1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andreyandreev [35.5K]
4 years ago
10

Which graph represents a linear function? A coordinate plane is shown with a way line beginning along the x axis and continuing

along the graph. It curves up and down reaching y equals 1 and y equals negative 1 in a steady pattern along the horizontal axis A coordinate plane is shown with a parabola opening in a downward U shape. The vertex of the parabola is at y equals 7 point 5 and opening downward on either side of the y-axis from there A coordinate plane is shown with a line crossing through the y axis at negative 3 and the x axis at 2. A coordinate plane is shown with a line that begins to the left of the y axis passing through negative 1 comma negative 4, then curving right and passing through the y-axis at negative 4. It curves again and continues upward, passing through the x axis at around x equals 1.
Mathematics
2 answers:
Sliva [168]4 years ago
5 0
<span><span>-2-2 + 2 = 0(-2, 0)</span><span>-1-1 + 2 = 1(-1, 1)</span><span>00 + 2 = 2(0, 2)</span><span>11 + 2 = 3(1, 3)</span><span>22 + 2 = 4<span>(2, 4)</span></span></span>
Assoli18 [71]4 years ago
4 0

Answer:

A coordinate plane is shown with a line crossing through the y axis at negative 3 and the x axis at 2.

Step-by-step explanation:

The graph of a linear function is a straight line. So, we have to find the one graph that describes a straight line.

A coordinate plane is shown with a way line beginning along the x axis and continuing along the graph. It curves up and down reaching y equals 1 and y equals negative 1 in a steady pattern along the horizontal axis. This answer is incorrect because it does not describe a straight line, the line curves up and down between y = 1 and y = -1.

A coordinate plane is shown with a parabola opening in a downward U shape. The vertex of the parabola is at y equals 7 point 5 and opening downward on either side of the y-axis from there. This answer is incorrect because describes a parabola which is the graph of a quadratic function.

A coordinate plane is shown with a line crossing through the y axis at negative 3 and the x axis at 2. This is the correct answer because describes a straight line that passes through the points (0 , - 3) and (2 , 0).

A coordinate plane is shown with a line that begins to the left of the y axis passing through negative 1 comma negative 4, then curving right and passing through the y-axis at negative 4. It curves again and continues upward, passing through the x axis at around x equals 1. This answer is incorrect because it does not describe a straight line.

You might be interested in
The figures show the dimensions of a tennis court and a basketball court given in terms of the width in feet of the tennis court
Sholpan [36]

Answer:

a.  Perimeter of the tennis court = 6x + 12

Perimeter of the Basketball court = 7x + 36

b.  x + 24

c.  Length of the tennis court = 78 feet

Width of the tennis court = 36 feet

Length of the Basketball court = 94 feet

Width of the Basketball court = 50 feet

Step-by-step explanation:

a.  Perimeter of the rectangle = 2(length + width)

So, perimeter of the tennis court = 2[(2x + 6) + x]

= 2(3x + 6)

= 6x + 12

Perimeter of the Basketball court = 2[(3x - 14)+(\frac{1}{2}x + 32)]

= 6x - 28 + x + 64

= 7x + 36


b.  Perimeter of the Basketball court - perimeter of the tennis court

= (7x + 36) - (6x + 12)

= 7x + 36 - 6x - 12

= x + 24

So, perimeter of the basketball court is x + 24 feet greater than that of the tennis court


c.  It is given that the width of the tennis court = 36 feet

But, from the figure,

width of the tennis court = x

So, x = 36

Therefore, length of the tennis court = 2x + 6

= 2(36) + 6

= 72 + 6

= 78 feet

Width of the tennis court = x = 36 feet

Length of the basketball court = 3x - 14

= 3(36) - 14

= 108 - 14

= 94 feet

Width of the basketball court = \frac{1}{2} x+32

=\frac{1}{2} (36)+32

= 18 + 32

= 50 feet

7 0
3 years ago
Find all the missing sides or angles in each right triangles
astra-53 [7]
In previous lessons, we used the parallel postulate to learn new theorems that enabled us to solve a variety of problems about parallel lines:

Parallel Postulate: Given: line l and a point P not on l. There is exactly one line through P that is parallel to l.

