Answer:
[tex]p=1/2\ or\ 0.5\ inches[/tex]
Step-by-step explanation:
From the question we are told that
Equation of cross section is [tex]y+5= \frac{1}{2x^2}[/tex]
Generally the equation can be rewritten mathematically as
[tex]y+5= \frac{1}{2}x^2[/tex]
[tex]x^2=(y+5)2[/tex]
[tex](x-0)^2=(y-(-5))2[/tex]
Generally the equation of a parabola with vertical axis is mathematically given by
[tex](x - h)2 = 4p(y - k)[/tex]
Therefore comparing equations
[tex](x-0)^2=(y-(-5))2[/tex]
[tex]4p=2[/tex]
[tex]p=2/4[/tex]
The distance from the bulb to the vertex of the cross section is given by
[tex]p=1/2\ or\ 0.5\ inches[/tex]
Which answer choice below represents the greatest percent change? F. To earn a position on the school’s wrestling team, Colin increased his weight from 170 pounds to 185 pounds. G. A 42” flat screen television originally priced at $630 is now on sale for $441. H. Marshall grew from 60 inches to 66 inches over the summer break. J. Derrick cut a pipe measuring 17 feet so that it now measures 11 feet.
Answer:
f
Step-by-step explanation:
A man needed to sell a car. He priced it at 3500 the first day. The second day he reduced the price by 15%. What was the price of the car after this reduction?
Answer:
Step-by-step explanation:b
What is the measure of QS?
Answer:
21.9mm
Step-by-step explanation:
6.2+ 15.7 = 21.9
hope this helps....
a rectangle has a length of 22 feet less than 6 times its width. if the area is of the rectangle is 868 square feet,find the length of the rectangle
Answer:
Length=62 feet
Step-by-step explanation:
L x W =area area= 868 L=6W-22
868=W x (6W-22)
868=6W^2-22W
reorder equation
6W^2-22W-868=0
Factor
(3W-42)(2W+20.7)=0
3W=42
W=14, then L=6(14)-22=62
Check:
62x14=868
The length of the rectangle is 62 feet.
Given,
A rectangle has a length of 22 feet less than 6 times its width.
The area of the rectangle is 868 square feet.
We need to find the length of the rectangle.
What is the area of a rectangle?It is given by:
A = Length x width
What is middle-term factorization?We have,
ax² + bx + c
a x c = p x q
The sum of p and q must be equal to b.
Find the length of the rectangle.
L = 6W - 22 ______(1)
Find the width of the rectangle.
Width = W ______(2)
Find the area of the rectangle.
A = L x W
868 square feet = L x W
From (1) and (2)
868 = (6W -22) x W
868 = 6W² - 22W
6W² - 22W - 868 = 0
Solve for W.
6W² - 22W - 868 = 0
Using middle-term factorization.
2( 3W² - 11W - 434 ) = 0
3W² - 11W - 434 = 0
3W² - ( 42 - 31 )W - 434 = 0
3W² - 42W + 31W - 434 = 0
3W ( W - 14 ) + 31 ( W - 14 ) = 0
3W + 31 = 0
3W = - 31
W = - 31 / 3 ( Can not be a negative)
W - 14 = 0
W = 14
Putting W = 14 in (1)
L = 6W - 22
L = 6 x 14 - 22
L = 84 - 22
L = 62
Thus the length of the rectangle is 62 feet.
Learn more about finding the dimension of a rectangle here:
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Which math expression means "the sum of 33 and 18"? O A. 33 = 18 O B. 33. 18 O C. 33 - 18 O D. 33 + 18
Answer:
D. 33 + 18
Step-by-step explanation:
Sum in mathematics is the same as addition or plus.
As such the sum of two or more numbers is the addition of these numbers or the result obtained when the plus sign is placed in between the given numbers.
Hence, the sum of 33 and 18 may be expressed as
33 + 18
Option D is right
One number is 6 less than another. Their sum is 14. Find the numbers.
Answer:
4 and 10
Step-by-step explanation:
10-4=6
and 10 plus 4 equals 14
so the numbers are 4 and 10
HELP ME PLEASEEEEEE THANK YOU
Answer:
from shortest to longest
NR
RS
NS
Step-by-step explanation:
HOPE IT HELPS
5
4
2
1
O
3
4
5
A
Which equation best represents the line? (4 points)
Oy - 3x - 1
Oy - 3x + 1
Answer:
The equation best represents the line is:
y = 3x-1Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where
m is the slopeb is the y-interceptTaking the two points
(0, -1)(1, 2)Determining the slope between the points (0, -1) and (1, 2)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:-1\right),\:\left(x_2,\:y_2\right)=\left(1,\:2\right)[/tex]
[tex]m=\frac{2-\left(-1\right)}{1-0}[/tex]
Refine
[tex]m=3[/tex]
We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.
As we are given the point (0, -1)
It means at x = 0, y = -1
Thus, the y-intercept b = -1
now substituting b = -1 and m = 3 in the slope-intercept form
y = mx+b
y = 3x + (-1)
y = 3x-1
Therefore, the equation best represents the line is:
y = 3x-1Dawn enjoys exercising on the hiking trail by her house. She ran 2/5 of
the trail on Monday and then ran a different 1/3 of the trail on Tuesday.
