Apply the distributive property.
=a(a−2b)+b(a−2b)
=a2−2ab+ba−2b2
=a2−ab−2b2.
Volume of Prisms
1. A pool in the shape of a rectangular prism is being filled with water. The
length and width of the pool is 24 feet and 15 feet. If the height of the water
in the pool is 1 &1/3feet, what is the volume of the water in cubic feet?
Answer:
the answer is 480 cubic feet
Verify that triangle ABC is equal to DEF . Find the scale factor of triangle ABC to triangle DEF
Answer:
k = 6 : 5 : 4
Step-by-step explanation:
BC : AB : AC = 18 : 15 : 12 = 6 : 5 : 4
EF : DE : DF = 12 : 10 : 8 = 6 : 5 : 4
A student takes the same street from his home to the university every day. There are 3 streetlights along the way, and he has noticed the following Markov dependence. If he sees a green light at an intersection, then 77% of time the next light is also green. However, if he sees a red light, then 77% of time the next light is also red. (Assume the chance of him seeing a yellow light is zero.) If the first light is green, what is the probability that the third light is red
Answer:
0.3542 = 35.42% probability that the third light is red
Step-by-step explanation:
For each light:
If it is green, 77% probability that the next is green.
If it is red, 77% probability that the next is red.
If the first light is green, what is the probability that the third light is red?
These following outcomes are desired, for the second and third lights:
G - R(0.77, then 1 - 0.77 = 0.23 probability)
R - R(0.23, then 0.77 probability).
So the desired probability is:
[tex]p = 0.77*0.23 + 0.23*0.77 = 0.3542[/tex]
0.3542 = 35.42% probability that the third light is red
The net of a triangular pyramid is shown.
Each triangle in the net has a base length that measures 6 inches and a height that measures 4 inches. What is the surface area of the pyramid that can be formed from this net?
Answer:
48 in²
Step-by-step explanation:
4x1/2x4x6=48
Pls help
If a varies jointly as b and c, find a when b = 4 and c = -3.
a = -96 when b = 3 and c = -8
a=
Answer:
a=4bc
a=4(4)(-3)=-48
a= - 48 when b equals to 3 is equals to - 8
The required answer by direct variation a is equal to 96. In other words, when b = 4 and c = -3, the value of a is 96.
When a variable varies jointly as two other variables, it means that the relationship between the variables can be expressed using direct variation. In this case, we have that "a varies jointly as b and c."
To find the value of a when b = 4 and c = -3, we can set up the proportion based on the direct variation relationship:
a/bc = k
where k is the constant of variation.
Substituting the given values:
a/(4)(-3) = k
Simplifying, we have:
a/-12 = k
Now, we can find the value of a when b = 4 and c = -3 by substituting these values into the equation and solving for a:
a/(-12) = k
a/(-12) = -96/-12 (since k = -96 when b = 3 and c = -8)
a = 96
Therefore, the required answer by direct variation a is equal to 96. In other words, when b = 4 and c = -3, the value of a is 96.
Learn more about direct variation here:
https://brainly.com/question/29150507
#SPJ2
Which rational number represents a decrease in water level from 8 feet to 6 feet?
A.
6
B.
2
C.
−
2
D.
−
6
Answer:
C
Step-by-step explanation:
PLEASE HELP!!!!!!!! HELP NEEDED ASAP PLS PLS
Answer:
A
Step-by-step explanation:
It's correct but you don't show other answers
A small airplane used 7 1/3 gallons of fuel to fly a 3 hour trip. How many gallons were used each hour? Each day?
Answer:
approximately 2.44 per hour, and 175.92 per day
Step-by-step explanation:
We can use 7.33 as 7 and 1/3rd.
If you take 7.33 and divide by 3, representing 3 hours, it equals 2.44333333.
If you round this to the nearest hundredth, you get the answer 2.44
For each day, you take the original number, 7.33, and multiply it by 8 to assume that the trip was 24 hours.
7.33 * 24 = 175.92.
Answer:
Step-by-step explanation:
Can someone please help me I will mark u brilliant
Answer:
The answer is 7/20 miles.
Step-by-step explanation:
Just multiply 7/6 x 2/5, then you have the answer
1.1.4 practice scale drawing
Answer:
Question Unclear
Step-by-step explanation:
Is this relating to your topic?
1.1.4 Practice: Scale Drawings
Practice
Math 7 Sem 2
Points Possible:5
Name:
Date:
Tips for Success
Read the assignment carefully and make sure you answer each part of the question or questions.
Check your work when you're done.
Your Assignment
Jason and Adam are using a kit to build their own electronics board for a computer project. They use a scale drawing included in the instructions to help build the board.
