Answer:
Step-by-step explanation:
The number in consideration here is 45 and the integers that divide it evenly are known as the factors of 45. There are a total of six factors of the number 45: 1, 3, 5, 9, 15 and 45. The numbers that are multiplied in pairs to produce 45 are the factor pairs of 45.
Sam is training for a 5
km run. While training he runs for 6
minutes, then rests for 2
minutes, runs for 6
minutes, rests for 2
minutes, etc., until he finishes the 5
km. It takes him 26
minutes in total (with the rest periods) to finish the 5
km rum. If Sam runs at a constant speed (when he is not resting), what is this speed in kilometers per hour? (Recall there are 60
minutes in 1
hour.)
Answer:
15 km/h
Step-by-step explanation:
How many intervals of running and resting are needed to run and rest for 26 minutes?
Running is in parentheses, resting is not.
Each time he runs (6 minutes) and rests (2 minutes), he takes 8 minutes.
Three times this cycle is 24 minutes. He needs 2 more minutes of running to have a total of 26 minutes.
(6) + 2 + (6) + 2 + (6) + 2 + (2)
Add all the numbers in parentheses which are the times of running.
6 + 6 + 6 + 2 = 20
He ran for 20 minutes and rested for 6 minutes.
He ran 5 km in 20 minutes (of running).
speed = distance/time
speed = [5 km / (20 minutes)] × (60 minutes)/(1 hour)
speed = 15 km/h
Answer: 15 km/h
What is the volume of this
rectangular pyramid?
6 ft
8.4 ft
8.6 ft
The volume of the rectangular pyramid is 144.48 cubic feet.
What is a rectangular pyramid?A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.
The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.
The volume of a rectangular pyramid is given as:
[tex]\sf V = \dfrac{(l)(b)(h) }{3}[/tex]
[tex]\sf V = \dfrac{(8.4)(8.6)(6) }{3}[/tex]
[tex]\sf V = \dfrac{433.44 }{3}[/tex]
[tex]\sf V = 144.48 \ cubic \ feet[/tex].
Hence, the volume of the rectangular pyramid is 144.48 cubic feet.
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Ravi has two and one-fourth meters of rope. He gives ninety-three centimeters of the rope to his brother. How many centimeters of rope does Ravi have left?
If he gives ninety-three centimeters of the rope to his brother, Ravi has 132 centimeters of rope left.
Two and one-fourth meters of rope can be written as 2.25 meters. Since 1 meter is equal to 100 centimeters, we can convert 2.25 meters to centimeters by multiplying it by 100, giving us 225 centimeters.
If Ravi gives 93 centimeters of the rope to his brother, we can subtract it from the original length to find how much rope he has left.
225 cm - 93 cm = 132 cm
In general, to convert between meters and centimeters, you can multiply the number of meters by 100 to get the length in centimeters. To convert between centimeters and meters, you can divide the number of centimeters by 100 to get the length in meters.
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f(x) = (x − a) (x − b)
f(x) = (x − a) (x −b) (x-c)
Describe the relationship between these equations and
their graphs.
The relationship between graph of functions is described below.
Since we can see that,
Both equations are quadratic functions, meaning that their graphs are parabolic.
The first equation,
f(x) = (x - a)(x - b),
It represents a parabola that opens upwards or downwards depending on the values of a and b.
If a < b,
the parabola opens upwards,
and if a > b, it opens downwards.
To graph f(x),
we can first find its x-intercepts by setting f(x) = 0,
⇒ 0 = (x - a)(x - b)(x - c)
This gives us three x-intercepts,
⇒ x = a, x = b, and x = c.
The value of c is important because it determines the direction in which the parabola opens.
If c is greater than both a and b,
the parabola opens upwards, and if c is less than both a and b,
the parabola opens downwards.
If c is between a and b, the parabola has a minimum or maximum point.
Now, we can find the y-intercept by setting x = 0,
⇒ f(0) = (0 - a)(0 - b)(0 - c) = -abc
This tells us that the y-intercept is -abc.
To graph the parabola, we can plot the x-intercepts and the y-intercept, and then use the shape of the parabola to connect the points.
If the parabola opens upwards, it will have a minimum point at the vertex, and if it opens downwards, it will have a maximum point.
The second equation, f(x) = (x - a)(x - b)(x - c),
represents a cubic function,
meaning that its graph is a curve with either a local minimum or maximum.
