Find m (16x-3)
(3x-7)

If we write a quadratic in vertex form:

\(y=a(x-h)^2+k\)

Then:

\(\bold{a}\)   \(\longrightarrow\)    is the coefficient of \(x^2\)

\(\bold{h}\)   \(\longrightarrow\)    is the axis of symmetry.

\(\bold{k}\)   \(\longrightarrow\)    is the max/min value of the function.

Also:

If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.

\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.

For the given functions:

\(a < 0\)

\(f(x)=-(x-1)^2+5\)        this has a maximum value of \(\bold{5}\)

\(a > 0\)

\(f(x)=(x+2)^2-3\)           this has a minimum value of \(\bold{-3}\)

Answer: what unit is this?

Step-by-step explanation:yeah I’ll need the unit to solve this question

Complete Question

A political analyst believes that a senator's recent decision to support a bill resulted in a drop of approval ratings. To test this claim, he selects random cities in the state the senator represents and compares the approval ratings before the decision to the approval ratings after the decision. Suppose that data were collected for a random sample of 8 cities, where each difference is calculated by subtracting the percent approval rating before the decision from the percent approval rating after the decision. Assume that the ratings are normally distributed. Using a test statistic oft -3.935, the significance level Q=0.05, and the corresponding p-value less than 0.01, draw a conclusion for the appropriate hypothesis test, where the null hypothesis is \(H_o. :  \mu_d= 0\) and the alternative hypothesis is  \(H. : \mu_d < 0\)

a. Reject the null hypothesis.

b. Fail to reject the null hypothesis.

c. The conclusion of the hypothesis test is that there is sufficient evidence to suggest that there was a drop in approval ratings in cities after the decision to support the bill.

d. The conclusion of the hypothesis test is that there is insufficient evidence to suggest that there was a drop in approval ratings in cities after the decision to support the bill.

Answer:

The correct option is  a and  c

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  8  

    The  test statistics is t =  -3.935

    The level of significance is  \(\alpha =  0.05\)

    The  p-value  is \(p-value  =  0.01\)

From the data given we see that the \(p-value  <  \alpha\) hence

The decision rule is  

  Reject null hypothesis

The conclusion

There is sufficient evidence to suggest that there was a drop in approval ratings in cities after the decision to support the bill.

Answer:

\(C=27inch\ by\ 27inch\)

Step-by-step explanation:

Squares \(h=4inch\)

Volume \(v=1444in^3\)

Generally the equation for Volume of box is mathematically given by

 \(V=l^2h\)

 \(1444=l^2*4\)

 \(l^2=361\)

 \(l=19in\)

Since

Length of cardboard is

 \(l_c=19+4+4\)

 \(l_c=27in\)

Therefore

Dimensions of the piece of cardboard is

\(C=27inch\ by\ 27inch\)

Answer:

\(\frac{x^2}{3} - \frac{x}{3} - 44 =\frac{(x -12)(x+ 11)}{3}\)

Step-by-step explanation:

Given

\(\frac{x^2}{3} - \frac{x}{3} - 44\)

Required

Solve

Take LCM

\(\frac{x^2 - x - 132}{3}\)

Expand

\(\frac{x^2 +11 x -12x- 132}{3}\)

Factorize:

\(\frac{x(x+11) -12(x+ 11)}{3}\)

\(\frac{(x -12)(x+ 11)}{3}\)

Hence:

\(\frac{x^2}{3} - \frac{x}{3} - 44 =\frac{(x -12)(x+ 11)}{3}\)

There wouls be 18 geese in the pond

Hope this helps :)

Answer:

\(y=5x^2-80x+324\)

Step-by-step explanation:

12 pairs could he predict will contain at least one six using empirical probability formula.

The empirical probability formula generates a ratio between the total number of times the desired occurrence was attempted to and the number of times it actually occurred. As an illustration, consider the case where I rolled the dice three times and each time I got 12, giving the result a statistical probability of 12/12 or 100%.

Probability is a form of ratio where we measure the likelihood of a given occurrence in comparison to all other possible outcomes.

