Which values for h and k are used to write the function f of x = x squared + 12 x + 6 in vertex form?

h=6, k=36
h=−6, k=−36
h=6, k=30
h=−6, k=−30

Answer:

work is shown and pictured

C, infinitely many solutions.

B, one solution.

C, infinitely many solution.

A system of linear equations is a collection of one or more linear equations involving the same variables.

A system of linear equation has

According to the given questions

the given system of equations

(1). 2x+2y=3 and 4x+4y=6

if we see the graph of the above system of linear equations, the graphs are the" exact at same line".

Hence, they have infinitely many solution.

(2). 7x+5y=8 and 7x+7y =8

if we see the graph of the above system of linear equations, the graphs are intersecting at a single point.

Hence, there is only one solution.

(3). -2x+3y=7 and 2x-3y=-7

if we see the graph of the above system of linear equations, the graphs are exact at same line.

Hence, there is infinitely many solutions.

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Answer:

Half of its original

Step-by-step explanation:

When multiplying a denominator by a whole number, he value decreases accordingly, in other word, it changes inversely.

Examples:

In 1/2, if 2 is multiplied by 2, the value becomes 1/4, which is half of 1/2

In 1/4, if 4 is multiplied by 2, the value becomes 1/8 which is half of 1/4.

Hope this helps

Good luck

Answer: 9

Step-by-step explanation:

[tex]3^2 + \frac{3}{3}-1\\\\=9+1-1\\\\=9[/tex]

Answer:

0.8

Step-by-step explanation:

because the template should be axr^n-1

where r is the common ratio

r=0.8

Answer:

0.8

Step-by-step explanation:

Answer:

X=6/11

Step-by-step explanation:

8-(5x-2)=6-2(3x+1)

8-5x+2=6-6x-2

10-5x=4-6x

6=11x

x=6/11

Answer:

8-5x-2=6-6x+2

8-2-6-2=5x-6x

-10+8=-x

-2 =-x

x=2 ........×-1

x=2

Answer: w=5

Step-by-step explanation:

Answer:

A. 3

Step-by-step explanation:

ΔDEC is bigger than ΔABC by 5. For the hypotenuse, 25 is 5 times bigger than 5.

So, side DE on ΔDEC has to be 5 times bigger than side AB on ΔABC.

If side AB equals 3, side DE equals 18 - 3, which is 15.

15 is five times bigger than 3, so the answer is A. 3.

Hope that helps.

Answer:

336m^2

Step-by-step explanation:

The triangle area is half of base times height so: 1/2*8*12=48m^2

There are 4 triangles so 48*4=192

Then the square base area is side times side so: 12*12=144m^2

Then surface area of model is 192m^2+144m^2=336m^2

Answer:

336 m²

Step-by-step explanation:

We can find the surface area of this pyramid by finding the surface area of one of the sides, multiplying it by 4 (as there are 4 sides to the pyramid) then adding it to the surface area of the base.

Each side of this (excluding the base) is a triangle, and to find the area of a triangle we use the equation [tex]\frac{b \cdot h}{2}[/tex].

[tex]\frac{12 \cdot 8}{2}[/tex]

[tex]\frac{96}{2}[/tex]

48.

So, one side of this is 48. Multiplying it by 4 gets us 192.

Now we have to add the area of the base. The area of the bass is a square with side lengths of 12, so we can square 12 to get the area of the bass. 12² = 144.

Now let's add these numbers:

192+144 = 336

So, 336 m² is what this comes out to.

Hope this helped!

Answer:

[tex]p = \frac{1}{2}[/tex]

[tex]q = 5[/tex]

[tex]h^{-1}(h(3)) = 3[/tex]

Step-by-step explanation:

Given

[tex]h(x) = px - \frac{5}{2}[/tex]

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

Solving for p and q

Replace h(x) with y in [tex]h(x) = px - \frac{5}{2}[/tex]

[tex]y = px - \frac{5}{2}[/tex]

Swap the position of y and d

[tex]x = py - \frac{5}{2}[/tex]

Make y the subject of formula

[tex]py = x + \frac{5}{2}[/tex]

Divide through by p

[tex]y = \frac{x}{p} + \frac{5}{2p}[/tex]

Now, we've solved for the inverse of h(x);

Replace y with [tex]h^{-1}(x)[/tex]

[tex]h^{-1}(x) = \frac{x}{p} + \frac{5}{2p}[/tex]

Compare this with [tex]h^{-1}(x) = q + 2x[/tex]

We have that

[tex]\frac{x}{p} + \frac{5}{2p} = q + 2x[/tex]

By direct comparison

[tex]\frac{x}{p} = 2x[/tex] --- Equation 1

[tex]\frac{5}{2p} = q[/tex]  --- Equation 2

Solving equation 1

[tex]\frac{x}{p} = 2x[/tex]

Divide both sides by x

[tex]\frac{1}{p} = 2[/tex]

Take inverse of both sides

[tex]p = \frac{1}{2}[/tex]

Substitute [tex]p = \frac{1}{2}[/tex] in equation 2

[tex]\frac{5}{2 * \frac{1}{2}} = q[/tex]

[tex]\frac{5}{1} = q[/tex]

[tex]5 = q[/tex]

[tex]q = 5[/tex]

Hence, the values of p and q are:[tex]p = \frac{1}{2}[/tex];  [tex]q = 5[/tex]

Solving for [tex]h^{-1}(h(3))[/tex]

First, we'll solve for h(3) using [tex]h(x) = px - \frac{5}{2}[/tex]

Substitute [tex]p = \frac{1}{2}[/tex];  and [tex]x = 3[/tex]

[tex]h(3) = \frac{1}{2} * 3 - \frac{5}{2}[/tex]  

[tex]h(3) = \frac{3}{2} - \frac{5}{2}[/tex]

[tex]h(3) = \frac{3 - 5}{2}[/tex]

[tex]h(3) = \frac{-2}{2}[/tex]

[tex]h(3) = -1[/tex]

So; [tex]h^{-1}(h(3))[/tex] becomes

[tex]h^{-1}(-1)[/tex]

Solving for [tex]h^{-1}(-1)[/tex] using [tex]h^{-1}(x) = q + 2x[/tex]

Substitute [tex]q = 5[/tex] and [tex]x = -1[/tex]

[tex]h^{-1}(x) = q + 2x[/tex] becomes

[tex]h^{-1}(-1) = 5 + 2 * -1[/tex]

[tex]h^{-1}(-1) = 5 - 2[/tex]

[tex]h^{-1}(-1) = 3[/tex]

Hence;

[tex]h^{-1}(h(3)) = 3[/tex]

Answer:

(1.5,-3) and (4.5,-3)

Step-by-step explanation:

Answer: rotate 180 degrees and reflection across the line y=2

Step-by-step explan

Answer:

Step-by-step explanation:

Answer:

g = (h+a) - l

None of them

Step-by-step explanation:

Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters. Which of the following expressions always represents how far away the new oil level is from the previous oil level? H+G lGl none of them

Let

h = liters of oil in the morning

l= liters that has leaked

a= liters that were added during the day

g= amount of liters at the end of the evening

Total liters of oil in the evening= (litres of oil in the morning + litres of oil added during the day) - litres of oil that leaked

Substituting each variable into the formula, we have

g = (h+a) - l

Answer: 81

Step-by-step explanation:

First digit  and    Second digit    and    Third digit    and    Fourth digit

3 choices  x       3 choices          x        3 choices      x       3 choices     = 81

Answer:

The x value of the point 1/4 the distance from point C to point D is -0.25

Step-by-step explanation:

The given information are;

The location of point C = (1, 2)

The location of point D = (-4, -2)

The point 1/4 from point C to point D is the point 3/4 from point D to point C

Which gives;

The coordinate at point D + 3/4× The difference between the coordinates of point C and point D

Which is (-4 + 3/4×(1 - (-4),  - 2 + 3/4×(2 - (-2))

Which gives;

(-4 + 3.75, -2 + 3)  and (-0.25, 1)

The coordinates of the point 1/4 the distance from point C to point D is (-0.25, 1)

Therefore, the x value of the point 1/4 the distance from point C to point D = -0.25.

Answer:

for exapmle:  (2, 5)          {5=2•2.5}

                       (8, 20)        {20=8•2.5}  

                       (-5,  -12.5}    {-12.5=-5•2.5}

Step-by-step explanation:

    -3y+3x    -3y+3x

            ÷2     ÷2

Answer:

neither

Step-by-step explanation:

Answer:

your welcome and hope this helps

Answer:

Z = 0.87

Explanation:

Given the following data;

Sample 1:

n1 = 30

Mean, X = 2.36

Standard deviation, Ox = 0.96

Sample 2:

n2 = 60

Mean, Y = 2.19

Standard deviation, Oy = 0.66

The formula for test statistics for two population is;

[tex]Z = \frac{X-Y}{\sqrt{(\frac{Ox^2} {n_1} } +\frac{Oy^2}{n_2} )}}[/tex]

Substituting the values, we have;

[tex]Z = \frac{2.36-2.19}{\sqrt{(\frac{0.96^2} {30} +\frac{0.66^2}{60} )}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{(\frac{0.9216} {30} +\frac{0.4356}{60} )}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{(0.03072 +0.00726)}}[/tex]

[tex]Z = \frac{0.17}{\sqrt{0.03798}}[/tex]

[tex]Z = \frac{0.17}{0.19488}[/tex]

Z = 0.8723

The test statistics to 2 d.p is 0.87

Therefore, Z = 0.87

Answer:

The correct option is;

A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25

Please find attached the graphs of the table data

Step-by-step explanation:

Each of the given table data of in the tables are analysed to find direct variation;

Table 1

x,               -3,                 -1,                 2,                5,                10

y,              -4.5,              -3.0,             -1.5,             0.0,              1.5              

-4.5/-3  = 1.5 ≠ -3.0/-1 = 3

No direct variation

Table 2      

x,             -5.5,               -4.5,            -3.5,            -2.5,             -1.5

y,              10,                   8,                 6,              4,                  2

10/(-5.5) = -20/11  ≠ 8/(-4.5) = -16/9

However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2

Adjusted direct variation

Table 3              

x,              -5.5,               -5.5,             -5.5,           -5.5,            -5.5

y,              -3,                    -1,                 2,                5 ,              10                  

-3/(-5.5) ≠ -1/-5.5

No direct variation

Table 4

x,              -3,                    -1,                2,                  5,             10

y,              -7.5,                 -2.5,            5.0 ,              12.5,         25  

 -7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10

Direct variation exists        

Answer:

so D

Step-by-step explanation:

Answer:

Height of the kite = 86.60 meter (Approx)

Step-by-step explanation:

The angle of elevation to see a kite from a stone lying to the ground is 60 degrees. If a thread is tied with a kite and a stone, then that thread is 100 meters long, find the height of the kite.

Given:

Length of thread = 100 meter

Angle of elevation = 60°

Find:

Height of the kite.

Computation:

Using trigonometry application:

Height of the kite / Length of thread = Sin 60°

Height of the kite / 100 = √3 / 2

Height of the kite = [√3 / 2]100

Height of the kite = 50√3

Height of the kite = 86.60 meter (Approx)

Answer:

80 = EG

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

40 = 1/2 EG

Multiply each side by 2

80 = EG

Answer:

80 deg

Step-by-step explanation:

Theorem:

The measure of an inscribed angle is half the measure of the intercepted arc.

m<EFG = (1/2)m(arc)EG

40 deg = (1/2)m(arc)EG

m(arc)EG = 2 * 40 deg

m(arc)EG = 80 deg

Answer:

this. question is not clear please send clear question

We can conclude that -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have the following two functions -

y = -x

AND

y = x

Refer to the graphs attached for both the functions -

y = - x     and     y = x

The graphs as seen pass through the origin. One graph (y = x) has a slope of +1 while the other one (y = - x) has a slope of -1. The y - intercept of both the graphs will be 0.

We can conclude that -

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Answer:

3 degrees F

Step-by-step explanation:

if the temperature rose 1* for 7 hours, times 1 by 7. which is 7 and add to -10. which is -3. then, since the temperature rose by 2* for 3 hours, times 2 by 3 which is 6 and add to -3, which is 3.

i hope this helped?

Answer:

0.75

Step-by-step explanation:

The average length is given as the sum of all the lengths given divided by the number of lengths (frequency).

Mathematically:

Average = (Sum of lengths) / frequency

The lengths given are -3, 3, -4, -3, 4, -2, 6, 5. There are 8 lengths there.

The average is therefore:

Average = (-3 + 3 + (-4) + (-3) + 4 + (-2) + 6 + 5) / 8

Average = 0.75

Answer:

1/5

Step-by-step explanation:

2/9 * 9/10 = 2/10 = 1/5

Answer:

M(2, −4), N(−2, 4)

Step-by-step explanation:

Transformation is the movement of a point from one place to another. If an object is transformed, all the points of the object are being changed. There are different types of transformation which are: Reflection, rotation, translation  and dilation.

Reflection of a point is the flipping of a point. If a point A(x, y) is reflected across the x axis, the new point is A'(x, -y). If a point B(x, y) is reflected across the y axis, the new point is A'(-x, y).

