What is the factored form of 8x² + 12x?
O 4(4x² + 8x).
O 4x(2x + 3)
O8x(x + 4)
O 8x(x² + 4)

Using translation concepts, the transformations are given as follows:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The parent function is given by:

y = x².

The translated function is:

y = -2(x + 5)² - 3.

In this problem, we have that:

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James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.

Given that, James needs to mix a 10% acid solution with a 50% acid solution to create 100 millilitres of a 26% solution.

Let the acid solution needs to mix with 10% be x ml and the acid solution needs to mix with 50% will be 100 - x ml.

Now,

10% x + 50% ( 100 - x ) = 26% ×100

⇒[tex]\frac{10x}{100} +\frac{50(100-x)}{100}=\frac{2600}{100}[/tex]

⇒10x + 50( 100 - x ) = 2600

⇒10 x + 5000 - 50x = 2600

⇒10 x - 50 x = 2600-5000

⇒-40 x = -2400

⇒x=60

Therefore, James must mix 60 millilitres of 10% solution and 40 millilitres of 50% solution.

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Answer:

14

Step-by-step explanation:

AT/TB = AV/VC

5/7 = 10/VC

VC = 14

For the given figure length of VC = 14.

In the given figure,

We can see that,

ΔATV and ΔABC are similar triangle,

Since we know that,

Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion. The '' sign here denotes the resemblance of triangles.

Therefore,

AT/TB = AV/VC

It is given that,

AT = 5

TB = 7

AV = 10

Now put these values we get,

⇒ 5/7 = 10/VC

⇒ VC = 14

Hence,

Length of VC  is 14 units.

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Option D. If property taxes are decreased by $12000, the effect that it would have on the cost function is shifts downward by 12 units.

We have a function of this type

fx = Ax + B

where A = labor and material

B = fixed cost

We have a graph of this form. g(x) = ax + b - 12, with b and a representing costs in thousands of American currency.

A factory has a linear cost function f(x)=ax+b, where b represents fixed costs and a represents the labor and material costs of making one item, both in thousands of dollars. If property taxes (part of the fixed costs) are decreased by $12,000 per year, what effect does this have on the graph of the cost function? a. shifts to the left by 12 units b. shifts to the right by 12 units c. shifts upward by 12 units d. shifts downward by 12 units

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The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. The total number of students that are in the orchestra, the band, and the choir is 126.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

There are 32 students in the orchestra and twice that number in the band. Therefore the number of students in the band is:

Number of students in band = 2 (Number of students in Orchestra)

                                                = 2 × 32 = 64

The number of students in the Choir is the sum of the number of boys and girls. Therefore, the number of students in the Choir is,

Number of students in the Choir = 19 + 11 = 30

Total number of students = 32 + 64 + 30 = 126

hence, the total number of students that are in the orchestra, the band, and the choir is 126.

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Calculate the slope of the line between each pair of co-ordinates

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\LARGE\textsf{Question 1}}[/tex]

The points given are,

[tex]\begin{cases} \bf{(3,6)} \\ \bf{(4,-3) \end{cases}[/tex]

To find the slope [tex]\textbf{M}[/tex] of this line,

we will utilise the [tex]\textbf{Slope Formula}[/tex].

The first thing to do is

to put in the co-ordinates

of the two points given.

[tex]\bf{\dfrac{-3-6}{4-3}}[/tex] | subtract on top and bottom

[tex]\bf{\dfrac{-9}{1}}[/tex] | divide on top and bottom

[tex]\bf{-9}[/tex]

[tex]\LARGE\textsf{Question 2}[/tex]

The points given this time are,

[tex]\begin{cases} \bf{(-5,-3)} \\ \bf{(-3,-7)} \end{cases}}[/tex]

Last time we needed to

put in the co-ordinates.

Similarly, we ought to

put in the co-ordinates

in this problem.

[tex]\bf{\dfrac{-7-(-3)}{-3-(-5)}}[/tex] | simplify

[tex]\bf{\dfrac{-7+3}{-3+5}}[/tex] | add on top and bottom

[tex]\bf{\dfrac{-4}{2}}[/tex] | divide on top and bottom

[tex]\bf{-2}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                         [tex]\bf{\begin{cases}\bf{Slope=-9} \\ \bf{Slope=-2} \end{cases}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]

Answer:   [tex]\boldsymbol{(x + 4)^2 + (y + 6)^2 = 49}\\\\[/tex]

Work Shown:

[tex](h,k) = (-4,-6) = \text{center}\\\\r = 7 = \text{radius}\\\\(x - h)^2 + (y - k)^2 = r^2\\\\(x - (-4))^2 + (y - (-6))^2 = 7^2\\\\\boldsymbol{(x + 4)^2 + (y + 6)^2 = 49}\\\\[/tex]

To check the answer, you can use a graphing calculator like GeoGebra or Desmos or similar.

