what is the value of m
Answer:
114°--------------------------
Angle G is central angle and angle E is inscribed angle, both with same endpoints.
According to the inscribed angle theorem the inscribed angle is half of the central angle.
Hence the central angle G measures:
m∠G = 2(m∠E)m∠G = 2(57°)m∠G = 114°0.5(x-4)=4x-3(x-1)+37/5
Answer:
Multiply to remove the fraction, then set it equal to 0 and solve.
Exact Form: x = −124/5
Decimal Form: x = −24.8
Mixed Number Form: x = −24 4/5
Please give the brainliest, really appreciated. Thank you
Pls help I need help on this
Answer:
[tex]5a2b2/4[/tex]
Step-by-step explanation:
In the figure, m<1 = (x+6)°, m<2 = (2x + 9)°, and m<4 = (4x-4)°. Write an
expression for m<3. Then find m<3.
A. 180° -(x+6)°
B. 180° -(4x-4)°
C. 180° - [(2x+9)° + (x+6)°]
D. 180° + (x+6)°
m<3=
The expression for m<3 is 349° - 7x.
To find the measure of angle 3 (m<3), we need to apply the angle sum property, which states that the sum of the angles around a point is 360 degrees.
In the given figure, angles 1, 2, 3, and 4 form a complete revolution around the point. Therefore, we can write:
m<1 + m<2 + m<3 + m<4 = 360°
Substituting the given angle measures, we have:
(x + 6)° + (2x + 9)° + m<3 + (4x - 4)° = 360°
Combining like terms:
7x + 11 + m<3 = 360°
To isolate m<3, we subtract 7x + 11 from both sides:
m<3 = 360° - (7x + 11)
m<3 = 360° - 7x - 11
m<3 = 349° - 7x
Therefore, the expression for m<3 is 349° - 7x.
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A high school robotics club sold cupcakes at a fundraising event.
They charged $2.00 for a single cupcake, and $4.00 for a package of 3 cupcakes.
They sold a total of 350 cupcakes, and the total sales amount was $625.
The system of equations below can be solved for , the number of single cupcakes sold, and , the number of packages of 3 cupcakes sold.
Multiply the first equation by 2. Then subtract the second equation. What is the resulting equation?
x + 3y = 350
2x + 4= 625
Type your response in the box below.
$$
The resulting equation after multiplying the first equation by 2 and subtracting the second equation is:
-5y = -375
1. Given equations:
- x + 3y = 350 (Equation 1)
- 2x + 4y = 625 (Equation 2)
2. Multiply Equation 1 by 2:
- 2(x + 3y) = 2(350)
- 2x + 6y = 700 (Equation 3)
3. Subtract Equation 2 from Equation 3:
- (2x + 6y) - (2x + 4y) = 700 - 625
- 2x - 2x + 6y - 4y = 75
- 2y = 75
4. Simplify Equation 4:
-2y = 75
5. To isolate the variable y, divide both sides of Equation 5 by -2:
y = 75 / -2
y = -37.5
6. Therefore, the resulting equation is:
-5y = -375
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Evaluate the given expression for x=5
x² + 3x - 2
(5)² + 3 × 5- 2
25 + 15 - 2
40 - 2
38...
In the triangle below, which of the following best describes DH?
A. Angle bisector
B. Altitude
C. Median
D. Perpendicular bisector
Answer:
AStep-by-step explanation:Angle EDH=Angle FDH, so A must be correct.
Also, we don't have more information to prove B, C, D is right
Answer:
A.
Step-by-step explanation:
An angle bisector is a line, ray, or segment that divides an angle into two equal parts. It divides the angle into two congruent or equal angles. The angle bisector originates from the vertex of the angle and extends towards the interior of the angle. It essentially cuts the angle into two smaller angles of equal measure.
In order to compute a sample mean by hand, first the data values must be added up. Then the sum is divided by the
sample size.
x = xx
Given the data set below, compute the summation, identify the sample size, and calculate the sample mean.
