=\sf \dfrac{553.3}{67}[/tex]

[tex]\implies x= \tan^{-1} \left(\sf \dfrac{553.3}{67}\right)[/tex]

[tex]\implies x=83.09557654...^{\circ}[/tex]

Therefore, the angle of elevation is 83°  (to the nearest degree).

45 Points!
The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below.

A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the moon and
the Sun.

Answers

Answer:

by using pythagoras theorem

Step-by-step explanation:

the distance between sun and moon is hypoteneous

the distance between earth and sun is perpndicular

and distance between earth and moon is base

we can use,

tanx°=distance betwwen earth and sun/ distance betweenearth and moon

or,

sinx°= distance between earth and sun/ distance between sun and moon

we can use other formulas also same as above 2 examples

Hope ithelps

Answer:

The scientist can use trigonometry to figure out the distance between the Moon and Sun. More specifically, using sine (sin).

Step-by-step explanation:

Label the triangle first.

- x should be theta

- y would be opposite (o) as it is across/opposite from the side where x is

- the distance between the sun and moon would be hypotenuse (h), as it's opposite of the right angle.

The calculation that has o and h in it's formula is sine. The formula looks like :

Sin(Ф) = [tex]\frac{o}{h}[/tex]

To solve for the distance between the Sun and Moon, we plug it into the formula and solve

Sin(x) = [tex]\frac{d}{y}[/tex]

- where d is the distance between the Sun and Moon

hope this helps !! :D

Describe What Anime Is
(In 2 or 3 sentences)
Pls don’t copy and paste from G00gI3

Answers

Answer:

Anime is animation from japan

I NEED THIS NOW PLSSSSS

In terms of the number of moose, what is the relative frequency of male moose, female moose, adult moose, and baby moose? Write your answers as simplified fractions.

Elk Mountain Goat Deer Moose
Male 105 71 42 52
Female 120 93 63 34
Adult 173 103 72 58
Baby 52 61 33 28

Answers

The relative frequencies for the given table are:

Male → 13/44Female →  17/86Adult → 29/86Baby → 7/43

How to get the relative frequencies?

The relative frequency of a given element out of a set, is given by the quotient between the number of that element and the total number of the set.

Here we can see that the total number of moose is:

52 + 34 + 58 + 28 = 172

There are 52 male moose, then the relative frequency for male moose is:

M = 52/172 = 26/86 = 13/44

There are 34 female moose, then the relative frequency is:

F = 34/172 = 17/86

There are 58 adult moose, so the relative frequency is:

A = 58/172 = 29/86

There are 28 baby moose, so the relative frequency is:

B = 28/172 = 14/86 = 7/43

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what percent of their gross pay is being withheld

Answers

The total amount of deductions from an employee's gross pay is $83.20. If the gross pay is $378.18, what percent of their gross pay is being withheld?
a.
21%

b.
22%

c.
23%

d.
24%

Correct answer: b. 22%
The answers is 22 percent!

Here is a hexagon.
Work out the value of x.
150°
140°
56°

Answers

Answer:

x = 142

Step-by-step explanation:

The sum of the internal angles in a hexagon is 720°

2x° + 150° +56° + 140° +90° = 720

2x° + 436° = 720°

2x° = 720 - 436

x° = [tex]\frac{284}{2} =142[/tex]

Hope this helps

Which property justifies the following if angle A is congruent to angle B and angle b is congruent to angle C then angle a is congruent to angle c

Answers

Answer: Transitive property of congruence

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True A 6.1 foot tall camper is standing on a 98 foot cliff looking down at his tent. The tent is 65 feet from the base of thecliff, find the angle of depression to the nearest tenth. How do scientists answer questions?OA. By making observations and performing experimentsOB. By listening to the ideas of others and choosing the best oneOC. By writing papers that support their opinionsOD. By reading reliable sources on the subject they are interested in Somebody please help me with this question What is the measure of 1, 2 and 3? On Monday, 56 biographies werechecked out at the library. This is 8 lessthan twice the amount of fiction bookschecked out that day. How many fictionbooks were checked out on Monday? Which statement best defines the relationship between work and energy?Work can transfer energy between objects and increase radiant energy.Work can transfer energy between objects and cause a change in the form of energy.Work can transfer energy between objects and decrease nuclear energy.Work can transfer energy between objects and cause a change in the amount of total energy. . circle the letter of each sentence that is true about the light-dependent reactions. correct the false statements. a. they convert adp into atp. b. they produce oxygen gas. c. they convert oxygen into carbon dioxide. d. they convert nadp+ into nadph. e. photosynthesis begins when pigments in photosystem i absorb light In almost all multiple cash flow calculations, it is implicitly assumed that the cash flows occur at the _____ of each period. Drag each tile to the correct box.Match each Reconstruction plan to its description.Lincolns planthe Wade-Davis BillJohnsons Planrequired 50 percent of a Southern statesregistered voters to take an oath of loyaltyto the UnionarrowRightdenied amnesty to wealthy plantation ownersin the SoutharrowRightrequired 10 percent of a states registered votersto take an oath of loyalty to the UnionarrowRight Ali needs $60 to purchase a flute. She has $32. She can earn $4 an hour babysitting. Which equation could be used to find h, the number of hours Ali needs to babysit to earn enough money to purchase the flute?A. 60=(32 x 4)h B. 60=(32 x 4)h C. 60=(32 + 4)h D. 60=(32 - 4)h PLS HELP FAST PART B: Which detail from the text best supports the answer to Part A?A. "The Lincoln administration wrestled with the idea of authorizing the recruitment ofblack troops, concerned that such a move would prompt the border states to secede."(Paragraph 2)B. "By the end of the Civil War, roughly 179,000 black men (10% of the Union Army)served as soldiers in the U.S. Army and another 19,000 served in the Navy." (Paragraph4)C. "The July 1863 assault on Fort Wagner, SC, in which the 54th Regiment ofMassachusetts Volunteers lost two-thirds of their officers and half of their troops, wasmemorably dramatized in the film Glory." (Paragraph 5)D. Racial discrimination was prevalent even in the North, and discriminatory practicespermeated the U.S. military. (Paragraph 6) Two chemicals react in an endothermic reaction. what can be known about this reaction? the new substance will need more energy to form its chemical bonds than the old substance will release. more energy will be released from the old substance than the new substance will need to form its chemical bonds. a precipitate will form as a result of the reaction. a gas will form as a result of the reaction.