The standard form for the Parabola is given as
[tex]y=-\frac{1}{7} x^2+\frac{6}{7} x+\frac{33}{7}[/tex]
This is further explained below.
What are the steps to turn it into standard form?Generally, the equation for is mathematically given as
x^2-6 x+7 y-33=0
Solve for y.
Move all terms not containing y to the right side of the equation.
7 y=-x^2+6 x+33
Divide each term into 7 y=-x^2+6 x+33 by 7 and simplify.
[tex]y=-\frac{x^2}{7}+\frac{6 x}{7}+\frac{33}{7}[/tex]
To write a polynomial in standard form, simplify and then arrange the terms in descending order.
y=a x^2+b x+c
Reorder terms.
[tex]y=-\left(\frac{1}{7} x^2\right)+\frac{6}{7} x+\frac{33}{7}[/tex]
[tex]y=-\frac{1}{7} x^2+\frac{6}{7} x+\frac{33}{7}[/tex]
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The people go to a restaurant. Their bill comes to $78.00. They decide to split the cost. One person pays 4.50 the next person pays 3 time that amount. How much will the their person have to pay
Answer:
13
Step-by-step explanation:
u multiply 4.50 x 3 it makes it 13.5 so they basically need to pay more .
Two cars, initially at rest and 5 km apart at t=0 , simultaneously move toward each other. Car A travels at a constant speed of 55 km/hour, while car B travels at a constant speed of 12 km/hour. How far will car A travel before meeting car B in the middle?
Car A travel before meeting car B in the middle is 268 second.
Constant Speed Motion
An object is said to travel at constant speed if the ratio of the distance traveled by the time taken is constant.
Expressed in a simple equation, we have:
v= d/t
Where
v = Speed of the object
d = Distance traveled
t = Time taken to travel d.
From the equation above, we can solve for d:
d = v . t
And we can also solve it for t:
t = d/v
Two cars are initially separated by 5 km are approaching each other at relative speeds of 55 km/h and 12 km/h respectively. The total speed at which they are approaching is 55+12 = 67 km/h.
The distance of an object can be defined as the complete path travelled by an object. For example. if a car travels east for 5 km and takes a turn to travel north for another 8 km, the total distance travelled by car shall be 13 km.The time it will take for them to meet is:
t = 5/67
t = 0.0746 hours
Converting to seconds: 0.0746*3600 = 268.56
Therefore the closest answer is d. 268 s.
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Suppose the height of Rodrigo's triangle in the Example is doubled. Will the area of the triangle also double? Explain how you know.
Yes, area of the triangle also get doubled when the height of the triangle is doubled.
As given in the question,
Let 'b' be the base of the triangle
'h' be the height of the triangle
Area of the triangle = (1/2) × b × h
Base of the new triangle = b
Height of the new triangle doubled =2h
Area of new triangle = (1/ 2) × b × 2h
= 2 {(1/2) × b × h}
= 2 Area of original triangle
Therefore, area of the triangle also get doubled when the height of the triangle is doubled.
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A random sample of students were surveyed as to how much non-school screen time
they had each week (for purposes of the survey, screen time was defined as: time
spent online, on social media, watching TV, or playing video games) and if their grade
average was above or below 80.
Screen Time
Answer:
above below
9
9
16
15
17
less than 4 hours
4-8 hours
8-12 hours
more than 12 hours 14
%
11
What percent of the students who spend less than 4 hours a week on screens reported
a grade average below 80? Round your answer to the nearest whole number percent.
20
Submit Answer
p
attempt 2 out of 2
The percentage of students who spend less than 4 hours a week on screens which reported a grade average below 80 is 50%
Given, we have the report representing children spending time online, on social media or watching T.V, which has there effect on there grades as above or below 80.
By the question we know that the number of students who spends less than 4 hours a week on screen is:
9 + 9
= 18
And among the 18 students there are 9 students whose grade average is below 80.
So the percentage of the students who spends 4 hours a week on screen is:
= 9 ÷ 18 × 100%
= 100/2
= 50%
hence 50% students spend less than 4 hours a week on screens.
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On April 11, Maria's checking account balance was $922. She wrote a check on April 29 for $280, withdrew
$40 on May 1, and deposited $150 into her account on May 14. What is her account balance on May 15?