To graph f(x), we can use the same process as above to find the x-intercepts and y-intercept, and then use the shape of the curve to connect the points.
After plotting can see, the cubic function has two local minima and one local maximum.
It also has a point of inflection at x = (a + b + c)/3.
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Find the inverse of y = log₂x
Answer: 2ˣ = y
Step-by-step explanation:
In order to find the inverse of any function, switch the x and the y, then solve for y.
y = log₂x >swap/switch variables and solve for y
x = log₂y >rewrite in exponential form
2ˣ = y
Find the value of 20x when x = 10.
(a) 200
(c) 2
(b) 30
(d) 5
a prime number that is between 48 and 58
Answer:
53 is prime. How are you in collage?
A prime number is a number that is only divisible by 1 and the number itself (examples include 3, 11, 19). The prime numbers between 40 and 60 are 41, 43, 47, 53, and 59.
A ring was purchased in 2012 for $900the value of the ring increases by 7% each year, find the value of the ring in 2030. Round to the nearest cent
The value of the ring in 2030 would be; 2,034
Given that the Purchase price of the Diamond ring= $900
Value of ring increase by 7% each year.
First find a number of the year between 2012 and 2040,
Time period= 2030 - 2012
∴ Time period of value appreciation is 18 years.
Now, finding the value of a diamond ring increased after 28 years.
The value of ring increased after 18 years= 900 x 0.07 x 18
∴ Increased value of diamond ring after 18years= $1,134
Next, Value of diamond ring after 18 years= 1,134 + 900
Hence, value of a diamond ring in 2030 is $2,034
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Last year, the Ross family spent $3,336 for electricity. They are opting to use balanced billing for next year. What will their monthly payment be?
Using balanced billing, the monthly payment is $278
What will be their monthly payment?Using balanced billing to determine their monthly payment, we simply need to divide their total annual payment by the total number of months in a year. This will result to dividing the entire annual bill by 12 to determine the monthly payment.
Given that the Ross family spent $3,336 for electricity last year, we can calculate their monthly payment as follows:
Monthly payment = Total cost / Number of months
Monthly payment = $3,336 / 12
Monthly payment = $278
Therefore, the Ross family's monthly payment for balanced billing will be approximately $278.
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Find the slope of the line through the points (4, 8) and (5, 10).
A. -1/2
B. 2
C. 1/2
D. -2
Answer:
2, answer choice B
Step-by-step explanation:
Slope = rise/run = (y2-y1)/(x2-x1).
You are given points (4,8) and (5,10).
slope = (8-10)/(4-5)
slope = (-2)/(-1)
slope = 2
1. If an object has a mass of 12kg, it has a weight of
Answer:
weight = gxg = 12kg to g = 0.12 and then using formula we get 0.12x0.12 = 1.44 is the weight
Step-by-step explanation:
Answer:
Therefore, the weight of the object is approximately 117.72 Newtons.
Step-by-step explanation:
The weight of an object is given by the formula:
weight = mass x acceleration due to gravity
The acceleration due to gravity on Earth is approximately 9.81 m/s².
So, the weight of an object with a mass of 12 kg is:
weight = 12 kg x 9.81 m/s² = 117.72 N
Therefore, the weight of the object is approximately 117.72 Newtons.
7. Mark wants to put a circular swimming
pool in his backyard. The base of the
pool has an area of 615.44 square feet,
and the rectangular section of the
yard where he wants to put the pool is
25 feet by 35 feet. Use this information
to answer Parts A and B.
Yes, the circular pool will fit into the rectangular section of the yard.
Part A: Given that, the base of the pool has an area of 615.44 square feet.
We know that, the area of a circle is πr².
Here, πr²=615.44
3.14r²=615.44
r²=615.44/3.14
r²=196
r=14 feet
Therefore, the diameter is 14×2=28 feet
Part B: The rectangular section of the yard where he wants to put the pool is 25 feet by 35 feet.
Area of a rectangular section = Length×Breadth
= 25×35
= 875 square feet
Yes, the circular pool will fit into the rectangular section of the yard.
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"Your question is incomplete, probably the complete question/missing part is:"
Mark wants to put a circular swimming pool in his backyard. The base of the pool has an area of 615.44 square feet, and the rectangular section of the yard where he wants to put the pool is 25 feet by 35 feet. Use this information to answer Parts A and B.
Part A: What is the diameter of the swimming pool?
Part B: Will the pool fit in the rectangular section of the yard?
need help with two part edulastic question
What is 50% of half of 10?
