Answer:
8=t/d
Step-by-step explanation:
a. Before a basketball game, a referee noticed that the ball seemed under-inflated. She dropped it from 6 feet and measured the first bounce, as 36 inches and the second bounce as 18 inches. Write an exponential function to model the height of the ball.
The exponential function to model the height of the ball is
h = 72*[tex](1/2)^{n}[/tex]
According to the question we have been given that
at first bounce the height of the ball is = 36 inches
and at the second bounce the ball is at the height = 18 inches
The exponential model is given as
h = a.[tex]b^{n}[/tex] (1)
where h = height of the ball
n = number of bounces
Putting the different values of h and n in equation (1) and getting the value of a and b, we get
when h = 36 and n=1
36 = a.[tex]b^{1}[/tex]
36 = a.b (2)
when h = 18 and n =2
18 = a.[tex]b^{2}[/tex]
18 = a.b.b
18 = 36.b
b = 1/2
substituting the value of b in equation (2) we get
a = 72
Hence putting the value of a and b in equation (1), the exponential function to model the height of the ball is
h = 72*[tex](1/2)^{n}[/tex]
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Simplify the following expression: -9x+8+2x-6*
Answer:
7x+2
Step-by-step explanation:
-9x+8+2x-6
8-6
-9x+2+2x
combine like terms
-9x+2+2x
-9+2
7x+2
Use the Change of Base Formula to evaluate each expression.
log₃33
Using the change of base formula the evaluated value of [tex]log_{3} 33[/tex] is 3.184
Change of base formula is used to change the base of logarithm. It is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm.
According to the change of base formula :
[tex]log_{a} b = \frac{log_{x} b}{log_{x} a}[/tex]
where base x is base 10
According to the question, we have to find the value of [tex]log_{3} 33[/tex]
Thus applying change of base formula we get
[tex]log_{3} 33 = \frac{log_{10} 33}{log_{10} 3}[/tex]
calculating the value of log from the calculator we get,
[tex]log_{3} 33 = \frac{1.519}{0.477}\\log_{3} 33 = 3.184[/tex]
Thus using the change of base formula the evaluated value of [tex]log_{3} 33[/tex] is 3.184
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I NEED HELP!!! MARKING BRAINLIEST LATER
Answer:
what is the question?
Step-by-step explanation:
There is no picture or question
Answer: Question
Step-by-step explanation:
help me with this !! please
we get the graph of the quadratic function by plotting the points on the graph paper.
We are given the quadratic function as:
f (x) = x²
We need to graph the function and find the values of the function for some given points of x.
For x = - 2, we get that:
f (x) = x²
f (- 2) = (- 2)²
f (- 2) = 4
For x = - 1, we get that:
f (x) = x²
f (- 1) = (- 1)²
f (- 1) = 1
For x = 0, we get that:
f (x) = x²
f (0) = (0)²
f (0) = 0
For x = 1, we get that:
f (x) = x²
f (1) = (1)²
f (1) = 1
For x = 2, we get that:
f (x) = x²
f (2) = (2)²
f (2) = 4
Plotting these points on the graph, we obtain the graph of the quadratic function.
Therefore, we get the graph of the quadratic function by plotting the points on the graph paper.
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Solve the inequality and describe the graph of the solution. 3x+27>=-5
The solution to the inequality is x ≥ -10 2/3. On the graph, the solution to the inequality is to the right of the line
From the question, we are to solve the given inequality
The given inequality is
3x + 27 ≥ -5
Solving the inequality
3x + 27 ≥ -5
Subtract 27 from both sides of the inequality
3x + 27 -27 ≥ -5 - 27
3x ≥ -32
Divide both sides of the inequality by 3
3x/3 ≥ -32/3
x ≥ -10 2/3
The graph of the inequality is shown below
Hence, the solution to the inequality is x ≥ -10 2/3. On the graph, the solution to the inequality is to the right of the line
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MP Persevere with Problems Explain how
you can write 25 % as a decimal.
25% in the decimal number system is 0.25.
