Problems 5-9, Find the value of the variable to the nearest tenth of each triangle.

[tex]\dfrac{2x-3}x = \dfrac{14}{x+5}\\\\\implies (2x-3)(x+5) = 14x\\\\\implies 2x^2 +10x -3x -15 -14x=0\\\\\implies 2x^2-7x-15=0\\\\\text{Apply quadratic formula,}~~x= \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}.\\\\\text{In this case,}~ a=2, b=-7~ \text{and}~ c = -15. \\\\\\x = \dfrac{-(-7) \pm \sqrt{(-7)^2 -4\cdot 2 \cdot (-15)}}{2(2)}\\\\\\\implies x = \dfrac{7 \pm \sqrt{169}}{4}\\\\\\\implies x = \dfrac{7 \pm 13}4\\\\\\[/tex]

[tex]\text{Hence} ~x = \dfrac{7+13}{4} = \dfrac{20}4 = 5 ~\text{or}~ x = \dfrac{7-13}4 = -\dfrac{6}4 = -\dfrac 32[/tex]

Answer:

16z

Step-by-step explanation:

z = the unknown number of pounds

16 ounces in 1 pound.

So  z pounds =  16z    

or   it can be given as a proportion;

[tex]\frac{16 ounces}{1 pound} (z)[/tex]

Answer:

f(x) = [x] - 2 + 8

[x] is the notation for 'greatest integer function'

f(-1.8) = [-1.8] - 2 + 8 = -2 -2 + 8 = 4

The answer is 4

Step-by-step explanation:

The value of the function  f(x) = [x] - 2 + 8 when x = -1.8 is 12

Given the function f(x) =[x] - 2 + 8, we need to find f(-1.8)

To get the value of f(-1.8), we will simply substitute x = -1.8 into the function to have:

f(-1.8) = -1.8 - 2 + 8

f(-1.8) = -3.8 + 8

f(-1.8) = 11.8

Since x is in a square bracket, we will round the value up to the nearest whole number, hence;

f(-1.8) = 12

Therefore the value of the function  f(x) = [x] - 2 + 8 when x = -1.8 is 12

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Dynamite blue fire red grape purple

Answer:

z = 56

Step-by-step explanation:

z = 7(8)

Answer:

<NLO and <OLN

Step-by-step explanation:

These two angle names are the same. the letters are simply reversed. it's like saying 1+2=3 and 2+1=3. the same. only reversed but still fluent in simplicity.

Answer:

Step-by-step explanation:

Determine which climbed at a constant rate

A constant rate would produce a straight line.  The slope is the same for all the data for that climber.  We can either calculate the slope between the first and last intervals and see if the slope changes.  Or we can graph the points, which I chose to do.  See the attachment.

Note that Joe's rate is not constant.  It appears as though he's wearing down.  Both Zas and Stephon have constant slopes, so their climbing rates are constant over the period measured.

The slope is the climbing rate:

Joe:           Not Constant

Zas:            2.5 feet/sec

Stephon:     4.0 feet/sec

Time to Reach 30 feet

Joe:           Unknown - he's slowing down at an unpredictable rate.

For Zas and Stephen, use their slopes in the expression:

Use m for slope (ft/sec):  y = m(t) where t is time in seconds

Zas:            2.5 feet/sec:  y = 2.5(t)  Time to reach 30 is 30/2.5 or 12 sec.

Stephon:     4.0 feet/sec:  y = 4.0(t)  Time to reach 30 is 30/4.0 or 7.5 sec.

Answer:

Step-by-step explanation:

[tex]\frac{\sqrt{36x^3y^4}}{2x^{2/3}y^{-4}}=\frac{6x^{3/2}y^2}{2x^{2/3}y^{-4}}=3x^{5/6}y^6[/tex]

a=3, b=5/6, c=6

3*(5/6)*6= 15

Answer:

15.6

Step-by-step explanation:

10.7+4.9=15.6

Answer:

15.6

Step-by-step explanation: I took the test

The reasonable estimate for the length of side DE is 3 units

Find the diagram of the question attached. The given triangle ABC and BDE are similar triangles.

