The equation of h(x) in vertex form is given as follows:
h(x) = (x + 2)² - 3.
How to define the quadratic function given it's vertex?The quadratic function of vertex(h,k) is given by the rule presented as follows:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.The vertex is the turning point of the function, where it changes from decreasing to increasing, or vice versa, hence it's coordinates are given as follows:
(-2,-3).
Then the equation is:
h(x) = a(x + 2)² - 3.
When x = 0, h(x) = 1, hence the leading coefficient a is obtained as follows:
1 = a(2)² - 3
4a = 4
a = 1.
Hence the equation is:
h(x) = (x + 2)² - 3.
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A line passes through the points in this table.
X
4
5
6
7
y
24
19
14
9
What is the slope of the line?
Write your answer as an integer or simplified fraction.
The slope of the line passing through the given points is -2.5.
To find the slope of a line passing through two points, we need to use the formula:
Slope = (Change in y) / (Change in x
We can choose any two points from the given table to find the slope of the line. Let's choose the points (4, 19) and (6, 14).
Change in y = 14 - 19 = -5
Change in x = 6 - 4 = 2
Slope = (-5) / 2 = -2.5
Therefore, the slope of the line passing through the given points is -2.5.
The slope of a line represents the steepness of the line. If the slope is positive, the line is increasing as we move from left to right. If the slope is negative, the line is decreasing as we move from left to right. A slope of 0 represents a horizontal line, while an undefined slope represents a vertical line.
In this case, the slope of -2.5 indicates that the line is decreasing at a moderate rate as we move from left to right. The higher the absolute value of the slope, the steeper the line.
It is important to note that the slope is constant for any two points on a straight line. Therefore, we can choose any other two points from the table to find the slope, and we will get the same result.
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How many ways are there to construct a string of 4 digits if numbers cannot be repeated?
Answer:
The number of ways to construct a string of 4 digits without repetition can be found using the permutation formula.
The formula for finding the number of permutations of n objects taken r at a time without repetition is:
P(n, r) = n! / (n - r)!
Where n is the total number of objects and r is the number of objects being chosen.
In this case, we have 10 digits (0-9) to choose from, and we need to choose 4 digits without repetition. Therefore, the number of ways to construct a string of 4 digits without repetition is:
P(10, 4) = 10! / (10 - 4)!
P(10, 4) = 10! / 6!
P(10, 4) = (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1)
P(10, 4) = 10,080
Therefore, there are 10,080 ways to construct a string of 4 digits without repetition using the digits 0-9.
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Select the correct answer.
Weight/Calories per Day 1000 to 1500 cal. 1500 to 2000 cal. 2000 to 2500 cal. Total
120 lb. 90 80 10 180
145 lb. 35 143 25 203
165 lb. 15 27 75 117
Total 140 250 110 500
Based on the data in the two-way table, which statement is true?
The correct probability from the two-way table is given as follows:
B. P(120 lb | 2,000 - 2,500 cal) is different of P(120 lb).
How to calculate a probability?
A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Then the probabilities are given as follows:
P(1,000 - 1,500 cal | weight of 165 lb) = 15/117.P(1,000 - 1,500 cal) = 140/500 -> item a is false.P(120 lb | 2,000 - 2,500 cal) = 10/110 = 1/11.P(120 lb) = 180/500.Hence statement B is true.
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Find the missing value that makes the ratio equivalent to 1:5
4:___ And ___:65
Answer: 4:20 and 13:65
Step-by-step explanation: First one is 4 x 5 and second one you would do 65/5
14. Which is NOT a part of your budget? (1 point) fixed expenses Ogross pay Odiscretionary expenses Orealized income
Realized income is NOT part of your budget.
Income that has really been received or generated within a certain period is referred to as realized income. It stands for the money that has been made or acquired through a variety of sources, including work, investments, or commercial ventures.
Realized income is a crucial part of a budget since it shows the actual cash that a person or organization has available for budgeting and financial planning.
The income is what may be used for a variety of costs, savings, investments, or other financial objectives.
