Final answer:
To find the length of the hallway, divide the area (280 square feet) by the width (8 feet), resulting in a hallway that is 35 feet long.
Explanation:
The student's question involves the calculation of the length of a hallway when given the area and the width. To solve for the length, we use the formula for the area of a rectangle, which is area = length imes width. Since the area of the hallway is 280 square feet and the width is 8 feet, we divide the area by the width to find the length:
Length = Area / Width
Length = 280 sq ft / 8 ft
Length = 35 feet
Therefore, the hallway is 35 feet long.
A greengrocers sells mangoes for 77p each.
a)
Find the greatest number of mangoes you can buy for £5.
b) How much change should you receive?
Answer:
6 mangoes
0.38 or 38p
Step-by-step explanation:
Apparently the value of the mango is £ 0.77, which means that to get the number of mangoes you can buy, you must divide this value to the amount of money you have, that is, £ 5
5 / 0.77 = 6.49
which means that it is enough for 6 mangoes.
To know the change, multiply the value of one by 6 and subtract it with £ 5, it would be the change.
6 * 0.77 = 4.62
5 - 4.62 = 0.38
That is, the change is £ 0.38 or 38p
Answer:
(a) 6 mangoes
(b) £0.38
Step-by-step explanation:
(a) The greengocers sell the mangoes for 77 p.
The greatest number of mangoes you can buy for £5 can be gotten by dividing £5 by the price of each mango (77 p). We will only pick the whole number part because number of mangoes can only be whole number.
First, we convert £5 to pence:
£1 = 100 pence
=> £5 = 5 * 100 = 500 pence
Hence, the greatest number of mangoes that can be bought is:
500 / 77 = 6.49
Since we are only picking the whole number part, the answer is 6 mangoes.
(b) The price of 6 mangoes is:
6 * 77 = 462 pence
Hence, if you take £5 (500 pence) to the store, your change should be:
500 - 462 = 38 pence
38 pence is the same as £0.38
Manual collects $45.18 for a fundraiser. Gerome collects $18.07 more than Manual. Cidny collects 2 times as much as Gerome. How much money does Cidny collect for the fundraiser
Answer:
$126.5
Step-by-step explanation:
45.18+18.07=67.25
67.25*2=126.5
Riley and Jace work at a dry cleaners ironing shirts. Riley can iron 25 shirts per hour, and Jace can iron 30 shirts per hour. Riley worked 3 more hours than Jace and they ironed 460 shirts between them. Write a system of equations that could be used to determine the number of hours Riley worked and the number of hours Jace worked. Define the variables that you use to write the system.
Answer:
25r +30j = 460r - j = 3Step-by-step explanation:
Let r and j represent Riley's hours and Jace's hours, respectively. The equations could be ...
25r +30j = 460
r - j = 3
__
The solution is (r, j) = (10, 7).
The system of equations that could be used to determine the number of hours Riley and Jace worked is: R = J + 3 and 25R + 30J = 460, where R represents the number of hours Riley worked, and J is the number of hours Jace worked.
Explanation:Let's define our variables first. Let's let J represent the number of hours Jace worked and R represent the number of hours Riley worked.
From the information given, we know that Riley worked 3 more hours than Jace. So we can write this as an equation: R = J + 3.
We also know that between them, they ironed 460 shirts. We can express this as another equation by multiplying their per-hour output by the number of hours they worked, then adding the two together: 25R + 30J = 460.
So our system of equations is: R = J + 3 and 25R + 30J = 460.
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Consider Circle Y with radius 3 m and m XYZ=70
What is the approximate length of minor arc XZ? Round to the nearest tenth of a meter.
Answer:
4.9m
Step-by-step explanation:
In circle Y:
Radius=4m
Central Angle of XYZ=70°
Length of an arc[tex]=\frac{\theta}{360^\circ}X2 \pi r [/tex]
Therefore, Length of minor arc XZ
[tex]=\frac{70^\circ}{360^\circ}X2X4 X \pi [/tex]
=4.9m (correct to the nearest tenth)
Choose ONE of the equations to solve. SHOW DETAILED WORK & give the answer.
Answer:
x=3
Step-by-step explanation:
9x+5+2x = 38
Combine like terms
9x+2x +5 = 38
11x+5 = 38
Subtract 5 from each side
11x+5-5 = 38-5
11x = 33
Divide each side by 11
11x/11 = 33/11
x = 3
Answer:
3(2n + 10) = 54
n = 4
Step-by-step explanation:
3(2n + 10) = 54
Divide both sides by 3
2n + 10 = 18
Subtract 10 form both sides
2n = 8
Divide both sides by 2
n = 4
In Prodigy, Luigi's inventory weighs 3 grams. He is collecting old socks,
each sock weighs grams.
