Answer: Summary: The equation which represents the inverse of the function f(x) = 4x is h(x) = 1/4 x.
Step-by-step explanation: THERE IS NO EXPLANATION
(hope this helps) :)
3-3k+7k=5b solve for x
Hey there!
[tex]3-3k+7k=5b[/tex]
Assuming you're trying to solve for b or k, I'll solve both.
Solve for b:
[tex]3-3k+7k=5b[/tex]
We will need to flip the equation:
[tex]5b=4k+3[/tex]
Now, let's divide both sides by 5:
[tex]\frac{5b}{5} =\frac{4k+3}{5}[/tex]
[tex]b=\frac{4}{5} k+\frac{3}{5}[/tex]
Solve for k:
[tex]3-3k+7k=5b[/tex]
Let's add -3 to both sides:
[tex]4k+3+-3=5b+-3\\4k=5b-3[/tex]
Now, let's divide both sides by 4:
[tex]\frac{4k}{4} =\frac{5b-3}{4}[/tex]
[tex]k=\frac{5}{4} b+\frac{-3}{4}[/tex]
Now, we've solved for b and k.
Hope this helps!
A student claimed that reflect a triangle in a line, translating a triangle , rotating a triangle, and reflecting it in a point result in an image that is congruent to the original( pre-image) triangle. explain why they are correct.
If we reflect a triangle in a line, translate a triangle, rotate a triangle, and reflect it in a point result in an image that will be congruent to the original( pre-image) triangle.
This is a problem from triangular geometry. We can solve this problem by following a few steps.
Here a triangle ABC is given and the triangle is at first reflected and then translated, thereafter it rotates and is later reflected.
After all, these processes the value of ∠A, ∠B, and ∠ C remains the same as usual concerning ∠A''', ∠B''', ∠ and C'', as they just changes coordinates not geometric structures.
After all these processes the length of the triangle AB, AC, BD, and A'''B''', B'''C''', C'''A''' remains the same as usual.
∵ We can conclude that ΔABC ≅ ΔA'''B'''C'''
( As AB = A'''B''', BC = B'''C''', ∠ABC = ∠ A'''B'''C''' )
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Four pencils held together with a band
Step-by-step explanation:
The length of the band is the number of units it covers
The actual length of the band is: \mathbf{40 + 10\pi}40+10π
The diameter of 1 pencil is given as:
\mathbf{d = 10}d=10
The circumference of 1 pencil is:
\mathbf{C = \pi d}C=πd
So, we have:
\mathbf{C = 10\pi }C=10π
Multiply by 4, to calculate the circumference of all pencils
\mathbf{4C =4 \times 10\pi }4C=4×10π
\mathbf{4C =40\pi }4C=40π
The rubber band covers a quarter of the 4 pencils.
So, we divide by 4
\mathbf{C = 10\pi }C=10π
The length of the band on one pencil is:
\mathbf{L = 10}L=10
Multiply by 4, for the 4 pencils
\mathbf{L = 40}L=40
So, the actual length of the band is:
\mathbf{Length = 40 + 10\pi}Length=40+10π
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What is the probability that A occurs given that B occurs ?
This is an instance of conditional probability and the formula to use is;
[tex]P(\text{AIB)}=\frac{P(A\cap B)}{P(B)}[/tex]Where:
P(A|B) = the probability of event A occurring given that event B occurred
P(A ∩ B) = the probability that both events A and B occur
P(B) = the probability of event B
[tex]\begin{gathered} P(\text{AnB)}=\frac{1}{3} \\ P(B)=\frac{2}{5} \end{gathered}[/tex][tex]P(\text{AIB)}=\frac{\frac{1}{3}}{\frac{2}{5}}=\frac{1}{3}\times\frac{5}{2}=\frac{5}{6}[/tex]Therefore, the probability that A occurs given that B occurs is 5/6
can anyone help me with these questions
Answer:
Nah
Step-by-step explanation:
The melting point of nitrogen is -210 °C. The melting point of magnesium is 650 °C.
What is the difference in melting points of the two elements?
Answer:
860 degrees
Step-by-step explanation:
-210+210=0
0+650=650
650+210=860
You plan to retire in 35 years, and would like to have 1,000,000$ in investments. How much money would you have to invest today at a 7% annual interest rate compounded daily to reach your goal in 35 years. Assume all years have 365 days round your answer to the nearest cent
Given:
You plan to retire in 35 years and would like to have 1,000,000$ in investments.
