20) g(a) = a² - 2
h(a) = -3a
Find g(a) + h(a)

Answer: [tex]50^{\circ}[/tex]

Step-by-step explanation:

[tex]m\angle FDE=25^{\circ}+25^{\circ}=50^{\circ}[/tex]

Answer:

C. order

Step-by-step explanation:

The associative property of addition allows you to change the of numbers without affecting the sum.

Answer: Grouping

Step-by-step explanation:

Changing the grouping of addends does not change the sum. For example, ( 2 + 3 ) + 4 = 2 + ( 3 + 4 ) (2 + 3) + 4 = 2 + (3 + 4) (2+3)+4=2+(3+4)left parenthesis, 2, plus, 3, right parenthesis, plus, 4, equals, 2, plus, left parenthesis, 3, plus, 4, right parenthesis.

Answer: the area of triangle PQR is 7.5 square units

Step-by-step explanation:

[tex]\displaystyle\\A_{PQR}=\frac{PR*QS}{2} \\\\1.\ (3,-3)\ \ \ \ \ (5,-2)\\\\PR=\sqrt{(5-3)^2+(-2-(-3))^2}\\\\PR=\sqrt{2^2+(-2+3)^2} \\\\PR=\sqrt{4+1^2} \\\\PR=\sqrt{4+1}\\\\ PR=\sqrt{5} \ units[/tex]

[tex]\diplaystyle\\2.\ (8,7)\ \ \ \ \ (11,1)\\\\QS=\sqrt{(11-8)^2+(1-7)^2} \\\\QS=\sqrt{3^2+(-6)^2} \\\\QS=\sqrt{9+36} \\\\QS=\sqrt{45}\\\\QS=\sqrt{9*5} \\\\QS=\sqrt{3^2*5} \\\\QS=3\sqrt{5}[/tex]

[tex]\displaystyle\\Hence,\\A_{PQR}=\frac{\sqrt{5}*3\sqrt{5} }{2} \\\\A_{PQR}=\frac{(\sqrt{5}*\sqrt{5}) *3 }{2} \\\\A_{PQR}= \frac{5*3}{2}\\\\A_{PQR}=\frac{15}{2}\\\\A_{PQR}=7.5 \ units^2[/tex]

150 - 5.5n= 95 equation to model when the balloon will reach an altitude of 95 meters above the ground.

Two or more expressions with an Equal sign is called as Equation.

Given that,

A hot air balloon is cruising at an altitude of 150 meters above the ground when it begins its descent.

The balloon descends at a rate of 5.5 meters per minute.

We need to write an equation to model when the balloon will reach an altitude of 95 meters above the ground.

The equation is 150 - 5.5n= 95

Hence 150 - 5.5n= 95 equation to model when the balloon will reach an altitude of 95 meters above the ground.

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The next place value on the right should be used to round a number to the closest tenth (the hundredths). Simply take away all the digits to the right if it's 4 or fewer. Remove all the digits to the right after adding 1 to the digit in the tenths position if the number is five or above.

To what decimal place do you round?

Examine the hundredth number to determine the decimal number's nearest tenth. Add one to the tenth value if the number is more than 5. Remove all the numbers that are present after the tenth place if the value is less than 5, but keep the tenth place value in place otherwise. As an illustration, if you want to round up to the nearest.

Triangle Area Solver

A=hbb

2

b Base

Enter value

hb Height

Enter value

γ

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Variance inflation factor can have a value as low as one (absence of multicollinearity). A VIF number greater than 5 or 10 generally denotes collinearity that is problematic.

The variance of bj is not inflated at all if the VIF is 1, which indicates that there is no association between the jth predictor and the other predictor variables.

VIF equal to 1 signifies that there is no correlation between the variables. A VIF of 1 to 5 indicates a moderate correlation between the variables. Variables are highly linked when the VIF is greater than correlated2.

VIF = 1.0 if all independent variables are orthogonal to one another. VIF = infinity if there is perfect correlation.

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Given,

5(2)+15v=00

where v is the number of vans.

Solving,

15v=90

v=6

Thus the correct answer is 6 vans are needed to transport students.

Answer:

d = 4

Step-by-step explanation:

4d - 5 = 11

a) Subtract 5 from both sides.

-5 + 5 = 11 + 5

4d = 16

b) Divide both sides by 4.

4d/4 = 16/4

16/4 = 4

Therefore, you're answer will be 4.

Answer:

Exterior angle = 20 degrees

Interior angle = 160 degrees

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

Explanation:

The phrasing "Each exterior angle measure is one eighth the measure of each interior angle" means,

exterior = (1/8)*(interior)

That rearranges to

interior = 8*(exterior)

Let's say x is the measure of the unknown exterior angle. That makes 8x the measure of the interior angle

The two must add to 180 to form a straight line.

interior + exterior = 180

8x + x = 180

9x = 180

x = 180/9

x = 20 is the measure of the exterior angle

8x = 8*20 = 160 is the measure of the interior angle

Note how 160+20 = 180 to verify our answers.

