here is the complete and correct question. Colton bounces a ball 3.268 feet in front of his feet. The path of
the ball from the time it hits the ground until it lands on the floor is represented by
f(x) =-4(x - 5)2 + 12
Assuming that Colton's feet are located at the origin, (0, 0), what is the maximum height of the ball (in feet)?
Answer:
12ft
step by step explanation:
This equation has been written in vertex form, and it has its vertex at (5, 12). Because the scale factor is not positive, it has a negative value, the graph for the question is going to open downward, such that the vertex,
that is the maximum height is 12 ft.
we have The equation of a parabola with vertex (h, k) to be
f(x) = a(x -h)² + k
when put in Comparison to your question function, we get that
a=-4
h=5
k=12
so the vertex (h, k) = (5, 12).
PLEASE HELP QUICK
The costume jewelry and accessories for the show are bought from sales racks at two different stores on different days. Use x to represent the price of each item on the sales rack at the first store and y to represent the price of each item on the sales rack at the second store.
On the first day, the students spent $30 on 4 items from the first store and 7 items from the second store. On the second day, the students spent $22 on 3 items from the first store and 5 items from the second store. On the third day, the students need to buy 10 items from the first store and 17 items from the second store.
What is the amount of money the students will need on the third day? Find your answer by creating and solving a system of linear equations based on the first day and the second day. Explain your reasoning.
Answer:
74
Step-by-step explanation:
Using linear equations, we are given two equations from the questions:
4x +7y=30 from day one and 3x +5y=22 from day two
Multiply the first equation by 3 and second by 4 giving us
12x +21y=90 and 12x +20y=88. Minus both equations.
12x - 12x +21y - 20y= 90 - 88, Gives you y=2,
You can now use the value of y to find x.
4x + 7y = 30
4x + 7(2)= 30
4x + 14= 30. Minus 14 on both sides giving you
4x=16. Divide both sides by 4.
x=4
Now use both values to find how much money is needed on the third day.
10x + 17y
=10(4) + 17(2)
=40 +34
=74
Draw triangle ABC by first drawing segment BC six inches long. Then draw a 60° angle at vertex B and a 60° angle at vertex C. Extend the segments so that they intersect at point A.
Answer:
Step-by-step explanation:
Given that segment BC is the base of the triangle, this drawing shows that triangle ABC is an equilateral triangle.
Since;
<B = <C = 60°
Then,
<A + <B + <C = [tex]180^{o}[/tex]
<A + 60° + 60° = [tex]180^{o}[/tex]
<A = [tex]180^{o}[/tex] - [tex]120^{o}[/tex]
= 60°
Thus,
AB = BC = AC = 6 inches
The construction is attached to this answer.
If the sinø=7/12, what is cosø?
Answer:
If the sinø=7/12, cosø is [tex]\frac{\sqrt{95} }{12}[/tex]
Step-by-step explanation:
We are given sinФ = 7/12
We need to find cosФ
The basic trigonometric functions of right triangle are:
[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]
[tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex]
We need values of adjacent and hypotenuse to find cosФ
Using Pythagoras theorem we can find the value of adjacent
[tex](Hypotenuse)^2= (Opposite)^2+(Adjacent)^2[/tex]
We have Hypotenuse= 12 and Opposite = 7 (because [tex]sin\theta=\frac{opposite}{hypotenuse}[/tex] and we are given [tex]sin\theta=\frac{7}{12}[/tex]
Inserting values and finding adjacent:
[tex](Hypotenuse)^2= (Opposite)^2+(Adjacent)^2\\(12)^2=(7)^2+(Adjacent)^2\\144=49+(Adjacent)^2\\144-49=(Adjacent)^2\\95=(Adjacent)^2\\\sqrt{(Adjacent)^2} =\sqrt{95}\\Adjacent=\sqrt{95}[/tex]
So, value of Adjacent is [tex]\sqrt{95}[/tex]
Now finding cosФ
[tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex]
Adjacent = [tex]\sqrt{95}[/tex], hypotenuse = 12
[tex]cos\theta=\frac{\sqrt{95} }{12}[/tex]
So, If the sinø=7/12, cosø is [tex]\frac{\sqrt{95} }{12}[/tex]
65.6g of sugar is needed to make 8 cakes how much is needed to make 5
Answer:
41g
Step-by-step explanation:
65.6/8= 8.2g per cake
8.2*5 cakes= 41g
Answer:
41g of sugar.Step-by-step explanation:
65.6g = 8 cakes
We need to find the sugar for 1 cake:
65.6 ÷ 8= 8.2 (gram for 1 cake)
The sugar for 5 cakes:
8.2 × 5= 41 (gram for 5 cakes)
whats 851,708 to the nearest hundred-thousand
Answer:
900,000
Step-by-step explanation:
because when you round number from 1-4 you put it down example: 1223
round to nearest thousand it is 1000 but when 5-9 is higher example: 1566 it is 2000
Answer:
900,000
Step-by-step explanation:
Bc The Ten Thousandths place is over 4
Graph the equation.