19
10
15
17
16
a.) Ex =
b.) n =
c.) x =
a) The summation (Ex) of the given data set, we add up all the values
Ex = 77
b) n = 5
c) x = 15.4
a) To compute the summation (Ex) of the given data set, we add up all the values:
19 + 10 + 15 + 17 + 16 = 77
b) The sample size (n) is the total number of data points in the set. In this case, there are 5 data points, so:
n = 5
c) To calculate the sample mean (x), we divide the summation (Ex) by the sample size (n):
x = Ex / n
x = 77 / 5
x = 15.4
Therefore, the answers are:
a) Ex = 77
b) n = 5
c) x = 15.4
The summation is 77, the sample size is 5, and the sample mean is 15.4.
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Question 11 of 26
Given the diagram below, what is cos(45)?
Triangle not drawn to scale
A. √2
O B.
√3
C. 3-√2
45⁰
OD.
Answer:
chemical reaction that releases heat energy to the surroundings is known as endothermis reaction
MLMS4 Day 3 (1 hour) SBA Task: Project November 2023 Which sides of the rectangle (that formed the sides of the cylinder) has the same length as the circumference of the circles? Which sides of the rectangle has the same length of the height of the cylinder. What do you notice between your model and the practical calculation.
The sides of the rectangle that have the same length as the circumference of the circles are the sides parallel to the bases of the cylinder. The sides of the rectangle that have the same length as the height of the cylinder are the sides perpendicular to the bases. While the model provides a simplified representation, practical calculations might have slight differences due to real-world factors.
In a cylinder, the two circular bases are connected by a curved surface, forming a three-dimensional shape. The rectangular shape that wraps around the curved surface of the cylinder is called the lateral surface or the lateral area.
To determine which sides of the rectangle have the same length as the circumference of the circles, we need to understand the geometry of a cylinder. The circumference of a circle is calculated using the formula:
Circumference = 2πr,
where r is the radius of the circle. In a cylinder, the bases are identical circles, so the circumference of each base is equal. Therefore, the sides of the rectangle that are parallel to the bases have the same length as the circumference of the circles.
Now, let's consider the height of the cylinder. The height is the distance between the two bases and is perpendicular to the bases. In the rectangular representation of the cylinder, the sides that are perpendicular to the bases represent the height. Hence, the sides of the rectangle that are perpendicular to the bases have the same length as the height of the cylinder.
When comparing the model (rectangular representation) with practical calculations, we may notice some differences. The model provides a simplified representation of the cylinder, assuming that the lateral surface is perfectly wrapped around the curved surface. However, in practical calculations, there might be slight variations due to factors like material thickness, manufacturing processes, or measuring precision. These variations can result in minor deviations between the model and the practical calculations.
It's important to consider that the model is an approximation and serves as a visual aid to understand the basic properties of the cylinder. In real-life applications or engineering calculations, precise measurements and considerations of tolerances are crucial.
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(5/8x+y^5)(y^5- 5/8x) write the expression as a polynomial
100 points for this
Answer:
y^10 + (5/8xy^5 - 5/8xy^6) - (25/64x^2)
Step-by-step explanation:
To simplify the given expression, we can expand it using the distributive property:
(5/8x + y^5)(y^5 - 5/8x)
Expanding the expression yields:
= (5/8x * y^5) + (5/8x * -5/8x) + (y^5 * y^5) + (y^5 * -5/8x)
= (5/8xy^5) - (25/64x^2) + y^10 - (5/8xy^6)
Combining like terms, we have:
= y^10 + (5/8xy^5 - 5/8xy^6) - (25/64x^2)
Hope this help! Have a good day!
4x-5 2x+7 Find the value of x
answers should be from
27
37
47
57
Please answer ASAP I will brainlist
Answer:
X intercepts: (-2, 0), (2, 0)
Y intercept: (0, 4)
Edited because I forgot to put in point form earlier. Depends on whether your teacher wants it in point form. If not, ignore the 0s.
Step-by-step explanation:
X intercepts are the points where a line crosses the x axis. Y intercepts are the points where a line crosses the y axis.
Answer:
A. x-intercept: (-2,0), (2,0)
A. y-intercept: (0,4)
Step-by-step explanation:
If you want to find the x and y-intercept of a line, you need to know its equation. But don't worry, it's not as hard as it sounds. Here are some tips to help you out.
One type of equation is y = mx + c, where m is the slope and c is the y-intercept. This means that the line crosses the y-axis at c. To find the x-intercept, just plug in y = 0 and solve for x. You'll get x = -c/m. Easy peasy!
For example, if the equation is y = 2x + 4, then the y-intercept is 4 and the x-intercept is -2.
