Answer:
The dimensions of the new rectangle will be 10 cm by 12 cm.The new perimeter will be 4 times the original perimeter.The new area will be 16 times the original area.The new perimeter will be 44 cm.Step-by-step explanation:
Given dimensions of original rectangle , length(l)=3 cm and width(w)=2.5 cm
We know that after dilation with scale factor (k), the dimension of new figure = k times the original dimensions.
Thus width of new rectangle=[tex]4\times2.5=10\ cm[/tex]
length of new rectangle=[tex]4\times3=12\ cm[/tex]
∴The dimensions of the new rectangle will be 10 cm by 12 cm.
Now, Perimeter of original rectangle=[tex]2(l+w)=2(3+2.5)=2(5.5)=11\ cm[/tex]
Thus, Perimeter of new rectangle=[tex]2(4l+4w)=2(12+10)=2(22)=44\ cm[/tex]
⇒ Perimeter of new rectangle=44 cm=[tex]4\times11\ cm[/tex]
∴The new perimeter will be 4 times the original perimeter.
Now, Area of original rectangle=[tex]lw=3\times2.5=7.5\ cm^2[/tex]
Thus, Area of new rectangle=[tex]4l\times4w=12\times10=120\ cm^2[/tex]
Area of new rectangle=[tex]16lw=16(lw)[/tex]
⇒The new area will be 16 times the original area.
19. if a vechicle was purchased for $32345. there's a 6% sales tax on automobile sales, how much tax will be added to the price of the car
If a 12-student class averaged 90 on a test, and a 20-student class averaged 80 on the test, then all 32 students averaged
2. Give an example of how you use positive and negative numbers in the real world. Be sure to explain the meaning of 0 in your example.
A wall in Marcus's bedroom is 8 2/5 feet high and 16 2/3 feet long. If he paints 1/2 of the wall blue, how many square feet will be blue?
Marcus's wall has an area of 140 square feet. If he paints half of it blue, 70 square feet will be blue.
To find the area of the wall, we multiply its height by its length:
[tex]\[ \text{Area of the wall} = \text{Height} \times \text{Length} \][/tex]
First, convert the mixed numbers to improper fractions:
- Height: [tex]\(8 \frac{2}{5} = \frac{42}{5}\) feet[/tex]
- Length: [tex]\(16 \frac{2}{3} = \frac{50}{3}\) feet[/tex]
Now, multiply:
[tex]\[ \text{Area} = \left( \frac{42}{5} \right) \times \left( \frac{50}{3} \right) \][/tex]
[tex]\[ \text{Area} = \frac{42 \times 50}{5 \times 3} = \frac{2100}{15} = 140 \text{ square feet} \][/tex]
If Marcus paints half of the wall blue, the area painted blue is:
[tex]\[ \text{Blue area} = \frac{1}{2} \times 140 = 70 \text{ square feet} \][/tex]
Therefore, 70 square feet of the wall will be blue.
Consider the equation 22+3x/3x+7=2 How do you begin isolating the variable x to one side of the equation?
You have 22+3x/3x+7=2. That 3x/3x raises eyebrows; is this what you meant, with the result that 3x/3x = 1? or did you mean
3x
22 + ------------- + 7 = 2?
3x+7
If you meant the latter, then simplify the equation by subtracting 2 from both sides:
3x
27 + ---------- = 0
3x+7
Multiply all three terms by (3x+7), obtaining
27(3x+7) + 3x = 0
Then 21x + 3x + 189 = 0, so that 24x = -189, or x = -189/24 = -7 7/8
Help me (once again!)
The base of a rectangular pyramid has sides 3 feet long and 7 feet long. The pyramid is 4 feet tall. A second, larger pyramid has dimensions that are 3 times the dimensions of the smaller pyramid. What is the difference between the volumes of the two pyramids?
Answer:
The difference between the volumes is 728 ft³.
