The translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.
What is translation and reflection?
In mathematics, the translation shift the coordinates either on the horizontal axis or on the vertical axis. It compress the expression also. Similarly, in reflection, the expression get reflected on the coordinate axis either on the upper side or downward side.
According to the question, the given expression for the translation as well as for the reflection are as follows:
h(x)=a |b(x) + c| + d
g(x)=1/3 | x + 3| - 4
And the given condition state that the translation is for 7 units and reflection is on the y-axis. Translation shift the expression and reflection reflects the expression.
Translation expression: h(x+7)=a |b(x+7) + c| + d
Reflection expression: g(-x)=1/3 | -x + 3| - 4 = 1/3 | x + 3| - 4
Therefore, the translation shift the coordinates of the expression in the right side. And there is no change in the reflection based equation because of the absolute symbol.
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team A and team B play in a competition
team A has twelve more points than team B
team A has five times as many points as team B
how many points does each team have
Answer:
A = 15
B = 3
Step-by-step explanation:
Since Team A has 12 more points than team B, then,
A - 12 = B
A = B + 12 ( equation 1 )
team A has 5 times as many points as team B, so,
5B = A. ( equation 2 )
Substitute equation 1 into equation 2
A = B + 12
5B = B + 12
5B - B = 12
4B = 12
B = 3
we'll substitute the answer into equation 2
5B = A
5(3) = A
A = 15
I hope this helps :D
have a nice day dear...
The measures of the angles of a triangle are shown in the figure below. Solve for x.
74°
(8x-19)°
45°
Answer:
x = 10
Step-by-step explanation:
The internal angles of a triangle sum 180°
74° + 45°+ (8x-19)° = 180°
119 + 8x - 19 = 180
119 - 19 + 8x = 180
100 + 8x = 180
8x = 180 - 100
8x = 80
x = 80/8
x = 10
Check:
74 + 45 + (8x-19) = 180
1100 + 8*10 = 180
100 + 80 = 180
Charis invested 140$ . She earned a simple interest of 3%per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charis received at the end of two years?
The amount of interest would be $8.4 Charis received at the end of two years.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
We have been given data as:
Principal (P) = $140
Rate of Interest (R) = 3% = 3/100 = 0.03
Time (T) = 2 years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
⇒ Simple interest = 140 × 0.03 × 2
⇒ Simple interest = $8.4
Therefore, the amount of interest would be $8.4 Charis received at the end of two years.
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HELP
A toy rocket is launched from a 2.1 m high platform in such a way that its height, h (in meters), after t seconds is given by the
equation h = -4.9t² + 14.0t+2.1. How long will it take for the rocket to hit the ground?
Answer:
3 seconds
Step-by-step explanation:
The height of the rocket when it hits the ground will be zero meters.
Therefore, set the equation to zero and solve for t by using the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Given equation:
[tex]-4.9t^2+14t+2.1=0[/tex]
Therefore:
[tex]a=-4.9, \quad b=14, \quad c=2.1[/tex]
Substitute the values into the quadratic formula:
[tex]\implies t=\dfrac{-14 \pm \sqrt{14^2-4(-4.9)(2.1)}}{2(-4.9)}[/tex]
[tex]\implies t=\dfrac{-14 \pm \sqrt{196+41.16}}{-9.8}[/tex]
[tex]\implies t=\dfrac{-14 \pm \sqrt{237.16}}{-9.8}[/tex]
[tex]\implies t=\dfrac{-14 \pm15.4}{-9.8}[/tex]
Therefore:
[tex]\implies t=\dfrac{-14 +15.4}{-9.8}=\dfrac{1.4}{-9.8}=-\dfrac{1}{7}[/tex]
[tex]\implies t=\dfrac{-14-15.4}{-9.8}=\dfrac{-29.4}{-9.8}=3[/tex]
As time is positive, t = 3 s only.
Therefore, it will take 3 seconds for the rocket to hit the ground.
x^5/x^2 can be simplified to what
Answer:
x^3
Step-by-step explanation:
Because they are the same base in a division question, you subtract the exponents.
5-2=3.
Answer = x^3
Hope this helps!
Btw, if this is right, please give me brainliest, thanks!
Answer:
x^3
Cancel the common factor of x^5 and x^2.
Hope you have a wonderful day :)
Using the Pythagorean theorem! Need to be in simplest radical form
The simplest radical form of the hypotenuse of the given right-angled triangle is therefore discovered to be [tex]6\sqrt{2}[/tex] units.