So, the time = 35 years
And A = 1,000,000
compounded daily, n = 365
Rate of the interest = r = 7% = 0.07
We will find the initial investment = P
We will use the following formula:
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]Substitute with the values of A, r, n, and t
[tex]\begin{gathered} 1000000=P\cdot(1+\frac{0.07}{365})^{365\cdot35} \\ \end{gathered}[/tex]Solve the equation to find P
[tex]\begin{gathered} 1000000=P\cdot11.5856 \\ \\ P=\frac{1000000}{11.5856}=86,313.86 \end{gathered}[/tex]So, the answer will be $86,313.86
Max is designing a hot tub for a local spa.
He wants the hot tub to have a diameter of 90 inches, what is the approximate area required for the installation of the hot tub? (Use 3.14 for.)
The area of the hot tub to be installed for local spa is 6358.5 in².
What is defined as the circle?A circle is a round figure with no corners as well as edges.A circle is defined in geometry as a closed, double curved shape.The center of the a circle is the point in a circle where all distances to the circle's points are equal. This distance is known as the circle's radius.The diameter of a circle is a line segment that passes through center of a circle and has its endpoints just on circle.Diameter = 2 × radiusFor the given question;
The diameter of the hot tub to be installed for local spa is 90 inches.
Then, radius is 90/2 = 45 inches.
The area of the circle is;
Area = πr²
Where, π = 3.14
Put the values;
Area = 3.14×45²
Area = 6358.5
Thus, the area of the hot tub to be installed for local spa is 6358.5 in².
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M
Given the diagram below, solve for x.
X%
87° 87°
Xº
87
N
Acute Geometry Class, 2021
The angle x= 33 degree.
What is an angle?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "" is used to denote angles. The Greek letter,,, etc. can be used to represent the angle measurement between the two rays. If different types of angles, such as a positive angle and a negative angle.
Positive Angle: If angle goes in counterclockwise, then it is called a positive angle.
Negative Angle: If angle goes clockwise direction, then it is called a negative angle.
360= 87*3+3x
360-261=3x
33=x
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are lines AC and DF parallel explain
Answer:
yes
Step-by-step explanation:
ac goes straight forever and df does straight forever and they are parallel
Help!! i’ll give brainlest
The equivalent expression is 54 divided by 18, and the quotient is 3.
A car rental service charges an initial fee of $250 and 25$ for every hour using the car. If a customers bill totals $1,275 then how long did they rent the car for?
======================================================
Explanation:
x = number of hours
y = total cost
The equation is y = 25x+250 since 250 is the initial cost, aka y intercept, and 25 is the slope telling us how much the cost goes up per hour (aka rate of change).
I recommend making a table of values to help see how/why that equation works out.
Plug in y = 1275 and isolate x.
y = 25x+250
1275 = 25x+250
1275-250 = 25x
1025 = 25x
25x = 1025
x = 1025/25
x = 41 hours
----------------
Check:
If the customer rents the car for 41 hours, then they pay 25*41 = 1025 dollars on top of the initial fee of $250.
The total cost is therefore 1025+250 = 1275 dollars to confirm the answer.
----------------
Extra info:
41 hours = 24 hours + 17 hours = 1 day + 17 hours
41 hours = 41/24 = 1.70833 days approximately
1.2x10-8 x 4.0×10-3
Scientific Notation
Answer:
−3.11×10^2
Step-by-step explanation:
standard to intercept form
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + 1[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 5y - 6x = 5[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 5y = 6x + 5[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + \frac{5}{5} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
3. At a carnival, of the games cost $1. Another 2.5% of the games cost $2. What
percent of the games do not cost $1 or $2?
Percent of the games do not cost $1 or $2 is 35%.
What is percentage?
A fraction of a number out of 100% is referred to as a percentage, sometimes known as a percent. Percentage refers to a portion of a total amount and signifies "per 100." For instance, 45% signifies 45% of the total or 45 out of 100.
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
Given,
games = 58
5/8 is 62.5%
2.5% + 62.5% = 65%
100%-65% = 35%
A third of the games (35%) are free.
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Complete question -
At a carnival, 58 of the games cost $1. Another 2.5% of the games cost $2. What percent of the games do not cost $1 or $2?
What’s the term for 5 _ 13
The nth term for the given series is given by 4n-3.
What is meant by series?
The fundamental concepts in mathematics are series and sequence. A series is the total of all elements, but a sequence is an ordered collection of elements for which repetitions of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression. A series can be finite or infinite in length and has a length that corresponds to the number of terms.The number series is 1, 5, 9, 13, 17,...
Common deviation (d)=5-1=4
A=1 is the first phrase.
A+(n1)d=1+(n1) is the formula for the nth term.
4=4n−3
∴tn =4n−3
The nth term for the given series is given by 4n-3.