Jason will use the scale factor to find the board's actual length and width, then multiply those dimensions to find the board's area.
Adam says he knows another way.
Answer the questions to show how Adam could find the area of the scale drawing, and then use this strategy to find the area of the electronics board.
1. What is the area of the board shown on the scale drawing? Explain how you found the area.
Write your answer in the space below.
2. How can Adam use the scale factor to find the area of the actual electronics board? Remember, he uses a different method than Jason.
Write your answer in the space below.
3. What is the area of the actual electronics board?
Write your answer in the space below.
2 to the 4th power divided by [(3.35 x 0.8) + 5.32]
Answer:
2Step-by-step explanation:
First we need to rewrite this part word problem completely into numbers
2⁴ ÷ [(3.35 × 0.8) + 5.32]
Now we must solve. Remember to do parenthesis first.
3.35 × 0.8 = 2.68
2.68 + 5.32 = 8
Now we need to find the value of 2⁴
2⁴ = 2 × 2 × 2 × 2 = 16
Finally we need to divide 16 by 8
16 ÷ 8 = 2
So our final answer is 2
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius ?
Step-by-step explanation:
Cone Volume = 1/3 ×( π r² h) h = 2 × diameter = 2 × 2 × r
Cone Volume = 1/3 ×( π r² h) h = 2 × diameter diameter = 2r
= 2 × (2 × r)
= 4r
Cone Volume = 1/3 ×( π r² 4r)
= (4 π r³ / 3)
HELP PLEASE ALGEBRA 1
Answer: See below. I did the first one as an example
Step-by-step explanation:
to find slope between 2 points use the formula
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
1) (19,-16) ( -7,-15)
the first value in each pair is the x, the 2nd value is the y
19= x1
-7-x2
-16=y1
-15=y2
[tex]m=\frac{-15--16}{-7-19} \\m=\frac{1}{-26} \\m=-\frac{1}{26}[/tex]
help me please thank you
......... what even is the question?????
Answer:
30
Step-by-step explanation:
you just simply add all numbers then the two thtas there beside the box add it with all the numbers and you get 3mm
Brad has a garden with dimensions 12 feet long x 7 feet wide. He wants to enlarge the garden to an area of 119 square feet. How much farther will he need to extend the length of the garden to attain his desired area?
Answer:
he needs to increase the length to 17 feet
Step-by-step explanation:
[tex]12 \times 7 \\ = 84 \\ to \: get \: {119}^{2} feet \: he \: must \: say \: \\ 119 \div 7 \\ = 17 \\ = 17 \times 7 = 119 \\ [/tex]
Answer:
28
Step-by-step explanation:
f58t85h85y8578
If p is inversely proportional to the square of q, and p is 25 when q is 3, determine p
when q is equal to 5.
Answer:
p = 9 when q = 5.
Step-by-step explanation:
p is inversely proportional to the square of q
This means that:
[tex]p = \frac{k}{q^2}[/tex]
In which k is a constant multiplier.
p is 25 when q is 3
We use this to find k.
[tex]p = \frac{k}{q^2}[/tex]
[tex]25 = \frac{k}{3^2}[/tex]
[tex]k = 25*9 = 225[/tex]
So
[tex]p = \frac{225}{q^2}[/tex]
Determine p when q is equal to 5.
[tex]p = \frac{225}{q^2} = \frac{225}{5^2} = 9[/tex]
p = 9 when q = 5.
question is in the image I put!
Help me I having a hard time with This one
Answer:
4
Step-by-step explanation:
4 students studied 4 hours or more.
Answer:
8
Step-by-step explanation:
at least means minimum so how many students studied a minimum of 4 hours?
i’m confused? this lesson was so confusing
Answer:
A. leg
Step-by-step explanation:
No files plz help with answer
Answer:
20°
Step-by-step explanation:
60 = (x + 40) (opposite angles are equal)]
x = 60 - 40 = 20°
Answer:
=> x = 20°
Step-by-step explanation:
here's your solution
==> both are vertical angle ,so both are equal
==> 60° = x + 40°
==> - x = -60° + 40°
==> - x = - 20°
==> x = 20°
[tex]hope \: it \: helps[/tex]
Each evening, Billy jogs around the high school track at a constant rate. The following equation describes the relationship between t, the time he jogs in hours, and d, the distance he jogs in kilometers. d = 7t Which graph represents the relationship between the amount of time Billy jogs and the distance he jogs?
The slope of the given line d = 7t is 7 kilometers per hour. Then the correct option is A.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
Each evening, Billy jogs around the high school track at a constant rate.
