QUESTION 2
A board is 86 cm. in lenght and must be cut so that one piece is 20 cm. longer than the other piece
Find the lenght of each piece.
A26 cm and 60 cm
b. 33 cm and 53 cm
C 30 cm and 56 cm
d. 70 cm and 16 cm
One piece will be length x and the other piece will be 20 cm longer, so it will be x + 20 cm long.
Added together the length of these two boards will equal 86 cm. So you can write an equation:
x + (x + 20) = 86
Remove the parentheses and add the two x's together to get:
2x + 20 = 86
Subtract 20 from both sides:
2x = 66
Divide both sides by 2 and you have:
x = 33
The short piece is 33 cm and the other piece is 20 cm longer or 33 + 20 = 53 cm.
14feet 23feet round each measurement to the nearest ten
What is the domain of the function Y = In
-X+3
2
0x62
O x32
O X<3
O
X> 3
ASAP
Answer:
i think 1/58 is correct
i hope its help you
Find the missing side of the right triangle.
Answer:
√65
Step-by-step explanation:
you have to use the pythagoras theorem to find x which is the hypotenuse
x²=7²+4²
x²=49+16
√x²=√65
x=√65
I hope this helps
40 percent of the teachers at a meeting are male.
Of the male teachers at the meeting, 20 percent
teach mathematics. Which of the following
could be the possible number of teachers at the
meeting?
(A) 60
(B) 64
(C) 72
(D) 75
(E) 80
Answer:
D. 75
Step-by-step explanation:
To find the possible number of teachers at the meeting, find which answer choice creates a whole number answer when calculating the 40% of teachers that are male and the 20% of them that teach math.
This number is answer choice D, 75.
40% of 75 is 30.
Of those 30 teachers, 20% of 30 is 6.
So, since each quantity is a whole number, this could be the possible number of teachers at the meeting.
The correct answer is D. 75
I need you guy’s help answer thanks so much
Answer:
D
Step-by-step explanation:
inverse just means opposite so if its shown dividing it first then adding, then the inverse is multiplying then subtracting
how many degrees are there in the angle made by the heart hand and the minute hand of a clock when it is 9 o'clock
both angles are 90 degrees
A building security code has 2 numeric
digits, O through 9, followed by 2 letters.
What is the probability that the first digit
is 9 and the last letter is A?
Answer:
Step-by-step explanation:
First number is 1/10
Last letter is 1/26
The second digit is 1/9
The first letter is 1/25
1/10 * 1/26 * 1/9 * 1/25
0.00001709
This assumes no duplication is allowed,
If there are duplications
then 1/10 * 1/10 * 1/26 * 1/26
0.000014782
What's the value of n if 13+19= n+25
.
.
..
.
.............
Answer:
[tex]13+19=n+25[/tex]
[tex]n+25=13+19[/tex]
Add 13+19= 32
[tex]n+25=32[/tex]
Now Subtract 25 from both sides
[tex]n+25-25=32-25[/tex]
[tex]n=7[/tex]
OAmalOHopeO
A restaurant operator in Accra has found out that during the lockdown,if she sells a plate of her food for Ghc 20 each,she can sell 300 plates but for each Ghc5 she raises the price,10 less plates are sold. A.Draw a table relating 5 different price levels with their corresponding number of plates sold.
B.Use the table to find the slope of the demand
C.Find the equation of the demand fraction.
D.Use your equation to determine the price in Ghc if she sells one plate of food to maximize her revenue
The demand equation illustrates the price of an item and how it relates to the demand of the item.
The slope of the demand function is -1/2The equation of the demand function is: [tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]The price that maximizes her revenue is: Ghc 85From the question, we have:
[tex]Plates = 300[/tex]
[tex]Price = 20[/tex]
The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:
[tex]\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}[/tex]
The slope (m) is calculated using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{25-20}{290-300}[/tex]
[tex]m = \frac{5}{-10}[/tex]
[tex]m = -\frac{1}{2}[/tex]
The equation of the demand is as follows:
The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).
Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).
