a) The quadratic x² - 4x-21 can be written in the form (x + a)² + b
Find the values of a and b.
quadratic formula

By using the fact that EBC and ABE are supplementary angles, we will see that the measure of angle EBF is 106 degrees.

First, we can notice that angles EBC and ABE are supplementary angles, which means that their measures add up to 180°.

Then we can write:

m∠EBC + m∠ABE = 180°

Replacing what we know we get:

3y + 10 + 2y - 20 = 180°

Now we can solve this linear equation for y, we will get:

5y - 10 = 180

5y = 180 + 10

y = 190/5 = 38

Then we have that:

EBC = 3*38 + 10 = 124°

ABE = 2*38 - 20 = 56°

Now, in the image it says that:

ABE = 2b = 56°

then b = 56°/2 = 28°

And ABF = 7b - 24 = 162°

Then:

EBF = ABF - ABE = 162° - 56° = 106°

We conclude that the measure of angle EBF is 106 degrees.

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[tex]\sin^2\left(\frac{\pi }{6}-x \right)\implies \left[ ~~ \sin\left(\frac{\pi }{6}-x \right) ~~ \right]^2 \\\\\\ \stackrel{\textit{\LARGE Chain Rule}}{2\left[ ~~ \sin\left(\frac{\pi }{6}-x \right) ~~ \right]^1 \left[ ~~ \cos\left(\frac{\pi }{6}-x \right) ~~ \right] (-1)}\implies \boxed{-2\sin\left(\frac{\pi }{6}-x \right)\cos\left(\frac{\pi }{6}-x \right)}[/tex]

Answer: -15

Step-by-step explanation:

x=-5

g(-5)=3(-5)

g(-5)=-15

The evaluation of  (2-a)³+(2-b)³+(2-c)³-3(2-a)(2-b)(2-c) is mathematically given as

a^3+3 a b c-b^3-c^3+6 a^2-6 a b-6 a c+6 b^2-6 b c+6 c^2

This is further explained below.

(2-a)^3+(2-b)^3+(2-c)^3-3(2-a)(2-b)(2-c)

Use the Binomial Theorem.

2^3+3 * 2^2(-a)+3*2(-a)^2+(-a)^3 +(2-b)^3+(2-c)^3  -3(2-a)(2-b)(2-c)

8-12 a+6 a^2-a^3+(2-b)^3+(2-c)^3 -3(2-a)(2-b)(2-c)

Use the Binomial Theorem.

8-12 a+6 a^2-a^3+2^3+3 * 2^2(-b)+3 * 2(-b)^2+(-b)^3+(2-c)^3-3(2-a)(2-b)(2-c)

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +(2-c)^3-3(2-a)(2-b)(2-c)

Use the Binomial Theorem.

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+2^3+3 \cdot 2^2(-c)+3 \cdot 2(-c)^2+(-c)^3-3(2-a)(2-b)(2-c)

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +8-12 c+6 c^2-c^3-3(2-a)(2-b)(2-c)

Apply the distributive property.

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3+(-3 * 2-3(-a))(2-b)(2-c)

Multiply -3 by 2 .

&8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3 +(-6-3(-a))(2-b)(2-c)

Multiply -1 by -3.

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +8-12 c+6 c^2-c^3 +(-6+3 a)(2-b)(2-c)

Expand (-6+3 a)(2-b) using the FOIL Method.

Combine the opposite terms in

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3-24+12 c+12 b-6 b c+12 a-6 a c-6 a b+3 abc

8+6 a^2-a^3+8+6 b^2-b^3+8+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 abc

Simplify by adding numbers.

6 a^2-a^3+6 b^2-b^3+24+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 abc

Combine the opposite terms in

6 a^2-a^3+6 b^2-b^3+24+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 a b c

6 a^2-a^3+6 b^2-b^3+6 c^2-c^3-6 b c -6 ac-6 ab+3 abc

Re odrder

a^3+3 a b c-b^3-c^3+6 a^2-6 a b-6 a c+6 b^2-6 b c+6 c^2

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Answer:

2nd power

Step-by-step explanation:

3rd is cubed and 1st is: example 3^1 = 3

square root is √

The ratios are equivalent

Ratio shows the relationship that exists between values. It shows the proportion of one value in another value.

In other words, ratios says how much of one thing there is compared to another thing.

