explain why the sum of two angles of any triangle always equals the exterior angle of the third.

Answer:

d

Step-by-step explanation:

Answer:

Down below

Step-by-step explanation:

150 - (2 + x)^3

150 - (2 + 2)^3

150 - (4)^3

150 - 64

= 86

I would check my math but I believe this is correct.

Answer:

86

150-(2+x)^3

⇒ x = 2

2 + 2 = 4

4^3(4 • 4 • 4) = 64

150 - 64 = 86

Answer:

Complete the following statements.

The functions f and g have the same axis of symmetry.

The y-intercept of f is greater than the y-intercept of g.

Over the interval [-6, -3], the average rate of change of f is less than the average rate of change of g.

Step-by-step explanation:

speed = distance/time

we know the speed and the time (11:45am to 1:45pm = 2 hours).

distance = speed × time = 56 m/h × 2 h = 112 miles

The expressions equivalent to kara's expression are 0.7p and p-0.3p

Discount price expression = p(1 - 0.3)

= p - 0.3p

= 0.7p

Check for equivalent expression

p - 0.3

Not equivalent

1 - 0.3p

Not equivalent

0.7p

Equivalent

p - 0.3p

Equivalent

1.3p

Not equivalent

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Answer:

  200 miles

Step-by-step explanation:

Each inch represents 50 miles, so 4 times 1 inch will represent 4 times 50 miles.

  4(1 in) ⇔ 4(50 mi)

  4 in ⇔ 200 mi

It is about 200 miles from Chelsea to New York City according to the map.

Answer:

x=3, Aly is correct.

Step-by-step explanation:

a. angle YWZ

b. ZY = 9

c. the triangles are congruent so 7x-20=2x-5, 5x=15, and x=3

Answer & step-by-step explanation:

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign. As you can clearly see here, there is no equal sign connecting anything here, thus, it is an expression.

Because for it to be called an equation you need to have the equal symbol (=) comparing two epressions.

Example of expression:

 2x - 4y + 14

Example of equation:

   -3y - 2 = -2x - 8

⇔ -3y = -2x + 6

⇔ -y = -[tex]\frac{2}{3}[/tex]x + 2

⇔ y = [tex]\frac{2}{3}[/tex]x - 2

Answer:

G = 1.60 x 1.5, G = 1.5 x 1.60, and G ÷ 1.5 = 1.60

Step-by-step explanation:

^ ^

original equation

[tex]\frac{x}{2}-\frac{3x}{4}+\frac{x}{6}=-\frac{2}{3}[/tex]

multiply by lcd

[tex]12(\frac{x}{2})-12(\frac{3x}{4})+12(\frac{x}{6}) =-12(\frac{2}{3})\\\\6x-9x+2x=-8[/tex]

isolate for x

[tex]-1x=-8\\\\x=8[/tex]

verify

[tex]\frac{8}{2}-\frac{3(8)}{4}+\frac{8}{6}=-\frac{2}{3}\\\\4-6+\frac{4}{3}=-\frac{2}{3}\\\\4-2+\frac{4}{3}=-\frac{2}{3}\\\\-\frac{2}{3}=-\frac{2}{3}\\\\LS=RS[/tex]

Answer:

-4 and 7

Step-by-step explanation:

-4 + 7 = 3

-4•7 = -28

The equation k(x) = x^2 is quadratic equation, and the value of n in p (x) = k (x) + n is -6

The equations are given as:

k(x) = x^2

p (x) = k (x) + n

From the graph, we can see that the graph of k(x) is shifted down by 6 units.

This means that the equation of p(x) is

p (x) = k (x) - 6

By comparison;

n = -6

Hence, the value of n in p (x) = k (x) + n is -6

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Answer:

Step-by-step explanation:

In the question, there's an quadrilateral whose sum of all exterior angle is 360°.

140° + 34° + 56° + x = 360°

➝ 230° + x = 360°

➝ x = 360° - 230°

➝ x = 130°

Thus, The value of x is 130°.

Answer:

60 ft

Step-by-step explanation:

3 times 20 is 60 ft so there is your answer

Answer:

C

Step-by-step explanation:

Diameter is 3 feet, and the radius is half the diameter.

Circumference

Distance travelled in 20 rotations

3x + 2y=-10 equation 1

y=-x -4 equation 2

use the substitution method of elimination to get the answer to the question.