Answer:
2.5
Step-by-step explanation:
half of 10 is 10/2 = 5
so 50% of 5 is 2.5
Rachel has discovered the perfect recipe for icing that she wants to put on top of her cinnamon buns. The recipe calls for 5 tablespoons (tbsp) of sugar for every 2 teaspoons (tsp) of milk. Rachel already made her cinnamon buns and is ready to put on the icing. She has 7 teaspoons of milk for her next batch. How many tablespoons of sugar does she need?
Answer:
Step-by-step explanation:
Rachel already has 7 teaspoons of milk.
so 7 x 5 = 35
So Racheal will need 35 teaspoons of surger.
graphing stuff needs done soon
The value of x in each equation is:
a) x = -1
b) x = 3
c) x = 3
d) x = 9
e) x = -45
We have,
Substitute y = 2 in each equation.
a)
y = 6x + 8
2 = 6x + 8
2 - 8 = 6x
-6 = 6x
x = -1
b)
y = 2/3 x
2 = 2/3 x
x = 3
c)
y = -x + 5
2 = -x + 5
2 - 5 = -x
-3 = -x
x = 3
d)
y = 3/4 x - 2(1/2)
2 = 3/2 x - 5/2
2 + 5/2 = 3/2 x
9/2 = 3/2 x
x = 9
e)
y = 1.5 x + 11
2 = 1/5x + 11
2 - 11 = 1/5 x
-9 = 1/5 x
x = -45
Thus,
The value of x in each equation is:
a) x = -1
b) x = 3
c) x = 3
d) x = 9
e) x = -45
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need help with edualastic question answer a b c or d
the amount of cubic feet(Volume) the tent can hold is 165 ft³.
What is volume?Volume is the space occupied by an object.
To caculate the amount of cubic feet(Volume), the tent can hold, we use the formula below.
Formula:
V = bhL/2..................... Equation 1Where:
V = Volume of the tenthb = Base of the triangleh = Height of the triangleL = Height of the tentFrom the question,
Given:
b = 5 fth = 6 ftL = 11 ftSubstitute these values into equation 1
V = 5×6×11/2V = 165 ft³Hence, the right option is (A) 165 ft³.
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Kevin got the following scores on his math tests this semester.
85, 94, 98, 88, 85, 92, 97, 81
What is his mean score so far?
ANSWERED
What score will Kevin need to get on his next test to raise his mean score to exactly 91?
Kevin will need to get a score of 109 on his next test to raise his mean score to exactly 91.
To find out what score Kevin will need to get on his next test to raise his mean score to exactly 91, we can use the formula for the mean:
mean = (sum of all scores) / (number of scores)
We know the current mean score is:
mean = (85 + 94 + 98 + 88 + 85 + 92 + 97 + 81) / 8
= 89.5
To raise the mean to 91, we can set up the equation:
(85 + 94 + 98 + 88 + 85 + 92 + 97 + 81 + x) / 9 = 91
where x is the score Kevin needs to get on his next test.
Multiplying both sides of the equation by 9, we get:
85 + 94 + 98 + 88 + 85 + 92 + 97 + 81 + x = 819
Simplifying, we get:
710 + x = 819
Subtracting 710 from both sides, we get:
x = 109
Therefore, Kevin will need to get a score of 109 on his next test to raise his mean score to exactly 91.
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(4,2)
I
5
(x, y)
Given that the circle to the left has a center at
point (4,2), and point (x, y) is on the
circle,write the equation for the distance (x, y)
is away from the center. Rearrange this
equation so it contains no radicals.
The equation for the distance of the point (x, y), from the center of the circle is; (x - 4)² + (x - 2)² = 5²
What is the general form of the equation of a circle?The general form of the equation of a circle with center (h, k) is; (x - h)² + (y - k)² = a², where the radius of the circle is; a
The radius of a circle is the distance from the center to a point (x, y) on the circumference, therefore, the equation for the distance of the point (x, y) from the center of the circle, is equivalent to the equation for a circle, where the distance of the point (x, y) from the center is the radius.
The coordinates of the center of the circle, (h, k) = (4, 2)
The radius of the circle, r = a = 5
The equation for the distance (x, y) from the center, which radius of the circle, with center (4, 2), is therefore;
Equation of a circle; (x - h)² + (y - k)² = a²
Equation from the center; (x - 4)² + (y - 2)² = 5²
Where;
5 = The radius, a = The distance from the center of the circle
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What are the measure of angels 1 to 8
Let's just compare the angles to start - - - these are two parallel lines cut by another line (transversal), so there are a lot of equal angles.
