The best estimate of the lateral area of a cube with 2.1-inch edges is 17.64 square inches, calculated by squaring the edge length to find the area of one side (4.41 square inches) and then multiplying by four since there are four lateral faces.
The question asks for the best estimate of the lateral area of a cube with edges that are 2.1 inches long.
To calculate the lateral area of a cube, we need the formula for the lateral area, which is the sum of the areas of all the sides excluding the top and bottom faces. Since a cube has six faces, we have four lateral faces to consider.
The area of one face of a cube is obtained by squaring the length of one edge. In this case:
Area of one side = edge length × edge length = 2.1 inches × 2.1 inches = 4.41 square inches
Since there are four sides whose areas we need to count for the lateral area, we multiply the area of one side by four:
Lateral area = 4 × Area of one side = 4 × 4.41 square inches = 17.64 square inches
Therefore, the best estimate of the lateral area of the cube is 17.64 square inches.
Final answer:
The best estimate of the lateral area of a cube with 2.1-inch edges is approximately 17.64 square inches, calculated by squaring the edge length and multiplying by four since a cube has four lateral faces.
Explanation:
The goal is to estimate the lateral area of a cube with edges that are 2.1 inches long. The lateral area of a cube is the sum of the areas of all the sides of the cube, excluding the top and bottom faces. Since the cube has six faces and we only need the sides, we calculate for four faces.
Each face of a cube is a square, so to find the area of one face, we square the length of the edge:
Area of one side = Edge length × Edge length
Area of one side = 2.1 inches × 2.1 inches
Area of one side = 4.41 square inches
Since there are four sides whose area we are considering for the lateral area:
Lateral area = 4 × Area of one side
Lateral area = 4 × 4.41 square inches
Lateral area = 17.64 square inches
So, the best estimate of the lateral area of the cube is approximately 17.64 square inches.
For which value of x would this model make the least sense
to use? A.-2.75 B.0.25 C.1.75 D.2.25
Answer: A
Explanation: x is your independent variable and is time, so it is unlikely to have negative amounts of time.
The time will be 2.25 seconds. Then the correct option is D.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The function is given below.
h(x) = – 16x² + 100
Where x is the time in seconds and h(x) is the height at x.
Let the height is y feet.
Then the value of y will be
y = 84 – 65
y = 19 feet
Then the time will be
19 = – 16x² + 100
16x² = 100 – 19
16x² = 81
4x = 9
x = 2.25 seconds
Then the correct option is D.
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Plz help meeeee plzzzz
Answer:
-4p³+3p²-17p
Step-by-step explanation:
(-3p³+5p²-2p)+(-p³-8p²-15p)
-3p³+5p²-2p-p³-8p²-15p
-3p³-p³+5p²-8p²-2p-15p
=-4p³+3p²-17p
can someone please help i need to write the equation of the green line
f(x) = ax + b
(0, -4):
f(0) = a•0 + b
f(0) = b ⇒ b = -4
(12, 0):
0 = a•12 + b
0 = 12a - 4
4 = 12a
[tex]a=\frac4{12}=\frac13[/tex]
The equation of the green line:
[tex]\underline{\,y=\frac13x-4\,}[/tex]
or: [tex]y=\frac13x-4[/tex]
[tex]-\frac13x+y+4=0\\\\\underline{x-3y-12=0}[/tex]
Plz help me love you
Answers)
27=6
30=82
33=24
Question: Solve it using the proportion method.
risha wants to buy a computer for $775. She already has $275 saved and earns $100 a week babysitting. a. Use w to represent weeks and write an inequality that could be used to determine how many weeks she would have to work to afford the computer. b. How many weeks does she have to work?
Answer
Inequality=100x+275≥775 Answer=5 or more
Step-by-step explanation:
The circumference of a circle is 24π ft. What is the area, in square feet? Express your answer in terms of
π
π.
Answer:
[tex]144\pi[/tex]
Step-by-step explanation:
Circumference = [tex]\pi d[/tex]
Diameter = [tex]2r[/tex]
Area of a circle = [tex]\pi r^2[/tex]
From our first equation, we can find our value for our diameter:
We do this by dividing [tex]24 \pi[/tex] by [tex]\pi[/tex] to get 24.
[tex]c=\pi d[/tex]
[tex]d=\frac{c}{\pi } = \frac{24\pi }{\pi } =24[/tex]
Using our second equation, we can find out the value for our radius:
[tex]d=2r[/tex]
[tex]r=\frac{d}{2} =\frac{24}{2} =12[/tex]
Now we have a value for our radius, we can use our third equation to find out our area:
[tex]A=\pi 12 ^2 = 144 \pi[/tex]
Given that:
The circumference of a circle is 24π ft.To Find:
What is the area, in square feet?We know that:
Circumference of a circle = 2πRArea of a circle = πR²Where,
Radius is denoted as R.Finding the radius of the circle:
Circumference of a circle = 24π
⟶ 2πR = 24π
⟶ 2πR = 2π × 12
Cancelling 2π.
