The first three steps in determining the solution set of the system of equations, y = –x2 – 2x + 8 and y = 2x + 11, algebraically are shown in the table.



Which represents the solution(s) of this system of equations?

(–3, –1)
(–3, 5)
(–3, 5) and (–1, 9)
(1, 13) and (3, 20)

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

Answer:

A)2

Step-by-step explanation:

we would like to integrate the following definite Integral:

[tex] \displaystyle \int_{0} ^{1} 5x \sqrt{x} dx[/tex]

use constant integration rule which yields:

[tex] \displaystyle 5\int_{0} ^{1} x \sqrt{x} dx[/tex]

notice that we can rewrite √x using Law of exponent therefore we obtain:

[tex] \displaystyle 5\int_{0} ^{1} x \cdot {x}^{1/2} dx[/tex]

once again use law of exponent which yields:

[tex] \displaystyle 5\int_{0} ^{1} {x}^{ \frac{3}{2} } dx[/tex]

use exponent integration rule which yields;

[tex] \displaystyle 5 \left( \frac{{x}^{ \frac{3}{2} + 1 } }{ \frac{3}{2} + 1} \right) \bigg| _{0} ^{1} [/tex]

simplify which yields:

[tex] \displaystyle 2 {x}^{2} \sqrt{x} \bigg| _{0} ^{1} [/tex]

recall fundamental theorem:

[tex] \displaystyle 2 ( {1}^{2}) (\sqrt{1} ) - 2( {0}^{2} )( \sqrt{0)} [/tex]

simplify:

[tex] \displaystyle 2 [/tex]

hence

our answer is A

Answer:

[tex](60\times 50)\div 3[/tex]

Step-by-step explanation:

We are given that

Length of roll of sod, l=3 feet

Width of roll of sod, b=1 feet

Length of courtyard, L=60 feet

Breadth of courtyard, B=50 feet

Area of rectangle=[tex]Length\times breadth[/tex]

Using the formula

Area of roll of sod=[tex]3\times 1 feet^2[/tex]

Area of roll of sod=3 square feet

Area of courtyard=[tex]60\times 50[/tex] square feet

Number of rolls of sod needed=[tex]\frac{Area\;of\;courtyard}{area\;of\;roll\;of\;sod}[/tex]

Using the formula

Number of rolls of sod needed=[tex]\frac{60\times 50}{3}[/tex]

Number of rolls of sod needed=[tex](60\times 50)\div 3[/tex]

This is required expression which represents the number of rolls of sod needed.

Answer:

She will need 41.22 meters.

Step-by-step explanation:

She knows that one leg of the triangle is 11 meters long and that the angle formed by that leg and the hypotenuse is 50 degrees .

The leg is adjacent to the hypothenuse. We know that the cosine of an angle [tex]\theta[/tex] is given by:

[tex]\cos{\theta} = \frac{l}{h}[/tex]

In which l is the length of the adjacent side and h is the hypothenuse.

Considering that we have [tex]\theta = 50, l = 11[/tex], we can find the hypothenuse.

Looking at a calculator, the cosine of 50 degrees is 0.6428.

So

[tex]0.6428 = \frac{11}{h}[/tex]

[tex]0.6428h = 11[/tex]

[tex]h = \frac{11}{0.6428}[/tex]

[tex]h = 17.11[/tex]

The other leg:

In a right triangle, with legs [tex]l_1[/tex] and [tex]l_2[/tex], and hypothenuse h, the pythagorean theorem states that:

[tex]l_1^2 + l_2^2 = h^2[/tex]

We already have one of the legs and the hypothenuse, so:

[tex]11^2 + l^2 = 17.11^2[/tex]

[tex]l^2 = 17.11^2 - 11^2[/tex]

[tex]l = \sqrt{17.11^2 - 11^2}[/tex]

[tex]l = 13.11[/tex]

How many meters will she need?

This is the perimeter of the garden, which is the sum of its dimensions, of 11 meters, 13.11 meters and 17.11 meters. So

[tex]P = 11 + 13.11 + 17.11 = 41.22[/tex]

She will need 41.22 meters.

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

Answer:

The answer is "This direct variant (-4,2) is part of it".

Step-by-step explanation:

The equation expresses its direct variation relation

[tex]y = mx ........ (1)[/tex]

Where x and y vary directly, and k vary continuously.

Now so the point (4,-2) is in the direct relation of variation, so from equation (1) we are given,[tex]-2 = 4m[/tex]

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

The equation (1) is therefore converted into

[tex]\to y=-\frac{1}{2}x \\\\\to x + 2y = 0 ......... (2)[/tex]

Then only the point (-4,2) satisfies the connection with the four possibilities (2). Therefore (-4,2) is a direct variant of this.

