Complete the square to transform the expression x2 + 4x + 2 into the form a(x − h)2 + k.

Answer:

Step-by-step explanation: just did it on apex

The pairs of triangles appear to be congruent are Triangles 1 and 4,  Triangles 1 and 3 and  Triangles 3 and 4, that is option B, option C and option E. This can be obtained by understanding the concept of congruence.

In the question, Triangle 2 is larger than the other triangles.

Triangle 1, Triangle 3 and Triangle 4 appears to have the same size and shape.

Thus Triangle 1, Triangle 3 and Triangle 4 appears to be congruent to each other.

Hence the pairs of triangles appear to be congruent are Triangles 1 and 4,  Triangles 1 and 3 and  Triangles 3 and 4, that is option B, option C and option E.

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Step-by-step explanation:

Step-by-step explanation:

To answer the question you have t the square of the differences.

So this means that (x-3)^2= x^2-9x+9

Next youmultiply 3 on both sides which says…

x^2-9x+9=27

x^2-9x=18

So, x equals

9/2+3/2 square root 17

OR

9/2-3/2 square root 17

A Vertex is the point that 2 or more lines connect.

When an angle is written given the letters of the lines/ points, the point where the lines connect are always the middle letter.

For ∠XYZ, the vertex would be point Y, because it is the middle letter.

An angle is formed by two rays that have a common endpoint which is known as the vertex of the angle

The vertex of the angle ∠XYZ is point Y

The reason the above selection is correct is as follows;

There are three methods used in naming an angle, including;

. The given angle is ∠XYZ, therefore, the middle letter, Y, is the vertex

The vertex point is Y

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Answer:

7+16= 23

23*2=46. ..........

Answer:

y=-2x+4

Step-by-step explanation:

2x+y-1=0

2x+y=0+1

2x+y=1

y=1-2x

y=-2x+1

y=mx+b where m=slope and b=y-intercept

parallel means same slope,

so the slope would still be -2.

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

y-y1=m(x-x1)

y-2=-2(x-1)

y=-2x+2+2

y=-2x+4

Question 21: 24 minutes

[tex]\frac{3}{\frac{3}{2} } = \frac{x}{12}[/tex]

x = [tex](\frac{3}{\frac{3}{2} })(12)[/tex]

x = 24

Question 22: 20 centimeters

x = one side of the square

x² = 25

x = 5

4x = perimeter

4(5) = perimeter

20 = perimeter

Question 23: 17 sides

Hexagon = 6 sides

Octagon = 8 sides

Triangle = 3 sides

Total amount of sides = 6 + 8 + 3

Total amount of sides = 17

the equation is S=30w+450

to find the answer just replace the w by 14

multiply 30 by 14 to get 420 and add 450 to it to get 870

The equation relating the total amount of money 'S' in the savings account to the number of weeks 'W' that Ryan has been saving is S = 450 + 30W. By substituting W with 14 in this equation, we find that Ryan will have $870 in his savings account after 14 weeks.

In this case, Ryan had started with $450 in his savings account. His weekly contribution to the savings is $30. So the total amount of money 'S' in the savings account after 'W' weeks could be represented by the equation S = 450 + 30W.

Now, if you want to find out the total amount of money in the savings account after 14 weeks, just substitute W = 14 into the equation. Thus the equation becomes S = 450 + 30*14 = 450 + 420 = $870.

Therefore, Ryan will have $870 in his savings account after 14 weeks.

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[tex]\dfrac{1}{3}+x=\dfrac{1}{12}\\\\\dfrac{4}{12}+x=\dfrac{1}{12}\\\\x=-\dfrac{3}{12}=-\dfrac{1}{4}[/tex]

Answer:

1/4

Step-by-step explanation:

The LCD here is 12.  Subtract 1/3, or 4/12, from 7/12, to obtain the missing fraction.  7/12 - 4/12 = 3/12, or 1/4.  The missing fraction is 1/4.

Answer:

3x+4 Ralph is currently 12 years old.

Step-by-step explanation:

You can find the equation by reading the scenario given. When you read it, it says that Ralph is 3 times as old as Sara and since her current age is going to be used to represent x you will first get 3x. That automatically eliminates the second and third choice given. It then says the equation is for Ralph's age in four years which means to add four to the equation. This gives you 3x+4 as your equation.