180°

Considering the definition of an inequality, the correct answer is option C. the inequiality $0.70x + $10.00 < $34.50 symbolize this situation

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

The solution of an inequality is the set of numbers that make the inequality true.

In this case, you know that:

Being "x" the number of cookies Britany can buy, the inequality that expresses the previous relationship is

10 + 0.70x <34.50

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The value of x for the given triangle is 30°.

According to the question,

We have the following information:

We have a triangle.

Three angles of the triangle are x°, 65° and (x+55)°.

We know that the sum of all the three angles of a triangle is 180°.

So, the sum of these angles will be 180°.

Now, adding three angles:

x° + 65° + (x+55)° = 180°

(2x+120)° = 180°

2x = 180-120

2x = 60

x = 60/2 (2 was in the multiplication on the left hand side. So, it is in the division on the left hand side.)

x = 30°

Hence, the value of x in the angles of the given triangle is 30°.

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For the given parallel lines with transversal ,and the pair of interior angles 72° and (7x +24)°, the value of x = 12°.

As given in the question,

Two parallel lines with transversal are given.

72° and (7x +24)°are pair of interior angles

Simplify the given relation to get the value of x we have,

72° + (7x +24)° =180°

⇒ 7x + (72 +24)° =180°

⇒ 7x + 96° = 180°

⇒ 7x = 180° - 96°

⇒ 7x = 84°

⇒ x = 84° /7

⇒ x = 12°

Therefore, for the given parallel lines with transversal ,and the pair of interior angles 72° and (7x +24)°, the value of x = 12°.

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The measure of ∠ A is 44 degrees.

Given that:-

∠ A and ∠ B are complementary angles.

∠ A = (6x +2) degrees

∠ B = (4x + 18) degrees

We have to find the measure of ∠ A.

We know that the sum of two complementary angles is 90 degrees.

Hence, we can write,

(6x + 2) + (4x + 18) = 90

(6x + 4x) + (2 + 18) = 90

10x + 20 = 90

10x = 90 - 20

10x = 70

x = 70/10

x = 7 degrees

Hence,

∠ A = 6*7 + 2 = 42 +2 = 44 degrees.

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Answer:

y > -1

Step-by-step explanation:

8y+9 > 1

   -9    -9

8y > -8

/8    /8

y > -1

We are given a graph and we are asked to determine if it is a function or not. To do that we will use the vertical line test. We will draw a vertical line and if the line touches the graph in more than two places in any given value of "x" then it is not a function. Therefore, the vertical line we get is:

Since the vertical line touches the graph in two axes this means that the given graph is not a function.

Answer:Triangle EFG is dilated by a scale factor of 2 centered at (0, 2) to create triangle E'F'G'. Which statement is true about the dilation? segment EG ≅ segment E prime G prime. The slope of segment EF is the same as the slope of segment E prime H prime.

Step-by-step explanation:

Based on the yards of fabric used by Jan for the quilt squares, the total fabrics used by Jan was 1 ¹ / ₅₆ yards

The yards of fabric used by Jan were 7 / 8 of a yard and 1 / 7 of another yard.

The total yards used by Jan can be found by adding these fractions up. To add both fractions, you first need to find the common denominator of 8 and 7 which is 56.

Then the numerators can be found by dividing 56 by the denominator and then multiplying the numerator by the result.

Fraction 7 / 8 yards:

= 56 / 8 x 7

= 49 / 56

Fraction 1 / 7:

= 56 / 7 x 1

= 8 / 56

The total number of yards used is:
= 49 / 56 + 8 / 56

= 57 / 56

= 1 ¹ / ₅₆ yards

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From the figure, angle ACB anf angle BCD are complementary, that is,

∠ACB + ∠BCD = 90°

Replacing with data

61° + ∠BCD = 90°

∠BCD = 90° - 61°

∠BCD = 29°

From the picture, angle BCD and angle FCE are vertical angles, then they are congruent, which means that:

∠FCE = ∠BCD = 29°

Angle FCA is a right angle, that is, ∠FCA = 90°. Therefore:

∠FCE + ∠FCA = ∠ACE

29° + 90° = ∠ACE

119° = ∠ACE

Answer: slope = [tex]\frac{y}{x}[/tex]

Step-by-step explanation:
Slope means gradient which is given by change in y
                                                                      change in x
on the graph, change in y = 100-0 = 100
                        change in x = 95-45 = 50
so, gradient is 100/50
                      = 2

The oil prospector drills wells with a success probability of 0.15. The probability of finding the first productive well in the third attempt is 0.108375 and the probability that the prospector fails to find productive well in the first 5 attempts is  0.26724 or 26.724%

Let Y be the number of drilling trials on which the prospector will find the first productive well. As Y is a geometric random variable with p=0.15 where p is the probability of being successful on any drilling. Let q = 1- p be the probability of being unsuccessful in drilling a well. q = 1 - 0.15 = 0.85

The probability that the first productive well is found on the third attempt is when outcomes are independent

