Answer:
Step-by-step explanation:
'
The length of a rectangle is 6 inches longer than it is wide. If the area is 160 square inches, what are the dimensions of the rectangle?
Answer:
L = 16
w = 10
Step-by-step explanation:
Givens
Area = 160 sqr inches
width = x
length = x + 6
Equation
Area = L * w
Solution
Substitute in the equation all of the givens.
160 = x(x + 6) Remove the brackets
160 = x^2 + 6x Subtract 160 from both sides.
160-160 = x^2 + 6x - 160
0 = x^2 + 6x - 160
This equation factors. Turn it around first
x^2 + 6x - 160 = 0
(x - 10)(x + 16) = 0
Answer
x (width) = 10
x + 16 = 16
Answer:
The length is 16 inches and the width is 10 inches.
Step-by-step explanation:
The speed of an object in space is shown in the graph.
A graph titled Speed of Object has Time in Minutes on the x-axis and Distance in Miles on the y-axis. A line goes through points (0.2, 3) and (0.4, 6).
What is the slope of the line?
A) 10
B) 15
C) 20
D) 25
The slope of the linear equation is 15, so the correct option is B.
How to get the slope of the line?
A linear equation can be written as:
y = a*x + b
Where a is the slope and b is the intercept.
For a line that passes through the points (x₁, y₁) and (x₂, y₂), the slope can be written as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we have the two points (0.2, 3) and (0.4, 6), so the slope is:
[tex]a = \frac{6 - 3}{0.4 - 0.2} = 15[/tex]
So the slope of the line is 15, which means that the correct option is B.
If you want to learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Drag each tile to the correct box. a с C b A David proved the Law of Cosines with reference to AABC using a different method. Arrange the steps of his proof in the correct sequence. k² = c² - (b − x)² In AABD, (Pythagorean Theorem) In ABCD, k² = a² - 1² (Pythagorean Theorem) c² (6²-26x + x²) = a² — 1² (on simplification) Similarly, prove that a2b² + c² - 2bccos A and 82 6² = a² + c²2accos B B
Big question:
where is the question here
Date:
Name:
Refocus
Directions: Solve the problems by building the figure with algebra tiles and writing an equation.
A rectangle has a length that is twice the width. The perimeter of the rectangle is 12 feet.
What is the width? What is the length?
Equation:
Width:
Length:
Answer:
Equation: 2w + 2(2w) = 12
width = 2
length = 4
Step-by-step explanation:
Width is w
Length is 2 * width = 2w
Perimeter is 2w + 2l
Substitute 2w for L.
Perimeter is now 2w + 2(2w) = 12
Distribute the 2 to the parentheses.
2w + 4w = 12
Combine Like terms
6w = 12
Divide by 6 to solve for w.
w = 2
If w = 2, then the length = 4.
Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true
The correct answer is option D which is f(x) is decreasing for all the values of x < 3.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The value of the function [tex]f(x) = \dfrac{x+6}{x^2-9x+18}[/tex] is represented on the graph in the graph we can see that at x>6 the value of the function is decreasing and at x<3 the value of the function is increasing.
Therefore the correct answer is option D which is f(x) is decreasing for all the values of x < 3.
To know more about function follow
https://brainly.com/question/25638609
#SPJ1
suppose 2/5 of the marbles in a bag are red. how many marbles would you expect to pick before picking 10 reds
Find a3, a4, and a5.
a₁ = 5
a₂ = 2
an =-2an -1 + an-2
Answer:
A1 5×3 = 15
A2 = 2×4= 8
an=I don't know that one
Question 2 A birthday cake in the shape of the right-circular cylinder of radius 15cm and thickness 10cm is cut into smaller pieces. One of the piece is shown. 15 cm 30° 10 cm a) What is the volume of this piece to the nearestcm³? (2 marks)
The volume of a piece of the cake will be 588.75 cm³.
The complete question is attached below.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A birthday cake in the shape of the right-circular cylinder of radius 15 cm and thickness 10 cm is cut into smaller pieces.
One of the piece is shown.
