SOLUTION
Equation of a parabola is given by the equation
[tex]y=a(x-h)^2+k[/tex]Where (h, h) are the coordinates of the vertex.
From the question given, the vertex is (2, 0)
So, h = 2, k = 0.
The y-intercept is given as (0, 12).
So, this means that x = 0 and y = 12
Substituting the values for h, k, x and y into the equation we have
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ 12=a(0-2)^2+0 \\ \\ 12=a\times-2^2+0 \\ \\ 12=4a \\ \\ a=\frac{12}{4} \\ \\ a=3 \end{gathered}[/tex]Now, let's substitute the value of a into the equation to get equation for the parabola.
This becomes
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ y=3(x-2)^2+0 \\ \\ y=3(x-2)^2 \\ \\ \end{gathered}[/tex]Jena's income is $3800 a month, and she plans to budget 13 of her income for savings and 16 of her income for groceries.
What fraction of her income does she plan to spend each month on these two items together?
The fraction of Jena's income does she plan to spend each month on these two items together is 1/2
The fraction of her income does she plan to spend each month on the two itemsJena's income for the month = $3800Fraction of Jena's income for savings = 1/3Fraction of Jena's income for groceries = 1/6Amount of Jena's income spent on savings = 1/3 × $3800
= 1266.666666666666
Approximately,
= $1,266.67
Amount of Jena's income spent on groceries = 1/6 × $3800
= 633.3333333333333
Approximately,
= $633.33
Amount spent on the two items = $1,266.67 + $633.33
= $1900
Fraction of Jena's income spent on the two items = 1/3 + 1/6
= (2+1) / 6
= 3/6
= 1/2
So therefore, Jena spent 1/2 of her income on savings and groceries.
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[tex]k(x) = 3(2) {}^{x} - 8[/tex]. Is the function linear, quadratic, exponential or neither?
An exponential function is defined as a function of the form:
[tex]f(x)=a(b)\placeholder{⬚}^x+c[/tex]where a, b and c are constants.
We notice that the function given has this form, therefore the function given is an exponential function.
Please help me with this, show full work for all questions, thank you!Question 3
Answer:
0.375
Explanation:
The probability of red and purple can be calculated as the frequency for rean and purple over the total frequency
Red has a frequency of 4
Orange has a frequency of 1
Yellow has a frequency of 1
Green has a frequency of 7
Blue has a frequency of 1
Purple has a frequency of 2
The total frequency is
4 + 1 + 1 + 7 + 1 + 2 = 16
And the frequency for red and purple is
4 + 2 = 6
Then, the probability is equal to
P = 6/16 = 0.375
So, the answer for question 3 is 0.375
A shirt costs ₹(a2 –ab -b2 ) , a pair of trousers cost ₹(2a2 +8ab-2b2 ) and a pair of shoes cost ₹(a2 –3ab+4b2 ) .After collecting these three items from the store, Ranjan paid ₹(2a+b )2 .What balance will Ranjan receive from the cashier ?
The balance Ranjan will receive from the cashier is ₹ 0
How to determine the balanceBased on the information given, we have that;
shirt costs ₹(a² –ab -b² ) pair of trousers cost ₹(2a² +8ab-2b² ) pair of shoes cost ₹(a² –3ab + 4b² ) Ranjan paid ₹(2a+b )2Now, expand the bracket for the payment, we have;
(2a+b )²
(2a +b) (2a + b)
Multiply through
4a² + 2ab + 2ab + b²
Add like terms
4a² + 4ab + b²
Now, let's add the amount for the items bought
a² –ab -b² + 2a² +8ab-2b² + a² –3ab + 4b²
add like terms
4a² + 4ab + b²
Now, subtract the amounts
4a² + 4ab + b² - 4a² + 4ab + b²
₹ 0
Hence, the balance is ₹ 0
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Determine the equation of the line that passes through the points (0,−10) and (−8,1).
