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SOLVING QUADRATIC EQUATIONS BY FACTORING

Answer:

16 and 3

Step-by-step explanation:

Let x and y represent the positive integers. We know that

[tex]x + y = 19[/tex]

[tex]xy = 48[/tex]

Isolate the top equation for the x variable.

[tex]x = 19 - y[/tex]

Substitute into the second equation.

[tex](19 - y)y = 48[/tex]

[tex]19y - {y}^{2} = 48[/tex]

[tex] - {y}^{2} + 19y = 48[/tex]

[tex] - {y}^{2} + 19y - 48[/tex]

[tex](y - 16)(y - 3)[/tex]

So our values are

16 and 3.

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Answer:

Step-by-step explanation:

1 are = 100 m²

Assuming the ten squares are congruent, the area of each square is 160/10 = 16 are

16 are × 100 m²/are = 1600 m²

each side is √1600 = 40 m

The length of side of plot is 40 meters.

The total space occupied by a flat (2-D) surface or shape of an object is known as area.

Draw a square on a piece of paper with a pencil. It has two dimensions. The term "area" refers to the area that the shape occupies on the paper.

Now picture your square as being comprised of smaller unit squares. The number of unit squares required to cover a 2-D shape's total surface area is used to calculate its area.

Given the area of 10 square plot is 160 are,

here 1 are = 100 m²

area of 10 square plot = 160 x 100 = 16,000 m²

area of 1 square plot = 16000/10 = 1600 m²

area of square is "a²"

where a is side of square

area = a² = 1600 m²

a = √1600

a = 40 m

Hence the length of side of each plot is 40 meters.

Learn more about area;

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Answer:

15 years

Step-by-step explanation:

Given the quadratic regression model:

y = 8x² - 40x+6 ; where

y = Number of people attending graduate school ;

x = number of years

The value of x when y = 1206

The equation becomes :

1206 = 8x² - 40x+6

1206 - 6 = 8x² - 40x

1200 = 8x² - 40x

Divide through by 8

150 = x² - 5x

x² - 5x - 150 = 0

x² - 15x + 10x - 150 = 0

x(x - 15) + 10(x - 15)

x - 15 = 0 or x + 10 = 0

x = 15 or x = - 10

Number of years can't be negative,

Hence, x = 15 years

Answer:

y = 3x+2

Step-by-step explanation:

First find the slope using the slope formula

m= (y2-y1)/(x2-x1)

   = ( -1 - -4)/(-1 - -2)

   = (-1 +4)/ (-1 +2)

   = 3/1

  = 3

The slope intercept formula is

y = mx+b where m is the slope and b is the y intercept

y = 3x+b

Using the point (-1,-1) and substituting into the equation

-1 = 3(-1)+b

-1 = -3+b

-1+3 = b

2 = b

y = 3x+2

9514 1404 393

Answer:

  geometric sequence

Step-by-step explanation:

The terms of the sequence have a common ratio of -12/3 = -4, so the sequence is geometric. The general term is ...

  an = 3(-4)^(n-1)

so the sum can be written as ...

  [tex]\displaystyle\sum_{n=0}^\infty3(-4)^n[/tex]

(Note the summation starts at n=0, corresponding to a first term of 3.)

Answer:

30.2

Step-by-step explanation:

We know that quadrilateral KLMN is larger than quadrilateral GHIJ by a scale factor. In order to figure out that scale factor, we must divide a value of a side of KLMN by the value of the side that it corresponds to on GHIJ. One said side is NM, because we know it corresponds to JI on GHIJ. The value of NM is 56, and the value of JI is 13, so to figure out the scale factor, we must divide 56 by 13. We have the scale factor as 56/13, so to figure out the measure of side NM, we must find the side it corresponds to on GHIJ. The side it corresponds to is side JG, which has a value of 7. To get the value of NK, we must multiply the scale factor by 7, and the scale factor is 56/13. 56/13 times 7 is equal to 392/13. Rounding to the nearest tenth, we have the answer as 30.2

Answer:

this and that and that is this

Step-by-step explanation:

step by step

Cost of jacket = $20

No. Of jackets = 1

Let the cost of shirt be x

No of shirts = 5

ATQ

5x + 1(20) = 95

5x + 20 = 95

5x = 95 - 20

5x = 75

x = 75/5

x = 15

Therefore cost of each shirt was $15

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Answer:

110 feet

Step-by-step explanation:

Take x as the width of the field.

4x = 440 feet

x = 440 feet ÷ 4

x = 110 feet

So, the field is 110 feet wide #

Answer:

1.46 dollars per pound

Step-by-step explanation:

Take the total cost and divide by the number of pounds

7.30 dollars / 5 pounds

1.46 dollars per pound

Answer:

1.46

Step-by-step explanation:

Unit rate is the amount for only one pound. To do this, divide 7.30 and 5.

Divide:

7.3 / 5 = 1.46

Each pound is $1.46

Hope this helped.

Answer: Yes you are correct. The answer is choice A

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Explanation:

If you used the z-table, you should find that P(Z < 1) = 0.84 approximately.

So by symmetry, P(Z > -1) = 0.84 approximately as well.

We'll convert the z score z = -1 into its corresponding x score

z = (x-mu)/sigma

-1 = (x-180)/15

-15 = x-180

x-180 = -15

x = -15+180

x = 165

We don't land on any of the answer choices listed, but we get fairly close to 165.2, which is choice A. So you are correct.

I have a feeling that the table you have is probably more accurate than the one I'm using, so it's possible that you'd land exactly on 165.2 when following the steps above.

