Answer:
The value of the expression is 4.
Step-by-step explanation:
Consider the provided information.
We have given that:
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20[/tex]
Now we need to find the value of:
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{5}{8} } =?[/tex]
Consider the provided fact:
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20[/tex]
Multiply [tex]\frac{1}{5}[/tex] both sides.
[tex]\dfrac{1}{5}\times \dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20\times\dfrac{1}{5}[/tex]
[tex]\dfrac{1\times2\dfrac{1}{2} }{5\times\dfrac{1}{8} } =20\times\dfrac{1}{5}[/tex]
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{5}{8} } =4[/tex]
Hence, the value of the expression is 4.
solve the equation, and check the solution. 1/3s =1/5
Answer:
3/5
Step-by-step explanation:
1/3s=1/5
s=(1/5)/(1/3)
s=(1/5)(3/1)
s=3/5
Answer: s = 3/5 = 0.600
Step-by-step explanation:s = 3/5 = 0.600
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
1/3*s-(1/5)=0
Step by step solution :
Step 1 :
1
Simplify —
5
Equation at the end of step 1 :
1 1
(— • s) - — = 0
3 5
Step 2 :
1
Simplify —
3
Equation at the end of step 2 :
1 1
(— • s) - — = 0
3 5
Step 3 :
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 3
The right denominator is : 5
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
3 1 0 1
5 0 1 1
Product of all
Prime Factors 3 5 15
Least Common Multiple:
15
Calculating Multipliers :
3.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 5
Right_M = L.C.M / R_Deno = 3
Making Equivalent Fractions :
3.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. s • 5
—————————————————— = —————
L.C.M 15
R. Mult. • R. Num. 3
—————————————————— = ——
L.C.M 15
Adding fractions that have a common denominator :
3.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
s • 5 - (3) 5s - 3
——————————— = ——————
15 15
Equation at the end of step 3 :
5s - 3
—————— = 0
15
Step 4 :
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
5s-3
———— • 15 = 0 • 15
15
Now, on the left hand side, the 15 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
5s-3 = 0
Solving a Single Variable Equation :
4.2 Solve : 5s-3 = 0
Add 3 to both sides of the equation :
5s = 3
Divide both sides of the equation by 5:
s = 3/5 = 0.600
One solution was found :
s = 3/5 = 0.600
BTW YOu can but the answer as 0.600 or 3/5
If there are 21 chickens on the farm and 10 die, how many are still left on the farm?
Answer:
11 live chickens and 10 dead chickens
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
21-10=11
RIP chickens
Ratio of girls to boys is 3:8. if there are 48 boys, how many girls are there
Answer:
18 girls
Step-by-step explanation:
if the r 48 boys u know that 8 times 6 is 48. So now u have to multiply 6 on the other side. And this action would result in the number of girls to be 18
At how many points does the graph of the function below intersect the x-
axis?
y = 4x2 - 6x +1
Apex
Answer:
2 points
Step-by-step explanation:
Answer:
THE ANSWER IS 2 POINTS
Step-by-step explanation:
A
P
E
X
what is the area of the composite figure ? enter your answer in the box . use 3.14 for pi
Answer:
The area of the composite figure = 12.785 square units
Step-by-step explanation:
The figure composite of :
A ⇒ Rectangle with coordinates (0,0) , (0,5) , (2,5) and (2,0)
B ⇒ Rectangle with coordinates (2,0) , (2,1) , (4,1) and (4.0)
C ⇒ Quarter of a circle with coordinates (2,1) , (2,2) and (3,1)
Area of A: Length = 5 and Width =2
Area of A = Length times the width = 5*2 = 10 square units
Area of B: Length = 2 and Width =1
Area of B = Length times the width = 2*1 = 2 square units
Area of C: radius = 1
Area of C = 0.25 * pi * r² = 0.25 * 3.14 * 1² = 0.785 square units
Total Area = 10 + 2 + 0.785 = 12.785 square units
Answer:
the answer is 12.785
Step-by-step explanation:
i took the test
Mona stopped at a gas station where the price per gallon was $2.80. She spent $14 to fill up her car. What equation would represent how much gas Mona purchased? How many gallons of gas did Mona purchase? If Mona’s car gets 20 miles per gallon, how many miles did she drive since the last time she filled up her tank?
Answer:
1. A
2. A
3. D
Step-by-step explanation:
Stay safe❤️
Mona purchased 5 gallons of gas and 5 gallons of gas would give her 100 miles of driving.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Mona stopped at a gas station where the price per gallon was $2.80
Mona spent $14 to fill up her car.
