Answer:
Step-by-step explanation:
3x2.25=6.75
4x4=16
16+6.75=22.75
The area of a rectangle is 27 m”, and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.
Answer:
[tex]L = 6[/tex] --- Length
[tex]W = 4.5[/tex] --- Width
Step-by-step explanation:
Given
Let: [tex]L = Length; W = Width[/tex]
[tex]Area = 27m^2[/tex]
[tex]L = 2W- 3m[/tex]
Required
Find the dimensions of the rectangle
Area (A) is calculated as:
[tex]A = L * W[/tex]
This gives:
[tex]27 = (2W - 3) * W[/tex]
Open bracket
[tex]27 = 2W^2 - 3W[/tex]
Express as a quadratic function
[tex]2W^2 - 3W - 27 = 0[/tex]
Expand
[tex]2W^2 + 6W - 9W - 27 = 0[/tex]
Factorize:
[tex]2W(W + 3) - 9(W + 3) = 0[/tex]
[tex](2W - 9)(W + 3) = 0[/tex]
This gives:
[tex]2W - 9 = 0\ or\ W + 3 = 0[/tex]
[tex]2W = 9 \ or\ W = -3[/tex]
Width can not be negative.
So:
[tex]2W = 9[/tex]
[tex]W = 4.5[/tex]
Recall that:
[tex]L = 2W- 3m[/tex]
[tex]L = 2 * 4.5 - 3[/tex]
[tex]L = 6[/tex]
A builder could get 9 sheets of Sheetrock for $20. If he bought 15 sheets, how much money would he have spent?
Given: BC ≅ DA, ∠CBD ≅ ∠ADB
Prove: △BCD ≅ △DAB
Answer:
Step-by-step explanation:
Side-angle-side.
570 milliliters equal how many centiliters
Answer:
It equals 57 centiliters.
Step-by-step explanation:
The reason why is because any number that has a 0 is subtracted to less without the 0, so for example lets say 1,680 milliliters equal how many centiliters the answer would be 1,680. Take out the 0 out of any number u add to if you want to know the centiliter
Answer: 57
Step-by-step explanation:
We can set up a proportion to solve for the number of centiliters.
1ml/ 570ml = 0.1 centiliter/ xcentiliter
Now, we cross multiply to solve for our unknown x:
x centiliter ≈ 570 ml / 1 ml * 0.1 centiliter → x centiliter ≈ 57.0 centiliter
Conclusion:
570ml ≈ 57.0 centiliter
Find the area of the triangle.
Answer:
to find the area, multiply the base times the height and divide it by two. we do not have the picture of the triangle, so we cannot answer this but here is the formula
(BxH)/2 = A
You can use this rule to work out the total cost of hiring a car. Total cost = £4 per hour plus £12. Arun hires a car for 5 hours. Work out the total cost.
Answer:
£32
Step-by-step explanation:
12 + 4(5) = 32
Stay safe! <3
PLEASE ANSWERRR! FIRST CORRECT ANSWER WILL VOTE BRAINLIEST
For a certain value of k, the system
x + y + 3z = 10,
-4x + 3y + 5z = 7,
kx + z = 3
has no solutions. What is this value of k?
Answer:
k = 7/4Step-by-step explanation:
Given system:
x + y + 3z = 10, -4x + 3y + 5z = 7, kx + z = 3Substitute z in the first two equations with z = 3 - kx:
x + y + 3(3 - kx) = 10 ⇒ (1 - 3k)x + y = 1 ⇒ y = (3k - 1)x + 1-4x + 3y +5(3 - kx) = 7 ⇒ -(4 + 5k)x + 3y = -8 ⇒ y = 1/3(5k + 4) - 8In order the two equations above not to have a solution, the lines should be parallel. Parallel lines have equal slopes.
Solve the following equation for k:
3k - 1 = 1/3(5k + 4)9k - 3 = 5k + 44k = 7k = 7/4Question 5 Multiple Choice Worth 1 points)
(05.02 MC)
Find the measure of angle x in the figure below:
A - 35
B - 47
C - 51
D - 62
Answer:
C because to get y u do 180 - 57+61 than for x u do 180 - 62+67
Answer:
x=51
Step-by-step explanation:
y+57+61=180 linear pair
y=180-118=62
in triangle
x+y+67=180sum of interior angle of the triangle is 180
x+62+67=180
x=180-129=51
help please and thanks <3
Answer:
x<14
Step-by-step explanation:
7+7>x by triangle inequality theorem
14>x or x<14
The stock market gained 45 points on Tuesday and lost 32 points on Wednesday. It had closed on Monday at 2760 points. Where did the market close on Wednesday?
Answer:
The market closed with a rating of 2773 points on Wednesday.