Solution:
Given the points below;
[tex]\left(0,−10\right)\text{ }and\text{ }(−8,1)[/tex]To find the equation of the line that passes through the points, we will apply the formula below
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)=(0,-10) \\ (x_2,y_2)=(-8,1) \end{gathered}[/tex]Substitute the values of the coordinates into the formula above
[tex]\begin{gathered} \frac{y-(-10)}{x-0}=\frac{1-(-10)}{-8-0} \\ \frac{y+10}{x}=\frac{1+10}{-8} \\ \frac{y+10}{x}=-\frac{11}{8} \\ Crossmultiply \\ 8(y+10)=-11(x) \\ 8y+80=-11x \\ 11x+8y+80=0 \end{gathered}[/tex]Hence, the equation of the line is
[tex]11x+8y+80=0[/tex]The graph is shown below with the points indicated using a graphing tool
In the expression below, what operation should be done first?
4 + 8 ÷ 2
Answer:
Division
Step-by-step explanation:
Using the tool PEMDAS, you will see the order that you must complete an equation in, P=Parenthesis E=Exponents M=Multiplication D=Division Addition S=Subtraction
solve x=y+4, where x=3
if x=3 we get
[tex]3=y+4\rightarrow y=3-4=-1[/tex]Find the slope between the points with coordinates
(-2,3) and (4, 5).
Answer:
1/3 or 2/6
Step-by-step explanation:
you just plug the coordinates into a calculator and look at the rise over run.
The registrars office at Acc predicts that 90% of the 6,950 spaces open on various math classes will be available during the first week of registrationA. The percent of spaces that will be filled after the first week of registration is %B. A good estimate of the number of spaces that will be filled after the first week of registration is Spaces
A: 10%
B: 6950*10%=695
The midpoint of segment AB is (2,4). If the coordinates of point B are (5,7), find the coordinates of point A.
A (1, 1)
B (-1, 1)
C (1, -1)
D (-1, -1)
Answer:
I don't know why you asking me??
Answer:-1,1
Step-by-step explanation:
-1,1
triangle ABC has a>b>c. if one of the angles in the triangle is 60 degrees, name the angle that can be equal to 90degrees
Answer:
Angle a
Step-by-step explanation:
the sum of the interior angles of a triangle is 180. If one angle is 60 and another angle is 90, then the third angle has to be 30.
60 + 90 + 30 = 180
90>60>30
Need help with this ASAP Ignore the top video.
The average rate of change of the function is found as 1.
What is termed as the rate of change of function?The rate of change function has been described as the rate during which one quantity changes in relation to another. The rate of change from y coordinates to x coordinates can be calculated as Δy/ Δx = (y2 - y1)/ (x2 - x1 ).For the given question;
The function is given by the equation;
g(x) = -x² - 9x + 27
The interval of the function lies as;
-9 ≤ x ≤ -1.
Let,
a = -1 ans b = -9
Then,
g(a) = g(-1), Put x = -1 in the function.
g(-1) = -(-1)² - 9(-1) + 27
g(-1) = 35
Now, g(b) = g(-9), Put x = -9 in the function.
g(-9) = -(-9)² - 9(-9) + 27
g(-9) = 27
Thus, the average rate of change of the function is-
Average rate of change = [g(a) - g(b)]/[a - b]
= [35 - 27]/[-1 + 9]
= 8/8
= 1
Thus, the average rate of change of the function is found as 1.
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Find the surface area of each figure. Round your answers to the nearest hundredth. DO
NOT leave in terms of pi.
The surface area of the figure is calculated as 150.72 [tex]mi^2[/tex] and when rounded off to the nearest hundredth, it comes out as 151 [tex]mi^2[/tex].
What is Surface area?A solid object's surface area can be stated as a measurement of the overall space that the object's surface takes up. As an alternate, surface area can also be described as the area of the entire outer part, or which is said as the uppermost layer of any kind of 3D object.
Square units are used in the calculation. The total area of all the outside surfaces makes up the surface area of a three-dimensional object, which is also expressed in square units.