The coordinates of point L on a coordinate grid are (−2, −4), if Point L is reflected across the y-axis to obtain point M, the coordinates of M is at (2, -4).

if Point L is reflected across the x-axis to obtain point N, the coordinates of N is at (-2, 4).

Answer: M(2, −4), N(−2, 4) So D can i get branliest

Step-by-step explanation:

Answer:

The bank offering simple interest at rate of 3% for four years

Step-by-step explanation:

Hello,

To find out which deal would be better, we have to find how much accrued on the simple and compound interest.

Data;

Principal (P) = $7,000

Time = 4 years

Simple interest rate = 3%

S.I = PRT / 100

S.I = (7000 × 3 × 4) / 100

S.I = $840

In four years, he would have $7000 + $840 = $7840.

For compound interest,

C.I = P(1 + r/n)^nt

Where n = number of time compounded = 1 (since it's annually)

rate = 2.5% = 2.5/ 100 = 0.025

C.I = 7000(1 + 0.025/1)⁽¹*⁴⁾

C.I = 7000 (1 + 0.025)⁴

C.I = 7000×(1.025)⁴

C.I = 7000 × 1.1038

C.I = $7726.6

In four years he would have $7,726.6

After calculating and evaluating both option, it's advisable for him to select the bank offering a simple interest of 3% for four years

Answer:

SOLUTION SET ={a/a≥20}

Step-by-step explanation:

[tex]\frac{2a}{5}-2\geq\frac{a}{4}+1[/tex]

[tex]adding 2 on both sides[/tex]

[tex]\frac{2a}{5}-2+2\geq \frac{a}{4}+1+2[/tex]

[tex]now subtracting \frac{a}{4} on both sides[/tex]

[tex]\frac{2a}{5}-\frac{a}{4}\geq 3[/tex]

[tex]takig LCM as 20\\\frac{8a}{20}-\frac{5a}{20}\geq 3[/tex]

[tex]\frac{3a}{20}\geq 3[/tex]

[tex]by cross-multiplication[/tex]

3a≥3×20

3a≥60

dividing 3 on both sides

3a/3≥60/3

a≥20

SOLUTION SET ={a/a≥20} is the answer

i hope this will help you :)

Answer:

B. y= -x^2+50x-300

Step-by-step explanation:

A. y^2=4x^2-100

B. y= -x^2+50x-300

C. x=-y^2-400

D. x^2=-6y^2+200

we are to find profits (y) when the company sells x items

Option A can be used to calculate the profit (y) squared

Option B can be used to calculate profits (y)

Option C can be used to calculate items sold(x)

Option D can be used to calculate items sold squared(x^2)

We are asked to find the weekly profit (y) function which eliminate options A, C and D leaving us with option B

Therefore, the weekly profits (y) function in thousands of dollars when the company sells x items is

B. y= -x^2+50x-300

Answer:

[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]

Step-by-step explanation:

The interior angle of a regular heptagon = = 900/7° = 128.57°

Therefore, angle DAB = 128.57°

The interior angle of the square = 90°

Therefore, angle DAC = 90°

Therefore, we have

angle DAB+ angle DAC + angle BAC = 360° (sum of angles at a point (A))

Angle BAC = 360° - angle DAB - angle DAC =  360° - 900/7° - 90° = 990/7°

Angle BAC = 141.43°

Expressing 141.43° as a common fraction gives;

[tex]141.43 ^{\circ}= \dfrac{990}{7} ^{\circ}=141\frac{3}{7} ^{\circ}[/tex]

[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]

 The degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex]

Given, A square and a regular heptagon are coplanar as shown in below figure attached.

We have find the exterior angle of BAC.

We know that, The formula that gives the interior angle measure for a regular polygon with any number of sides is,

[tex]\frac{180(n-2)}{n}[/tex]  where n is the number of sides.  

Since the heptagon has 7 no. of sides.

So regular heptagon's interior angle measures,

[tex]\frac{180(7-2)}{7}=128\frac{4}{7}[/tex]

Hence [tex]\angle A[/tex] will be[tex]128\frac{4}{7}[/tex] degrees.

We know that a square's interior angle is 90 degrees and a heptagon's interior angle is  128.57 degrees. We will subtract those from 360 degrees to find angle BAC.

[tex]\angle BAC = 360 - (\angle A + 90)\\[/tex]

[tex]\angle BAC = 360 - (128\frac{4}{7} + 90)\\\angle BAC=141\frac{3}{7} ^\circ[/tex]

Hence the degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex].

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