The following equation describes the relationship between t, the time he jogs in hours, and d, the distance he jogs in kilometers.
d = 7t
The slope of the line will be 7,
Then graph A is correct.
More about the linear system link is given below.
https://brainly.com/question/20379472
Use the given information to write the standard form equation of a circle:
a) x²+y²+10x+14y+70=0 translated 1 unit to the right and 2 units down.
Answer:
The formula for the equation of a circle is (x – h) 2 + (y – k) 2 = r 2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.
Step-by-step explanation:
What is the area of this?
Answer:
just multiply 95 times 1.2 which is 114
I dont understand
NOOOOO LINKSSSSSS
Answer: 4.40
Step-by-step explanation: 10 divided by 4 is 2.5 and 2.5 times 4.40=11
so 4.40x2.5=11
Tyler sold a total of $115,000 of exercise equipment last month. If his commission is 6.5% of sales, how much commission did he earn?
A.
$2,342
B.
$7,475
C.
$12,719
D.
$115,065
Answer:
B
Step-by-step explanation:
Do 115000/100x6.5 You get 7.475k
A welder is making a metal sphere. The diameter will be 130 inches. What is the surface area of the metal sphere? Use 3.14 for π and round to the nearest tenth.
Answer:
53092.92 square inches
Step-by-step explanation:
Surface Area of a Sphere = 4πr2
Radius = ½D = 130÷2 = 65
4 × 3.14 × 65² = 53092.92
29:07
Using the patterns of inverse variation, complete the following table if y is inversely proportional to the cube of x:
x
0.5
64
2
Y
16
a.
1
0.037
4
b.
2
C.
d.
8
Please select the best answer from the choices provided
A
B
С
D
9514 1404 393
Answer:
a. 1
Step-by-step explanation:
"y is inversely proportional to the cube of x" means ...
y = k/x³
The value of k can be found from ...
k = x³y
The second table entry lends itself to easy computation of k:
k = 1³·8 = 8
Then the third table entry is ...
y = 8/2³
y = 1 . . . . matches choice A
Answer:
its a.) 1
Step-by-step explanation:
i got 100 on the test
please help with these questions
Answer:
False, False, True, False
Step-by-step explanation:
1. False. D and F are not parallel as they are intersecting in the diagram.
2. False. Angles 1 and 3 are not corresponding. They are opposite. A pair of corresponding angles would be angles 1 and 5.
3. True. A transversal line is a line that passes through two other lines.
4. False. Angle 6 = 63˚ through corresponding angles. Angle 6 + Angle 7 = 180. 63 + Angle 7 = 180. Angle 7 = 117˚.
i hope this helped :)
Find the volume of the figure below. Use 3.14 for π, and round your final answer to the nearest tenth.
Answer:
79.25 mm³
Step-by-step explanation:
The figure can be decomposed into 2 different half cylinders and a rectangular prism
Volume of the figure = volume of the smaller half cylinder + larger half cylinder + rectangular prism
✔️Volume of smaller half cylinder = ½(πr²h)
r = ½(2) = 1 mm
h = 5 mm
π = 3.14
Volume of smaller half cylinder = ½(3.14*1²*5)
= 7.85 mm³
✔️Volume of larger half cylinder = ½(πr²h)
r = ½(4) = 2 mm
h = 5 mm
π = 3.14
Volume of smaller half cylinder = ½(3.14*2²*5)
= 31.4 mm³
✔️Volume of rectangular prism = L*W*H
L = 5 mm
W = 4 mm
H = 2 mm
Volume = 5*4*2 = 40 mm³
✅Volume of the figure = 7.85 + 31.4 + 40
= 79.25 mm³
The pupils in my class work very quickly. Jasleen answers four questions every
30
seconds and Ella answers five questions every
40
seconds.
Last week, Jasleen took exactly
1
hour to answer a large set of questions.
How many minutes more than Jasleen did Ella take to answer the same set of questions?
Answer:
4 mins more would be taken by Ellina
Step-by-step explanation:
Given that
Jasleen answers 4 questions every 30 seconds
And, Ella answers 5 questions every 40 seconds
And, last week Jasleen took exactly 1 hour for answering a large set of questions
We need to find out the number of more minutes taken by Ella
As Jasleen answers four questions every 30 seconds
So, Jasleen answers 8 questions for every 1 minutes
Now
Jasleen answers time taken
= 60 × 8
= 480 questions for every 60 minutes or 1hr
On the other hand
Ella answers five questions every 40 seconds.
So, 1 questions in 8 sec
Now for 480 Questions , it would take
= 480 × 8 secs
= 480 × 8 ÷ 60 min
= 8 × 8
= 64 mins
Hence 4 mins more would be taken by Ellina