In this lesson we extend these results to learn about special line segments within triangles. For example, the following triangle contains such a configuration:

Triangle <span>△XYZ</span> is cut by <span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span> where A and B are midpoints of sides <span><span>XZ</span><span>¯¯¯¯¯¯¯¯</span></span> and <span><span>YZ</span><span>¯¯¯¯¯¯¯</span></span> respectively. <span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span> is called a midsegment of <span>△XYZ</span>. Note that <span>△XYZ</span> has other midsegments in addition to <span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span>. Can you see where they are in the figure above?

If we construct the midpoint of side <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span> at point C and construct <span><span>CA</span><span>¯¯¯¯¯¯¯¯</span></span> and <span><span>CB</span><span>¯¯¯¯¯¯¯¯</span></span> respectively, we have the following figure and see that segments <span><span>CA</span><span>¯¯¯¯¯¯¯¯</span></span> and <span><span>CB</span><span>¯¯¯¯¯¯¯¯</span></span> are midsegments of <span>△XYZ</span>.

In this lesson we will investigate properties of these segments and solve a variety of problems.

Properties of midsegments within triangles

We start with a theorem that we will use to solve problems that involve midsegments of triangles.

Midsegment Theorem: The segment that joins the midpoints of a pair of sides of a triangle is:

<span>parallel to the third side. half as long as the third side. </span>

Proof of 1. We need to show that a midsegment is parallel to the third side. We will do this using the Parallel Postulate.

Consider the following triangle <span>△XYZ</span>. Construct the midpoint A of side <span><span>XZ</span><span>¯¯¯¯¯¯¯¯</span></span>.

By the Parallel Postulate, there is exactly one line though A that is parallel to side <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span>. Let’s say that it intersects side <span><span>YZ</span><span>¯¯¯¯¯¯¯</span></span> at point B. We will show that B must be the midpoint of <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span> and then we can conclude that <span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span> is a midsegment of the triangle and is parallel to <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span>.

We must show that the line through A and parallel to side <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span> will intersect side <span><span>YZ</span><span>¯¯¯¯¯¯¯</span></span> at its midpoint. If a parallel line cuts off congruent segments on one transversal, then it cuts off congruent segments on every transversal. This ensures that point B is the midpoint of side <span><span>YZ</span><span>¯¯¯¯¯¯¯</span></span>.

Since <span><span><span>XA</span><span>¯¯¯¯¯¯¯¯</span></span>≅<span><span>AZ</span><span>¯¯¯¯¯¯¯</span></span></span>, we have <span><span><span>BZ</span><span>¯¯¯¯¯¯¯</span></span>≅<span><span>BY</span><span>¯¯¯¯¯¯¯¯</span></span></span>. Hence, by the definition of midpoint, point B is the midpoint of side <span><span>YZ</span><span>¯¯¯¯¯¯¯</span></span>. <span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span> is a midsegment of the triangle and is also parallel to <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span>.

Proof of 2. We must show that <span>AB=<span>12</span>XY</span>.

In <span>△XYZ</span>, construct the midpoint of side <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span> at point C and midsegments <span><span>CA</span><span>¯¯¯¯¯¯¯¯</span></span> and <span><span>CB</span><span>¯¯¯¯¯¯¯¯</span></span> as follows:

First note that <span><span><span>CB</span><span>¯¯¯¯¯¯¯¯</span></span>∥<span><span>XZ</span><span>¯¯¯¯¯¯¯¯</span></span></span> by part one of the theorem. Since <span><span><span>CB</span><span>¯¯¯¯¯¯¯¯</span></span>∥<span><span>XZ</span><span>¯¯¯¯¯¯¯¯</span></span></span> and <span><span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span>∥<span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span></span>, then <span>∠<span>XAC</span>≅∠<span>BCA</span></span> and <span>∠<span>CAB</span>≅∠<span>ACX</span></span> since alternate interior angles are congruent. In addition, <span><span><span>AC</span><span>¯¯¯¯¯¯¯¯</span></span>≅<span><span>CA</span><span>¯¯¯¯¯¯¯¯</span></span></span>.

