The scale factor from the smaller figure to the larger figure is found by taking the cube root of the ratio of their volumes, which is the cube root of 216/343.
Explanation:The student asked: Which of the following could represent the scale factor of the smaller figure to the larger figure? When comparing the volumes of two geometric figures, we can determine the scale factor of their linear dimensions by understanding the relationship between volume and linear scale factor.
Given that the smaller figure's volume is 216 cubic inches and the larger figure's volume is 343 cubic inches, we are looking for the cube root of the ratio of these volumes to find the linear scale factor.
To find the scale factor from the smaller figure to the larger figure, divide the volume of the smaller figure by the volume of the larger figure and then calculate the cube root: Scale factor = ∛(216/343). This calculation will give you the scale factor of the linear dimensions from the smaller figure to the larger figure.
which statement can be proved if you are given that SK≌LR?
Answer:
C
Step-by-step explanation:
The correct answer is C.[tex]$\overline{SL}\cong\overline{KR}$[/tex]
Given that [tex]$\overline{SK}\cong\overline{LR}$[/tex] , we can see that triangle SKL is congruent to triangle LRP by the Side-Side-Side (SSS) congruence postulate. This means that all corresponding sides and angles of the two triangles are congruent.
Since [tex]$\overline{SK}\cong\overline{LR}$[/tex]is given, we know that [tex]$\overline{SL}\cong\overline{KR}$[/tex] must also be true. The other answer choices do not necessarily follow from the given information.
The complete question is: Which statement can be proved if you are given that SK≌LR?
I need help with this
If A(0, 0), B(3, 3), C(9, 3), and D(6, 0) are the vertices of a quadrilateral, do the points form a parallelogram? Justify your answer.
A. Yes, it is a parallelogram because the slope of segment AB equals the slope of segment DC, which equals 1, and AB = DC = square root of 18.
B. Yes, it is a parallelogram because the slope of segment AB equals the slope of segment DC, which equals −1, and AD = CD = 3 units.
C. Yes, it is a parallelogram because the midpoint of the diagonals of segment AC and segment BD is (4.4, 1.5).
D. No, it is not a parallelogram because the slope of segment AB = 1 and the slope of segment DC = −1.
For what values of b will F(x) = logb x be an increasing function?
A. b < 0
B. b > 0
C. b < 1
D. b > 1,
Final answer:
The logarithmic function F(x) = logb x is an increasing function when the base b is greater than 1, because the value of logb x increases as x increases for b > 1.(Option D)
Explanation:
The question asks for what values of b will F(x) = logb x be an increasing function. To determine this, we need to understand the behavior of logarithmic functions based on their base value (b). A logarithmic function is increasing if the base of the logarithm is greater than 1. This is because as x increases, the value of logb x increases when b>1. Conversely, if b<1 (but b>0), the function is decreasing because the power to which b must be raised to produce x decreases as x increases. We also know that the base of a logarithm cannot be negative or zero, as this would not produce a valid logarithmic function.
Therefore, the correct answer is D. b > 1, where the logarithmic function F(x) = logb x is an increasing function.
Choose the situation that represents a function. The number of raisins in an oatmeal raisin cookie is a function of the diameter of the cookie. The inches of rainfall is a function of the day’s average temperature. The time it takes to cook a turkey is a function of the turkey’s weight. The number of sit-ups a student can do in a minute is a function of the student’s age.
The time it takes to cook a turkey is a function of the turkey’s weight. Then the correct option is C.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
Choose the situation that represents a function.
An intake and an outlet are both present in a function. Each unique supply is converted into a result as per the concept of a function.
The amount of the turkey determines how long it will take to cook.
Oversized turkeys will take longer to prepare than smaller turkeys, and vice versa.
The time it takes to cook a turkey is a function of the turkey’s weight.
Then the correct option is C.
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Each test grade in Sara's science class counts for 1/6 of the final grade. The final exam counts for 1/2. Sara's test scores are 72, 84, and 90. Her final exam score is 90.
What is Sara's final grade for the class?