Write your answer as a whole dollar amount, such as: $148.
Circle the problem in which you need to regroup use the strategy that is easier to find the sum. a 496 + 284. B 482 + 506
Correct answer is B. In A, there is no number from which to regroup (all the numbers may be added together), so you must regroup. In B, the number 6 cannot be added to the number 2, therefore you must regroup.
What is regrouping in mathematics?Making groups of ten while doing math operations like addition or subtraction is known as regrouping. This frequently occurs while dealing with double digits. Technically speaking, it also happens whenever you get a response that is more than 10.
Additionally, if the numbers you are adding result in a two-digit number and they are not in the farthest left column, you must regroup. When the numbers you are subtracting from are more than the ones you are subtracting from, you regroup.
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10n + 2 =43 what is the value of n
Answer:
n = 41/10 OR 4.1
Step-by-step explanation:
10n + 2 =43
10 + 2 - 2 = 43 - 2
10n = 43 - 2
10n = 41
10n/10 = 41/10
n = 41/10
Answer:
n = 41/10Step-by-step explanation:
10n + 2 = 43 what is the value of n
10n + 2 = 43
10n = 43 - 2
10n = 41
n = 41/10
-------------------
check
10 * 41/10 + 2 = 43
41 + 2 = 43
43 = 43
the answer is good
A small business office uses 307 pieces of paper every 3 days. Which is a reasonable estimate for the pieces of paper the business office uses in 7 days?
A.
600
B.
2,100
C.
900
D.
700
700 is a reasonable estimate for the pieces of paper the business office uses in 7 days
How to calculate the estimate ?The office uses 307 pieces of paper every 3 days
The first is to calculate the number of paper used per day
= 307/3
= 102.3
The number of paper used in 7 days can be calculated as follows
= 7 × 102.3
= 716
Hence 700 is a reasonable estimate for the pieces of paper the business office uses in 7 days
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Assuming a linear relationship, find the missing value in the table below.
The missing value in the table below assuming a linear relationship is 18
How to find the missing value in the table below assuming a linear relationship?The table of values represents the given parameters
From the question, we understand that the relationship is a linear relationship.
This means that the x and y values change at constant rate
From the table, we have
As x increases by 1, y increases by 2
So, the missing value is
Missing value = 16 + 2
Evaluate
Missing value = 18
Hence, the missing value in the table below assuming a linear relationship is 18
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Using the approximation 3.14 for I, what is the radius of a circle with circumference 44 m?
The radius is m. (Round to the nearest tenth as needed.)
Given the value of the circumference, the radius of the circle to the nearest tenth is 7.0m.
What is the radius of the given circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The circumference of a circle is expressed mathematically as;
C = 2πr
Where r is radius and π is constant pi ( π = 3.14 ).
Given the data in the question;
Circumference of the circle C = 44mConstant pi π = 3.14Radius r = ?Plug the given values into the circumference formula above and solve for r.
C = 2πr
44m = 2 × 3.14 × r
44m = 6.28 × r
Reorder the equation and divide both sides by 6.28
6.28 × r = 44m
( 6.28 × r )/6.28 = 44m/6.28
r = 44m/6.28
r = 7.0m
Given the value of the circumference, the radius of the circle to the nearest tenth is 7.0m.
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A person earns 16000 one year and gets a 5% raise in salary. What is the new salary?
Answer:
The new yearly salary is $16,800
Step-by-step explanation:
Amount of raise.
5% = 0.05
Multiply the original salary times the percentage of the raise.
$16000 * 0.05 = $800
New salary .
$16000 + $800 = $16,800
One-step Solution
$16000+($16000 * 0.05) =$16,800
if u arent beinggreat simply dont answer :)
Answer:
Step-by-step explanation:
The exponent is -3, making it 10 to the power of negative 3. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 3 times:
9.2 -> 0.0092
The answer is D.
Answer:
0.0092.
Step-by-step explanation:
I have an explanation on this same question. Apparently, you have a duplicate of this.
The admission fee to a carnival is $5.00, and each game costs an additional $1.50 to play. The carnival also has a
special admission price of $14 that includes unlimited games. What is the minimum number of games a customer
must play to make the special admission price less than paying for each game separately?