How much of the trail had she covered on the two days?
Answer:
11/15 of the trail
Step-by-step explanation:
Step one:
given data
She ran 2/5 of the trail on Monday
Then ran a different 1/3 of the trail on Tuesday
Required
The total distance covered for Monday and Tuesday
Step two:
Total= 2/5+1/3
lcm= 15
Total= 6+5/15
Total= 11/15
At the beach, a child is filling a plastic bucket with sand. If the bucket is in the shape of a cylinder, with a height of 9 inches and a radius of 4.5 inches, approximately how much sand will fill the bucket? (Use 3.14 as an approximate of pi.)
A) 254.3
B) 508.7
C) 572.3
D) 2,289.1
Answer:
Volume of a Cylinder = πr²h
v = 3.14 * (0.5)² * 2.5
v = 3.14 * 0.25 * 2.5
v = 1.96 Ft³
Step-by-step explanation:
Answer:
Step-by-step explanation:
a
Please helpppp meeee
================================================
Explanation:
Let's go through the answer choices one at a time.
A) The AA postulate is only used for similar triangles, and not congruent triangles. We need information about at least one pair of sides. Using the angles only isn't enough. We can rule out choice A.B) The HL postulate only applies to right triangles. These triangles are acute triangles, so we can rule out choice B.C) This is the answer as we can rule out choice D, so this is the only thing left. Also, if we know that angle A = angle A'' and angle B = angle B'', then we could use the ASA theorem to prove the triangles congruent.D) This is not a valid congruence theorem. This is because we could have ambiguous cases that arise and lead to confusion. Also, it is possible that if we know two sides and a non-included angle, then a triangle may not be able to be formed. It will depend on the angle and side values. Therefore, we can rule out choice D.Z/7=8 what is the missing number and how do you figure it out
Answer:
56
Step-by-step explanation:
Multiply 7 to both sides to get x by itself.
z/7=8
z=8(7)z=56Check:
56/7=8What is the slope of the line whose equation is 12=4x−6y?
Enter your answer in the box.
Solve for y in the equation C = 5x² +y
Answer:
y=C-5x^2
Step-by-step explanation:
like to have some leftovers. I've discovered that the proper ratio of turkey to people is 12 pounds of turkey for every 8 people. If 36 people are going to be eating, how many pounds of | turkey do I need to buy?
Answer:
A
Step-by-step explanation:
Took the test
There is a need for 58.5 pounds of turkey for 36 people.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The proper ratio of turkey to people is 12 pounds of turkey for every 8 people.
Let the number of pounds would be x for 36 people
According to the given situation, we can write the ratio would be as:
12 pounds of turkey : 8 people = x pounds of turkey : 36 people
⇒ 12 / 8 = x / 36
Apply the cross-multiplication operation,
⇒ 8x = 13 × 36
Apply the multiplication operation,
⇒ 8x = 468
⇒ x = 468/8
Apply the division operation,
⇒ x = 58.5
Therefore, there is a need for 58.5 pounds of turkey for 36 people.
Learn more about the Ratio here:
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What is the area of the figure below?
A 22 cm
B 24 cm2
C 48.5 cm2
D 56 cm
Simplify 2 + 3/5x - 1 - 1/5x
Answer:
6
Step-by-step explanation:
6 is the answer to your question
A coach throws a football from a height of 4 feet with an initial velocity of 59 feet per second at an elevation angle of 45 degrees. Which parametric equation represents the path of the football
Answer:
[tex]x=(59cos 45\textdegree)t,y=4+(v_0sin45\textdegree)t-16t^2[/tex]
Step-by-step explanation:
From the question we are told that
Height [tex]h=4feet[/tex]
Initial velocity of[tex]v_0=59 feet/sec[/tex]
Angle [tex]\theta= 40\textdegree[/tex]
Generally the parametric equation for projectile motion is mathematically given by
[tex]x=(v_0cos\theta)t,y=y_0+(v_0sin\theta)t-16t^2[/tex]
Therefore
[tex]x=(59cos 45\textdegree)t,y=4+(v_0sin45\textdegree)t-16t^2[/tex]
The parametric equation that represents the path of the football
[tex]x=(59cos 45\textdegree)t,y=4+(v_0sin45\textdegree)t-16t^2[/tex]
Answer:
C
Step-by-step explanation:
Michael's High School is selling tickets to its spring musical. On the first day of ticket sales the school sold 1 adult ticket and 3 student tickets for a total of $38. The second day of sales, the school sold 5 adult tickets and 1 student ticket for a total of $78
Write a system of equations to represent the number of tickets sold each day
Determine the price of an adult ticket and a student ticket
Answer:
adult ticket price: $14
student ticket price: $8
Step-by-step explanation:
x = adult ticket
y = student ticket
system equations:
[tex]x + 3y = 38 \\ 5x + y = 78[/tex]
elimination method:[tex]x + 3y = 38 |multiple \: by \: 1\\ 5x + y = 78|multiple \: by \: 3 \\ \\ x + 3y = 38 \\ 15x + 3y = 234 \\ subract \: them: \\ - 14x = - 196[/tex]
substitute:[tex] - 14x = - 196 \\ - x = \frac{ - 196}{14} \\ - x = - 14 \\ x = 14[/tex]
find the y using substitution method:
x+3y=38
14+3y=38
3y=24
y=24/3
y=8
so the price of an adult ticket is $14 and the price of student ticket is $3
What is the reason that absolute value is always written as a positive?