As an example, we can take that in order to find the exact surface area of a cuboid, we have to add the areas of all 6 faces.
In this figure, we can see that it can be stated as a cylinder.
So, as we know the formula of the surface area of a cylinder can be written as:
2[tex]\pi[/tex]rh + 2[tex]\pi r^2[/tex]
Here r = 8/2
=4 mi
h = 2 mi
Thus, putting the values, we have,
Surface area = [2 x 3.14 x 4 x 2] + [2 x 3.14 x 4 x 4]
= 50.24 + 100.48
= 150.72 [tex]mi^2[/tex]
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Question 4 of 10 What is the scale factor from ABC to DEF? A BO 72 42 35 65 B 66 O A. 2 OB. O O D. 6 Ico
Answer:
C
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{EF}{BC}[/tex] = [tex]\frac{11}{66}[/tex] = [tex]\frac{1}{6}[/tex]
The local grocery store is having a sale on sports drinks. For a particular brand ofsports drink, a 12-pack of 16-ounce bottles costs $10. 76. What is the unit price(per ounce) for the sports drink? Round your answer to the nearest cent.
The 12-pack contains bottles of 16 ounces each.
The total content of sports drinks is 12 × 16 = 192 ounces.
The unit price per ounce is the ratio of the total price to the total contents:
[tex]p=\frac{10.76}{192}=0.06[/tex]The unit price per ounce is $0.06
Which of the following best describes AD?17D17сA. MedianB. AltitudeC. Perpendicular bisectorD. Angle bisector
The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side thus bisecting that side.
Hence, Median best describes the line.
Option A is the correct option,
Which answers choice correctly illustrates the quotient as a fraction A) 913 ÷ 29 = 31 14/29B) 852 ÷ 16 = 53 5/16C) 200 ÷ 46 = 4 8/25D) 852 ÷ 16 = 53.25
Using long division:
So:
[tex]\begin{gathered} \frac{913}{29}=_{\text{ }}Quotient\frac{remainder}{_{\text{ }}divisor} \\ so\colon \\ \frac{913}{29}=31\frac{14}{29} \end{gathered}[/tex]Answer:
A
Let h(x) = (fog)(x) =
f(x) =
4
(x-7) ²
Find f(x) given g(x) = x − 7.
-
F(x)= ?
Answer:
[tex]\frac{4}{x2}[/tex]
Step-by-step explanation:
h (x) = log (N) = [tex]\frac{4}{x -2} {2}[/tex]
g (x) = (x - 1)
g (x) = [tex]\frac{4}{x2}[/tex]
Question
Which expression is equivalent to -40(4) +2³?
The expression equivalent to -40(4) +2³ is -152 by the concept of BODMAS Rule.
What is equivalent expression?It is generally understood that two things are equivalent if they are the same. Similar to this, analogous mathematical expressions are those that are the same even if they appear to be different. However, when the values are plugged into the expression, both expressions provide the same outcome.
What is BODMAS rule?BODMAS is formally known as Brackets (Numbers inside the Bracket always comes first)
Priority for brackets is Orders in a bar (the power)
Division
Multiplication
Addition
Subtraction
To solve the above expression, follow the above order
-40(4) +2³ = -160+8 = -152
Therefore, the expression equivalent to -40(4) +2³ is -152.
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Describe a series of transformations Matt can perform to device if the two windows are congruent
A transformative sequence is a particular arrangement of transforming events. This suggests that a series of transformations may manage more than one transition, and that the order in which they occur is crucial. A and B are similar in this case.
Congruent is what?When two figures or objects in geometry have the same shapes, sizes, or are mirror images of one another, they are said to be congruent.
Formally, two sets of points are said to be congruent if, and only if, an isometry, which is a collection of rigid motions including translation, rotation, and reflection, can transform them into one another.
This shows that resizing an object will not allow it to be properly aligned with another object, only by moving and reflecting it. Therefore, two independent plane figures on a piece of paper are congruent if we can cut them out and then precisely line them up. The paper might be distributed.
