Mathematics College

Solve the equation by using the quadratic formula.
8x2 – 2x - 15 =0

Answers

Answer 1

Answer:

x = 3/2 or x = -5/4

Step-by-step explanation:

Solve for x over the real numbers:

8 x^2 - 2 x - 15 = 0

Using the quadratic formula, solve for x.

x = (2 ± sqrt((-2)^2 - 4×8 (-15)))/(2×8) = (2 ± sqrt(4 + 480))/16 = (2 ± sqrt(484))/16:

x = (2 + sqrt(484))/16 or x = (2 - sqrt(484))/16

Simplify radicals.

sqrt(484) = sqrt(4×121) = sqrt(2^2×11^2) = 2×11 = 22:

x = (2 + 22)/16 or x = (2 - 22)/16

Evaluate (2 + 22)/16.

(2 + 22)/16 = 24/16 = 3/2:

x = 3/2 or x = (2 - 22)/16

Evaluate (2 - 22)/16.

(2 - 22)/16 = -20/16 = -5/4:

Answer: x = 3/2 or x = -5/4

Related Questions

Cheryl and her sister Diane walk to school along the same route. Cheryl walks at an average of
80 steps per min while Diane walks at an average of 90 steps per min. Cheryl takes steps
of 81 cm each. She takes 12 min to walk to school.
a) What is the distance between their house and the school (Give your answer in metres) ?

metres
b) If each of Diane's steps in 72 cm, how long does Diane take to walk to school?

minutes
c) If Diane takes 16 min to walk to school, how long is each of her steps?

Answers

The distance between their house and the school from the information given will be 777.60 meters.

How to calculate the distance?

The distance between their house and the school will be:

= 80 × 81 × 12

= 77760cm

= 777.60 meters.

When Diane takes 16 min to walk to school, the length of her steps will be:

= 77760/(16 × 90)

= 54 cm

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Pendulum A is 20 cm long and has a 5 g mass on it. Pendulum B is 30 cm long and has a 10 g mass on it. Which one has a faster period?

Answers

The formula for the period T of a pendulum is T = 2π Square root of√L/g, where L is the length of the pendulum and g is the acceleration due to gravity.

Find the measure of angle x in the figure below:

A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 56 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 51 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 72 degrees. The interior angle on the left is labeled as x.

35°
47°
73°
78°

Answers

Answer:

I took the Test it is 72

You measure 20 dogs' weights, and find they have a mean weight of 41 ounces. Assume the population standard deviation is 11.9 ounces. Based on this, what is the maximal margin of error associated with a 99% confidence interval for the true population mean dog weight.

Give your answer as a decimal, to two places

Answers

Answer:

(34.15, 47.85)

Step-by-step explanation:

[tex]n = (\frac{z*stddev}{ME} )^{2}[/tex]

stddev = 11.9

z = invNorm(

area = (1 + confidence interval)/2

mean = 0

stddev = 1

)

= invNorm(

0.995

)

≈ 2.576

n = 20

square root both sides

[tex]\sqrt{20} = 2.576 * 11.9 / ME[/tex]

multiply both sides by ME, divide both sides by √20 to isolate ME
ME = 2.576 * 11.9/√20

≈ 6.85

interval = mean ± ME
= (41-6.85, 41+6.85)

= (34.15, 47.85)

which product is less than 111
31/55x111
31/31x111
55/55x111
55/31x111

Answers

Answer:

31/55 * 111

Step-by-step explanation:

For all the other products, the number before the slash is greater than, or equal to the number after the slash. This means that the fraction is greater than or equal to 1 and thus a bigger product. For 31/55 however, the value is less than 1 (0.56) and thus, the actual product will be less than 111.

plot the points on the coordinate plane and answer the questions k (11,...),L(....,11), and M(40,....) are on that line, too what are the missing coordinates

Answers

The missing coordinates on the line after plotting the points are k(11, 0), L(0, 11) and M(40, 40).