Absolute Value is talking about numbers so it must be positive
Absolute Value is like a clock it has only positive numbers
Absolute value does not always have to be positive
Absolute value is talking about distance (Distance from zero); distance is always
measured by positive numbers.
Answer:
Absolute value is talking about distance (Distance from zero); distance is always measured by positive numbers.
Find the equation of a line that contains the points (0,4) and (3,7). Write the equation in slope-intercept form.
Answer:
y=mx+b
y= 1x + 4
Step-by-step explanation:
m= y2-y1/x2-x1
m= 7-4/3-0
m= 3/3
m=1
y=mx+b
7= 1*3+b
7=3+b
-3 -3
4=b
y=1x+4
A school has 840 pupils, if the school hall has seats 85% of the pupils, how many pupils will have no seats?
Answer:
126
Step-by-step explanation:
So theres 840 people and 85% got a seat
We just do 840 * 85% = 714
then to find the people without the seat
840 - 714 = 126
x2+y2=r2 Solve for y
Answer: [tex]y=\sqrt{r^{2} -x^{2} }[/tex]
Step-by-step explanation:
x^2+y^2=r^2 --> subtract x^2 to other side
y^2=r^2-x^2 --> square root both sides
y=sqrt(r^2-x^2)
What is the graph of g(x) = 2^x-1 + 3
Answer: its D
Step-by-step explanation:
Mariam Ali
0.1 Express the ratio as a fraction in simplest form:18 ounces to 3 cups
2 points
O 6 to 1
O 1/6
O 18/3
O 3/18
[tex]\huge\star{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}\star[/tex]
18 ÷ 3
= 6/1
Option [a] 6 to 1 is correct !
can someone help me figure this out
Answer:
I think the answer is Z is 45 degrees
hope this helps!
Answer:
The value of tangent Z is
[tex] \frac{3}{4} [/tex]
Note that the question asks for the value of tan z NOT angle z.
Step-by-step explanation:
[tex] \tan(z) = \frac{opposite}{adjacent} = \frac{21}{28} = \frac{7 \times 3}{7 \times 4} = \frac{3}{4} [/tex]
WORTH 20 POINTS PLS HELP!!!
On a windy morning, a hot air balloon starts rising and flying away from the top of a hill. The altitude, h, in feet, of the balloon x hours after starting its ascent from the hill, can be modeled by the function:
Part B: There is a positive and negative x intercept for this function. What is the positive x-intercept?
Explain what this x-intercept represents in the given situation.
h(x)=-16x2+64x+80
Here the positive intercept should be considered as the -1 and 5.
Calculation of the positive intercept:Since X-Intercept shows the landing point i.e. bottom of the cliff since all x intercepts contains a y value of 0.
In this case it would be 0 feet.
So,
[tex]h(x)= -16x^2-16x+80x+80[/tex]
h(x)= -x(16x-16) +5(16x+16)
h(x)= (-x+5)(16x+16)
x intercepts = -1 and 5
Learn more about intercept here: https://brainly.com/question/15546484
find the value of x in the figure below
Answer:
24
Step-by-step explanation:
cuz its an iscosceles triangle so the angles are the same so
2x-4=44 and solve
What is the value of x in the equation Negative two-fifths x minus 2 = 18? –50 –40 –8 –6
Answer:
A. -50
Step-by-step explanation:
your welcome!
Brandi rolls a fair Six-sided Number cube flips a fair coin, and then rolls the number cube again. Which outcome is part of sample space?
Answer:
Options aren't given but explanation and answer is below:
Step-by-step explanation:
First action/trial - Rolling a fair dice (6-sided number cube)
Second action - Flipping a fair coin
Third action - Rolling a fair dice
In this experiment, all the equipment are fair. What this means is that there is no bias; every face of each equipment has an equal chance of emerging tops.
In your options, you should have three values per option.
The first would be the number resulting from the first throw of dice.
The second would be head or tail; which are the only two faces of a coin.
The third would be the number resulting from the second throw of dice.
So ONE of those options will be a part of the sample space, which is enlisted below:
Trial A: {1, 2, 3, 4, 5, 6}
Trial B: {Head, Tail}
Trial C: {1, 2, 3, 4, 5, 6}
* If there's an option like {9, Tail, 2} it will be wrong, because it has an element "9" which does not fall within the prescribed sample space.
* Also, if we follow the order in which Brandi conducted this experiment, an option like {Head, 6, 5} will be wrong, since the elements are wrongly placed.