We need to find the equation would represent how much gas Mona purchased.
2.8x = 14 is the equation
Divide both sides by 2.8
x=5
Mona purchased 5 gallons of gas.
Now multiply 5 by the price per gallon of $2.80
5×2.8=14
Since Mona's car gets 20 miles per gallon, 5 gallons of gas would give her 100 miles of driving.
Hence, Mona purchased 5 gallons of gas and 5 gallons of gas would give her 100 miles of driving.
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Bridget takes a 5-inch by 4-inch rectangle of fabric and cuts from one corner of the piece of fabric to the diagonally opposite corner. Now Bridget has two equally sized triangles of fabric. What is the perimeter of each triangle? If necessary, round to the nearest tenth.
Answer:
Perimeter of each triangles are equivalent to 15.4 inches.
Step-by-step explanation:
Given:
A rectangle :
Length of the rectangle = 5 inches
Width of the rectangle =4 inches
As Bridget cuts it from one corner to the other corner,its forms two right angled triangle.
The diagonal will be treated as the hypotenuse.
Lets say that the length of the hypotenuse is 'x'.
Using Pythagoras formula:
⇒ [tex](hypotenuse) = \sqrt{(perpendicular)^2+(base)^2}[/tex]
Plugging the values:
⇒ [tex]hypotenuse = \sqrt{5^2+4^2}[/tex]
⇒ [tex]hypotenuse = \sqrt{25+16}[/tex]
⇒ [tex]hypotenuse =\sqrt{41}[/tex]
⇒ [tex]hypotenuse = 6.40[/tex] inches
Now we have to find the perimeter :
Perimeter = Summation of length of all sides.
So,
Perimeter of each triangle = (length + width + hypotenuse)
⇒ [tex]Perimeter =(5+4+6.4)[/tex]
⇒ [tex]Perimeter =15.4[/tex] inches
Perimeter of each triangle, as they are equally sized are same that is 15.4 inches.
2 to the 3rd power times 4 divided by 2 plus 2
Answer: 18
Step-by-step explanation: 2 x 2 x 2= 8
8 x 4 = 32
32 / 2 = 16
16 + 2 = 18
What is the value of -36÷(-4/9)
The value of -36 divided by (-4/9) is 81, which is found by multiplying -36 with the reciprocal of (-4/9), giving the result 324/4, which simplifies to 81.
To find the value of -36 divided by (-4/9), you can think of division by a fraction as multiplication by its reciprocal. So, the problem changes from division to multiplication: -36 * (-9/4). To solve this:
First, multiply the numerators: -36 * -9 = 324.
Then, multiply the denominators: 1 * 4 = 4.
Now, divide 324 by 4 to get 81.
Therefore, the value of -36 divided by (-4/9) is 81.
Write the inequality shown in the graph below:
Step 1) Identity two points on the boundary line.
Two such points are (0,7) and (1,5)
-----------------------------
Step 2) Find the slope of the line through those two points
m = (y2-y1)/(x2-x1)
m = (5-7)/(1-0)
m = -2/1
m = -2
The slope is -2
-----------------------------
Step 3) Use the point slope form to get the y = mx+b form
y - y1 = m(x - x1) ..... point slope form
y - 7 = -2(x - 0)
y - 7 = -2x
y = -2x+7
A quicker way is to just note that 7 is the y intercept as visually shown, so b = 7. Which allows us to go from y = mx+b to y = -2x+7
-----------------------------
Step 4) The boundary line is y = -2x+7. This is a dashed line so we will use either a less than sign, or a greater than sign. There will be no "or equal to" as part of the inequality sign.
The shaded region is below the dashed boundary line, so we use a less than sign.
Change y = -2x+7 into y < -2x+7
----------------------------
Step 5) Change into standard form (optional)
y < -2x+7
2x+y < 7 ... add 2x to both sides
==========================================
Final Answer: y < -2x+7 or 2x+y < 7The answer will depend on if you want slope intercept form or standard form.
PLEASE HELP , TRYING TO BE ON HONOR ROLL !
What is the solution to this system of equations?