Another type of equation is ax + by + c = 0, where a, b and c are constants. To find the x-intercept, plug in y = 0 and solve for x. You'll get x = -c/a. To find the y-intercept, plug in x = 0 and solve for y. You'll get y = -c/b. Piece of cake!
For example, if the equation is 3x + 2y - 6 = 0, then the x-intercept is 2 and the y-intercept is -3.
Now you know how to find the x and y-intercept of a line from its equation.Let us understand the calculations to find the x and y intercept, through the steps in the below table.
Please help! Will give brainliest
The z - score z = (x - μ)/σ equals z = (p' - p)/[√(pq/n)]
What is z-score?The z-score is the statical value used to determine probability in a normal distribution
Given the z-score z = (x - μ)/σ where
x = number of successes in a sample of nμ = np and σ = √npqWe need to show that
z = (p' - p)/√(pq/n)
We proceed as follows
Now, the z-score
z = (x - μ)/σ
Substituting in the values of μ and σ into the equation, we have that
μ = np and σ = √(npq)So, z = (x - μ)/σ
z = (x - np)/[√(npq)]
Now, dividing both the numerator and denominator by n, we have that
z = (x - np)/[√(npq)]
z = (x - np) ÷ n/[√(npq)] ÷ n
z = (x/n - np/n)/[√(npq)/n]
z = (x/n - p)/[√(npq/n²)]
z = (x/n - p)/[√(pq/n)]
Now p' = x/n
So, z = (x/n - p)/[√(pq/n)]
z = (p' - p)/[√(pq/n)]
So, the z - score is z = (p' - p)/[√(pq/n)]
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Which is equivalent to 4/9 1/2x*?
92x
9 1/8x
Answer:
B. [tex] 9^{\frac{1}{8}x} [/tex]
Step-by-step explanation:
[tex] \sqrt[4]{9}^{\frac{1}{2}x} = [/tex]
[tex] = ({9}^{\frac{1}{4}})^{\frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{4} \times \frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{8}x} [/tex]
(a) Un ángulo mide 47°. ¿Cuál es la medida de su complemento?
(b) Un ángulo mide 149°. ¿Cuál es la medida de su suplemento?
El supplemento y el complemento de cada ángulo son, respectivamente:
Caso A: m ∠ A' = 43°
Caso B: m ∠ A' = 31°
¿Cómo determinar el complemento y el suplemento de un ángulo?De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:
Ángulo y su complemento
m ∠ A + m ∠ A' = 90°
Ángulo y su suplemento
m ∠ A + m ∠ A' = 90°
Donde:
m ∠ A - Ángulom ∠ A' - Complemento / Suplemento.Ahora procedemos a determinar cada ángulo faltante:
Caso A: Complemento
47° + m ∠ A' = 90°
m ∠ A' = 43°
Caso B: Suplemento
149° + m ∠ A' = 180°
m ∠ A' = 31°
ObservaciónEl enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.
The statement is written in Spanish and its answer is written in the same language.
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If the mean of a negatively skewed distribution is 122, which of these values could be the median of the distribution
118 be the median of a positively skewed distribution with a mean of 122. Option D.
To determine which of the given values could be the median of a positively skewed distribution with a mean of 122, we need to consider the relationship between the mean, median, and skewness of a distribution.
In a positively skewed distribution, the tail of the distribution is stretched towards higher values, meaning that there are more extreme values on the right side. Consequently, the median, which represents the value that divides the distribution into two equal halves, will typically be less than the mean in a positively skewed distribution.
Let's examine the given values in relation to the mean:
A. 122: This value could be the median if the distribution is perfectly symmetrical, but since the distribution is positively skewed, the median is expected to be less than the mean. Thus, 122 is less likely to be the median.
B. 126: This value is higher than the mean, and since the distribution is positively skewed, it is unlikely to be the median. The median is expected to be lower than the mean.
C. 130: Similar to option B, this value is higher than the mean and is unlikely to be the median. The median is expected to be lower than the mean.
D. 118: This value is lower than the mean, which is consistent with a positively skewed distribution. In such a distribution, the median is expected to be less than the mean, so 118 is a plausible value for the median.
In summary, among the given options, (118) is the most likely value to be the median of a positively skewed distribution with a mean of 122. So Option D is correct.
