The volume of the rectangular prism will increase by 33% if the width, length, and height are each increased by 10%.
Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
The formula for the volume of a rectangular prism is:
V = l x w x h
where
“l” is the base length
“w” is the base width
“h” is the height of the prism
If the width, length, and height are each increased by 10%, the equation will now become:
[tex]V_{2}= 1.10 l * 1.10 w*1.10h[/tex]
[tex]V_{2}= 1.331* l*w*h[/tex] V = l*w*h
[tex]V_{2}= 1.331* V[/tex]
Hence, if the width, length, and height are each increased by 10%, the volume of the rectangular prism will increase by 33%.
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write the equation for a parabola with a focus at (6,-4)(6,−4)left parenthesis, 6, comma, minus, 4, right parenthesis and a directrix at y
The equation of the parabola is (x - 6)² = 6(y + 5.5).
Given that, a focus at (6,-4) and a directrix at y= -7.
We need to find the equation for a parabola.
What are focus and directrix?Parabolas are commonly known as the graphs of quadratic functions. They can also be viewed as the set of all points whose distance from a certain point (the focus) is equal to their distance from a certain line (the directrix).
The standard form of the equation of the parabola is (x - h)² = 4p(y - k), where
The vertex of the parabola is (h , k)
The focus is (h, k + p)
The directrix is at y = k - p
∵ The focus of the parabola is at (6, -4)
The coordinates of the focus are (h, k + p)
∴ h = 6
∴ k + p = -4 ⇒ (1)
∵ The directrix of the parabola is at y = -7
The directrix is at y = k - p
∴ k - p = -7 ⇒ (2)
Solve the system of equations to find k and p
Add equations (1) and (2) to eliminate p
∴ 2k = -11
Divide both sides
∴ k = -5.5
Substitute the value of k in equation (1) to find p
∵ -5.5 + p = -4
Add 5.5. to both sides
∴ p = 1.5
∵ The form of the equation is (x - h)² = 4p(y - k)
Substitute the values of h, k, and p in the form
∴ (x - 6)² = 4(1.5)(y - -5.5)
∴ (x - 6)² = 6(y + 5.5)
Therefore, the equation of the parabola is (x - 6)² = 6(y + 5.5).
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Your question is incomplete, probably the complete question/missing part is:
Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7
write equation in the standard form then identify the terms and the values of a,b and c
The sum of the squares of two consecutive integers is 25 find the integers
In a food court there are people eating hamburgers, burritos & pizza. P(h) = 0. 38 and P(b) = 0. 31. If there are 35 people eating pizza, what is the total number of people in the food court?
Answer should be rounded to the nearest WHOLE NUMBER
The total number of people in the food court eating pizza, burritos, and hamburgers is 113 (Approximate) or (Whole number)
People eating hamburger P(h) =0.38
People eating burritos P(b) = 0.31
Number of people eating pizza = 35
Let's suppose the total number of people is 1
So,
By adding the total number of people eating hamburgers and burritos
= 0.38+0.31
= 0.69
The ratio of the total number of people eating pizza = 1.00 - 0.69
= 0.31
So total number of people eating pizza = 0.31 = 35
By solving :
1 = 35 / 0.31
= (35*100)/31
= 3500/31
= 112.9 (we have to write it down in the nearest whole number)
Here we writing the approximate value of 112.9 = 113 (Approximate)
Hence, the total number of people in the food court in the nearest whole number is 113
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solve (x-3)(x+8)+(2x-x^2)
The required solution of the given expression is 7x-24.
What is expression?
An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined.
Given:
The given expression is
[tex](x-3)(x+8)+(2x-x^{2} )[/tex]
According to given question we have
By the expansion theorem we have
The expression is
[tex](x-3)(x+8)+(2x-x^2)\\\\=x^{2} +8x-3x-24+2x-x^{2} \\\\=7x-24[/tex]
Therefore, the required solution of the given expression is 7x-24.
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Joel is buying packs of baseball cards to add to his collection. He wants to have at least 65 total. He already has 15 and each pack has 5 cards, c, in it. How many packs will Joel need to buy in order to have at least 65 total cards?
Answer:
10 cards
Step-by-step explanation:
In order to find how many packs Joel needs to buy we need Make an equation
Equation = 5c + 15 = 65
where,
c = cards5c+15=65
Step 1: Subtract 15 from both sides.
5c+15−15=65−15
5c=50
Step 2: Divide both sides by 5.