Then the volume of piece of the cake will be
V = (30 / 360) x π x 15² × 10
V = 588.75 cm³
More about the geometry link is given below.
https://brainly.com/question/7558603
#SPJ1
A square is inscribed in a quarter of a circle,calculate the quarter circle.
Answer:
Step-by-step explanation:
Mr. Simmons figures he can paint his house in 5 days. If his son helps, together they can paint it in 2 days. How long will it take his son to paint the house if he works alone?
Answer:
3 hrs 20 min
Step-by-step explanation:
1/5 + 1/x = 1/2
x = 10/3
Houa bought 11 chicken wings for $23.10 . How much does each wing cost
Answer:
Answer = $2.10
Step-by-step explanation:
To solve this we take the total cost divided by the total number of chicken wings to get $2.10.
Hope that helps! :)
Answer:
1 wing = $2.10
Step-by-step explanation:
11 wings = $23.10
Let 1 wing = x
11x = 23.10
To solve for x, we divide both sides by 11 :
11x÷ 11 = 23.10 ÷11
x = 2.1
So 1 wing = $2.10
Hope this helped and brainliest please
Solve for x: -8 < 3x + 1 ≤ 13
Answer: If you’re doing algebra, -3<x or x<_4.
Another answer is -3<x<_4
Answer:
-3 < x <_4
Step-by-step explanation:
-8 < 3x+1 <_13
First solve for the left side: -8 < 3x + 1
Subtract 1 from each side
-9 < 3x
Divide each side by 3
-3 < x
Solve for the right side: 3x+1 <_13
Subtract 1 from each side
3x <_ 12
Divide each side by 3
x<_4
Put it together for your answer
-3 < x <_4
Question 18
Let set A = { even numbers}
set B = {odd numbers}
Find A U B
Answer: all integers
Step-by-step explanation:
[tex]A \cup B[/tex] denotes the union of the two sets, and is thus the set of all integers.
What is the slope of the line that cuts through the points (1, 2) and (5, 4)? a. 2 c. One-half b. -2 d. Negative one-half Please select the best answer from the choices provided A B C D
The slope of the line is 1/2 or one-half if the line that cuts through the points (1, 2) and (5, 4) option (c) One-half is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have a line that cuts through the points (1, 2) and (5, 4).
The slope of a line:
[tex]\rm m =\dfrac{4-2}{5-1}[/tex]
m = 2/4
m = 1/2
Thus, the slope of the line is 1/2 or one-half if the line that cuts through the points (1, 2) and (5, 4).
Learn more about the slope here:
brainly.com/question/3605446
#SPJ1
Can someone pls help quickly?
From the question given above, the ratio of L : W in simplified form is given as: 6 : 5. See the explanation below.
What is a ratio?A ratio, simply, can be defined as the quantitative relationship that exists between two values which is indicative of the number of times one value can be obtained from the other.
What is the explanation for the solution above?Step 1 - Indicate your assumptionsLet X be the width of one of the rectangles and let its height be Y.
It is clear from the image that:
4X = 3Y
Hence
(4/3)X = Y
Therefore,
Lenght (L) = 3Y
= 3 (4/3)X
= 4X
Width (W) = Y + 2X
= (4/3)X + 2X
= (10/3)X
Therefore,
L : W = 4X: 10/3X
= 4:10/3
To remove the fraction, multiply both sides of the ratio by 3
= 12 : 10, furhter simplify by halving each value, and we have
= 6:5
Hence, the ratio L: W in simplified form is 6 : 5.
Learn more about ratios at:
https://brainly.com/question/2328454
#SPJ1
8 19. Marcus claims that fractions with denominators 1 through 10 follow a pattern
when they are converted to decimal form. If any one fraction can be converted
to a terminating decimal, then all of the fractions with that same denominator
will also convert to terminating decimals. On the other hand, if one fraction
converts to a repeating decimal, then all fractions with that same denominator
will convert to a repeating decimal. Is Marcus correct? Explain.
Answer:
No
Step-by-step explanation:
Marcus is not correct because 1/12 converts to the repeating decimal 0.8333... but 3/12 converts to 0.25 which is not a repeating decimal.
A manufacturer of kitchen utensils and gadgets is considering changing the design of the salt and pepper shakers. Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder. the figure shows both designs.