What is the theory of the Pythagorean Theorem?The Pythagorean Theorem states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the triangle's legs.
A simplest radical form is defined as what?If the number or algebraic expression under the radical has no factors that are perfect nth powers, then the radical is said to be in its simplest radical form.
The given right angled triangle has sides 6 units each.
We need to determine the hypotenuse using the Pythagorean theorem.
Hypotenuse = [tex]\sqrt{(side 1)^{2} + side 2)^{2} }[/tex]
[tex]=\sqrt{6^{2} + 6^{2} } \\\\= \sqrt{72}\\ \\= 6\sqrt{2}[/tex]
Therefore, the hypotenuse of the given right angled triangle is found to be [tex]6\sqrt{2}[/tex] units which is the simplest radical form.
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HELP PLS IM MARKING BRAINLEIST
The formula for the volume of a sphere is 4/3πr³. The formula for r is d/2. We know d, so we can substitute this for r.
4/3(3.14)(32/2)^3
4/3(3.14)(16)^3
4/3(3.14)4096
4.19(4096
17612.24 cm^3
[tex]\huge\boxed{\sf 17157.28} \\\\\\\displaystyle \sf Converting\ the\ diameter\ to\ radius\\\\r=\frac{d}{2} =\frac{32}{2} =16\\\\Finding\ the\ volume \\\\V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times 16^{3} \approx 17157.28 \\\\[/tex]
Which of the following is a correct way to solve 4 = 13 – 3x ?
A. 4 + 13 = 13 - 3x + 13. 17 = -3x. 17/-3 = -3x/-3. x = -17/3.
B. 4 - 13 = 13 - 13 - 3x. -9 = -3x. -9/-3 = -3x/-3. x = 3.
C. 4 - 13 = 13 - 13 - 3x. -9 = -3x. -9/-3 = -3x/-3. x = -3.
D. 4 - 13 = 13 - 13 - 3x. -9 = -3x. -9/3 = -3x/3. x = -3.
The solution of the equation 4 = 13 – 3x is x = 3 which is the correct answer would be an option (B).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
We have been given an equation as
4 = 13 – 3x
Rearrange the terms non-variables and variables,
3x = 13 - 4
Apply the subtraction operation,
3x = 9
x = 9/3
Apply the division operation, and we get
x = 3
Therefore, the correct answer would be an option (B).
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help i need help with this question
guys please help ive been trying to figure it out for like an hour. i need to khow whats the value of x khowing that the perimeter is 51 cm
Answer:
x=4
Step-by-step explanation:
first, you have to add all of the sides up:
x+2x+x+3x+7+5x-4=12x+7-4=12x+3
12x+3=51. now, we can subtract 3 from both sides, so that we can isolate x.
-3 -3
12x=48
x=4
A stadium has 52,000 seats. Seats sell for $28 in Section A, $24 in Section B, and $20 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium
takes in $1,307,200 from each sold-out event. How many seats does each section hold?
Section A holds seats.
The number of seats in Section A is 26000 ,The number of seats in Section B is 14800 and, The number of seats in Section C is 11200.
What is a equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
Let the number of seats in Section A is "a".
Let the number of seats in Section B is "b".
and, Let the number of seats in Section C is "c".
Now using the statement "stadium has 52,000 seats"
we can make equation: a + b + c = 52000
Now using the statement "Seats sell for $28 in Section A, $24 in Section B, and $20 in Section C" and "stadium takes in$1,307,200 from each sold out event".
we can make equation: 28a + 24b + 20c = $1,307,200
Now using the statement "he number of seats in Section A equals the total number of seats in Sections b and C"
we can make equation: a = b + c
Solving these three equations. We get,
a = 26000 , b = 14800 and c = 11200
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Solve and graph the solutions of the inequality - |x - 2| + 9 > 6.
i solved it
you graph it :)
Need help pls y’all will help me
The correct description regarding each table is given as follows:
1. Rate of change of 4, linear.
2. Rate of change of -2/3, linear.
3. Rate of change of 1/4, linear.
4. Rate of change of -1, linear.
5. Not linear.
6. Rate of change of 3, linear.
Linear functionsA linear function has the definition presented as follows:
y = mx + b.
In which:
m is the slope, which is the constant rate of change.b is the y-intercept.A data-set will only be classified as linear if the rate of change is constant.
