The function g(x) is defined as g(x) = -2x^2 - 4x + 2 The value of g(-3)

The value of x in the vertical angles is 12.

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.

In other words, vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

Vertically opposite angles are congruent.

Therefore, the vertical angles measures 84 degrees and 8x - 12.

Let's find the value of x using the principle of vertically opposite angles.

Therefore,

84 = 8x - 12

add 12 to both sides of the equation

84 + 12 = 8x - 12 + 12

96 = 8x

divide both sides by 8

x = 96 / 8

x = 12

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Answer:

3=6 5=10 7=14

Step-by-step explanation:

here's how to do it u wwould have to sum (+) up all the ratios then it would give u 15 after then u divide the sum by 15 hen u multiply by ratios .

The measure of ∠C is 121 degrees.

Given that:-

There is a triangle ABC.

m∠A = (x + 6)°

m∠B = (3x - 15)°

m∠C = (5x + 36)°

We have to find the measure of ∠C.

We know that,

The sum of all the angles of a triangle is 180 degrees.

Hence, we can write,

m∠A + m∠B + m∠C = 180 degrees

(x + 6)° + (3x - 15)° +  (5x + 36)° = 180 degrees

(x + 3x + 5x) + (6 - 15 + 36) = 180 degrees

9x + 27 = 180 degrees

9x = 180 - 27

9x = 153 degrees

x = 153/9 degrees

x = 17 degrees

Hence,

The measure of ∠C = 5x + 36 = 5*17 + 36 = 85 + 36 = 121 degrees.

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Dividing 7 and 2 over 3 ÷ negative 3 and 1 over 5 will give a quotient of  negative 2 and 19 over 48

information gotten from the question include

Divide 7 and 2 over 3 ÷ negative 3 and 1 over 5.

Division is a basic mathematical operator that performs the function of sharing

division of fraction is done as follows

7 and 2 over 3

= 7 2/3

= 23/3

negative 3 and 1 over 5.

= -3 1/5

= -16/5

= 23/3 ÷ -16/5

= 23/3 * -5/16

= -115/48

= -2 19/48

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Answer:

with?

Step-by-step explanation:

We want to find the places where the line

2x - 3y = 12

intercepts y-axis and x- axis

When the line intercepts y axis, we know that x=0, we replace it in the equation so we can find y value:

2x - 3y = 12

↓

2 · 0 - 3y = 12

↓

0 - 3y = 12

-3y = 12

y = 12 / -3

y = -4

In the same way, we find the interception with x- axis when y = 0. We find the value of x replacing y by 0 in the equation:

2x - 3y = 12

↓

2x - 3 · 0 = 12

↓

2x - 0 = 12

2x=12

x = 12 / 2

x = 6

We locate both points: y = -4 and x = 6:

Finally, we join the points with a straight line

Answer:

12 ft

Step-by-step explanation:

To find the base (b), you would first need to sketch a right triangle using the following:

a = 9

c = 15

Using the Pythagorean theorem [tex]a^{2} +b^{2} =c^{2}[/tex], you would change it to [tex]c^{2} -a^{2} =b^{2}[/tex]  to fit the question. Next, you would plug in the numbers to the corresponding letter.

[tex]15^{2} -9^{2} =b^{2}[/tex]

[tex]225-81=144^{2}[/tex]

[tex]\sqrt{144} =b[/tex]

[tex]12=b[/tex]

The horizontal distance from the tent pole to the rope along the ground will be equal to 12 feet.

According to the Pythagoras theorem, if a triangle has a straight angle (90 degrees), the hypotenuse's square is equal to the total of its other two sides' squares.

As per the given in the question,

Height of tent pole, p = 9 feet

Height of rope, h = 15 feet

Let the horizontal distance from pole to rope is b.

Use Pythagoras' theorem,

h² = p² + b²

15² = 9² + b²

b² = 225- 81

b = √144

b = 12 feet.

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The domain of the function will be; [0 ∞) and the domain is continuous.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

The number c of calories consumed is a function of the number b bars

eaten is represented by the linear function b = 130c

The domain of the linear function would be [0 ∞).

A whole number or a decimal number may be c.

Any data which can be expressed as a decimal is continuous data.

Therefore, the domain of the function will be; [0 ∞) and the domain is continuous.

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The sample proportion is option(d) i.e, 0.32

What is Proportion?

A proportion is an equation in which two ratios are set equal to each other.