Let the total weight of his inventory be represented by i.
Let the number of old socks collected be represented by s.
An equation that represents this scenario is:
i = s +3
What is the total weight of his inventory if he collects 27 socks?
Answer as a decimal.
Final answer:
The total weight of Luigi's inventory if he collects 27 socks is 30 grams.
Explanation:
The equation i = s + 3 represents the scenario where Luigi's inventory weight is represented by i and the number of old socks collected is represented by s. According to the equation, the total weight of Luigi's inventory is equal to the number of socks collected plus 3 grams.
If Luigi collects 27 socks, we can substitute s with 27 in the equation to find the total weight of his inventory.
i = 27 + 3 = 30 grams.
Can someone help me finger out my homework please
Answer:
(1) w = 6.4
(2) w = -67
(3) q = 336
(4) z = -14
(5) x = 9
(6) y = 3
(7) x = 8
(8) x = -16
(9) x = 54
(10) x = 13.5
Step-by-step explanation:
Ik u need it quick so mb for not explaining. Good luck
Answer:
the first one is 6.4 i cant help with others srry im not smart either.
Step-by-step explanation:
30 points!!!
AOC and BOD are diameters of a circle, centre O. prove that triangle ABD and triangle DCA are congruent by RHS.
Triangle ABD and triangle DCA can be proven congruent using the RHS congruence criterion.
Explanation:To prove that triangle ABD and triangle DCA are congruent using the RHS (Right Angle, Hypotenuse, Side) congruence criterion, we need to show that they have a right angle, an equal hypotenuse, and an equal side adjacent to the right angle.
Since AOC and BOD are diameters of the circle, we know that they are perpendicular to their respective radii.Therefore, angle AOB is a right angle, and triangle AOB is a right triangle.Since AO and BO are radii of the same circle, they have the same length, making the hypotenuse AB of triangle ABD equal to the hypotenuse BD of triangle DCA.Furthermore, angle ABD and angle CDA are both subtended by the same arc AD, so they are equal in measure.Finally, the adjacent sides to the right angles, AB and DC, are also equal as they are radii of the circle.Therefore, by the RHS criterion, triangle ABD and triangle DCA are congruent.
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He fills the pencil holder with sand before he wraps it to make it feel like a heavy, expensive gift. How much sand will he need to "borrow" from his sister's sandbox to fill the pencil holder? *
1 point
a) 21 cubic inches
b) 7.5 cubic inches
c) 9.375 cubic inches
d) 10.5 cubic inches
e) 15 cubic inches
Answer:
Answer choice d
Step-by-step explanation:
To find the volume of this triangular prism, you first need to find the area of the triangular base. The formula for the area of a triangle is bh/2, which in this case is 3*2/2=3 square units. Multiplying this by the height of the prism, 3.5, you get a total of 10.5 cubic inches, or answer choice d. Hope this helps!
Fill in the blank: 3 feet = __________ inches
Answer:
3 feet
Step-by-step explanation:
There are 36 inches in 3 feet. (there are 12 inches in a foot)
Answer:
3 ft = 36 inches
Step-by-step explanation:
We know that 1 foot = 12 inches
Multiply each side by 3
3 * 1ft = 3 *12 inches
3 ft = 36 inches
please help it is an 100 point test first person gets brainlyist :)
An A-frame house is 45 feet high and 32 feet wide. Find the measure of the angle that the roof makes with the floor. Round to the nearest degree.
Answer:
Angle, [tex]\theta=70.4^{\circ}[/tex]
Step-by-step explanation:
We have, an A-frame house is 45 feet high and 32 feet wide. It is required to find the measure of the angle that the roof makes with the floor.
The attached figure shows the A frame. Let [tex]\theta[/tex] is the angle that the roof makes with the floor. So,
[tex]\tan\theta=\dfrac{45}{16}\\\\\tan\theta=2.81\\\\\theta=\tan^{-1}(2.81)\\\\\theta=70.4^{\circ}[/tex]
So, the angle of 70.4 degrees is the angle that the roof makes with the floor.
Final answer:
To find the angle an A-frame house roof makes with the floor, one needs to use trigonometry. By dividing the width of the house by 2 to work with a right triangle and using the tangent function, the angle is calculated to be approximately 70 degrees.