So, the demand equation is:
[tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]
Open the brackets to calculate the maximum revenue
[tex]R(x) =6000 + 1500x - 200x - 50x^2[/tex]
[tex]R(x) =6000 + 1300x - 50x^2[/tex]
Equate to 0
[tex]6000 + 1300x - 50x^2 =0[/tex]
Differentiate with respect to x
[tex]1300 - 100x =0[/tex]
Collect like terms
[tex]100x =1300[/tex]
Divide by 100
[tex]x =13[/tex]
So, the price at maximum revenue is:
[tex]Price= 20 + 5x[/tex]
[tex]Price= 20 + 5 * 13[/tex]
[tex]Price= 85[/tex]
In conclusion:
The slope of the demand function is -1/2The equation of the demand function is: [tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]The price that maximizes her revenue is: Ghc 85Read more about demand equations at:
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At a sale this week, a desk is being sold for $312. This is a 35% discount from the original price.
What is the original price?
Answer:
$480
Step-by-step explanation:
Let original price be x
{Original price - discount amount = sale price}
So, x - (x * 35/100) = 312
x - 35x/100 = 312
100x - 35x / 100 = 312
65x/100 = 312
65x = 31200
x = 31200/65
x = $480
So I think the original price of desk was $480
The original price of the desk is $480.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Given that, a desk is being sold for $312.
Let the original price of the desk be x.
Here, x-35% of x =312
x- 35/100 ×x=312
x-0.35x=312
0.65x=312
x=312/0.65
x=480
Therefore, the original price of the desk is $480.
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Which proportion would you use to solve the following problem?
A map has a scale of 1 cm : 5 km. Determine how far apart two cities are if they are 4 cm apart on the map.
A.
B.
C.
D.
Answer:
20 km
Step-by-step explanation:
We can use ratios to solve
1 cm 4 cm
-------- = ------------
5 km x km
Using cross products
1 * x = 4 * 5
x = 20
20 km
Answer:
1/5 = 4/x
Step-by-step explanation:
Each cm on the map represents 5 km. If it shows 4 cm apart of the map, you can use the proportion 1 cm : 5 km = 4 cm : x km.
simplify the following without using calculator
√50 + √98
Answer:
The exact answer is 12*√2, if you need approximately answer it is 12*1.4= 16.8
Step-by-step explanation:
√50 + √98 = √(25*2)+√(49*2)= √25√2+√49*√2= 5√2+7*√2=12*√2
please help !!!!
i would really appreciate it
Answer: A
Step-by-step explanation: x=-2, y=3, z=-3
Answer:
A. -2, 3, -3
Step-by-step explanation:
x = 7 - 2y + z
y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =
= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z
13y = 63 + 8z
y = (63 + 8z)/13
2x + 2y - 3z = 11
2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11
2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11
14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11
-2×(63 + 8z)/13 - z = -3
-2×(63 + 8z) - 13z = -39
-126 - 16z - 13z = -39
-29z = 87
z = -3
y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3
x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2
What is the length of the hypothenuse of the triangle?
Answer:
26ft
Step-by-step explanation:
10^2 +24^2 =AB^2
AB=26
Answer: 26 ft
Step-by-step explanation:
a^2+b^2=c^2
10^2+24^2 = c^2
100+576=c^2
Sqrt 676 = c
C = 26
Which table represents a linear function?
Answer:
the the 3rd one Is the one
A physician orders Diflucan oral suspension 200 mg now followed by 100 mg daily for a total of two weeks. How many 35 mL bottles of Diflucan 10 mg/ml suspension are needed to fill this prescription?
Answer:
Step-by-step explanation:
Total amount = 200 mg + (13 days)×(180 mg)/day = 2620 mg
One 35 mL bottle contains (35 mL)×(10 mg)/mL) = 350 mg of medication.
(2620 mg)×(1 bottle)/(350 mg) ≈ 7.5 bottles
8 bottles are needed.
Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. That tree can be seen when one walks 14 bu from the south gate, turns west and walks 1775 bu. Find the length of each side of the city.