Therefore,

Ratio of peanuts to raisins in the first version = 3 : 2

divide both numbers by 2

1.5 : 1

Ratio of peanuts to raisins in the second version = 4.5 : 3

divide both numbers by 3

1.5 : 1

The ratios of the first and second trail mix are equivalent because they are both 1.5 : 1

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Answer:

r = S/(2πh)

Step-by-step explanation:

S = 2πrh

divided by (2πh)

r = S/(2πh)

The x-intercept of the line is -3

y-intercept: None

From the question, we are to find the y-intercept and x-intercept of the given line

The x-intercept of a line is the point where the line crosses the x-axis on a cartesian plane

The y-intercept of a line is the point where the line crosses the y-axis on a cartesian plane

From the graph, we can observe that the line only crosses the x-axis at the point (-3, 0). That is, at the point where x = -3

Thus,

The x-intercept of the line is -3

The graph does not cut through the y-axis

Thus,

There is no y-intercept

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We get the consecutive numbers as 257 and 258 from the equation 2 x + 1 = 515.

We are given that,

The sum of 2 consecutive numbers is 515.

Consecutive numbers:

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1 and 2 are consecutive numbers, 34 and 35 are also consecutive numbers.

Here let the first number be x

Second number will be:

x + 1

We need to find their sum:

x + x + 1 = 515

2 x + 1 = 515

2 x = 515 - 1

2 x = 514

x = 514 / 2

x = 257

x + 1 = 257 + 1 = 258

Therefore, we get the consecutive numbers as 257 and 258 from the equation 2 x + 1 = 515.

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Answer:

yes

Step-by-step explanation:

-24 is. a whole number so it would be greater

The water in the rectangular pool which has a depth of 3/4 of the pool's depth has a volume of 2250 cubic feet.

If the depth of the water is 3/4 of the depth of the pool and the depth of the pool is 60 inches, then

depth of the water = 3/4 of the depth of the pool

depth of the water = 3/4(60 inches)

depth of the water = 45 inches = 3.75 feet

Volume is defined as the amount of space any object occupies. The volume for a rectangular prism is given by the formula:

V = lwh

where v is the volume

l is the length

w is the width

h is the height

Since the water occupies the inside of the rectangular pool, to solve the volume of the water, use the formula for the volume of a rectangular prism.

V = lwh

V = 20 feet(30 feet)(3.75 feet)

V = 2250 cubic feet

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The simplification of the expression ∛(1/16) × (-54/1) is -27√4/32.

Rationalization is the process of removing a radical as well as imaginary number from of the denominator of an arithmetic fraction. That is, in a fraction, remove the radicals so that the denominator just includes a rational number.

Now the expression is given as;

= ∛(1/16) × (-54/1)

= -54/ ∛16

Taking cube root of 16.

= -54/(4√4)

= -27/2(√4)

By the process of rationalization, multiply the numerator and denominator by the a radical that removes the radical from the denominator which is √4.

= -27×√4/2(√4×√4)

Simplifying the equation;

= -27√4/32

Therefore, the simplification of the expression is -27√4/32.

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Answer:

18.48

7.39 divided by 0.4 is 18.475

rounded to hundredth is 18.48 because 5 or above you round up

Answer:2.909

Step-by-step explanation:hope this helps

Statement a : "The standard deviation measures the variation of the data. If the standard deviation is 0, then there is some variation, so all the data are different" is false.

Statement b : "All the data must be equal to the mean because the sum of the squares of the differences of the data from the mean is 0. So, all the data take the same value" is true

This is a term in statistics that represent the amount of variation in a data set or simply put the spread of the data set. Standard deviation is solved from the mean of the data, that is we get mean first before solving for standard deviation.

From the definition, if all the data is the same then the data should be equal to the mean. If the data is equal to the mean there will be no spread or variation leading to a zero standard deviation.

Hence we can conclude that statement b is true and statement a is false

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The probability that a student who can drive is a college student is 0.2771 or 27.7%

It will be sooved using Baye's theorem -

P(college) = P(C) / 1/5 = 0.2

P(high school students) = P(H) = 4/5 = 0.8

P(college drives) = 0.23

P(high school drives) = 0.15

We have to find, probability that a student who drives is a college student.

That is, we have to find P(C/D).

P(C/D) = P(C ∩ S)/P(S)

Since P(C ∩ S) is an independent event.

P(C ∩ S) = P(C) × P(S)

P(C ∩ S) = 0.2 × 0.23

= 0.046

Using bayes's theorem, we will get

P(C/D) = 0.2771 or 27.7%

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Answer: It is likely B

Step-by-step explanation:

1. Subtract 6:
6 -6 + 3y < 9 -6

2. Divide by 3:
3y/3 < 3/3

3. Simplify:
y < 1

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

1. Subtract 3y:
4y -3y < 3y -3y + 2

2. Simplify:
y < 2

(i) So the answer is likely B

Answer:

Step-by-step explanation:

Since zero of a polynomial function is a value of the variable at which the function's value is 0, 0=4(-1)^3+k(-1)^2-(-1)-1, for the given polynomial q(y)=4y^3+ky^2-y-1

simplifying the above gives: 0= -4+k+0

k=4

Answer:

-5

Step-by-step explanation:

Let's assume the you are moving horizontally along the number line. If you start at -4 and jump to -6, you have made 2 jumps to the left(-4;-5;-6). So halfway between them (the midpoint) is 1 jump (half of 2 jumps).