Hence the tables in this problem are classified as follows:
Table 1: Linear, as for each two points, the change in the output y divided by the input x has a result of 4, which is the rate of change.Table 2: Linear, as for each increase of 3 in x, there is a decay of 2 in y, hence the rate of change is of -2/3.Table 3: Linear, as for each increase of 4 in x, there is a increase of 1 in x, hence the rate of change is of 1/4.Table 4: Linear, as for each increase of 1 in x, there is a decay of 1 in y, hence the rate of change is of -1.Table 5: Not Linear, as from x = 1 to x = 2 an increase of 1 in x resulted in a an increase of 2 in y, while from x = 2 to x = 3 an increase of 1 in x resulted in a an increase of 4 in y.Table 6: Linear, as an increase of 2 in x results in an increase of 6 in y, hence the rate of change is of 6/2 = 3.Learn more about linear functions at https://brainly.com/question/24808124
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can someone help with my homework? Thank you !
Answer:
1000-0=1/2(2000-0)
y= 1/2x
-1x + 2y = 0
A cylindrical hollow metal pipe is 16 cm long.
It has an external diameter of 10 cm and an internal diameter of 8 cm.
The density of the metal from which the pipe is made is 8 grams per cm3
What is the mass of the pipe in grams?
Answer:
3617.28 grams
Step-by-step explanation:
Find the volume of the metal as following:
[tex]V_{metal}=V_{external}-V_{internal}[/tex][tex]V_{external} = \pi d_{external}^2h/4=\pi *10^2*16/4=1256[/tex] cm³[tex]V_{internal} = \pi d_{internal}^2h/4=\pi *8^2*16/4=803.84[/tex] cm³[tex]V_{metal}=1256-803.84 = 452.16[/tex] cm³Find the mass:
[tex]mass = volume*density[/tex][tex]mass = 452.16*8=3617.28[/tex] gramsAnswer:
3619.1 grams (nearest tenth)
Step-by-step explanation:
Volume of a cylinder
[tex]V=\pi r^2 h[/tex]
where:
r is the radius.h is the height.The radius of a circle is half its diameter.
Find the volumes of the external and internal cylinders by substituting the given values into the formula for volume of a cylinder:
[tex]\implies \textsf{Volume of the external cylinder}&=\pi \cdot 5^2 \cdot 16=400 \pi \; \sf cm^3[/tex]
[tex]\implies \textsf{Volume of the internal cylinder}&=\pi \cdot 4^2 \cdot 16=256 \pi \; \sf cm^3[/tex]
Find the volume of the cylindrical hollow metal pipe by subtracting the volume of the internal cylinder from the volume of the external cylinder:
[tex]\begin{aligned}\implies \textsf{Volume of the metal pipe}&=\sf Volume_{external}-Volume_{internal}\\&=400 \pi - 256 \pi\\& = 144 \pi \sf \; cm^3\end{aligned}[/tex]
Density formula
[tex]\rho=\dfrac{m}{V}[/tex]
where:
ρ = densitym = massV = volumeGiven:
ρ = 8 g/cm³V = 144π cm³Substitute the given values of density and the found volume into the density formula and solve for m:
[tex]\begin{aligned}\implies \rho&=\dfrac{m}{V}\\8&=\dfrac{m}{144 \pi}\\m&=8 \cdot 144\pi\\m&=1152 \pi \\m&=3619.11473...\\m&=3619.1\; \sf g \;(nearest\;tenth)\end{aligned}[/tex]
Therefore, the mass of the pipe is 3619.1 grams (nearest tenth).
Note: I have used the exact value of π (not a rounded value).
Please help!
Choose the mathematical sentence that most accurately expresses the
information in the problem, and would be most helpful in solving it.
After taking 4 pieces of fruit out of a bag, 12 pieces of fruit remained. How
many pieces of fruit were in the bag to start?
A. 12 + f = 4
B. 12 ÷ f = 4
C. 4+ f = 12
D. 12 - 4 = f
E. F ÷ 4 = 4
F. F - 4 = 12
Answer:
Option F
F - 4 = 12Step-by-step explanation:
According to given information
1) You had F fruits and took 4 pieces out of a bag, it is:
F - 42) Then you have 12 pieces of fruit remained:
F - 4 = 12This equation matches the answer choice F.
What’s x??