Answer:
The length of each side of the city is 250b
Step-by-step explanation:
Given
[tex]a = 20[/tex] --- tree distance from north gate
[tex]b =14[/tex] --- movement from south gate
[tex]c = 1775[/tex] --- movement in west direction from (b)
See attachment for illustration
Required
Find x
To do this, we have:
[tex]\triangle ADE \sim \triangle ACB[/tex] --- similar triangles
So, we have the following equivalent ratios
[tex]AE:DE = AB:CB[/tex]
Where:
[tex]AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775[/tex]
Substitute these in the above equation
[tex]20:x/2 = 20 + x + 14: 1775[/tex]
[tex]20:x/2 = x + 34: 1775[/tex]
Express as fraction
[tex]\frac{20}{x/2} = \frac{x + 34}{1775}[/tex]
[tex]\frac{40}{x} = \frac{x + 34}{1775}[/tex]
Cross multiply
[tex]x *(x + 34) = 1775 * 40[/tex]
Open bracket
[tex]x^2 + 34x = 71000[/tex]
Rewrite as:
[tex]x^2 + 34x - 71000 = 0[/tex]
Expand
[tex]x^2 + 284x -250x - 71000 = 0[/tex]
Factorize
[tex]x(x + 284) -250(x + 284)= 0[/tex]
Factor out x + 284
[tex](x - 250)(x + 284)= 0[/tex]
Split
[tex]x - 250 = 0 \ or\ x + 284= 0[/tex]
Solve for x
[tex]x = 250 \ or\ x =- 284[/tex]
x can't be negative;
So:
[tex]x = 250[/tex]
Sierra used the following steps to copy angle ABC:
1. Draw a ray with the endpoint D.
2. Place the compass on point B. Swing an arc that intersects rays BA and BC that creates point E on BA and Fon BC.
3. Keeping the compass at the same width, place it on point D, and swing an arc that creates point G on the ray.
4. Open the compass to the distance between points A and E.
5. Keeping the compass at the same width, place it on point G and swing an arc that intersects the arc created from point D.
6. Label the intersection of the arcs created from point D with point H, and draw a ray from point D through point H.
In which step did the error occur? Explain. (1 point)
Step 2. She did not set the proper compass length.
O Step 2. She drew an arc Instead of a circle.
Step 3. She placed the compass at an incorrect point.
Step 4. She measured the incorrect length.
The process of copying an angle through construction involve ensuring
that the distance between the two rays forming the angle is the same or
equal in the original and copy of the angle at a given equal distance from
the vertex of both angles
The step where the error occur is step 4. She measured the incorrect length
The reason for the above selection is as follows:
The steps to copy an angle are as follows;
Draw the initial line, l, (the working line) of the copy of the angle as a ray with an endpoint, DIn the given angle ∠ABC, with the compass placed at point B, construct an arc that intersect the two sides of the given line (BA at point E, and BC at point F) by opening the compass to a radius, rPlace the compass at the point D on the line l and with the radius r from above, draw an arc (D, r) that intersects the line l at the point GPlace the compass at point E on line AB, and construct an arc passing through point F, therefore having radial length EFPlace the compass at point G and construct an arc with radial length EF that intersects the arc (D, r) at point H and draw a ray from the point D passing through point H to complete the constructionA critical step in the copying process involves the finding the distance
between the initial line and the terminal line EF at a given distance DG =
AE from the angle vertex
The step where the error occur is in step 4. by opening the compass
between points A and E which are points on the same line and placing the
compass at point G on line l to draw an arc intersecting the arc created
from point D at H, thereby making the radial distance between the two lines
forming the angle, in the copied angle at a distance E from the vertex,
equal to AE rather than EF
Therefore, the error occurred in step 4. She measured the incorrect length
Learn more about the steps to copy an angle here:
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Factor the following expressions completely. Show and check all work on your own paper.
x^2+169
Y= 3x-1
2x+6=y substitution method
Answer: (7, 20)
Concept:
There are three general ways to solve systems of equations:
EliminationSubstitutionGraphingSince the question has specific requirements, we are going to use substitution to solve the equations.
Solve:
Given equations
y = 3x - 1
2x + 6 = y
Substitute the y value since both equations has isolated [y]
2x + 6 = 3x - 1
Add 1 on both sides
2x + 6 + 1 = 3x - 1 + 1
2x + 7 = 3x
Subtract 2x on both sides
2x + 7 - 2x = 3x - 2x
[tex]\boxed{x=7}[/tex]
Find the value of y
y = 3x - 1
y = 3(7) - 1
y = 21 - 1
[tex]\boxed{y=20}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Solve this inequality: 14 <-7x
Answer:
x > -2
Step-by-step explanation:
14 <-7x
or, 14/-7=-7x/-7
or, -2 < x
pls help! I need the answer quickly! thank you!
