Type the correct answer In each box. Use numerals instead of words. What is the equation of the quadratic function that has a minimum at (7,-3) and goes through (9.9)​

Step-by-step explanation:

AAS means angle angle side. so, we need 2 angles and 1 side.

the diagram shows us 1 angle in each triangle to be equal or congruent (C and G).

it also shows us implicitly, that the side AB is shared and is therefore truly the same for each triangle.

that means we need one more angle. either the one at A or the one at B. you pick.

Answer:

(4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75

(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x

Step-by-step explanation:

a) Use the formula a²-2ab+b²= (a-b)² (You need to make squared expression because it is always positive)

Consider 4x² as a² and -6x=-2ab

4x²=a² a=2x  ab=3x 2x*b=3x

b=1.5

Express 4x² -6x+9= (4x² -6x+1.5²) +9-1.5²= (2x-1.5)²+9-2.25= (2x-1.5)²+6.75

(2x-1.5)² is greater or equal to 0 , 6.75>0 so expression is positive for all real numbers x

Answer:

x =7/ 3

Step-by-step explanation:

5x+  22=  2x+  29

⇔5x - 2x= 29 - 22

⇔3x = 7

⇔x = 7/3

Answer:

x=0

Step-by-step explanation

I think that's what you're looking for :l/

Answer:

a. The number of pounds of the meat required is 3 pounds and the number of pounds of cheese required is 2 pounds.

b. $ 16.7

Step-by-step explanation:

a. How many pounds of each are needed in order to minimize the cost and still meet the minimum requirements?

Let c represent the carbohydrate units and p the protein units.

For the meat portion M, we have 2 units of carbohydrates and 2 units of protein per pound. So, M = 2c + 2p

For the cheese portion K, we have 3 units of carbohydrates and 1 units of protein per pound. So, K = 3c + p.

Let x be the number of pounds of meat required and y be the number of cheese pounds required. The total number of pounds required is T

So, we have xM + yK = x(2c + 2p) + y(3c + p)

= 2xc + 2xp + 3yc + yp

= 2xc + 3yc + 2xp + yp

= (2x + 3y)c + (2x + y)p

Since the required number of units, R is 12 units of carbohydrates and 8 units of protein, we have R = 12c + 8p

Since T = R, we have

(2x + 3y)c + (2x + y)p = 12c + 8p

Equating coefficients, we have

2x + 3y = 12 (1) and 2x + y = 8 (2)

Subtracting (2) from (1), we have

2x + 3y = 12 (1)

-

2x + y = 8 (2)

2y = 4

y = 4/2

y = 2

Substituting y = 2 into (2), we have

2x + y = 8

2x + 2 = 8

2x = 8 - 2

2x = 6

x = 6/2

x = 3

Since x = 3 and y = 2

The number of pounds of the meat required is 3 pounds and the number of pounds of cheese required is 2 pounds.

What is the minimum cost?​

Since meat costs $3.70 per pound and the cheese costs $2.60 per pound and we have 3 pounds of meat and 2 pounds of cheese, the total cost of meat is C = $3.70/pound × 3 pounds = $ 11.1.

The total cost of cheese is C' = $2.60/pound × 2 pounds = $ 5.2.

So, the minimum cost C" = C + C' = $ 11.1 + $ 5.2 = $ 16.7

Answer:

Step-by-step explanation:

Answer:

B Trevor isn't correct because -2i must also be a root

Step-by-step explanation:

A Trevor is correct.

B Trevor is not correct because –2i must also be a root.

C Trevor is not correct there cannot be an odd number of roots.

D Trevor is not correct because there cannot be both rational and complex roots.

statements^^^^^^

The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Since one of the roots is complex (2i), it follows that the coefficients of f(x) must be complex as well, and therefore f(x) must be a polynomial with complex coefficients.

However, it is possible for f(x) to have a higher degree than 3.

For example,

The polynomial (x + 7)(x - 2i)(x + 2i)(x - 7) has degree 4 and has the given roots of -7, 2i, and 7. Therefore, f(x) could be a polynomial with degree 4 or higher.

Thus,

The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.