In order to appropriately reflect the financial resources available for controlling spending and making financial decisions, realized income is often included as part of a budget.
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Convert 2553 base 10 to base 16
Step by step explanation
How did I get my answer?
3+2=25
5+4=81
2+2=16
The pattern involves squaring the sum of the given numbers.
Here's the process for each equation:
3+2=5, then [tex]5^2=25[/tex]
5+4=9, then [tex]9^2=81[/tex]
2+2=4, then [tex]4^2 = 16[/tex]
How to solveOn careful analysis of the given pattern and answers, I am able to observe that this is a pattern-based numerical puzzle where the standard rules of arithmetic do not apply.
In this case, the pattern involves squaring the sum of the given numbers.
Here's the process for each equation:
3+2=5, then [tex]5^2=25[/tex]
5+4=9, then [tex]9^2=81[/tex]
2+2=4, then [tex]4^2 = 16[/tex]
So, the answer is obtained by first adding the numbers and then squaring the result.
This puzzle demonstrates that the logic behind the equations is different from traditional arithmetic, showcasing the importance of understanding the pattern to get the correct answer.
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I need some help please
The earthquake registered 3.6 on the Richter scale.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is given as follows:
R = log(A/0.0001)
The amplitude of the earthquake was of 0.3954, hence the magnitude of the earthquake is obtained as follows:
R = log(0.3954/0.0001)
R = 3.6.
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help pls i need this like rn
The probability of just thunder is 0.196.
We have,
The probability of rain P(A) = 1/2
The probability of thunder and raining P(A ∩ B) = 1/3
The probability of rain and thunder P(A U B) = 11/30
Now,
Using the addition rule of probability.
P(A U B) = P(A) + P(B) - P(A∩B)
Substituting.
11/30 = 1/2 + P(B) - 1/3
11/30 - 1/2 + 1/3 = P(B)
P(B) = 0.196
The probability of just thunder is 0.196.
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need help with this problem
The solution to the system of equations is given as follows:
x = 3z + 3.y = -2z + 4.z = z.How to solve the system of equations?Considering the augmented matrix, the system of equations is defined as follows:
x + y - z = 7.2x + 3y = 18.-5x - 7y + z = -43.Adding the first and third equations, we have that:
-4x - 6y = -36.
From the second equation, we have that:
2x + 3y = 18.
The addition equation is a multiple of this equation, hence the system has an infinite number of solutions.
From the second equation, we have that:
2x + 3y = 18.
x + 1.5y = 9
x = 9 - 1.5y.
The definition for z is given as follows:
z = x + y - 7.
Hence the variable y is:
y = z - x + 7.
The variable x is of:
x = 9 - 1.5(z - x + 7)
x = 9 - 1.5z + 1.5x - 10.5
0.5x = 1.5 + 1.5z
x = 3z + 3.
The variable y is:
y = z - 3z - 3 + 7
y = -2z + 4.
Hence the solution is:
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Point O is the center of the circle in the diagram. What is
mzBCA?
A. 80°
B. 75°
C. 70°
D. 65°
Thanks in advance for any assistance! Assume that θ is a positive acute angle.
Given: cosθ = 45/53
Find: cos2θ
Answer:
1≠0.346485
Step-by-step explanation:
Please fast!!!!!!!!!!!!!!!! Triangle 1 and triangle 2 are similar right triangles formed from a ladder leaning against a building.
Triangle 1 Triangle 2
The distance, along the ground, from the bottom of the ladder to the building is 12 feet. The distance from the bottom of the building to the point where the ladder is touching the building is 18 feet. The distance, along the ground, from the bottom of the ladder to the building is 8 feet. The distance from the bottom of the building to the point where the ladder is touching the building is unknown.
Determine the distance from the bottom of the building to the point where the ladder is touching the building for triangle 2.
27 feet
18 feet
12 feet
5 feet
The distance from the bottom of the building to the point where the ladder is touching the building for triangle 2, obtained using trigonometric ratio of tangent is 12 feet. The correct option is therefore;
12 feet
What are the trigonometric ratios?The trigonometric ratios are the value relationship between an interior angle of a right triangle and two of the sides of the triangle.