The perimeter of a triangle is the summation of the three sides of the triangle. Base on the assumed values, the length of side BD is 2.
For [tex]\triangle ACD[/tex], the sides are: AC, AD and CD
So, the perimeter is:
[tex]P_{\triangle ACD} = AC + AD + CD[/tex]
For [tex]\triangle ABD[/tex], the sides are: AB, AD and BD
So, the perimeter is:
[tex]P_{\triangle ABD} = AB + AD + BD[/tex]
The difference in the perimeters is:
[tex]P_{\triangle ACD} - P_{\triangle ABD} =1 + \sqrt 3[/tex]
So, we have:
[tex](AC + AD + CD) - ( AB + AD + BD) =1 + \sqrt 3[/tex]
Open brackets
[tex]AC + AD + CD - AB - AD - BD =1 + \sqrt 3[/tex]
Evaluate like terms
[tex]AC + CD - AB - BD =1 + \sqrt 3[/tex]
Make BD the subject
[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex]
The solution cannot be completed because the side lengths of [tex]\triangle ACD[/tex] and [tex]\triangle ABD[/tex] are not given; so, I will assume the following values.
[tex]AC =2; CD = 1; AB = \sqrt 3[/tex]
[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex] becomes
[tex]BD = 2 + 1 + \sqrt 3 - (1 + \sqrt 3)[/tex]
Open bracket
[tex]BD = 2 + 1 + \sqrt 3 - 1 - \sqrt 3[/tex]
Evaluate like terms
[tex]BD = 2[/tex]
Base on the assumed values, the length of side BD is 2.
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GIVING 25 POINTS AND BRAINIER IF ANSWERED!
What is one thing you would not do when finding the question in a word problem?
A. Look for a problem similar to the word problem you are trying to solve.
B. The question may not be directly stated.
C. So you can understand what the facts are in the word problem.
D. To define your strategy or game plan to solve the word problem.
Answer:
B. The question may not be directly stated.
find the surface area of the prism HURRY HURRY
Answer:
should be 192
Step-by-step explanation:
Evaluate the expression 2x-xy if x= -1/2 and y=8
Answer:
3
Step-by-step explanation:
2x-xy
2(x)-(x)(y)
2(-1/2)-(-1/2)(8)
-1 - (-4)
-1 + 4
3
Answer:
3
Step-by-step explanation:
2x-xy
Let x = -1/2 and y = 8
2(-1/2) - (-1/2)(8)
Multiply
-1 - (-4)
Subtracting a negative is like adding
-1+4
Add
3
The perimeter of a square is 14 cm. Find the area
Step-by-step explanation:
A = 12.25cm2
P perimeter 14cm
Answer:
A=12.25cm²
P=14
Which of the following is not a rational number?
What are all possible integer solutions for b & p in the equation?
Answer:
4
Step-by-step explanation:
7+sqrt(7) is an irrational number
Answer:
p = 8 when b = 16 and p = -8 when
b = -16
Step-by-step explanation:
x² + bx + 64 = x² + 2px + p²
Cancel x² on both sides,
bx + 64 = 2px + p²
Now, by comparing both sides, you'll get the following equations,
1. b = 2p
2. p² = 64
From equation (2),
p = ±√64
= 8 or -8
Substitute p = 8 and p = -8 into equation (1),
b = 2(8) and b = 2(-8)
b = 2(8) and b = 2(-8) = 16 = -16
Therefore, p = 8 when b = 16 and p = -8 when
b = -16
(4m-n-3). 12n13
8m 20
Answer:
24n^7/m^16
Step-by-step explanation:
Just simplify and rewrite what ever you get simplify again 2 times and now make the calculation as you see every big number is a whole number and is a pair.
What are the solutions?
It's the third option.
Completing the square yields
x ² + 9x + 7 = 0
(x ² + 9x + 81/4) + 7 = 81/4
(x + 9/2)² + 7 = 81/4
Now solving for x gives
(x + 9/2)² = 53/4
x + 9/2 = ± √(53/4) = ± √53/2
x = (-9 ± √53)/2