Learn more about functions here:

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Solution :

a). The test is a left tailed test.

b). The sample proportion is :

[tex]$\hat p = \frac{x}{n}$[/tex]

[tex]$\hat p = \frac{17}{258}$[/tex]

  = 0.065

Determining the Z statistics using the formula :

[tex]$Z=\frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]

[tex]$Z=\frac{0.065 - 0.11}{\sqrt{\frac{0.11(1-0.11)}{258}}}$[/tex]

   = -2.31

∴ Z statistics value is -2.31

c). Using the excel function, the P-value is :

P-value = Normsdist(-2.31)

             = 0.0104441

d). The null hypothesis is [tex]$H_0: P = 0.11$[/tex]

    The level of significance is 0.01

    We fail to reject the null hypothesis as the P value is less than or equal to the significant level.

Answer:

D

Step-by-step explanation:

x- coordinate = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]

y- coordinate = sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]

That is ( [tex]\frac{\sqrt{2} }{2}[/tex] , [tex]\frac{\sqrt{2} }{2}[/tex] ) → D

Answer:

honestly i dont know but i bet someone will

Answer:

1/11 of a gallon

Step-by-step explanation:

He used 2/11 of 1/2 gallon

2/11 * 1/2 = 1/11 of a gallon

Answer:

[tex]\frac{1}{11}[/tex]

Step-by-step explanation:

Step 1:  Find how much of a gallon he used

[tex]\frac{2}{11} * \frac{1}{2} =\frac{2}{22}[/tex]

[tex]\frac{2}{22}=\frac{1}{11}[/tex]

Answer:  [tex]\frac{1}{11}[/tex]

Answer:

D or -1

Step-by-step explanation:

It says that f(x) is equal to -3.

f(x) is the same as y-values, and x is the same as the x-values on a coordinate grid because x is the independent variable, meaning y is the dependent variable, where f(x) depends on the value of x to find y.

So if y is -3, it can be found on the graph on the 4th line, so x = -1 when y = -3

Answer:

m∠1 = 105°

m∠2 = 75°

Step-by-step explanation:

From the picture attached,

Two lines 'a' and 'b' are parallel and a transversal 't' is intersecting these lines at two distinct lines.

Therefore, m∠2 = 75° [Corresponding angles measure the same]

m∠1 + m∠2 = 180° [Linear pair of angles are supplementary]

m∠1 + 75° = 180°

m∠1 = 105°

Answer:

The parabola x²=8y has,

vertex: (0,0)

focus: (0,2)

directrix: y=-2

so that option is the answer,

btw, the parabola opens up to the top and axis of symmetry is x=0

Answer:

It's A!

Step-by-step explanation:

Got it correct on my test! :)

Answer:

m<1=145

m<2=35

m<3=35

Step-by-step explanation:

measure one is supplementary(the angles add to 180) to measure four.

so we do 180-35=145

measure 2 is congruent to measure four because they are corresponding angles

so measure 2=35

and measure 3 is also congruent to measure 4 because the are corresponding angles

so m<3=35

f(x, y) = x ² - 4xy + 5

has critical points where both partial derivatives vanish:

∂f/∂x = 2x - 4y = 0   ==>   x = 2y

∂f/∂y = -4x = 0   ==>   x = 0   ==>   y = 0

The origin does not lie in the region R, so we can ignore this point.

Now check the boundaries:

• x = 1   ==>   f (1, y) = 6 - 4y

Then

max{f (1, y) | 0 ≤ y ≤ 2} = 6 when y = 0

max{f (1, y) | 0 ≤ y ≤ 2} = -2 when y = 2

• x = 4   ==>   f (4, y) = 12 - 16y

Then

max{f (4, y) | 0 ≤ y ≤ 2} = 12 when y = 0

max{f (4, y) | 0 ≤ y ≤ 2} = -4 when y = 2

• y = 0   ==>   f (x, 0) = x ² + 5

Then

max{f (x, 0) | 1 ≤ x ≤ 4} = 21 when x = 4

min{f (x, 0) | 1 ≤ x ≤ 4} = 6 when x = 1

• y = 2   ==>   f (x, 2) = x ² - 8x + 5 = (x - 4)² - 11

Then

max{f (x, 2) | 1 ≤ x ≤ 4} = -2 when x = 1

min{f (x, 2) | 1 ≤ x ≤ 4} = -11 when x = 4

So to summarize, we found

max{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = 21 at (x, y) = (4, 0)

min{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = -11 at (x, y) = (4, 2)

Answer:

The third graph

Step-by-step explanation:

What the translation is saying is that for each value of f(x) = |x|, the graph is translated 4 units in the negative x direction and 3 units for the positive y direction. Another way to say this is that for each f(x), we can add (-4) (or subtract 4) to its x value and add 3 to its y value.