Plotting the points on the coordinate planes

The points can be plotted on coordinate planes as shown below in the graph uploaded.

The missing coordinates are determined as follows;

k (11, 0)L (0, 11)M (40, 40)

Thus, the missing coordinates on the line after plotting the points are k(11, 0), L(0, 11) and M(40, 40).

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A Ferris wheel contains 16 cars evenly spaced on a circle with a radius of 20 feet. What is the distance between any two cars on the Ferris wheel?

Answers

Answer:

230.4

feet

Explanation:

arc length

circumference

fraction of circle

165

360

165

360

230.4

feet to nearest tenth

Answer:

Step-by-step explanation:

the answer is 22.5 but rounded to the nearest whole which is 23

3 of 8
If x = -8 and y = 4, evaluate the
-
following expressions:
i) (4y)² - (2x)²=
ii) 4y²– 2x²=

Answers

Answer:

Step-by-step explanation:

i) (4*4)^2-(2(-8))^2=256-(16)^2=256-256=0

ii) (4*16)-2*(-8)^2=64- 2(16)= 64-32=32

find an equation of the line through the given points. give the final answer in slope-intercept form (-2,2) (4,-1)

Answers

to get the equation of any straight line, we simply need two points off of it, let's use the points in the picture below.

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-2)}}}\implies \cfrac{-3}{4+2}\implies \cfrac{-3}{6}\implies -\cfrac{1}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{-\cfrac{1}{2}}(x-\stackrel{x_1}{(-2)}) \\\\\\ y-2 = -\cfrac{1}{2}(x+2)\implies y-2=-\cfrac{1}{2}x-1\implies y=-\cfrac{1}{2}x+1[/tex]

please help with this

Answers

Answer:

Step-by-step explanation:

This is pretty straight forward. Here are the answers verified:

A. Incorrect. Pretty much not even close to 2°. If it was, then it would've been a very small triangle.B. Incorrect. It is kind of close to it, but it is not 28°. Once again, it would've been small.C. Correct. Angle just about right to reach 62°.D. Incorrect. This triangle would've been kind of big. Though it is not 88°, it is not big.

Correct choice is C.

In the problem 7/10 – 3/4, what is the LCM you can use as the denominator in both fractions?

Answers

1 ) Multiply the largest number (10) by 1.

Can the smallest (4) go into this number evenly?

10 x 1 = 10

10/4 = 2.5 ❌

2 ) Now multiply the largest number by 2.

Can the smallest go into this number evenly?

10 x 2 = 20

20/4 = 5 ✅

The LCD is 20

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Nadia wants to estimate the mean driving range for her company's new electric vehicle. She'll sample vehicles and measure each of their driving ranges to construct a confidence interval for the mean driving range. She wants the margin of error to be no more than 10 kilometers at a 90% level of confidence. A pilot study suggests
that the driving ranges for this type of vehicle have a standard deviation of 15 kilometers.

Which of these is the smallest approximate sample size required to obtain the desired margin of error?

A) 5 vehicles
B) 7 vehicles
C) 10 vehicles
D) 15 vehicles
E) 30 vehicles

Answers

Using the z-distribution, it is found that the smallest sample size required is given by:

B) 7 vehicles.

What is the margin of error for a z-distribution confidence interval?

It is given by:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

z is the critical value.[tex]\sigma[/tex] is the population standard deviation.n is the sample size.

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The margin of error and the population standard deviation are given by, respectively:

[tex]M = 10, \sigma = 15[/tex].

Then, we solve for n to find the needed sample size.

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]10 = 1.645\frac{15}{\sqrt{n}}[/tex]

[tex]10\sqrt{n} = 1.645 \times 15[/tex]

[tex]\sqrt{n} = 1.645 \times 1.5[/tex]

[tex](\sqrt{n})^2 = (1.645 \times 1.5)^2[/tex]

[tex]n = 6.1[/tex]

Rounding up, 7 vehicles have to be sampled, hence option B is correct.