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Note the complete question is
If the mean of a positively skewed distribution is 122, which of these values could be the median of the distribution?
A. 122
B. 126
C. 130
D. 118
What are the new coordinates of point A when
it is rotated about the origin by
a) 90° clockwise?
-4
b) 180°?
c) 270° clockwise?
-3 -2 -1
Y
4-
3-
ΤΑ
2.⁰⁰
1
0
-1-
-2-
--3-
-4-
1
N.
2
3 4
X
The different coordinates after respective rotation are:
1) A'(2, 0)
2) A'(0, -2)
3) A'(-2, 0)
What are the coordinates after rotation?There are different methods of transformation such as:
Translation
Rotation
Dilation
Reflection
Now, the coordinate of the given point A is: A(0, 2)
1) The rule for rotation of 90 degrees clockwise is:
(x, y) →(y,-x)
Thus, we have:
A'(2, 0)
2) The rule for rotation of 180 degrees is:
(x, y) → (-x,-y)
Thus, we have:
A'(0, -2)
3) The rule for rotation of 180 degrees is:
(x, y) → (-y,x)
Thus, we have:
A'(-2, 0)
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PLSPLSS PLSSMSL HELP ME
Answer:
1. x = 18
2. x = 31
Step-by-step explanation:
1. Angles in a quadrilateral sum to 360°.
360 -(60 +130 +70) = 360 -260 = 100
So, x +82 = 100. x = 100 -82 = 18
2. Angles in a triangle sum to 180°. 180 -(29 +75) = 180 -104 = 76.
So, -17 +3x = 76. 3x = 93. x = 93/3 = 31
2.3.5 Quiz: Cross-Sections of Geometric Solids
OA. Triangle
OB. Circle
OC. Trapezoid
OD. Rectangle
The cross section of the geometric solid is (d) rectangle
How to determine the cross section of the geometric solidFrom the question, we have the following parameters that can be used in our computation:
The geometric solid
Also, we can see that
The geometric solid is a cylinder
And the cylinder is divided vertically
The resulting shape from the division is a rectangle
This means that the cross section of the geometric solid is (d) rectangle
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The shape of the cross-section for the geometric solid given in the diagram is a rectangle.
The cross section of the geometric solid represents the shape which extends beyond the actual geometric solid which is a cylinder.
A rectangle has opposite side being equal. This means that the width and and length are of different length.
Therefore, the shape of the cross-section is a rectangle.
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please help quick
Which of the following are solutions to the quadratic equation? Check all that
apply.
The solutions to the quadratic equation 2x² + 6x - 10 = x² + 6 are -8 and 2.
What are the solutions to the quadratic equation?Given the quadratic equation in the question:
2x² + 6x - 10 = x² + 6
First, reorder the quadratic equation in standard form:
2x² + 6x - 10 = x² + 6
2x² - x² + 6x - 10 - 6 = x² - x² + 6 - 6
2x² - x² + 6x - 10 - 6 = 0
x² + 6x - 10 - 6 = 0
x² + 6x - 16 = 0
Next, factor the equation using the AC method:
( x - 2 )( x + 8 ) = 0
Equate each factor to 0 and solve for x:
( x - 2 ) = 0
x - 2 = 0
x = 2
( x + 8 ) = 0
x + 8 = 0
x = -8
Therefore, the solutions are -8 and 2.
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Given the following equation of a line x+6y= 3, determine the slope of a line that is perpendicular.
The slope of a line that is perpendicular to the given line x + 6y = 3 is 6.
To determine the slope of a line that is perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.
The equation of the given line is x + 6y = 3.
To find the slope of the given line, we can rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope:
x + 6y = 3
6y = -x + 3
y = (-1/6)x + 1/2
From the equation y = (-1/6)x + 1/2, we can see that the slope of the given line is -1/6.
To find the slope of a line that is perpendicular, we take the negative reciprocal of -1/6.
The negative reciprocal of -1/6 can be found by flipping the fraction and changing its sign:
Negative reciprocal of -1/6 = -1 / (-1/6) = -1 * (-6/1) = 6
Therefore, the slope of a line that is perpendicular to the given line x + 6y = 3 is 6.
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Solve it for me please
1a.) The amount that the eldest son received would be =GHç 1,360
b .) The amount received by the daughter would be =G Hç 2176
c.) The difference between the amount the two sons received would be =GHç1,904
How to calculate the amount received by the eldest son?For 1a.)
