To write a linear equation in point-slope form for a given graph:

First, find the
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of the line using riserun or the
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.
Next, substitute the
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and the
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into the point-slope formula.
Finally, remember to
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if possible.

Answer:

a = 6 , b = - 44

Step-by-step explanation:

x² + 12x - 8

using the method of completing the square

add/subtract ( half the coefficient of the x- term)² from x² + 12x

x² + 2(6)x + 36 - 36 - 8

= (x + 6)² - 44 ← in the form (x + a)² + b

with a = 6 and b = - 44

Answer:

The height of the flagpole is about 25.6 feet.

Step-by-step explanation:

The figure is omitted--please sketch it.

Put your calculator in degree mode.

Let h be the height of the flagpole.

[tex] \tan(52) = \frac{h}{20} [/tex]

[tex]h = 20 \tan(52) = 25.6[/tex]

a) The test statistic is: t = -1.11.

b) The p-value is: 0.1342.

c) The conclusion is that the null hypothesis is not rejected.

d) The final conclusion is that there is not sufficient evidence to conclude that the population mean is of 6.

The standard deviation for the population is unknown, only the sample standard deviation is known, hence the t-distribution is obtain the test statistic.

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the variables of the equation are given as follows:

For this problem, the values of these parameters are as follows:

[tex]\overline{x} = 5.83, \mu = 6, s = 2.11, n = 189[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{5.83 - 6}{\frac{2.11}{\sqrt{189}}}[/tex]

t = -1.11.

The p-value is obtained using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less a value, with 189 - 1 = 188 df and t = -1.11, hence it is of 0.1342.

Since the p-value is greater than the significance level of 0.10, it is found that:

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The equation of the line  in slope-intercept form is y = -x/12 + 23/4

Given that: the line is perpendicular to the line y= 12x−2 and it contains the (−3,6).

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The slope-intercept form of a straight line is:

y = mx + c,

where m is the slope and c is the y-intercept

When the two lines are perpendicular, the product of their slope is -1 i.e.

m₁ x m₂ = -1

where m₁ and m₂ represent the slope of the lines

Let the slope of the given line be m₁ and the slope of the unknown line be m₂

Line1(given):

y = 12x−2   and m₁ x m₂ = 12

m₁ x m₂ = -1

12 x m₂ = -1

m₂= -1/12

Line 2(unknown) with the point (−3,6):

y = mx + c

6 = -1/12 (-3) + c

6 = 1/4 + c

c = 6 -1/4 = 23/4

y = -x/12 + 23/4

Therefore, the slope-intercept form of the equation of the line is y = -x/12 + 23/4

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When red is the first one , blue the second and green the third one (and as you can see, all of them share the vertex (-2, 3)).

The vertex of a quadratic equation:

a[tex]x^{2}[/tex]+bx + c = y

is located at :

x = -b/2a.

In this case, x = -2

Then,

-b/2a = -2

And we also have that:

a[tex](-2)^2[/tex] -2b + c = 3

Then we have two equations:

-b/2a = -2

a[tex](-2)^2[/tex] -2b + c = 3

We have only equations and 3 variables, So we can just give the variable c different values and we will find different quadratic equations that are not equivalent.

Let's begin with c = 0 ,Our equations are:

-b/2a = -2

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

In the first equation we can isolate b and get :

b = 4a

Now we can replace this in the other equation and solve this for a.

4a + 4a x -2 = 3

-4a = 3

a = -3/4

then:

b = 4a = 4 x -3/4 = -3

The first quadratic equation is:

(-3/4)[tex]x^{2}[/tex] - 3x = y

Now, To find the second let's use a different value of c.

c = 1

b = 4a

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

Let's solve in the same way as before:

4a + 4a x -2 + 1= 3

-4a = 2

a = 2/-4 = 1/-2

b = 4 x -1/2 = -2

Then our equation is :

(-1/2)[tex]x^{2}[/tex] -2x + 1 = y

For the last equation, let's use c = 2

then our equation are:

b = 4a

a(-2)^2 - 2b +2 = 3

Same as before, replace the first equation in the second

4a + 4a x-2 +2 = 3

-4a +2 = 3

-4a = 1

a = -1/4

Then:

b = 4 x (-1/4) = -1

Our third equation is :

(-1/4)x^2 - x + 2 = y

Now, Below you can see all of them graphed.

When red is the first one , blue the second and green the third one (and as you can see, all of them share the vertex (-2, 3)).

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_____________________

[tex]\huge\blue{\mid{\fbox{\tt{Answer}}\mid}}[/tex]

[tex]\huge\blue{\mid{\fbox{\tt{Explanation}}\mid}}[/tex]

Multiplication - Multiplication, otherwise known as the inverse of division repeats a certain number's value into what it has been multiplied by. Ex. [tex]4\cdot4=16[/tex]

Fraction - A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters.