Each box is the same size in terms of length and width. The only change is where the figure is located.
Transformations can be divided into four categories: translation, rotation, reflection, and dilation.
Two figures are said to be "congruent" if they can be positioned perfectly over one another. Congruent refers to things that are exactly the same size and shape.
Hence, A and B are congruent.
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Please answer this question with an explanation. Thank you. :)
The rate is positive because she is withdrawing funds from her account. So, Option C is the correct option.
What is the rate of change?The momentum of a variable is represented by the rate of change, which is used to mathematically describe the percentage change in value over a defined period of time.
How do you calculate the slope's rate of change?The slope of a graphed function is determined using the average rate of change formula. Divide the change in y-values by the change in x-values to find the average rate of change.Jessica's savings account balance is plotted against the number of months.
Rate of withdrawal from her account is given as:
Amount in Savings account/Number of months
= 1000/10
= 100 dollars/month
Therefore, Jessica is withdrawing 100 dollars per month from her savings account.
As a result, the rate is positive because she is taking money out from her account. Option C is thus the right option.
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Find the image of D (0, -2) after the composition of translations
(x, y) → (x+10, y − 8) and (x, y) → (x − 7, y + 15).
The ordered pair that represents the image of the point after the transformation is (3, 5)
How to determine the transformation of the point?The ordered pair of the point is given as
D = (0, 2)
The above point is an ordered pair on a coordinate plane
The sequence of transformations of the points is given as
(x, y) → (x+10, y − 8) and (x, y) → (x − 7, y + 15).
When the above transformations are applied on the point, we have:
So, we have the following equation
(x, y) → (x + 10 - 7, y − 8 + 15)
Evaluate the sum and the difference
So, we have the following equation
(x, y) → (x + 3, y + 7)
Recall that
D = (0, -2)
So, we have
D' = (0 + 3, -2 + 7)
Evaluate
D' = (3, 5)
Hence, the image of point D is (3, 5)
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please hurry. I need help on all three questions. please show working clearly.
Aisha and her children went into a bakery and will buy cupcakes and brownies. Each cupcake costs $3 and each brownie costs $2.25. Aisha has a total of $15 to spend on cupcakes and brownies. Write an inequality that would represent the possible values for the number of cupcakes purchased, c, and the number of brownies purchased, b.
The inequality equation is 3c + 2.25b <=15 which represents the possible values of cupcakes and brownies that can be purchased by Aisha with the given amount of money.
Cost of each cupcake = $3
Cost of each brownie = $2.25
Total money available with Aisha to spend on cupcakes and brownies = $15
Let c represent the number of cupcakes purchased by Aisha and b represent the number of brownies purchased by Aisha
Formulating the inequality equation we get the following:
Cost of each cupcake*Number of cupcakes purchased + Cost of each brownie*Number of brownies purchased <= Total money available with Aisha
3c + 2.25b <=15
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A man realizes he lost the detailed receipt from the store and only has the credit card receipt with the after-tax total. If the after-tax total was $1,253.07, and the tax rate in the area is 7.1%, what was the pre-tax subtotal?
To answer this question, we can proceed as follows:
1. We have that the after-tax total was $1,253.07.
2. We have that the tax rate in the area is 7.1%.
3. Then to find the pre-tax subtotal, we can proceed as follows:
[tex]7.1\%=\frac{7.1}{100}=0.071[/tex]Therefore, we have:
[tex]x+0.071x=1253.07[/tex]4. Finally, we need to add the like terms as follows:
[tex]1.071x=1253.07[/tex]And using technology, we can divide both sides by 1.071:
[tex]\begin{gathered} \frac{1.071}{1.071}x=\frac{1253.07}{1.071} \\ \\ x=1170 \\ \end{gathered}[/tex]Therefore, the pre-tax subtotal is $1,170.
What’s the slope I need help
Answer:
-8/3
Step-by-step explanation:
You want the slope of the line shown in the graph.