The amount that the land is worth= $8,600
The amount received for various purposes= $1,800
The remaining amount shared to the sons= 8,600-1800= $6,800
The percentage amount received by the eldest son= 20% of 6800
That is;
= 20/100×6800/1
= 136000/100
= $1,360
The remaining amount= 6800-1360= $5,440
For 1b.)
The ratio that the remaining amount was shared between the other son and the daughter = 3 : 2 respectively.
The total ratio= 3+2=5
For daughter= 2/5× 5440
= 10880/5 = 2176
The other son= 5440-2176 = 3264
For 1c.)
The difference between the amount the two sons received would be =3264-1,360 = GHç1,904.
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The average student loan debt for college graduates is $25,200. Suppose that that distribution is normal and that the standard deviation is $11,200. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar.
a. What is the distribution of X? X - N
b Find the probability that the college graduate has between $27,250 and $43,650 in student loan debt
c. The middle 20% of college graduates loan debt lies between what two numbers? Low: $ High: $
a) The distribution of X, the student loan debt of a randomly selected college graduate, is normal with a mean of $25,200 and a standard deviation of $11,200. b) The probability is approximately 7.28%.
c) The middle lies between approximately $22,164 and $28,536.
How to Find Probability?a. The distribution of X, the student loan debt of a randomly selected college graduate, is a normal distribution (bell-shaped curve) with a mean (μ) of $25,200 and a standard deviation (σ) of $11,200. We can represent this as X ~ N(25200, 11200).
b. To find the probability that the college graduate has between $27,250 and $43,650 in student loan debt, we need to calculate the z-scores for these two values and then find the area under the normal curve between those z-scores.
First, we calculate the z-score for $27,250:
z1 = (X1 - μ) / σ = (27250 - 25200) / 11200 ≈ 1.8304
Next, we calculate the z-score for $43,650:
z2 = (X2 - μ) / σ = (43650 - 25200) / 11200 ≈ 1.6518
Now, we need to find the area under the normal curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this area.
Using a standard normal distribution table or a calculator, the probability is approximately P(1.6518 ≤ Z ≤ 1.8304) ≈ 0.0728.
c. To find the middle 20% of college graduates' loan debt, we need to find the range of values that contain the central 20% of the distribution. This range corresponds to the values between the lower and upper percentiles.
The lower percentile is the 40th percentile (50% - 20%/2 = 40%) and the upper percentile is the 60th percentile (50% + 20%/2 = 60%).
Using a standard normal distribution table or a calculator, we can find the z-scores corresponding to these percentiles:
For the lower percentile (40th percentile):
z_lower = invNorm(0.40) ≈ -0.2533
For the upper percentile (60th percentile):
z_upper = invNorm(0.60) ≈ 0.2533
Now, we can convert these z-scores back to the corresponding loan debt values:
Lower debt value:
X_lower = μ + z_lower * σ = 25200 + (-0.2533) * 11200 ≈ $22,164
Upper debt value:
X_upper = μ + z_upper * σ = 25200 + 0.2533 * 11200 ≈ $28,536
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what is this solution to the problem of ? 12÷132
Answer:
0.090909
Step-by-step explanation:
I used a calculator
whats the answer pls
Answer:
Step-by-step explanation:
Two models R1 and R2 are given for revenue (in millions of dollars) for a corporation. Both models are estimates of revenues from 2030 through 2035, with t = 0 corresponding to 2030.
R1 = 7.23 + 0.25t + 0.03t^2
R2 = 7.23 + 0.1t + 0.01t^2
How much more total revenue (in millions of dollars) does that model project over the six-year period ending at t = 5? (Round your answer to three decimal places.)
Step-by-step explanation:
To find the difference in total revenue projected by the two models over the six-year period ending at t = 5, we need to calculate the revenue for each model from t = 0 to t = 5 and subtract the results.
