(a) 14x - 3x + 16 = 7(x - 4)

Solve the linear equation

Answer:

Step-by-step explanation:

To find the vertex, we need to put this into vertex form, which is done by completing the square on the quadratic. Begin by moving the 8 over to he other side of the equals sign:

[tex]3x^2-6x=-8[/tex]

Now factor out the 3:

[tex]3(x^2-2x)=-8[/tex]

Now take half the linear term, square it, and add it to both sides. Our linear term is 2. Half of 2 is 1, and 1 squared is 1:

[tex]3(x^2-2x+1)=-8+3[/tex]

We added a 3 on the right because 3 times the 1 we added in is 3. Cleaning that up a bit gives us the perfect square binomial on the left and -5 on the right:

[tex]3(x-1)^2=-5[/tex]

and when we move the -5 back over by adding we have

[tex]3(x-1)^2+5=y[/tex] and our vertex is seen to be (1, 5)

Answer:

Step-by-step explanation:

The volume of the rectangular prism is:

Answer:

16v

Step-by-step explanation:

3x + 11 = 4x - 5

11+5 = 4x -3x

x = 16

I hope im right!!

Answer:

The correct option is (c).

Step-by-step explanation:

The given expression is :

[tex]14(\dfrac{3}{2}\times \dfrac{1}{4})[/tex]

We need to use the associative property to make it easier.

The associative property for multiplication is as follows :

[tex]A\times (B\times C)=(A\times B)\times C[/tex]

We have,

[tex]A=14, B=\dfrac{3}{2}\ and\ C=\dfrac{1}{4}[/tex]

[tex]14(\dfrac{3}{2}\times \dfrac{1}{4})=(14\times \dfrac{3}{2})\times \dfrac{1}{4}[/tex]

Hence, the correct option is (c).

Answer:

119 cm

Step-by-step explanation:

20 - 3 = 17

(140/20)(17) = 119 cm

Answer:

3.......................

Answer:

150

Step-by-step explanation:

The element a₁₂ represents the first row and second column which is 100. Then the correct option is B.

A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij} element in a matrix, such as M, refers to the i-th row and j-th column element.

Record the data in a table with the rows representing the week and the columns representing the type of music.

The element a₁₂ represents the first row and second column which is 100. Then the correct option is B.

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Answer:

R = -0.8908

R² = 0.7935

Step-by-step explanation:

Given the data:

X :

5

3

6

3

4

4

6

8

Y :

13

15

7

12

13

11

9

5

Using technology, we could obtain the correlation Coefficient (R) using the Pearson correlation Coefficient calculator :

R = -0.8908 ; This means that there is a strong negative relationship between x and y. That is, an increase in x will lead to a corresponding decrease in y and vice versa.

The Coefficient of determination (R²) ; is obtained by taking the squared value of R

R² = (-0.8908)² = 0.7935 ; This means that about 79.35% of the variation is y is explained by the regression line.

Answer:

A sample of [tex]n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2[/tex] is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In a previous study of 1012 randomly chosen respondents, 374 said that there should be such a law.

This means that [tex]n = 1012, \pi = \frac{374}{1012} = 0.3696[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How large a sample size is needed to be 95% confident with a margin of error of E?

A sample size of n is needed, and n is found when M = E.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]E = 1.96\sqrt{\frac{0.3696*0.6304}{n}}[/tex]

[tex]E\sqrt{n} = 1.96\sqrt{0.3696*0.6304}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.3696*0.6304}}{E}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2[/tex]

[tex]n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2[/tex]

A sample of [tex]n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2[/tex] is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

Answer:

you would make 400 each week

Step-by-step explanation:

Answer:

<2 = 133degrees

<1 = 135degrees

Step-by-step explanation:

From the diagram, the angle <2 and 47 are supplementary, hence;

<2 + 47 = 180

<2 = 180 - 47

<2 = 133degrees

To get <1;

47 = 1/2(<1 - 41)

47 * 2 = (<1 - 41)

94 = <1 - 41

<1 = 94 + 41

<1 = 135degrees

Answer:

B x >= 11

Step-by-step explanation:

80 miles total, 14 miles already done => 80-14=66 miles left.

66 miles distributed evenly across 6 days means 66/6=11

Answer:

(-3,3) and (4,0) are inside the triangle.

Answer:

0.5 ft per min

Step-by-step explanation:

in 80 minutes the radius expanded by 40%

we can set up a proportion of percent change over minutes:

.4/80 = r/1

cross-multiply to get:

80r = .4

r = .005 or 1/2 of a foot per minute.

Hope It Helps :)

The radius of the spill changing between the time of the spill was noticed and the arrival of the response team is 2/7.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Let the radian of the spill at time t be μ(t).

Since, radian increases at a constant rate, we have,

dμ/dt = k

r(t) = kt + c

At t = 0, r = 60 m

60 = k(0) + c

c = 60

At, t = 70, r(70) = 80 m

80 = k(70) + 60

20 = 70k

k = 20/70

k = 2/7

Then, r(t) = 2/7t + 60 and the rate of change of radian of the spill is 2/7 per min.

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Answer:

the required number of telephone orders to complete the 400 interviews is 3433

Step-by-step explanation:

Given the data in the question;

Let us represent the telephone numbers the researcher orders to complete the 400 interviews with Y.

Thus, The working phone numbers = 70% × Y

Now, number of ATM users = 45% × The working ph0ne numbers

⇒ 45% × ( 70% × Y )

number of ATM users = 0.45 × 0.70 × Y = 0.315Y

Thus; Number of people contacted that agrees to complete the survey will be;

⇒ 37% × number of ATM users

⇒ 0.37 × 0.315Y = 0.11655Y

so, since the researcher needs at least 400 interviews

Hence;

0.11655Y ≥ 400

Y ≥ 400 / 0.11655

Y ≥ 3432.0034 ≈ 3433

Therefore, the required number of telephone orders to complete the 400 interviews is 3433

Answer:

A function is a mathematical relationship where all inputs must have exactly one output. If there is more then one output for one input, then the relationship is not a function.

x is most of the time the input and y the output for an equation:

y = 2x

of course the input and output could be any variable.

Step-by-step explanation:

Have a nice day!

We have four copies of '2' and one copy of '5' multiplied together

This is the same as saying 2^4*5

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

Explanation:

Divide 80 over the smallest prime factor, which is 2

80/2 = 40

Divide that result over 2

40/2 = 20

Keep going until you cannot divide by 2 anymore

20/2 = 10

10/2 = 5

We stop here because 5/2 isn't a whole number. We also stop here since 5 is prime. Circle all the primes that show up and you should have four copies of 2 and one copy of 5.

Therefore: 2*2*2*2*5 = 80

In shorthand, this condenses to 2^4*5 = 80

The factor tree is shown below. Other factor trees are possible.

Answer:

462

Step-by-step explanation:

(11)C(6) = 11! ÷ 6! 5!

= (11 x 10 9 x 8 x 7) / (5 x 4 x 3 x 2)

= 462

Answer: B

Step-by-step explanation:

Answer:

(-3,2)

Step-by-step explanation:

Answer:

C. 12.04 inches

Step-by-step explanation:

Diagonal of a prism cam be solved using the extension of Pythagorean theorem which is given as:

d² = x² + y² + z²

x = 10 in.

y = 6 in.

z = 3 in.

d² = 10² + 6² + 3²

d² = 100 + 36 + 9

d² = 145

d = √145

d = 12.0415946

d = 12.04 inches (nearest hundredth)

Answer:

$34,500

Step-by-step explanation:

1% of 550,000 = 5,500

33,000÷ 5,500 = 6%

1% of 575,000 = 5,750

5,750 x 6 = 34,500

9514 1404 393

Answer:

  2 11/12 yards

Step-by-step explanation:

Sometimes it works best to use improper fractions when multiplying mixed numbers and/or fractions.

  1/3(8 3/4) = 1/3(35/4) = 35/12 = 2 11/12

Carol will need 2 11/12 yards of the material for the dress.

Answer:

2 11/12 yards

Step-by-step explanation:

Answer:

I think it is 1/4x not sure but try it

Answer:

$66

Step-by-step explanation:

Let the money that you started off with be called x.

You spend $62 on a game: x-62

You receive $50 for painting a fence: x-62+50 = x-12

You give $10 to your friend: x-12-10 = x-22

You have $44 left: x-22=44, x=44+22=66

Answer:

b

Step-by-step explanation:

Answer:

since in second quadrant cos θ is negative.

Cos θ=b/h=2/3

b=2

h=3

p=√(3²-2²)

p=√5

Now

Tan θ=p/b=√5/2

since in second quadrant tanθ is negative

so

Tanθ=-√5/2

b. - (sqrt 5)/2

In second Quadrant cos is negative

So

b=2 and h=3

Perpendicular

tanØ=-p/b =-√5/2