Answer:
9.3333333
Step-by-step explanation:
14÷1.50=9.333333
According to a cookie recipe, I need 3 large eggs if I need to make 38 cookies.
Now, you want to make 300 cookies for a bake sale. How many eggs do I need?
O 25
O24
O22
O 23
Answer:
24
Step-by-step explanation:
Because 300 cookies / 38 cookies = 7.89,..
Then 7.89,... x 3 = 23.68,...
round to the nearest tenths= 24
In order to meet the demand for the bake sale, a total of 300 cookies will be prepared, requiring the use of precisely 24 fresh eggs.
To calculate how many eggs you need to make 300 cookies, set up a proportion based on the information given in the cookie recipe:
Number of eggs / Number of cookies = Constant ratio
Let the number of eggs needed for 300 cookies as "x."
So, x eggs / 300 cookies = 3 eggs / 38 cookies
Now, cross-multiply and solve for "x":
x * 38 = 3 * 300
38x = 900
x = 900 / 38
x = 23.6842
x ≈ 24
Therefore, you need 24 eggs to make 300 cookies for the bake sale.
Thus, option (b) is correct.
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Which expression could represent the product of 15 and the quantity 12 more than the number of wailles?
Use w-4 to solve once you have the correct expression! Does your expression make sense????
a. 15+12-w
bw(15+12)
45(w+12)
d. 15-12+w
15x+180 is the required expression. Let the number be 'x'. For more than we would use addition.
A mathematical expression is the collection of mathematical symbols that results from the valid combination of numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.
2x + 3 is an illustration of a mathematical expression with a variable. Each and every variable needs to have a coefficient, or a value multiplied by the variable. The number 2 is the coefficient of x in the expression 2x + 3, which translates to 2x times plus 3.
Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.
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Odessa and Daxton are making a table that is 3 1/3m high and has an area of 32m2. What is the width?
Answer: 9.6 meters
Step-by-step explanation:
See attached image
Do the 3 lengths form a triangle? 5, 17, 29 *
yes or no
Answer:
No they do not because it does not qualify for a triangle due to the extreme differences in messurments
Step-by-step explanation:
Drag and drop the range of each data set into the boxes.
PLEASEE
The range of data set 1 is 4
The range of data set 2 is 4.
What is the range?A line plot is a graph that is made up of a number line and check marks above the number line. The check mark above the number represents the frequency of the number in the data set. For example, if the number 3 on the number line has 2 checkmarks above it, it means 3 has a frequency of 2.
The range is the difference between the highest number in a dataset and the smallest number in the dataset. Range is a measure of variation.
Range = highest number - lowest number
The range of data set 1 = 7 - 3 = 4
The range of data set 2 : 7 - 3 = 4
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A model of the total cost C, in dollars, to produce n cell phones is given by
C = 240n + 800.
Find the C-intercept and the n intercept
Answer:
C intercept is 800, n intercept is -3.3333...
Step-by-step explanation:
C = 240n + 800 is a linear equation (the graph is a line)
C-intercept is the point with the coordinates ( 0, C-intercept ) where the line C = 240n + 800 is intersecting the vertical C-axis and
n-intercept is the point with the coordinates (n-intercept, 0) where the line C = 240n + 800 is intersecting the horizontal n-axis.
Find the C-intercept:
n has to be 0 for our line to intercept the C-axis, so substitute n = 0 in our given equation
C = 240n + 800
C = 240·0 + 800
C = 800
Find the n-intercept:
C has to be 0 for our line to intercept the n-axis, so substitute C = 0 in our given equation
C = 240·n + 800
0 = 240·n + 800, subtract 800 from both sides
-800 = 240 ·n, divide both sides by 240
-800/240 = n
-3.(3) = n
if sin 22.6°=5/13, what is cos 67.4° ?
The value of cos 67.4° is 5/13.