⟶ R = 12
∴ Radius of the circle = 12 ft.
Finding the area of the circle:
⟶ Area = πR²
⟶ Area = π(12)²
⟶ Area = π × 12 × 12
⟶ Area = π × 144
⟶ Area = 144π
Hence,
Area of the circle is 144π square feet.
An equation for the depreciation of a car is given by y = A(1-r)^twhere y = current value of the car, A = original cost, r = rate of
depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately
how old is the car?
Answer: The car is 6.6 years old.
Step-by-step explanation:
Hi, to answer this question we have to replace the values in the equation given:
Y = 1/2 (half the value)
A = 1 (total value)
r =10% = 0.10 (decimal form)
Replacing:
y = A(1-r)^t
1/2 = 1 (1-0.10)^t
Solving for t:
(1/2)/1 = 0.9^t
1/2 = 0.9^t
log 1/2 = log 0.9^t
log 1/2 = (t) log 0.9
(log 1/2)/ log 0.9 = t
6.57 =t
6.6 years (rounded)
Cameron sent a chain letter to his friends, asking them to forward the letter to more friends.
The relationship between the elapsed time t, in days, since Cameron sent the letter, and the number of people, P(t), who receive the email is modeled by the following function:
P(t) = 100 · (1.83) ^ t/2.5
Complete the following sentence about the rate of change in the number of people who receive the email.
Every _______ days, the number of people who receive the email increases by 83%.
A.) 0
B.) 1.83
C.) 100
D.) 2.5
Answer:
Step-by-step explanation:
Answer:
2.5
Step-by-step explanation:
Which function has a domain of all real numbers
Functions with all real numbers as their domain include polynomial functions, sine and cosine functions, and exponential functions. For example, the function f(x)=x², f(x) = sin(x), or f(x) = cos(x) and f(x)=a^x (where a>0).
Explanation:In Mathematics, the domain of a function is the set of values that can be plugged into the function. There are multiple functions that have a domain of all real numbers, some of them are polynomial functions, sine and cosine functions, and exponential functions.
For example, the function f(x)=x² is a polynomial function where any real number can be inputted for x, hence its domain is set of all real numbers.
Similarly, sine and cosine functions, represented as f(x) = sin(x) or f(x) = cos(x), have a domain of all real numbers, because sine and cosine are periodic and their values repeat over every interval of 2π.
Furthermore, the exponential functions, represented in the form f(x)=a^x (where a>0), have also their domains as the set of all real numbers.
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pls pls pls pls help ;(
Answer the problem below. Show all your work/thinking.
1. Find the surface area of the following figure, then explain the steps of your solution in
paragraph form.
Answer:
Around 202.08
Step-by-step explanation:
The formula for the surface area of a pyramid is [tex]a^2 +2a\sqrt{\frac{a^2}{4}+h^2}=9^2+2\cdot 9\sqrt{\frac{9\cdot 9}{4}+5^2}=81+18\sqrt{45.25}\approx 202.08[/tex]. Hope this helps!
Ice cream sandwiches are wrapped in white paper before they are put in
a box to be sold. How many ice cream sandwiches can be wrapped with
500 square inches of paper?
A picture frame measures 9 inches high and 5.4 Inches wide. It will be proportionately enlarged so the height will be 15 inches. How wide will the frame be?
Answer:
Width: 9 inches
Step-by-step explanation:
1. We can see that the height increased by 6 inches, provided a difference of 15 and 9. If the question states that the frame's dimensions were proportionately enlarged, perhaps the height's enlargment could be benificial
2. If we were to take a ratio where the increased height is over the previous height (height enlargment/prior height) that would be 6/9, or in other words, can be simplified to be 2/3
3. We can see that if the width were to be enlarged, we might be able to determine how much it should be enlarged through a proportionality, provided the frame's dimensions are proportionately enlarged. Now if x ⇒ the width enlargment: 2 / 3 = x / 5.4
4. Through cross multiplication, let us solve for x:
2 * 5.4 = 3 * x,
10.8 = 3 * x,
x = 3.6 inches by which the width should be enlarged
5. If we are to determine the new width of the frame after enlargment, add 5.4 to 3.6 ⇒ the width of the frame ⇒ 9 inches
The number of students enrolled at a college is 14,000 and grows 5% each year.
Answer:
14000/100*105 = 14,700
Step-by-step explanation:
In an assembly line, 56 out of 60 randomly selected parts have no faults. Predict the number of parts that will have no faults in a similar batch of 12,000 parts.
We have been given that in an assembly line, 56 out of 60 randomly selected parts have no faults. We are asked to predict the number of parts that will have no faults in a similar batch of 12,000 parts.