The right triangles are similar, therefore, the tangent of the angle the ladder makes with the ground are the same, which indicates;
tan(θ) = (Length of the side facing the angle θ) ÷ (Length of the side adjacent to the angle θ)
The side facing the angle is the distance from the bottom to the point where the ladder touches the building.
The adjacent to the angle is the horizontal distance from the bottom to the ladder to the building.
Therefore; tan(θ) = 18/12 = x/8
Where x = The distance from the bottom of the building to the point the ladder touches the building for triangle 2
18/12 = x/8
x = 18/12 × 8 = 12
The distance, x = 12 feet
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Answer:
12?
Step-by-step explanation:
I'm not too sure! I am in the middle of taking the test right now.
A bakery wanted to make their muffins more uniform in size. They reworked their equipment to do so. To test the changes, they made 25 muffins then measured each one. Which of the following should they use to determine whether or not the equipment changes worked?
Select one:
a.
mean
b.
mode
c.
range
d.
interquartile range
The equation n = 0.03t² -0.6t+ 3.93, models, n , the number (in millions) of people who moved to another state in the year that is t years since 1990. The table below shows some of the data that were used to find this model. Year 1995 1998 2001 2004 2006 Number of People Who Moved to Another State (millions) a. When t O what is the value of n ? What does it mean in this situation? Select an answer 1.7 1.1 1.0 1.5 2.1 b. Estimate the number of people who moved to another state in 2005. million (Round to the nearest tenth of a million.) c. Predict the number of people who moved to another state in 2014. million (Round to the nearest tenth of a million.)
When t = 0, the value of n is approximately 3.93 million. The estimated number of people who moved to another state in 2005 is approximately 1.68 million. The predicted number of people who moved to another state in 2014 is approximately 6.81 million.
we need to substitute the given values of t (years since 1990) into the equation n = 0.03t² - 0.6t + 3.93. Let's calculate the values accordingly:
a. When t = 0 (which corresponds to the year 1990), we substitute this value into the equation:
n = 0.03(0)² - 0.6(0) + 3.93
n = 0 + 0 + 3.93
n ≈ 3.93
So, when t = 0, the value of n is approximately 3.93 million. In this context, it means that in the year 1990, around 3.93 million people moved to another state.
b. To estimate the number of people who moved to another state in 2005 (t = 2005 - 1990 = 15), we substitute this value into the equation:
n = 0.03(15)² - 0.6(15) + 3.93
n = 0.03(225) - 9 + 3.93
n = 6.75 - 9 + 3.93
n ≈ 1.68
Therefore, the estimated number of people who moved to another state in 2005 is approximately 1.68 million.
c. To predict the number of people who moved to another state in 2014 (t = 2014 - 1990 = 24), we substitute this value into the equation:
n = 0.03(24)² - 0.6(24) + 3.93
n = 0.03(576) - 14.4 + 3.93
n = 17.28 - 14.4 + 3.93
n ≈ 6.81
Hence, the predicted number of people who moved to another state in 2014 is approximately 6.81 million.
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Samantha wants to enclose 1680 ft² for a rectangular horse pen. The length will be 2 ft longer than the width. Find the dimensions of the pen. (Hint: A = lw)
The dimensions of the rectangular horse pen are 40 feet (width) and 42 feet (length).
What are the dimensions of the rectangular horse pen?The area of a rectangle is expressed as:
Area = length × width
Given that, the length of the pen will be 2 feet longer than the width, so the width is x feet and the length can be expressed as (x + 2) feet.
Using area of rectangle:
Area = length × width
1680 = (x + 2) × x
Simplify
1680 = x² + 2x
x² + 2x - 1680 = 0
Solve for x:
Using factoring
(x + 42)(x - 40) = 0
Hence:
x + 42 = 0 or x - 40 = 0
x = -42 or x = 40
Since we are dealing with dimensions, we use the positive value:
The valid solution is x = 40.
This represents the width of the horse pen.