Algebra - Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all mathematics

Reciprocal - In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by [tex]\frac{1}x[/tex] or x⁻¹, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction [tex]\frac{a}b[/tex] is [tex]\frac{b}a[/tex]. For the multiplicative inverse of a real number, divide 1 by the number.

_____________________

Trey, Raina, and Deandre have $21,$31, and $93 in their wallets respectively.

From the question the sum of the money in their wallets is:

Raina  +  Trey +Deandre=$145

      R   +    T    +       D      =$145................(i)

Raina has $10 more than Trey= ($10 + T)

Deandre has 3 times more Raina =3($10 + T)

substituting the values of Raina and Deandre in Eqn (i) we have

R   +    T    +       D      =$145

($10 + T) +  T  +{3$(10 + T)}=$145

$10 +T   +T+  $30   + 3T    =$145

                     5T   +$40    =  $145

                                5T   =   $145   -  $40

                                 5T     =    $105

                                    T      = $105/5

                                     T     =   $21

i.e  Trey   =  $21

Raina has $10 more than Trey= ($10 + T)

i.e                                               = ($10 + $21)    

                                      Raina  =$31    

Deandre has 3 times more Raina =3($10 + T)

                                                        =3($10 + $21)

                                                        =$30   +$63

                                       Deandre  =$93

Therefore the total sum of money in thier wallet is:

        Raina  +  Trey +Deandre=$145

             $31  + $21   +  $93=    $145

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Answer:

$69.98

Step-by-step explanation:

8.5% of 64.50 is around 5.48 or to be exact, 5.4825 which there are no more dollar denominations beyond the hundredth place so it would be 5.48. 64.50+5.48 is $69.98.

Answer:

$69.98

Step-by-step explanation:

It is percent increase.

So, 100% + 8.5% = 108.5% which is 1.085.

64.50 × 1.085 = 69.9825

we need to round to 2 decimal places

$69.98

Simon bought a $48 table on sale. The price of the table can be estimated by $50.

The sale propose 30% off, then an estimate for the discount can be calculated using proportion:

$50 -- 100%,

$x -- 30%

that is mathematically

Find x:

Answer: correct choice is B

The probability that student will pass the test is 2/7.

So, the probability that the student will pass the test:

Probability Formula: P(E) = Favourable events/Total events

Now, calculate as follows:

Therefore, the probability that student will pass the test is 2/7.

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32 inches more of tape students need.

Given that,

Students in Dave's science class are trying to build the tallest structure. Ten newspapers and two yards of tape are given to each group of kids. The decision is made by Dave's group to roll up each newspaper. Then, they use 4 inches of tape to seal each roll.

We have to find how many more inches of tape are there.

We know that,

1 yard is 36 inches.

So,

2 yards is 2 times 36 is 72 inches.

The inches of the tape they need is 10 times 4 is 40.

So,

72-40 is 32 inches

Therefore, 32 inches more of tape students need.

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Answer:

(10, -1)

Step-by-step explanation:

x + 2x = 3x

-y + y = 0

11 + 19 = 30

3x = 30

3/3 x = 30/3

x = 10

10 - y = 11

y = -11 + 10

y = -1

Answer:

C and A

Step-by-step explanation:

The equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.

According to the question,

We have the following information:

The line is parallel to y = -4/3x + 11 and passes through the point (–6, 2).

Now, we know that the following formula is used to find the equation of the line:

y-y' = m(x-x')

In this case, m is the slope of the line.

m = -4/3

We have the following values:

x' = -6 and y' = 2

Now, we have the following expression:

(y-2) = -4/3(x+6)

y-2 = -4x/3-8

Adding 2 to both sides of the equation:

y = -4x/3-8+2

y = -4x/3-6

Hence, the equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.

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If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.

What is a value function?

The value function represents the optimal payoff of the system over the interval [t, t1] when started at the time- t state variable x(t)=x.

What is a variable?

A quantity that could take on any of a number of different values. : a sign that denotes a variable. : anything has a range. : a variable that might alter in a scientific experiment.

Here, we have

x = -4 and y = 3

then by putting the value of a function in a given equation, we get

1/2*(-4) + 3*(-4)*(3)²

= -110

Hence, If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.

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The probability of P(A AND B) when Josh visit his aunt's house is 0.36.

Probability is the likelihood that an event will occur or take place.

Let A = the event that he walks his dog at his aunt's house

Let B = the event that he plays darts at his aunt's house.

When A and B are independent events with P(A)=0.9 and P(B)=0.4, the probability of P(A AND B) will be:

= P(A) × P(B)

= 0.9 × 0.4

= 0.36

The probability is 0.36.