More can be learned about the z-distribution at https://brainly.com/question/25890103

The market sells 1 dozen bagels
for $7.00. The bagel shop sells
bagels for $0.60 each. Which is
the better buy?

Answers

Answer:

market

Step-by-step explanation:

Market

1 dozen bagels = 12 bagels

⇒ Cost per bagel = $7.00 ÷ 12 = $0.58 (nearest cent)

Bagel shop

Cost per bagel = $0.60

As $0.58 < $0.60 the market is a better buy

Find the length of the missing side of the right triangle.

Answers

Answer:

b=8

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 =c^2 where a and b are the legs and c is the hypotenuse

6^2 + b^2 = 10^2

36+b^2 = 100

Subtract 36 from each side

b^2 = 100-36

b^2 = 64

Take the square root of each side

sqrt(b^2) = sqrt(64)

b = 8

What’s the median for 28,30,30,30,30,31,31,31,31,31,31,31,31

Answers

Answer:

Step-by-step explanation:

The median is the number that we find in the middle of the data.

So if we have a sequence of {1,2,3}

Then 2 is the median

If we have a sequence of {1,2,3,4,5}

Then 3 is the median

We look in the middle of 28,30,30,30,30,31,31,31,31,31,31,31,31

and we find 31 in the middle.

Note:

If the middle is something with 2 terms in the middle like

1,2,3,4

Then the median is the average of the two middle terms which is

(2+3)/2 = 2.5

can someone help me with this? please

Answers

Answer:

14.4 feet

Step-by-step explanation:

There are 62 seats on a train. 31 of the seats are empty. What percentage of the seats on the train are empty?

Answers

Answer:

50%

Step-by-step explanation:

31/62 of the train seats are empty,meaning there is 50%

3x-4=8 what does X equal to?

Answers

Hey there,

Solve the equation:

Answer :

x = 4 ✅

Explanations :

3x - 4 = 8

>> Add 4 to both sides :

3x - 4 + 4 = 8 + 4

3x = 12

>> Divide both sides by 3 :

3x/3 = 12/3

Therefore, your answer is x = 4

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Answer:

x = 4

Step-by-step explanation:

Given equation:

3x - 4 = 8

To determine the value of "x", we need to isolate the "x" variable and it's coefficient. This can be done by adding 4 to both sides of the equation.

⇒ 3x - 4 + 4 = 8 + 4⇒ 3x = 12

The next step in determining the "x" variable is to isolate the coefficient from the "x" variable. This can be done by dividing 3 both sides of the equation.

⇒ 3x/3 = 12/3⇒ x = 4

Therefore, the solution (x) is 4.

Please help around 60 points

Answers

Answer:

i don't know do you play any games

Convert 21 inches to feet using dimensional analysis round to 2 decimal places necessary

Answers

1 foot = 12 inches = 1/12

21/1 x 1/12 = 21/12 = 1.75 feet

Answer: 1.75 feet

what is the exact value of tan(19pi/12)

Answers

Answer:

the answer is -2-√3

Step-by-step explanation:

[tex] \tan( \frac{19\pi}{12} ) \\ \tan( \frac{19 \times 180}{12} ) \:\:we \: know \: that \: \pi = 180 \\ \\ \tan(285) \\ = - 2 - \sqrt{3} [/tex]

16/x 45/3 find the value of x round to the nearest tenth

Answers

Answer:

x would be equal to 1.1

Step-by-step explanation:

Step 1: Determine the value of x

I assume that the equation looks like this: 16/x = 45/3

Therefore, using the cross multiply method we can do (16*3) = (x*45)

This will give us 48 = 45x

Then we divide both sides by 45 so we can isolate x by itself

45x/45 = 48/45

x = 1.0667

Then we round to the nearest tenth

x = 1.0667

x = 1.1

Answer: x would be equal to 1.1

Answer:

x = 16/15, or (to the nearest tenth) x = 1.1

Step-by-step explanation:

Note: there must be an " = " sign between the two fractions:

16 45

------- = -------

x 3

Also note that 45/3 reduces to 15: 16/x = 15

Multiplying both sides by x yields 16 = 15x, so that x must be x = 16/15 = 1.1

Slope-intercept form that passes through (9, 3) and has a slope of -

Answers

Step-by-step explanation:

Let m and c be the slope and y-intercept respectively,

(y-3)/(x-9) = m

y-3 = mx-9m

y= mx - 9m+3

y = mx + 3(1-3m)

Select the correct answer.
Which of these is a non-real complex number?

Answers

Answer:

Step-by-step explanation:

[tex]\dfrac 83 +\sqrt{-\dfrac 73}\\\\=\dfrac 83 + \sqrt{-1} \sqrt{\dfrac 73}\\\\=\dfrac 83 +i\sqrt{\dfrac 73}~~~~~~;\left[i =\sqrt{-1}\right]\\\\\text{It is now in the standard form of complex number (a+bi).}[/tex]

What is x .
ABC~ DEF

Answers

Answer:

Dado, △ABC∼△DEF

Por lo tanto

A.C

Así que

2x−1

3x+9

2x+2

Ahora tomando

2x−1

tenemos

2x−1

o 4x−2=18 o x=5

Por lo tanto, AB=2×5−1=9,

BC=2×5+2=12,CA=3×5=15,

DE=18,EF=3×5+9=24

y FD=6×5=30

Por lo tanto

AB = 9 cm, BC = 12 cm, CA = 15 cm, DE = 18 cm, EF = 24 cm y FD = 30 cm

What is the slope-intercept equation for this line?
--1
y = [?]=x +
Enter the correct
symbol,+ or -.
-2
-3

Answers

Answer:

y = -1/2x - 2

Step-by-step explanation:

Slope Intercept form: y=mx+b

You need to find the slope and y-intercept.

(0,-2) is the y-intercept which is the point on the y-axis that is intersected by the linear equation which is our slope line.

Now, we need to find our slope.

*This line is a negative slope*

Starting at our y-intercept [ (0,-2) ] we need to go to a point where the line intersects.

The red dot on the coordinate plane clearly represents it.

(2,-3) is the red point in which we need to go down 1 and over 2 to get there.

So our slope should be -1 / 2

Lastly, write in slope-intercept form:
y = -1/2x - 2

If the sides of a triangle are 8 and 11 in units and the angle between them is 37 degrees, then the length of the third side is: Options :
A 6.1 B 6.4 C 6.7 D 6.9

Answers

The question is an illustration of the laws of cosine, the length of the third side is 6.7 units

How to determine the third side?

The measure of the third side is calculated using the following law of cosine

a^2 = b^2 + c^2 - 2bc * cos(A)

So, we have:

a^2 = 8^2 + 11^2 - 2 * 8 * 11 * cos(37)

Evaluate the expression

a^2 = 44.44

Take the square root of both sides

a = 6.7

Hence, the length of the third side is 6.7 units

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Answers

Answer:

Step-by-step explanation:

Perimeter of a triangle is the total of sides a+b+c
11+5+13=29

I NEED HELP WITH PERCENT PROBLEM

Answers

Answer:

76$

Step-by-step explanation:

114=.6y; y= original price

y=190, original price

190-114=76

i need help asap please

Answers

Answer:

x = 52 due to vertical angle theorem

Step-by-step explanation:

Vertical angles mean that the angles are congruent.

If we know that one angle is 52 the other one shall be 52 as well because vertical angles state that ones that are directly across are congruent known as equal.

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Solve the equation by using the quadratic formula. 8x2 – 2x - 15 =0

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Solve the equation by using the quadratic formula.
8x2 – 2x - 15 =0