Answer:
length = [tex]8\frac{1}{6}[/tex] inches
Step-by-step explanation:
A rectangle is a quadrilateral which has opposite sides to be equal.
Area of a rectangle = length × width
Given that: Area = [tex]36\frac{3}{4}[/tex] square inches, width = [tex]4\frac{1}{2}[/tex] inches, length = l. Thus;
[tex]36\frac{3}{4}[/tex] = l × [tex]4\frac{1}{2}[/tex]
[tex]\frac{147}{4}[/tex] = l × [tex]\frac{9}{2}[/tex]
divide both sides by [tex]\frac{9}{2}[/tex],
l = [tex]\frac{147}{4}[/tex] ÷ [tex]\frac{9}{2}[/tex]
= [tex]\frac{147}{4}[/tex] x [tex]\frac{2}{9}[/tex]
= [tex]\frac{49}{6}[/tex]
l = [tex]8\frac{1}{6}[/tex]
Therefore, the length of the rectangle is [tex]8\frac{1}{6}[/tex] inches.
What is the simplified expression for 5 to the power of 4 multiplied by 5 to the power of 3 over 5 to the power of 5
Answer:
25
Step-by-step explanation:
5^4 x 5^3/5^5
5^(3+4)/5^5
5^7/5^5
5^(7-5)
5^2
25
Answer:
5 to the power of 2.
Step-by-step explanation:
someone help me
i will give u 5 star..
Answer:
Step-by-step explanation:
Start 3 end 10 what present did it go up
PLS answer will mark brainliest⦁ The average age of a family of 5 is 30 years. The average of the 3 children in the family is 12 years. If the mother is 4 years as young as the father, calculate the age of the father.
Answer:
20
Step-by-step explanation:
(X+9)(x-2)-9x-6 equivalen to
Answer:
hrheje
Step-by-step explanation:
bdhsjsiskskdkdhdhennsjss
what is the average speed of a train that covers 80 km in 1 hour, 200 km in 2 hours and 420 kn in 4 hours
Answer:
95
Step-by-step explanation:
80+(200 divided by 2)+(420 divided by 4)=285
285 divided by 3=95
Write an expression with a negative exponent that has a value between 0 and 1/2. Please answer ASAP, thank you!
Answer:
4^-2
Step-by-step explanation:
Answer:
[tex] 2^{-2} [/tex]
Step-by-step explanation:
1/4 is between 0 and 1/2.
[tex] \dfrac{1}{4} = \dfrac{1}{2^2} = 2^{-2} [/tex]
Andre and Morgan are both headed to Florida for vacation. Andre will drive 70 miles per hour. Morgan will drive 55 miles per hour but will leave 3 hours earlier than Andre. How many hours will Morgan have been driving before Andre catches up with her?
Answer:
The number of hours Moran wold have driven before Andre catches up with him is 14 hours
Step-by-step explanation:
The given information are;
The speed with which Andre will drive = 70 miles per hour
The speed with which Morgan will drive = 55 miles per hour
The time of departure of Morgan = 3 hours before Andre departs
Let the time at which Andre catches up with Morgan be, t
We have, from the definition of distance traveled;
Distance traveled =Speed × Time
The distance Morgan would have driven in t hours = 55 × t
Given that to catch up with Morgan, Andre has to travel the same distance, and that Andre starts 3 hours late, we have;
The distance Andre would drive when Morgan has driven for t hours = 70 × (t - 3)
Therefore, since the distance at the point they meet is the same distance for them both, we have;
55 × t = 70 × (t - 3)
55 × t = 70 × t - 210
210 = 70 × t - 55 × t = 15 × t
t = 210/15 = 14 hours
Therefore, Morgan would have driven for 14 hours before Andre catches uo with him.
Answer:
Morgan walks 2 miles per hour.
Step-by-step explanation:
took the test. ;)
An experienced carpenter can frame a house twice as fast as an apprentice. Working together, it takes the carpenters 2 days. How long would it take the apprentice working alone?
