The first three steps in determining the solution set of the system of equations algebraically are shown.

y = x2 − x − 3
y = −3x + 5



What are the solutions of this system of equations?

(−2, −1) and (4, 17)
(−2, 11) and (4, −7)
(2, −1) and (−4, 17)
(2, 11) and (−4, −7)

Answer:

x=4

Step-by-step explanation:

sqrt(x+5) = sqrt(x)+1

Square each side

(sqrt(x+5))^2 = (sqrt(x)+1)^2

x+5 = (sqrt(x)+1)^2

Foil

x+5 = (sqrt(x)) ^2 + sqrt(x) + sqrt(x) + 1

x+5 = x + 2 sqrt(x) + 1

Subtract x from each side

5 = 2 sqrt(x) + 1

Subtract 1 from each sdie

4 = 2 sqrt(x)

Square each side

4^2 = (2 sqrt(x))^2

16 = 4 x

Divide by 4

16/4 = 4x/4

4 =x

Check to see if it is extraneous

sqrt(4+5) = sqrt(4)+1

sqrt(9) = sqrt(4) +1

3 = 2+1

3=3

It is a valid solution

Answer:

[tex]\boxed{x=4}[/tex]

Step-by-step explanation:

[tex]\sqrt{x+5} = \sqrt{x}+1[/tex]

Take the square on both sides.

[tex]x+5=( \sqrt{x}+1)^2[/tex]

Expand brackets.

[tex]x+5=( \sqrt{x}+1) ( \sqrt{x}+1)[/tex]

[tex]x+5= \sqrt{x} ( \sqrt{x}+1) +1 ( \sqrt{x}+1)[/tex]

[tex]x+5= x+ \sqrt{x}+ \sqrt{x}+1[/tex]

[tex]x+5= x+ 2 \sqrt{x}+1[/tex]

Subtract 2√x, x, and 5 on both sides.

[tex]x- 2 \sqrt{x} -x= 1-5[/tex]

[tex]-2 \sqrt{x} = -4[/tex]

Cancel negative signs.

[tex]2\sqrt{x} = 4[/tex]

Divide both sides by 2.

[tex]\sqrt{x} =2[/tex]

Square both sides.

[tex]x=2^2[/tex]

[tex]x=4[/tex]

Check if the solution in the equation works.

[tex]\sqrt{x+5} = \sqrt{x}+1[/tex]

Let [tex]x=4[/tex]

[tex]\sqrt{4+5} = \sqrt{4}+1[/tex]

[tex]\sqrt{9} = 2+1[/tex]

[tex]3=3[/tex]

The value of x as 4 works in the equation.

Answer:

Option (A).

Step-by-step explanation:

[tex]8\frac{4}{5}[/tex] is a mixed fraction and can be written as,

[tex]8\frac{4}{5}=8+\frac{4}{5}[/tex] [Combination of a whole number and a fraction]

When we multiply this mixed fraction by 7,

[tex]7\times 8\frac{4}{5}=7\times (8+\frac{4}{5})[/tex]

          [tex]=(7\times 8)+(7\times \frac{4}{5})[/tex] [Distributive property → a(b + c) = a×b + a×c]

          [tex]=56+\frac{28}{5}[/tex]

          [tex]=56+5\frac{3}{5}[/tex]

          [tex]=56+5+\frac{3}{5}[/tex]

          [tex]=61+\frac{3}{5}[/tex]

          [tex]=61\frac{3}{5}[/tex]

Therefore, [tex]7\times 8\frac{4}{5}=61\frac{3}{5}[/tex] will be the answer.

Option (A) will be the correct option.

Answer:

Option C

Step-by-step explanation:

A line has a 2-Fold rotational symmetry because if we rotate the line about 180, The resulting thing will be the same line.

Answer:

[tex]\boxed{\mathrm{C}}[/tex]

Step-by-step explanation:

A line has two-fold rotational symmetry.

The line rotated two times from a central point remains the same.

Or the line rotated 180 degrees from a central point remains the same.

Answer:

1. 31.67 degrees

2. 38 degrees

3.

PNQ  = 117 degrees

LKQ =  102 degrees

4. XYV = 120 degrees

Step-by-step explanation:

1. Using sum of angles of a triangle = 180

angle ACB = 180 - 55.14 - 93.19 = 31.67

2.

FDE = 180-GDE = 180 - 135.11 = 44.89   [angles on a line are supplementary]

FED = HEJ = 97.11         [vertical angles]

DFE = 180-FDE-FED = 180 - 44.89 - 97.11 = 38 degrees

3.