*using substitution

substitute equation 2 in one and we get

3x +2(-x-4)=-10

3x- 2x-8=-10

x=-2 and y=-2

Answer:

B

Answer:  Choice A

(-2, -2)

=============================================================

Explanation:

I'll use the substitution method to solve this system.

Replace y in the first equation with -x-4. This is because y = -x-4 is mentioned in the second equation.

So,

3x + 2y = -10

3x + 2( y ) = -10

3x + 2( -x-4 ) = -10 .... substitution

3x - 2x - 8 = -10

x - 8 = -10

x = -10+8

x = -2

Then use this to find y

y = -x-4

y = -(x) - 4

y = -(-2) - 4

y = 2 - 4

y = -2

We have x = -2 and y = -2 pair up together

They form the ordered pair solution (x, y) = (-2, -2)

This shows why Choice A is the answer.

Another way to see this is to graph each equation given using a tool like Desmos. It's a free graphing app.

See below.

The two lines intersect at (-2, -2) which is the solution.

The roots of the equation [tex]x^{2}[/tex]-15x +2 =0 are 14.865 and 0.135

Completing the square method is one of the methods to find the roots of the given quadratic equation.

Given equation is:

[tex]x^{2}[/tex]-15x +2 =0

Using Completing the Square method we have

[tex]x^{2}[/tex]-15x +2 + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] =0

Now,

[tex]x^{2}[/tex]-15x + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] +2=0

or, [tex][x-(\frac{15}{2})]^{2}[/tex] - 225/4 +2 =0

or,  [tex][x-(\frac{15}{2})]^{2}[/tex] -217*4 =0

or,  [tex][x-(\frac{15}{2})]^{2}[/tex] = 217/4

or,  [tex]x[/tex] = [tex]\pm \frac{14.73}{2} + \frac{15}{2}[/tex]

or, [tex]x_1[/tex]= 14.865, [tex]x_2[/tex]= 0.135

Thus, the roots of the quadratic equation are: 14.865 and 0.135

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Answer:

first one is the valid probability distribution

Answer:

1) x² + x

2) Check Below.

Explanation:

Hence sequence can be created:

2, 6, 12

Find difference:

2, 6, 12

 4   6

    2

Find Equation:

Then,

Then,

So Equation:

With Step Increasing, The step number multiplies the step number and plus the step number. That is the number of squares.

Step-by-step explanation:

1 min 4 cals

60 cals how many mins?

1min. 60cals

____. × _______ = 15 mins

4cals. ?mins

we simplify the matter by simplifying 60 with 4 and striking out cals... then we will have 15 on the top right and then we multiply 1 and 15 together at the end we add the mark of the answer which is (min).

Answer:

   41. (2) x² - 3x - 4 =0

Step-by-step explanation:

Question 41

Standard form of polynomial

Answer:

(2)  [tex]x^2-3x-4=0[/tex]

Step-by-step explanation:

Standard form of a quadratic equation:  [tex]ax^2+bx+c=0[/tex]

When factoring a quadratic (finding the roots) we find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], then rewrite [tex]b[/tex] as the sum of these two numbers.

So if the roots sum to 3 and multiply to -4, then the two numbers would be 4 and -1.

[tex]\implies b=1+-4=-3[/tex]

[tex]\implies ac=1 \cdot -4[/tex]

As there the leading coefficient is 1, [tex]c=-4[/tex].  

Therefore, the equation would be:  [tex]x^2-3x-4=0[/tex]

Proof

Factor  [tex]x^2-3x-4=0[/tex]

Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].

The two numbers that multiply to -4 and sum to -3 are:  -4 and 1.

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies x^2-4x+x-4=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies x(x-4)+1(x-4)=0[/tex]

Factor out the common term  [tex](x-4)[/tex]:

[tex]\implies (x+1)(x-4)=0[/tex]

Therefore, the roots are:  

[tex](x+1)=0 \implies x=-1[/tex]

[tex](x-4)=0 \implies x=4[/tex]

So the sum of the roots is:  -1 + 4 = 3

And the product of the roots is:  -1 × 4 = -4

Thereby proving that  [tex]x^2-3x-4=0[/tex]  has roots whose sum is 3 and whose product is -4.