Explanation:

12/10 * 10 = 6/5 * 10

               = 12.

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Answer:

Step-by-step explanation:

Leon visited Chicago, which is located on the shore of

Lake Michigan. The lake has a volume of about 4,920

km cubed. Chicago was a major gateway to the west in

1825 when the Erie Canal was completed. When built,

the Erie Canal was 680 long and only 100 or

10 deep. While in Chicago, Leon visited the Sear

Tower. One of the tallest buildings in the world, the

Sears Tower is 443 tall

during Leon's visit was about 7

Answer:

y = 40x + 30

Step-by-step explanation:

The equation for a linear function is given by:

y = mx + b;

where y and x are variables, m is the slope or rate of change of the function and b is the initial value of y at x = 0 (that is y intercept).

Let y represent the total cost and x represent the number of hours worked.

The electrician charges 110 after 2 hours of work and 190 for 4 hours of work.

Representing in coordinate form as (x, y) we get:

(2, 110) and (4, 190)

The equation of the function can be gotten using the formula:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

Therefore:

\(y-110=\frac{190-110}{4-2}(x-2)\\\\y-110=40(x-2)\\\\y-110=40x-80\\\\y=40x-80+110\\\\y=40x+30\)

Answer:

It is right

Step-by-step explanation:

Because the hypotenuse must be greater than all the legs, we have that \(17\) is the hypotenuse. So, we want to determine if \(8^2+15^2=17^2\).

\(8^2=8*8=64\\15^2=15*15=225\\17^2=17*17=289\\225+64=289\\\)

This means the triangle is indeed right!

Answer:

The area of the trapezoid is 238 \(m^2\).

Step-by-step explanation:

The formula to use in order to calculate the area of a trapezoid is \(\frac{h}{2}(b_{1} +b_{2})\) where \(b_{1}\) and \(b_{2}\) are the lengths of the top and bottom bases of the trapezoid, and \(h\) is the height of the trapezoid. In this case, we can rewrite the formula by inserting the corresponding values into the expression. The area of the trapezoid will be \(\frac{14}{2} (15+19)=7*34=238m^2\).

Answer:

238m^2

Step-by-step explanation:

1/2(15+19)*14

1/2(34)*14

17*14

238

Answer:

44u-36

Step-by-step explanation:

42u-36+2u

44u-36

Answer:

12 11/20

Step-by-step explanation:

the answer to the question is 12 11/20

It seems that the sequence you provided is the sequence of triangular numbers. The function that generates this sequence could be defined as:

f(n) = n*(n+1)/2

Where n is the position of the number in the sequence.

So, for example:

f(1) = 1*(1+1)/2 = 1

f(2) = 2*(2+1)/2 = 3

f(3) = 3*(3+1)/2 = 6

and so on.

Answer:

4.9

Step-by-step explanation:

multiple the same as that

Answer:

134 deg

Step-by-step explanation:

x + 46 = 180

v + 46 = 180

Solve

The two given rectangles are proportional to each other since they have a width to length ratio of 2 and the area ratio between them is equal to 9.

Two rectangles are proportional to each other when both have the same length to width ratio. The area ratio is defined by the following formula:

r' = (l' · h')/(l · h)      (1)

Where:

Now we determine the length to width ratio of each rectangle:

Original rectangle

s = 4/2

s = 2

Enlarge rectangle

s' = 12/6

s' = 2

The two rectangles have the same length to width ratio.

And the area ratio is:

r' = (12 · 6)/(4 · 2)

r' = 72/8

r' = 9

The statement is incomplete and complete statement cannot be found. We modify the statement towards the determination of the length to width ratio of a rectangle and the areas ratio.

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Answer: A, B, D, is the correct answer.   :) Hope this helped.

StartFraction width original over length original EndFraction = StartFraction width enlargement over length enlargement EndFraction.

StartFraction length original over length enlargement EndFraction = StartFraction width original over width enlargement EndFraction.

StartFraction width enlargement over length enlargement EndFraction = StartFraction width original over length original EndFraction.

