How to solve this geometry?
Step by step solution please.

Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

The solution of the given inequality is h > 4.5 and it is shown by the blue-shaded line in the number line.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

As per the given inequality,

2 > 8 - (4/3)h

Subtract both sides by 2

0 > 8 - 2 - (4/3)h

0 > 6 - (4/3)h

Subtract 6 on both sides,

-6 > -(4/3)h

Multiply by -3/4

-6(-3/4) <-(4/3)(-3/4)h   (since inequality sign changes by multiplying with negative)

h > 18/4

h > 4.5

The plot of this region in the number line is shaded with a blue line.

Hence "The solution of the given inequality is h > 4.5 and it is shown by the blue-shaded line in the number line.".

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Answer:

The ratio of red sweets to yellow sweets is 12.

Step-by-step explanation:

let the number of red sweet = 2x

number of yellow sweet = 3x

according to question:

red sweets + yellow sweets = total sweet

2x +3x = 30

5x = 30

x = 30/5 = 6

red sweet = 2x = 2× 6 = 12

yellow sweet = 3x = 3× 6 = 18

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The integer variable bonus is assigned a value based on the value of the integer variable score

score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

First, we need to analyze the conditions:

score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

Writing the above as programming instructions, we have:

if(score > 100){//This represents the first condition

bonus = 2 * score;

}

else if(score >=50 && score<=100){//This represents the second

bonus = score;

}

else{//This represents the last condition

bonus = 0;

}

Hence, if score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

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Answer:

z= 125 because they are congruent and y = 55 because they are congruent

I hope this is good enough:

If a = 3 and b = 5, find a/(a+b).

\( \bf \frac{a}{a + b} = \\ \\ \bf = \frac{3}{3 + 5} = \\ \\ \bf = \red { \boxed{ \bf \frac{3}{8}} } \)

Answer:

hope it helps...

have a great day!!

Answer:

m = 0

Or Slope intercept form of y = mx+b

y=-5

Step-by-step explanation:

Answer: true

Step-by-step explanation:

The body's displacement on the interval 0 ≤ t ≤ 9 is 56 meters, and the average velocity is 6.22 m/s. The body's speed at t = 0 is 3 m/s, and at t = 9 it is 15 m/s. The acceleration at both endpoints is 2 m/s². The body changes direction at t = 3/2 seconds during the interval 0 ≤ t ≤ 9.

a. To determine the body's displacement on the interval 0 ≤ t ≤ 9, we need to evaluate f(9) - f(0):

Displacement = f(9) - f(0) = (9^2 - 3*9 + 2) - (0^2 - 3*0 + 2) = (81 - 27 + 2) - (0 - 0 + 2) = 56 meters

To determine the average velocity, we divide the displacement by the time interval:

Average velocity = Displacement / Time interval = 56 meters / 9 seconds = 6.22 m/s (rounded to two decimal places)

b. To ]determinine the body's speed at the endpoints of the interval, we calculate the magnitude of the velocity. The velocity is the derivative of the position function:

v(t) = f'(t) = 2t - 3

Speed at t = 0: |v(0)| = |2(0) - 3| = 3 m/s

Speed at t = 9: |v(9)| = |2(9) - 3| = 15 m/s

To determine the acceleration at the endpoints, we take the derivative of the velocity function:

a(t) = v'(t) = 2

Acceleration at t = 0: a(0) = 2 m/s²

Acceleration at t = 9: a(9) = 2 m/s²

c. The body changes direction whenever the velocity changes sign. In this case, we need to find when v(t) = 0:

2t - 3 = 0

2t = 3

t = 3/2

Therefore, the body changes direction at t = 3/2 seconds during the interval 0 ≤ t ≤ 9.

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Answer: 2289.06

Step-by-step explanation:

math expert

Answer:

r = 169.56 in. / 2π ≈ 27 in.

Now we can use the radius to find the area:

Area = πr^2 ≈ π(27 in.)^2 ≈ 2289.06 in^2

So the area of the circular table is approximately 2289.06 square inches, rounded to the nearest hundredth. The answer is option C.

Answer:

do you need the answer or do you already have the answer? you put answer D on there and that confuses me.

Step-by-step explanation:

Answer:hahaha are you just trying to thro some one off

Step-by-step explanation:

(a) The equation z = z^2 does not have a well-defined graph. (b) The equation y² + 2² = 1 + x² represents a cylinder with radius 2 and its axis parallel to the z-axis.

(a) The equation z = z^2 represents a paraboloid.

To sketch the graph of this equation, we can plot some points and observe the shape of the paraboloid. However, it's important to note that the equation z = z^2 is not a well-defined equation as it leads to multiple interpretations and can cause mathematical inconsistencies. The equation implies that z is equal to either 0 or 1, but it does not specify a specific relationship between x, y, and z.