The length can be found by adding 2 to the width:
Length = x + 2
Plug in x = 40
= 40 + 2
= 42
Therefore, the length is 42 feets.
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Please help me it’s due today!!!!
(a) The sum of the interior angles of a regular octagon is 1,080⁰.
(b) The measure of one interior angle is 135⁰.
(c) The sum of the exterior angles of the octagon is 360⁰.
What is the sum of the interior angles of a regular octagon?The sum of the interior angles of a regular octagon is calculated as follows;
The formula for sum of interior angles is given as;
sum of interior angles = (n - 2) x 180
where;
n is the number of sidesThe number of sides of a regular octagon = 8
sum of interior angles = (n - 2) x 180
sum of interior angles = (8 - 2) x 180
sum of interior angles = 1,080⁰
The measure of one interior angle = 1,080 / 8 = 135⁰
The sum of exterior angles of a polygon = 360⁰, so the sum of the exterior angles of the octagon is 360⁰.
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does anyone knows the solution of this
The complete solution to the system is 25/17, 61/17, 2/17 respectively.
How to find solution to a matrix system?Using the Gauss-Jordan elimination method to find the solution of the system of linear equations represented by the given augmented matrix:
Starting matrix:
[1 -2/3 -1/3 | 1]
[1 -2 6 | -17]
[-3 -7 3 | -43]
Add Row 1 to Row 2 and Row 3:
[1 -2/3 -1/3 | 1]
[0 -4/3 17/3 | -18]
[0 -1 0 | -40]
Multiply Row 2 by -3/4:
[1 -2/3 -1/3 | 1]
[0 1 -17/4 | 27/2]
[0 -1 0 | -40]
Add Row 1 to Row 2 and Row 3:
[1 0 -7/4 | 19/2]
[0 1 -17/4 | 27/2]
[0 0 -17/4 | -13/2]
Multiply row 3 by -4/17:
[1 0 -7/4 | 19/2]
[0 1 -17/4 | 27/2]
[0 0 1 | 2/17]
Add Row 3 to Row 1 and Row 2:
[1 0 0 | 25/17]
[0 1 0 | 61/17]
[0 0 1 | 2/17]
Therefore, the solution of the system of linear equations is:
x = 25/17
y = 61/17
z = 2/17
So the solution is [25/17, 61/17, 2/17].
Thus the completed augmented matrix is:
[1 0 0 | 25/17]
[0 1 0 | 61/17]
[0 0 1 | 2/17]
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The correct statement is the center of the circle does not lie on the x-axis or the y-axis.
Given the equation of a circle, x² + y² – 2x – 8 = 0. Transform this equation in standard form of equation of circle
The standard form of the equation is (x – 1)² + y² = 8, and the radius of this circle is not the same as the radius of the circle whose equation is x² + y² = 9. Also, the center of the circle does not lie on the x-axis or the y-axis.
Therefore, the correct statement is the center of the circle does not lie on the x-axis or the y-axis.
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I need help. please help me with this question.
Answer:
1,000 - 50x > 600
-50x > -400
$0.00 < x < $8.00
Can someone please help me?
Answer:
90Y + 36
Step-by-step explanation:
just multiply the length by the width.
9 X (8y + 4 + 2y)
= 9 X (10y + 4)
= 90Y + 36
b). A pupil solved a fraction task as follows: 3/5 + 1/2 = 4/7. Identify what the child did wrongly. Explain how you would solve the task correctly, leaving your answer as a common fraction.
The correct answer to the fraction task is 3/5 + 1/2 = 11/10 expressed as a fraction and 4/7 is incorrect answer
The pupil made an error in their addition of 3/5 and 1/2, resulting in an incorrect answer of 4/7.
To solve the task correctly, we need to find a common denominator for 3/5 and 1/2.
The least common multiple of 5 and 2 is 10, so we can rewrite the fractions with a denominator of 10 as follows:
3/5 = 6/10
1/2 = 5/10
Now we can add the fractions:
6/10 + 5/10 = 11/10
Hence, the correct answer to the fraction task is 3/5 + 1/2 = 11/10 expressed as a fraction.