What are decimal numbers?The base-10 number system, arguably the most widely used number system, is referred to as decimal. The ten single-digit numbers in the decimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number following nine is 10. 19 is followed by 20, and so on.Decimal fractions and recurring (repeating or non-terminating, like) decimals are the three different types of decimals (a.k.a. converting a decimal into a fraction whose denominator is a power of ten).So, we need to divide the number by 100 and we want to convert a number in percentage into decimals.
Then,
25/100 = 0.25Therefore, 25% in decimals is 0.25.
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If a serving size of
corn is ½ cup and
contains 45 calories,
how many calories in
3.5 servings?
Answer:
78.75 or 78 3/4
Step-by-step explanation:
Point I is on line segment HJ. Given IJ = 3 and HI = 14, determine the length
НЈ.
The length of hJ is 17.
Given, the line HJ has a length
HJ = ?
HI = 14
IJ = 3
Since line HJ = HI + IJ
= 14+3
=17
Therefore the length of HJ will be 17.
A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
the measurement or extent of something from end to end; the greater of two or the greatest of three dimensions of a body is called length.
In geometry, a line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.
Types of Line Segment
Parallel Line. Two lines in the same plane either meeting each other or not.
Intersecting Lines.
Concurrent Lines.
Collinear Points.
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What is the best description of the relationship in the scatterplot below?
A) Positive linear association
B) Negative linear association
C) Nonlinear association
D) No association
Ebony is cutting dough for pastries in her bakery. She needs all the pieces to be congruent triangles and has ensured that segment EF ≅ segment ON and ∠MON ≅ ∠GEF. What would Ebony need to compare in order to make sure the triangles are congruent by ASA?
segment EG and segment OM
∠EFG and ∠ONM
segment NM and segment FG
∠EGF and ∠OMNEbony is cutting dough for pastries in her bakery. She needs all the pieces to be congruent triangles and has ensured that segment EF ≅ segment ON and ∠MON ≅ ∠GEF. What would Ebony need to compare in order to make sure the triangles are congruent by ASA?
segment EG and segment OM
∠EFG and ∠ONM
segment NM and segment FG
∠EGF and ∠OMN
Answer:
NM=FG
Step-by-step explanation:
Answer:
Segment EG and segment OM
Step-by-step explanation:
Comparing the lengths of segment EG and segment OM satisfies the side-side correspondence required for AAS congruence.
Question
What value of x makes the equation x+5=2x true?
Answer:
5
Step-by-step explanation:
5+5=2(5)
10=10
please help me thank u
What is the base if the portion is $4,560 and the rate is 65%? Solve for the base (in $). Round to hundredths when necessary.
The base of the $4,560 which is 65% of the base is $7,015.38.
What is percentage?This represented by the symbol %, is the division of any number by 100. The expression 25%, for example, means that 25 parts of a whole were divided into 100 parts.
The portion of 65% means that the amount given as $4,560 is only a part of the whole amount known as base, which is unknown as the base, in other words, the base amount can be determined the portion divided by the percentage of the portion:
65%=$4560
1%=$4560/65
1%=$70.1538461538462
100%=$70.1538461538462*100
100%=$ 7,015.38
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Determine whether each logarithm is a common logarithm.
b. (log 64)
The logarithm function ( log 64 ) is not a common logarithm function as it does not have a base 10 but ahs a base e.
In mathematics, the common logarithm is the logarithm with base 10.
It is also known as the decadic logarithm and as the decimal logarithm function.
Here, we have the logarithm function as:
( log 64 )
Now, we can see that:
It does not have a base.
So, we will take the base as e.
So, it will not be a common logarithm function as having base 10 is an important characteristic of a common logarithm function.
Therefore, we get that, the logarithm function ( log 64 ) is not a common logarithm function as it does not have a base 10.
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Round 12,345.6789 to the nearest hundred
Answer:
12,300
Step-by-step explanation:
To round to the nearest hundred look at the tens place and if the number is a 5 or above add 1 to the hundreds place, in this case though the number is below 5 so you drop all the numbers behind it and nothing happens to the hundreds place
12,(3)46.6789
this is the hundreds place
12,3[4]6.6789
go to the tenths place and since the number is a 4 you drop it and the other numbers behind it.
Giving you the answer 12,300
Two men shared the cost of a business in the ratio 2:3. if the smaller share is 75000, find the total cost of the business?