When something is tripled and then in a few years it is doubled, it is easiest to first try the number that is being added. So in this case the number is four. When you multiply 4 by 3 you get 12. If Sara is 4 she'll turn eight in four years and if Ralph is 12 he'll turn 16 in four years. 16 divided by 2 is 8 which shows you that Ralph is currently 12

Step-by-step explanation:

ΔACX is an isosceles triangle, so ∠AXC = ∠XAC.  We'll call the measure of this angle x°.

∠AXC and ∠BXC are supplementary, so ∠AXC + ∠BXC = 180.  That means ∠BXC = 180 − x.

ΔBXC is an isosceles triangle, so ∠XBC = ∠XCB.  We'll call the measure of this angle y°.

Angles of a triangle add up to 180, so:

y + y + (180 − x) = 180

2y = x

y = x/2

∠ACX and ∠XCB are complementary, so ∠ACX + ∠XCB = 90.

x + y = 90

x + x/2 = 90

3/2 x = 90

x = 60

Therefore, ∠AXC = ∠XAC = 60°.

Answer:

Length = x-5

Step-by-step explanation:

Length= Area/width

Length = x³-5x²+3x-15/ x²+3

Re-arrange the numerator:

Length=x³+3x-5x²-15/x²+3

Take common from the numerator:

Length=x(x²+3) -5(x²+3)/x²+3

Length=(x²+3)(x-5)/x²+3

Length = x-5

Thus the answer is x-5 ....

Answer:

a. x = t, y = -[tex]\frac{3}{2}t[/tex] + [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

The answer is a. x = t, y = -3/2t + 5/2

The parametric equations of the line with the equation 3x + 2y = 5 is mathematically given as

x=t

y = (5-3t)/2

Question Parameter(s):

the line with the equation 3x + 2y = 5.

Generally, the equation for the equation in slope-intercept  is mathematically given as

 y = 3x -5/ 2

Therefore

y = (5-3t)/2

While

x=t

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Answer:

Hi there!

The answer to this question is: C

Farah would packs 10 outfits for a 9 day vacation.

Step-by-step explanation:

It follows the pattern having one more outfit than the number of vacation days

Answer:

Number line graph with closed circle on 30 and shading to the left

Step-by-step explanation:

we know that

The algebraic expression of the phrase " An unknown number x is at most 30" is equal to

[tex]x\leq 30[/tex]

The solution is the interval ------> (-∞,30]

All real numbers less than or equal to 30

Number line graph with closed circle on 30 and shading to the left

see the attached figure

Explanation

Answer

First option: 1/3x = y - 3

Answer:

y = - 34

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = - 51 when x = 3

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{-51}{3}[/tex] = - 17

y = - 17x ← equation of variation

When x = 2, then

y = - 17 × 2 = - 34

Final answer:

To find the value of y when x = 2 in a direct variation relationship, determine the constant of variation first and then substitute the given values to find the unknown.

Explanation:

The relationship given is that y varies directly with x. To find y when x = 2, you can use the direct variation formula.

First, find the constant of variation by using the values given: y = kx. Plug in y = -51 and x = 3 to find k.

Once you have k, solve for y when x = 2 using y = kx.

Therefore, when x = 2, y = -34.

Answer:

B.

Step-by-step explanation:

Let's plug in and find out.

A. y-4<3x-5 with (x,y)=(0,0)

   0-4<3(0)-5

     -4<-5

This is false because -5 is not bigger than -4.

B. y-5<3x-4 with (x,y)=(0,0)

   0-5<3(0)-4

     -5<-4

This is true because -4 is bigger than -5.

C. y+5<3x+4 with (x,y)=(0,0)

   0+5<3(0)+4

       5<4

This is false because 4 is not bigger than 5.

D. y+5<3x-4 with (x,y)=(0,0)

    0+5<3(0)-4

        5<-4

This is false because -4 is not bigger than 5.

The only true inequality I got from plugging in (0,0) for (x,y) was B so that your answer.

Answer:

Nina's rate in miles per hour is 2.7 miles/hour

Nina bikes faster

Step-by-step explanation:

we know that

1 hour=3,600 seconds

1 mile=5,280 feet

Convert feet to miles

63,360 feet=63,360/5,280=12 miles

Convert seconds to hours

3,400 sec=3,400/3,600=0.94 hours

Find Nina's rate in miles per hour

12/0.94=12.7 miles/hour

Sophia's rate in miles per hour is 10 miles/hour

Compare the rates

12.7 miles/hour > 10 miles/hour

therefore

Nina bikes faster

Answer:

12.7 mph

Nina

Step-by-step explanation:

Answer:

25/81

Step-by-step explanation:

1000³ = (10³)³ = 10⁹ = 2⁹ × 5⁹

For a factor to be a perfect square, the exponents must be even.  For example:

2⁰ × 5⁰, 2⁰ × 5², 2² × 5⁰, etc.