We will use proportions to solve our given problem.
[tex]\frac{\text{Not faulty parts}}{\text{Total parts}}=\frac{56}{60}[/tex]
[tex]\frac{\text{Not faulty parts}}{12,000}=\frac{56}{60}[/tex]
[tex]\frac{\text{Not faulty parts}}{12,000}\times 12,000=\frac{56}{60}\times 12,000[/tex]
[tex]\text{Not faulty parts}=56\times 200[/tex]
[tex]\text{Not faulty parts}=11,200[/tex]
Therefore, approximately [tex]11,200[/tex] parts will have no faults in a similar batch of 12,000 parts.
The measure of XYZ is 45. The length of radius YZ is 6 inches. What is the area of sector XYZ?
(Use 3.14 for I.)
Answer:
area of a sector = 14.13 yards²
Step-by-step explanation:
XYZ is a sector of a circle. The radius YZ is 6 inches .The angle of the sector is given as 45°. The area of the sector can be solved as follows.
area of a sector = ∅/360 × πr²
where
r = radius
∅ = center angle
r = 6 inches
∅ = 45°
area of a sector = 45/360 × 3.14 × 6²
area of a sector = 45/360 × 3.14 × 36
area of a sector = 45/360 × 113.04
area of sector = 1/8 × 113.04
area of a sector = 14.13 yards²
Answer:
14.13
Step-by-step explanation:
i know
2/3+q=1/2 what is Q
Q=rational number=1/6
2/3+q=1/2=1/6
which set of side lengths form a right triangle?
A. 8 cm, 17 cm, 14 cm
B. 50 in., 48 in., 14 in.
C. 53 m, 48 m, 24 m
D. 3 ft, 6 ft, 5 ft
Answer:
I think the answer is B.
Answer:
b.) [tex]50,48,14[/tex]
Step-by-step explanation:
To find if a set of lengths makes a right triangle, use the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
If a and b squared equal c squared, then the set makes a right triangle. C (the hypotenuse) is the largest number of the set because the hypotenuse is always the largest side in a right triangle.
Use the options:
a.) insert values:
[tex]8^2+14^2=17^2\\64+196=289\\260\neq 289[/tex]
260 does not equal 289, so a is wrong.
b.) insert values:
[tex]14^2+48^2=50^2\\196+2304=2500\\2500=2500[/tex]
2,500 equals 2,500, so b is correct.
Finito.
I WILL GIVE BRAINLIEST
Solve the inequality:
10x - 3 ≥ 2
A. x ≤ 1/2
B. x ≤ 2
C. x ≥ 1/2
D. x ≥ 2
10x−3+3≥2+3
10x≥5
(10x10)/2≥(5/10)
x≥1/2
Need this answer in fraction form these are the answer choices
A.8/15
B.15/16
C.16/15
D.15/8
Answer:
Option B 15/16
Step-by-step explanation:
calculate the volume of the cone and the volume of the cylinder and then put them in a fraction with the cone over the cylinder, afterwards put that fraction in a calculator and see what you get. once you get the answer input each one of the options into the calculator until one of the fractions gives you the same product as the cone/cylinder fraction.
please mark brainliest :)
The diameter of a golf ball is about 4 centimeters. Which of these is the closest to the volume of a golf ball?
16.75 cm^3
33.51 cm^3
100.53 cm^3
268.08cm^3
The volume is approximately 33.51 [tex]cm^3[/tex], option B.
The question asks us to determine the closest volume to a golf ball with a diameter of approximately 4 centimeters. To find the volume of a sphere (which is the shape of a golf ball), we use the formula:
V = (4/3)π[tex]r^3[/tex],
where r is the radius of the sphere. Since the diameter of the golf ball is given as 4 cm, the radius would be half of that, which is 2 cm. Plugging in the radius into the formula, we have:
[tex]V = (4/3)\pi(2 cm)^3 = (4/3)\pi(8 cm^3) = (32/3)\pi cm^3,[/tex]
Now, we calculate the value using the approximation π = 3.14:
V = (32/3) × 3.14 [tex]cm^3[/tex] = 33.51 [tex]cm^3[/tex] (approximately).
Therefore, the volume that is closest to the actual volume of the golf ball is 33.51 [tex]cm^3[/tex], option B.
A golfer hits a ball from a starting elevation of 7 feet with a velocity of 70 feet per second down to a green
with an elevation of -2 feet. The number of seconds t it takes the ball to hit the green can be represented
by the equation - 16t2 + 70t +7=-2. How long does it take the ball to land on the green?
It takes the ball ___
seconds to land on the green.