(b) The equation y² + 2² = 1 + x² represents a cylinder.

To sketch the graph of this equation, we can treat it as a three-dimensional equation and interpret it as a cylinder. The equation implies that the sum of the squares of y and 2 is equal to 1 plus the square of x. This equation describes a right circular cylinder with its axis parallel to the z-axis and centered at the origin. The radius of the cylinder is 2, and it extends infinitely in the positive and negative directions along the x-axis. The graph would be a cylinder with circular cross-sections.

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Answer: m= 1/2

Step-by-step explanation:

It rises +3 and shifts right 6, and if simplified gives you 1/2.

The center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

The equation of the circle is given as x² + y² - 32x+24y +396 = 0.

Comparing the given equation with general equation of circle, x² + y² + 2gx + 2fy + c = 0.

The center of circle is C = (-g, -f)

The radius of circle is r = √g² + f² - c

Therefore, from the given equation,

2g = -32

g = -16

2f = 24

f = 12

C( -16, 12)

And the radius is

r = √(-16)² + (12)² - 396

= √256 + 144 -396

=√4

= 2

Hence, the center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

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Is {x}^{3} + { x }^{3} = {x}^{6}: B. No, because you are not multiplying the bases, so exponent rules don't apply.

Simplifying x^{4} × x^{10} by using exponent rules is equal to: C. x^{-6}.

In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;

bⁿ

Where:

the variables b and n represent numerical values or an algebraic expression.

From the information provided, we can logically deduce the following mathematical expression:

Expression = {x}^{3} + { x }^{3}

Therefore, exponent rules does not apply to the given expression because you are not multiplying the bases.

Next, we would apply exponent rules to the second expression because the bases are being multiplied:

Expression = x^{4} × x^{10}

Expression = x^{4 - 10}

Expression = x^{-6}

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The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

Answer:

8.41

Step-by-step explanation:

8.14+3.45=11,59

20-11,59=8.41

In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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Answer:

12/3=4 ..............

Answer:

Step-by-step explanation:

A+C+B>35

A = 7

B = 14

C = 2

A+B+C<35=

23<35

Answer:

7 + x/9 = 3

x/9 = -4, so x = -36

You can order 6 different one-topping pizzas. You can order 15 different one-topping pizzas.

What is the combination?

A combination is a method of selecting items from a collection where the order of selection is irrelevant.

The combination is defined as "an arrangement of objects in which the order in which the objects are chosen is unimportant." The combination means "selection of things," where the order is irrelevant.

The formula of combination is nCr = n!/[r!(n-r)!]

Where n is the total number of objects and r is the number of objects those are selected.

Case 1: one-topping pizzas

The number of different toppings is 6.

Selecting one topping is ₆C₁  = 6!/[1!5!] = 6

Case 2: two-topping pizzas

The number of different toppings is 6.

Selecting two topping is ₆C₂  = 6!/[2!4!] = 15

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Answer:

y = 0x

Step-by-step explanation:

y=-4x-b

0 = -4(0) + b

0 = 0 + b

0

Answer:

467.65

Step-by-step explanation:

Answer:

A. x = 6.08, x = -0.58

Step-by-step explanation:

1. Factor the denominator.

2. Multiply the leftmost fraction by (x-6)/(x-6) to get common denominators.

3. Simplify.

4. Combine like terms.

5. Multiply the right side of the equation by (x-4)/(x-4).

6. Simplify.

7. "Cancel" out the denominators because they are equivalent.

8. Set the equation equal to 0.

Quadratic formula:

9. Factor using the quadratic formula.

10. Multiply and simplify.

11. Plug this into your calculator and solve for x.

The correct answer is A. x = 6.08, x = -0.58.

Answer:

20

Step-by-step explanation:

To evaluate the expression for a= 3, replace (or 'substitute') every 'a' you see with a '3' in the expression.

Given expression: 32 -4a

When a= 3,

32 -4a

= 32 -4(3)

= 32 -12

= 20

Answer:

Step-by-step explanation:

In the question we're given with an expression that is 32 - 4a , value of a is 3 . And we are asked to evaluate the expression for a = 3 .

Solution : -

\( \longmapsto \: 32 - 4a\)

Step 1 : Substituting value of a in given expression :

\( \longmapsto \:32 - 4(3)\)

Step 2 : Multiplying 4 with 3 :

\( \longmapsto \:32 - 12\)

Step 3 : Subtracting 12 from 32 :

\( \longmapsto \: \red{\boxed{ \frak{20}}}\)