MLN = 180 - 82 = 98   [angles on a line are supplementary]

PNQ = 360 - 67 - 78 - 98 = 117  [sum of exterior angles of a polygon = 360]

LKQ = 180 - 78 = 102  [angles on a line are supplementary]

4.

WXY+YXZ = 180 [angles on a line are supplementary]

=>

3x + x = 180

=>

x = 180/4 = 45

Now solve for XYV

XYV = 360 - 135 - 60 - 45 = 120  [sum of interior angles of quadrilateral = 360]

Note: In the future, please limit the number of problems per question to three.

Answer:36

Step-by-step explanation: first I did

9÷5=1.80 per box.

so then I did 1.80 x 20 which = 36

Answer:

20 boxes cost $36

Step-by-step explanation:

Using proportions,

5 boxes cost 9$

20 boxes cost X$

Cross multiply

X = 9/5 * 20 = 36$

Answer:

18

Step-by-step explanation:

8r - r s

r=6 and s=5

8*6 - 6*5

48 - 30

18

Answer:

you first take the equation 8r-rs and you substitute r=6 s=5, which will look like this 8(6)-6(5).

after that you distribute 8*6 and 6*5

and then you'll get 48-30

finally you subtract the two numbers which will leave you with = 18

Step-by-step explanation:

C. A line has one dimension, length.

E. A plane consists of an infinite set of lines.

Answer:

a   1 : 5

Step-by-step explanation:

Blue mables: 3

green and red marbles: 8 + 7 = 15

then, the radio blue:(green+red) is:

3 : 15

simplified unit rate is:

3/3 = 1

15/3 = 5

then:

3:15

is equal to:

1:5

Answer:

a   1 : 5

Answer:

No there is not  enough evidence to support the claim that the mean expenditure for auto insurance is less than the 2002 amount at the α = 0.05 level of significance

Step-by-step explanation:

Sample Mean = μ1 = $806

Sample Mean = μ2 = $ 781

Standard Deviation= S= σ =39.13

n= 32

Confidence Interval = 95 %

α= 0.05

z∝=± 1.96

We state the null and alternative hypotheses as

H0: μ1 = $806  and Ha: μ1 ≠ $806  two sided tail test

z= μ1 -μ2/σ/√n

z= 806-781/ 39.13/√32

z= 806-781/ 39.13/5.6568

z=806-781/ 6.92

z= 25/6.92

z= 3.613

Z> z∝

3.613 > ± 1.96

No there is not  enough evidence to support the claim that the mean expenditure for auto insurance is less than the 2002 amount at the α = 0.05 level of significance

Step-by-step explanation:

c^2( c^2-10c+25)

=c^4 - 10c^3 + 25c^2

Answer:

[tex]a^2+3\,a\,b-5\,a\,b-15\,b^2=(a-5\,b)\,(a+3\,b)[/tex]

Step-by-step explanation:

Work via factoring by groups:

!) re arrange the terms as follows:

[tex]a^2-5ab+3ab-15b^2[/tex]

then extract the common factor for the first two terms (a), and separately the common factors for the last two terms (3 b):

[tex]a^2-5ab+3ab-15b^2\\a\,(a-5\,b)+3\,b\,(a-5\,b)[/tex]

Now notice that the binomial factor (a-5 b) is in both expressions, so extract it:

[tex]a\,(a-5\,b)+3\,b\,(a-5\,b)\\(a-5\,b)\,(a+3\,b)[/tex]

which is the final factorization.

Answer:

[tex] \boxed{\sf (a + 3b)(a - 5b)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf Grouping \: like \: terms, \\ \sf {a}^{2} + 3ab - 5ab - 15 {b}^{2} = {a}^{2} + (3ab - 5ab) - 15 {b}^{2} : \\ \sf \implies {a}^{2} + (3ab - 5ab) - 15 {b}^{2} \\ \\ \sf 3ab - 5ab = - 2ab : \\ \sf \implies {a}^{2} - 2ab - 15 {b}^{2} \\ \\ \sf The \: factors \: of \: - 15 \: that \: sum \: to \: - 2 \: are \: 3 \: and \: - 5. \\ \\ \sf So, \\ \sf \implies {a}^{2} + (3 - 5)ab - 15 {b}^{2} \\ \\ \sf \implies {a}^{2} + 3ab - 5ab - 15 {b}^{2} \\ \\ \sf \implies a(a + 3b) - 5b(a + 3b) \\ \\ \sf \implies (a + 3b)(a - 5b)[/tex]

Answer:

the Probability of Fair coin = 0.2664=26.64 % and

Probability of Bent coin = 0.7336= 73.36 %

Step by step Explanation:

The fair coin has a 60% probability of coming up heads, same thing with the bent coin , when the coin was thrown up ten times,it comes up heads 8 times,

Here we were told to find the probability fair coin vs. probability bent coin

A)THE FAIR COIN::

The probability of getting Head Coin = 1/2

Probability of getting tail Coin = 1/2

Then the Probability of head 8 times out of 10 can be calculated using combination

= ¹⁰C₈ × (1/2)⁸ ×(1/2)²

= 45/1024

= 0.0439

Therefore, the Probability of head 8 times out of 10= 0.0439

B)BENT COIN

the probability of getting Head Coin = 0.6

= 6/10

= 3/5

NOTE: 60%=0.6

The probability of getting tail Coin = 1 - 3/5

= 2/5

Then, the probability of getting head 8 times out of 10 can be calculated using combination;

= ¹⁰C₈ × (3/5)⁸ × (2/5)²

= 45 × 6561 ×( 4 / 5¹⁰)

= 0.1209

Therefore, the probability of getting head 8 times out of 10 = 0.1209

We can now calculate the Probability of Fair coin

(Probability of head 8 times out of 10 in fair coin )/(Probability of head 8 times out of 10 in fair coin )+(the probability of getting head 8 times out of 10 in bent coin)

= (0.0439 )/(0.0439 + 0.1209)

= 0.2664

Probability of bent coin can as well be calculated as 0.1209 /(0.0439 + 0.1209)

= 0.7336

Therefore, the Probability of Fair coin = 0.2664=26.64 % and

Probability of Bent coin = 0.7336= 73.36 %

Answer:

subtraction; division

Step-by-step explanation:

the first step is to subtract 7/2 from both sides.

the second step is to divide by -2

Answer:

✔ Subtraction

✔ Division

Step-by-step explanation:

It's right in Edgen

Answer:

Step-by-step explanation:

If EG is parallel to the side of the rectangle then lenght of EG is equal to width of rectangle.

If F and H are midpoints of sides of rectangle then FH is parallel to the side of rectangle {wich is perpendicular to the side parallel to EG}. That means the lenght of FH is equal to lenght of rectangle, and FH is perpendicular to EG.

Then FH is sum of hights of triangles EFG and EHG [tex](FH=H_{_{\Delta EFG}}+H_{_{\Delta EHG}})[/tex], and the area of EFGH is sum of areas of triangles EFG and EHG [tex](A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}})[/tex].

So the area of the rectangle:  [tex]\bold{A_{rectangle}=EG\cdot FH}[/tex]

The area of the kite:

                                  [tex]A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}}\\\\A_{kite}=\frac12 EG\cdot H_{_{\Delta EFG}}+\frac12 EG\cdot H_{_{\Delta EHG}}\\\\ A_{kite}=\frac12 EG\cdot (H_{_{\Delta EFG}}+H_{_{\Delta EHG}})\\\\A_{kite}=\frac12 EG\cdot FH\\\\A_{kite}=\frac12 A_{rectangle}[/tex]

No matter the height of the triangles, so no matter the location of the EG

Answer:

11

Step-by-step explanation:

Prime factor: 43659 = 3*3*3*3*7*7*11

Pair: √43659 = √3²×3²×7²×11

11 is odd therefore 11 must be divided by 43659

Answer:  A) 1       B) [tex]\sqrt5[/tex]

Step-by-step explanation:

[tex]A)\quad \dfrac{2\sqrt3}{\sqrt{12}}=\dfrac{2\sqrt3}{2\sqrt3}=1\\\\\\\\B)\quad \dfrac{5\sqrt7}{\sqrt{35}}=\dfrac{5\sqrt7}{\sqrt5\cdot \sqrt7}=\dfrac{5}{\sqrt5}\bigg(\dfrac{\sqrt5}{\sqrt5}\bigg)=\dfrac{5\sqrt5}{5}=\sqrt5[/tex]

First find height using Pythagorean theorem.

[tex]h^2+4^2=13^2\implies h=\sqrt{153}\approx12.37[/tex].

Then use cone surface area formula and compute the result:

[tex]A=\pi r(r+\sqrt{h^2+r^2})\approx\boxed{68\pi}\mathrm{units^2}[/tex].

Hope this helps.

Answer:

3x (x - 2) (x + 3)

Answer 4

Hope this helps :)

The solution is where the two red lines cross. This is the point (3,-4)

If you knew the equation of each red line, you can plug (x,y) = (3,-4) into each equation. You should find the two equations lead to true statements.

Answer:

88

Step-by-step explanation:

mother's age = 12+24

= 36

father's age = 12+40

=52

add the parent age= 36+52

= 88

Answer: (0, -2) & (1, -2)

Step-by-step explanation:

There are an infinite number of coordinates on y = -2.