Answer:
[tex]t \approx 4.501\,s[/tex]
Step-by-step explanation:
The second-grade equation must be rearragend into its standard form:
[tex]-16\cdot t^{2} + 70\cdot t + 9 = 0[/tex]
Roots can be found with the help of the General Equation for Second-Order Polynomial:
[tex]t = \frac{-70\pm \sqrt{70^{2}-4\cdot (-16)\cdot (9)}}{2\cdot (-16)}[/tex]
[tex]t = 2.188 \pm 2.313[/tex]
[tex]t_{1} \approx 4.501\,s[/tex]
[tex]t_{2} \approx -0.125\,s[/tex]
Only the first root offers a reasonable solution.
[tex]t \approx 4.501\,s[/tex]
rnhymfrtyunryhbxdgveZvf
Answer: part of the alphabet
Step-by-step explanation: nice
Simplify 5+ W equals eight
Answer:
3
Step-by-step explanation:
5+3=8
8-5=w
What is the simplified form of the expression?
Answer:
The answer is A - a. -6a^2/b b. 5y^3
The Royal Fruit Company produces two types of fruit drinks. The first type is 60% pure fruit juice, and the second type is 85% pure fruit juice. The company is
attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 160
pints of a mixture that is 70% pure fruit juice?
Answer: 96 pints of the first fruit drink (60% pure fruit juice) and 64 pints of the second fruit drink (85% pure fruit juice).
Step-by-step explanation:
This question is a system of equations. First, we will define our variables:
Let x= number of pints of the first fruit drink (60% pure fruit juice), and then y = the number of pints of the second fruit drink(85% pure fruit juice).
We know that there are 160 total pints of the mixture. Therefore,
x + y = 160 .......... equation i
We are also aware that 70% of those 160 pints will be pure fruit juice, and they will come from either x or y.
For x pints of the first juice, there is
0.6x of pure fruit juice and for y pints of first juice, there is 0.85y of pure fruit juice. Therefore, we will have:
0.6x + 0.85y = 160 × 0.7
0.6x + 0.85y = 112
Multiply through by 100 to remove decimal. This will be:
60x + 85y = 11200 ........... equation ii
Combine both equations
x + y = 160 .......... i
60x + 85y = 11200 ........ ii
Multiply equation i by 60
Multiply equation ii by 1
60x + 60y = 9600 ........ iii
60x + 85y = 11200 ......... iv
Subtract iv from iii
-25y = -1600
y = 1600/25
y = 64
Since x + y = 160
x = 160 - 64
x = 96
Therefore , we will need 96 pints of the first fruit drink (60% pure fruit juice) and 64 pints of the second fruit drink (85% pure fruit juice).
Factor polynomial p^2-20p+100
Answer:
[tex](p-10)^2[/tex]
Step-by-step explanation:
[tex]p^2-20p+100=\\(p-10)^2[/tex]
Hope this helps!
p − 10 ) 2
Step-by-step explanation:
Which set of ordered pairs represents y as a function of x? A) {(0, 0), (−1, 2), (−1, −2), (−2, 4), (−2, −4)} B) {(0, 0), (1, 1), (2, 4), (3, 9), (3, 16)} C) {(0, 0), (0, 1), (0, 2), (0, −1), (0, −2)} D) {(0, 0), (−1, −0.5), (−2, −1), (−3, −1.5), (−4, −2)}
Answer: D
Step-by-step explanation:
No two coordinates can have to same input(x) and different outputs(y)
Option A represents y as a function of x because each x-value is associated with only one y-value.
Explanation:To determine if a set of ordered pairs represents y as a function of x, we need to check if each x-value is associated with a unique y-value. In option B) {(0, 0), (1, 1), (2, 4), (3, 9), (3, 16)}, we can see that the x-value 3 is associated with two different y-values, 9 and 16. Therefore, option B) does not represent y as a function of x.
The correct answer is option A) {(0, 0), (-1, 2), (-1, -2), (-2, 4), (-2, -4)}. In this set, each x-value is associated with only one y-value. For example, x = -1 is associated with y = 2 and y = -2. Since no x-value is repeated with different y-values, this set represents y as a function of x.
Option C) {(0, 0), (0, 1), (0, 2), (0, -1), (0, -2)} and option D) {(0, 0), (-1, -0.5), (-2, -1), (-3, -1.5), (-4, -2)} both have repeated x-values with different y-values, so they do not represent y as a function of x.
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log8x=2 solve for x by converting the logarithm to an exponential equation. (i already know the answer is 12.5 but i need the written steps that it takes to solve this problem in order for my answer to count.) please help!!!!1
Answer:
pooooooo
Step-by-step explanation:
What is the radius of the circle x^2+6x + y^2– 12y = 36?
Answer:
Step-by-step explanation:
hello :
x²+6x + y²– 12y = 36
completed to suqard :(x²+6x) + (y²– 12y) = 36 means :
(x²+6x+9)-9 + (y²– 12y+36)-36 = 36
(x+3)²+(y-6)² = 9².... standard form when the radius is : 9