Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fourth) squared + thirteen-eighths y = negative 6 (x minus one-fourth) squared + nineteen-eighths y = negative 6 (x minus one-half) squared + seven-halves

Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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Answer:

3.6

Step-by-step explanation:

18/5 =3.6

5/5 = 1

18 - 15 =3. 15/5= 3

the remaining

3/5 = 0.6

3+0.6=3.6

Answer:

30°

Step-by-step explanation:

angles on a straight line add up to 180°.

angles in a triangle add up to 180°.

XYZ = 180 - 105 = 75°.

angle YZX = 180 - 2x.

so we have YZX + 2x = 180, YZX = 180 - 2x.

angles in triangle add up to 180:

x + YZX + 75 = 180,

x + (180 - 2x) + 75 = 180,

-x + 180 + 75 = 180,

-x = 180 - 180 - 75 = -75,

x = 75°.

YZX = 180 - 2x = 180 2(75) = 180 - 150 = 30

Answer:

H= -35/4

Decimal form: -8.75

Explanation:

Answer:

the integers are either -3 , -2. or

2,3

Step-by-step explanation:

\(x \times x + 1 = {x}^{2} + 1 \\ x + x + 1 = (2x + 1)3 = 6x + 3 \\ 6x + 3 - 3 = {x}^{2} + 1 \\ 6x = {x}^{2} + 1 \\ {x}^{2} - 6x + 1 = 0 \\ (x + 3)( x - 2) \\ x = - 3 \: x = 2 \\ \)

Answer:

3, 3.024, 3.04, 10

I'm sorry if I misunderstood.

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Answer:

15.98 dollars

Step-by-step explanation:

its really easy

we need to subtract the total amount that she has spent from the total amount that she had in her purse

the total amount in Megan's purse=$45.12

total amount that Megan spent=$7.89+$21.25 =$29.14

now,

the exact amount that Megan has left = $45.12-$29.14=$15.98

Answer:

30 ft²

Step-by-step explanation:

Area of trapezium = 1/2 (a + b)h

a = 6 ft , b = 9 ft , h = 4 ft

Area = 1/2 (6 + 9) 4

= 30 ft²

Answer:

D

Step-by-step explanation:

For two ratios to form a proportion they have to be equal.

To see if two ratios are equal we express them in their simplest form.

In this case we notice that in the first ratio both numbers are multiples of five, then:

In the second case we notice that both numbers are multiples of 2, then:

Since both ratios can be simplified to the same final ratio, they form a proportion.

Answer:

x+y=12

Step-by-step explanation:

Standard form is ax+by=c

Given, y-8 = -(x-4)

y-8=-x+4

x+y=4+8

x+y=12

Answer:

x + y = 12

Step-by-step explanation:

Standard form is Ax+By=C

so the goal is to get the y and the x on the same side without and negatives or fractions on that side.

y - 8 = - (x - 4)  first, start by simplifying

y - 8 = -x +4  next, because it is negative, we are going to add x to -x on the right side to get it to cancel out and we'll add x to y on the left side

x + y - 8 = 4  now we need to get rid of that eight so we'll add 8 to -8 so it cancels out and we'll add 8 to 4

x + y = 12 now it is in standard form

Answer:

perpendicular

Step-by-step explanation:

This question only asks about the slope of the line, so the intercept doesn't matter. You can see that the slope of one line is 3x and the other is -3x so they're perpendicular

The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:

The functions have the same range.

The functions have the same domain.

The functions have the same x-intercepts.

Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.

Here are the options:

The functions have the same graph.

The functions have the same range.

The functions have the same domain.

The functions have the same vertex.

The functions have the same y-intercept.

The functions have the same x-intercepts.

The functions have the same graph:

This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).

Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).

The functions have the same range:

This statement is true.

Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.

The functions have the same domain:

This statement is true.

The domain of both functions, unless restricted by any other factors, is all real numbers.

Quadratic functions have a domain of (-∞, ∞).

The functions have the same vertex:

This statement is false.

The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).

Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).

The functions have the same y-intercept:

This statement is false.

The y-intercept of a function is the value of y when x = 0.

For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.

For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3

= 3.

Their y-intercepts are different.

The functions have the same x-intercepts:

This statement is true.

To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.

The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.

Both functions have the same x-intercepts.

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Answer:

y= -2(-6) +5

y= 12+5

y= 17

y= -2(-3) +5

y= 6 +5

y= 11

y= -2(0) +5

y= 0+5

y=5

y= -2(3) +5

y= -6 +5

y= -1

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

An inclinometer or clinometer is an instrument used for measuring angles of slope, elevation, or depression of an object with respect to gravity's direction.

