A student needs to make a square cardboard piece. The cardboard should have a perimeter equal to at least 92 inches. The function f(s) relates the perimeter of a cardboard piece, in inches, to the length of its side in inches. Which of the following shows a reasonable domain for f(s)?
a 23 < s < 46
b 23 < s < 92
c s ≥ 92
d s ≥ 23
Answer: d. s ≥ 23
Step-by-step explanation:
Let s be the side of the square.
We know that the perimeter of a square =4s
Let f(s)=4s
If the cardboard should have a perimeter equal to at least 92 inches, the inequality would look like
[tex]4s\geq 92[/tex]
Divide both sides by 4, we get
[tex]s\geq\frac{92}{4}\\\Rightarrow\ s\geq23[/tex]
Thus, d. is the right answer. The reasonable domain of f(s) is [tex]s\geq23[/tex]
the product of 7 and a nimber increased by 3 is equal to twice the number subtracted from 39
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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Write the linear equation 5x-15y=-8 in slope-intercept form?
What is the range of function y=√(-2cos^2x+3cosx-1)
Which of the following side lengths can form a triangle?
16 cm, 21 cm, and 47 cm
1 in, 2 in, and 3 in
34 mm, 75 mm, and 100 mm
8 ft, 24 ft, and 33 ft
Convert 0.79 tons to pounds?
write a story problem that can be solved using the equation: 18.50÷0.5=x
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
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
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.
NEED HELP FAST!!!!!
4.
How many solutions does the equation 5p – 4p – 8 = –2 + 3 have? (5 points)
One
Two
None
Infinitely many
the smaller of two numbers is 7/8 of the larger. Their sum is 30. Find the two numbers
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?
A mule deer can run one over four of a mile in 25 seconds. At this rate, which expression can be used to determine how fast a mule deer runs in miles per hour? A. twenty-five seconds over one-fourth mile = 36 miles per hour B. one-fourth mile over twenty-five seconds = 36 miles per hour C. one-fourth mile over twenty-five seconds = 100 miles per hour D. twenty-five seconds over one-fourth mile = 100 miles per hour
Answer:
At this rate, which expression can be used to determine how fast a mule deer runs in miles per hour. A 25 seconds/ 1/4 mile = 36 miles per hour
Answer:
B) one-fourth mile over twenty-five seconds = 36 miles per hour
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.
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.
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 rectangular prism is completely packed with 84 cubes of edge length 1 over 3 inch without any gap or overlap
The question involves finding the dimensions of a rectangular prism packed with 84 smaller cubes of a certain size. The answer requires understanding of volume and consideration of the physical characteristics of a rectangular prism.
Explanation:The problem presents a rectangular prism completely packed with 84 cubes of edge length 1 over 3 inch. To find the dimensions of the prism, we must first understand the volume. Given the volumes of the small cubes (edge length cubed), we can multiply this by the number of cubes (84) to find the total volume of the prism.
Next, we use this total volume to derive the possible dimensions of the rectangular prism. The dimensions should be factors of the total volume, keeping in mind the shape of a physical rectangular prism (which usually has length longer than width and height).
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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 table represents the same linear relationship as the equation y = 3x +5?
Help me (once again!)
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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Ariana has 2/3 quart of milk. She uses 3/4 of it in a cookie recipe. How much milk did Ariana use In her recipe?
Three less than the sum of four times a number and six is eight. Find the number.
Determine the equation of the line through (-1,2) and perpendicular to the line 2x-3y+5=0
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?
Use pascal's triangle to find (8 4)
I don't get how to do this can some one help me please!!
round 345276 to the nearest thousand