The coordinates can have any x-value, but must have -2 for the y-value.

Answer:

True

Step-by-step explanation:

Answer:

[tex]\boxed{D = 15.8\ units}[/tex]

Step-by-step explanation:

The coordinates are (0,9) and (-8,-4)

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

D = [tex]\sqrt{(-8-0)^2+(-4-9)^2}[/tex]

D = [tex]\sqrt{(-8)^2+(-13)^2}[/tex]

D = [tex]\sqrt{81+169}[/tex]

D = [tex]\sqrt{250}[/tex]

D = 15.8 units

Answer:

15.3

Step-by-step explanation:

The coordinates are (0,9) and (-8,-4)

Distance of two points formula:

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

Plug in the values.

[tex]D=\sqrt{(-8-0)^2+(-4-9)^2}[/tex]

[tex]D=\sqrt{(-8)^2+(-13)^2}[/tex]

[tex]D=\sqrt{64+169}[/tex]

[tex]D=\sqrt{250}[/tex]

[tex]D= 15.264338...[/tex]

[tex]D \approx 15.3[/tex]

Answer:

x=10 y=12

Step-by-step explanation:

just multiply 15 and 18 by 1/3 because both triangle are similar.

Answer:

x = 10; y = 12

Step-by-step explanation:

find the scale factor ratio using corresponding sides: 9 / 6 = 3/2 so the ratio is 3:2

from large triangle to small triangle you will get:

1. 15 / x

2. 18 / y

to implement the ratio, set the side length ratio equal to the scale factor:

1. [tex]\frac{15}{x}[/tex] = [tex]\frac{3}{2}[/tex]

2. [tex]\frac{18}{y}[/tex] = [tex]\frac{3}{2}[/tex]

cross multiply:

1. 30 = 3x

2. 36 = 3y

divide:

1. x = 10

2. y = 12

Answer:

664

Step-by-step explanation:

651 - - 13

Negative times negative is positive.

651 + 13

Add.

664

Answer:

664

Step-by-step explanation:

651 - (-13)

Do the keep , change , change method

So , it will be :

651 + 13 = 664

Hope this helps and plsss plss amrl as brianliest and THNXX :)

Answer:

125

Step-by-step explanation:

1 x 1  x 1 = 1

5 x 5 x 5 = 125

125 / 1 = 125

125 is your answer

Answer:

B

Step-by-step explanation:

You have to use cos because you are using the adjacent and hypotenuse

So

cos38=x/14

multiply each side by 14

14cos38

Answer:

D.

Step-by-step explanation:

A function is when each x-value has only 1 y-value.

A: When x = 5, there are two values for y.

B: When x = -3, there are two values for y.

C: When x = -4, there are two y-values.

D: Each x-value has exactly one y-value.

So, your answer should be D.

Hope this helps!

Option (D) is accurate since the fourth option's x value has exactly one y value.

D. {(₋7,9), (₋4,₋9), (5,15), (7,19)}

What are functions?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

When we say that a variable quantity y is a function of a variable quantity x, we indicate that y depends on x and that x's value determines what y's value will be. This reliance can be expressed as follows: y = f (x)

Given,

In the first case, y has two different values of 13 and 17, which is not permitted in a function, with the same value of x = 5. The first case is not a function as a result.

For the same value of x = 3 in the second case, y has two different values of 1 and 1, which is not permitted in a function. The second example is therefore not a function.

In the third case, for the same value of x = ₋4, y has two different values of 52 and 16 which is not allowed in a function. Therefore, third case is not a function.

Here, in the fourth situation, no x value is identical and there is only one possible y value.

Hence we get the answer as {(₋7,9), (₋4,₋9), (5,15), (7,19)} which represents the function.

Learn more about "functions" here-

brainly.com/question/10439235

#SPJ2

Answer:

$20, 533.33

Step-by-step explanation:

From the question, we are given the following values

Principal = $20000

Rate = 8% = 0.08

Time( in years) = 120days = 4 months = 4/12 years = 1/3 years

Interest = Principal × Rate × Time

Interest = 20,000 × 0.08× (1/4)

Interest = $533.33

Hence, the proceeds to Aster Corporation are

$20000 + $533.33

= $20,533.33

Answer:

3,500 tons

Step-by-step explanation:

We know that 1,400 tons is 2/5 of the Consolidated Brick Company's output.

This means that 1/5 must be equal to 700 tons if 2/5 is 1,400.

So, we can find the total output by multiplying 700 by 5, since 700 is 1/5 of the total.

700(5) = 3,500 tons