A) 83
B) 86
C) 87
D) 89,
Which pair of times has the longest elapsed time between the two times?
3:05 to 9:40
8:35 a.m. to 2:35 p.m.
4:25 to 10:45
7:10 p.m. to 1:40 a.m.
What is the elapsed time between 9:30 p.m. and 2:15 a.m.?
7 hours and 45 minutes
5 hours and 15 minutes
4 hours and 45 minutes
4 hours and 15 minutes
Subtract 1 hour, 50 minutes from 4 hours, 10 minutes.
2 hours, 20 minutes
2 hours, 40 minutes
3 hours, 40 minutes
3 hours, 30 minutes
What is the value of x?
simplify 6/x-6+3x/x+5-1/(x-6)(x+5)
To simplify a complex algebraic expression, you handle fractions first by bringing them to a common denominator. However, the resources provided seem misplaced as they pertain to calculus rules and Chemistry, which are not relevant to this algebra question.
Explanation:The student's question is asking to simplify a complex algebraic expression: 6/x-6+3x/x+5-1/(x-6)(x+5). To simplify such an expression, it's best to deal with fractions first. Note that the given expression can also be expressed as three separate fractions summed together, i.e., (6/x-6) + (3x/x+5) - [1/(x-6)(x+5)]. Dealing with fractions in simplification, we combine them to a common denominator and rationalize the numerator and denominator. After that, simplify the resulting expression. However, with provided reference, it seems that there is a misunderstanding or a misplacement of information because resources given are about calculus rules and Chemistry which are not relevant in simplifying this algebraic expression.
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How far does a ball that is hit from a height of 3 feet at a speed of 120 feet per second travel before it hits the ground if it is hit at an angle of 45 degrees? Round your answer to the nearest integer.
A) 376 Feet
B) 395 Feet
C) 426 Feet
D) 453 Feet
What number belongs in the blank space in the formula??
If 5x-4=26 what does the x equal
Help Help Help!!! :)
solve the system of equations y=2x^2-3 y=3x-1
-7x^6*(-2x^8) will mark as brainiest
SIMPLIFY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
DO NOT SOLVE FOR X
Part 1.] Identify the transformations that describe the graph of an odd function. Select all that apply.
reflection over the x-axis;
reflection over the y-axis;
reflection over the line y = x;
90° rotation around the origin;
180° rotation around the origin
Part 2.] Prove that if f(x) and g(x) are both even functions, then h(x) = f(x) + g(x) is an even function.
HELP ASAP WILL MARK AS BRAINILEST TO WHOEVER GETS IT RIGHT
Can someone graph it for me and answer a or b???
Can anyone help me!?!?!?!?! Here is my question:
Compare the functions shown below:
f(x) = 4 sin (2x − π) - 1
g(x)
x y
-1 6
0 1
1 -2
2 -3
3 -2
4 1
5 6
h(x) = (x − 2)2 + 4
Which function has the smallest minimum y-value?,
Kevin goes fishing every Saturday. The table below shows the number of fish he caught each week for the last six weeks.
Fish Caught
Week Number of Fish
1 4
2 0
3 2
4 8
5 4
6 6
What is the mean absolute deviation of the data above?
A. 8
B. 2
C. 4
D. 1
Tom caught 4 fish and his son caught 12 fish.
The number of fish that Tom caught was what percent of the number of fish that his son caught?
Evaluate the function below for x = 2 F(x) = 4x3 - x2 - 5x + 7
Answer:
The value of the given function is 25 for x = 2.
Step-by-step explanation:
Given function is,
[tex]F(x) = 4x^3 - x^2 - 5x + 7[/tex]
At x = 2,
The value of the function is,
[tex]f(2)=4(2)^3-(2)^2-5(2)+7[/tex]
[tex]=4(8)-4-10+7[/tex]
[tex]=32 - 7[/tex]
[tex]=25[/tex]
Hence, the value of the given function is 25 for x = 2.