The total cost of business is 1,87,500
We are given the ratio of shares of two men. So, let the share of first person be 2x and share of second person be 3x.
It is also stated that smaller share is 75000. Out of the two shares, 2x is the smaller one. So, relating the two statements -
2x = 75000
x = 75000 ÷ 2
Performing division
x = 37500
So, finding the larger share now -
Larger share = 3x
Larger share = 3×37500
Performing multiplication
Larger share = 112500
Total cost of business = Smaller share + Larger share
Total cost of business = 75000 + 112500
Total cost of business = 1,87,500
Hence, the total cost of business is 1,87,500.
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expanded form of which decimal. Santo chose C as the correct answer.How did he get that answer?
Applying proportions, the decimal value is given by:
B. 32.064.
Santo got the wrong answer because he counted 6 and 4 as the tenths and hundredths digits, instead of hundredths and thousandths.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for digit values in a number.
For this problem, we just have to apply the digit values of the number to find the decimal value, adding the factors, hence:
3 x 10 = 30. (3 tens)2 x 1 = 2 (2 ones).6 x 1/100 = 0.06 (6 hundredths).4 x 1/1000 = 0.004 (4 thousandths).Hence:
30 + 2 + 0.06 + 0.004 = 32.064.
The decimal value is given by:
B. 32.064.
Santo got the wrong answer because he counted 6 and 4 as the tenths and hundredths digits, instead of hundredths and thousandths.
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B is the midpoint of AB. If the coordinates of B are (11,20) and A are (3,8) what are the coordinates of C?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad C(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +3}{2}~~~ ,~~~ \cfrac{ y +8}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE B}}{(11~~,~~20)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +3}{2}=11\implies x+3=22\implies \boxed{x=19} \\\\\\ \cfrac{ y +8}{2}=20\implies y+8=40\implies \boxed{y=32}[/tex]
Perpendicular to the line y = 3x + 8; passes through (-4, 1)
The slope intercept form of the equation become y = (-1/3)x - 1/3.
According to the statement
We have to find that the slope intercept equation.
So, For this purpose, we know that the
Slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
From the given information:
y - 3x = 8
y = 3x + 8
Slope = 3
And
Perpendicular lines have slopes that are negative reciprocals of each other. So, the new line will have a slope of = -1/3.
P(-4,1)
y - 1 = (-1/3)(x +4)
y - 1 = (-1/3)x - 4/3
y = (-1/3)x - 1/3.
So, The slope intercept form of the equation become y = (-1/3)x - 1/3.
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CAN SOMEONE HELP I DONT UNDERSTAND (CRYS)
Answer:
1) [tex]m[/tex]∠JKL = 145°
2) [tex]m[/tex]∠IHG = 164°
3) [tex]m[/tex]∠NME = 50°
4) [tex]m[/tex]∠TUV = 178°
I hope this helps! (✿◠‿◠)
Every weekend, Sue bikes to the park to play disc golf with her friends. Before leaving home, she fills her water bottle to the top. This weekend, Sue drinks of a liter on the way to the 1 2 park. Now there is only of a liter remaining in Sue's water bottle. 4 Use an equation to find the amount of water that Sue's water bottle holds. To write a fraction, use a slash (/) to separate the numerator and denominator. liters
The equation is [tex]\frac{1}{2}x + \frac{1}{2}x[/tex]
Let the amounts of water that Sue's water bottle holds = x
According to the question,
given that,
Sue's water bottle holds the water = [tex]\frac{1}{2}x + \frac{1}{2}x[/tex] = [tex]\frac{2}{2}x[/tex] = x
Thus, assumption is true
Hence, the equation is [tex]\frac{1}{2}x + \frac{1}{2}x[/tex]
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.
Different Types of Equations:
Some of the math equations used in algebra are:
Linear Equation
A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
Quadratic Equation
This is a second-order equation. In quadratic equations, at least one of the variables should be raised to exponent 2.
Example:
[tex]a x^{2}[/tex] + b x + c = 0
Cubic Equation
This is a third-order equation. In cubic equations, at least one of the variables should be raised to exponent 3.
Example:
[tex]a x^{3}[/tex] + [tex]b x^{2}[/tex]+ cx + d = 0
[tex]a^{3}[/tex] – 27 = 0
Rational Equation
A rational equation is an equation that contains fractions with a variable in the numerator, denominator, or both.
