The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new function? (x – 11)2 + 58 (x + 22)2 – 121 (x + 7)2 – 47 (x – 15)2 + 94

Step-by-step explanation:

the triangle is obtuse...has an angle greater than 90deg

also it is scalene...all 3 sides are different length

The triangle is a scalene and obtuse triangle

A scalene triangle is a type of triangle with three different length sides and three interior angles that add up to 180 degrees. Scalene triangles have no equal of parallel sides , hence there is no line of symmetry. The interior angles of a scalene triangle can be acute , right or obtuse angles.

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of sides of the triangle are

The measure of side AB = 11.9

The measure of side BC = 7

The measure of side AC = 6

And , the measure of ∠ABC = 132°

So , the sides of the triangle are having different lengths so it can be classified as a scalene triangle

And , the angle is obtuse , so it is also an obtuse triangle

Hence , the triangle is scalene

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Answer:

810.58 dollars per year

Step-by-step explanation:

Ok, so we are given that P=5000, so that makes our function A(t)=5000(1.06)^t .

The average rate of change is really the slope of the line going through (15,y1) and (20,y2).

We can find the corresponding y values by plugging the x's there to A(t)=5000(1.06)^t.

So let's do that:

y1=A(15)=5000(1.06)^(15)=11982.79097

y2=A(20)=5000(1.06)^(20)=16035.67736

Now the slope of a line can be found by using the formula:

(y2-y1)/(x2_x1) or just lining up the points and subtracting vertically and remember y difference goes over x difference.

Like so:

 ( 15  , 11982.79097 )

- ( 20 , 16035.67736)

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

 -5          -4052.886391

So the average rate of change is whatever -4052.886391 divided by -5 is.....

which is approximately 810.58 dollars per year.

Answer:

The average rate of change in dollars per year between years 15 and 20 is:

[tex]m=\$810[/tex]

Step-by-step explanation:

First we calculate the profit of the investment for the year 15

So

[tex]P=5000\\t=15[/tex]

[tex]A(15)=5000(1.06)^{15}[/tex]

[tex]A(15)=11982.79[/tex]

Now we calculate the profit of the investment for the year 20

So

[tex]P=5000\\t=20[/tex]

[tex]A(20)=5000(1.06)^{20}[/tex]

[tex]A(20)=16035.68[/tex]

Now the average rate of change m is defined as:

[tex]m=\frac{A(20) - A(15)}{20-15}[/tex]

Therefore:

[tex]m=\frac{16035.68-11982.79}{20-15}[/tex]

[tex]m=\frac{4052.89}{5}[/tex]

[tex]m=\$810.58[/tex]

Answer:

25

Step-by-step explanation:

Since she predicts that 80% of the invited people come, she needs to invite a number greater than 20, so that 80% of that number is 20.

Let the number of invited people be x.

80% of x must be 20.

80% * x = 20

0.8x = 20

Divide both sides by 0.8

x = 25

Answer: She should invite 25 people.

Check: Let's find 20% of 25. If it is 20, then 25 is correct.

80% of 25 = 0.8 * 25 = 20

Since 80% of 25 is 20, the answer, 25, is correct.

Answer:

80/100=.80

.80x=20

x=25

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Let the unknown number be n.  Then 0.60n = 30, and n = 30/0.60 = 50.

Answer:

60 divided by 2 =30

100 divided by 2 = 50 so your answer will be c

Step-by-step explanation:

hope your having a good day guys

Set up a ratio with the height over the shadow.

Let the height of the tower be X

The ratio of the tower is x/120

The ratio if the sign is 10/8

Set them to equal and solve for x:

x/120 = 10/8

Cross multiply:

8x = 1200

Divide both sides by 8:

x = 1200/8

x =150

The answer is B. 150 ft.

Answer:

B.  150 feet.

Step-by-step explanation:

The tower and the street sign and their shadows form 2 similar triangles.

So the corresponding lengths are in the same ratio, then:

120 / 8 = h / 10  where h is the height of the tower.

8h = 120 * 10

h = 120 * 10 / 8

= 150 feet.

Answer:

C) XZ is your best answer.

Step-by-step explanation:

Note that all the other choices are not line segments:

YZ is an arc segment, and is not your answer.

WY is also an arc segment, and is not your answer.

WZ is not a straight line, which does not make it a "line segment" (a straight line that is terminated on both ends by points).

~

Answer: The answer is C

Answer:

True

Step-by-step explanation:

The prefix "co" means together, and the base "linear" means line. Therefore co-linear means together on a line

Answer:

AB = 3

Step-by-step explanation:

Since AB is a perpendicular bisector then Δ is isosceles and AD = AC, that is

4x - 1 = 2x + 3 ( subtract 2x from both sides )

2x - 1 = 3 ( add 1 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

Hence AB = x + 1 = 2 + 1 = 3

Answer:

AB=3

Step-by-step explanation:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We ahve the slope m = 1/2 and the point (-2, 1). Substitute:

[tex]y-1=\dfrac{1}{2}(x-(-2))[/tex]

[tex]y-1=\dfrac{1}{2}(x+2)[/tex] - point-slope form

Covert to the slope-intercept form (y = mx + b):

[tex]y-1=\dfrac{1}{2}(x+2)[/tex]          use the distributive property

[tex]y-1=\dfrac{1}{2}x+1[/tex]          add 1 to both sides

[tex]y=\dfrac{1}{2}x+2[/tex]   - slope-intercept form

Convert to the standard form (Ax + By = C):

[tex]y=\dfrac{1}{2}x+2[/tex]     multiply both sides by 2

[tex]2y=x+4[/tex]        subtract x from both sides

[tex]-x+2y=4[/tex]         change the signs

[tex]x-2y=-4[/tex]   -  standard form

Convert to the general form (Ax+By+C=0):

[tex]x-2y=-4[/tex]        add 4 to both sides

[tex]x-2y+4=0[/tex]   - general form

Answer:

he correct answer is 4.

Step-by-step explanation:

Answer:

The correct answer is 20.

Step-by-step explanation:

Can I get brainliest?

Answer: Each kid would receive 13 pieces of candy

Step-by-step explanation: Since Carlene has 104 pieces of candy and she wants to distribute them evenly to 8 kids she would have to do division and divide 104 with 8 which equals to 13 which means 13 pieces of candy are going to each kid.

Answer: Our required equation would be

[tex]\dfrac{\text{Number of pieces of candy}}{\text{Number of kids}}[/tex]

and each kid would get 13 pieces of candy.

Step-by-step explanation:

Since we have given that

Number of pieces of candy left over from halloween = 104

Number of kids in which she would like to distribute = 8

As every student get pieces of candy evenly.

So, Number of pieces of candy each kid would get is given by

[tex]\dfrac{\text{Number of pieces of candy}}{\text{Number of kids}}\\\\=\dfrac{104}{8}\\\\=13[/tex]

Hence, our required equation would be

[tex]\dfrac{\text{Number of pieces of candy}}{\text{Number of kids}}[/tex]

and each kid would get 13 pieces of candy.

The equation of a circle is written as (x-h)^2 + (y-k)^2 = r^2

Where the center point of the circle is (h,k) and r is the radius.

In the given equation 16 = r^2

To find r take the square root of both sides:

r = √16

r = 4

The answer is A.

Answer: OPTION A.

Step-by-step explanation:

The equation of a circle in center-radius form  is:

[tex](x - h)^2 + (y- k)^2 = r^2[/tex]

Where the center is at the point (h,k) and "r" is the radius.

Then, given the equation of the circle:

[tex](x - 3)^2 + (y + 1)^2 = 16[/tex]

You can idenfity that:

[tex]r^2=16[/tex]

Therefore, in order to find the radius, you need to solve for "r".

Then, this is:

[tex]r=\sqrt{16}\\\\r=4[/tex]

Answer:

The conjecture is that the sum is [tex]30^2+30=930[/tex].

Step-by-step explanation:

I don't see your table... but let's see if we can make a conjecture about the sum of the first 30 positive even numbers.

What is the sum of the first even number? 2=2

What is the sum of the first two even numbers? 2+4=6

What is the sum of the first three even numbers? 2+4+6=12

What is the sum of the first four even numbers? 2+4+6+8=20

What is the sum of the first five even numbers? 2+4+6+8+10=30

What is the sum of the first six even numbers? 2+4+6+8+10+12=42

Alright, let's stop there for a second.

So we have the following sequence of numbers to find a pattern for:

2,6,12,20,30,42,...

Let's look at the common differences:

6-2 ,  12-6 , 20-12 , 30-20, 42-30,...

 4  ,    6     ,  8      ,   10     , 12

No common difference here so let's move on too the second common differences:

6-4  ,  8-6,   10-8,   12-10

 2   ,    2  ,     2  ,     2

So there is a 2nd common difference which means the pattern is a quadratic.

So our expression is of the form [tex]ax^2+bx+c[/tex]

Let's plug in our numbers to come up with a system to solve:

If x=1 , then [tex]ax^2+bx+c=2[/tex]

That is, [tex]a(1)^2+b(1)+c=2[/tex] .

Simplifying this gives: [tex]a+b+c=2[/tex].

If x=2, then [tex]ax^2+bx+c=6[/tex]

That is, [tex]a(2)^2+b(2)+c=6[/tex]

Simplifying this gives: [tex]4a+2b+c=6[/tex].

If x=3, then [tex]ax^2+bx+c=12[/tex]

That is [tex]a(3)^2+b(3)+c=12[/tex]

Simplifying this gives: [tex]9a+3b+c=12[/tex].

So we have this system of equations:

 a+  b+  c=2

4a+2b+  c=6

9a+3b+  c=12

I'm going to set this up as a matrix:

[ 1    1    1    2 ]

[4   2    1    6 ]

[9   3    1    12]

Multiply first row by -4:

[ -4   -4    -4    -8 ]

[  4     2     1     6 ]

[  9     3     1     12]

Add equation 1 to 2:

[ -4    -4    -4     -8]

[   0    -2    -3    -2]

[   9    3      1      12]

Divide first row by -4:

[ 1     1        1       2]

[ 0    -2     -3     -2]

[9      3      1       12]

Multiply top row by -9:

[-9    -9      -9    -18]

[0    -2      -3       -2]

[ 9    3       1         12]

Add equation 3 to 1:

[0    -6      -8     -6]

[0    -2      -3      -2]

[9     3        1        12]

Multiply the second equation by -3:

[ 0    -6     -8     -6]

[0      6      9      6]

[9       3      1     12]

Add equation 1 to 2:

[0      -6    -8    -6]

[0       0     1       0]

[9       3      1       12]

Let's stop there the second row gives us c=0.

So the first row gives us -6b-8c=-6 where c=0 so -6b-8(0)=-6.

Let's solve this:

-6b-8(0)=-6

-6b-0=-6

-6b    =-6

  b    =1

So we have b=1 and c=0 and we haven't used that last equation yet:

9a+3b+c=12

9a+3(1)+0=12

9a+3+0=12

9a+3=12

9a=9

a=1

So your expression for the pattern is [tex]x^2+x+0[/tex] or just [tex]x^2+x[/tex].

Let's test it out for one of our terms in our sequence:

"What is the sum of the first four even numbers? 2+4+6+8=20"

So if we plug in 4 hopefully we get 20.

[tex]4^2+4[/tex]

[tex]16+4[/tex]

[tex]20[/tex]

Looks good!

Now we want to know what happens when you plug in 30.

[tex]30^2+30[/tex]

[tex]900+30[/tex]

[tex]930[/tex]

If you don't like this matrix way, I can think of something else let me.

Answer:

(4x -1  ) ( x  +5  )

Step-by-step explanation:

4x2 + 19x-5

(4x   ) ( x    )

We need to get -5    The factors are -1 and 5  and 1 and -5

4*5 = 20  

so the 5 will be on the outside  We do this because we have +19 on the inside

(4x -1  ) ( x  +5  )

Lets check

FOIL

4x^2 +20x -x -5 = 4x^2 +19x-5  

Answer:

The factors are (4x-1)(x+5).

Step-by-step explanation:

4x^2+19x-5

Break the middle term:

First multiply the coefficient of first term by the constant.

4*5=20

Now find any two numbers whose product = 20 and whose sum is equal to the middle term.

20*1 = 20

20-1 = 19

Now break the middle term:

4x^2+20x-x-5

Now group the first two terms and last two terms:

(4x^2+20x)-(x+5)

Now take the common from each group.

4x(x+5)-1(x+5)

(4x-1)(x+5).

Thus the factors are (4x-1)(x+5).....

Answer:

1

Step-by-step explanation:

(8^1)^0

We know that a^b^c = a^ (b*c)

8^1 ^0 = 8^(1*0) = 8^0 =

Anything raised to the 0 power is 1

=1

Using the slope-intercept form, the equation of the line with slope 6 passing through the point (7,49) is obtained as y = 6x + 7.

To find the equation of a line given the slope and a point it passes through (7,49), we'll use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Since we are given the slope to be 6, we can substitute this into the equation, getting y = 6x + b. To find b, the y-intercept, we substitute the coordinates of the given point into the equation: 49 = 6(7) + b. After solving, we get b = 49 - 42, which simplifies to b = 7. Therefore, the complete equation of the line is y = 6x + 7.

Answer:

Step-by-step explanation:

[tex]2x-3(x+4)=-5\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\2x+(-3)(x)+(-3)(4)=-5\\\\2x-3x-12=-5\qquad\text{add 12 to both sides}\\\\-x=7\qquad\text{change the signs}\\\\x=-7[/tex]

Answer:

x = 40

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Consider the triangle on the left and calculate the third angle

Subtract the sum of the 2 angles from 180

third angle = 180° - (75 + 50)° = 180° - 125° = 55°

Consider the triangle on the right

The third angle = 55° ( vertical angles )

Subtract the sum of the 2 angles from 180

x = 180 - (55 + 85) = 180 - 140 = 40

Answer:

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

Step-by-step explanation:

The given parent function is:

[tex]f(x) = {x}^{2} [/tex]

If we shift to the right by 1 unit, the function becomes:

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

If we stretch by a factor of 5, the function becomes,

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

Finally reflecting over the x-axis gives:

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

Answer:

f'''(x)=-5(x-1)^2

Step-by-step explanation:

Given:

f(x)= x^2

Shifting 1 unit to right means subtracting 1 from the function i.e

f(x-1)=(x-1)^2

f'(x)=(x-1)^2

now vertically stretching above f'(x)  by a factor of 5:

5f'(x)=5(x-1)^2

f''(x)=5(x-1)^2

finally reflecting above f'''(x) over the x-axis:

-f''(x)=-5(x-1)^2

f'''(x)=-5(x-1)^2 !

The required simplified solution of the given expression is 8x + 9.

Given that,
To determine the simplified solution of the expression 3(2x+1)+2(x+3).

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let,
y = 3(2x+1)+2(x+3)
y = 6x + 3 + 2x + 6
y = 8x + 9

Thus, the required a simplified solution of the given expression is 8x + 9.

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Answer:

12.53

Step-by-step explanation:

x = x₂ - x₁ = -6 - 0   = -6

y = y₂ - y₁ =  7 - (-4) = 11

We can use the Pythagorean theorem to calculate the distance.

z² = (-6)² + 11² = 36 + 121 = 157

z = √157 ≈ 12.53

The distance between the two points is 12.53.

Answer:

y-22=14(x-1)

Step-by-step explanation:

Since we are looking for a line parallel to y=14x-3 then we are looking for a line that has the same slope as y=14x-3.

The slope of y=14x-3 is 14.

So the slope of our line is 14.

So we know our equation is in the form y=14x+b.

We can find b by using a point (x,y) on the line. We know (x,y)=(1,22) is a point on the line we are looking for.

So I'm going to replace x with 1 and y with 22 in the equation y=14x+b giving me

22=14(1)+b

22=14   +b  

Subtract 14 on both sides

8=b

The equation of the line is y=14x+8. That is slope-intercept form.  I will leave this here just in case you are curious of this.

I was do point-slope form now since that is what your question says.

We know the slope is 14 so m=14.

The point-slope form is y-y1=m(x-x1).

We know (x1,y1)=(1,22) so now we substitute.

y-22=14(x-1)

Answer:

[tex]h= 116.616[/tex]

Step-by-step explanation:

we have

[tex]h= 105sin (0.0698(90+1)) + 105[/tex]

step 1

Solve (90+1)

[tex]h= 105sin (0.0698(91)) + 105[/tex]

step 2

Solve 0.0698(91)

[tex]h= 105sin (6.3518) + 105[/tex]

step 3

Solve sin (6.3518)

[tex]h= 105(0.11063) + 105[/tex]

step 4

Solve 105(0.11063)

[tex]h= 11.616 + 105[/tex]

step 5

Solve 11.616 + 105

[tex]h= 116.616[/tex]

Answer:

(g-f)(3) = 23

Step-by-step explanation:

f(x) = 4-x^2

g(x) = 6x

we need to find g-f(3)

Put the value of x = 3 in g(x) and f(x) and subtract f(x) from g(x) i.e

(g-f)(3) = g(3) - f(3)

(g-f)(3) = 6(3) - {4-(3)^2}

(g-f) (3)=18-(4-9)

(g-f)(3) = 18-(-5)

(g-f)(3) = 18+5

(g-f)(3) = 23

so, (g-f)(3) = 23

Answer:

23

Step-by-step explanation:

(g-f)(3)=g(3)-f(3)

So we need to find g(3) and f(3). Then subtract.

g(3)=6(3)=18.

f(3)=4-(3)^2=4-9=-5.

(g-f)(3)=g(3)-f(3)=18-(-5)=18+5=23

The answer is option "D. Figure U"

f(x) = 2x + 7 and f(x) = -1

Replace f(x) with -1:

-1 = 2x +7

Subtract 7 from both sides:

-8 = 2x

Divide both sides by 2:

x = -8 /2

x = -4

Answer:

There are infinite numbers that added or multiplied will give the same answer. But, if the require this two numbers to be the same, then we need to solve the following equation to see what we found out:

x + y = x * y

Given that we want the numbers to be equal, then y=x.

x + x = x * x

2x = x^2

x^2 - 2x = 0

x(x-2) = 0

We find that NOT only x=2 meets this requirement but also x=0.

Therefore, there is another number that when added, multiplied or squared gives the same result. The other number is zero!

We can prove it:

0 × 0 = 0

0 + 0 = 0

Answer: It’s D

5x

25x can still be simplified all the way down to 5x

(D) 5x Is the correct answer

Answer:

The quotient to the problem 806 ÷ 6 is 134.3333 and so forth.

The quotient of the expression 806 ÷ 6 will be 134.33.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

The expression is,

806 ÷ 6

Now, Solve the expression by using long division as;

6 ) 806 ( 134.333.....

  - 6

---------

    20

  - 18

 -----------

      26

   -  24

    -------

         20

       - 18

       -------

           2

Thus, The quotient of the expression 806 ÷ 6 will be 134.33.

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Answer:

60

Step-by-step explanation:

Answer:

$10.

Step-by-step explanation:

Let x represent the original cost of bag of cat food.

We have been given that a pet store owner set the price of a bag of cat food at 50% above the cost. So the cost of cat food would be x plus 50% of x.

[tex]x+\frac{50}{100}*x\rightarrow x+0.5x=1.5x[/tex]

We are further told that the price was reduced by 20%, when it did not sell. So price of cat food after reduction would be [tex]1.5x[/tex] minus 20 percent of [tex]1.5x[/tex].

[tex]1.5x-(\frac{20}{100}\times 1.5x)[/tex]

[tex]1.5x-(0.20\times 1.5x)[/tex]

[tex]1.5x-(0.3x)[/tex]

[tex]1.2x[/tex]

Since price after reduction was $12, so we will equate [tex]1.2x[/tex] with 12 as:

[tex]1.2x=12[/tex]

[tex]\frac{1.2x}{1.2}=\frac{12}{1.2}[/tex]

[tex]x=10[/tex]

Therefore, the original cost of cat food was $10.