Instructions: Find the missing side. Round your answer to the nearest
tenth.
63°
19
х
X =

Hi!

-4(x - 5) + 8x = 9x - 3

-4x + 20 + 8x = 9x - 3

-4x + 8x - 9x = -3 - 20

-5x = -23

Answer: B

Answer:

B

Step-by-step explanation:

-4x +20 +8x = 9x -3. That's equall to 4x+20=9x-3. subtract 9x both sides, -5x+20=-3. subtract 20 both sides, -5x=-23.

Answer:

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Step-by-step explanation:

euwwuwjw

Answer:

[tex]x^3-3x^2-12x+19[/tex] is divisible by [tex]x^2+x-6[/tex]  when [tex]2x+5[/tex] is added to it.

Step-by-step explanation:

Let [tex]p(x)=x^3-3x^2-12+19[/tex]  &  [tex]q(x)=x^2+x-6[/tex]

By division algorithm, when p(x) is divided by q(x), the remainder is a linear expression in x

So, let [tex]r(x)=ax+b[/tex] is added to [tex]p(x)[/tex] so that [tex]p(x)+r(x)[/tex] is divisible by [tex]q(x)[/tex]

Let, [tex]f(x)=p(x)+r(x)[/tex]

⇒ [tex]f(x)=x^3-3x^2-12x+19+ax+b[/tex]

⇒ [tex]f(x)=x^3-3x^2+x(a-12)+b+19[/tex]

We have,

[tex]q(x)=x^2+x-6=(x+3)(x-3)[/tex]

Clearly, [tex]q(x)[/tex] is divisible by [tex](x-2)[/tex] and [tex](x+3)[/tex]

{ [tex](x-2)[/tex] and [tex](x+3)[/tex] are factors of [tex]q(x)[/tex] }

We have,

[tex]f(x)[/tex] is divisible by [tex]q(x)[/tex]

⇒ [tex](x-2)[/tex] and [tex](x+3)[/tex] are factors of [tex]f(x)[/tex]

From factors theorem,

If [tex](x-2)[/tex] and [tex](x+3)[/tex] are factors of [tex]f(x)[/tex]

then [tex]f(2)=0[/tex] and [tex]f(-3)=0[/tex] respectively,

⇒ [tex]f(2)=0[/tex] ⇒ [tex]2^3-3(2)^2+2(a-12)+b+19=0[/tex]

⇒ [tex]8-12+2a-24+b+19=0[/tex]

⇒ [tex]2a+b-9=0[/tex]

Similarly,

[tex]f(-3)=0[/tex] ⇒ [tex](-3)^3-3(-3)^2+(-3)(a-12)+b+19=0[/tex]

⇒ [tex]-27-27-3a+36+b+19=0[/tex]

⇒ [tex]b-3a+1=0[/tex]

Subtract (1) from (2)

[tex]b-3a+1-(2a+b-9)=0-0[/tex]

⇒ [tex]b-3a+1-2a-6+9=0[/tex]

⇒ [tex]-5a+10=0[/tex] ⇒ [tex]5a=10[/tex] ⇒ [tex]a=2[/tex]

Put [tex]a=2[/tex] in equation 2

⇒ [tex]b-3[/tex] × [tex]2+1=0[/tex] ⇒ [tex]b-6+1=0[/tex] ⇒ [tex]b-5=0[/tex] ⇒ [tex]b=5[/tex]

∴ [tex]r(x)=ax+b[/tex] ⇒ [tex]r(x)=2x+5[/tex]

Hence, [tex]x^3-3x^2-12x+19[/tex] is divisible by [tex]x^2+x-6[/tex] when [tex]2x+5[/tex] is added to it.

Hope this helps...

Answer:

11

Step-by-step explanation:

because line AD divided the triangle ABC into two equal halves

Answer:

A.

Step-by-step explanation:

Basically.. when you draw a line from the vertex of a right triangle's 90 degree angle to its hypotenuse, it'll make two triangles with the same angles. Then you can use ratios to discern the size of said rectangles. I hope that helps.