Answer:
6 days
Step-by-step explanation:
Let the time taken by Carpenter working alone = [tex]C[/tex] days
Then time taken by apprentice alone = Twice as that of taken by Carpenter = 2[tex]C[/tex] days
Time taken working together = 2 days
Work done in one day working together = [tex]\frac{1}{2}[/tex]
Work done in one day by Carpenter working alone = [tex]\frac{1}{C}[/tex]
Work done in one day by apprentice working alone = [tex]\frac{1}{2C}[/tex]
Work done in one day by Carpenter working alone + Work done in one day by Carpenter working alone = [tex]\frac{1}{C}[/tex]+[tex]\frac{1}{2C}[/tex] = Work done in one day working together = [tex]\frac{1}{2}[/tex]
[tex]\dfrac{1}{C}+\dfrac{1}{2C}=\dfrac{1}{2}\\\Rightarrow \dfrac{2+1}{2C}=\dfrac{1}{2}\\\Rightarrow C = 3\ days[/tex]
Time taken by Carpenter alone to complete the work = 3 days
Time taken by Apprentice alone to complete the work = 3 [tex]\times[/tex] 2= 6 days
We are required to calculate the number of days it would take the apprentice working alone
The number of days it takes the apprentice working alone is 6 days
let
Number of days taken for the carpenter to work alone = x
Number of days taken by the apprentice to work alone = 2x
Number of days taken to work together = 2 days
Work done per day Carpenter = 1/x
work done per day apprentice = 1/2x
work done per day together = 1/2
So,
work done per day together = Work done per day Carpenter + work done per day apprentice
1/2 = 1/x + 1/2x
1/2 = (2 + 1) / 2x
1/2 = 3/2x
cross product
1(2x) = 2(3)
2x = 6
x = 6/2
x = 3 days
Therefore,
Number of days taken by the apprentice to work alone = 2x
= 2(3)
= 6 days
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Susie ran a race. She ran 555 miles an hour, and the race took her ttt hours to complete. How long was the race? Write your answer as an expression.
Answer:
5t
Step-by-step explanation:
m−4=2m What would M=
Answer:
m = -4
Step-by-step explanation:
m - 4 = 2m
Switch sides.
2m = m - 4
Subtract m from both sides.
m = -4
Answer:
-4
Step-by-step explanation:
cause mafs
If x2 + ax + b = (x – 9)(x + 9), what is the value of
ab?
A) -81
B)
0
C)
81
D) 1458
Step-by-step explanation:
X2+ax+b=(x-9)(x+9)
X2+ax+b=x2-9x+9x-81
X2+ax+b=x2-81
therefore,a=0,b=(-81)
Then , ab = 0×-81 = 0
Answer:
B) 0Step-by-step explanation:
x² + ax + b = (x – 9)(x + 9)
x² + ax + b = x² – 9x + 9x – 81
x² + ax + b = x² + 0x – 81
x²=x² +ax = +0x +b = -81
a = 0 b = -81
ab = 0(-81) = 0
congruence transformation what is y
Answer:
-4.
Step-by-step explanation:
The bracket should be (-4) as AD which is height +2 has been shifted down to EF which is height -2.
One root of f(x)=x^3-4x^2-20x+48 is x = 6. What are all the factors of the function? Use the Remainder Theorem.
A. (x + 6)(x + 8)
B. (x – 6)(x – 8)
C. (x – 2)(x + 4)(x – 6)
D. (x + 2)(x – 4)(x + 6)
Answer:
(x - 6)(x + 4)(x - 2)
Step-by-step explanation:
since x = 6 is a root then (x - 6) is a factor
x³ - 4x² - 20x + 48 ÷ (x - 6)
= (x - 6)(x² + 2x - 8)
= (x - 6)(x + 4)(x - 2) ← factors of f(x)
By using the Remainder Theorem, all the factors of the function are,
⇒ (x - 6) (x + 2) (x - 4)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
One root of function f (x) = x³ -4x² -20x + 48 is, x = 6.