For R1:
R1 = 7.23 + 0.25t + 0.03t^2
Substituting t = 5:
R1(5) = 7.23 + 0.25(5) + 0.03(5^2)
R1(5) = 7.23 + 1.25 + 0.75
R1(5) = 9.23 + 0.75
R1(5) = 9.98 million dollars
For R2:
R2 = 7.23 + 0.1t + 0.01t^2
Substituting t = 5:
R2(5) = 7.23 + 0.1(5) + 0.01(5^2)
R2(5) = 7.23 + 0.5 + 0.25
R2(5) = 7.73 + 0.25
R2(5) = 7.98 million dollars
To find the difference, we subtract R2(5) from R1(5):
Difference = R1(5) - R2(5)
Difference = 9.98 - 7.98
Difference = 2 million dollars
Therefore, the model R1 projects 2 million dollars more in total revenue than R2 over the six-year period ending at t = 5.
Write the correct measurement for A-F (Example 2.2, 5.9, 9)
Answer:
9
Step-by-step explanation:
For a recent year, 52.7 million people participated in recreational boating. Sixteen years later, that number increased to 57.3
million. Determine the percent increase. Round to one decimal place.
The percent increase was approximately
%.
The percent increase in recreational boating participation over the sixteen-year period is approximately 8.72%. This means that the number of participants increased by around 8.72% from 52.7 million to 57.3 million.
To determine the percent increase in recreational boating participation over the sixteen-year period, we can use the following formula:
Percent Increase = ((New Value - Old Value) / Old Value) * 100
Using the given information, we have an old value of 52.7 million and a new value of 57.3 million.
Percent Increase = ((57.3 million - 52.7 million) / 52.7 million) * 100
= (4.6 million / 52.7 million) * 100
= 0.0872 * 100
= 8.72%
This increase indicates a positive trend in recreational boating, reflecting a growing interest in this activity over time. Factors such as improved accessibility, marketing efforts, and increasing disposable income may have contributed to this upward trend.
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(08.01 MC)
The function h(x) is a continuous quadratic function with a domain of all real numbers. The table
x h(x)
-6 12
-57
-4 4
-3 3
-24
-1 7
What are the vertex and range of h(x)?
The vertex of h(x) is (-3, 3), and the range is y ≥ 3.
To find the vertex of the quadratic function h(x), we can use the formula x = -b/2a, where the quadratic function is in the form [tex]ax^2 + bx + c[/tex].
From the given table, we can observe that the x-values of the vertex correspond to the minimum points of the function.
The minimum point occurs between -4 and -3, which suggests that the x-coordinate of the vertex is -3. Therefore, x = -3.
To find the corresponding y-coordinate of the vertex, we look at the corresponding h(x) value in the table, which is 3. Hence, the vertex of the function h(x) is (-3, 3).
To determine the range of h(x), we need to consider the y-values attained by the function.
From the table, we see that the lowest y-value is 3 (the y-coordinate of the vertex), and there are no other y-values lower than 3. Therefore, the range of h(x) is all real numbers greater than or equal to 3.
The vertex of h(x) is (-3, 3), and the range is y ≥ 3.
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The vertex of the quadratic function is (-4, 12).
The range of h(x) is [3, ∞).
To find the vertex and range of the quadratic function h(x) based on the given table, we can use the properties of quadratic functions.
The vertex of a quadratic function in the form of f(x) = ax² + bx + c can be determined using the formula:
x = -b / (2a)
The domain of h(x) is all real numbers, we can assume that the quadratic function is of the form h(x) = ax² + bx + c.
Looking at the table, we can see that the x-values are increasing from left to right.
Additionally, the y-values (h(x)) are increasing from -6 to -4, then decreasing from -4 to -1.
This indicates that the vertex of the quadratic function lies between x = -4 and x = -3.
To find the exact x-coordinate of the vertex, we can use the formula mentioned earlier:
x = -b / (2a)
Based on the table, we can choose two points (-4, 4) and (-3, 3).
The difference in x-coordinates is 1, so we can assume that a = 1.
Plugging in the values of (-4, 4) and a = 1 into the formula, we can solve for b:
-4 = -b / (2 × 1)
-4 = -b / 2
-8 = -b
b = 8
The equation of the quadratic function h(x) can be written as h(x) = x² + 8x + c.
Now, let's find the y-coordinate of the vertex.
We can substitute the x-coordinate of the vertex, which we found as -4, into the equation:
h(-4) = (-4)² + 8(-4) + c
12 = 16 - 32 + c
12 = -16 + c
c = 28
The equation of the quadratic function h(x) is h(x) = x² + 8x + 28.
The range of the quadratic function can be determined by observing the y-values in the table.
From the table, we can see that the minimum y-value is 3.
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