Given,

Number of successful outcomes  = 16

Total number of outcomes = 50

The sample proportion =

Number of successful outcomes / Total number of outcomes

Sample proportion = 16 / 50

                               = 0.32

Hence, the sample proportion is option(d) i.e, 0.32

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[tex]\frac{dx}{dy} = \frac{5}{3}. 4\frac{ft}{s} = \frac{20}{3}\frac{ft}{s}[/tex] is moving at the speed of the shadow

x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole. I assume the man and pole are standing straight up, which means the two cases are similar.

[tex]\frac{y-x}{y} = \frac{6}{15}[/tex]

15(y-x) = 6y

9y = 15x

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

differentiate both sides with respect to t or time.

[tex]\frac{dx}d{y} = \frac{5}{3}\frac{dx}{dt}[/tex]

you know [tex]\frac{dx}{dy} = 4\frac{ft}{s}[/tex] because the man is walking that speed away from the pole. you want to find [tex]\frac{dx}{dy}[/tex] , how fast the tip of the shadow is moving.

that means

[tex]\frac{dx}{dy} = \frac{5}{3}. 4\frac{ft}{s} = \frac{20}{3}\frac{ft}{s}[/tex]

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Answer:

     y

-------------

  x²¹ z⁵

Step-by-step explanation:

 (x⁻⁹ y³ z⁻²)²

-------------------

   x³ y⁵ z

   x⁻¹⁸ y⁶ z⁻⁴

-------------------

   x³ y⁵ z

        y⁶

-------------------

 x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴

      y

-------------------

     x²¹ z⁵

I hope this helps!

After simplification by rule of exponent solution is,

⇒ y /  x²¹ z⁵

We have to given that;

The expression is,

⇒ (x⁻⁹ y³ z⁻²)² /  x³ y⁵ z

Now, We can simplify by rule of exponent as;

⇒ (x⁻⁹ y³ z⁻²)² /  x³ y⁵ z

⇒  x⁻¹⁸ y⁶ z⁻⁴ / x³ y⁵ z

⇒ y⁶ / x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴

⇒ y /  x²¹ z⁵

Thus, After simplification by rule of exponent solution is,

⇒ y /  x²¹ z⁵

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The angle between north and south = 180°. The angle between East and South = 90°. The angle between South and West is 90° and between South and East is also 90°. So the sum of these two angles is equal to 180°. Since these two angles are adjacent to each other so they form a linear pair.

Triangle xyz, z=61 degree, its nearest length If leg an is the missing side and xz=17.3 cm and xy=15.2 cm,

then change the equation to its original form when an is on one side and calculate the square root: a = √(c² - b²)

Leg b is undetermined if. For a missing hypotenuse c, the formula is b = (c2 - a2). c = √(a² + b²)

How do you calculate a triangle's third side?

Different Methods to Determine a Triangle's Third Side?

Use the Pythagorean Theorem while forming a right triangle. Use the isosceles triangle area formula to determine the area of a triangle. Use the law of cosines or the law of sines if you are familiar with some of the angles and other side lengths.

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The order of the outcomes is irrelevant when calculating the total outcomes of an event using combinations. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations.

15 different 2-member committees are possible.

C(6,2) = 6!/(4!2!) = 15.

15 different 2-member committees are possible.

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In order to get the volume of the irregular figure, let's cut it into two regular figures. See the cut below.

First, let's calculate the volume of the upper part.

The dimensions of the upper part are 7cm by 3 cm by 3 cm. Since the shape is a rectangular prism, let's multiply 7, 3, and 3.

Hence, the volume of the upper figure is 63 cm³.

Let's now calculate the volume of the lower figure.

The dimensions of the lower figure are 5cm by 4 cm by 3 cm. Since this is a rectangular prism too, let's multiply the dimensions.

The volume of the lower figure is 60 cm³.

Let's add the volume of the two figures to get the volume of the entire irregular figure.

Therefore, the entire volume of the given irregular figure is 123 cm³.

Answer:

See below.  I added words tro the first question "Is a" so that I could answer it.

Step-by-step explanation:

f(x) = -3x³ + 9x² - 5x + 15

f(x) = -(x-3)(3x² + 5)

x((9-3x)x-5)+15

-3(x-1)[tex]x^{3}[/tex] + 4(x-1) + 16

=======

a) Is a [ghost happy]?

O Yes  Yes, as long as it can haunt.

