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The equation in vertex form would be y = [tex]2(x+5)^{2}[/tex] -6

The vertex of a parabola is the point where the parabola crosses its axis of symmetry.  If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape.  If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.

The standard equation of a parabola is

y=a[tex]x^{2}[/tex]+bx+c .

But the equation for a parabola can also be written in "vertex form":

y= a(x-h)² +k

if the curve passes through (-3, 2) and the coordinates of vertex h = -5, K= -6, then we can find a by simple substitution

2 = a[tex](-3 + 5)^{2}[/tex] - 6

2 = a([tex]2^{2}[/tex]) - 6

2 = 4a - 6

collecting like terms

4a = 2 + 6

4a = 8

dividing both sides by 4

a = 8/4

a = 2.

So the equation of parabola in vertex form is y = 2[tex](x+5)^{2}[/tex] - 6

In conclusion, the equation of parabola in vertex form is 2[tex](x+5)^{2}[/tex] - 6

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Answer:

1/2 teaspoon of salt per 1 teaspoon of baking soda.

Step-by-step explanation:

If you're starting with 1/2 tsp of baking soda and 1/4 tsp of salt, you can multiply that by two and still have the same ratio of salt to baking soda.

:)

Required correct statement is n+ 8 could be positive or negative or zero.

What is a negative number?

A negative number is any number less than zero. For example, -8 is a number that is seven less than 0. It may seem odd to say that a number is less than 0. After all, we often think that zero means nothing.

Option A: n + 8 is always positive is not correct since n is negative and adding a positive number (8) to a negative number will give a negative or zero result.

Option B: n + 8 is always negative is not correct since adding a positive number (8) to a negative number will give a negative or zero result, not always negative.

Option C: n + 8 cannot be zero is a wrong statement, if we put value of n = -8 then we will get zero as answer.

Option D: n + 8 could be positive or negative or zero is correct since it depends on the value of n.

If n is a large negative number, n + 8 could still be negative. If n is a small negative number or zero, n + 8 could be positive or zero.

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Correct question is "n is a negative number.

Which statement is correct?

Choose only one answer.

A) n +8 is always positive

B) n +8 is always negative

C) n + 8 cannot be zero

D) n+ 8 could be positive or negative or zero"

Answer:

$2940

Step-by-step explanation:

30 percent *4200 =

(30:100)*4200 =

(30*4200):100 =

126000:100 = $1260

4200-1260=$2940

The division of 5.375 divided by 0.25 results to 21.5

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created,

for instance, if 30 students need to be separated into groups of five for a sporting event?

In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome.

Given:

5.375 divided by 0.25

Now, dividing the above decimal

= 5.375/ 0.25

= 5375 x 100 / 25 x 1000

= 215 / 10

= 21.5

Hence, the division results to 21.5

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The set of ordered pairs that represent 90 degrees counter clockwise rotation about he origin is

3) A' (-6, 1) B' (-6, 6) C' (-2, 1)

Rotation is a from of transformation that involves circular movement about an axis.

There two types of rotation

The transformation rule for 90 degrees clockwise rotation is as follows

(x, y) for a scale factor of r → (-y, x)

From the graph the coordinates are read and following the given transformation rule we have

preimage   image

A (1, 6)   →   A' (-6, 1)

B (6, 6)  →  B' (-6, 6)  

C (1, 2)  →   C' (-2, 1)

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The rule for given translation is (x,y)→(x + 3, y - 4).

In mathematics, the phrases translation, rotation, and reflection are all used to describe the change of forms. This refers to a form moving beyond a mirror line or a fixed point. While being translated, rotated, or reflected, the shape doesn't change. The constant rotation of a shape around a fixed point or across the mirror line is known as translation. Rotation defines the way a form moves about a central axis. Shapes can be rotated by a specific number of degrees either clockwise or counterclockwise.