P(Y=3) = q * q * p = 0.85^2* 0.15 = 0.108375

We want to find the probability that 5 wells are drilled and not a productive one is found. That is we need to find p(Y>5). Y is a binomial random variable with several wells drilled at most as n. Given n=5 and p=0.15, q = 0.85

We know the geometric probability is p(y) = [tex]q^{y-1}[/tex]p

Then corresponding probabilities are added

p(Y≤ 5 ) = p(0) + p(1) +p(2) + p(3) +p(4) +p(5)= 0.73276

Using the complement rule:

p(Y>5) = 1 - p(Y≤5) = 1- 0.73276 = 0.26724 = 26.724 %

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The equation of the line in slope-intercept form would be; y = -12x + 18

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

y = MX +c

To find the slope of a line, we the rate at which the value of 'y' is increasing as we increase the value of 'x' by one unit.

We have been given the point (1,6) and (2,-6)

y-y₁ = m(x-x₁)

m = (-6-6)/(2 -1)

m = -12/1

Now substitute;

y-y₁ = m(x-x₁)

y- 6 = -12(x- 1)

y- 6 = -12x + 12

y = -12x + 18

Hence, the equation of the line in slope-intercept form would be; y = -12x + 18

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a) 10 men are selected at random, the probability their average height is above 72 inches is 0.0122.

b) Exactly one man is selected at random, the probability his average height is above 72 inches is 0.0122.

c) The 80th percentile for the average height of 10 men is 0.0097%.

d) The probability the average height of 10 men is between 70 and 71 inches is 0.13607.

Mean = 69.7 inches

Standard Deviation = 2.8 inches

a) Using normal distribution,

P(Y > 72) = P(Y - mean > 72 - mean)

P(Y > 72) = P((Y - mean ÷ SD) > (72 - mean ÷ SD))

P(Y > 72) = P(Z > (72 - mean ÷ SD))

P(Y > 72) = P(Z > (72 - 69.7 ÷ 2.8))

P(Y > 72) = P(Z > 2.25)

P(Y > 72) = 1 - P(Z  ≤ 2.25)

P(Y > 72) = 0.0122

b) P(man's height is above 72 inches) = 0.0122

c) (80 × 0.0122) ÷ 100

= 0.0097%

d) P( 70 > Y > 71) = P(70 - mean > Y - mean > 71 - mean)

P( 70 > Y > 71) = P((70 - mean ÷ SD) > (Y - mean ÷ SD) > (71 - mean ÷ SD))

P( 70 > Y > 71) = P((70 - mean ÷ SD) > Z > (71 - mean ÷ SD))

P( 70 > Y > 71) = P((70 - 69.7 ÷ 2.8) > Z > (71 - 69.7 ÷ 2.8))

P( 70 > Y > 71) = P(0.107 > Z > 0.464)

P( 70 > Y > 71) = 0.13607

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On the z-score metric, the standard deviation of the behaviour scores is 3.

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Answer: 11

Step-by-step explanation:

[tex]A-B=\{2\}[/tex].

Since there is 1 element in this set, the answer is 1.

The two consecutive odd integers are -7 and -5, then the greater integer is -5.

Let's say that the smaller integer is x and the larger one is y.

Such that if both of these are odd and consecutive, then y = 2 + x.

We can now write:

8*y - x = -33

Replacing y by x + 2 we get:

8*(x + 2) - x = -33

8x + 16 - x = -33

7x = -33 - 16  = -49

x = -49/7 = -7

that is the smaller integer, then the next one is:

y = x + 2 = -7 + 2 = -5

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The required value of the greater integer among the two consecutive odd integers is - 5.

An integer is a real number that has no decimal part.

suppose we have specified a particular odd no. 'O' then the consecutive odd integers are those numbers that arrive after every two numbers.

Given, an integer is subtracted from 8 times the next consecutive odd integer, the difference is -33.

Assuming the first odd integer to be 'n'.

So, the next consecutive odd integers are (n + 2), (n + 4)...

∴ 8(n + 2) - n = - 33.

8n + 16 - n = - 33.

7n = - 33 - 16.

7n = - 49.

n = - 49/7.

n = - 7.

So, the two integers are -7 and (-7 + 2) = - 5.

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The system of quadratic equations obtained on solving general equation of parabola are

a. 5=36a - 6b +c

   -2=64a+8b+c

    3=16a+4b+c

b. 1=289a+17b+c

   -1=81a-9b+c

  2=11025a+105b+c

the equation parabola

the general equation of Parabloa is written as-

y=a[tex]x^{2}[/tex]+bx+c

if the parabola passes through the point. then this point must satisfy the equation of the parabola. so, by putting the value of points we get a set equations-

5=a[tex]6^{2}[/tex]+b(-6)+c

5=36a - 6b +c

and for other two points we get equations

-2=64a+8b+c

and 3=16a+4b+c

and for other three points we get the equations

1=289a+17b+c

-1=81a-9b+c

2=11025a+105b+c

so on solving we get these three set of quadratic equations.

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