Angles 1 and 5 are the same
Angles 2 and the 65 degree angles are the same.
Angles 4 and 8 are the same.
And 3 and 7 are the same.
There are even more similar angles:
1 and 3 are the same. 2 and 4 are the same.
5 and 7 are the same, and 8 and the 65 degree angle are the same.
So without any math, Angles 2, 4 and 8 are all 65 degrees.
So Angle 65 + Angle 5 = 180. Therefore Angle 5 = 115.
Therefore angle 7 is 115. (You could also say that 65+ Angle 7 = 180.)
Since angle 7 is 115, so is angle 3 and angle 1.
So in conclusion
Angle 1: 115
Angle 2: 65
Angle 3: 115
Angle 4: 65
Angle 5: 115
Angle 7: 115
Angle 8: 65
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of x will be 16.
Given ,
Parallelogram with two sides:
side 1 = 3x + 20
side 2 = 5x - 12
In parallelogram the opposite side are equal and parallel.
Thus,
side 1 and side 2 will be equal and parallel.
Equating both sides to get the value of x,
3x + 20 = 5x - 12
x = 16
Hence the value of x can be found out by property of parallelogram.
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x^2 -5x + 29 = 8x -6
Answer:
Step-by-step explanation:
x²-5x+29=8x-6
x²-13x+35=0
[tex]x=\frac{13 \pm\sqrt{(-13)^2-4(1)(35)} }{2(1)} \\x=\frac{13 \pm\sqrt{169-140} }{2} \\x=\frac{13 \pm\sqrt{29} }{2}[/tex]
This week laptops are 25% off the original price. If the original price of a laptop was $300, what is the new sale price?
Answer:
$255
Step-by-step explanation:
25% in decimal form is 0.25
300 x 0.25 = 75
25% off means 300 - 75 = 255
answer is $255
Danielle Stevenson receives a commission of 6.5% for selling a $160,000 house. One-half of the commission goes to the broker, and one-half of the remainder to another salesperson. Stevenson receives the rest. Find the amount she receives.
Answer:
Danielle Stevenson receives $2,600 from selling the $160,000 house.
Step-by-step explanation:
To find the amount Danielle Stevenson receives from selling the house, we'll follow these steps:
Calculate the commission earned by Danielle Stevenson: Commission = 6.5% * $160,000.
Commission = 0.065 * $160,000 = $10,400.
Determine the broker's share: Broker Share = 0.5 * Commission.
Broker Share = 0.5 * $10,400 = $5,200.
Calculate the remaining amount after the broker's share: Remaining Amount = Commission - Broker Share.
Remaining Amount = $10,400 - $5,200 = $5,200.
Determine the salesperson's share: Salesperson Share = 0.5 * Remaining Amount.
Salesperson Share = 0.5 * $5,200 = $2,600.
Finally, calculate the amount Danielle Stevenson receives, which is the remaining portion after the broker and salesperson's shares: Amount Danielle Receives = Remaining Amount - Salesperson Share.
Amount Danielle Receives = $5,200 - $2,600 = $2,600.
Therefore, Danielle Stevenson receives $2,600 from selling the $160,000 house.
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The arc length of a 330° sector is 33π. Find the area of the sector
The area of the sector is 297π units squared.
How to find the area of a sector?The arc length of a 330° sector is 33π. Therefore, let's find the area of the sector.
Let's find the radius of the circle.
length of arc = ∅/ 360 × 2πr
where
∅= central angler = radiusTherefore,
33π = 330 / 360 × 2π × r
cross multiply
660πr = 11880π
divide both sides by 660π
r = 11880π / 660π
r = 18 units
Therefore,
area of the sector = 330 / 360 × π × 18²
area of the sector = 106920 / 360 π
area of the sector = 297π units²
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A rectangular prism.
What are the shapes of the cross sections formed by a plane slicing the rectangular pyramid?
A plane intersects the pyramid parallel to its base. The cross section is a
._____
A plane intersects the pyramid perpendicular to its base and through the top vertex. The cross section is a
_________
A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. A plane intersects the pyramid parallel to its base. The cross section is a rectangle A plane intersects the pyramid perpendicular to its base and through the top vertex. The cross section is a triangle
A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. Let's explore the two scenarios you mentioned:
Plane parallel to the base: When a plane intersects the rectangular prism parallel to its base, the resulting cross section is also a rectangle. The shape of the cross section will have the same dimensions as the base of the rectangular prism.