1 jump to the left of -4.... You land at -5.

Schweet!

The derivative is f'(x) = 5.

The limit definition of the derivative tells us that the derivative of a function is f is

f' (x) = [tex]\lim_{h \to \0} 0[/tex] [tex]\frac{f(x+h)-f(x)}{h}[/tex]

For this, f(x) = 5x and f(x + h) = 5(x + h)

So:

f'(x) = [tex]\lim_{h \to \}0[/tex] [tex]\frac{5(x+h)-5x}{h}[/tex]

        = [tex]\lim_{h \to \}0[/tex] [tex]\frac{5x+5h-5x}{h}[/tex]

       = [tex]\lim_{h \to \}0[/tex] [tex]\frac{5h}{h}[/tex]

       = [tex]\lim_{h \to \}0[/tex] 5

       = 5

So, when f(x) = 5x , we see that its derivative is f'(x) = 5.

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Here is the completed table:

x       y            y/x

3       30          10 / 1

5       50           10 / 1

7        70           10 / 1

9       90             10 / 1

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s). The sign used to represent ratios are :.

The ratio of y to x : change in value of y / change in the value of x

(50 - 30) / (5 - 3) = 20 / 2 = 10 / 1

(70 - 50) / (7 - 5) = 20 / 2 = 10 / 1

(90 - 70) / (9 - 7) = 20 / 2 = 10 / 1

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Answer:

hola

Step-by-step explanation:

Using the vertical angles theorem, the value of x = 2.

Given that angles A and B are vertical angles pair, based on the vertical angles theorem, both angles are congruent to each other.

Therefore:

m<A = m<B [vertical angles theorem]

m<A = (5x + 1)°

m<B = (4x + 3)°

Substitute

(5x + 1)° = (4x + 3)°

Solve for x

5x + 1 = 4x + 3

5x + 1 - 1 = 4x + 3 - 1

5x = 4x + 2

5x - 4x = 4x + 2 - 4x

x = 2

Therefore, using the vertical angles theorem, the value of x = 2.

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The Total amount to pay including the tax will be $132.52

In the given question, For the Total amount, we know that we have to add the Tax rate to the Principal amount. It is mentioned that the Principal amount P = $123.28 and the Tax rate is 7.5%. Firstly we have to calculate what amount of interest is to be charged upon the Principal amount. To calculate Interest we have the formula :

=>  I = (P * R)/100 , where I = Interest, P = Principal Amt, R = Interest Rate

=>  I = (123.28 * 7.5)/100   => I = 9.24

We get Interest amount = $9.24

To calculate the Total amount, We have the formula: T = P + I

where, T = Total Amount, P = Principal Amount, and I = Interest Amount

=>  T = 123.28 + 9.24  => T = 132.52

Hence, the Total Amount is $132.52

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The solution to the system of equations is (-7, 5)

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2x + y = -9

3x + 5y = 4

Make y the subject in 2x + y = -9

So, we have

y = -2x - 9

Substitute y = -2x - 9 in 3x + 5y = 4

So, we have

3x + 5(-2x - 9) = 4

Open the bracket

So, we have

3x - 10x - 45 = 4

Evaluate the like terms

-7x = 49

Divide both sides by -7

x  = -7

Substitute x  = -7 in y = -2x - 9

y = -2(-7) - 9

Evaluate

y = 5

Hence, the solution to the system of equations is (-7, 5)

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Answer:

3/4 x 8 1/2 = 6.375

the image of the point ( 0 , - 9 ) after a translation of right 5 units and down 1 unit will be ( 5 , - 10 ).

We are given a point:

( 0 , - 9 )

We will first translate it to the 5 units right.

So, we get that:

( 0 + 5 , - 9)

= ( 5 , - 9)

Now, we will translate it 1 unit to the down.

So, we get that:

= ( 5 , - 9 - 1)

= ( 5 , - 10 )

Image will become:

( 5 , - 10 )

Therefore, we get that, the image of the point ( 0 , - 9 ) after a translation of right 5 units and down 1 unit will be ( 5 , - 10 ).

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The car with the speed of 50 Km/h travels the fastest.

We have given with three choices for selecting the fastest speed from them. The three choices are

First choice is 50 Km/h.

Second Choice is  car b travels a distance of d kilometers in h hours, based on the equation 55 h = d , h, equals, d.. So from this be can conclude that this car is moving with the speed of (1/55)km/h.

Third choice is  car c travels 135 kilometers in 3 hours. So from this be can conclude that this car is moving with the speed of (135/3) Km/h i.e., 45 Km/h.

So, from the given choices we can conclude that the car with the speed of 50 Km/h travels the fastest.

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