The rule for translation of given figure will be,

We need to move x for 3 units to left and y for 4 units downwards to get the translation, so the rule is:

(x,y)→(x + 3, y - 4).

Therefore, the rule for given translation is (x,y)→(x + 3, y - 4).

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Answer:

B. $1.52 for 8 oz

Step-by-step explanation:

$1.26/6=$0.21

$1.52/8=$0.19

$2.30/10=$0.23

$2.40/12=$0.2

$0.19<$0.2<$0.21<$0.23

" I hoped I helped you : - ) "

Answer:

slope = - [tex]\frac{7}{13}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (9, - 10 ) and (x₂, y₂ ) = (- 4, - 3 )

m = [tex]\frac{-3-(- 10)}{-4-9}[/tex] = [tex]\frac{-3+10}{-13}[/tex] = [tex]\frac{7}{-13}[/tex] = - [tex]\frac{7}{13}[/tex]

The expression below using the MathQuill function is 2x^3+42^3-\sqrt\left(49\right).

Given expression:

= 2x³+42³-√49

Expression:

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

After using MathQuill function:

2x³+42³-√49 = 2x^3+42^3-\sqrt\left(49\right).

Therefore The expression below using the MathQuill function is 2x^3+42^3-\sqrt\left(49\right).

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The number of possible pair that could be chosen for duet is  1540 .

In the question ,

it is given that ,

total number of females in the choir group = 56 women

for duet the number of females that are required = 2 ,

the number of possible pair that can be chosen for the duet = ⁵⁶C₂ ,

⁵⁶C₂ = (56 × 55 × 54!)/2! × (56 - 2)!

= (56 × 55 × 54!)/2! × 54!

cancelling out the common factor 54! , we get

= (56 × 55)/2          .... because 2!= 2

= 28 × 55

= 1540

Therefore , The number of possible pair that could be chosen for duet is  1540 .

The given question is incomplete , the complete question is

56 women makes up an all female choir in a church. Two women are chosen to sing together for a duet. How many possible pair could be chosen for the duet ?

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Answer: The slope is 0

Step-by-step explanation:

Use the slope formula. -5-(-2)/-3-(-3)

-5+2/-3+3=0

Answer:

d) [tex]4x+23=10x-1[/tex]

Step-by-step explanation:

This is an isosceles triangle, which is defined as having two equal sides, and two equal angles corresponding to those sides.

Given this definition, it can be said that [tex]4x+23[/tex] is equal to [tex]10x-1[/tex]. Therefore,

[tex]4x+23=10x-1[/tex]

The average speed for the whole journey is 95.3km/hour

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction.

Average speed = Total distance/total time taken

The distance covered in the first journey is 75km and the time spent is calculated as Distance/speed

= 75/110 = 0.68hour

The time used for the second journey is

= distance/speed

= 7/40 = 0.18 hour

The total time spent = 0.68+0.18 = 0.86 hour

The total distance traveled = 75+7 = 82km

Therefore the average speed = 82/0.86 = 95.3 km/hour.

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Step-by-step explanation:

between the student and the flagpole we create a trapezoid with the line of sight to the top of the flagpole and the ground connection between the student's feet and the flagpole being the other 2 sides.

and between the flagpole and the building we create a similar trapezoid.

the line of sight to the top of the building and the ground connection between the flagpole and the building are the other 2 sides.

since both shapes are created from the same projection (the "projector" is somewhere behind the student on the ground), they are truly and mathematically similar.

that means that the angles of one trapezoid are the same as in the other trapezoid.

and - there must be one constant scale factor between all the sides (or for any other lengths in or on the trapezoids) of one trapezoid to the sides of the other trapezoid.

we know the ground distances and how they relate :

20 ft to 60 ft

that means 20/60 = 1/3

so, any length of the first (smaller) trapezoid is 1/3 of the corresponding length of the second (larger) trapezoid.

so, we know the height of the flagpole (35 ft).

the height of the building must follow the same ratio (scaling factor) as the ground distances.

flagpole height = building height × 1/3

3× flagpole height = building height = 3×35 = 105 ft

the building is 105 ft tall.