y-1 = -2(x-2)
Answer:
y-1 = -2(x-2) graph:
Answer:
Graph is below
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope:
−
2
y-intercept:
(
0
,
5
)
x
y
0
5
5
2
0
At a certain bookstore, you get a $5 coupon for every 4 books you buy. What is the least number of books you could buy to get $15 in coupons? Show your work.
Answer:
12books
Step-by-step explanation:
4 books → 1 $5 coupon
$15 coupon = $15 / $5 = 3times of $5 coupons
3 $5 coupons → 4 x 3 = 12 books
this is a topic on forming and solving equations. If you wish to explore more into this topic you can give me a follow on Instagram (learntionary) I'll be posting notes for many topics and will also be posting some tips :)
The number of books for $ 15 coupon is 12 books
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
From the bookstore :
Number of books for $ 5 coupon = 4 books
So ,
Number of books for $ 15 coupon = Number of books for $ 5 coupon x 3
Number of books for $ 15 coupon = 4 x 3 books
Number of books for $ 15 coupon = 12 books
Therefore , the number of books is 12
Hence , the number of books for $ 15 coupon is 12 books
To learn more about equations click :
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WILL MARK branniest answer if gotten right
Answer:
Line MN is the answer
Step-by-step explanation:
Image SQ as a line that extends forever, if you took line segment and also made it extend forever, then it would become parallel to line segment SQ, never touching or intersecting and going at the same angle.
Need help will mark brainliest
0Answer:
1) Exterior Angle Therorem
2) Isosceles Triangle Theorem
Step-by-step explanation:
Jada has time on the weekends to earn some money. A local bookstore is looking for someone to help sort books and will pay $12.20 an hour. To get to and from the bookstore on a work day, however, Jada would have to spend $7.15 on bus fare.
how would I write an equation for this? use e for her earnings and h for hours worked
What is the cost of making one burrito? (Remember that costs are negative.) Explain how you found your answer.
Answer:
it cost 5.99
Step-by-step explanation:
it all depends on the type of burrito
Will give brainliest if correct.
Answer:
y=(-9-2x)/3
Step-by-step explanation:
Last year, Summerfield Steel sold 6.5×104 pounds of steel to private businesses and 2.5×105 pounds of steel to government agencies. This year, they expect to sell 3 times that amount. How much steel would that be?
Answer:
9.45 × 10⁵ pounds of steel
Step-by-step explanation:
Last year, Summerfield Steel sold 6.5×10⁴ pounds of steel to private businesses and 2.5×10⁵ pounds of steel to government agencies.
Total amount of steel sold last year = (6.5 × 10⁴ + 2.5 × 10⁵) pounds = 315000 pounds = 3.15 × 10⁵ pounds
This year, they expect to sell 3 times that amount.
This year = 3 × 3.15 × 10⁵ pounds
= 9.45 × 10⁵ pounds of steel
please help and if you don't know the answer the don't put a random one thank you :(
hi i think the answers C z<=16.1 good luck:)
pls don't hate on me if im wrong:(
Answer:
Your answer will be C z<=16.1
Step-by-step explanation:
How to solve this would be to divide -4 from both sides and because you are dividing a negative you have to flip the sign.
i’ll give brainliest if it’s right
Answer:
bruh i cant see it
Step-by-step explanation:
Answer: what does the display say
A solid cylindrical metal is melted and recast into cubes of metal of side 3cm the base radius of the initial cylindrical metal is 10.5 and height is 63cm . how many cubes will be Madeline
Answer:
A solid cylindrical metal is melted and recast into cubes of metal of sides 3cm . The base radius of the initi… Get the answers you need, ... is melted and recast into cubes of metal of sides 3cm . The base radius of the initial cylindrical metal is 10.5cm and height is 63cm. How many cubes will be made.
Step-by-step explanation:
hope this is right!
HELP PLEASE Can you please give an explication when you answer
The temperature at 4:00 am was -3°C, and the temperature rose 9°C during the morning. What was the temperature by noon?