Plane perpendicular to the base and through the top vertex: In this case, the cross section will be a triangle. The shape of the cross section will be determined by the intersection of the plane with the three sides of the rectangular prism. The base of the triangle will be formed by the side of the rectangular prism, while the other two sides will be formed by the edges connecting the top vertex of the pyramid to the corresponding vertices of the base.
It's important to note that a rectangular prism is different from a pyramid. A rectangular prism has six rectangular faces, while a pyramid has a polygonal base (in this case, a rectangle) and triangular faces converging to a single point called the apex or top vertex.
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When Mrs Munyai wanted to swim in her new pool, the temperature of the wate 19 °C and she said she would only swim if the temperature of the water was 25 °C temperature must increase by 6 °C. Calculate what the temperature change would be in °F. You may use the following formula: (°F-32) ÷ 1,8 = °C +
The temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.
The formula to convert the temperature from Celcius to Fahrenheit is:
[tex]\textdegree F = (\textdegree C * 1.8) + 32[/tex]
We need to calculate the temperature change of [tex]6 \textdegree C[/tex] in Fahrenheit:
[tex]\Delta \textdegree C = 6\\\Delta \textdegree F = \Delta \textdegree C * 1.8 = 10.8[/tex]
The temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.
We can calculate the Fahrenheit temperature of the water and the desired temperature in Fahrenheit:
[tex]^{\circ}C = 19\\^{\circ}F = (19 * 1.8) + 32 = 66.2[/tex]
[tex]^{\circ}C = 25\\^{\circ}F = (25 * 1.8) + 32 = 77[/tex]
The current temperature of the pool is [tex]66.2 ^{\circ} F[/tex] and the desired temperature is [tex]77 ^{\circ} F[/tex].
Therefore the temperature needs to be increased by:
[tex]\Delta ^{\circ}F = 77 - 66.2 = 10.8 ^{\circ}F[/tex]
which is the same temperature change we calculated earlier in Fahrenheit.
Therefore, the temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.
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The vertices of △JKL are J(−3, −2), K(1, 4), and L(4, 2). Find the vertices of the image of △JKL under the dilation centered at the origin with scale factor 5.
J′ = (
,
)
K′ = (
,
)
L′ = (
,
)
The vertices of the image triangle △JKL under the dilation centered at the origin with a scale factor of 5 are:
J′ = (−15, −10)
K′ = (5, 20)
L′ = (20, 10)
To find the vertices of the image of triangle △JKL under the dilation centered at the origin with a scale factor of 5, we need to multiply the coordinates of each vertex by the scale factor.
Let's apply the dilation to each vertex:
J(−3, −2) → J′ [tex]= (5 \times -3, 5 \times -2)[/tex] = (−15, −10)
K(1, 4) → K′ [tex]= (5 \times 1, 5 \times 4)[/tex] = (5, 20)
L(4, 2) → L′ [tex]= (5 \times 4, 5 \times 2)[/tex] = (20, 10)
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SECTION B - Skills Analysis Question 8 Use the diagram to determine the sum of the series 1 + 3 + 5 + 7 + ... + (2n-1) in terms of n. Show your reasoning and explanation fully. n : [4]
Answer:
weel you have to start by addition of tose numbers and after you're done with the addition if the numbers you do 2n-1 which is equal to n so you use this formula to solve it hope this helps
What the surface area
Step-by-step explanation:
the surface area is the sum of all areas of the individual outside faces/sides.
so, what do we see here, what outside sides do we have here ?
of course, we have to assume that this is a regular object (left and right sides are the same).
2 right-angled triangles (left and right).
1 rectangle in the back.
1 rectangle at the bottom.
1 times rectangle in the front.
the area of a right-angled triangle is
leg1 × leg2 / 2
in our case that is
6 × 2.5 /2 = 3 × 2.5 = 7.5 mm²
we have 2 of these triangles :
2×7.5 = 15 mm²
the area of the rectangle in the back is
8 × 6 = 48 mm²
the area of the rectangle at the bottom is
8 × 2.5 = 20 mm²
the area of the rectangle in the front is
8 × 6.5 = 52 mm²
the surface of the object is the sum of all that :
15 + 48 + 20 + 52 = 135 mm²