3x + 6y = 1
x - 4y = 1
A. ( 0, -1/4)
B. (2/9 , 1/18)
C. (1/2 , -1/8)
D. (5/9, -1/9)
Option A
The solution is [tex](0, \frac{-1}{4})[/tex]
Solution:
Given system of equations are:
3x + 6y = 1 ------ eqn 1
x - 4y = 1 ------ eqn 2
We have to find solution to system of equations
We can use substitution method
From eqn 2,
x = 1 + 4y -------- eqn 3
Substitute eqn 3 in eqn 1
3(1 + 4y) + 6y = 1
3 + 12y + 6y = 1
18y = 1 - 3
18y = -2
Divide both sides by 18
[tex]y = \frac{-2}{18}\\\\y = \frac{-1}{4}[/tex]
Substitute the above value of y in eqn 3
[tex]x = 1 + 4 \times \frac{-1}{4}\\\\x = 1-1\\\\x = 0[/tex]
Thus solution is [tex](0, \frac{-1}{4})[/tex]
Alice is planning her next vacation. She budgeted 110 for travel expenses, and she expects to spend 120 each day for food and lodging. Her total budget for the trip is 710 . How many days can Alice have for her vacation without exceeding her budget?
Answer:
5 days to spend exactly $710
Step-by-step explanation:
Answer:
5 days
Step-by-step explanation:
5 x 120 = 600
600 + 110 = 710
use limits to find the area of the region bounded by the graph f(x)=4-2x^3 , the x-axis , and the vertical lines x=0 and x=1
A) 7
B) infinity
C) 7/2
D) 7/4
Answer:
[tex]\frac{7}{2}[/tex] square units.
Step-by-step explanation:
We have to use limits to find the area of the region bounded by the graph [tex]f(x) = 4 - 2x^{3}[/tex] , the x-axis, and the vertical lines x=0 and x=1.
So, the area will be
A = [tex]\int\limits^1_0 {(4 - 2x^{3})} \, dx[/tex]
= [tex][4x - \frac{x^{4}}{2} ]^{1} _{0}[/tex]
= [tex]4 - \frac{1}{2}[/tex]
= [tex]\frac{7}{2}[/tex] square units. (Answer)
how do you write 11% as a decimal?
Answer: 0.11
Step-by-step explanation: To write a percent as a decimal, first remember that a percent is a ratio that compares a number to 100.
So we can think of 11% as the ratio 11 to 100 or 11 divided by 100.
Dividing by 100 moves the decimal point 2 places to the left so 11 divided by 100 would move the decimal point 2 places to the left which would give us .11 or 0.11.
So 11% can be written as the decimal 0.11.
at dinner jermey and his friend spent $24. They left a 20% tip and then slpit the cost? How much did eacj person pay
Answer: They each paid $2.40.
Find an equation for the parabola with focus at (-5,-4) and vertex at (-5,-3)
Answer:
[tex](x+5)^{2}=-4(y+3)[/tex]
Step-by-step explanation:
Given:
Focus point = (-5, -4)
Vertex point = (-5, -3)
We need to find the equation for the parabola.
Solution:
Since the x-coordinates of the vertex and focus are the same,
so this is a regular vertical parabola, where the x part is squared. Since the vertex is above the focus, this is a right-side down parabola and p is negative.
The vertex of this parabola is at (h, k) and the focus is at (h, k + p). So, directrix is y = k - p.
Substitute y = -4 and k = -3.
[tex]-4 = -3+p[/tex]
[tex]p=-4+3[/tex]
[tex]p=-1[/tex]
So the standard form of the parabola is written as.
[tex](x-h)^{2}=4p(y-k)[/tex]
Substitute vertex (h, k) = (-5, -3) and p = -1 in the above standard form of the parabola.
So the standard form of the parabola is written as.
[tex](x-(-5))^{2}=4(-1)(y-(-3))[/tex]
[tex](x+5)^{2}=-4(y+3)[/tex]
Therefore, equation for the parabola with focus at (-5,-4) and vertex at (-5,-3)
[tex](x+5)^{2}=-4(y+3)[/tex]
9 pounds for $1.50 how many pounds for $1.00
1. Find how much one pound is.
- to do this, divide 1.50 by 9. This will give you one pound.
2. Figure out how many times 1 pound can go in a dollar.
proportion
[tex]\frac{9}{1,5} = \frac{x}{1} \\[/tex]
1.5x=9*1
1.5x=9
x=[tex]\frac{9}{1.5}[/tex]
x=6
Draw 2 supplementary angles. One angle is x-15 degrees and one is 2x degrees. What is the value of x in degrees?
Answer:
Step-by-step explanation:
Since they are supplementary, it means the addition of both angles gives 180 degree.
[tex]x - 15 + 2x = 180\\3x = 180 + 15\\3x = 195\\x = \frac{195}{3} \\x = 65[/tex]
Please help with question number three. Only first and third. I appreciate your help, I am lost!
I'll do the first part to get you started.