Step-by-step explanation:
Our first step will be to find the volume of the smaller pyramid. Notice that we have all the necessary dimensions. The formula for the volume of a pyramid is
[tex]V = \frac{A_bh}{3},[/tex]
where [tex]h[/tex] stands for the height and [tex]A_b[/tex] for the area of the basis. In this case [tex]h=4 ft[/tex], and the area of the basis, which is a rectangle, is [tex]A_b = 3 ft * 7 ft = 21 ft².[/tex] Then,
[tex]V = \frac{(21 ft²)(4 ft)}{3} = 28 ft³.[/tex]
Now, two calculate the volume of the second pyramid, recall that it has dimensions three times larger. This means, [tex]h=3*4 ft=12 ft[/tex] and [tex]A_b = (3*3 ft) *(3* 7 ft) = 9*21 ft² = 189 ft².[/tex] Then,
[tex]V = \frac{(189 ft²)(12 ft)}{3} = 756 ft³.[/tex]
Finally, we only need to substract the values of the volumes:
756 ft³-28 ft³= 728 ft³.
ABC is a right triangle in which B is a right angle, AB= 1, AC=2 and BC= square root of 3. Cos C x sin A=
Applying the cosine and sine ratios, the value of cos C × sin A = 3/4.
What is the Cosine and Sine Ratios?Cosine ratio: cos ∅ = adj/hyp
Sine ratio: sin ∅ = opp/hyp.
Find cos C using the cosine ratio:
cos C = √3/2
Find sin A using the sine ratio:
sin A = √3/2
cos C × sin A = √3/2 × √3/2
= 3/4
cos C × sin A = 3/4
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What is the range of function y=√(-2cos^2x+3cosx-1)
the height of a ball thrown directly up with a velocity of 40 feet per second from a initial height of 5 ft is given by the equation h(t)=-16t2+40t+5, where t is the time in seconds and h is the balls height, measured in feat. when will the ball hit the ground?
which of the following best explains why cos 2pi/3 is not equal to cos 5pi/3
A.The angles do not have the same reference angle.
B.Cosine is negative in the second quadrant and positive in the fourth quadrant.
C.Cosine is positive in the second quadrant and negative in the fourth quadrant.
D.The angles do not have the same reference angle or the same sign.
In this exercise we have to use the knowledge of cosine quadrants, like this:
Letter B
We have that the quadrant of the cosine is given by:
The two quadrants on the right are positive.The two quadrants on the left are negative.So we know that:
[tex]cos (2\pi/3)[/tex] If it's in quadrant three, that's negative.
[tex]cos(5\pi/3)[/tex] If you're in quadrant four, that's positive.
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The correct answer is option B. Cosine is negative in the second quadrant and positive in the fourth quadrant.
To determine why [tex]cos(\frac{2\pi }{3})[/tex] is not equal to [tex]cos(\frac{5\pi }{3})[/tex], we can analyze the properties of cosine in different quadrants.
Reference Angles: The reference angle for both [tex]\frac{2\pi }{3}[/tex] and [tex]\frac{5\pi }{3}[/tex] is [tex]\frac{\pi }{3}[/tex].Quadrants: [tex]\frac{2\pi }{3}[/tex] is in the second quadrant, while [tex]\frac{5\pi }{3}[/tex] is in the fourth quadrant.Sign of Cosine: In the second quadrant, cosine is negative. In the fourth quadrant, cosine is positive.Thus, because cosine is negative in the second quadrant and positive in the fourth quadrant, [tex]cos(\frac{2\pi }{3})[/tex] is not equal to [tex]cos(\frac{5\pi }{3})[/tex]. Therefore, the best explanation is: Cosine is negative in the second quadrant and positive in the fourth quadrant.
5/9 ÷ 5/7 plz a short answer doing it now o i hate math plz help so bad at it
5/9 / 5/7 =
5/9 * 7/5 = 35/45 reduce to 7/9
Reflection across the x-asis?
A recipe for buttermilk biscuits calls for 3 and 1/3 cups of flour. How many cups of flour do you need for 1/2 the recipe.
Convert 0.79 tons to pounds?
Suppose you are driving to visit a friend in another state. You are driving at an average rate of 50 miles per hour. You must drive a total of 345 miles. If you have already driven 145 miles, how much longer will it take you to reach your destination?
1. 7.2 aliens =1 monster. 1 monster= 15.5 oranges. Using the conversion above, about how many oranges are equal to 1 alien?
2. In a scaled drawing, 1 millimeter represents 150 meters. How many square millimeters on the drawing represents 1 square meters?
3. While driving with his father, Amit holds his breath whenever they pass through a particular tunnel. Amit counts the number of seconds he holds his breath, from the beginning of the tunnel to the end of the tunnel, and finds that he holds his breath, on average for about 8 seconds. If his father drives the car at 60 mph through the tunnel, according to the average time, Amit holds his breath, about how long is the tunnel.