Step-by-step explanation:
Lets start with what we know:
Monday at close it had a rating of 2760 points.
Tuesday it gained 45 points.
Wednesday it had lost 32 points.
Once written out it becomes less intimidating to answer.
Monday + Tuesday + Wednesday = Answer
2760 + 45 - 32
= 2805 - 32
= 2773
Tania bought 9.6 gallons of gas for $27.36. Find an equation that can be used to determine x, the price of each gallon of
gas? What is the price of each gallon of gas? Show work.
Answer:
9.6(x)= 27.36 27.36÷9.6=x x=2.85
These 10 blocks are separated into 2 groups. Which equation represents how to find the number of blocks in each group?
A. 10 ÷ 2 = 5
B. 10 ÷ 5 = 2
C. 5 ÷ 2 = 10
D. 2 ÷ 5 = 10
Answer:
A) would be the answer
Step-by-step explanation:
this is the answer because 2 groups with 10 blocked all together has to have 5 blocks each group, also 5+5=10
An arrow is shot up in the air from a height of 3 feet. The height of the arrow, in feet,can be modeled with the function h= -2t^2+12t+3where his the height in feet and is the time in seconds.Enter the average rate of change, in feet per second, from 1 second to 4 seconds
Answer:
The average rate of change is two feet per second.
Step-by-step explanation:
The height of an arrow shot up into the air from a height of three feet is given by the function:
[tex]h(t)=-2t^2+12t+3[/tex]
And we want to find its average rate of change from one second the four seconds.
The average rate of change is synonymous with the slope. Therefore, we can evaluate the height of the arrow after the first and fourth seconds, and find the slope between them.
After the first second, the height of the arrow is:
[tex]h(1)=-2(1)^2+12(1)+3=13[/tex]
And after the fourth second, the height of the arrow is:
[tex]h(4)=-2(4)^2+12(4)+3=19[/tex]
This yields two points: (1, 13) and (4, 19).
The slope between them is:
[tex]\displaystyle m=\frac{19-13}{4-1}=\frac{6}{3}=2[/tex]
Therefore, the average rate of change from one second to four seconds is two feet per second.
Todd had 6 gallons of gasoline in his motorbike. After driving 150 miles, he had 3 gallons left. Compute the slope, or rate of change in the amount of gasoline.
The rate of change is __ miles per gallon.
Answer:
50 miles per gallon, 50/1
Step-by-step explanation:
I was training the cross country team. Every week I expected the students to run 12 3/4 miles every week. If the kids ran
for 5 days that week, how many miles would they need to run each day to meet my expectations ?
Answer:
x = 2.55 miles per day
Step-by-step explanation:
In English: 5 days * 'x' miles per day = 12 & 3/4 miles total
In algebra: 5x = 12.75
x = 12.75 ÷ 5
x = 2.55 miles per day
Find x Question is attached:
PLease I need the answer fast!!!
Answer:
Step-by-step explanation:
(-3)ˣ⁻² = -243
(-3)ˣ⁻² = (-3)⁵
x-2 = 5
x = 7
F(x)=1/ x shift 9 units right and 4 units down
Answer:
g(x) = 1/(x-9) - 4
Step-by-step explanation:
f(x) shift 9 units right -> f(x-9) = 1/(x-9)
further shift 4 units down: 1/(x-9) - 4
Arithmetic mean of nine observations is calculated as 38. But in doing so, mistakenlythe observation 27 is taken instead of 72. Find the actual mean of the data.
Answer:
Actual Mean = 43
Step-by-step explanation:
Given Mean = 38
No of observations = 9
we know,
Mean = Sum / N
38 = Sum/ 9
Sum = 38 x 9 = 342
Since the observation 27 was mistakenly taken instead of 72, we subtract 27 from the sum and add 72.
New sum = 342 - 27 = 315 again, 315 + 72 = 387
The no. of observations stays the same.
Actual mean = New Sum / N
= 387/9
=43
Step-by-step explanation:
arithmetic mean =38
n=9
mean=sum/n
sum=mean×n=38×9=342
mistakenly observation 27 is taken instead of 72
new sum becomes =342+72-27=387
now
new mean =new sum/n=387/9=43
the actual mean of the data is 43.
Can someone help out with this question
Eric's water bottle holds 500 mL. He drinks 4 bottles of water at soccer practice.
How many liters of water does he drink?
A.2 L
B.5 L
C .2L
D.5L
2 litres of water. A
Eric's drink 2 liters of water.
What is liter?
" Liter is a basic unit which is used to measure volume of any liquid."
According to question,
Capacity of one water bottle = 500mL
Capacity of 4 water bottles = [tex]500[/tex] × [tex]4[/tex]
= 2000mL
1000mL = 1Liter
2000mL =2L
Hence we conclude that Option A is correct.