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A study on the average minutes spent by students on internet usage is 300 with a standard deviation of 102. Answer the following questions assuming a bell-shaped distribution and using the empirical rule. What percentage of students use the internet for more than 402 minutes?.
The percentage of students that use the internet for more than 402 minutes = 16%
Percentage
Percentage, often referred to as percent, is a fraction of 100. Percentage means "per 100," and denotes part a total amount. For example, 45% represents 45 out of 100.
calculate the percentage-
The empirical rule states that
68% of the population lies within 1 standard deviation of the mean
95% of the population lies within 2 standard deviations of the mean
99.7% of the population lies within 3 standard deviations of the mean
Standard Deviation
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
The percentage will be illustrated in this:
P(X > 402) = P(X > 30 + 1 × 102)
= (1-0.68) / 2
= 0.32/2
= 16%
The percentage of students that use the internet for more than 402 minutes = 16%.
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Help me out please :))
Answer:
The answer is C
Step-by-step explanation:
4.7.4 pt. 2 Modeling Pumpkin launch, we were covering graphs of quadratic functions please help! Thank you, all the info you need is on part 1 on my account
Considering that the pumpkin is on the ground at x = 0 and x = 50, it is found that:
5. The roots of the quadratic function are: r1 = 0, r2 = 50.
6. The function is written as follows: y = a(x - 0)(x - 50).
7. The leading coefficient is a = -0.0992.
8. The function is: y = -0.0992(x - 0)(x - 50).
9. Applying the distributive property, the function is: y = -0.0992(x² - 50x).
10. The graph is given at the end of the answer.
Building a quadratic function from it's rootsA quadratic function of roots x' and x'' is defined as follows:
y = a(x - x')(x - x'').
In the context of this problem, the roots are the values of x when the pumpkin is on the ground, hence:
x' = 0, x'' = 50.
Hence, considering the roots, the function is written as:
y = a(x - 0)(x - 50).
The maximum height obtained by the pumpkin is of 62 feet, after a horizontal distance of 25 feet(mean of the roots), hence the vertex is given by these following coordinates:
(25, 62)
The coordinates are used to find the value of a, which is the leading coefficient of the function, as follows:
62 = a(25² - 50 x 25)
62 = -625a
a = -62/625
a = -0.0992.
Then the equation is written as:
y = -0.0992(x - 0)(x - 50).
The distributive property means that the outer term multiplies each the inside terms, and then the common terms are added, hence the function is:
y = -0.0992(x² - 50x).
Which is sketched at the end of the answer.
Missing informationThe pumpkin is on the ground when x = 0 and x = 50.
The maximum height obtained by the pumpkin is of 62 feet, after a horizontal distance of 25 feet.
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Find the multiplicative inverse of −1 x -3/10.
Step-by-step explanation:
-1 × -3/10
=> 3/10
Multiplicative Inverse/Reciprocal of 3/10 = 10/3
Which equation represents a proportional relationship? responses 14x y=10 fraction 1 over 4 end fraction x plus y equals 10 y=14x y equals fraction 1 over 4 end fraction x y=13x 1 y equals fraction 1 over 3 end fraction plus 1 i don't know.
We identify the proportional relationship because it does not have a constant term, the correct option is:
y = (1/4)x
Which equation represents a proportional relationship?
A proportional relationship between two variables x and y is written as:
y = k*x
Where k is called the constant of proportionality.
Here the options are:
(1/4)x + y = 10 (this is a linear equation)y = (1/4)*x (this is a proportional relation)y = (1/3)*x + 1 (this is a linear equation)The only option that has not a constant term is the second one:
y = (1/4)*x
And that is the proportional relationship.
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Answer:
y=(1/4)x
Step-by-step explanation:
I took the test :)
can someone please help?
Answer:
No
Step-by-step explanation:
Write the equation of each parabola in vertex form
Answer: 9. y=[tex](x+4)^2-3[/tex]
10. y=[tex]-(x-5)^2+5[/tex]
11. y=[tex](x-2)^2+1[/tex]
12. y=[tex]x^2-3[/tex] or y=[tex](x-0)^2-3[/tex]
Step-by-step explanation:
Which point would describe the rate of change for the line modeled by y = 4/3x+2?
A. Vertical change of 2 units for each horizontal change of 1 unit
B. Vertical change of 1 unit for each horizontal change of 2 units
C. Vertical change of 4 units for each horizontal change of 3 units
D. Horizontal change of 4 units for each horizontal change of 3 units
The point which describe the rate of change for the line modeled by y = 4/3x+2 would be; C. Vertical change of 4 units for each horizontal change of 3 units
How to find the rate of change of a linear equation?Suppose that the considered linear equation is of the form y=mx+c
Then, when we change x by 1 unit, then:
[tex]y + \delta y = m(x + 1) + c\\mx + c + \delta y = mx + c + m\\\delta y = m[/tex]
where [tex]\delta y[/tex] shows the change in y as x changes by 1 unit.