Hence, <span>△<span>AXC</span>≅△<span>CBA</span></span> by The ASA Congruence Postulate. <span><span><span>AB</span><span>¯¯¯¯¯¯¯¯</span></span>≅<span><span>XC</span><span>¯¯¯¯¯¯¯¯</span></span></span> since corresponding parts of congruent triangles are congruent. Since C is the midpoint of <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span>, we have <span>XC=CY</span> and <span>XY=XC+CY=XC+XC=2AB</span> by segment addition and substitution.

So, <span>2AB=XY</span> and <span>AB=<span>12</span>XY</span>. ⧫

Example 1

Use the Midsegment Theorem to solve for the lengths of the midsegments given in the following figure.

M, N and O are midpoints of the sides of the triangle with lengths as indicated. Use the Midsegment Theorem to find

<span><span> A. <span>MN</span>. </span><span> B. The perimeter of the triangle <span>△XYZ</span>. </span></span><span><span> A. Since O is a midpoint, we have <span>XO=5</span> and <span>XY=10</span>. By the theorem, we must have <span>MN=5</span>. </span><span> B. By the Midsegment Theorem, <span>OM=3</span> implies that <span>ZY=6</span>; similarly, <span>XZ=8</span>, and <span>XY=10</span>. Hence, the perimeter is <span>6+8+10=24.</span> </span></span>

We can also examine triangles where one or more of the sides are unknown.

Example 2

<span>Use the Midsegment Theorem to find the value of x in the following triangle having lengths as indicated and midsegment</span> <span><span>XY</span><span>¯¯¯¯¯¯¯¯</span></span>.

By the Midsegment Theorem we have <span>2x−6=<span>12</span>(18)</span>. Solving for x, we have <span>x=<span>152</span></span>.

<span> Lesson Summary </span>
8 0
3 years ago
You save for retirement over 30 years by investing $850/month in a stock account that yields 10%. You invest $350/month in a bon
sergejj [24]

Answer:

  $13,287.70

Step-by-step explanation:

The future value of the stock account is computed as the sum of a geometric series. This computation assumes that the annual yield is compounded monthly.

  FV = p((1+r/12)^(12n) -1)/(r/12)

For the stock account, p=850, r=0.10, n=30, so the future values is ...

  FV = 850((1+.10/12)^360-1)/(.10/12)) = 1,921,414.74

For the bond account, p=350, r=.06, n=30, so the future value is ...

  FV = 350((1+.06/12)^360 -1)/(.06/12) = 351,580.26

The combined account value at the end of 30 years is ...

  $1,921,414.74 + 351,580.26 = $2,272,995.00

_____

The monthly payment that can be made over a 25 year period is given by the amortization formula.

  A = P(r/12)/(1 -(1 +r/12)^(-12n))

  = $2,272,995.00(.05/12)/(1 -(1+.05/12)^-300) = $13,287.70

You can withdraw $13,287.70 each month assuming a 25-year withdrawal period.

6 0
4 years ago
There are 45 students in Mr. Griffin's class. One day, 27 students played the drums. What was the ratio of students who played t
Zolol [24]
I am pretty sure that it is 27:20

5 0
3 years ago
Read 2 more answers
Tara runs an amusement park ride and needs to count the people who get on the ride. At the beginning of her shift, 132 people ha
DanielleElmas [232]
Y= the number riders over time
x= hours into Tara's shift
y= 33x + 132
6 0
4 years ago
Read 2 more answers
Other questions:
  • EASY POINTS! (50)
    6·2 answers
  • Evaluate the expression below for x = 4, y = –5, and z = 2.
    6·2 answers
  • 8×3÷(4²-13)+5²+4×3<br> Arrange the steps in the order in which they are preformed
    7·1 answer
  • The following data shows the weight, in pounds, of 5 boxes:
    11·1 answer
  • Question:
    9·2 answers
  • Solve and graph: -x+8&lt;6
    7·1 answer
  • What is the mode of the following data values? 54, 78, 36, 46, 36
    12·2 answers
  • What is the location of D on the decimal number line below?
    14·1 answer
  • How to solve 15x^3/4
    11·2 answers
  • How do i find these in surface area with work??
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!