Answer:

531,441

Step-by-step explanation:

3^2=9

9^6=531,441

Answer:

[tex] \sqrt{ {2}^{6 } } = 27 if thats what you meant here is another answer{ {2}^{6} = 64[/tex]

The answer is:

(-2/9, 35/9) in rounded decimal form is (-0.22, 3.89)

x = - 2 / 9 which in decimal form as well as rounded is -0.22

y = 35 / 9 which in decimal form as well as rounded is 3.89

Hope this helps...

Answer:

here is the required answer hope it help u

Step-by-step explanation:

−2(−5n+6)+5(2−7n)

10n-12+10-35n

-25n-2

Answer:

[tex]x\approx-0.7149[/tex]

Step-by-step explanation:

[tex]\displaystyle 6^{x+2}=10\\\\\log_6(6^{x+2})=\log_6(10)\\\\x+2=\frac{\log(10)}{\log(6)}\\\\x+2\approx1.2851\\\\x\approx-0.7149[/tex]

Recall that the change of base formula is [tex]\displaystyle \log_a(b)=\frac{\log(b)}{\log(a)}[/tex]

Answer:

22 pounds of watermelon

Step-by-step explanation:

First find cost per pound
19.60/8=2.45
$2.45 per pound
Then divide $53.90 by $2.45 to determine how many pounds you can buy
53.90/2.45=22
22 pounds of watermelon

Answer:

4

Step-by-step explanation:

Mean is another way to say the average of a set of numbers. To find the average you need to add all the numbers in the set together, and then divide by the amount of numbers that where given.

In this case:

6 + 8 + 2 + 0 + 4 + 5 + 3 = 28

there are 7 numbers given in the set, so you divide 28 by 7 to get your mean.

28 / 7 = 4

Answer:

4

Step-by-step explanation:

To find the mean of a set of numbers, you add up all the numbers and then divide them by the amount of numbers there are.

So, let's add up these numbers.

6 + 8 + 2 + 0 + 4 + 5 + 3 = 28

Now, there are a total of 7 numbers, so we divide 28 by 7.

28 / 7 = 4

Therefore, the mean of this data set is 4. I hope this helps! Have a lovely day!!

The -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

5⁻³ = 1/5³ = 1/125

-5⁻³ = -1/5³ = -1/125

(-5⁻³)⁻¹ = (-1/5³)⁻¹ = (-1/125)⁻¹ = -125

(-5⁻³)⁰ = 1   [tex]\rm (a^0 = 1)[/tex]

Thus, the -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.

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Answer:

[tex]\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}[/tex]

[tex]\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}[/tex]

[tex]\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}[/tex]

[tex]\sf{4)\ \left(-5^{-3}\right)^{0}=1[/tex]

Step-by-step explanation:

Exponent Property Rules:

⟹ Zero Exponent Property - ex: x⁰ = 1

An integer (excluding 0) with an exponent of zero equals one.

⟹ Negative Exponent Property - ex: x⁻ⁿ = [tex]{\dfrac{1}{x^n}[/tex]

Any number raised to a negative power is equivalent to the reciprocal of the number's positive exponent.

⟹ Power of Product Property - ex: (xy)ⁿ = xⁿ × yⁿ

To find the power of a product, multiply the power of each factor.

[tex]\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}[/tex]

[tex]\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}[/tex]

[tex]\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}[/tex]

[tex]\sf{4)\ \left(-5^{-3}\right)^{0}=1[/tex]

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The slope and length of segment DE in the given triangle are: 0.5, and 1.6 units respectively.

The slope of lines that are parallel to each other are always the same.

Segment DE is parallel to segment BC in triangle ABC.

Since slope of BC is 0.5, slope of DE would also be: 0.5.

Since E and D are the the midpoints of AC and AB respectively, it means that:

Length of DE = 1/2(length of BC)

Length of DE = 1/2(3.2)

Length of DE = 1.6 units

Therefore, slope of DE is: 0.5

Length of DE is: 1.5 units.

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Answer:

C. Slope = 0.5, length = 1.6 units.

Hope this helps!

Step-by-step explanation:

Answer:

262 1/2 liters

Step-by-step explanation:

Remaining water in tank :

Answer:

262.5 litres

Step-by-step explanation:

Water taken from the tank

⇒ 11 × 12.5 litres = 137.5 litres

Water left in tank

⇒ 400 - 137.5 = 262.5 litres