It is found that this change is the value of 'm' called slope of the line this equation represents (each linear equation represents a line).
We have been given that the line modeled by y = 4/3x+2
The slope is given as m = 4/3
The point which describe the rate of change for the line modeled by y = 4/3x+2 would be;
C. Vertical change of 4 units for each horizontal change of 3 units
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an ice cream cone has a diameter of 8 cm and a slant height of 8.4 cm. find the lateral surface area of the cone. use 3.14 for π. round your answer to the nearest tenth.
an ice cream cone has a diameter of 8 cm and a slant height of 8.4 cm. find the lateral surface area of the cone then The lateral surface area of the cone is 105.2 cm².
What is lateral surface area?
The lateral surface area is the area of all the sides of a 3-dimensional object excluding its base and top.
Lateral surface area = πr√(h² + r²)
Where:
π = pi = 3.14
r = radius = 8/2 = 4cm
h = √8.4² - 4² = 7.38
3.14 x 4 x √(7.38² + 4²)
= 105.4 cm
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Describe all the x-values within or including a distance of the given value.
(Enter your answer using interval notation.)
Distance of 2 units from the number 7
The range of values, in interval notation is [-6,14] .
What is interval notation in math?
Continuous sets of real numbers can be represented by the integers that bound them using interval notation. When written, intervals resemble ordered pairs in several ways. They don't necessarily indicate a particular point, though. They are intended to serve as a shortened manner of expressing an inequality or system of inequalities.the values with a distance of 10 units from 4.
Maximum value to the right, 10 units from 4 is 4+10 = 14
Maximum value to the left, 10 units from 4 is 4 - 10 = -6
So, all the range of values, in interval notation is [-6,14]
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Justin has nine fudge popsicles.
He sells two popsicles to Sidney and three to Doryin.
What fraction of popsicles does Justin have left to eat?
Justin has sold 5 popsicles so from the original 9 if we take away 5, he has 4 popsicles left to eat.
1. You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week. How long
will it be before you and your sister have the same amount of money? Write an equation and solve.
It will take 30 weeks to have to have the same amount of money as my sister if I have $60 and my sister has $120. I am saving $7 per week and my sister is saving $5 per week.
How to write equation?A mathematical sentence that uses the equal sign, =, to show that two expressions are equal is known as an equation. Look for key words or phrases such as "is," "the same as," or "equals" to determine where to place the equal sign when writing a word sentence as an equation. Make an equation out of the word sentence.
What is equation?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.
The given condition,
You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week.
Let x be the time period in weeks. So we need same amount of money.
60+7x=120+5x
This is the equation needed.
2x=60
x=30 weeks
If I have $60 and my sister has $120, it will take 30 weeks for me to have the same amount of money as my sister. I save $7 per week, and my sister saves $5 per week.
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URGENT PLEASE HELP
A triangle is translated 6 units left and then dilated by a factor of 0.5.
Which statement about the triangle's image and pre-image is correct?
A) The image and pre-image are congruent figures because one of the transformations is a rigid transformation, and the other
is not.
B) The image and pre-image are congruent figures because both transformations are rigid transformations.
C) The image and pre-image are not congruent figures because one of the transformations is a rigid transformation, and the
other is not.
D) The image and pre-image are not congruent figures because both transformations are rigid transformations.
A triangle is translated 6 units left and then dilated by a factor of 0.5. the statement about the triangle's image and pre-image that is correct is: The image and pre-image are not congruent figures because one of the transformations is a rigid transformation, and the other is not.
What is a rigid transformation?Transformation is a term that refers to movement of an image from one position to the other.
When the intervals or distances between the points of the image being moved is not altered then the transformation is rigid transformation. However when the interval is altered it is a rigid transformation.
Translation is a rigid transformation while dilation is a non rigid transformation.
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Answer for both A, B, and C. Need help asap!!! Giving brainliest.
Answer:
Step-by-step explanation:
Question a: Solve for c
0.9c = 17.01 - 18.9r
c = 17.01-18.9r/0.9
c = 18.9 - 2.1r
Question b: Solve for r
18.9r = 17.01-0.9c
r = 9 - [tex]\frac{0.9}{18.9}[/tex]c
r = -10/21c + 9
(0.9/18.9 = 10/21)
Question c:
It will be best to use the equation that solves for c because this helps us determine how much chicken is bought.
c = 18.9 - 2.1r
Substitute r with 3.25
c = 18.9 - 2.1(3.25)
c= 18.9 - 6.825
c = 12.075