Learn more about Liters of water here
https://brainly.com/question/22384228
#SPJ2
What's the area of a circle with diameter 18 units? Question 8 options: A) 9π units2 B) 81π units2 C) π units2 D) 18π units2
Answer:
B) 81π units²
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Radius of a Circle Formula: r = d/2
r is radiusd is diameterArea of a Circle Formula: A = πr²
Step-by-step explanation:
Step 1: Define
Diameter d = 18 units
Step 2: Manipulate Variables
Radius r = 18 units/2 = 9 units
Step 3: Find Area
Substitute in r [Area of a Circle Formula]: A = π(9 units)²[Area] Evaluate exponents: A = π(81 units²)[Area] Multiply: A = 81π units²Find the size of angle XYZ. Give your answer to 1 decimal place.
Answer:
45
Step-by-step explanation:
Because this is a triangle all angles must add up to 180. so we already know 90 so 180-90=90 and 90/2 = 45. Hope this helps
Step-by-step explanation:
1. Label each side of the Triangle
Using the SOH CAH TOA method we can label zy as H (the longest line is always H). We can label xz as O (it is opposite the angle). We can label xy as A (it's the remaining side).
2. Cross out the 'useless' side
Now, we need to cross out the label which doesn't have an appointed piece of information to it. Meaning that A will remain as it labels 7cm. H will also remain as it labels the angle. O does not label anything and so we can cross it out.
3. Decide which method is correct
We are using the SOH CAH TOA method, this means we can either use SOH, CAH, or TOA to solve the problem. We know which method to use by seeing which of them does not contain the letter we crossed out. CAH does not contain O so it is the correct method.
4. Know the formula
Now we will use the formula of our found method. CAH begins with C and so does Cos. Therefore, Cos is our formula.
Cos( ) = A/H
5. Substitute in your numbers
Then, we will put in our numbers into the formula. The first slot we must fill in is within the brackets. Usually the angle goes inside of the brackets during trigonometry but we obviously do not know it. This means we will use 'x' inside of the brackets. Our formula now looks like this:
Cos(x)
Substitute in A and H. A will be the information appointed to the side we labelled A. H will be the information appointed to the side we labelled H.
Our formula will look like this:
Cos(x) = 7/12
6. Reverse it and calculate
Now we need to input an equation into our calculator. I don't know why but we will need to reverse our previous formula and type it into the calculator as:
cos-^1(7/12)
The result should say 54.31466529.
7. Round
Now we will round it by 1 decimal place. To do this we need to look at the number next to 3, it is not 5 or above 5. This means we will not round up,
our answer is 54.3 degrees.
cual es valor absoluto de -7
Answer: -7
Step-by-step explanation:
−7
=−7
Maria wants to buy a new car. She will choose a green car
or a silver car. The green car costs $16,898, and the silver
car costs $1,059.75 less than the green car. What is the
cost of the silver car?
please help do today
Answer:
1,059.75
Step-by-step explanation:
well the silver car is less then a green car right but just add them up
If f(x)=4x-1 , what is f(1) ??
Answer:
f(1) = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
f(x) = 4x - 1
f(1) is x = 1
Step 2: Evaluate
Substitute in x [Function]: f(1) = 4(1) - 1Multiply: f(1) = 4 - 1Subtract: f(1) = 3Help please!!!
Thanks
Answer:
25.6
Explanation:
t = 2 seconds
h = 8 + 40.8(2) - 16(2)^2
Solve for h by simplifying both sides of the equation, then isolating the variable.
h = 25.6
A stone is thrown upward, its height h meters after t seconds is given by this formular h=30t-5t². Find t when it is at a height of 25m, why are there two answers, what do they mean?
Answer:
the answer is
T¹=5s
T²=1s
Am not sure about why there's two times , although perhaps the two times indicate the starting time and the other indicate the time when the stone hits 25m above the ground
Step-by-step explanation:
the solving steps are in the picture.
How do I tell my mom I have depression so she will stop hurting me with hurtful words-
Answer:
Just tell her and if she says you dont tell her that you do. If she continues to hurt you then probaly call the police.
Step-by-step explanation:
Answer:
try to find someone close to you like a relative or best freind and tell them about her. After that try to confront her about it, and bring that close one with you to make you feel more strong. if she says you dont
have it and contiues hurting you tell the police.
Identify the slope and y intercept of the function y=4x-9
help pls what is the area of this shape?
Answer:
I think 15 I dont see it in the options but im going to explain my answer
Step-by-step explanation:
4 + 4 = 8, 13 - 8 = 5 x 6 = 30 divided by 2 is 15
SO 8 x 13 = 104 - 15 = 89 so therefore its 89!