Answer:

57.5

Step-by-step explanation:

20x - (10 x 110) = 50

=> 20x - 1100 = 50

=> 20x = 1150

=> x = 1150/20

=> x = 115/2

=> x = 57.5

In this question, two houses have an initial value of $179,000, and the projected values are given in the tables for houses 1 and 2.

Part a:

If the absolute value of the change is always the same, it is linear.

If the rate is the same, it is exponential.

House 1:

We have that:

193,606.4 - 186,160 = 7446.4

201,350.66 - 193,606.40 = 7744.26

Let's try exponential:

[tex]\frac{193,606.4}{186,160} = 1.04[/tex]

[tex]\frac{201,350.66}{193,606.40} = 1.04[/tex]

For house 1, the rate of change is the same, and thus, it is exponential.

House 2:

212,000  - 201,000 = 201,000 - 190,000 = 11,000.

Absolute value of change is the same, so linear.

Thus, for house 1, an exponential function is used, as the rate of change is the same, and for house 2, as the absolute value of change is always the same, it is linear.

Part B

House a:

Exponential function, with initial value of $179,000, and exponential growth rate of 1.04 - 1 = 0.04. Thus:

[tex]f_a(x) = 179000(1+0.04)^x[/tex]

[tex]f_a(x) = 179000(1.04)^x[/tex]

House b:

Linear function, with initial value of $179,000, increasing by $11,000 each year. So

[tex]f_b(x) = 179000 + 11000x[/tex]

Part c:

House a after 30 years:

[tex]f_a(30) = 179000(1.04)^30 = 580,568[/tex]

House b after 30 years:

[tex]f_b(30) = 179000 + 110000(30) = 509,000[/tex]

In 30 years, house a will have a value of $580,568, while house b will have a value of $580,568. House a will have a higher value, due to exponential growth.

For more about linear/exponential growth, you can check https://brainly.com/question/14983998

Answer:

0.2210

Step-by-step explanation:

If p = 0.04

then 1-p = 1 - 0.04 = 0.96

So we have the probability distribution value

as;

n C r * p^r * (1-p)^(n-r)

Thus;

64 C 3 * p^3 * (1-p)^(64-3)

= 64 C3 * 0.04^3 * 0.96^61

where 64 C 3 is 64 combination 3

= 41,664 * 0.04^3 * 0.96^61

= 0.2210

Answer:

[tex]2*3^{2} *5[/tex]

Step-by-step explanation:

90 = 45 = 15 = 5

        2       3     3

                  2    3

                         2

Answer:

1,2,3,4

Step-by-step explanation:

I'm not sure, but i think it is

Answer:

The angle between his home, his friends house and grocery store

Step-by-step explanation:

The given angle are;

The angle between the bus stop, the park and his home

The Angle Angle Similarity Theorem can be used to determine if the streets are parallel by verifying if there are congruent corresponding angles  on the streets between his friends house and the grocery store and the street between the park and the bus stop

Therefore, the angle he needs to know is the angle between his home, his friends house and grocery store which are same side interior angles and they should sum to 180° to give the angle between the road and the other side of his friend's house

Answer:

B could be (4,8), (6,11), (8,14), (10,17), (12,20), etc.

Step-by-step explanation:

quick mafhs

Answer:

90.2

Step-by-step explanation:

Assuming that you can use a calculator, you would need to type in the square root symbol and type in the value 8136.04.

The square root of 8136.04 is 90.2.

Answer:

The inequality is 0.6x < 12.5

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

Step-by-step explanation:

14 gallons-1.5 gallons=12.5 gallons    

we know that  

If the remaining fuel is greater than  1.5 gallons Diego's father can drive the car without the warning light coming on    

so  

Let  

x ----> the number of days

0.6x < 12.5 inequality that represent the situation  

Solve for x

x < 12.5/0.6

x < 20.8 days

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

Answer:

one side should be given.

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

hope it helps...

have a great day!!

Answer:

The answer is D.

Step-by-step explanation:

D is the only choice that properly connects each part of the equation, such as 6*50-6 -> 300-6.

Answer:

10000000

Step-by-step explanation:

gitcy is good for your spleen

Answer:

Rs. 28,571.4

Step-by-step explanation:

Let

Cost price = x

Profit = 5% of x

= 0.05x

Selling price = Rs.30, 000

Profit = Selling price - cost price

0.05x = 30,000 - x

Collect like terms

0.05x + x = 30,000

1.05x = 30,000

x = 30,000/1.05

x = Rs. 28,571.428571428

Approximately,

Cost price = x = Rs. 28,571.4

Answer: B) ^6√2

Both expressions equal 1.22

Step-by-step explanation:

Answer:

A.) 6.4 units

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of AB.

If we find the horizontal and vertical distance of A and B, we form a triangle, with leg lengths of 5 and 4.

Now, we just solve using the Pythagorean theorem.

5^2 = 25

4^2 = 16

25 + 16 = 41

sqrt 41 ≈ 6.4 units.

Hope this helps!

If there is something wrong, just let me know.

x=119

hope it doesn't help you!!

Complete Question

The reading speed of second grade students in a large city is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm.

What is the probability that a random sample of 12 second grade students from the city in a mean reading rate of more than 96 words per minute?

Answer:

[tex]P(\=x >96 )=0.01884[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=12[/tex]

Sample mean [tex]\=x =90[/tex]

Standard Deviation [tex]\sigma=10[/tex]

Generally

[tex]\sigma_x=\frac{\sigma}{\sqrt{10}}[/tex]

[tex]\sigma_x=\frac{10}{\sqrt{12}}[/tex]

[tex]\sigma_x=2.887[/tex]

Generally the equation for P(\=x >96 ) is mathematically given by

[tex]P(\=x >96 )=P(Z>\frac{\=x-\mu_x}{\sigma_x})[/tex]

[tex]P(\=x >96 )=P*(Z>\frac{90-96}{2.887})[/tex]

[tex]P(\=x >96 )=1-P(Z<2.08)[/tex]

[tex]P(\=x >96 )=1-0.98116[/tex]

[tex]P(\=x >96 )=0.01884[/tex]

Answer:

1) It is given that line AB is tangent to the circle at A.

∴ ∠CAB = 90º (Tangent at any point of a circle is perpendicular to the radius throught the point of contact)

Thus, the measure of ∠CAB is 90º.

Step-by-step explanation:

the equation is

3n-1 = 5n-7

2n= 6

n= 3

Part A

Explanation:

A histogram is best because it helps show how the scores breakdown for the various bins or intervals or classes. It's effectively a visual summary of a grouped frequency table.

A dot plot would not work because we don't know the specific scores, but rather just the general region of where they fall.

A box plot doesn't work well either because we lose information on how the distribution is broken down. Sure we get the five number summary out of it, but we don't see how the bins are set up.

============================================================

Part B

We have the categories or bins of 0-4, 5-9, 10-14, 15-19, 20-24. Each bin will correspond to a bar that tells us how frequently the values show up. It tells us how frequent or how many scores we got in that sub-interval.

And so on. This all leads to the histogram shown below.

Answer:

Part A is a histogram.

Part B draw a histogram

Step-by-step explanation:

This is because a dot plot and a box plot are too specific for how the data was given. We don't know the exact number for each student.

Part B The x axis would be labeled by the groups, 0-4, 5-9, 10-14, 15-19, 20-24. The y axis would be labeled number of students. Then you could color in the area matching the correct number of students for each category.

y = 42°

Because the angle at the side of right angle will also be right angle or 90°

Sum of all angles of a triangle = 180°.

So, 48° + 90° + y = 180°

=> 138° + y = 180°

=> y = 180° - 138°

=> y = 42°

Angles on a straight line are 180. Therefore, 180 - 90 (right angle) = 90

Angles in a triange add to 180.

90 + 48 = 138

180 - 138 = 42

—————— (not sure if you need this, but:)

To work out x, you would do:

Angles on a straight line add to 180.

180 - 48 = 132

132/2 = 66

To work out z:

Angles in a triangle add to 180. You know x is 66, so

66 + 90 (right angle) = 156

180 - 156 = 24

Answer:

25%

Step-by-step explanation:

We know that there are ten purple popsicles. Together without the purple popsicles, there are 40 popsicles in total. Therefore there is a 10/40 chance to get purple. We need to turn this into a percentage so we do (10 / 40) x 100. This would equal to 25%, therefore, there is a 25% probability to get a purple popsicle.