According to trigonometric identities used in mathematics, sin of an angle is equal to cos of 90 - the given angle. Mathematically, this means that, suppose we have an angle x, then-
sin(90 - x) = cos x
Here, we are given that sin 22.6° = 5/13. As we can observe that (90 - 67.4) is equal to 22.6, and we need to find the value of cos 67.4° only. Thus we can write the given equation as follows-
sin22.6° = sin(90 - 67.4°)
= cos 67.4°
Thus, sin 22.6° = cos 67.4°
Hence, cos 67.4° = 5/13
Thus, the value of cos 67.4° comes out to be 5/13.
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PLEASE HELP ASAP! I am struggling piece wise function
Answer:
[tex]f\left(x\right)=\begin{cases}2x\:+\:10&-6\:\le x\: < \:-3\\ -x\:+\:1&-3\: < \:x\: < \:2\end{cases}[/tex]
Step-by-step explanation:
Looking at the graph we can see that it is a linear graph of the form
y = mx + b where m is the slope and b is the y intercept.
In one region the slope is positive and the other region it is negative
Interval 1 is -6 ≤ x < -3
How do I know that one uses a ≤ and the other uses a <?
A filled circle means that the point is included in the domain(range of x values) and therefore (≤, ≥) and an unfilled circle means it is not(<, >)
Find the slope of line in this interval
Take two points, say (-5, 0) and (-3, 4)
Slope = rise/run = (4 - 0)/(-3 - (-5) = 4/2 = 2
So slope of line is 2 and its equation in slope-intercept form is
y = 2x + b
Choose any point, plug in values, solve for b
Point (5, 0) is chosen
0 = 2(-5) + b
0 = -1 + b
or
b = 10
So equation of line in the interval (-6 ≤ x < -3) is
y = f(x) = 2x + 10
Interval 2: -3 < x < 2
We see this line intersects the y axis at y = 1
So b = 1
Equation is y = mx + 1
Choose point x = 0, y = 1 to find slope m
At x = 0, y = m(1) + 1 = m + 1
So m + 1 = 0
m = -1
So equation of this line is
y = f(x) = -1x + 1 in the interval -3 < x < 2
Putting all these together we get the piecewise function as:
[tex]f\left(x\right)=\begin{cases}2x\:+\:10&-6\:\le x\: < \:-3\\ -x\:+\:1&-3\: < \:x\: < \:2\end{cases}[/tex]
Calculate the paychecks of the following people. They make time and a half for any hours beyond 40. Round all values to two decimal places.
Answer:
Sue Black: 40 hours, $270
Jerry Atrix: 30 hours, $154.50
Sam Ting: 38.75 hours, $339.06
Step-by-step explanation:
Firstly, 40 hours is a workweek of 8-hour shifts. It's good to remember. Otherwise, we can multiply 8 by 5 and get 40 anyway. That's the hours of Sue Black, and she earns:
40*$6.75 = $270
Jerry worked for (note you can easily add in memory if you do the fractions first):
7.25+3+6.75+8+5 = 7.25+6.75 + 3+8+5 = 14 + 16 = 30
Earnings:
30*$5.15 = $154.50
Sam worked a quarter of an hour less than Sue each day. That means that his total time was:
40 - 5 * 0.25 = 40 - 1.25 = 38.75
Earnings:
38.75*$8.75 = $339.0625 ≈$339.06
Using inductive reasoning, what is the most reasonable conjecture for the number of triangles in the eighth figure in the pattern? Enter your answer as a number.
The most reasonable conjecture for the number of triangles in the eighth figure in the pattern is that there are 8 triangles in the eighth figure in the pattern
How to determine the most reasonable conjecture for the number of triangles in the eighth figure in the pattern?The given figure represents the given parameter
From the figure, we have the following parameters
Pattern 1 = 4 trianglesPattern 2 = 6 trianglesPattern 3 = 8 trianglesWhen represented as a sequence, we have the following terms
4, 6, 8.....
The above sequence represents an arithmetic sequence with the following properties
First term, a = 4
Common difference, d = 2 i.e. 6 - 4
The most reasonable conjecture for the number of triangles in the eighth figure in the pattern is calculated by the following arithmetic sequence formula
Tn = a + (n - 1) * d
So, we have
T8 = 4 + (8 - 1) * 2
Evaluate
T8 = 18
Hence, the most reasonable conjecture for the number of triangles in the eighth figure in the pattern is that there are 8 triangles in the eighth figure in the pattern
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Two steamers leave a port on river at the same time traveling in opposite directions each is traveling 20mph how long will it take for them to be 140 miles apart
The correct answer is 3.5.