Solve for x
5x+2=7x-4
Answer:
x = 3
Step-by-step explanation:
[tex]{ \rm{5x + 2 = 7x - 4}}[/tex]
- First, using equality order by collecting like terms of x together and constants together;
Using subtraction property of equality on constant 2 [subtracting 2 from both sides][tex]{ \rm{(5x + 2) { \green{- 2}} + = (7x- 4){ \green{ - 2}}}} \\ { \rm{5x = 7x - 6}}[/tex]
Using subtraction property of equality on term 7x [subtracting 7x from both sides][tex]{ \rm{5x - { \blue{7x}} = (7x - 6) - { \blue{7x}}}} \\ { \rm{ - 2x = - 6}}[/tex]
- Using division property of equality, by dividing -2 on both sides;
[tex]{ \rm{ \frac{ - 2x}{ \orange{ - 2}} } = \frac{ - 6}{ \orange{ - 2}} } \\ \\ { \rm{x = 3}}[/tex]
[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \mathfrak{ \: \: creed}}}[/tex]
Answer:
x = 3Step-by-step explanation:
What’s x??
Solve for x
5x+2=7x-4
2 + 4 = 7x - 5x
6 = 2x
x = 6 : 2
x = 3
--------------
check
5 * 3 + 2 = 7 * 3 - 4
17 = 17
the answer is goodGiven the domain (-5,-1,3,5) find the first number in the range of the function f(x)=-2x -3 .
The first number in the range of the function is 7
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the range of the function?The function is given as
f(x) = -2x - 3
Also, we have the domain to be
(-5,-1,3,5)
The first value in this domain is
x = -5
So, we have
f(-5) = -2 x -5 - 3
Evaluate
f(-5) = 7
This represents the first number in the range
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please help me find how many solutions there are
Answer:
A. No solutionStep-by-step explanation:
Use a distributive property.
Distributive property:
A(B+C)=AB+AC
A(B-C)=AB-AC
First, expand by distributive property from multiply the numbers from left to right.
-9j=-9(j-20)
-9(j-20)
-9*j=-9j
9*20=180
=-9j+180
-9j=-9j+180
Add by 9j from both sides.
-9j+9j=-9j+180+9j
Solve.
0=180
No solution.
Therefore, the correct answer is A. no solution.
I hope this helps, let me know if you have any questions.
Carlson Middle School has a total of 500 students in sixth, seventh, and eighth grades. The table below shows the number of students in each grade.
Grade Number of Students
Sixth 203
Seventh 126
Eighth 171
The principal randomly selects 25 students to receive a free school lunch today. What is the most likely number of sixth graders in the group of 25 selected by the principal?
There is also a picture down below
Answer: Around 10 sixth graders would get free lunch.
Step-by-step explanation: first, divide 500/25 to find the percentage of students receiving free lunches. You should get 0.05, or 5%. Then, multiply the number of sixth graders (203) by 5%. Your answer is 10.15, rounded down to 10. (Because it is impossible to have 0.15 of a student)
8 is 20% of what number?
Answer: 40
Step-by-step explanation:
Which relation represents a function?
The relation that represents a function is the mapping in: B.
How to Determine if a Relation is a Function?A relation is defined as a function if each of the x-value (domain element of input) in the relation corresponds to exactly one y-value (range element of output).
The relation in option A is not a function because it has two different y-values, 7 and 5 that corresponds to an x-value, 6. The relations in option C and D do not represent a function also.
The mapping in option B shows a relation where each x-value (domain element) is related or corresponds to only one y-value (range element). Therefore, it is a function.
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Rewrite with Common Denominator
-⅗ + -7/10
By multiplying 2 on both the numerator and denominator of [tex]\frac{-3}{5}[/tex] .
The expression [tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] with a common denominator can be written as
[tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]
What is a fraction?A fraction is written with a numerator and a denominator where the numerator is less than the denominator.
Example: 1/3 is a fraction
We have,
[tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex]
We have different denominators and we need to make the denominator the same.
We will multiply 2 on both the numerator and denominator of [tex]\frac{-3}{5}[/tex].
= [tex]\frac{2 \times -3}{2 \times 5}[/tex]
= [tex]\frac{-6}{10}[/tex]
We see that,
The denominator in [tex]\frac{-6}{10}[/tex] and [tex]\frac{-7}{10}[/tex] is the same.
i.e 10.
Now,
[tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] can be written as [tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]
Thus,
By multiplying 2 on both the numerator and denominator of [tex]\frac{-3}{5}[/tex] .
The expression [tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] with a common denominator can be written as
[tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]
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The number of ounces of chocolate chips per batch of cookies can be represented with the equation y = 8x, where y represents ounces of chocolate chips and x represents batches of cookies.
Determine how many batches of cookies can be made using 28 ounces of chocolate chips.