Answer:

measure of angle V + measure angle W = VUF

Answer:

∠ VUF = 94°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles

∠ VUF is an exterior angle of the triangle, then

∠ VUF = 71° + 23° = 94°

Answer:

he is correct

Step-by-step explanation:

to have 2 liters means it has to have 2000 milliliters of solution

(1000milliliters = 1 liter)

2 beaker  * 350+2 beaker * 400 + 1 beaker* 500 =

700+800+500=2000 milliliters

Answer:

$7.58/lb

Step-by-step explanation:

raw roast: $5.99 per lb

deli roast: $2.99 for 100g

We know the price per lb of the raw roast.

Let's find the price per lb of the deli roast.

1 lb = 454 grams

454 grams / 100 grams = 4.54

1 lb is 4.54 times 100 g

If we multiply the price of 100g of deli roast by 4.54, we get teh price per lb.

$2.99/lb * 4.54 = $13.57/lb

raw roast: $5.99/lb

deli roast: $13.57/lb

difference in price of 1 lb: $13.57 - $5.99 = $7.58

Answer: $7.58/lb

Answer:

.01669 $/g or $7.57 $/lb

Step-by-step explanation:

$2.99/100g = .0299 $/g

1 lb = 453.59237 g.

$5.99/453.59237 g= .0132$/g

Answer:

2y² - 4y - 24

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

3(2y - 8) - 2y(5 - y)

Step 2: Simplify

Answer:

The capital is $ 309365.

Step-by-step explanation:

What is the capital that I need, if I want to obtain a profit of $ 9745 in 5 months applying a rate of 6.3?

Let the capital is P.

Simple interest, I =$ 9745

Rate, R = 6.3 %

Time, T = 5 months

Use the formula of the simple interest.  

[tex]9745=\frac{P\times 6.3\times 5}{1200}\\\\P = 309365[/tex]

Answer:

4x - 2

Step-by-step explanation:

Given

- 2x + 3 - (5 - 6x) ← distribute parenthesis by - 1

= - 2x + 3 - 5 + 6x ← collect like terms

= 4x - 2

The expression -2x + 3 – (5 – 6x) simplifies to 4x - 2.

The correct way of simplifying expressions is first solving what are inside the brackets.Then solving divisions then multiplications then additions and last subtractions.This way of solving order has a short name which is BODMAS order.

According to the given question we have to simplify the expression

-2x + 3 – (5 – 6x).

First we'll solve what are inside the brackets.

-2x + 3 - 5 + 6x.  (negative sign distributed to get a positive).

= 4x - 2.

= 2(2x - 1).

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Answer: 3

Step-by-step explanation:

Points (-3,-4) and (6,2) give you slope of (-4-2)/(-3-6)=-6/-9=2/3

Y=2/3x+k. Substitute first point, you get -4=2/3(-3)+k. -4=-2+k, so k=-2. When y=0, x value is the x intercept. 0=2/3x-2, 2/3x=2, so x=3.

Answer:

7[tex]\sqrt{x}[/tex] = 14, D

Step-by-step explanation:

A radical equation is defined by having a variable under a radical sign. This is the only option with a variable (x) under the radical sign. Hence, 7[tex]\sqrt{x}[/tex] = 14 is the correct option.

Answer:

the lines are parallel they are 10 units apart

Step-by-step explanation:

The shortest distance between these two parallel lines is 2.5

Given equations:

3x + 4y + 10 = 0 ----- (1)

3x + 4y + 20 = 0 ---- (20)

To find:

the shortest distance between the two lines

The slope  and y-intercept of the first equation is calculated as;

3x + 4y + 10 = 0

4y = -3x - 10

[tex]y = \frac{-3x}{4} - \frac{10}{4} \\\\y = \frac{-3x}{4} - \frac{5}{2}[/tex]

The slope = -³/₄ and the y-intercept = - ⁵/₂ = - 2.5

The slope  and y-intercept of the second equation is calculated as;

3x + 4y + 20 = 0

4y = -3x  - 20

[tex]y = \frac{-3x}{4} - \frac{20}{4} \\\\y = \frac{-3x}{4} - 5[/tex]

The slope = -³/₄ and the y-intercept = - 5

The two equations have the same slope = -³/₄

This shows that they are parallel with different y-intercepts

The shortest distance between the two lines is at their y-intercepts

The shortest distance between these two lines is calculated as;

[tex]distance = \sqrt{(-5 - (-2.5) )^2} \\\\distance = \sqrt{(-5+ 2.5)^2} \\\\distance = \sqrt{(-2.5)^2 } \\\\distance = \sqrt{6.25} \\\\distance = 2.5[/tex]

Thus, the shortest distance between these two parallel lines is 2.5

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Answer:

Step-by-step explanation:

e) 3√2 (-3√6 -2 -6)

3√2 (-3√6 - 8)

-9√12 - 24√2

-9√(2^2 * 3) - 24√2

-18√3 - 24√2

or

6(-3√3 - 4√2)

f) -5√2 (3 + 2√2 - 6 - 1)

-5√2(-4 + 2√2)

20√2 - 20

or

20(√2 - 1)

Answer:

= 7. 343 × 10^19 ×81

= 1.377 × 10^21

9514 1404 393

Answer:

  B.  log_b(a) - log_b(d)

Step-by-step explanation:

The applicable rule of logarithms is ...

  log(a/b) = log(a) -log(b)

All the logs need to have the same base.