The value of x in the given expression is; x = wz/y

We are given the expression;

w/x = y/z

Now, we want to find the value of x which means we want to make x the subject of the formula. Thus;

Multiply both sides of the given expression by x to get;

(w/x)*x = (y/z)*x

⇒ w = xy/z

Now, multiply both sides by z/y to get;

w(z/y) = (xy/z) * (z/y)

wz/y = x

Thus, the value of x in the given expression is;

x = wz/y

The correct question is;

If w/x = y/z, then what is the value of x

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Answer: 45.5yds

Step-by-step explanation:

- the radius is simply half of the diameter so: 91 / 2= 45.5yd

- so the radius is 45.5yds

hope this helps :)

r= d/2 = 91/2 =45.5yd

Answer:

D. Write an equation

Step-by-step explanation:

x = The time of Sand Diego

t = Current designated time

n = The difference in time

So the equation is x = t+/-n.

You can determine if it would be + or - based of the word problem.

For this word problem the equation is x = 1:00pm - 2hrs

Hope this helps.

Answer:

Step-by-step explanation:

eq of line perpendicular to 3x+5y=10 is

5x-3y=a

where a is constant.

it passes through (3,2)

5(3)-3(2)=a

a=15-6=9

reqd. eq. is 5x-3y=9

or

3y=5x-9

y=5/3 x-3

gradient=5/3

y-intercept=-3

or

5y=-3x-10

y=-3/5 x-2

slope=-3/5

slope of reqd. line=-1/(-3/5)=5/3

eq. of line through (3,2) is

y-2=5/3(x-3)

3y-6=5x-15

3y=5x-15+6

3y=5x-9

y=5/3 x-3

Answer: A, B, C, D

Step-by-step explanation:

A. This is true because all rhombi are parallelograms, and diagonals of a parallelogram bisect each other.

B. This is true because the diagonals of a rhombus are perpendicular.

C. This is true because diagonals of a rhombus bisect the angles from which they are drawn,

D. This is true because all sides of a rhombus are congfruent.

E. This is not always true - all rhombi are parallelograms, and adjacent angles of a parallelogram are supplementary, but not always congruent.

F. This is not always true - diagonals of a rhombus are not always congruent.

Answer:

20

Step-by-step explanation:

Correct option is A)

let the number be x.

∴75% of x=15

∴

100

75

×x=15

∴x=15×

3

4

∴x=20

The value of x is 20.

Answer:

A) 65

B) 60

Step-by-step explanation:

64.9963 rounds to 65

To the nearest 10 it would round down as the second intiger the 4 is below 5 meaning as a result it rounds down

After rounding  the given number 64.9963:

(a) Near 2 decimal places is: 64.70

(b) And the nearest 10 is: 60

When you round a number to a certain digit, you have to check the value of the digit before the place you want to round off to.

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

The given number is:

64.9963

To round off the nearest 2 decimal places:

Since the third digit after the decimal is 6 which is greater than 5.

Add 1 to their previous digit.

Therefore,

After rounding near to 2 decimal places the number becomes:

64.70

To round off the nearest 10:

Since the tense digit is 4 and it is less than 5

Therefore,

The number after rounding off the nearest 10 is:

60.

Hence, after rounding the number:

Near 2 decimal places is: 64.70

And the nearest 10 is: 60

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The composite function of the paintings Jenny completes in a year is

[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

A composite function is a function made of other functions, where the output of one function is the input to the other function.

An example of the composite functions 2x+3 and [tex]x^{2}[/tex] together make the composite function [tex](2x+3)^{2}[/tex]

We have [tex]P(w)=\frac{1}{2}w+1[/tex]

Here, P(w) represents the number of paintings Jenny completes in some w weeks. and

J(y)  represents the number of weeks per year.

As J(y) is the number of weeks spent per year in painting, we can calculate the paintings completed in a year by substituting

w as J(y) in the equation we have

Then the equation becomes:[tex]P(J(y))=\frac{1}{2}J(y)+1[/tex]

Hence this is the composite function that would represent the number of paintings Jenny completes in a year.

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The expression is equivalent to 2 , option C is the right answer.

An expression in maths is a statement that contains , constants , variables and mathematical operators.

The expression given in the question is

[tex]\rm \dfrac { 4^{\frac{5}{4}} * 4^{\frac{1}{4}}} {4^{\frac{1}{2}}}[/tex]

Applying exponent rule

[tex]\rm a^m * a^n = a^{m+n}[/tex]

[tex]\rm \dfrac { 4^{\frac{5}{4} +\frac{1}{4}}} {4^{\frac{1}{2}}}[/tex]

Applying exponent rule

[tex]\rm \dfrac{a^m}{a^n} = a^{m-n}[/tex]

[tex]\rm { 4^{\frac{5}{4} +\frac{1}{4} -{\frac{1}{2}}}[/tex]

On solving the exponents

=(6/4) -(1/2)

=4/4

=1

=[tex]\rm 4^{\frac{1}{2}}[/tex]

= 2

Therefore the expression is equivalent to 2 , option C is the right answer.

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Answer:

AABC and AXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle

Answer: A

tan= Opposite ÷ Alternate

tan B= 16 (which is the opposite side of B) ÷ 7 (it's the side beside B, excluding 17.46 as it's the hypotenuse)

Therefore 16÷7 = 2.285714286

= 2.29 (3sf)

Answer:

just choose one

Answer:

b elephants and zebras

Step-by-step explanation:

Answer:

Step-by-step explanation:

Comment

I'll give you the answer, but my guess is the question will be deleted because it is in the wrong place.