Using the similarity theorem of a triangle, this is expressed as:

AC = DE

Using the pythagoras theorem to get the length of AC:

AB^2 = AC^2 + BC^2

5^2 + AC^2 + 4^2

AC^2 = 25 - 16

AC^2 = 9

AC= 3

Since AC = DE, hence the reasonable estimate for the length of side DE is 3 units

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Answer:

5/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Formula

tn = a1 + (n-1)* d

Givens

tn = 67 (it is the last term or the nth term

n = 10

a1 = 4

find d

Solution

67 = 4 + (10 - 1)*d

67 = 4 + 9*d               Subtract 4 from both sides

67 - 4 = 9d            

63 = 9d                      Divide by 9

63/9 = 9d/9              

7  = d

Remark: This is a fundamental application of the arithmetic sequence. You pretty much have to know how to juggle it's parts.

Answer:

1000

Step-by-step explanation:

5% of my 20000 is 1000 so 21000 total or 1000 anually

40 dollars

Step-by-step explanation:

Answer:

y = 8 + 4x

Step-by-step explanation:

y is the total cost of 1 skating experience.

y = 8 + 4x

This can be read as:  the total cost, y, is equal to the admission, $8, plus $4 times the number of hours the skates are rented.  No snacks included.

Answer:

A - Exponential

Step-by-step explanation:

Exponential is the best fitting model because there's a $500 raise in salary each year, so $500 is added to the salary of the previous year.

The statement that best describes the line segment drawn in relation to the y-axis is (c) the y-axis is a bisector of the segment drawn.

The transformation rule is given as:

[tex](x,y) \to (-x,y)[/tex]

When the triangle is reflected to form triangle H'A'M', the vertices of triangle H'A'M' would be:

[tex]H'A'M' = (-x,y)[/tex]

So, the distance from point A to the y-axis is equidistant to the distance from point A' to the y-axis.

This, in other words means that the y-axis bisects the line segment AA'.

Hence, the relation between the segment and the y-axis is (c)

Read more about reflection at:

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Answer:

C. The y-axis is a bisector of the segment drawn.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

3(x +1) =3x +3

Plug it in

3(5+1)=3(5)+3

3(6)=15+3

18=18

Answer:

0.8 km per day

Step-by-step explanation:

5 3/5 is the same as 5.6, so

5.6/7

= 0.8 km per day

Step-by-step explanation:

x = number of hours A

y = number of hours B

x + y = 23

5.7x + 7.1y = 143.7

from the first equation we get

x = 23 - y

and that we use in the second equation

5.7×(23 - y) + 7.1y = 143.7

131.1 - 5.7y + 7.1y = 143.7

1.4y = 12.6

y = 12.6/1.4 = 9

x = 23 - y = 23 - 9 = 14

she was working 14 hours on job A and 9 hours on job B.

Answer:

she is rich

Step-by-step explanation:

Answer:

54 units^2

Step-by-step explanation:

Answer:

Point B is

Step-by-step explanation:

Answer:

B (-2,-4)

Step-by-step explanation:

Answer:

You can use the scale factor to determine if a picture is an enlargement if the scale factor is greater than 1. If it is less than 1 like 0.9 then the picture would be a reduction because you would be multiplying the number by a number smaller than 1. Now if we have a scale factor greater than 1 let's say 3. Then the picture would be an enlargement because the number is greater than 1.

Step-by-step explanation:

Answer:

not a function. domain = -2, 3, 8 (you don't have to write them in any specific order and you also don't need to write -2 twice)

Step-by-step explanation:

to be a function, all of the x's must be different

Answer:

4 are left. or 1/3 are left

Answer:

N/A; 32; -8

Step-by-step explanation:

4) You have to graph this equation... basically pick two points on the line and connect them. I'd do (0,4) and (4,1) because they're the easiest

5) Just plug -2 into the equation! -3x³+2x², so when you substitute x for -2, you get -3*(-2)³+2*(-2)²=-3*(-8)+2*4=24+8=32

6) -6m+6+6=4-7m, so m=-8

Answer:

graph the slope and the -2

Step-by-step explanation:

first, plot a point at (0,-2) because of the -2 as the y intercept

then, start graphing ur slope

ur next points should be

(2,-1), (4,0) (6,1) and so on

Answer:

62.5

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

-7x-3x+2= -8x - 8

Add like terms

-7x-3x=-10x

-10x+2=-8x-8

+8x       +8x

-2x+2=-8

     -2  -2

-2x=-10

Divide by -2 to isolate the variable

x=5

Answer:

Step-by-step explanation:

what is the answer to the equation

-7x - 3x + 2= -8x - 8

-7x - 3x + 8x = -10

2x = -10

x = 5

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

check

-7 * 5 - 3 * 5 + 2 = -8 * 5 - 8

-48 = -48

the answer is good

Answer:

No factors.

3 - x^2 is prime.

Step-by-step explanation: