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Answer:

Measure of ∠8 is 130°.

Step-by-step explanation:

We can solve for ∠8 in multiple steps:

∠1 = 50°

∠5 = 50° due to corresponding angles being equivalent

180° - m∠5 = m∠8 due to supplementary angles

180° - 50° = m∠8 = 130°

Therefore, the measure of ∠8 is 130°.

Answer: The measure of angle 8 is 130 degrees.

Step-by-step explanation:

Angle 8 and angle 4 has the same measures.  The same way angle 1 and angle 5 also have the same measures.So we know that angle 1 is 50 degrees so angle 5 is also 50 degrees. Angle 5 and  8 lies on a straight line.And straight lines have a measure of 180 degrees.So we know that angle 5 is 50 degrees so what angle measure will 50 degrees add up to get 180 degrees.

Use the equation

50 + x =180  solve for x

-50       -50

x = 130

This means angle 8 is 130 degrees .

Answer:

The skeleton is 1150 yrs old.

Step-by-step explanation:

To get this answer you would take 5750 and divide by 5 because the problem say 1/5th. This would give you the equation 5750/5 = 1150.

Answer:

The solutions of 2·cos(θ) - √3 = 0in the interval [0, 2pi) are;

π/6,  13/6·π

Step-by-step explanation:

The given that the equation is 2·cos(θ) - √3 = 0

The solution of the above equation in the interval [0, 2pi) are required

Therefore, the domain includes 0 ≤ θ < 2pi

2·cos(θ) - √3 = 0

2·cos(θ)  = √3

cos(θ)  = √3/2

Therefore;

θ = cos⁻¹(√3/2)

The values are;

[tex]\theta =\dfrac{12 \cdot \pi \cdot n_1 +\pi }{6} \, or \, \theta =-\dfrac{12 \cdot \pi \cdot n_1 +\pi }{6}[/tex]

Where the domain is 0 ≤ θ < 2pi, we have;

π/6,  13/6·π

Answer:

84 km... Mark me as BRAINLIEST

Step-by-step explanation:

Refer to the pic...

Hope it helped you!

Step-by-step explanation:

Since it takes 6 trips to cover 24 km -

1 trip = 24/6

Therefore 1 trip is -

4 km

Now, the distance for 21 trips is -

21*4 = 84

Therefore, Brad has walked -

84 km

HOPE YOU FIND THIS HELPFUL

Answer:

60 mph

Step-by-step explanation:

Let 'S' be the velocity of the southbound car and 'E' be the velocity of the eastbound car. The distances traveled by each car are:

[tex]D_E=3E\\D_S=3S=3(E+15)\\D_S=3E+45[/tex]

The distance between both cars is given by:

[tex]D^2=D_S^2+D_E^2\\225^2=(3E+45)^2+(3E)^2\\50,625=9E^2+270E+9E^2+2,025\\18E^2+270E-48,600=0\\[/tex]

Solving the quadratic equation for the velocity of the eastbound car:

[tex]18E^2+270E-48,600=0\\E^2+15E-2,700\\E=\frac{-15\pm\sqrt{15^2-4*1*(-2,700)}}{2}\\E=45.0\ mph[/tex]

The velocity of the southbound car is:

[tex]S=E+15=45+15\\S=60\ mph[/tex]

The southbound car is driving at 60 mph.

Answer:

1. 44 + 3x

2. 2y - 8

3. x - 6

15. [tex]5\frac{7}{8}[/tex]

16. [tex]6\frac{1}{3}[/tex]

17. [tex]3\frac{7}{9}[/tex]

Step-by-step explanation:

1. 7² + 2² - 5 - 4 + 3x

   49 + 4 - 5 - 4 + 3x

       53 - 5 - 4 + 3x

           48 - 4 + 3x

              44 + 3x

2. - y - 5 + y + 2(2y-y) - 3

     -y - 5 + y + 4y - 2y -3

      -y - 5 + 5y - 2y - 3

          4y - 2y - 5 - 3

                2y - 8

3. 5x -3 - x - 3(x + 1²)

    5x - 3 - x - 3x - 3

      4x - 3x - 3 -3

           x - 3 -3

             x - 6

15.  [tex]7\frac{1}{4} - 1\frac{3}{8}[/tex]

   = [tex]7 \frac{2}{8} - 1\frac{3}{8}[/tex]

   = [tex]\frac{58}{8} - \frac{11}{8}[/tex]

   = [tex]\frac{47}{8}[/tex] → [tex]5\frac{7}{8}[/tex]

16.  [tex]9 - 2\frac{2}{3}[/tex]

   = [tex]\frac{54}{6} - 2\frac{4}{6}[/tex]

   = [tex]\frac{54}{6} - \frac{16}{6}[/tex]

   = [tex]\frac{38}{6}[/tex] → [tex]6\frac{2}{6}[/tex] → [tex]6\frac{1}{3}[/tex]

17.  [tex]10\frac{1}{3} - 6\frac{5}{9}[/tex]

   =  [tex]10 \frac{3}{9} - 6\frac{5}{9}[/tex]

   =    [tex]\frac{93}{9} - \frac{59}{9}[/tex]

   =     [tex]\frac{34}{9}[/tex] → [tex]3\frac{7}{9}[/tex]

Hope this helps.

Answer:

27π Sq in.

Step-by-step explanation:

Circle A is equal to 9π sq inches. (Radius squared times Pi), Segment BC is a radii of Circle B and the diameter of Circle A. Meaning Circle B's radius is 6 inches. The area of circle B would be 36π sq inches. Now we subtract Circle A's area from Circle B's area(36π sq in. - 9π sq in.), the area of the shaded region is 27π sq in.

Answer:

C = 314 m

Step-by-step explanation:

The circumference of a circle is given by

C = pi * d

Using 3.14 for pi

C = 3.14 * 100

C = 314 m

Answer:

The answer is option D.

Step-by-step explanation:

Circumference of a circle = πd

Where d is the diameter

From the question

d = 100m

Circumference of the circle is

100π

= 314.2

Which is 314m to the nearest whole number

Hope this helps you

Answer:

what is the questions.

Answer:

64 : 216

Step-by-step explanation:

Given the ratio of the heights = a : b, then

ratio of volumes = a³ : b³

Here the ratio of heights = 4 : 6 = 2 : 3 ← in simplest form, thus

ratio of volumes = 4³ : 6³ = 64 : 216 = 8 : 27 ← in simplest form

Answer:

[tex]a^{\frac{1}{3} }[/tex]

Step-by-step explanation:

Apply rule:  [tex]\displaystyle \sqrt[n]{x} =x^{\frac{1}{n}[/tex]

[tex]\sqrt[3]{a} =a^{\frac{1}{3} }[/tex]

Answer:

B. [tex]15x^{4}[/tex] + 2x³ - 8x² - 22x - 15

Step-by-step explanation:

1. (3x² - 2x - 3)(5x² + 4x +5)

[tex]15x^{4}[/tex] + 12x³ + 15x² - 10x³ - 8x² - 10x - 15x² - 12x - 15

2. Combine like terms

[tex]15x^{4}[/tex] + 2x³ - 8x² - 22x - 15

Answer:

Step-by-step explanation:

3x + 45 = 4x + 21

45 - 21 = 4x - 3x

24 = x

Answer:

Step-by-step explanation:

[tex]3x + 45 = 4x + 21 \\ collect \: like \: terms \\ 3x - 4x = 21 - 45 \\ - x = - 24[/tex]

[tex]x = 24[/tex]

Answer:

             [tex]\bold{A_{_{\Delta XYZ}}=927.5\ cm^2}[/tex]

Step-by-step explanation:

m∠Z = 180° - 118° - 28° = 34°

[tex]\sin(28^o)\approx0.4695\\\\\sin(118^o)=\sin(180^o-62^o)=\sin62^o\approx0.8829 \\\\\sin(34^o)\approx0.5592\\\\[/tex]

[tex]\dfrac{\overline{XY}}{\sin Z}=\dfrac{\overline{YZ}}{\sin X}\\\\\\\overline{XY}=\dfrac{\overline{YZ}}{\sin X}\cdot\sin Z\\\\\\\overline{XY}=\dfrac{42}{0.4695}\cdot0.5592\\\\\overline{XZ}=50.024281...\\\\\\A_{_{\Delta XYZ}}=\frac12\cdot\overline{XY}\cdot\overline{YZ}\cdot\sin(\angle Z)\\\\\\A_{_{\Delta XYZ}}\approx\frac12\cdot50.0243\cdot42\cdot0.8829=927.4955...\approx927.5[/tex]

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{8}{7} \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

The solutions are, for a positive discriminant:

   [tex]\dfrac{-b\pm\sqrt{\Delta}}{2a} \ \text{ where } \Delta=b^2-4ac[/tex]

Here, we have a = -21, b = -11, c = 40, so it gives:

[tex]\Delta =b^2-4ac=11^2+4*21*40=121+3360=3481=59^2[/tex]

So, we have two solutions:

[tex]x_1=\dfrac{11-59}{-42}=\dfrac{48}{42}=\dfrac{6*8}{6*7}=\dfrac{8}{7} \\\\x_2=\dfrac{11+59}{-42}=\dfrac{70}{-42}=-\dfrac{14*5}{14*3}=-\dfrac{5}{3}[/tex]

We only want x > 0 so the solution is

   [tex]\dfrac{8}{7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

25

Step-by-step explanation:

a=15

2(15)-5=25

30-5=25

Answer:

25

Step-by-step explanation:

The problem substituting a for 15 would be 2(15)-5

2*15 is 30, then -5 is 25.

Answer:

it is C.

Step-by-step explanation:

The common difference is -7

-27 -(-20)= -27 + 20 = -7

-34 -(-27)= -34 + 27 = -7

-41 -(-34)= -41 + 34 = -7

-48 -(-41)= -48 + 41 = -7

Answer:

$95.42  more

Step-by-step explanation:

To find out how much money was made with Investment A after 2 years:

First, we are told that 160 dollars is saved per month for 2 years.  There are 24 months in 2 years, so we have to multiply $160 by 24 months.

160 *24=$3840 after 2 years.

Next, we learn thar 2.5% interest rate is added to the total amount saved in those two years.  So, we must turn 2.5% in to a decimal, which is 0.025.

Now, multiply 3840*0.025 to get $96.

We have to add that on the the amount saved, so 3840+96=$3936.

Investment A made $3936 after 2 years.

To find out how much money was made with Investment B.

So, we have to find compound interest.  The formula for compound interest is:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

In this problem: P=3800, r=3% or 0.03, n=1, and t=2.

So, lets write it out: [tex]A=3800(1+\frac{0.03}{1} )^{2*1}[/tex]

That becomes: [tex]A=3800(1.03)^{2}[/tex]

Simplify it even further: [tex]A=3800(1.0609)[/tex]

Multiply the last two numbers to get: [tex]A=4031.42[/tex]

Investment B made $4031.42 after 2 years.

The question asks us to find out how much more money Investment B made than Investment A after 2 years.  It's simple.  Just subtract Investment A's amount from Investment B's amount.

4031.42-3936=95.42

Investment B made $95.42 more than Investment A after 2 years.

Answer:

answer Z

Step-by-step explanation:

Look for a graph that contains the following zeros: x = 1, x = 2 , x= 3, following the info derived by the binomial factors that the function contains. Also look ate the fact that the function in question has for leading term positive [tex]x^3[/tex] , then this function must go towards plus infinity when x becomes large. This is the case for the graph option Z (the last graph of the group)

Answer:

h(x) = -15.6(x - 3.8)² + 241

Step-by-step explanation:

if you were to graph these equations, you can see that the second equation has a lower maximum than the rest of equations, including the original. therefore, that answer can be eliminated.

or simply recognize the equation is in vertex form and realize that 222 is the y-value of the vertex. and 222 < 230. (230 being the y-value of the parent function's vertex)

the a-value (-15.9 for the parent/original function) of the new equation must be less than the parent function's a-value. this is the rate at which the pumpkin is decreasing. the lower the value, the slower the pumpkin moves. this is an advantage, as the length it travels increases. therefore, the third and fourth options are eliminated, leaving the first option as the answer.

Answer: 93

Step-by-step explanation:

To solve this we need to follow BIDMAS.

The order of calculations is brackets, division, then multiplication, then addition, then subtraction.

1) (4 + 3) = 7

2) Division: 8 / 2 = 4

3) Multiplication: 3 * 32 = 96

This leaves us with:

96 + 4 - 7

This equals 93.

Answer:

93

Step-by-step explanation:

3 · 32 + 8 ÷ 2 − (4 + 3)

PEMDAS says parentheses first

3 · 32 + 8 ÷ 2 − (7)

Then multiply and divide from left to right

96 + 4 -7

Then add and subtract

100-7

93

Answer:

A.  x = 36

B.  x = 10

C.  x = 36

D.  x = 25

E.  x = 60

Step-by-step explanation:

A.  Since it is a straight line, the total degrees will be 180.  Add the two angle values and set them equal to 180.

2x + 3x = 180

5x = 180

x = 36

B.  This is right angle, meaning that the total degrees will be 90.  Add the two angle values and set them equal to 90.

4x + 5x = 90

9x = 90

x = 10

C.  The angles are around a point, meaning that the total degrees will be 360.  Add the angle values and set them equal to 360.

x + 2x + 3x + 4x = 360

10x = 360

x = 36

D.  Like part A, the straight line has 180 total degrees.  Add the angle values and set them equal to 180.

3x - 5 + x + 20 + 65 = 180

4x - 5 + 20 + 65 = 180

4x + 80 = 180

(4x + 80) - 80 = 180 - 80

4x = 100

(4x)/4 = 100/4

x = 25

E.  Like part A, the angles around the point have 360 total degrees.  Add the angles values and set them equal to 360.

x + 2x + 2x + 60 = 360

5x + 60 = 360

(5x + 60) - 60 = 360 - 60

5x = 300

(5x)/5 = 300/5

x = 60

Answer:

a = 36°

b = 20°

c = 36°

d = 25°

e = 60°

Step-by-step explanation:

A)

2x + 3x = 180° (angles on a straight line = 180°)

5x = 180°

X = 180 / 5

x = 36°

B) 4x + 5x = 90° (sum of two acute angles in a right angle triangle = 90°)

9x = 90

x = 90 / 9

x = 10°

C) 2x + x + 4x + 3x = 360° (sum of angles at a point = 360°)

10x = 360°

x = 360 / 10

x = 36°

D) (3x - 5) + (x + 20) + 65 = 180 (sum of angles on a straight line = 180)

Open brackets

3x - 5 + x + 20 + 65 = 180

4x + 80 = 180

Collect like terms

4x = 180 - 80

4x = 100

X = 100 / 4

x = 25°

E)

x° + 60° + 2x° + 2x° = 360° (angle at a point = 360°)

5x° + 60° = 360°

Collect like terms

5x° = 360° - 60°

5x° = 300°

x = 300 / 5

x = 60°

Answer:

The answer is option D

Step-by-step explanation:

32m + 56mp

First factor out the HCF out

The HCF of 32and 56 is 8

So we have

8 ( 4m + 7mp)

next factor m out

We have the final answer as

Hope this helps you

Answer:

13/25

Step-by-step explanation:

The total number of people is 20 + 6 + 17 + 7 = 50.

Of these, the number that have brown or green eyes is 20 + 6 = 26.

So the probability is 26/50, which reduces to 13/25.

The probability that a person chosen at random from this group has brown or green eyes is; 13/25

From the given data values, we can deduce that;

Total number of people = 20 + 6 + 17 + 7 = 50.

Now, the total number of people that have brown or green eyes is;

Total(brown or green eyes) = 20 + 6 = 26.

Thus, the probability that a person chosen at random from this group has brown or green eyes is;

P(brown or green eyes) = 26/50 =  13/25.

Read more about Probability at; https://brainly.com/question/251701

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Answer:

A. 2 real roots:  (2, 7) and (1, 4).

Step-by-step explanation:

y = x^2 + 3

y = 3x + 1

So equating the right sides:

x^2 + 3 = 3x + 1

x^2 - 3x  + 2 = 0

(x - 2)(x - 1) = 0

So there are 2 roots.

They are x = 2 , y = 3(2) + 1 = 7 and

x = 1, y = 3(1) +1 = 4.

Answer:

The correlation between hour of the day and the speed over the limit at which the motorist is ticketed is weak positive correlation.

Step-by-step explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

The types of correlation coefficient are:

The correlation coefficient value between the hour of the day and the speed over the limit at which the motorist is ticketed is:

r = 0.12.

The value of r lies between:

0 < 0.12 < 0.30

Thus, the correlation between hour of the day and the speed over the limit at which the motorist is ticketed is weak positive correlation.

Answer:

you want to follow PEMDAS so you would multiply 27 by 1/3 to get 81.003, which you would round to 81, then you would multiply 8 to the third power and you would get 512.

Step-by-step explanation:

27(1/3)^3

81^3

512

Answer:

5x +3

Step-by-step explanation:

f(x) = 2x-6

g(x) = 3x+9

(f+g) (x) = 2x-6+ 3x+9

Combine like terms

            = 5x +3

We are given the following two equations:

[tex]f(x)=2x-6[/tex]

[tex]g(x)=3x+9[/tex]

To find (f+g)(x), we just add f(x) and g(x) and simplify:

[tex](f+g)(x)=f(x)+g(x)[/tex]

[tex]=2x-6+3x+9[/tex]

[tex]=5x+3[/tex]

Let me know if you need any clarifications, thanks!

Answer:

? = 57

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos ? = adj/ hyp

cos ? = 14/26

Taking the inverse cos of each side

cos ^-1 ( cos ?) = cos ^-1 ( 14/26)

? = 57.42102961

To the nearest degree

? = 57