There are 5 even exponents between 0 and 9 for each 2 and 5.  So the number of perfect square factors is 5×5 or 25.

The total number of factors is 9×9 or 81.

So the fraction of positive integer factors that are perfect squares is 25/81.

25/81 is the fraction of the positive integer factors of 1000^3,

1000^3 = (10^3)^3 = 10^9 = 2^9 x 5^9

Perfect square factors have even exponents.

There are 5 even exponents between 0 and 9 for each 2 and 5.

Number of perfect square factors: 5x5 =25

Total number of factors: 9x9 =81

Fraction: 25/81

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Answer: OPTION A

Step-by-step explanation:

It is important to remember the "Angle Addition Postulate" in order to solve this exercise.

You have this larger angle:

 [tex]\angle AVB[/tex]

According to the "Angle Addition Postulate", if the point "C"  is in the interior of [tex]\angle AVB[/tex], then the measure of this angle can be obtained by adding the angle [tex]\angle AVC[/tex] and the angle [tex]\angle CVB[/tex].

You can observe in the figure that:

 [tex]m\angle AVC=39\°\\\\\mangle CVB=23\°[/tex]

Then you get that:

[tex]m\angle AVC+m\angle CVB=m\angle AVB\\\\39\°+23\°=62\°[/tex]

Therefore, the correct answer is Option A.

Answer:answer is actually C

Answer:

3x over x+1 MULTIPLIED by 1 over x+1 Letter choice will be A On ingenuity  

Step-by-step explanation:

For this case we must find an expression equivalent to:

[tex]\frac {\frac {3x} {x + 1}} {x + 1}[/tex]

Applying double C we have:

[tex]\frac {3x} {(x + 1) (x + 1)} =\\\frac {3x} {(x + 1) ^ 2}[/tex]

Finally, an equivalent expression is:

[tex]\frac {3x} {(x + 1) ^ 2}[/tex]

Answer:

[tex]\frac {3x} {(x + 1) ^ 2}[/tex]

Answer:

1)3/5=60%

2)7/8=87.5%

3)4/25=16%

4)27/50=54%

fractions

1)50%=0.5

2)34%=0.34

3)56%=0.56

4)331/3%=1.1033

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Answer:

7/15

Step-by-step explanation:

first recognise that 3/3 is a whole pizza and so is 5/5.

Secondly make all the numbers to have the same denominator

So times both denominators of the fractions together; 5x3=15

Now find 1/3 of 15. Do this by dividing 15 by 3. This equals 5.

So 1/3 is equal to 5/15

Now do the same for 1/5. 15 divided by 5, this equals 3.

So 1/5 is equal to 3/15

Now that we know that the whole pizza is 15/15

We minus 1/3 from 15.

15-5=10.  So we now have 10/15 left.

now we know that 'x' is representative of the amount of pizza Tom gave to his bother.

10/15 - 3/15 = x

x = 7/15

So out of the whole pizza (15/15), tom ate 5/15 and was left with 3/15 meaning he gave 7/15 to his brother.

Final answer:

Tom ate 1/3 of the pizza and was left with 1/5 of it, so he gave away 2/15 of the pizza to his brother.

Explanation:

The question is asking which fraction of a pizza Tom gave to his brother. To find out, we know Tom ate 1/3 of the pizza and ended up with 1/5 of it. The fraction that Tom gave his brother is the difference between what he had after eating and what he was left with, thus:

1/3 - 1/5 = (5 - 3) / 15

So, 2/15 of the pizza was given to Tom's brother.

Answer:

Choice C

Step-by-step explanation:

Because,

50 is min

75 is middle

100 is max

The correct data set is {50, 60, 60, 75, 75, 85, 85, 100}

Given,

The box plot with number line titled percent with 50 as the minimum, 60 as quartile 1, 75 as the median, 85 as quartile 3, and 100 as the maximum.

We need to determine the following data sets are represented in the box plot.

Let us segregate the following data set by taking the help of a minimum value.

Now, we require a data set that has a minimum value of 50.

There is only one data set given in the option that is a minimum value of 50.