--------------------
Area = 1/2
Length = 7/8
Width = W
Area of rectangle = Length*Width
A = L*W
1/2 = (7/8)*W
(8/7)*(1/2) = (8/7)*(7/8)*W .... see note1 below
(8*1)/(7*2) = (8*7)/(7*8)*W .... see note2
8/14 = (56/56)*W
4/7 = 1*W .... see note3 and note4
W = 4/7Final Answer: 4/7--------------------
Foot notes
note1: I multiplied both sides by the reciprocal of 7/8, that way the "7/8" on the right side cancels out (as you'll see in a few steps later)note2: I used the rule (a/b)*(c/d) = (a*c)/(b*d)note3: the 56/56 turns into 1, and later on 1*W becomes just Wnote4: 8/14 reduces to 4/7 after dividing both parts by 2f(x) = 4x + 6, g(x) = 2x2
Find (fg)(x).
We know x in f(x) is g(x) which is 2x^2 because we are to find (fg)(x)
f(x)=4(2x^2)+6
f(x)=8x^2+6
So (fg)(x) is 8x^2+6
Hope this helped!
(4x+6)(2x^2) = 8x3 + 12x2
There are 14 books on a shelf. 9 of these books are new.
(a) What is the ratio of all books to used books?
(b) What is the ratio of used books to new books?
Answer:
all books to new books- 14:5
used books to new books- 5:9
Step-by-step explanation:
Answer: a. 14:5 b. 5:9
Step-by-step explanation:
There are 14 books and 9 are new so subtract 9 from 14 and get 5 and your ration would be 14:5. Once you have the answer to a you know how many new books there are and how many old books there are, so you can easily figure out the ratio would be 5:9.
Mr Davis buys 30 tickets for the drama club to attend a play. The tickets cost n dollars each for a total of $360
Answer:
the answer is F. because n x 30 would = 360 and the n would be 12 so he paid 12 dollars per ticket and I got that answer by dividing the two numbers 30 and 360
brainliest plz
The answer is F.
Given: Mr. Davis buys 30 tickets for the drama club to attend a play. The tickets cost n dollars each for a total of $360.
How to find out the equation that can be used to find n?
As n x 30 would = 360 and the n would be 12 so he paid 12 dollars per ticket and I got that answer by dividing the two numbers 30 and 360.
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Find the number of sides of a polygon who’s interior angles add up to 3780
Set up this equation: 180(n-2)=3780
n is the number of sides of the polygon
Solved:
180(n-2)=3780
n-2=21
n=23
So the polygon will have 23 sides, also called a 23-gon
Hope this helped!
The sum of two numbers is 100 and their difference is -20. What are the two numbers?
Answer:
x=40 and y= 60
Step-by-step explanation:
step:1
Let 'x' and 'y' are two numbers
given data the sum of two numbers is 100
x+y = 100......(1)
Given difference of two numbers are
x - y = -20 ......(2)
Step :2
solving the equation (1) and (2)
adding the equations (1) and (2)
x+y+x-y=100-20
cancelling 'y' terms are
2 x = 80
dividing "2" on both sides, we get
x = 40
Step :3
substitute x = 40 in equation (1)
x + y =100
40 + y = 100
subtracting "40" on both sides, we get
40 + y - 40 = 100 -40
y = 60
Final answer:-
The two numbers are x = 40 and y= 60
Find the equation of a line that is parallel to line g that contains (P, Q).
the coordinate plane has a line g that passes through the points (-3,2) and (0,5).
3x − y = 3P − Q
3x + y = Q − 3P
x − y = P − Q
x + y = Q − P
Correct option:
[tex]\boxed{x-y=P-Q}[/tex]
Explanation:
Given that the line we are looking for is parallel to g, then the slope of that line and g is the same, therefore:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ (x_{1},y_{1})=(-3,2) \\ \\ (x_{2},y_{2})=(0,5) \\ \\ \\ m=\frac{5-2}{0-(-3)}=1[/tex]
So we can write the point-slope form of the equation of the line as follows:
[tex]y-y_{0}=m(x-x_{0}) \\ \\ (x_{0},y_{0})=(P,Q) \\ \\ \\ y-Q=1(x-P) \\ \\ y-Q=x-P \\ \\ \\ Arranging: \\ \\ P-Q=x-y \\ \\ \boxed{x-y=P-Q}[/tex]
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A linear equation is in the form:
y = mx + b
where y, x are variables, m is the slope and b is the y intercept.