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9. Lucy is designing a block for a quilt. She measured one of the
angles. Use the numbers and symbols on the tiles to write and
solve an equation to find the unknown angle measure.
? 110
40° 70° 110° 180° +
Equation:
Solution: ? =
= ?
The unknown angle measure is 70 degrees.
We are given that;
The values 40° 70° 110° 180°
Now,
One possible equation to find the unknown angle measure is:
180 - 40 - 70 = ?
This equation is based on the fact that the sum of the angles in a triangle is 180 degrees. To solve for ?, we can subtract 40 and 70 from both sides of the equation:
180 - 40 - 70 = ? - 40 - 70 180 - 110 = ? 70 = ?
The solution is ? = 70 degrees.
Therefore, by equation the answer will be 70 degrees.
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7. Is (s + t)^2 equivalent to s^2 + 2st + t^2? Explain or show your reasoning.
Answer:
Yes, (s + t)^2 is equivalent to s^2 + 2st + t^2. This can be shown through the process of expanding the expression (s + t)^2 using the FOIL method (multiplying first, outer, inner, and last terms).
First, we can rewrite (s + t)^2 as (s + t)(s + t).
The first terms are s and sThe outer terms are s and tThe inner terms are t and sThe last terms are t and tNow, we do the multiplication and combine like terms:
s*s + s*t + t*s + t*t
s^2 + st + st + t^2
s^2 + 2st + t^2
7) Line BC is a tangent to the circle. Find angle ACB.
The measure of the angle BCA is 50 degrees.
How to find the angle BCA?The angles at the circumference subtended by the same arc are equal.
The angles at the circumference on the same segment theorem states that angles in the same segment of the circle are equal.
Therefore, let's use the theorem to find the angle ∠BCA in the circle.
Hence,
∠BCA = ∠BOA
Finally,
∠BCA = 50 degrees.
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WILL GIVE BRAINLIEST IF CORRECT
The value of x is 5.
Using Angle Sum Property
The sum of the angles in a triangle is always 180 degrees. So, we can set up an equation:
9x-1 + 62 + 74 = 180
Simplifying the equation:
9x + 135 = 180
9x = 45
x = 5
Therefore, x is 5.
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I really dont get this ,can yall help me out
Graph XY with endpoints X(-3, 1) and Y(4,-5) and its image after the composition.
Translation: (x, y)→(x, y + 2)
Rotation: 90° about the origin
The graph of its image after the composition is shown in graph.
We have to given that;
XY with endpoints are,
⇒ X (-3, 1) and Y (4,-5)
Now, After Translation (x, y)→(x, y + 2) we get;
X = (- 3, 1)
X' = (- 3, 1 + 2) = (- 3, 3)
Y = (4, - 5)
Y' = (4, - 3)
And, After Rotation: 90° about the origin.
That is, (x, y) = (y, - x)
The points of image are,
X'' = (3, 3)
Y'' = (- 3, - 4)
Thus, The graph of its image after the composition is shown in graph.
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What are the x and y coordinates so i can graph it
Answer:
Step-by-step explanation:
X is the horizontal line and Y is the vertical line. :)
The pair of solids is similar. Find the volume of each solid. Round to the nearest tenth, if necessary.
The volume of small solid is 24 cm³ and volume of big solid is 216 cm³.
Given that
Height of small solid = 4 cm = h₁
Width of small solid = 2 cm = w₁
Length of small solid = 3 cm = L₁
Width of big solid = 6 cm = w₂
Let,
Height of small solid = h₂
Length of small solid = L₂
Since we know that volume of solid = length x width x height
Therefore, volume of small solid = 4x2x3 = 24 cm³
Since both the solids are similar,
So,
⇒ w₁/w₂ = h₁/h₂
⇒ 2/6 = 4/h₂
⇒ h₂ = 12 cm
Also,
w₁/w₂ = L₁/L₂
⇒2/6 = 3/L₂
⇒ L₂= 9 cm
Hence , the volume of big box = 6x12x9
= 216 cm³
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