Thus, data set is {50, 60, 60, 75, 75, 85, 85, 100}.

Cross-checked the above data set with more information that is already given in the question.

We required 60 as quartile 1, 75 as the median, 85 as quartile 3, and 100 as the maximum.

Thus, all the above requirements are fulfilled by the data set {50, 60, 60, 75, 75, 85, 85, 100}.

Hence, the correct data set is {50, 60, 60, 75, 75, 85, 85, 100}

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Answer:

11

Step-by-step explanation:

Ok so we aren't looking to maximize profits which is equivalent to finding the vertex of the parabola.

But we want to know what is the highest number of x so that our we aren't losing money.  We aren't losing money when our profit is 0.

So we are asked to solve P(x)=0 for x and take the highest x of that equation.

[tex]P(x)=0[/tex]

[tex]-10x^2+120x-150=0[/tex]

I'm going to divide both sides by -10 to make the numbers easier to work with later.

[tex]x^2-12x+15=0[/tex]

I'm going to use the quadratic formula.

[tex]x^2-12x+15=0[/tex] when compared to [tex]ax^2+bx+c=0[/tex] gives us [tex]a=1,b=-12,c=15[/tex].

We are going to plug this into our quadratic formula:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].

[tex]x=\frac{12\pm \sqrt{(-12)^2-4(1)(15)}}{2(1)}[/tex]

[tex]x=\frac{12\pm \sqrt{144-60}}{2}[/tex]

[tex]x=\frac{12\pm \sqrt{84}}{2}[/tex]

[tex]x=\frac{12}{2} \pm \frac{\sqrt{84}}{2}[/tex]

[tex]x=6 \pm \frac{\sqrt{84}}{2}[/tex]

I'm ready to put this into my calculator.

The one with the plus gives me 10.5826 approximately.

The one with the minus gives me 1.4174 approximately.

The 10.5826 is the higher number.

So about 11 dollars.

Answer:

C $11

Step-by-step explanation:

If a company found that its monthly profit, P, is  given by P = -10x2 + 120x - 150 where x is the  selling price for each unit of the product, the best estimate of  the maximum price per unit that the company  can charge without losing money is $11.

Answer:

5 jumps

Step-by-step explanation:

Personally I would write it out, although there surely is a formula for it.

3 fall to 2 - 5 fall to 4 - 7 fall to 6 - 10 fall to 9 - 12.

This makes 5 jumps, since once he is out he won't fall back in.

Answer:

-1/8

Step-by-step explanation:

(-2)^-3

The negative exponent means it's the inverse.

1 / ((-2)^3)

-2 cubed is -8.

1 / (-8)

So the simplified answer is -1/8.

Answer:

-8

Step-by-step explanation:

=(-2)^-3

= -2 ×-2 ×-2

= -8

Answer:

[tex]\large\boxed{f(x)=(x+1)^2-4}[/tex]

Step-by-step explanation:

[tex]\text{The vertex form of a quadratic equation}\ f(x)=ax^2+bx+c:\\\\f(x)=a(x-h)^2+k\\\\(h,\ k)-\text{vertex}\\=====================================[/tex]

[tex]\bold{METHOD\ 1:}\\\\\text{convert to the perfect square}\ (a+b)^2=a^2+2ab+b^2\qquad(*)\\\\f(x)=x^2+2x-3=\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-3\\\\f(x)=(x+1)^2-4\\==============================[/tex]

[tex]\bold{METHOD\ 2:}\\\\\text{Use the formulas:}\ h=\dfrac{-b}{2a},\ k=f(k)\\\\f(x)=x^2+2x-3\to a=1,\ b=2,\ c=-3\\\\h=\dfrac{-2}{2(1)}=\dfrac{-2}{2}=-1\\\\k=f(-1)=(-1)^2+2(-1)-3=1-2-3=-4\\\\f(x)=(x-(-1))^2-4=(x+1)^2-4[/tex]

Answer:

4x²+ 3x - 7

Step-by-step explanation:

(4x²-2x)+(5x-7)

= 4x²- 2x + 5x - 7

= 4x²+ 3x - 7

The sum of Expressions is 4x² +3x -7.

An expression is a mathematical statement consisting of variables, constants and mathematical operators.

The sum of the expression  (4x²-2x) and (5x-7) has to be determined

(4x²-2x)+(5x-7)

4x² -2x+5x -7

4x² +3x -7

Therefore, the sum of Expressions is 4x² +3x -7.

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