Line g passes through (-3,2) and (0,5). hence:
[tex]Slope\ of\ line\ g=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{0-(-3)}=1[/tex]Two lines are parallel if they have the same slope. Hence:
Line parallel to line g has a slope of 1. Since it passes through (P, Q), hence:
[tex]y-y_1=m(x-x_1)\\\\y-Q=1(x-P)\\\\y-Q=x-P\\\\x-y=P-Q[/tex]
The equation of a line that is parallel to line g that contains (P, Q) is x - y = P - Q
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How many cubic feet of concrete are needed to pour 4 cylindrical pillars 5 feet high with a diameter of 4 inches?
Answer: 1.75 cubic feet concrete is needed.
Step-by-step explanation:
Alright, lets get started.
The volume of the pillar is : [tex]\pi r^2h[/tex]
We have given the height is 5 feet.
We have given the diameter is 4 inches.
So the radius will be : [tex]\frac{4}{2}=2 \ inches[/tex]
Converting inches into feet.
The radius will be : [tex]\frac{2}{12} \ feet[/tex] [tex]= 0.167 feet[/tex]
So the volume of the cylinder will be : [tex]\pi * 0.167^2*5[/tex]
So the volume of the cylinder will be : [tex]0.4380 \ cubic \ feet[/tex]
As there are 4 pillars, so total volume will be : [tex]4*0.4380[/tex]
So, total volume will be : [tex]1.75 \ cubic \ feet[/tex]
Hence 1.75 cubic feet concrete is needed. : Answer
Hope it will help :)
Answer:
1.75 cubic feet
Step-by-step explanation:
Measure the diameter of the cylinder. ...
Hope this helps
GIVING BRAINLIEST. Write a proportion that could be used to solve for each variable. Then solve. 12 balls in 2 boxes 78 balls in x boxes a. 12/2 = 78/x; x = 13 c. 12/2 = 78/x; x = 12 b. 2/12 = 78/x; x = 468 d. 12/2 = x/78; x = 458
Answer:
B. 2/12 = 78/x ; x = 468
Step-by-step explanation:
12/2 = 78/x
6 = 78/x
6 x 78 = x
468
Multiply each equation by a constant that would help to eliminate the y terms.
2 x minus 5 y = negative 21. 3 x minus 3 y = negative 18.
What are the resulting equations?
6 x minus 15 y = negative 63. Negative 15 x + 15 y = 90.
6 x minus 15 y = 63. Negative 15 x + 15 y = 90.
6 x minus 15 y = negative 63. Negative 15 x + 15 y = negative 90.
6 x minus 15 y = negative 63. Negative 15 x + 15 y = 90.
Answer:
Therefore the required resulting equation is
[tex]6x-15y=-63\\-15x+15y=90[/tex]
6 x minus 15 y = negative 63.
Negative 15 x + 15 y = 90
Step-by-step explanation:
Given:
[tex]2x-5y=-21[/tex] ......................Equation ( 1 )
[tex]3x-3y=-18[/tex] ......................Equation ( 2 )
To Find:
Expression after multiplying to eliminate y term,
Solution:
So to eliminate 'y' term we need to multiply equation 1 by a constant 3 and equation 2 by a constant -5, such that equations becomes
[tex]3(2x-5y)=3\times -21\\\\6x-15y=-63[/tex] .....( 1 )
[tex]-5(3x-3y)=-5\times -18\\\\-15x+15y=90[/tex] .....( 2 )
so now by adding new equation one and two we can eliminate y term that means -15y and +15y will get cancel,
Therefore the required resulting equation is
[tex]6x-15y=-63\\-15x+15y=90[/tex]
6 x minus 15 y = negative 63.
Negative 15 x + 15 y = 90
Answer:
It's A
Step-by-step explanation:
Got it right on the test
answer the question Please ASAP
The independent variable is
A: Number of friends (f)
B: Number of cost (c)
The dependent variable is
A: Number of friends (f)
B: Number of cost (c)
The equation that can be used to represent this relationship:
A: c = 20f
B: f = 20c
C: c = 10f
D: f = 10c
Answer:
Independent variable is A.
Dependent variable is B.
The equation that can be used to represent the relationship is B. F=20c
Step-by-step explanation:
To answer the question, the independent variable is A. Number of friends (f). Because we know the cost is $20. And the dependent variable is B. because we know the cost so that's the dependent variable. The equation that can be used to represent this relationship is B. F=20c because we need to know how many friends are gonna be at Hank's party.
Find the value of the expression:
a
p^2q^2+pq–q^3–p^3 for p=1 and q=−1
Answer:
0
Step-by-step explanation:
Put the numbers where the letters are and do the arithmetic.
(1)^2(-1)^2 +(1)(-1) -(-1)^3 -(1)^3
= 1·1 -1 -(-1) -1
= 1 - 1 + 1 - 1 = 0
The value of the expression is 0.