O No

b) Is x + 1 a factor of f(x)?

O Yes  Yes

No

1 a factor of f(x)?  

Always

c) Is a 3 a factor of f(x)?

O Yes

O No    No, as far as I can see.

ok

Equations : 4x + y = 2 x - y = 3

Equation 1 4x + y = 2 x - y = 3

x y x y

-2 10 -2 -5

-1 6 -1 -4

0 2 0 -3

1 -2 1 -2

2 -6 2 -1

The point where both lines cross is (1, -2) so it is the solution.

Answer:

The missing number is 3.

Step-by-step explanation:

1. For the sake of the equation, let's represent the missing number as y. Then write the equation: 4*7=(4*10)-4*y

2. Follow according to the order of operations, then you should get the result of 28=40-4y

3. Swap -4y and 28 in the equations: 4y=40-28 which goes to 4y=12.

4. Find y by dividing the rest of the equation by 4: y=3

a) (2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex]) in standard form

The number in standard form is 345

explanation:

The given two multiplication of the numbers is :

(2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex])

First we multiply the non exponential terms as shown below

2.3 × 1.5 = 3.45

Now we multiply the exponential terms as shown below

[tex]$10^4[/tex] × [tex]$10^{-2}[/tex] = 100

Now multiplying the exponential and non exponential term we get the number in standard form as shown below

(2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex])  in standard form 345

(3.6 × [tex]10^-5[/tex])÷(1.8 × 10²) in standard form 0.0000002

(8 ×  10^-3) ×  (2 ×  [tex]10^-4[/tex] in standard form  1.6 × [tex]10^-6[/tex]

(6 × 10²)/(3 × 10-5) in standard form 20,00,0000

5.1 × [tex]$10^-1[/tex] in ordinary number is 0.51

(1.7 × [tex]10^4[/tex]) × (8.5x ×[tex]0^-2[/tex]) in standard form  1.445 × 10³.

3.45 x  100 = 345

Therefore, the number in the standard form is 345

b) (3.6 × [tex]10^-5[/tex])÷(1.8 × 10²) in standard form

The number in standard form is 0.0000002

explanation:

By dividing 3.6 by 1.8 we get “2”, hence the above equation becomes,

(2 × [tex]10^-5[/tex]) /[tex]10^2[/tex]

We know that

[tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex]

Therefore the above equation becomes,

2 × [tex]10^-7[/tex]

since the exponent of 10 is negative , therefore 7 zeros are written on the left hand side of the number = 0.0000002

Therefore, the number in the standard form is 0.0000002

c) (8 × [tex]10^-3[/tex]) × (2 × [tex]10^-4[/tex]) in standard form

The number in standard form is 1.6 × [tex]10^-6[/tex]

explanation:

Given the product of scientific notations:

(8 ×  [tex]10^-3[/tex]) ×  (2 ×  [tex]10^-4[/tex])

This can be expressed as:

(8 × 2) ×  ([tex]10^-3[/tex] × [tex]10^-4[/tex])

= 16 ×  [tex]10^-3[/tex]-4

= 16 × [tex]10^-7[/tex]

= 1.6 × [tex]10^1[/tex] × [tex]10^-7[/tex]

= 1.6 × [tex]10^-6[/tex]

Therefore, the number in the standard form is 1.6 × [tex]10^-6[/tex]

d) (6 × 10²)/(3 × 10-5) in standard form

The number in standard form is 20,00,0000

e)  5.1 × 10^-1 as an ordinary number

The ordinary number is 0.51

usual form of 5.1 × [tex]10^1[/tex] is

5.1 ×  1/ [tex]10^1[/tex]

= 5.1/10

= 0.51

Therefore , ordinary number is 0.51

f) (1.7 × [tex]10^4[/tex]) × (8.5 × [tex]10^-2[/tex])  in standard form.

The number in standard form is 1.445 × 10³.

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The answers to the subparts of the arithmetic sequence are shown:

So, the formula is: aₙ = 5 + 3 (n − 1)

So, 5th term or n = 5:

Similarly, the 9th term or n = 9:

Therefore, the answers to the subparts of the arithmetic sequence are shown:

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The correct question is given below:

Consider the arithmetic sequence an = 5 + 3 (n − 1)

a. What are the first 5 terms of the sequence?

b. What is the 9th term in the sequence?