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Answer:

b

Step-by-step explanation:

because you solve it and you get B

Answer:

Step-by-step explanation:

rate of change

[tex]=\frac{f(b)-f(a)}{b-a} \\=\frac{f(9)-f(1)}{9-1} \\=\frac{28-20}{8} \\=\frac{8}{8} \\=1[/tex]

Answer: The missing values in the ratio table will be 0.666 and 5.33 inches.

Step-by-step explanation:

As the ratio of the terms is equal. The value of x and y is ,

2/3 = x/1

x=2/3

x=0.66 inches

In order to obtain y,

2/3 = y/8

y=2×8/3

y=16/3

y=5.33 inches.

84.78 mm² is area of circle .

What is a circle ?

radius of the circle = 27 mm

area of the circle = πr²

                          =  3.14 * 27

                         =  84.78 mm²

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We will need 7 quart package if we want 62 strawberries

What is division?

Division is one of the basic arithmetic computation which divide a value in equal sets of smaller values. The other basic arithmetic computations are addition, subtraction, multiplication. We use long division method to find the quotient and remainder.

We are given that there are 9 strawberries in a quart package

Also we want 62 strawberries

Then how many quart will be required

Now we perform division to find the number of quart

62/9 = we get a value of 8.88

Which is very close to nine

Hence we will need 9 quart packages if we want 62 strawberries

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Answer:

C (the one which starts with x = -2 and y = -1)

Step-by-step explanation:

because for every x value there is only an y value

solution

3x+18/18

ans4

The probability that more than one-fourth of them will have low levels of literacy as described above is 0.3043.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given: A study conducted by the Institute of Education Sciences from 1992 to 2003 found that about 22% of adult Americans had low levels of literacy and were “not able to locate information in text,” could not “make low-level inferences using printed materials” and were unable to “integrate easily identifiable pieces of information.”

A simple random sample of 50 adult Americans is collected.

n(p) = 50(0.22)

n(1 - p) = 50(1 - 0.22)

The CLT would hold here.

n = 50

p = 0.22

p cap = 0.25

The test statistic, z = (p cap - p) / (√p (1 - p) / n)

z = (0.25 - 0.22)/(√0.22(1-0.22)/50)

z = 0.51

The p-value is 0.3043.

Hence, The probability that more than one-fourth of them will have low levels of literacy as described above is 0.3043.

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Option C: The relationship between the statement cannot be determined.

What is Conditional statement?

Two independent statements can be related to each other in a logic structure called a conditional statement.

The first statement is presented with “if,” and is referred to as the hypothesis.

The second statement is linked with “then”, and is known as the conclusion.

The notation associated with conditional statements typically uses the variable p for the hypothesis statement, and q for the conclusion.

                                     p → q

Explanation for the answer:

So, from the above we can clearly see that the both the statement 1 and statement are not start with "if" and "then".

Therefore, their relationship cannot be determined.

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let the number be = x

[tex] = > \frac{3x}{5} = 150[/tex]

[tex] = > 3x = 150 \times 5[/tex]

[tex] = > 3x = 750[/tex]

[tex] = > \frac{3x}{3} = \frac{750}{3} [/tex]

[tex] = > x = 250[/tex]

The number can be found by multiplying 150 by 5 and then dividing the result by 3. Therefore, the number is 250 by solving equations.

To find the number, we can set up the equation: (3/5) * x = 150. To isolate x, we multiply both sides of the equation by 5/3, resulting in x = 250. This means that the number is 250.

Start with the equation: (3/5) * x = 150.

To isolate x, multiply both sides of the equation by the reciprocal of (3/5), which is 5/3. This yields (5/3) * (3/5) * x = (5/3) * 150.

Simplify the left side of the equation: x = (5/3) * 150.

Multiply 5 by 150 and divide the result by 3: x = (750/3).

Simplify the fraction by dividing the numerator (750) by the denominator (3): x = 250.

Therefore, the number is 250.

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The logarithmic expression given as logₙ(1/63) has its value to be -4.143

From the question, the given parameters are

logₙ(7) = 1.946

logₙ(9) = 2.197

logₙ(16) = 2.773

The logarithmic expression to calculate is given as

logₙ(1/63)

Express 1/63 as 1/7 * 1/9

So, we have the following representation

logₙ(1/63) = logₙ(1/7 * 1/9)

Apply the product of logarithm

This gives

logₙ(1/63) = logₙ(1/7) + logₙ(1/9)

Apply the exponent of logarithm

This gives

logₙ(1/63) = -logₙ(7) - logₙ(9)

Substitute logₙ(7) = 1.946 and logₙ(9) = 2.197 in logₙ(1/63) = -logₙ(7) - logₙ(9)

logₙ(1/63) = -1.946 - 2.197

Evaluate

logₙ(1/63) = -4.143

Hence, the value of the logarithmic expression is -4.143

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