Let t be the amount of time each steamer takes.
Two steamers that are headed in opposite directions depart a port on a river at the same time, according to the information provided.
Given that both steamers move at the same speed, they would cover the same distance in t hours.
Given that both steamers covered 140 miles, we can write the following equation to reflect this data:
rate time distance
First stream 20 t 20t
Second stream 20 t 20t
140
setting the equation ,
20t + 20t = 140
40t = 140
t = 140/40
t = 3.5
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the equation of the line parallel to y=-X+11 through the point (-3,5)?
Step-by-step explanation:
I guess the result is needed again in slope-intercept form.
this is in general
y = ax + b
"a" being the slope, "b" being the y-intercept (y value when x = 0).
when a line is parallel to another line, this means they both have the same slope.
so, we can use the same "a" from the original line : -1
to get "b" we use the given point coordinates :
5 = -1×-3 + b = 3 + b
2 = b
so, the full equation is
y = -x + 2
to lose 1 lb of body fat you need to burn 3.500 calories. If you burn 450 more calories than you take in each day, how long will it take to lose 1 lb? What about 10 lb?
Step-by-step explanation:
1 pound is equivalent to 3500 calories.
if you burn 450 more calories per day, it will take as many days as the times 450 fits into 3500 :
3500 / 450 = 7.77777777... days
for 10 pounds we need to burn 10×3500 = 35000 calories.
35000 / 450 = 77.77777777... days (10 times more logically than for 1 pound).
Jamal has 34 toy soldiers. He wants to arrange the soldiers into one or more equal-sized lines. Which list shows all the possibilities for the number of toy soldiers Jamal could place in each line
The list that shows all the possibilities for the number of toy soldiers Jamal could place in each line is 1, 2, 17 and 34.
How to illustrate the information?From the information, Jamal has 34 toy soldiers. He wants to arrange the soldiers into one or more equal-sized lines.
It should be noted that the factors of 34 are 1, 2, 17, and 34.
Therefore, the list that shows all the possibilities for the number of toy soldiers Jamal could place in each line is 1, 2, 17 and 34.
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Given f\left(x\right)=8-3xf(x)=8−3x, find the following
The value of the function f(2) for the function with the equation f(x) = 8 - 3x is 2
How to determine the value of the function?The function value is given as
f(x) = 8 - 3x
The above is a linear function
As a general rule
Linear functions are function that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
From the question, we have the value to be
f(2)
The above means that we determine the value of the function when x = 2
i.e., f(x) = ? when x = 2 or we substitute 2 for x in f(x)
Next, we test the above function with the x value
So, we have
f(x) = 8 - 3x
Substitute 2 for x in f(x)
f(2) = 8 - 3 x 2
Evaluate the product in the above equation
So, we have
f(2) = 8 - 6
Evaluate the difference in the above equation
So, we have
f(2) = 2
Hence, the value of the function f(2) for the function with the equation f(x) = 8 - 3x is 2
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Possible question
Given f(x)=8−3x, find the following: f(2)
Brenda and Jenna saved up $81.75 and $45.25 respectively to buy a gift for Mother's Day. How
much money in all have the sisters set aside for the gift?
Answer: $127
Step-by-step explanation: $81.75+$45.25=$127
Shelby measured the volume of a cylinder and determined it to be 58.8 cm³. The teacher told her that she
was 4.98% too high in her determination of the volume. What is the actual volume of the cylinder?
The actual volume of the cylinder is 61.73 cm³
Percentage error is the error introduced in a measurement. The formula for the error is given as :
Error = Percentage error * measured volume
According to the question we have been given that
determined volume of cylinder = 58.8 cm³
Percentage error = 4.98%
thus, error = 4.98% * 58.8
= 0.0498 * 58.8
= ±2.93 cm³
The formula for the actual volume is given as
Actual volume = measured volume ± error
= 58.8 ± 2.93 cm³
As the error is high we will do addition we get
= 58.8 + 2.93 cm³
= 61.73 cm³
hence the actual volume is 61.73 cm³
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