5c/5 = 50/5
c=10
Therefore, Joel need to buy total of 10 cards in order to have at least 65 total cards
Please help and please hurry I have to submit it soon: The price of Stock A at 9 A.M. was $15.01. Since then, the price has been increasing at the rate of $0.13 each hour. At noon the price of Stock B was $15.76. It begins to decrease at the rate of $0.09 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
Answer: 8.3 hours
Step-by-step explanation: 15.76-15.01 is 0.75
Now just divide 0.75 from 0.09 and you get 8.3
Answer:
Step-by-step explanation:
Stock A= $15.01 increases by $0.13 an hour. $15.14
Stock B =$15.76 decreases by $0.09 an hour $15.65
15.65-15.14= 0.51
Use the diagram shown to answer the question. What
are the sine and cosine values of a 60° angle?
Answer: sin(60°)= [tex]\frac{\sqrt{3}} 2[/tex] and cos(60°)=[tex]\frac{1} 2[/tex]
Step-by-step explanation:
sine means opposite/hypothenus (SOH)
opposite=[tex]\frac{\sqrt{3}} 2[/tex] and hypothenus is 1
sin(60°) = [tex]\frac{\sqrt{3}} 2[/tex] ÷ [tex]\frac{1} 1[/tex]
= [tex]\frac{\sqrt{3}} 2[/tex] × [tex]\frac{1} 1[/tex]
= [tex]\frac{\sqrt{3}} 2[/tex]
cosine means adjacent/hypothenus (CAH)
adjacent= [tex]\frac{1} 2[/tex] and hypothenus is 1
cos(60°) = [tex]\frac{1} 2\\[/tex] ÷ [tex]\frac{1} 1[/tex]
= [tex]\frac{1} 2[/tex] × [tex]\frac{1} 1[/tex]
= [tex]\frac{1} 2[/tex]
- The circles are identical. Find the circumference of each circle. Round your
answer to the nearest tenth.
4x
6x - 6
Answer:
Circumference = 75.4
Step-by-step explanation:
Since the circles are identical, that means that the radii must be equal.
4x=3x+3
x=3
That means that radius = 12
The formula for the circumference = 2pi × radius
2pi × 12 = 24pi ≈ 75.4
Answer:
75.4 (nearest tenth)
Step-by-step explanation:
The diameter of a circle is the distance from one side of the circle to the other through the center. The diameter is the widest part of the circle.
The radius of a circle is the distance from the center to the circumference. The radius is half the diameter of a circle.
We have been given the radius of the circle on the left: r = 4x.
Therefore, as the diameter is twice the radius, the diameter of the circle on the left is: d = 2(4x) = 8x
We have been given the diameter of the circle on the right: d = 6x + 6
Equate the two diameters and solve for x:
⇒ 8x = 6x + 6
⇒ 8x - 6x = 6x + 6 - 6x
⇒ 2x = 6
⇒ 2x ÷ 2 = 6 ÷ 2
⇒ x = 3
Substitute the found value of x into one of the diameter expressions to find the diameter of both circles:
⇒ d = 8x
⇒ d = 8(3)
⇒ d = 24
Circumference of a circle
C = πd
(where d is the diameter)
Substitute the found diameter into the circumference formula:
⇒ C = πd
⇒ C = 24π
⇒ C = 75.39822...
⇒ C = 75.4 (nearest tenth)
Therefore, the circumference of each circle is 75.4 units (nearest tenth).
mav is older than justin. Their ages are consecutive integers find mavs age if the product of their age is 42
Answer:
7
Step-by-step explanation:
hope this works :)
consecutive numbers means 2 numbers next to eachother like 8 and 9 or 3 and 4
product means basically the result of numbers multiplying together, e.g. the product of 8×9 = 72
so if you use trial and error you will find 6 × 7 = 42 and since mav is older she must be 7 years old
Answer:
mav is 7
Step-by-step explanation:
let justin's age be n then mav is n + 1 and the product is
n(n + 1) = 42
n² + n = 42 ( subtract 42 from both sides )
n² + n - 42 = 0 ← in standard form
(n + 7)(n - 6) = 0 ← in factored form
equate both factors to zero and solve for n
n + 7 = 0 ⇒ n = - 7
n - 6 = 0 ⇒ n = 6
since n > 0 then n = 6
mav is n + 1 = 6 + 1 = 7
HELP I LITTERALLY DO NOT UNDERSTAND
Answer: what are the options tho?
Step-by-step explanation:
The quotient of a number and negative six plus eight is twenty-four
Answer:
the number is ..let X
X/-6+8=24X/2=24criss cross the number and we get 48Evaluate.
Quickly please!
Answer:
819,200
Step-by-step explanation:
First start by raising all the numbers to the power indicated:
5^4 = 625
8^5 = 32768
2^9 = 512
5^2 = 25
Then divide the numerators by the denominators:
625 / 8 = 78.125
32768 / 64 = 512
512 / 25 = 20.48
Finally, multiply all the numbers together
78.125 * 512 * 20.48 = 819200
(b) Find the equation of the straight line which passes through 81 +88 (i) the point (3, 2) and makes an intercept on the x-axis is twice as long as that on the y-axis. (ii) the point (-1, 3) whose intercept on the y-axis is thrice that on x-axis.