Hence, (x - 6) is divide the function f (x) = x³ -4x² -20x + 48 as;
(x - 6) ) x³ -4x² -20x + 48 ( x² + 2x - 8
x³ - 6x²
--------------
2x² - 20x
2x² - 12x
-----------------
- 8x + 48
- 8x + 48
----------------
0
Hence, We get;
f (x) = x³ -4x² -20x + 48
f (x) = (x - 6) (x² + 2x - 8)
⇒ f (x) = (x - 6) (x² - 4x + 2x - 8)
⇒ f (x) = (x - 6) (x(x - 4) + 2(x - 4))
⇒ f (x) = (x - 6) (x + 2) (x - 4)
Thus., By using the Remainder Theorem, all the factors of the function are,
⇒ (x - 6) (x + 2) (x - 4)
Learn more about the function visit:
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Solve the literal equation −cy+2=3d+7y for y.
Answer:
y = (2-3d)/(7+c)
Step-by-step explanation:
-cy + 2 = 3d + 7y
To solve this equation in terms of y, we must first move all of the terms containing a y to one side of the equation and move all of the other terms to the other side.
Our first step is going to be to add cy to both sides of the equation.
- cy + cy + 2 = 3d + 7y + cy
2 = 3d + 7y + cy
Next, we can subtract 3d from both sides of the equation.
2 - 3d = 7y + cy
Next, we can factor out a y from the right side of the equation.
2 - 3d = y (7 + c)
Finally, we can divide both sides by the quantity (7+c) to get the y alone on the right side of the equation.
(2-3d)/(7+c) = y
Therefore, your answer is y = (2-3d)/(7+c).
Hope this helps!
please help me solve this question
Step-by-step explanation:
5/(x + 2) + 3/(x - 4) = 2
5(x - 4) + 3(x + 2) = 2(x + 2)(x - 4)
5x - 20 + 3x + 6 = 2x^2 - 4x - 16
8x - 14 = 2x^2 - 4x - 16
4x - 7 = x^2 - 2x - 8
x^2 - 6x - 1 = 0
By using the quadratic formula, x = (-6 +/-√40)/2.
Simplify. 3(2a+4b+7) +6a *Plz explain your answer*
Answer:
3(2a+4b+7)+6a = 12a+12b+21
help me please with this question
Answer:
second option
Step-by-step explanation:
Given
A = 4xy ( to isolate x divide both sides by 4y )
[tex]\frac{A}{4y}[/tex] = x , that is x = [tex]\frac{A}{4y}[/tex]
Susan will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $70 and costs an additional $0.40 per mile driven. The second plan has no initial fee but costs $0.60 per mile driven. How many miles would Susan need to drive for the two plans to cost the same?
Answer:
350 miles
Step-by-step explanation:
Let x represent the miles driven
The cost with the first plan will be represented by 0.40x + 70
The second plan will be represented by 0.60x
Set these 2 expressions equal to each other and solve for x:
0.40x + 70 = 0.60x
70 = 0.20x
350 = x
So, Susan will have to drive 350 miles for the cost to be the same
You own a fish store with 478 fishes. You put the same number of fish into 17 tanks, but there are 2 fishes left over. How many fishes are in each tank?
Answer:
10
Step-by-step explanation:
478-2=476
476÷17= 10
therefore you put 10 fish in each tank.
Let me know if this helps:)
Answer:
10
Step-by-step explanation:
Math problem giving brainlist and points!
Answer:
2c + 15 = 25
Step-by-step explanation:
The total he wants to earn is $25, so we know the equation must be an expression that equals 25.
____ = 25
He earns a fixed $15. He also earns $2 per customer.
The total he earns is the sum of the fixed amount ($15) and the amount he earns per customer. Let the number of customers be c. The amount he earns from the number of customers is 2c.
fixed amount + amount per customer = 25
15 + 2c = 25
2c + 15 = 25
Answer: 2c + 15 = 25
If LaTeX: m\angle ABF=8s-6m ∠ A B F = 8 s − 6 and LaTeX: m\angle ABE=2\left(s+11\right)m ∠ A B E = 2 ( s + 11 ), find LaTeX: m\angle EBFm ∠ E B F. LaTeX: m\angle EBF=m ∠ E B F = [measure]LaTeX: ^\circ
Answer:
2(3s-14)Step-by-step explanation:
Given the angles ∠ABF=8s-6, ∠ABE = 2(s + 11), we are to find the angle ∠EBF. The following expression is true for the three angles;
∠ABF = ∠ABE + ∠EBF
Substituting the given angles into the equation to get the unknown;
8s-6 = 2(s + 11)+ ∠EBF
open the parenthesis
8s-6 = 2s + 22+ ∠EBF
∠EBF = 8s-6-2s-22
collect the like terms
∠EBF = 8s-2s-22-6
∠EBF = 6s-28
factor out the common multiple
∠EBF = 2(3s-14)
Hence the measure of angle ∠EBF is 2(3s-14)
What is the volume of the triangular prism?