One way to find which graph works is to take a point, figure out where it should be, and work from there.

One example of this is (-1,1). If x=-1, |x| is 1, so in the original graph, our point is (-1, 1). In our translated graph, we need to subtract 4 from the x component (the first number, which is -1 in this case) and add 3 to the y component (the second number, or 1 in this case). Our new point comes to

(-1-4 , 1+3)

= (-5, 4)

Therefore, one point on the resulting graph is (-5, 4). We can look through each graph and see if it has the point.

Looking at each graph, it is clear that the graph in the bottom left, or the third graph, contains the point.

The equation of the translated function will be f(x) = |x + 4| + 3. Then the correct option is C.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The absolute function is given as

f(x) = | x – h | + k

The function is given below.

f(x) = |x|

Then the function is translated 4 units in the negative x-direction and 3 units in the positive y-direction. Then the vertex will be at (-4, 3). Then the equation of the function will be

f(x) = |x + 4| + 3

Then the graph is given below.

Then the correct option is C.

More about the absolute function link is given below.

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Answer:

$240

Step-by-step explanation:

A year has 12 month in it so lets multiply the 10 by 12 which is $120,Mean a year is $120 so 2years will be $120×2 which is $240

Answer:

x+1/5x

Step-by-step explanation:

Because the eqaution would be x+10%=x+1/10+10%=1/5+x

Then the equation equals x+1/5

Answer: Passes out in slow

Step-by-step explanation:

Step 1 be Einstein

Answer:

their distance is increasing at the rate of 41.6 miles/hr

Step-by-step explanation:

Given the data in the question;

first we determine the distance travelled by the first boat in 10 min when the second boat was crossing its path;

⇒ ( 30/60 ) × 10 = 5 miles

so as illustrated in the diagram below;

y² = x² + ( x + 5 )²

2y[tex]\frac{dy}{dt}[/tex] = 2x[tex]\frac{dx}{dt}[/tex] + 2(x+5)[tex]\frac{dx}{dt}[/tex]

y[tex]\frac{dy}{dt}[/tex] = ( 2x + 5 ) ][tex]\frac{dx}{dt}[/tex]

[tex]\frac{dy}{dt}[/tex] = [( 2x + 5 )/y ][tex]\frac{dx}{dt}[/tex]   ------ let this be equation 1

Now, given that, [tex]\frac{dx}{dt}[/tex]  = 30 miles/hr, when x = 10

so

y = √( 10² + 15² ) = √325

so from equation 1

[tex]\frac{dy}{dt}[/tex] = [( 2x + 5 )/y ][tex]\frac{dx}{dt}[/tex]

we substitute

[tex]\frac{dy}{dt}[/tex] = [( 2(10) + 5 ) / √325 ]30

[tex]\frac{dy}{dt}[/tex] = [ 25 / √325 ] × 30

[tex]\frac{dy}{dt}[/tex] = 41.6 miles/hr

Therefore, their distance is increasing at the rate of 41.6 miles/hr

Answer:

3.5g/ml or 3.5g/cm³

Step-by-step explanation:

1cm³=1ML

Volume of the irregular shaped stone = New Volume of water in cylinder -initial Volume of water in cylinder

Volume of irregular shaped stone = 8ml-2ml

Volume of irregular shaped stone =6ml

Denisty =Mass/Volume

Density = 21g/6ml

Density = 3.5g/ml

Answer:

no solution to the question

Answer:

4 2/3

Step-by-step explanation:

The two-step equation is solved regularly. The answer is 4 2/3.

9514 1404 393

Answer:

  zero

Step-by-step explanation:

3(2x) = x/2

5.5x = 0 . . . . subtract x/2

x = 0 . . . . . . . divide by 5.5

The number is zero.

Answer:

2x-1 = 5x-14

Step-by-step explanation:

5(2x−1) = 5(5x−14)

Divide each side by 5

5/5(2x−1) = 5/5(5x−14)

2x-1 = 5x-14

Answer:

A.

Step-by-step explanation:

5(2x−1) = 5(5x−14)

10x - 5 = 25x - 70

65 = 15x

x = 13/3.