The ____ is the vertical number line on the coordinate grid
50 POINTS!!!!! HELPFor the exponential function f(x)=a^x,a>0,a≠1 what is the domain? what is the range?
Paul has a tack stuck in his four-wheeler tire. If the tire has a diameter of 36 inches, how far does the tack travel in 62° of rotation?
A. 31π
B. 18π
C. 31 pi over 5
D. 31 pi over 90,
C. 31 pi over 5
~sbcardinals :)
hello there
your answer would be
C, 31 pi over 5
hope it helps
thank you
best regards Queen Z
Please help!! Show your work !!
What are the zeros of f(x) = 4x^2 - 12x + 8 (I need a clear explanation on how to solve it)
The zero of the quadratic function is therefore x = 1. Since both factors give the same zero, we have a repeated zero and f(x) only touches the x-axis at one point, x = 1.
The zeros of the quadratic function f(x) = 4x^2 - 12x + 8 are the values of x that make f(x) = 0. In this function, we can factor by finding two numbers that multiply to give the constant term (8 times 4, the coefficient of x^2) and add to give the coefficient of x (-12). Here, those numbers are -4 and -4, so we rewrite the middle term -12x as -4x - 4x, and factor by grouping:
4x^2 - 4x - 4x + 8 = 0
4x(x - 1) - 4(x - 1) = 0
(4x - 4)(x - 1) = 0
Now we have two factors equal to zero, which gives us two equations to solve:
4x - 4 = 0 or x - 1 = 0
x = 1
Using the given equation find the missing coordinates of the points and then find the slope of the line for each equation y=3.5x+4; a(...; 5), b(10; ...)
A(2/7:5)
B(10:39)
The slope is 7/2.
The slope of the line y=3.5x+4 is 3.5, and the missing coordinates will be filled as a(0.28, 5) and b(10, 9)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given equation of line is y=3.5x+4
When we compare this with slope intercept form y=mx+b.
slope m=3.5
We need to find the value of x when y is 5
5=3.5x+4
1=3.5x
Divide both sides by 3.5
x=0.28
So a coordinates are (0.28, 5)
Now let us find y value when x is 10
y=3.5(10)+4
y=39
So b coordinates are (0.28, 39)
Hence, the slope of the line y=3.5x+4 is 3.5, and the missing coordinates will be filled as a(0.28, 5) and b(10, 9)
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Can someone plz explain Pythagoras theorem to me
(50 PTS) NEED HELP FAST ILL MARK BRAINLIEST AND RATE 5 STARS AND SAY THANK YOU
A tournament organizer recorded the number of people in different age groups who participated in the archery tournament. He then created the following histogram:Which of the following statements best compares the height of the bars of the histogram?
A.) There are more participants in the 20–39 age group than in the 0–19 and 60–79 groups combined.
B.) There are more participants in the 20–39 age group than in the 40–59 and 0–19 groups combined.
C.) There are twice as many participants in the 40–59 age group than in the 60–79 age group.
D.) There are twice as many participants in the 0–19 age group than in the 60–79 age group.
Answer:
d
blessed have one
Consider the function y = 1.05(x/12), which represents the growth of capital in a bank account.
The annual interest is __%,
a. 12
b. 105
c. 1.05
d. 5
and the bank compounds the interest__ .
a. annually
b. continuously
c. daily
d. monthly
The balance of the account will grow __ .
a. logarithmically
b. exponentially
c. asymptotically
d. linearly
Answer:
The annual interest is,
Option d is correct
5%
The bank compounds the interest_
Option a is correct.
Annually.
The balance of the account will grow,
Option b is correct
exponentially
Step-by-step explanation:
Exponential growth function is given by:
[tex]y=(1+r)^x[/tex] .....[1]
where,
r is the annual interest in decimal
x is the number of periods.
As per the statement:
Consider the function:
[tex]y=(1.05)^{\frac{x}{12}}[/tex] where, x represents the time in months.
On comparing with [1] we have;
[tex]1+r = 1.05[/tex]
Subtract 1 from both sides we have;
r = 0.05 = 5%
The annual interest is, 5%
and
the bank compounds the interest annually.
The balance of the account will grow exponentially