4. Lea's car travels on average of 30 miles per gallon of gas. If she spent $20.70 on gas for a 172.5 mile trip, what was the approximate cost of gas in dollars per gallon?
Which is an equation for the line that passes through (0, 2) and (-2, 0)?
f. y = -x
g.y = x - 2
h.y = x + 2
j.y = -x - 2
write a real-world problem in which you would need to find the number of units between -6 and 0 on a number line.
The precise measurement of distance between Junction A at -6 and Junction B at 0 is indispensable in urban planning, optimizing traffic flow, and ultimately enhancing the quality of life for city residents.
One real-world problem where finding the number of units between -6 and 0 on a number line is crucial is in urban planning and transportation engineering.
Imagine a city with two major traffic junctions, Junction A at position -6 and Junction B at position 0 on the number line. City officials need to optimize traffic flow between these junctions to reduce congestion and commute times.
To achieve this, engineers must calculate the exact distance between these junctions. This information is vital for designing efficient road networks, determining signal timings, and planning for public transportation routes. It also helps in estimating travel times for commuters and enables the implementation of traffic management strategies.
Accurate measurements between -6 and 0 on the number line ensure that resources are allocated efficiently, minimizing environmental impact, fuel consumption, and overall transportation costs.
This problem highlights how fundamental mathematical concepts like distance on a number line play a critical role in shaping the urban landscape and improving quality of life for city residents.
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Which expression is the result of the perimeter of rectangle b minus the perimeter of rectangle a
IS THE SQUARE ROUTE OF 7 OR 14/5 BIGGER
If a Rubik’s Cube has a volume of 384 cubic centimeters, how long is one side of the cube?
Determine the equation of the line through (-1,2) and perpendicular to the line 2x-3y+5=0
What is an equation that equals 58 explain!
Some equations that equal 58 include: 58x, 29 + 29, and y + 58x.
For example, 58x is equal to 58 because you can change x to 1, and 58 times 1 is 58. Therefore, it is equal to 58.
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Jose made 33 of the 88 baskets for basketball team.What percent did he no make?
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 1.5" by 2.25" on the drawing, how large is the bedroom?
The scale of the architectural drawing is such that 1/4" represents 1'. This means, if the room measures 1.5" by 2.25" on the drawing, it measures 6 feet by 9 feet in real life.
Explanation:In this scenario, the unit scale indicates that 1/4" on the drawing represents 1' in real life. So, to find the real-life dimensions of the room, you would need to convert the drawing dimensions to real-life dimensions.
For the length, 1.5" on the drawing would equate to 1.5 * 4 feet because every 1/4" equals 1 foot. Therefore, the length of the room is 6 feet.
The width of the room is similarly calculated. 2.25" on the drawing would equate to 2.25 * 4 feet which gives us a width of 9 feet.
So, the bedroom in real life is 6 feet by 9 feet.
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The bedroom is 6 feet by 9 feet in real life.
Explanation:To determine the actual size of the bedroom, we can use the scale given in the architectural drawing. The scale 1/4" = 1' means that every 1/4 inch on the drawing represents 1 foot in real life. In this case, the bedroom measures 1.5 inches by 2.25 inches on the drawing. To find the actual size, we can multiply these dimensions by the scale factor: 1.5 inches * (1 foot / 1/4 inch) = 6 feet, and 2.25 inches * (1 foot / 1/4 inch) = 9 feet. Therefore, the bedroom is 6 feet by 9 feet in real life.
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A barrel shaped like a cylinder is laid on its side and rolled up a ramp that is 92m long. The barrel has a circular base that turns 46 times in being rolled up the ramp. What is the diameter of the circular base?
Use pascal's triangle to find (8 4)
I don't get how to do this can some one help me please!!
Three less than the sum of four times a number and six is eight. Find the number.
HELP
Cynthia is finding the measures of the labeled angles in this image.
What is the least number of angle measures she needs to know to find the measures of all labeled angles in the image?
A.She only needs to know the measure of one angle, angle D.
B.She only needs to know the measure of one angle, angle A.
C.She only needs to know the measures of two angles, angles A and B.
D.She only needs to know the measures of two angles, but one of the angles must be one of the remote interior angles.