Answer:

194.9

Step-by-step explanation:

ON EDG

Step-by-step explanation:

We'll find the distance using the all-famous "Distance Formula." You'll probably come across it quite a bit, so it's best to have it written down somewhere.

The Distance Formula: [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

Our points are (8, -3) and (4, -7), so we'll plug in those numbers accordingly.

For reference:

x2 = 4

x1 = 8

y2 = -7

y1 = -3

The calculation:

(substitute)

[tex]\sqrt{(4-8)^2+((-7)-(-3))^2 }[/tex]

(simplify)

[tex]\sqrt{(-4)^2+(-4)^2 }[/tex]

(square things)

[tex]\sqrt{16+16 }[/tex]

(add)

[tex]\sqrt{32}[/tex]

Answer:

[tex]\sqrt{32}[/tex]

Answer:

[tex]\boxed {\boxed {\sf C. \sqrt{32}}}[/tex]

Step-by-step explanation:

The distance between 2 points can be determined with the following formula.

[tex]d= \sqrt{(x_2-x_1)^2+ (y_2-y_1)^2[/tex]

In this formula, (x₁, y₁) and (x₂, y₂) are the 2 points. We want to find the distance between the points (8, -3) and (4, -7). If we match the value with its corresponding variable, then we see:

Substitute the values into the formula.

[tex]d= \sqrt{(4-8)^2+(-7--3)^2[/tex]

Solve inside the parentheses.

[tex]d= \sqrt {(-4)^2+(-4)^2[/tex]

Solve the exponents.

[tex]d= \sqrt {16+16[/tex]

Add.

[tex]d= \sqrt {32}[/tex]

This radical can be simplified, but since it is an answer choice, we can leave it as is.

The distance between the points (8, -3) and (4, -7) is √32 and choice C is correct.

A perfect correlation is denoted by:

A. +1.0 and -1.0

Answer:

(0, 3)

Step-by-step explanation:

y = 3 is the horizontal tangent to y = x^2+3, and passes the parobala at (0, 3)

Answer:

it should be 3

Step-by-step explanation:

I hope this help

Answer:

y=2x+8

Step-by-step explanation:

Hope this helps

Answer:

The answer is "720"

Step-by-step explanation:

The amount of different slates candidates:

[tex]n=\frac{N!}{(N-k)!}\\\\[/tex]

   [tex]=\frac{10!}{(10-3)!}\\\\=\frac{10!}{7!}\\\\=\frac{10\times 9 \times 8 \times 7! }{7!}\\\\=10\times 9 \times 8\\\\=90\times 8\\\\=720[/tex]

Answer:

1.23

Step-by-step explanation:

Answer:

[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]

Step-by-step explanation:

Given

The above table

Required

The discrete probability distribution

The probability of each is calculated as:

[tex]Pr = \frac{Frequency}{Total}[/tex]

Where:

[tex]Total = 2140+ 2853 + 4734 + 4880 + 10715[/tex]

[tex]Total = 25322[/tex]

So, we have:

[tex]P(1) = \frac{2140}{25322} = 0.0845[/tex]

[tex]P(2) = \frac{2853}{25322} = 0.1127[/tex]

[tex]P(3) = \frac{4734}{25322} = 0.1870[/tex]

[tex]P(4) = \frac{4880}{25322} = 0.1927[/tex]

[tex]P(5) = \frac{10715}{25322} = 0.4231[/tex]

So, the discrete probability distribution is:

[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]

9514 1404 393

Answer:

  (5, -6)

Step-by-step explanation:

x-coordinates measure the distance to the right of the y-axis. Moving a point 4 units to the right adds 4 to its x-coordinate.

y-coordinates measure distance up from the x-axis. Moving a point 4 units down subtracts 4 from its y-coordinate.

  (1, -2) +(4, -4) = (1 +4, -2 -4) = (5, -6) . . . . image of translated point

Answer:

I really can't read this

Step-by-step explanation:

Answer:

(-6,0) and (0,-6) are the points on the graph

Answer: SS Error

Step-by-step explanation:

The SS Error refers to the sum of the squares of the deviations of the observations, from their mean. It is simply the total variance from the observations on the study.

In performing a one-way ANOVA, the SS Error measures the variability of the observed values around their respective means and this is done through the summation of the squared differences between each observed value of the response and its corresponding treatment mean.

Answer:

D.

Step-by-step explanation:

sin Y = opposite side / hypotenuse

= 38/63.

Answer:

D

Step-by-step explanation:

[tex]Sin \ y = \frac{opposite \ side}{hypotenuse}\\\\Sin \ y = \frac{38}{63}[/tex]

Answer:

45- s= 21

s= 45- 21

=24

so the answer is 24

Answer:

Consider the angle Ф.

the line opposite to Ф is the perpendicular -> PQ = 5cm

The base is the line with whom the perpendicular has 90° angle -> PR = 12cm

Finally, hypotenuse is the line opposite to the 90° which is QR= 13cm

Answer:

hypotenuse = QR = 13 cm

Perpendicular = PQ = 5 cm

Base = PR = 12 cm

Answer:

Step-by-step explanation:

Use the coordinates (30, 1) and (150, 5) to solve this. Time is always an x thing, while things like distance and weight and value are y things. Put them into the slope formula:

[tex]m(\frac{miles}{sec})=\frac{5-1}{150-30}=\frac{4}{120}=\frac{1}{30}[/tex]  This translates to:

The rocket is ascending at a constant rate of 1 mile every 30 seconds; or, conversely, for every 30 seconds the rocket is flying, it is traveling 1 mile.