3x+y=0 and x+2y=7
i)
a= intercept on x axis
b= intercept on y axis
from the question
a=2b
x/2b+ y/b=1
x+2y=2b
since it passes through the point (3,2)
then 3+4=2b
7/2=b
x+2y=7 putting the value of b
ii) given b =3a
then x/a+ y/ 3a =1
3x+y=3a
it passes through ( -1,3) then
-3+3=3a
a=0
3x+y=0
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the following are like terms and can be combined together through addition: 5x and 3y question 2 options: true false brainly
It is false that 5x and 3y are like terms. They can not be combined together through addition.
Like terms are those who encompass the same variables raised to the identical power. The most effective difference is within the numerical coefficients. only we are able to integrate like terms in an expression. To make algebraic formulation simpler to work with, we integrate like phrases to shorten and simplify them.to combine like phrases, upload the coefficients while retaining the variables consistent.We integrate like terms to form one term.in contrast to terms are algebraic words that don't have the equal coefficients and can't be raised to the identical strength.An algebraic expression with unlike phrases is 5x + 3y as it consists of wonderful variables, x and y, and they're not raised to the same power.To learn more about like terms, visit :
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Find the surface area of the figure
Answer: 208 in^2
Step-by-step explanation:
4 2*8 rectangles
1 8*8 square
4 5*8/2 triangles
4(2*8)+8*8+4(5*8/2)=
4(16)+64+4(5*4)=
64+64+4(20)=
128+80=208 in^2
If m∠j=91 m∠l=16 and m∠k=73 list the sides of ∆JLK in order from smallest to largest
Answer:
ikj
Step-by-step explanation:
In a triangle:
The shortest side is opposite the smallest angle.The longest side is opposite the biggest angle.When labeling angles and sides of triangles, it is convention to label the side opposite an angle with the same letter but in lower case.
Therefore in ∆JLK:
Side j is opposite angle J.Side l is opposite angle L.Side k is opposite angle K.As 16 < 73 < 91
⇒ m∠I < m∠K < m∠J
As the angles of ∆JLK in order from smallest to largest are IKJ, then the sides of ∆JLK in order from smallest to largest are ikj.
[tex] {x}^{2} + 70 = 17x[/tex]
solve
I really neeed this done asap
Answer: x=7 x=10
Step-by-step explanation:
[tex]x^2+70=17x\\x^2+70-17x=17x-17x\\x^2-17x+70=0\\x^2-7x-10x+70=0\\x(x-7)-10(x-7)=\\(x-7)(x-10)=0\\x-7=0\\x=7\\x-10=0\\x=10[/tex]
Answer:
x = 7, x = 10
Step-by-step explanation:
x² + 70 = 17x ( subtract 17x from both sides )
x² - 17x + 70 = 0 ← in standard form
consider the factors of the constant term (+ 70) which sum to give the coefficient of the x- term (- 17)
the factors are - 10 and - 7 , since
- 10 × - 7 = + 70 and - 10 - 7 = - 17 , then
(x - 10)(x - 7) = 0 ← in factored form
equate each factor to zero and solve for x
x - 7 = 0 ⇒ x = 7
x - 10 = 0 ⇒ x = 10
Systems of equations with graphing
For the equations 7 x - y = 7 and x + 2 y = 6, we get the solution as x = 4 / 3 and y = 7 / 3.
We are given the equations:
7 x - y = 7 … (1)
x + 2 y = 6
x = 6 - 2 y … (2)
Substitute equation (2) in equation (1), we get that:
7 ( 6 - 2 y ) - y = 7
42 - 14 y - y = 7
15 y = 35
y = 35 / 15
y = 7 / 3
x = 6 - 2 ( 7 / 3)
x = 18 - 14 / 3
x = 4 / 3
Therefore, for the equations 7 x - y = 7 and x + 2 y = 6, we get the solution as x = 4 / 3 and y = 7 / 3.
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Divide. 5/6 ÷ −2/3
−5/4
negative fraction 5 over 4
−5/9
, negative fraction 5 over 9,
5/9
5 over 9
5/4
5 over 9
Answer:
[tex] \frac{ - 5}{4} [/tex]
Step-by-step explanation:
[tex] \frac{5}{6} \div \frac{ - 2}{3} [/tex]
When dividing two fractions, we turn the second fraction upside-down and multiply two expressions instead.
[tex] \frac{5}{6} \times \frac{ - 3}{2} = \frac{ - 15}{12} [/tex]
Now simplify the fraction by dividing it with biggest common divisor which is 3 in this case.
