What is the slope of the line that passes through the points (1,3) and (5, -2)?

Recall that (a + b)² = a² + 2ab + b².

Let a = x² and b = y². Then

(x² + y²)² = (x²)² + 2x²y² + (y²)²

⇒   x⁴ + y⁴ = (x² + y²)² - 2 (xy)²

Given that x² + y² = 13 and xy = 6, we have

x⁴ + y⁴ = 13² - 2×6² = 97

Using the triangle sum theorem, the value of angle ACB in the triangle is: B. 50°.

According to the triangle sum theorem, the sum of all the angles in a triangle equals 180 degrees.

90 + 7x - 20 + 4x = 180

70 + 11x = 180

11x = 180 - 70

11x = 110

11x/11 = 110/11

x = 10

m∠ACB = 7x - 20

Plug in the value of x

m∠ACB = 7(10) - 20

m∠ACB = 50° (option B).

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Answer:

3

Step-by-step explanation:

got it on edge

Answer:

x = -2

Step-by-step explanation:

[tex]2x(x-5)-x(3+2x) = 26\\2x^{2} -10x-3x-2x^{2} = 26\\-13x=26\\x=\frac{26}{-13} \\=-2[/tex]

Its basically the order of operations, from left to right , evaluate brackets (if possible), then multiplication or division, lastly followed by addition or subtraction.

2x2-10x-3x-2x2=26

Eliminam opusele

reducem termenii

-13x=26

imparte ambele parti

x=-2

Step-by-step explanation:

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3900\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &9 \end{cases} \\\\\\ A=3900\left(1+\frac{0.075}{1}\right)^{1\cdot 9}\implies A=3900(1.075)^9\implies A\approx 7477.23[/tex]

Answer: 5%

Step-by-step explanation:

[tex]6615=6000(1+r)^{2} \\ \\ 1.1025=(1+r)^{2} \\ \\ 1.05=1+r \\ \\ r=0.05=\boxed{5\%}[/tex]

Answer:

=4x³-4x²+4x-3

Step-by-step explanation:

(f+g)(x)=4x³+2x²-6x²+4x-6+3

=4x³-4x²+4x-3

Answer:

[tex]g(x) = \sqrt[4]{x-7},~ x\geq 7[/tex]

Step by step explanation:

[tex]y= f(x) = x^4+7\\\\\text{Replace x with y and solve for y:}\\\\~~~~~~~x = y^4 +7\\\\\implies y^4 = x-7\\\\\implies y = \pm\sqrt[4]{x-7}\\\\ \implies f^{-1}(x) = \pm\sqrt[4]{x-7}[/tex]

The approximate difference in years for Calvin and Makayla is that B. Makayla invests her money 2 years longer.

Given:

We use the compound interest formula,

[tex]A= P(1 + r/t)^t[/tex]

[tex]658.8/400= (1205/1200)^1^2^c[/tex]

c= 10 years approx.

For Makayla,

We use the same formula:

[tex]A= P(1 + r/t)^t\\[/tex]

[tex]613.4/300= (1206/1200)^1^2^m[/tex]

m= 12 years approx.

Hence, the difference in the years would be:

12-10

= 2 years.

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Answer:

Makayla invests her money 2 years longer

Step-by-step explanation:

b on edge

Those two have both two formulas but when dealing with a not-right triangle which is a particular case you use this formula for sines.

[tex]\frac{SinC}{c} =\frac{SinR}{r}[/tex]

Substitute

Note: the capital letters are for the angles and the small letter are for the sides.

But since we used side R and there is no angle to substitute. you will basically have to find it by adding the two angles given and subtracting it by 180, which is a 100.

[tex]\frac{Sin(7)}{1.9} =\frac{Sin100}{x}[/tex]

now you do the butterfly method or cross multiplication method.

[tex]xsin(7)=1.9sin(100)[/tex]

You have to isolate the x

[tex]\frac{xsin(7)}{sin(7)} =\frac{1.9sin(100)}{sin(7)}[/tex]

now cancel and plug the right side of the equation into your calculator and u get the answer for the missing side.

[tex]x= 15.35[/tex] or if u want to round it [tex]15.4[/tex]

<R = 100 and side CK= 15.35 or 15.4

Hope I helped! ^w^

TheOneAndOnlyLara~

Answer:

122x + 37

Step-by-step explanation:

hope this helps u

Answer:

[3×2⁵+13×2]+2³(-2²+3²)-3=

[3×32+26]+2³(-4+9)-3=

[96+26]+2³(5)-3=

122+40-3

162-3=

159...

note:-a×(-b)=+ab

Answer: x = 0, 8

Step-by-step explanation:

x = 0

x - 8 = 0 ⇒ x = 8 (move 8 to the right)

x = 0, 8

Answer:

7. 13.6

8. 19.5

9. 6.5

10. 12.6

Step-by-step explanation:

Recall the three main trig functions

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

( remember hypotenuse = longest side length , opposite = side length opposite of angle , and adjacent = side length thats not the opposite or hypotenuse )

We will use these to solve each problem

7.

We are given :

When dealing with opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in opp = 11 and adj = x as well as given angle 39

tan(39) = 11/x

==> multiply both sides by x

xtan(39) = 11

divide both sides by tan(39)

x = 11/tan(39)

plugging this into a calculator , we get x = 13.6 ( rounded )

8.

We are given :

When dealing with adjacent and hypotenuse we use cos

We have cos = adj / hyp

==> plug in given angle 46 , adj = x and hyp = 28

cos(46) = x/28

==> multiply both sides by 28

x = 28cos(46)

plugging this into a calculator we get  x = 19.5 ( rounded )

9.