The inequality that represents the number of songs and albums that Jorge could download is:

$2*s + $12*a ≤ $50

Here we have the variables:

s = number of songs.

a = number of albums.

Then the total cost can be written as:

$2*s + $12*a

And we know that Jorge has a maximum of $50 to spend, so the total cost can be equal to or smaller than $50, so the inequality is:

$2*s + $12*a ≤ $50

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Answer:the last option

Step-by-step explanation:

Answer:

Step-by-step explanation: the distance is 6 but if you're talking decimal then the distance is 1.4142

Answer:

$712.50

Step-by-step explanation:

.95(750) = 712.5  If they give 5% to the seller, they get to keep 95%

Answer:

Step-by-step explanation:

Correct Answer: C.

First we can see that the slope is negative, meaning the graph is decreasing.

Then we go to the point (-1,0) and go down 2 and 3 right. if that point is on the line, then we know it's correct.

Answer:

The answer to your questions is 96.

Answer: 13g

Step-by-step explanation: because each gram is 1000 milligrams

Answer:

the answer is-7

Step-by-step explanation:

Answer:

Exact form: -31/4

Decimal form: -7.75

Mixed number form: -7 3/4

If  the price of a used car is discounted $200 each week then the grapg will be linearly decreasing in nature

A linear graph can be either increasing, decreasing or constant.

Here the price of the car is being discounted $200 every week, so as the number of weeks increase, the price of the car decreases

So, the graph for this situation will be linearly decreasing.

The slope of this kind of graph is negative/

Therefore, If  the price of a used car is discounted $200 each week then the grapg will be linearly decreasing in nature

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The value of 20,304 using exponents will be 2.0304 × 10⁴.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the value of 20,304 will be:

= 2.0304 × 10000

= 2.0304 × 10⁴.

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Answer:

6.481.

Square Root of 42 in Decimal Form: 6.481.

The 95% confidence interval for the mean weight per apple is calculated and the p value foe that particular interval is 0.1447

There is not sufficient evidence to reject the company's claim.

Z Test of Hypothesis for the Mean

Data

Null Hypothesis m =120

Level of Significance 0.05

Population Standard Deviation 12

Sample Size 49

Sample Mean 122.5

Intermediate Calculations

Standard Error of the Mean 1.7143

Z Test Statistic 1.4583

Two-Tail Test  

Lower Critical Value -1.9600

Upper Critical Value 1.9600

p-Value 0.1447

Do not reject the null hypothesis

Hence, the p value foe that particular interval is 0.1447

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The values of m<4 and m<6 are 160° and 20° respectively

To solve this problem, we need some angle geometry knowledge:

Given that: m<6 = 1/8 m<4

Since m<6 = 1/8 m<4. Thus, m<4 = 8.m<6

m<6+ m<4 =  m<6 + 8.m<6 = 9.m<6    (Algebra)

m<6+ 8.m<__ = 180° will be:

m<6+ 8.m<6 = 180°      

Note: m<6 + m<5 = 180° (angles on a straight line) and m<5 = m<6 (alternate angles)

m<6+ 8.m<6 = 180°

9.m<6 = 180°

m<6 = 180/9 = 20°

m<4 = 8 x m<6

m<4 = 8 x 20° = 160°

Therefore, the values of m<4 = 160° and m<6 = 20°

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Using the theories of quantitative​ variables, we got that Graphical display is the first thing that should be​ done when we are analyzing two quantitative​ variables.

Comparing the Two Quantitative Variables As we did when considering only one variable, we begin with the graphical display. A scatterplot is the most useful display technique for comparing the two quantitative variables. We plot on the y-axis the variable we consider for the response variable and on the x-axis we place the explanatory or the predictor variable.

Hence, When analyzing two quantitative​ variables,  the first thing that should be​ done is Graphical display.

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