[tex] \frac{ - 5}{4} [/tex]
is the final result.
find the area of the polygon with the given points A (-5,-2) B (4,-2) C (4, -7) D (-5, -7)
7. Which statements about the values of 7.055
and 70.55 are true? Select all that apply.
7.055 is 10 of 70.55.
7.055 is 100 of 70.55.
70.55 is 10 times 7.055.
70.55 is 100 times 7.055.
7.055 is 10 times 70.55.
The statement which is true to the values of 7.055 and 70.55 are true is:
70.55 is 10 times 7.055. is true.
Given, the values are 7.055 and 70.55
statement A.
7.055 is 10 of 70.55
= 70.55×1/10
= 705.5
⇒ 705.5 ≠ 7.055
Statement B.
7.055 is 100 of 70.55.
= 70.55×1/100
= 0.7055
⇒ 0.7055 ≠ 7.055
Statement C.
70.55 is 10 times 7.055.
= 10 × 7.055
= 70.55
⇒ 70.55 = 70.55
hence true.
Statement D.
70.55 is 100 times 7.055.
= 100 × 7.055
= 705.5
⇒ 705.5 ≠ 70.55
Statement E.
7.055 is 10 times 70.55.
= 10 × 70.55.
= 705.5
⇒ 705.5 ≠ 70.55
hence the correct option is 70.55 is 10 times 7.055.
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What is the scale factor from the drawing to the actual airplane
the scale factor is _
Answer: 2
Step-by-step explanation: I just did this lesson
A scale factor is a ratio between the scale of the original object in an actual sense and the prototype figure of the same object.
If the height of the actual airplane is 20m and the in the scale drawing the height is 10m.
The scale factor of the airplane is 200.
What is a scale factor?A scale factor is a ratio between the scale of the original object in an actual sense and the prototype figure of the same object.
We have
The height of the plane in scale drawing:
= 10 cm
The height of the plane in an actual airplane.
= 20 m
The scale factor of the height of the airplane:
= 20m / 10 cm
[ 1 m = 100 cm ]
= (20 x 100) cm / 10 cm
= 200
Thus,
The scale factor of the airplane is 200.
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4x = 0.5(2x- 12) solve for x
Answer: x = -2
Step-by-step explanation:
4x=0.5(2x−12)
Use the distributive property to multiply 0.5 by 2x−12.
4x=x−6
Subtract x from both sides.
4x−x=−6
Combine 4x and −x to get 3x.
3x=−6
Divide both sides by 3.
x= 3−6
Divide −6 by 3 to get -2.
HELP HELO
HELPPPPPP ASAP
On average, Leah's car gets 31.4 miles on every gallon of gasoline. If she fills up her tank for $2.18 per gallon, how much will it cost her to drive
358 miles?
Answer:
Step-by-step explanation:
Car drive 31.4 miles/gallon
for 358 miles, Leah needs 358/31.4 =~ 11.40 gallons
since it cost $2.18 / gallon, it will cost Leah 2.18 * 11.4 = $24.85
2[-3^(2)-(5)/(4-9)]+3(4-2^(3))
Answer:
-28
Step-by-step explanation:
How much weeks would I need to save up to get to $1000 if I get 35 one week, then 45 the next week (Every week for chores I get 35 and 45 every other week)
Example: week 1: +35
Week 2: + 45
Week 3: +35
Week 4: + 45
Answer:
12.857 aa 35 +12.222 as 25
Answer:
26 weeks (6 months)
Step-by-step explanation:
$35x + $45y = $1000
I don't know how to show the work but it would take 26 weeks to reach $1,040. That's exactly 6 months, so half a year.
A librarian's salary was $25000 in 2000 and $30500 in 2006. the librarians alary follow a linear growth pattern. What will the salary be in 2025
y=47,916.666 dollar after 25 years
librarian salary =25000 dollar in 2000
librarian salary=30500 dollar in 2006
in 6 years increment is 30500 - 25000= 5500dollar
in one year increment is 5500/6= 916.666
m= 916.666 each year
b= 25000
y=mx+b
y=916.666*25+25000 given x=25
y=47,916.666 dollar after 25 years
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Pls help me quickly!
Answer:
Step-by-step explanation:
answer number 3
is the answer
32. XY, given X(7, 2) and Y(2, 0)
Domain
Range
Based on the coordinates of XY which are X(7, 2) and Y(2, 0), the domain and range are:
Domain : (2, 7)Range: (0, 2)What are domain and range?The domain of a line refers to all the points on that line that the value of the x-axis can take.
In line XY, the only two x-axis values are 7 and 2. This means that the domain is therefore (2, 7).
The range of a line on the other hand, are all the points that the value on the y-axis can take.
The range in this case is therefore (0, 2).
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