We are given :

When dealing with the opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in 51 degrees for angle , opp = 8 and adj = x

tan(51) = 8/x

==> multiply both sides by x

xtan(51) = 8

==> divide both sides by tan(51)

x=8/tan51

plugging this into a calculator we get that x = 6.5 ( rounded )

10.

We are given:

When dealing with the opposite and hypotenuse we use sine

We have sin = opp / hyp

==> plug in angle as 24 , opp = x and hyp = 31

sin(24) = x / 31

==> multiply both sides by 31

31sin(24) = x

plugging this into a calculator we get that x = 12.6 ( rounded )

And we are done!

Let me know if you have any doubts in the comments ! : )

Answer: 60 square units

Step-by-step explanation: i hope that helps buddy :)

Answer:

35%

Step-by-step explanation:

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The percentage of people who supported the home team is 35%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

20% = 20/100 = 1/5

25% = 25/100 = 1/4

We have,

Number of people who attended the basketball game = 1940

Number of people who supported the home team = 679

Number of people who supported the visiting team = 1261

The percentage of people who supported the home team.

= [ Number of people who supported the home team / Total number of people who attended the basketball game ] x 100

= [679 / 1940] x 100

= 67900 / 1940

= 35%

Thus,

The percentage of people who supported the home team is 35%.

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After 10 years, there will be 108 rabbits left in the park.

An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Here, the given equation;

       R = 120 (0.99)ⁿ

where, n is the number of years

n = 10 years (given)

R = 120 (0.99)¹⁰

R = 120 X 0.904

R = 108.52

Thus, After 10 years, there will be 108 rabbits left in the park.

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50 students preferred science...

Explanation:

we can consider the numbers 5 and 4 in the ratio as units

now we need to know how much each unit represent

units = 5 + 4 = 9

my sample = 90 students

each unit = 90/9 = 10 students

so each unit represents 10 students

back to the ratio

who preferred science = 5

who preferred English = 4

Number of students choose Science = 5 * 10 = 50

Answer:

28

Step-by-step explanation:

[tex]sin=\frac{opp}{hyp}[/tex]

[tex]cos = \frac{adj}{hyp}[/tex]

[tex]cos^{-1}\left(\frac{45}{51}\right)[/tex]

which is 28.07 degree

[tex]sin\left(28.07\right)=\frac{x}{51}[/tex]

x= 23.99

23.99+4=h=28

The value of n from the triangle = 2.5

Perimeter of a triangle= a +b+c

Where,

a= n

b= 5n - 6

C= 2n + 1

P= 15

Therefore n

15 = n + 2n + 1 + 5n - 6

15 = 8n-5

8n= 15+5

8n = 20

n= 20/8

n= 2.5

Therefore, the value of n = 2.5

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Answer: See the screenshots below

I'm answering in this format because the questions aren't numbered, so its hard to reference them consistently (so we're both on the same page).

All decimal values are approximate. I decided to round to 4 decimal places, but feel free to use another level of precision.

Answer:

360 people out of 1200 are likely to have red hair.

Step-by-step explanation:

So I just saw that 100 x 120 equals 1200. So I just need to multiply 3 x 120 and I got 360. I think this is how to solve?

Answer:

the answer is  4.979

Step-by-step explanation:

Answer:

The answer is 4.979

Step-by-step explanation:

Answer: -7 < x < 3

Step-by-step explanation:

-21 < 3x < 9

-7 < x < 3

The class which has a greater percent of students who ride the bus is Walter's class

Walter's class:

Percentage of students who ride bus = 14 / 15 × 100

= 0.933 × 100

= 93.3%

Sasha's class:

Percentage of students who ride bus = 11 / 20 × 100

= 0.55 × 20

= 55%

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The area of the triangle will be 3240 square centimeters.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The diagram is given below.

The height of the triangle is 120 cm and the base of the triangle is 54 cm.

Then the area of the triangle will be

Area = 1 / 2 x 120 x 54

Area = 3240 square cm

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Answer:

0.324

Step-by-step explanation:

The area of a 2D form is the amount of space within its perimeter. The correct option is D.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of the L block will be the sum of the area of A and B. Therefore, the area can be written as,

Area of L block = Area of A + Area of B

                          = (7×2) units² + (1 × 5) units²

                          = 14units² + 5units²

                          = 19units²

Hence, the correct option is D.

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Answer:

a) 3x⁴-4x³-8x²-35x-10

Step-by-step explanation:

3x2(x²-3x-1)+5x(x²-3x-1)+10(x²-3x-1)

3x⁴-9x³-3x²+5x³-15x²-5x+10x²-30x-10

3x⁴-9x³+5x³-3x²-15x²+10x²-5x-30x-10

3x⁴-4x³-8x²-35x-10

The expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

An expression is combination of variables, numbers and operators.

The area (w) of Vanessa's patio can be found by multiplying the length and width expressions:

w = (3x² + 5x + 10)(x² – 3x - 1)

Expanding this expression using the distributive property, we get:

w = 3x⁴ - 4x³ - 8x² + 15x³ - 25x² - 10x + 10x² - 30x - 10

Simplifying this expression, we get:

w = 3x⁴ + 11x³ - 15x² - 40x - 10

Hence, the expression  3x⁴ + 11x³ - 15x² - 40x - 10 represents the area (w) of Vanessa's patio

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Answer:

i just need points

Step-by-step explanation:

sorrry ehburbvuygvuywhefe2b yvfb we

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

in our case

baseline × 5 / 2 = 20 in²

baseline × 5 = 40

baseline = 8 in