Explanation:
The question involves finding the angle that an A-frame house roof makes with the floor, given the height of the house is 45 feet and the width is 32 feet. To solve this, we can use trigonometry, specifically the tangent function, as we are dealing with a right-angled triangle where the house's height forms one leg (opposite) and half of the width forms the other leg (adjacent). The formula to find the angle (θ) is θ = arctan(opposite/adjacent).
First, halve the width to work with one side of the A-frame: 32 feet / 2 = 16 feet. Then, use the arctan function: θ = arctan(45 feet / 16 feet). Use a calculator to find θ, which gives us an angle of approximately 70.346 degrees. When rounded to the nearest degree, the angle is 70 degrees.
Therefore, the angle that the roof makes with the floor is 70 degrees.
The picture shows a triangle.
Side Lengths: 2.1in., 4.4in., 5in.
Angle Measures: 25°, 61°, 94°
Which choice describes another triangle that can be drawn?
A. Side Lengths: 4.2in., 8.8in., 10in.
Angle Measures: 25°, 61°, 94°
B.Side Lengths: 2.1in., 4.4in., 5in.
Angle Measures: 35°, 56°, 89°
C.Neither of these choices
Answer:
A
Step-by-step explanation:
I got it correct
On some other planet, Thor stands on a bridge and throws his hammer at his brother Loki, who is at ground level. The hammer’s height h (in meters above the ground), t seconds after Thor threw it, is modeled by:
Answer:
h(0) = 3600
t=60 when it hits the ground
max height at 4050
at 15 seconds
Step-by-step explanation:
h(t) = -2t^2 + 60t +3600
When it is thrown is t=0
h(0) = -2(0) +60(0) +3600 = 3600
When it hits the ground is h(t) =0
0 = -2t^2 + 60t +3600
Factor out -2
0 = -2 (t^2 -30t -1800)
Divide by -2
0 = (t^2 -30t -1800)
Factor. What 2 numbers multiply to -1800 and add to -30
0 = (t+30) (t-60)
Using the zero product property
t+30 = 0 t-60 =0
t = -30 t = 60
Since we do not have negative time
t=60
The maximum occurs halfway between the zeros
(-30+60)/2 = 30/2 = 15
Put this into the function to find the maximum value
h(15) = -2(15)^2 + 60(15) +3600
= -2 (225) +900+3600
=4050
Answer:
Thrown at: 3600
Ground after: 60
Max height: 4050
After: 15
Step-by-step explanation:
h(t) = -2t² + 60t + 3600
h(0) = 3600
-2t² + 60t + 3600 = 0
t² - 30t - 1800 = 0
t² - 60t + 30t - 1800 = 0
t(t - 60) + 30(t - 60) = 0
(t - 60)(t + 30) = 0
t = 60, -30(not possible)
h(t) = -2t² + 60t + 3600
-2(t² - 30t) + 3600
-2(t² - 2(t)(15) + 15² - 15²) + 3600
-2[(t - 15)² - 225] + 3600
-2(t - 15)² + 450 + 3600
-2(t - 15)² + 4050
The Distance Between London And Cardiff Is 150 Miles. What is The Distanec In Kilometeres
Answer:
241.402
Step-by-step explanation:
Answer:
241.402
Step-by-step explanation:
(3x3 - 2x2 - 7x + 6) = (x + 1) synthetic division
Answer:3/2
3x3-2x2-7x+6=x+1(Multiply the numbers)
9-4-7x+6=x-1(Calculate)
11-7x=x-1(Move the terms)
-7x-x=-1-11(Collect like terms&calculate)
-8x=-12(Divide both sides by -8)
x=3/2
Synthetic division is a process used to divide a polynomial by a linear expression. Using a step-by-step process, the polynomial 3x^3 - 2x^2 - 7x + 6 is divided by x + 1. The result is a new polynomial, which represents the quotient and a remainder.
Explanation:Synthetic division is used to divide a polynomial by a linear expression. In this case, we have the polynomial (3x^3 - 2x^2 - 7x + 6) and we want to divide it by (x + 1). Synthetic division follows a specific set of steps:
Write the coefficients of the polynomial in a row: 3, -2, -7, 6. Write the root of the divisor, which is the solution to x + 1 = 0. This root is -1. Drop down the leading coefficient, which is 3 in this case. Multiply the root by the number just brought down, and write the result under the next coefficient. So, (-1)*3 = -3. Add the numbers in that column to get the next number to bring down. (-2) + (-3) = -5. Repeat steps 4 and 5 until all coefficients have been processed.