Which set of additional details are the minimum required to ensure the new design will have the same volume as the original design?
For the current cylinder to have the same volume as the oblique cylinder, the height of both design must be the same and the base area of both designs must be the same.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Volume of cylinder = area of base * height
For the current cylinder to have the same volume as the oblique cylinder, the height of both design must be the same and the base area of both designs must be the same.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Answer:
C
Step-by-step explanation:
happened to do the test
How many classrooms would be necessary to hold 1,000,000 inflated balloons? (Assume one balloon is about 1 ft3 and a typical classroom is about 35 ft × 50 ft × 15 ft. Round your answer to the nearest number of classrooms.)
To hold 1,000,000 inflated balloons,
38 classrooms are needed.
What is volume?In three-dimensional space,
the amount of space taken by an object is the volume of that object.
The volume of the cubic,
= length x width x height
Given:
The dimensions of the normal classroom are 15 ft × 50 ft × 35 ft.
The volume of the classroom,
= 15 ft by 50 ft by 35 ft.
= 26250 cubic feet.
The number of classrooms,
= 1,000,000 / 26250
Simplifying the fraction,
we get,
= 38.09
≈ 38 to the nearest whole number.
Therefore, 38 classrooms are required.
To learn more about the volume;
https://brainly.com/question/23477586
#SPJ2
Divide x cubed minus 3 x squared minus 10 x + 24 by x minus 2. Step 1 - Fill in the missing number: A vertical line and horizontal line combine to make a L shape. There is one row of entries in the shape including 1, negative 3, negative 10, 24. On the outside to the left of the L shape is k. k = Step 2 - Fill in the missing number: A vertical line and horizontal line combine to make a L shape. There is one row of entries in the shape including 1, negative 3, negative 10, 24. On the outside to the left of the L shape is 2 and to the outside below 1 is a. a = ⇒ 1 Step 3 - Fill in the missing numbers: A vertical line and horizontal line combine to make a L shape. There are two rows of entries in the shape. The first row includes 1, negative 3, negative 10, 24. The second row includes blank, b, d, blank. On the outside to the left of the L shape beside row 1 is 2. On the outside below the L shape in the first column is 1 and in the second column is c. b = c = d =
The dividend that's represented by the synthetic division is 2x³ + 10x² + x + 5.
How to depict the dividend?From the information, given that the vertical line and a horizontal lines combined to form the L shape.
Row 1 has entries 2, 10, 1, 5.
Row 2 has entries -10, 0, -5.
In this situation, entry -5 is outside to the let of the shape.
Here, the dividend that's represented by the synthetic division is 2x³ + 10x² + x + 5.
Learn more about division on:
brainly.com/question/26410027
#SPJ1
Answer:
step 1: 2 Step 2: 1
Step-by-step explanation:
Step 3: 2, -1, -2
Complete the division. The remainder is 0. The quotient is x^2 - x - 12.
The universal set, &, and the sets A and B are defined below.
= {3, 4, 6, 8, 9, 12, 15, 16, 20}
A = {6, 9, 12, 15}
B = {multiples of 4}
Write down all the elements of AB'.
Answer:
wedg
Step-by-step explanation:
ed
BRAINLIEST AND 50 POINTS IF U ANSWER ALL PLSSS SOLVING REQUIRED PLSSS
#1
LSA
4(1/2BH)4(1/2×9×12)2(9)(12)216cm²TSA
LSA+9²216+81297cm²#2
LSA
3(1/2(13)(15))1.5(195)292.5cm²TSA
292.5+1/2(195)1.5(195)+0.5(195)2(195)390cm²#3
LSA
4(1/2(6)(16))2(96)192cm²TSA
LSA+6²36+192228cm²#4
LSA
2(1/2(8)(6))+2(1/2(6)(6.5))8(6)+6(6.5)48+3987cm²TSA
87+8(6)87+48135cm²#5
We know
TSA=LSA+Area of baseSo
LSA=TSA-Area of baseShe can use this formula
Solve for x
5x= -9
Give your answer as an improper
fraction in its simplest form.