Answer:

[tex] 7^2[/tex]

Step-by-step explanation:

Answer:

7²

Step-by-step explanation:

the product of a number and its multiplicative inverse is equal to 1 , that is

a ×[tex]\frac{1}{a}[/tex] = 1

given

[tex]7^{-2}[/tex] , then multiplicative inverse is [tex]\frac{1}{7^{-2} }[/tex] = 7² and

[tex]7^{-2}[/tex] × 7² = [tex]7^{0}[/tex] = 1

Answer:

see explanation

Step-by-step explanation:

since the dilatation is centred at the origin , then multiply each of the original coordinates by the scale factor of 2

Q (2, 2 ) → Q' (2(2), 2(2) ) → Q' (4, 4 )

P (0, 0 ) → P' (2(0), 2(0) ) → P' (0, 0 )

R (- 2, - 4 ) → R' (2(- 2), 2(- 4) ) → R' (- 4, - 8 )

S (4, - 2 ) → S' (2(4), 2(- 2) ) → S' (8, - 4 )

Answer:

Step-by-step explanation:

The formula is :

(y - y1) = m(x - x1)

the given values are x1 = 19, y1 = -12 and m = slope = -3

putting values

(y + 12)= -3(x-19)

y + 12 = -3x +57

y+ 3x - 35 = 0

This is the required equation.

Investor purchased 50 shares of stock in a company for $40.

So, the total initial amount he invested is

Then the rate of return is:

So, the requied rate of return is 10.0%.

We were told that the salary, t years after 2015 is given by the function,

S(t) = 3100t + 56000

When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2

We would substitute t = 2 into the function and find S(2)

Thus,

S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200

When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5

We would substitute t = 2 into the function and find S(2)

Thus,

S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500

Thus, we can say that

when

x1 = 2, y1 = 62200

when x2 = 5, y2 = 71500

Recall,

slope or average rate of change = (y2 - y1)/(x2 - x1)

average rate of change = (71500 - 62200)/(5 - 2) = 9300/3

average rate of change = 3100

The last option is correct

Let:

A = Rolling an odd number

B = Rolling a 5

N = Number of possible outcomes

so:

The most appropriate choice for exponent will be given by-

Fourth option is correct

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2\times 2\times 2 \times 2[/tex], here, 2 is multiplied by itself 4 times.

If  [tex]a^m = a\times a\times a \times.....\times a[/tex] (m times), a is the base and m is the index.

The laws of index are

[tex]a^m \times a^n = a^{m + n}\\\\\frac{a^m}{a^n} = a^{m-n}\\\\a^0 = 1\\\\(a^m)^n = a^{mn}\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\a^mb^m = (ab)^m[/tex]

Here,

For first option

[tex]\frac{4^{11}}{4^{14}}\\\frac{1}{4^{14 - 11}}\\\frac{1}{4^3}\\\frac{1}{64} < 1[/tex]

For second option

[tex](5^4)^2 \times 5^{-11}\\5^8 \times 5^{-11}\\5^{8-11}\\5^{-3}\\(\frac{1}{5})^3\\\frac{1}{125} < 1[/tex]

For the third option,

[tex](2^3)^{-2}\\2^{-6}\\(\frac{1}{2})^6\\\frac{1}{64} < 1[/tex]

For the fourth option
[tex]\frac{(3^5)^2}{3^4}[/tex]

[tex]\frac{3^{10}}{3^4}\\3^{10 - 4}\\3^6\\ 729 > 1[/tex]

Fourth option does not have an expression greater than 1

Fourth option is correct.

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The coordinates of (6, -4) after a reflection in the line x = 2 are:

(-4, -4)

If we have a point (x, y) and we do a reflection in the line x = a, the new coordinates of the point will be:

(a - x, y)

In this case, we have (6, -4) and the line of reflection is x = 2, then the coordinates after the reflection are:

(2 - 6, -4) = (-4, -4)

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Rainfall anually table data

Then

Option A)

Half of the data are between 6 and 18

TRUE , because there are 8/2 = 4 data in the box plot

Option B)

Data point 27 ,could be an outlier

FALSE, because 27 is a black point. It means it belongs, is not out

Option C)

More points between 6,9 that between 9,18

FALSe,. Area between 6,9. Is smaller than area between 9,18

Option D)

Data are less spread out to the left

TRUE, because box plot is ubicated at left

Option E)

Only one data point is less than 6

TRUE, is data point 3