3.5 batches
8 batches
36 batches
224 batches
Answer: 3.5 batches is correct.
Step-by-step explanation: Take 28 and divide that by 8 and that equals 3.5
Hope this helps!
The number of batches of cookies that can be made using 28 ounces of chocolate chips is 3.5 batches.
The correct answer option is option a
How to find number of batches of cookies can be made using 28 ounces of chocolate chips?Equation:
y = 8x
Where,
y = ounces of chocolate chips and x = batches of cookiesIf there are 28 ounces of chocolate chips:
y = 8x
28 = 8 × x
28 = 8x
divide both sides by 8x = 28/8
x = 3.5 batches
So therefore, the
So therefore, 3.5 batches of cookies can be made using 28 ounces of chocolate chips.
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Lloyd is making a bouquets of flowers. He has 25c roses and 15v snapdragons.he divides flowers equally to make as many bouquets as possible . He uses all the flowers .what number snapdragons are in beach bouquet.
Answer:
A. 3
Step-by-step explanation:
45 + 15 + 25 = 85
There are 85 flowers.
There are 25 roses, 45 tulips, an 15 roses.
What are all 3 of these divisible by?
5!
That means that there will be 5 bouquets.
Let's divide each number by 5 to find out how many of each type of flower is in each bouquet.
25/5 = 5
5 roses in each bouquet
45/5 = 9
9 tulips in each bouquet
15/5 = 3
3 snapdragons in each bouquet
5 + 9 + 3 = 17
There are a total of 17 flowers in each bouquet.
Out of those 17 flowers, 3 are snapdragons.
A. 3
It takes 200 coins to get a bag upgrade in Pokémon Go. The creators decided to throw a sale on bag upgrades. For one day only anybody can upgrade their bag for 125 coins. Find the percent of change
price change: 125 - 200 = -75 coins
percent of change = price change/original price *100 = -75/200*100 = -37.5%
that is, a discount of 37.5%
The results of a survey about what 432 students would like as a career are shown below use the graph
We have in total 432 students.
8.
We know that 23% of the students want to be a teacher, this means that:
[tex]432\cdot0.23=99[/tex]99 students want to be a teacher.
9.
We know that 13% of the students want to be doctor or nurses, this means that 26% of them want to be one of those, then:
[tex]432\cdot0.26=112[/tex]112 students want to be doctor or nurses.
10.
Since 9% of the students want to be lawyers, this means that 91% of them did not want to be lawyers, then:
[tex]432\cdot0.91=393[/tex]393 students does not want to be lawyers.
Answer:
393 students do not want to be lawyers.
Step-by-step explanation:
What’s x??
Solve for X
5x-9=3x+3
Answer:
x = 6
Step-by-step explanation:
5x - 9 = 3x + 3 ( subtract 3x from both sides )
2x - 9 = 3 ( add 9 to both sides )
2x = 12 ( divide both sides by 2 )
x = 6
Which of the following whole numbers are perfect squares? (Please select ALL correct answers for full credit).
Answer: 9, 144, 225, 10,000
Step-by-step explanation:
9=3x3
144=12x12
225=15x15
10,000=100x100
The enrollment for a school in 2010 was 1245 students. in 2020, the enrollment was 715 students. find and interpret the rate of change in enrollment from 2010 to 2020
The rate of change in enrollment from 2010 to 2020 is -53 students per year.
Interpretation:
A negative rate of change (-53 students per year) means that the enrollment in the school decreased over the 10-year period from 2010 to 2020. On average, the school lost 53 students per year during this time frame. This decline in enrollment may have implications for the school's resources, budget, and programs, as it indicates a reduction in the student population over the given period.
Here, we have,
To find the rate of change in enrollment from 2010 to 2020, we can use the formula for calculating the rate of change:
Rate of change = (Change in enrollment) / (Time interval)
Where:
Change in enrollment = Enrollment in 2020 - Enrollment in 2010
Time interval = Year in 2020 - Year in 2010
Let's calculate the rate of change:
Change in enrollment = 715 - 1245 = -530
Time interval = 2020 - 2010 = 10 years
Rate of change = (-530) / 10 = -53
The rate of change in enrollment from 2010 to 2020 is -53 students per year.
Interpretation:
A negative rate of change (-53 students per year) means that the enrollment in the school decreased over the 10-year period from 2010 to 2020. On average, the school lost 53 students per year during this time frame. This decline in enrollment may have implications for the school's resources, budget, and programs, as it indicates a reduction in the student population over the given period.
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