A. -6°C
B. -12°C
C. 6°C
D. 12°C
Answer:
C. 6°C
Step-by-step explanation:
-3°C + 9°C = 6°C
To control an infection, a doctor recommends that a patient who weighs 92 pounds be given 320 milligrams of antibiotic. If the antibiotic is given proportionally according to the patient's weight, how much antibiotic should be given to a patient who weighs 138 pounds?
A 400 milligrams
B 480 milligrams
C 550 milligrams
D 600 milligrams
Answer:
480 milligrams
Step-by-step explanation:
92 pounds → 320 milligrams
138 pounds → 320/92 x 138 = 480 milligrams
A quadratic function has an axis of symmetry at x=4 and contains the points (2, -6) and (7, -11). Find the equation in standard form (y=ax2+bx+c). Then state the "a" value in the equation.
Answer:
The equation in standard form is [tex]y = -x^{2}+8\cdot x -18[/tex]. The "a" value is -1.
Step-by-step explanation:
A quadratic function is the standard form of the parabola. We can take advantage of the symmetry property of the parabola by using the following formula from the Analytical Geometry:
[tex]y - k = C\cdot (x-h)^{2}[/tex] (1)
Where:
[tex]C[/tex] - Parabola constant, dimensionless.
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Depedent variable, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex of the parabola, dimensionless.
If we know that [tex](x_{1},y_{1})=(2,-6)[/tex], [tex](x_{2},y_{2})=(7,-11)[/tex] and [tex]h = 4[/tex], then we have the following system of linear equations:
[tex](x_{1},y_{1})=(2,-6)[/tex]
[tex]-6-k = C\cdot (2-4)^{2}[/tex]
[tex]4\cdot C +k = -6[/tex] (2)
[tex](x_{2},y_{2})=(7,-11)[/tex]
[tex]-11-k =C\cdot (7-4)^{2}[/tex]
[tex]9\cdot C + k = -11[/tex] (3)
By clearing [tex]k[/tex] in (2) and (3) and equalizing each other, we get that:
[tex]-6-4\cdot C = -11-9\cdot C[/tex]
[tex]5\cdot C = -5[/tex]
[tex]C = -1[/tex]
And the remaining variable is calculated by substituting directly on (3):
[tex]k = -11-9\cdot C[/tex]
[tex]k = -11-9\cdot (-1)[/tex]
[tex]k = -2[/tex]
Then, the equation of the parabola is:
[tex]y+2 = -(x-4)^{2}[/tex]
And the standard form of the equation is obtained by algebraic handling:
[tex]y+2 = -(x^{2}-8\cdot x + 16)[/tex]
[tex]y + 2 = -x^{2}+8\cdot x -16[/tex]
[tex]y = -x^{2}+8\cdot x -18[/tex] (4)
The equation in standard form is [tex]y = -x^{2}+8\cdot x -18[/tex]. The "a" value is -1.
Write a rule for the translation of ABC to A' B' C'
Answer:
(x-2,y-4)
Step-by-step explanation:
Here, we want to calculate the rule for the translation
From the question, we can see that the new image was just formed as a movement of the old image by some particular units
The x-axis was move sideways while the y-axis was moved further down
The number of units is thus;
Y from 12 to 8
A movement of -4
For the x-axis
we have a movement of two units toward the left
So the rule is;
(x,y) to (x-2, y-4)
Which scatterplot would have a trend line with a negative slope?
Michael has a set of 24 math problems to do for homework. Michael completed 1/4 of his homework in 3/4 of an hour. If he continues at this rate , what fraction of his homework would he complete in one hour ? A. 3/8 B. 2/3 C. 4/3 D. 3/2
Given:
Total number of problems = 24
Michael completed [tex]\dfrac{1}{4}[/tex] of his homework in [tex]\dfrac{3}{4}[/tex] of an hour.
To find:
What fraction of his homework would he complete in one hour.
Solution:
We have,
Part of work done in [tex]\dfrac{3}{4}[/tex] of an hour [tex]=\dfrac{1}{4}[/tex]
Part of work done in an hour [tex]=\dfrac{4}{3}\times \dfrac{1}{4}[/tex]
[tex]=\dfrac{1}{3}[/tex]
Therefore, he complete [tex]\dfrac{1}{3}[/tex] of his homework in 1 hour. Hence, all options are incorrect.
if triangle ABC=triangle DEC, and angle b=3x and angle e=6x-39, what is x
The value of x in the expression is 13.
What is a Triangle?A polygon which has three sides and three vertices is called as triangle.
The sum of all the angles of the triangle is 180°.
Given:
The triangle ABC = triangle DEC,
and angle b=3x and angle e=6x-39.
To find the value of x:
We know,
b = e
So, substituting the values,
3x = 6x - 39
3x = 39
x = 13.