We proceed to solve the equation:
[tex]5x \: = \: 9[/tex]
We divide by 5 the two members that make up the equation.[tex]5x \: \div \: 5 \: = \: - 9 \: \div \: 5[/tex]
Since it is divided by itself, it is equal to 1.[tex]x \: = \: - 9 \: \div \: 5[/tex]
We transform it into an improper fraction:[tex]x \: = \: \boxed{ \bold{ - \frac{9}{5} }}[/tex]
MissSpanishplease help anyone i really need it
Answer:
Median: 21
Eric took the longest
Ed took 18 minutes longer than Mike
Oscar took the shortest amount of time to solve the puzzle
Step-by-step explanation:
The median is the middle amount of the numbers, line them up from smallest to largest and find the number in the middle...the largest number is the person who took the longest...subtract Ed's score (25) from Mike's score (4) to get the answer...and the smallest number is the person who took the shortest amount of time
Gerald will be finishing his payments on his 5-year, $45,000 student loan and wants to know the amount of interest that he
paid over the course of the loan. The student loan has a 4.1% fixed interest rate that is compounded monthly. Calculate the
total amount of interest Gerald paid, rounding to the nearest cent.
Answer: 538
Step-by-step explanation: en verdad no sé pero eso fuelo que me salio
Solve the following linear equation:
3(2x + 12) = 2(2x - 10)
8. Find the area of the shaded region.
Answer:
7
Step-by-step explanation:
did the math
Answer:
Answer:4π
Step-by-step explanation:
As we know,
Area of circle=πr^2
=π(2)^2
=4π=12.57m^2
9) A furniture store is having a spring sale-15% off of everything in the store.
What is the price of a table that regularly costs $159.98 if it is bought on sale?
Answer:
$135.98
Step-by-step explanation:
15% of $159.98 = 0.15 × $159.98 = $24.00
$159.98 - $24.00 = $135.98
Which statement is true?
a.All rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, all rectangles have 2 pairs of parallel sides.
b.Only some rectangles are parallelograms. Parallelograms have exactly 1 pair of parallel sides. Therefore, only some rectangles have exactly 1 pair of parallel sides.
c.Only some rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, only some rectangles have 2 pairs of parallel sides.
d.All rectangles are parallelograms. Parallelograms have exactly 1 pair of parallel sides. Therefore, all rectangles have exactly 1 pair of parallel sides.
Answer:
All rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, all rectangles have 2 pairs of parallel sides.
Step-by-step explanation:
Which of the following discribe an angle with a vertex at y
Answer:
The angle is referred to as a ∠ZYX angle, or ∠XYZ angle, because of the overall positioning. Think of it this way, you have a triangle with 3 angles. You have point X the high point, point Y the farthest point out, and point Z which makes the triangle complete. Connect these, and your angle becomes ZYX / XYZ.
Hope this helps!
why is the answer to this integral's denominator have 1+pi^2
It comes from integrating by parts twice. Let
[tex]I = \displaystyle \int e^n \sin(\pi n) \, dn[/tex]
Recall the IBP formula,
[tex]\displaystyle \int u \, dv = uv - \int v \, du[/tex]
Let
[tex]u = \sin(\pi n) \implies du = \pi \cos(\pi n) \, dn[/tex]
[tex]dv = e^n \, dn \implies v = e^n[/tex]
Then
[tex]\displaystyle I = e^n \sin(\pi n) - \pi \int e^n \cos(\pi n) \, dn[/tex]
Apply IBP once more, with
[tex]u = \cos(\pi n) \implies du = -\pi \sin(\pi n) \, dn[/tex]
[tex]dv = e^n \, dn \implies v = e^n[/tex]
Notice that the ∫ v du term contains the original integral, so that
[tex]\displaystyle I = e^n \sin(\pi n) - \pi \left(e^n \cos(\pi n) + \pi \int e^n \sin(\pi n) \, dn\right)[/tex]
[tex]\displaystyle I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n - \pi^2 I[/tex]
[tex]\displaystyle (1 + \pi^2) I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n[/tex]
[tex]\implies \displaystyle I = \frac{\left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n}{1+\pi^2} + C[/tex]