The answer is B. You might think it is D but those creatures are mostly in North America.

Answer: $36.68 or $35.97. Read below.

Step-by-step explanation: You need to multiply the 12 foot by 12 foot and you would get 144 sq feet. Then divide 47 into 144. You will be left with 3.06, and if you need to round, you can round that to 3. Then you need to multiply 3 by $11.99 and you will be left with the cost for the paint, which is $35.97 if you do round to a three, and $36.68 if you do not round the three. So your answer is either $36.68 or $35.97 depending on whether you round or not.

The required probability of success is given by 0.98906500

Assume the random variable X has a binomial distribution with the given probability of obtaining a success.
P(X<5), n=6, p=0.3

In binomial distribution for number trials we are investigating the probability of getting a success remain the same.

n = number of trails,
p = probability of success
x = the number of success

p(x<5) = P(x=0)+ p(x=1) + p(x=2)+p(x=3)+p(x=4)

= [tex]\binom{6}{0}(0.3)^0(1-0.3)^6+\binom{6}{1}(0.3)^1(1-0.3)^5+\binom{6}{2}(0.3)^2(1-0.3)^4+\binom{6}{3}(0.3)^3(1-0.3)^3+\binom{6}{4}(0.3)^4(1-0.3)^2[/tex]

p(x<5) = 0.98906500

Thus the required  probability of success is given by 0.98906500

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1) It's best to draw out a picture of a rectangle and label each corner with the coordinates given: Let's say (-5, 2) is point A, (-5, -2 1/3) is point B, (2 1/2, 2) is point C, and (2 1/2, -2 1/3) is point D.

2) That being said, line AB is one side of the rectangle, BC is another, CD is another, and lastly, AD is the fourth side.

3) We can use the distance formula and plug in the coordinates of each line to find how long every side is. Then you just need to solve it.

For example: if I want to find how long side AB is, I would use the point A (-5, 2) and B (2 1/2, 2) and plug them into the distance formula, where (-5, 2) is (x1, x2) and (2 1/2, 2) is (x2, y2) and solve that.

4) Repeat this process with side BC, CD, and AD, and add the results together. This will be your final answer; the perimeter of the rectangle.

Encourage children to recognize and talk about math in everyday situations, this statement teacher not recommendation.

What is mathematics?

Quality, structure, space, and change are the subjects of study in mathematics. The study of mathematics involves utilizing symbols and numbers to quantify and analyze the characteristics of quantities and sets.

It is impossible to encourage kids to understand and discuss arithmetic in normal contexts since the subject's solutions are based on numbers and symbols, which makes it inappropriate.

As a result, option (a) is correct.

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Answer:

Step-by-step explanation:

Complementary angles are angles that add up to 90°.

Let's say angle 1 is x, and angle 2 is 87.6 less than x.

We already know that angle 1 + angle 2 = 90, so we can just substitute x now.

We know that complementary angles add up to 90, so one of the angles is 90-x, and the other one is 90-x-87.6.

x = (90 - x) - 87.6

Simplifies to:

x = 2.4-x

Add x to both sides

2x = 2.4

Divide by 2

x = 1.2

To get the other angle, add 87.6 to 1.2

1.2+87.6 = 88.8

So, angle1 = 1.2, and angle2 = 88.8

Let's check our work.

88.8 + 1.2 = 90, so the angles are complementary and have a difference of 87.6

Hope this helps (:

Answer:

1.2°, 88.8°

Step-by-step explanation:

let one angle=x

other angle=y

y=x-87.6

also  

x+y=90

x+x-87.6=90

2x=90+87.6=177.6

x=88.8

other angle=88.8-87.6=1.2

If three diagonals are drawn inside a hexagon with each one passing through the center point, six triangles are formed.

There are nine diagonals in a regular hexagon

But for one with three diagonals drawn through the center, six equilateral triangles are formed.

Thus, if three diagonals are drawn inside a hexagon with each one passing through the center point, six triangles are formed.

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Answer:

Step-by-step explanation:

The best way to answer a question like this one is to use a graphing program on the internet. This graph was done with desmos

It looks to me that the equation is g(x)  = 10(x - 5)^2 - 37

I checked to see that this is correct, and thank goodness it is.

The graph is shown below.

Answer:

If you mean:

x² = 10

√x² = √10

x = √10

if you meant:

2x = 10

2x/2 = 10/2

x = 10/2

x = 5

hope this helps

If you mean x^2 then there would be no answer after all, 3^2= 9 and 4^2= 16 so

If you mean 2x then the answer would be 5

Step-by-step explanation:

:0

The equation for total pay is y = 10/8x.

Division is the mathematical operation that is used to determine the quotient of a number. In order to determine the total pay for hours from 0 to 8, the pay per hour has to be determined. To determine this value, divide $10 by 8.

Pay per hour = $10 / 8

y = 10/8x.

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