Therefore, the value of x is 13.
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Please please please help John wants to buy a new video game it cost $39.00. He has $14.00 in his piggy
bank. He works for farmer Jones down the street for $5.00 an hour. How many
hours will he need to work before he can buy his new video game? Make and equation
Answer:
5 hours
Step-by-step explanation:
39 - 14 = 25
5 x 5 = 25
14 + 25 = 39
Answer:
5 hours
Step-by-step explanation:
John needs $39.00, he has $14 now, and He earns $5 a week working. x= how many hours.
Start by setting the equation,
$39.00= $5x + $14.00
Then solve by
1) subtracting 14 from both sides;
39(-14)= 5x+14(-14), by subtracting 14 on both sides you cancelled out the 14;
39 -14 = 5x becomes $25= 5x (39 -14 =25)
2) divide both sides by 5 to get x alone
25 (/5)=5x (/5) which becomes 25/5=x
3) 25/5 is 5
John must work 5 hours to have enough money to buy his video game.
Help, Its due in 15 minuets!
Answer:
All Congruent Angle Pairs
1) ∠1 and ∠3 are congruent **
2) ∠2 and ∠4 are congruent
3) ∠6 and ∠8 are congruent
4) ∠5 and ∠7 are congruent
5) ∠1 and ∠7 are congruent
6) ∠2 and ∠8 are congruent **
7) ∠3 and ∠5 are congruent
8) ∠4 and ∠6 are congruent **
Step-by-step explanation:
1) Vertical pairs
2) Vertical pairs
3) Vertical pairs
4) Vertical pairs
5) Alternate exterior angles
6) Alternate exterior angles
7) Alternate interior angles
8) Alternate interior angles
the pairs are
< 1 and < 3
< 4 and < 5
I think 2 and 8
the square root of 84 is it closer to 9 or 10
Answer: It is closer to 9
Step-by-step explanation: The square root of 84 is 9.16515139
Answer:
9
Step-by-step explanation:
The square root of 84 rounded the hundredth is 9.17, making it closer to 9 than 10.
solve for x:x+3.17=12.78
A blueprint of a plot of land has a scale of 1 1/4 cm to 3 1/4 m the length of the land is 20 cm on the blueprint if i represents the length of the actual peace of land. What is i
Answer:
52metre
Step-by-step explanation:
Let us use proportion in solving this question, the land has a scale of 1 1/4 cm to 3 1/4 m then the proportion is
( 1 1/4)/ (3 1/4 ) =[blueprint of the plot of land/length of the actual peace of land]
But we need to convert those mixed fractions to improper fraction for easy simplification
1 1/4= [(4×1)+4]= 5/2
3 1/4=[(4×3)+1)]=13/4
Then we can proceed with simplification as
(5/2)/(13/4)=[blueprint of the plot of land/length of the actual peace of land]
But we were given length of the actual peace of land as 20 cm, then
(5/2)/(13/4)=[blueprint of the plot of land/20]
If we cross multiply we have
[blueprint of the plot of land] ×13/4 =5/2 ×20
[blueprint of the plot of land] =(5/2 ×20)÷(13/4)
= 50/(13/4)
=(4×13)/50
= 52
Therefore, the length of the actual peace of land is 52metre
Answer: B) 52 miles
Step-by-step explanation:
393.3 in 10 years investment
Step-by-step explanation:
The question is not well structured. We can say;
$393.3 in 10 years investment at rate of 10% is equivalent to what?
Given
Amount invested = $393.3 (principal)
Time = 10years
Rate = 10% (assumed rate)
Required
Amount after 10 years
Amount = Principal + Interest
First we need to get the simple interest using the formula
SI = PRT/100
SI = $393.3 * 10 * 10/100
SI = $393.3*100/100
SI = $393.3
Amount in 10years = $393.3 + $393.3
Amount in 10years = $786.6
Hence $393.3 in 10 years investment at rate of 10% is equivalent to $786.6.
Note that the rate was assumed. Any value of the rate can be used. Just employ the same calculation steps.
Inequality to Verbal
-3 < x < 7
A. The domain is greater than or equal to -3 and less than
or equal to 7.
B. The range is greater than -3 and less than 7.
C. The domain is greater than -3 and less than 7.
D. The range is greater than or equal to -3 and less than or
equal to 7.
Answer:
C. The domain is greater than -3 and less than 7.
Step-by-step explanation:
Just like the other one
x is domain
< = less than
≤ = less than or equal to
Answer:
c
Step-by-step explanation:
should b. cause most true usagw 'the domain'
good luck