Step-by-step explanation:

First, we need to perform the multiplication operation within the parentheses, following the order of operations:

2⅓ × 1¼ = (7/3) × (5/4) = 35/12

Now, we can substitute the values in the expression:

3½ - (2⅓ × 1¼) + ⅗ = 7/2 - 35/12 + 3/5

To add or subtract fractions with different denominators, we need to find a common denominator. The least common multiple of 2, 12, and 5 is 60, so we can rewrite the fractions with this denominator:

7/2 - 35/12 + 3/5 = (210/60) / (2/2) - (175/60) / (12/12) + (36/60) / (5/5)

Simplifying the fractions within the parentheses:

= 210/60 - 175/60 + 36/60

= 71/60

Therefore, 3½ - (2⅓ × 1¼) + ⅗ simplifies to 71/60.

Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.

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Since ∠BDA is an inscribed angle measuring 25°, the arc it intercepts, AB, must measure 50°. For the same reason, the arc intercepted by ∠BDA must measure 64°. That's a total of 114° out of the semicircle ABCD, which leaves 66° out of the 180° half-circle. That's the measure of arc BC.

Define measurement?

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Answer:

y = 5

Step-by-step explanation:

3(3y-8)=21

expand:

9y - 24 = 21

+24 to both sides to get 9y on its own.

9y = 45

divide both sides by 9 to get y on its own.

therefore

y = 5

hope this makes sense!

Answer: Solve for

y

by simplifying both sides of the equation, then isolating the variable.    

y≈−1.21698677,2.94165923

Step-by-step explanation:

Answer:

Step-by-step explanation:

Draw a picture, set up a trig equation. Use sine bc the info given is opposite and hypotenuse. You need a calculator to do trig calculations.

Answer:

answer = -1

Step-by-step explanation:

Answer:

twelve

Step-by-step explanation:

these are:

4 6 34 36 44 46 54 56 64 66 74 and 76

There are 56 ways for a group of 10 people to form a committee with at least 8 people on it.

To find the number of ways that a group of 10 people can form a committee with at least 8 people on it, we can use combinations.

First, we can find the number of ways to choose 8 people from the 10 available, which is:

C(10, 8) = 45

Next, we can find the number of ways to choose 9 people from the 10 available, which is:

C(10, 9) = 10

Finally, we can find the number of ways to choose all 10 people, which is:

C(10, 10) = 1

To get the total number of ways to form a committee with at least 8 people on it, we can add up these three cases:

45 + 10 + 1 = 56

Therefore, there are 56 ways for a group of 10 people to form a committee with at least 8 people on it.

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\(m\angle 1=35^{\circ}\) (alternate interior angles)

\(m\angle 2=24^{\circ}\) (adjacent angles of a parallelogram are supplementary)

\(m\angle 3=24^{\circ}\) (alternate interior angles)

A = 1 and 8

B = 2 and 4

C = 2 and 7

I’m pretty sure this is right? I’m still learning too :p

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

Explanations:

For the sake of simplicity, imagine that lines m and n are parallel. They don't necessarily need to be in order to answer this problem, but it might help with the terminology better.

When we use the term "interior" we basically mean the region between or inside the parallel lines. So "exterior" is everything but that, which is composed of two separate regions that don't overlap. Exterior angles shown in this diagram are

angle 1, angle 5, angle 4, angle 8

The "alternate" refers to the idea that we're on alternate sides of the transversal cutting line. One pair of alternate exterior angles is angle 1 and angle 8. We have angle 1 below the transversal while angle 8 is on the opposite side and above the transversal. For similar reasoning, angles 5 and 4 are alternate exterior angles as well.

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

Notice how each line crosses to form an X shape, producing 4 angles that share the same common vertex point. For instance, angles 1, 5, 6 and 2 are all around the same point.

Angle 1 and angle 3 are corresponding angles because they

So in short, they are both in the same corner of each four corner angle configuration. They are both in the bottom left corner. This is the full list of all corresponding angle pairs

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

As stated in the first section above, the interior region is between the parallel lines. Alternate interior angles alternate being above and below the transversal line.

So this applies to angle 2 and angle 7. It also works for angle 3 and angle 6.

Answer:

What function?

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

P(4)= 4^2 - (5*4)

      = 16 - 20

      = -4

Answer:

6x - 18

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define expression

(2x - 6) + 4(x - 3)

Step 2: Simplify