The numbers at the bottom are the coefficients of the quotient polynomial, and the remainder if any.
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a local small business will donate money to the students council based on the number of carnival tickets sold. the points shown on the graph repersent the model
Answer:
A = 5
B= 20
C= 15
D=20
Step-by-step explanation:
Answer:
A = 5
B= 20
C= 15
D=20
Step-by-step explanation:
Plzz
Answer quick plzzzz
Which of the following best describes the square root of 51?
Answer:
The [tex]\sqrt{51}[/tex] is between the [tex]\sqrt{49}[/tex] and [tex]\sqrt{64}[/tex] which simplified is 7 and 8.[tex]\sqrt{51}[/tex] equals 7.14142843...Step-by-step explanation:
Is there answer choices? If not here's my answer:
The [tex]\sqrt{51}[/tex] is between the [tex]\sqrt{49}[/tex] and [tex]\sqrt{64}[/tex] which simplified is 7 and 8.[tex]\sqrt{51}[/tex] equals 7.14142843...That's all that it should be.
Mr. Hayes has Ill straw bundles to use for bedding in his horse stalls. What is the
greatest number of stalls he can fill if each stall holds exactly 4 bundles of
straw?
We have been given that Mr. Hayes has 111 straw bundles to use for bedding in his horse stalls. We are asked to find the greatest number of bundles that he can fill if each stall holds exactly 4 bundles of straw.
To solve our given problem, we will divide 111 by 4.
[tex]\text{Greatest number of stalls that can be filled}=\frac{111}{4}[/tex]
[tex]\text{Greatest number of stalls that can be filled}=27.75[/tex]
Since 0.75 is not an integer, so Mr. Hayes cannot fill 0.75 of a stall. Therefore, the greatest possible number of stalls will be 27.
Leia cuts congruent triangular patches with an area of 15 square centimeters from a rectangular piece of fabric that is 10 centimeters long and 6 centimeters wide. How many of the patches can Leia cut from 33 pieces of the fabric?
Answer:
132 patches
Step-by-step explanation:
First we need to find the area of the rectangular piece, multiplying the length and the width:
Area of fabric: 10 * 6 = 60 cm2
If each triangular patch has 15 cm2 of area, a fabric of 60cm2 can make 60 / 15 = 4 triangular patches.
Then, if Leia uses 33 pieces of fabric, she can make a total of 33 * 4 = 132 patches.
Answer:
132
Step-by-step explanation:
Total area'A' of rectangular piece of fabric is given by
A= length 'l' x width'w'
A= 10 x 6=> 60cm²
As there are 33 such pieces, 33 x 60=1980cm²
In order to evaluate the umber of triangles that can be made, divide total area by the area of one triangular piece
n= 1980/15
n=132
Therefore, 132 triangles can be made
help pls??????????????????????????????????????????????????????????
The two events are Independent events. So, the selection of topics by different students does not influence each other's choices.
This is a question about whether the events of students selecting essay topics independently are dependent or independent. In this context, the two events are independent. Each student's choice of topic does not depend on the choices of other students, as they do not need to inform the teacher or each other beforehand. Therefore, the selection of topics by different students does not influence each other's choices.
What is the solution to this system? Enter the solution as an ordered pair,
(x, y).
Answer:
(-2, 5)
Step-by-step explanation:
The solution of a system is where the lines cross, or a common point they share. The lines meet at (-2, 5), so that is the solution to the system.
someone help me with this
Answer:
A -47
Step-by-step explanation:
(2-10)= -8*5= -40-7= -47
Answer:
-47.
Step-by-step explanation:
5(2-10)-7
--> 2-10= -8
5*-8-7
--> 5*-8= -40
--> -40-7 = -47
Here is the equation of a circle in standard form.
(x + 10)2 + (y + 9)2 = 100
What are the coordinates of the center?
A. (-10, -9)
B. (9, 10)
C. (-9, -10)
Answer:
A
Step-by-step explanation:
The equation is in the standard form of a circle:
(x – h)^2 + (y – k)^2 = r^2
where (h,k) is the center, and r is the radius.
If we compare the 2 equations:
(x – h)^2 + (y – k)^2 = r^2
(x + 10)^2 + (y + 9)^2 = 100
We can see that the center is (-10, -9).