3.2 cm
6 cm
5.4 cm
A. 8.64 cm
B. 17.28 cm3
C. 51.84 cm
D 103.68 cm
Answer:
C. 51.84 cm³
Step-by-step explanation:
Volume of traingular prism = Base Area * height of prism
Base Area = ½*base(b)*height(h)
Where, b = base of traingular base = 5.4 cm
h = height of triangular base = 3.2 cm
Base Area = ½*5.4*3.2 = 8.64 cm²
Height of prism is given as 6 cm
Therefore, volume of triangular prism =
8.64*6 = 51.84 cm³
Volume is C. 51.84 cm³
Which statement about the number −3 is true? Select all that apply.
A. It is a natural number.
B. It is a whole number.
C. It is an integer.
D. It is a rational number.
E. It is an irrational number.
Answer:
I'm pretty sure it's c and d
Which statement is true Every real number is an integer Every integer is a counting number Every integer is a rational number Every terminating decimal number is an irrational number
Answer:
C. Every integer is a rational number
Step-by-step explanation:
Integers are whole numbers which could be positive or negative and zero. Examples of integers are 330, 21, 10,052, 0, -425, -879, etc. Fractions are not integers. Rational numbers are numbers that are expressed as the ratio of two integers. So numbers that have integers as their numerators and denominators can be rightly said to be rational numbers. Examples are, 5/7, 10,111/880, -365/15.
Since both the numerators and denominators are whole numbers, the entire figures can be said to be rational numbers. So, fractions are rational numbers.
HELP 25 POINTS!!! MARK THE BRAINIEST!
Answer:
first option
Step-by-step explanation:
To find the product, that is
(4x + 1)(x² - 5)
Each term in the second factor is multiplied by each term in the first factor, that is
4x(x² - 5) + 1(x² - 5) ← distribute both parenthesis
= 4x³ - 20x + x² - 5
= 4x³ + x² - 20x - 5
Evaluate g(x) = 4 - 3x when x = -3, 0, and 5
The values of the given function when x = -3, 0, and 5 are 13, 4, and -11 respectively
From the question,
The given function is g(x) = 4 - 3x
We are to evaluate the function for the given values of x
For when x = -3put the value x = -3 into the function
That is,
g(x) = 4 - 3x becomes
g(-3) = 4 - 3(-3)
g(-3) = 4 + 9
g(-3) = 13
For when x = 0,Put the value x = 0 into the function
That is,
g(x) = 4 - 3x becomes
g(0) = 4 - 3(0)
g(0) = 4 - 0
g(0) = 4
For when x = 5,Put the value x = 5 into the function
That is,
g(x) = 4 - 3x becomes
g(5) = 4 - 3(5)
g(5) = 4 - 15
g(5) = -11
Hence, the values of the given function when x = -3, 0, and 5 are 13, 4, and -11 respectively
Learn more here: https://brainly.com/question/18684293
Please show all work and not just the answers.
Answer:
(-1, 6)
Step-by-step explanation:
Midpoint formula:
xm = (x1 +x2)/2ym = (y1+y2)/2For G(-7, 3) and H(5, 9) the midpoint:
((-7+5)/2, (3+9)/2) = (-1, 6)Answer:
(-1,6)
Step-by-step explanation
use the midpoint formula:
(x 1 + x2 /2 , y1 + y2/2)
(-7+ 5 /2, 3+ 9 /2)
after simplfying
(-1,6)
Simplify (-2V7)(3V28)
Answer:
v^2 -4v-21
Step-by-step explanation:
brainliest for correct answer
Answer:
m=14
n=32
p=64
Step-by-step explanation:
B=M, so 154=11m
m=154/11
m=14
E=P, so 118=n+86
n=118-86
n=32
A=L, so 116=180-p
p=180-116
p=64