Take Option A.

2x - 1 = 5x - 14

3x = 13

x = 13/3 so its this one.

B: 10x - 5 = 5x - 14

5x = -9

x = -9/5 so NOT B.

C. simplifies to x = 3. so NOT C.

Answer:

The answer is B) There is one proportional relationship

Step-by-step explanation:

The green line (the one at the top) does not go through the origin. This is not a proportional relationship.

Problem: It does not go through 0,0

----------------------------------------------------------------------------------------------------------------

The blue line (the one in the middle) is a straight line through the origin. This is a proportional relationship.

Reason: It goes through 0,0

----------------------------------------------------------------------------------------------------------------

The purple line (the one at the bottom) does not go through the origin. This is not a proportional relationship.

Problem: It does not go through 0,0

----------------------------------------------------------------------------------------------------------------

Conclusion: Since the green and purple lines are not proportional but the blue line is, this means only 1 line is proportional.

Note:

I know my answer is very late but I wanted to help anyone who needs it for future reference.

Answer:

α = 0.01 ; 2 - tailed

χ² = 16.998

Pvalue = 0.1497

Fail to reject H0

Step-by-step explanation:

Given the data above :

Number of People Making Contribution

Ethnic Group $1-50 $51-100 $101-150 $151-200 Over $200 Row Total

A 77 63 54 39 18 251

B 90 48 76 26 24 264

C 73 67 59 37 30 266

D 108 82 70 50 30 340

Column Total 348 260 259 152 102 1121

1.) The level of significance, α/2 = 0.01/2

2.)

The hypothesis :

H0 : Contribution and Ethnic group are independent

H1 : Contribution and Ethnic group are not independent

The Chisquare statistic :

χ² = (Observed - Expected)²/ Expected

The expected value for each cell is calculated thus :

(Row total * column total) / sum total

The expected values :

77.9197 58.2159 57.992 34.0339 22.8385

81.9554 61.231 60.9955 35.7966 24.0214

82.5763 61.6949 61.4576 36.0678 24.2034

105.549 78.8582 78.5549 46.1017 30.9367

Using the χ² formula above ;

χ² values for each cell are :

0.010855 0.393154 0.274794 0.724635 1.02509

0.789645 2.85902 3.69099 2.68108 0.0000191

1.11055 0.456179 0.098278 0.0240936 1.38826

0.056933 0.125176 0.93165 0.32963 0.028359

Taking the sum :

0.010855+0.393154+0.274794+0.724635+1.02509+0.789645+2.85902+3.69099+2.68108+0.0000191+1.11055+0.456179+0.098278+0.0240936+1.38826+0.056933+0.125176+0.93165+0.3293+0.028359

χ² = 16.998

To obtain the Pvalue :

df = (Row - 1)(column - 1) = (5-1)*(4-1) = 4 * 3 = 12

Pvalue(16.998 ; 12) = 0.1497

If Pvalue < α ; Reject H0 ;

Since Pvalue > α ; WE fail to reject H0

Answer:

A perpendicular line from a given point

Place your compass on the given point (point P).

From each arc on the line, draw another arc on the opposite side of the line from the given point (P).

Use your ruler to join the given point (P) to the point where the arcs intersect (Q).

Answer:

get the slope of original line

take the inverse of the slope and multiply by -1 (2/3 becomes - 3/2)

y = -b/a x + b

plug on y & x using the given point

calculate the "B"

go back to the y = -b/ax + calculated "B"

that is your answer

Step-by-step explanation:

What do you personaly feel like is most dificult.

For me its rembering minus signs

Answer:

y = -6x -6

Step-by-step explanation:

The general form of the equation of a line in the slope-intercept form may be given as

y = mx + c where

m is the slope and c is the intercept

Hence given the equation

18x + 3y = -18

subtract 18x from both sides

3y = -18x - 18

Divide both sides of the equation by 3

y = -6x -6

This is the equation in the slope - intercept form with -6 as the slope and -6 as the intercept

Answer:

12.65

Step-by-step explanation:

Pythagoras :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90 degree angle).

a and b are the side legs.

so, here we have

14² = 6² + b²

196 = 36 + b²

160 = b²

b = sqrt(160) = sqrt(16×10) = 4×sqrt(10) = 12.65