Step-by-step explanation:
the volume of a figure bases always on a calculation that multiplies 3 dimensions.
while a surface area bases always on a calculation that multiplies 2 dimensions.
since the figures are similar, that means that all dimensions or side lengths of one figure correlate to the corresponding dimensions or side lengths of the other figure via the same scale factor f.
and that means that
large side length = small side length × f.
and that means that f has to be multiplied in 3 times for the volume and 2 times for the surface area (once for every dimension).
so,
large volume = small volume × f × f × f =
= small volume × f³
1536 = 648 × f³
f³ = 1536/648 = 64/27
f = 4/3
and
large surface = small surface × f×f =
= small surface × f²
small surface = large surface / f² = 864 / 16/9 =
= 864 × 9/16 = 54 × 9 = 486 m²
In Exercise 3, one equation relating the times Eric spends running and walking to reach the goal of covering 1600 meters is 200x + 80y=1600. Suppose Eric runs and walks for a total of 12 minutes to reach his goal.
Answer + Step-by-step explanation:
let x be the time that Eric spends running
y be the time that Eric spends walking
a) the statement “Eric runs and walks for a total of 12 minutes to reach his goal” is equivalent to the equation: x + y = 12
b) the coordinates of the intersection point are (5.333... , 6.666...)
Interpretation:
the time that Eric spends running is 5.333... minutes
the time that Eric spends walking is 6.666... minutes
Answer:
Given equation:
[tex]200x+80y=1600[/tex]
where:
x = time Eric runs (in mins)y = time Eric walks (in mins)Part (a)If Eric runs and walks for a total of 12 minutes, then:
[tex]x+y=12[/tex]
Part (b)To graph:
Rewrite both equations to make y the subjectFind the x-interceptFind the y-interceptConnect the two points with a straight line[tex]200x+80y=1600 \implies y=20-\dfrac{5}{2}x[/tex]
[tex]\textsf{x-intercept}: \quad 20-\dfrac{5}{2}x=0 \implies x=8 \implies (8,0)[/tex]
[tex]\textsf{y-intercept}: \quad 20-\dfrac{5}{2}(0)=20 \implies (0,20)[/tex]
[tex]x+y=12 \implies y=12-x[/tex]
[tex]\textsf{x-intercept}: \quad 12-x=0 \implies x=12 \implies (12,0)[/tex]
[tex]\textsf{y-intercept}: \quad 12-0=12 \implies (0,12)[/tex]
Point of intersection (equate equations):
[tex]\begin{aligned}20-\dfrac{5}{2}x &=12-x\\20-12 &=\dfrac{5}{2}x-x\\8&=\dfrac{3}{2}x\\16 &=3x\\x &=\dfrac{16}{3}\end{aligned}[/tex]
[tex]y=12-\dfrac{16}{3}=\dfrac{20}{3}[/tex]
[tex]\implies \left(\dfrac{16}{3},\dfrac{20}{3}\right)[/tex]
The point of intersection tells us that Eric runs for 16/3 mins and walks for 20/3 minutes.
Lenny bought a motorcycle. He paid 12.5% in tax. The tax added $1437.50 to the price of the
motorcycle.
What was the price of the motorcycle, not including the tax?
Answer:
17963.13
Step-by-step explanation:
this is urgent!! please help!
Answer:
C=31.4mm
Step-by-step explanation:
Circumfrence formula: π*diameter
diameter =10mm (picture)
C=10mm*3.14
C=31.4 mm
Answer:
31.42
Step-by-step explanation:
use the formula C=2πr
Please help me answer this. Solve for X
Answer:
x = 14,641
Step-by-step explanation:
[tex] \sqrt{x} = 121 \\squaring \: both \: sides \\ \implies \: {( \sqrt{x}) }^{2} = {(121)}^{2} \\ \\ \implies \: x = 14,641[/tex]
In a company, there are 28 total employees. All employees who have worked there for more
than five years receive a gift.
If eleven employees have received the gift, what is the probability that a randomly
selected employee has received the 5-year gift?
The probability that a randomly selected employee has received the 5-year gift is 39.29%
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a randomly selected employee has received the 5-year gift = number of employees who have received the gift / total number of employees
11/28 x 100 = 39.29%
To learn more about probability, please check: https://brainly.com/question/13234031
The square root of 23
Answer:
4.796
Step-by-step explanation:
. Describe a set of transformations that would map the blue trapezoid ABCD onto the red trapezoid A’B’C’D’.
Answer:
1. Reflection across y=0
2. Shifted 6 units right
Answer:
Step-by-step explanation:
A translation of 6,-6 followed by a rotation of 180 degrees
3. Which of the following is the surface area of this right triangular prism? (
4 in.
8 in.
5 in.
106 in?
108 in?
.
2111 in 2
160 in?
Expand the following expression: 4 (2k + j)
Answer:
4(2k + j) = 8k + 4j
Step-by-step explanation:
4(2k + j)
Distribute in the 4.
4 * 2k + 4 * j
Multiply 4 and 2k.
8k + 4 * j
Multiply 4 and j.
8k + 4j
Answer:
[tex]\boxed{\sf{8k+4j}}[/tex]Step-by-step explanation:
Use the distributive property.
Distributive property:
⇒ A(B+C)=AB+AC
4(2k+j)First, multiply by expand.
→ 4*2k=8k
→ 4*j=4j
Rewrite the problem down.
= 8k+4j
[tex]\Longrightarrow: \boxed{\sf{8k+4j}}[/tex]
Therefore, the correct answer is 8k+4j.I hope this helps! Let me know if you have any questions.
HELP MY SISTER NEEDS HELP....AGAIN-
Answer:
96
Step-by-step explanation:
First solve (10-7)
Then use 21 and ÷ it by 3
Add 89 + 7 and then you'll get your answer
PLEASE HELP WILL MARK BRAINLIEST
(45x + 52y) + (-5x + 40y)
A.50x + 92y
B.40x + 92y
C.40x + 12y
D.50x + 12y
Find the average rate of change of each function on the interval specified.
i only need #5 thank you :)
The average rate of change (AROC) of a function f(x) on an interval [a, b] is equal to the slope of the secant line to the graph of f(x) that passes through (a, f(a)) and (b, f(b)), a.k.a. the difference quotient given by
[tex]f_{\mathrm{AROC}[a,b]} = \dfrac{f(b)-f(a)}{b-a}[/tex]
So for f(x) = x² on [1, 5], the AROC of f is
[tex]f_{\mathrm{AROC}[1,5]} = \dfrac{5^2-1^2}{5-1} = \dfrac{24}4 = \boxed{6}[/tex]
An irregular plane figure drawn on graph paper is framed 15 by 40 rectangle.To find its area,10,000 random points are generated,and 5,710 of them land inside the irregular region what is the area of the irregular region to the nearest integer
=========================================================
Explanation:
A = number of points that land inside the irregular figureB = number of randomly generated points totalIn this case,
A = 5,710B = 10,000Divide A/B to find the experimental probability of landing inside the figure
A/B = (5,710)/(10,000) = 0.571
There's about a 57.1% chance of landing inside the figure.
The entire region is 15 units by 40 units, giving an overall area of 15*40 = 600 square units.
Roughly 57.1% of this total area would be taken up by the irregular figure
57.1% of 600 = 0.571*600 = 342.6 which rounds to 343
The area of the irregular region is about 343 square units
What is the equation of the blue line
The Blue line is the translate in the direction of red line by,and therefore has equation y=3(x-4)+5
Jay went on a diet and lost 5 pounds each month. Find Jays net weight change in 6 months.
Answer:
30lbs
Step-by-step explanation:
5x6 i think lol maybe
the volume of this right trapezoidal prism is 380.25ft^3. what is the height ,x, of the prism? 5, 5, 8, 5.8, x.
Answer:
Hence, the height of the trapezoidal base is 7.2 ft.
Step-by-step explanation:
The height of the trapezoidal base is 7.2 ft.
Step-by-step explanation:
Consider the provided information.
The volume of trapezoidal prism is the area of the cross-section × the length.
Where B is the area of base, H is the length and V is the volume.
The length of the prism is 25.2ft and volume is 1279.152
Hence, the base area is 50.76 ft².
The base is trapezoid.
The area of trapezoid is
Substitute B=50.76, in above formula.
Hence, the height of the trapezoidal base is 7.2 ft.
What is 1.427381 rounded to the nearest hundred thousandths place?
1.427381
to find:the nearest hundredth thousandths place.
solution:if the the number right to the hundred thousandths place is 5 or more round up, if not keep it as it is.
= 1.42738
therefore, 1.427381 rounded to the nearest hundred thousandths is 1.42738
The answer is 1.42738
Describe the set 3 ≤ x ≤ 10
using interval notation.
B. [3,10]
D. (3,10]
A. (3,10)
C. [3,10)
Answer:
The answer is B, [3,10].
Step-by-step explanation:
Help guys I need this
Answer:
768 Square Inches
Step-by-step explanation:
10x18 = 180 (2 rectanlge faces)
12x8 = 96 (2 triangles)
12x18 = 216 (bottom face)
216 + 96(2) + 180(2) =
768
Jack and Diane want to meet for breakfast. Jack walks 1.5 mph and Diane walks 1 mph. They started 5 miles apart from each other. How long does it take them to meet up?
Answer:
jack take 3.33 hours and diane would take 5 hours
Step-by-step explanation:
choose all numbers that could be common denominators for 2/3 and 5/6
A right triangle is shown.
Enter the value of x.
ANSWE ASAPPP
Does the equation below represent a lunar relationship? Justify your response. 2x - 5y= -15
Answer:
Yes, the equation represents a linear relationship.
Step-by-step explanation:
If you graph it, it is a line.
Also, the exponent on the x and the y is exactly 1. There are no variables in the denominator, nor inside a radical. There are no squared, cubes or higher exponents. All these things will make an equation NOT linear.
A 14 ounce can of peaches cost $2.75 in a 24 ounce can of peaches cost $5.10 how much is the price per ounce of the 24 ounce can of peaches
Write an equation in slope-intercept form of the line shown.
An equation is
Answer:
y = -x - 4
Step-by-step explanation:
y = mx + b
m = rise/run = -5/5 = -1
b = y-intercept = (0, -4)
BRAINLIEST please if this helps!ol-
اد
Point Dis: Point E is
4.
D
E
Point Fis:
Point
5.
UL
G
0
6. Label each fraction on the number line below.
Answer:
I can't understand
Step-by-step explanation:
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
x = 15 , y = 15√(2)
Step-by-step explanation:
The triangle is isosceles where two angles are the same which mean two sides are also the same.
x = 15°
Pythagorean Theorem: a^2 + b^2 = c^2
15^2 + x^2 = y^2
15^2 + 15^2 = y^2
225 + 225 = y^2
450 = y^2
y = √(450) = 15√(2)
Answer:
x=15 and y=15root2
Step-by-step explanation:
tan45=p/b
1=x/15
x=15
again for right angle trangle
h=root (p+b)
=15root2 ans
If you roll a fair 6-sided die and then flip a fair coin, what is the probability that you roll greater than 1 and get heads with the coin?
Answer:
5/12
Step-by-step explanation:
The odds for the die are 5 positive out of 6 possible outcomes
-- 2,3,4,5,6 are the positive outcomes - the ones you want - but there are a total of 6 outcomes or ways the die could land
The odds for the coin are 1 positive outcome out of 2 possible outcomes (heads or tails)
Once you have 5/6 for the die and 1/2 for the coin, you multiply them together.
Differentiation in mathematics 2
Answer:
differentiation
Step-by-step explanation:
maths class