This is because (x- -10) will become (x+10), and (y- -9) will become (x+9).
So, choice A is correct
Answer:
A
Step-by-step explanation:
The equation of a circle in standard form is: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h, k) is the center and r is the radius.
Here, our equation is: [tex](x+10)^2+(y+9)^2=100[/tex] , which means that h = -10 and k = -9. Then, the center is (-10, -9).
The answer is A.
13.5-ounce bottle cost 2.19. A 29.2-ounce bottle costs 5.37 find the unit price for each size
Answer:
A)Unit prize is $0.162
B)Unit prize is $0.183
Step-by-step explanation:
A) 13.5-ounce bottle cost 2.19
Cost of 13.5 ounce bottle =2.19
Cost of 1 ounce bottle =[tex]\frac{2.19}{13.5}=0.162[/tex]
So, Unit prize is $0.162
B)29.2-ounce bottle costs 5.37
Cost of 29.2 ounce bottle = 5.37
Cost of 1 ounce bottle =[tex]\frac{5.37}{29.2}=0.183[/tex]
So, Unit prize is $0.183
The graph of r = 2cos5theta is symmetric about the __________.
a. y-axis only
b. x-axis only
c. origin only
d. no symmetry
The graph of r = 2cos5theta is symmetric about the x-axis only.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given function:
[tex]r=\ 2\ \cos\ \left(5\theta\right)[/tex]
Here, the graph shown below of this function.
As, seen from the graph.
The graph is symmetric about x- axis only .
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The distance around a circular dance hall room is 135 feet. What is the longest distance around the dance hall?
Answer: 43feet
Step-by-step explanation:
Perimeter= 135 feet
Since perimeter= 2πr
135 = 2πr
Recall that π = 3.14
135 = 2 × 3.14 × r
135 = 6.28 × r
135 = 6.28r
r = 135/6.28
r = 21.5
d = 2r
d = 2 × 21.5
d = 43 feet
Answer:
42.95 feet
Step-by-step explanation:
In this question, we are tasked with calculating the distance around the dance hall that is the greatest.
Now, to answer this, we must have at the back of our mind that the dance hall is circular in shape. Thus, the greatest distance that could arise is the distance from one edge of the dance hall to the other end of the dance passing exactly through the center of the dance hall.
This distance described above is the diameter of the dance hall.
Notice we were given a length in the question? This length refers to the circumference around the circular dance hall.
Reframing then question, we were just told to calculate the diameter of a circle given the circumference of the circle.
Mathematically, circumference C of a circle = 2 * pi * r
Recall, mathematically also 2r = D
so we can say C = pi * D
Using the value of 22/7 for pi and the value of the circumference in the question, we have;
135 = 22/7 * D
D = (7 * 135)/22
D = 42.95 feet
pls help me. question in picture
Answer:
a.) [tex](m+6)(m+10)[/tex]
Step-by-step explanation:
Factor [tex]m^2+16m+60[/tex]
Find what two numbers add up to 16, and equal 60 when multiplied:
[tex]6[/tex] and [tex]10[/tex]
[tex]6+10=16\\6*10=60[/tex]
Factor:
[tex](m+6)(m+10)[/tex]
Finito.
Answer:
(m+6)(m+10).
Step-by-step explanation:
To find this answer, we will need to determine factors of 60 that when added, they are equivalent to 16.
We can begin by listing some factors:
30 and 2
4 and 15
12 and 5
6 and 10
...
Then, we can determine which of these factors can be added together to become 16. From this, we can determine that only factors "6 and 10" become 16 when added together.
When we do this, we can see that only answer 1, (m+6)(m+10), is equivalent to the equation given.
Kristina received $125 for her birthday. Her parents offered to pay her 3.5% simple interest per year if she would save it for at least one year. How much interest could Kristina earn?
Answer:
4.375 a year
Step-by-step explanation:
The formula is
Interest earned= principal ×interest rate×time
I=125×0.035×1=4.375
Kristina could earn $4.375 in simple interest.
Explanation:To calculate the interest Kristina could earn, we can use the formula:
Interest = Principal × Rate × Time
where Principal is the initial amount, Rate is the interest rate, and Time is the duration in years.
Plugging in the values, we have:
Principal = $125Rate = 3.5% = 0.035 (expressed as a decimal)Time = 1 yearUsing the formula, we can calculate the interest:
Interest = $125 × 0.035 × 1 = $4.375
Therefore, Kristina could earn $4.375 in simple interest.
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