__

Here, the base is 'b', but the rule still applies:

  [tex]\log_b{\dfrac{a}{d}}=\log_b{(a)}-\log_b{(d)}[/tex]

Answer:

Step-by-step explanation:

θ=l/r

where θ is central angle in degrees.

l=length of arc.

r=radius of circle.

6=14/r

6r=14

r=14/6=7/3 =2 1/3 inches.

Answer:

103 is my answer.

Step-by-step explanation:

hope it helps

Step-by-step explanation:

in fraction it comes 36/121

and in decimal.it comes 0.3

Answer:

Step-by-step explanation:

6/11^2 = 6/11 * 6/11 = 36 / 121.

You cannot simplify 36/121

Step-by-step explanation:

Step 1: The factors of -60 that add up to -11 are -15 and 4.

Step 2:

[tex]( 6{x}^{2} - 15x)( 4x - 10)[/tex]

Step 3:

[tex]3x(2x - 5) + 2(2x - 5)[/tex]

[tex](3x + 2)(2x - 5) [/tex]

Answer:

A, B, C, E.

Step-by-step explanation:

.

Answer:

K=30

Step-by-step explanation:

120÷4 = 30

k=30

The value of k for selecting 40 teachers out of 120 is 1 / 3.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that there are 120 teachers in an ABC school and 40 teachers need to be selected,

The value of k will be calculated by the concept of probability as below,

k =  Number of favourable outcomes / Number of sample

k = 40 / 120

k = 1/3

Therefore, the value of k for selecting 40 teachers out of 120 is 1 / 3.

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Answer:

[tex]{ \bf{volume = \pi {r}^{2}h }} \\ = 3.14 \times {7.5}^{2} \times 20 \\ { \tt{volume = 3534.3 \: {cm}^{2} }}[/tex]

Complete question is;

Given a circle with (4. -3) and (2, 1) as the endpoints of the diameter.​ Write the equation of the circle.

Answer:

x² + y² - 6x + 2y + 5 = 0

Step-by-step explanation:

The end points of the diameter are;

(4. -3) and (2, 1).

Thus, the centre coordinates will be the midpoint of the diameter endpoints.

Thus;

Centre coordinates = ((4 + 2)/2), ((-3 + 1)/2) = (3, -1)

Diameter;

d = √(1 - (-3))² + (2 - 4)²)

d = √20

d = 2√5

Radius = ½ × diameter

Thus;

r = ½ × 2√5

r = √5

Equation of a circle is;

(x - a)² + (y - b)² = r²

Where;

(a, b) are coordinates of the centre of the circle

r is radius.

Thus;

(x - 3)² + (y - (-1))² = (√5)²

x² - 6x + 9 + y² + 2y + 1 = 5

x² + y² - 6x + 2y + 10 = 5

x² + y² - 6x + 2y + 10 - 5 = 0

x² + y² - 6x + 2y + 5 = 0

Answer:

In a product like:

a*b = 0

says that one of the two terms (or both) must be zero.

Here we have our equation:

x^2 + 12 = 7x

x^2 + 12 - 7x = 0

Let's try to find an equation like:

(x - a)*(x - b) such that:

(x - a)*(x - b)  = x^2 + 12 - 7x

we get:

x^2 - a*x - b*x  -a*-b = x^2 - 7x + 12

subtracting x^2 in both sides we get:

-(a + b)*x + a*b = -7x + 12

from this, we must have:

-(a + b) = -7

a*b = 12

from the first one, we can see that both a and b must be positive.

Then we only care for the option with positive values, which is x =3 or x = 4

replacing these in both equations, we get:

-(3 + 4) = -7

3*4 = 12

Both of these equations are true, then we can write our quadratic equation as:

(x - 3)*(x - 4) = x^2 + 12 - 7x

The correct option is the last one.

Answer:

d

Step-by-step explanation:

Answer:

4/5

SOH-CAH-TOA

sin = opposite / hypotenuse

Hypotenuse = sqrt(18^2 + 24^2)  = 30

sin 24/30 = 4/5

Step-by-step explanation:

Answer:

The third one i think

Step-by-step explanation:

Since a survey shouldn't be biased or anything.

Answer:

115°

Step-by-step explanation:

in a parallelogram vertically opposite angles are equal.

m∠MNK=m∠KLM=115°