Answer:

7x - 8

Step-by-step explanation:

eight less than product of seven and X

seven and x = 7x

eight less than = - 8

put it all together = 7x - 8

Answer:

7x - 8

Step-by-step explanation:

product of seven and X

7 X x = 7x

8 less than it

7X - 8

This is because we're looking for something that is smaller than 7X by 8

Answer:

47°

Step-by-step explanation:

Given that m<NLO = 41°, and m<NLM = 88°, according to angle addition postulate, m<OLM + m<NLO = m<NLM

Therefore, subtracting m<NLO from both sides will give us:

m<OLM = m<NLM - m<NLO

m<OLM = 88° - 41°

m<OLM = 47°

Answer:

2 doctors to 9 patients

Step-by-step explanation:

Divide each by 3. They cant be simplified more.

Answer:

Change the mixed numbers into an improper fraction:

\(2\frac16 \div 2\frac12=\dfrac{2 \times 6+1}{6}\div \dfrac{2 \times 2+1}{2}=\dfrac{13}{6}\div \dfrac{5}{2}\)

Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. (Reciprocal is when you swap the numerator and denominator).  Therefore,

\(\dfrac{13}{6}\div \dfrac{5}{2}=\dfrac{13}{6}\times\dfrac{2}{5}\)

Now we simply multiply the numerators and the denominators:

\(\dfrac{13}{6}\times\dfrac{2}{5}=\dfrac{13 \times 2}{6\times 5}=\dfrac{26}{30}\)

We can now reduce the fraction to its simplest form by dividing the numerator and denominator by 2:

\(\dfrac{26}{30}=\dfrac{26\div 2}{30 \div 2}=\dfrac{13}{15}\)

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

I'll assume it is \(\frac{21}{6}\)÷\(\frac{21}{2}\)

Not so sure if it is that or in mixed form

The division sign will become multiplication sign when two becomes the numerator and 21 becomes the denominator

\(\frac{21}{6}\)×\(\frac{2}{21}\)

21 will cancel out leaving \(\frac{2}{6}\)

=\(\frac{1}{3}\)

Answer and work down below. Let me know if you have questions

Answer:

2sqr3, the first option

Step-by-step explanation:

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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For this case the mapping diagram would be:

We have the following points given:

(1,8), (3,6) and (5,4)

Since we have a line pattern we can find the equation with this formula:

Where m is the slope and b the intercept:

And for the intercept we got:

And solving for b we got:

And the equation would be given by:

Answer:

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

Step-by-step explanation:

For a dilation at the origin, multiply each of the coordinates by the scale factor.

\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)

Correct option is A, the iS point-slope form of the line is y+ 8 = -4(x-2). A straight line's equation can be written as both a point slope form and a slope intercept form.

A line equation written using a single line point and the slope of the line is the simplest definition of the term "point-slope form." The slope is expressed in point form as the ratio of the change in y values to the change in x values, also known as the rise over run (x, y).

The point slope form is useful when there is a slope and one or more points are present. Standard form is often easier to employ while doing algebraic computations. Depending on our needs or our level of expertise, we can alter the form of an equation. Both the point slope form and the slope intercept form can be used to express the equation for a straight line. The point slope form highlights any point on the line as well as the slope. The slope and y-intercept of a line are only shown in slope intercept form.

Given,

the slope of line = - 4 and point = (2,-8)

The equation of line = y - yo = m (x - xo)

where m = slope and x,y are coordinates

y + 8 = - 4 (x - 2)

y + 8 = - 4x + 8

y = - 4x

Therefore, the correct answer is option A, y+ 8 = -4(x-2)

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The true statement on the height of the ball when thrown from a building, given the equation, can be found to be A. The ball reaches the ground in 3 seconds.

The equation given of the ball being thrown from a building, gives us the height when solved.

The height of the ball when it reaches the ground is 0 feet so we can insert this in the formula to find the time:
0 = - 5 ( t - 3 ) ( t + 5 )

We can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. So, we can set each factor equal to zero and solve for t:

t - 3 = 0 or t + 5 = 0

Solving for t in the first equation, we get:

t - 3 = 0

t = 3

Seeing as t is 3 seconds the first option is correct.

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