Slope from point coordinatesWhether counting grid squares on the graph, or using the slope formula, it is convenient to choose two points on the grid where the line crosses the intersection of grid lines.
It appears, the line passes through grid points (1, 4) and (4, -4). Using the slope formula, we find the slope of the line to be ...
m = (y2 -y1)/(x2 -x1)
m = (-4 -4)/(4 -1) = -8/3
The slope of the line is -8/3.
Counting grid squaresThe slope is the ratio of "rise" to "run" for the line. From the two points we see where the line crosses grid intersections, we have a "rise" of -1 from y=4 to y=-4, and a "run" of 3 from x=1 to x=4.
rise/run = -8/3 = slope of the line
Given that (3, 2, –6) and (–2, 5, 1) are solutions of two equations in a system of three linear equations, which of the following is true about the system?
The system can only be consistent and independent.
The system can be either inconsistent and independent or consistent and dependent.
The system can be either inconsistent and dependent or consistent and independent.
The system can only be inconsistent and dependent.
The statement which is true about the system of three linear equations is that: B. the system can be either inconsistent and independent or consistent and dependent.
What is a system of three linear equations?A system of three linear equations can be defined as a type of algebraic equation of the first order that has three (3) variables with each of its term having an exponent of one (1).
In Mathematics, a system of three linear equations is considered as a consistent system when it has at least one solution. However, a system of three linear equations is considered as an inconsistent system when it has no real solution.
Additionally, a system of three linear equations is considered as an independent system when it possesses exactly one solution while it is a dependent system if it has an infinite number of solutions.
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A person takes 50 minutes average to get to work. Time may vary by 10 minutes depending on traffic. Drag and drop the correct number or equation in each box to make the sentences true. "If the time taken by the person to get to work is T minutes, the equality that models this situation is_____ the minimum time taken by the person to get to work is _____min, the maximum time taken is____min.
Answer:
"If the time taken by the person to get to work is T minutes, the equality that models this situation is | t - 50 | = 10 the minimum time taken by the person to get to work is 40 min, the maximum time taken is 60 min.
Step-by-step explanation:
The difference between the time and 50 minutes is 10 minutes.
This can be expressed as:
|t - 50| = 10The minimum and maximum time can be found by solving the equation above:
t - 50 = 10 ⇒ t = 60 minutes,t - 50 = - 10 ⇒ t = 40 minutes.The blanks to be filled in as:
1) | t - 50 | = 10,2) 40,3) 60.Answer To this question so that we can move onto the next question so that we can get done with all this homework so we can go play
We need to transform a number that is written in scientific notation to the standard notation. For that we have to move the dot to the right, because the exponent of the power is positive, every time we do that we will subtract one from the exponent. When there is no more dot we will add zeros. This is done below:
[tex]\begin{gathered} 2.07\cdot10^5 \\ 20.7\cdot10^4 \\ 207\cdot10^3 \\ 2070\cdot10^2 \\ 20700\cdot10 \\ 207000 \end{gathered}[/tex]The correct answer is 207,000.
Please help which best explains an effect of the Diaspora on Jewish people?
The BEST explanation of the effect of the Diaspora on Jewish people is d) They developed new rituals to accommodate the loss of the Temple.
What new rituals were developed by the Diaspora Jews?Some of the new rituals developed by the Diaspora Jews included:
Accommodating plenty of other cultures from different geographies.Utilizing the Torah to represent the symbol of God.Elevation of prayer and deeds of lovingkindness as ways to connect to God instead of the Temple.The Diaspora did not affect the Jewish people by dividing their homeland, making the destroyed Temple of Jerusalem the center of their religiosity, or making Rabbis insignificant.
Thus, the Diaspora affected the Jewish people in Option D.
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Question Completion with Answer Options:a) Their homeland was divided into Israel and Judah.
b) The Temple of Jerusalem became the center of religious activity.
c) Rabbis no longer served as significant religious leaders.
d) They developed new rituals to accommodate the loss of the Temple.