Example:
[tex]\frac{x}{2}[/tex] = [tex]\frac{x + c}{4}[/tex]
How to prove an equation
One way to prove that an equation is true is to start with one side (say, the left-hand side) and to convert it, by a sequence of equality-preserving transformations, into the other side. But remember that a proof must be easy to check, so each step deserves a justification. We keep the steps elementary, based on known facts of algebra. Also, a proof should always start with a statement of the claim that is being proved.
.
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The temperature dropped 6 degrees celsius every hour for 6 hours. what was the total number of degrees the temperature changed in the 6 hours?
Answer:
36°C
Step-by-step explanation:
[tex]|-6(6)|=36[/tex]
I NEED HELP SOMEONE HELP ME!!
The grid above shows the graph of the parent
function f(x) = Ixl and a translated functions
graph.
Write the equation for the translated graph.
i need to write an equation pls help
Answer:
g(x) = | x + 2 | + 1
Step-by-step explanation:
the parent function f(x) = | x | has its vertex at the origin
the translated function has the form
g(x) = | x - h | + k
where (h, k ) are the coordinate of the vertex
the vertex of g(x) is at (- 2, 1 ) , then
g(x) = | x - (- 2) | + 1 , that is
g(x) = | x + 2 | + 1
Find the perimeter of the figure below, in centimeters.
May someone help with this?
Help please! (If you could explain too that would be great, no need to tho.)
8) What is their rate of
change (speed) in Section
D (Hours 7-
10)? Remember to
include units
Remember rate of
change = slope = rise/run
Answer:-2/1
Step-by-step explanation:
rise is -2 and 1 is run
What statement is true about the sum of two rational numbers
Answer: The sum is always a rational number.
Step-by-step explanation:
Step-by-step explanation:
Given, sum of two rational numbers is always a rational number
We have to determine if the given statement is true or false
Consider two rational numbers 2/3 and 4/5
Sum of two numbers = 2/3 + 4/5
= [2(5) + 4(3)]/3(5)
= (10 + 12)/15
= 22/15
22/15 is a rational number.
Consider two rational numbers 2/3 and 1/3
Here, the denominators are same
Sum of two numbers = 2/3 + 1/3
= (2 + 1)/3
= 3/3
= 1/1
1/1 is also a rational number
Therefore, the given statement is true.
64,000 divided by 10 to the 3rd power
Answer:
64
Step-by-step explanation:
10^3 is 1000
64000/1000=64
1/6y+3/8x=24 rate of change
The constant average rates of change of 1/6y + 3/8x = 24 is -9/4
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the constant average rates of change?The linear equation is given as
1/6y + 3/8x = 24
Multiply through the equation 1/6y+3/8x=24 by 24 to eliminate the fraction
So, we have
24 * 1/6y + 24 * 3/8x = 24 * 24
Evaluate the product
So, we have
4y + 9x = 576
Rewrite the equation as
So, we have
4y = - 9x + 576
Divide through the equation by 4
So, we have
y = - 9/4x + 144
A linear equation is represented as
y = mx + c
Where
m = rate of change
So, we have
m = -9/4
Hence, the constant average rates of change of 1/6y + 3/8x = 24 is -9/4
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find the distance between B and H
The distance between the points B and H on the coordinate plane is 4.48 units
What is the distance between the points B and H?See below for the complete question
The coordinates of the points B and H are given as:
(-2.63, 7) and (1.85,7)
Rewrite properly as
B = (-2.63, 7)
H = (1.85,7)
The distance between any two points on a coordinate plane is calculated using the following distance formula
d = √(x2 - x1)^2 + (y2 -y1)^2
Substitute the known values in the above distance equation
So, we have
d = √(-2.63 - 1.85)^2 + (7 - 7)^2
Evaluate the exponents
So, we have
d = √20.0704 + 0
Evaluate the sum
So, we have
d = √20.0704
Evaluate the exponent
So, we have
d = 4.48
Hence, the distance between the points B and H on the coordinate plane is 4.48 units
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Possible question
Find the distance between B (-2.63, 7) and H (1.85,7)