The factored expression of the expression given as 12b - 30 is 6(2b - 5)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to factor the expression by grouping?The expression is given as
12b - 30
Factor out the common factor from the expression
So, we have
12b - 30 = 3 * 4b - 3 * 10
Factor out 3 from the expression
So, we have
12b - 30 = 3(4b - 10)
Factor out 3 from the expression
So, we have
12b - 30 = 6(2b - 5)
The expression above cannot be further simplified
This means that the expression has been completely factored and cannot be further factored
Hence, the equivalent expression of the expression given as 12b - 30 when it is factored by grouping is 6(2b - 5)
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Find the value of x so that the line m is parallel to line n. Need answers
○ 35
○ 30
○ 40
○45
I really need help I hate Sparx maths
Answer:
[tex]x=\dfrac{1}{5}, \quad y=6[/tex]
Step-by-step explanation:
Given equations:
[tex]\begin{cases}y=10x+4\\2y+5x=13\end{cases}[/tex]
To solve the given equations by substitution, substitute the first equation into the second equation and solve for x:
[tex]\begin{aligned}\textsf{Equation 2}: \quad 2y+5x&=13\\\\y=10x+4 \implies 2(10x+4)+5x&=13\\20x+8+5x&=13\\25x+8&=13\\25x+8-8&=13-8\\25x&=5\\\dfrac{25x}{25}&=\dfrac{5}{25}\\x&=\dfrac{1}{5}\end{aligned}[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\begin{aligned}\textsf{Equation 1}: \quad y &=10x+4\\\\x=\dfrac{1}{5} \implies y&=10\left(\dfrac{1}{5}\right)+4\\y&=\dfrac{10}{5}+4\\y&=2+4\\y&=6\end{aligned}[/tex]
Therefore, the solution to the equations is:
[tex]x=\dfrac{1}{5}, \quad y=6[/tex]
Enter values to complete the table below.
For the given values of x and y, the value of y/x (that represents the slope of the equation) = 3/1, 3/1, 3
What does slope mean in math?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
Given are the values of the x and y
y/x represents the slope of the equation,
for x = -1 and y = -3,
y/x = 3/1
for x = 1 and y = 3
y/x = 3/1
for x = 2 and y = 6
y/x = 6/2 = 3
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You are working on a food budget for your family for the week. You know that you typically spend $90 at the grocery store, and you spend about $40 each time you go out to eat as a family. The graph of the relationship between the number of times you go out to eat and the total weekly budget for food is below.
Given the following question:
The family spends 90 dollars at a grocery store each week
The family spends 40 dollars each time they go out to eat.
Part one:
[tex]40\times4=160+90=250[/tex]If the family goes out to eat four times they would have spent 250 dollars.
Part two:
The final point on the graph is (6, 330)
Which means if the family goes out six times, the budget is 330 dollars.
So, your answer is 6.
[tex]6\times40=240+90=330[/tex]A window for a new house is shown. How many squares feet or glass does the window require? Enter your answer in the box
ANSWER
[tex]14.4ft^2[/tex]EXPLANATION
To find the number of square feet the window requires, we have to find the area of the shape.
The shape given is a kite, and the area of a kite is:
[tex]A=\frac{pq}{2}[/tex]where p and q are the diagonal lengths.
From the question given:
[tex]\begin{gathered} p=3.2+4 \\ p=7.2\text{ ft} \\ q=2+2 \\ q=4\text{ ft} \end{gathered}[/tex]Therefore, the area of the kite is:
[tex]\begin{gathered} A=\frac{7.2\cdot4}{2} \\ A=14.4ft^2 \end{gathered}[/tex]That is the number of square feet of glass that the window requires.
hello i need help on this
A rational number is a number that can be expressed as a ratio of two integers. Integers can be positive or negative. Rational numbers are simply fractions. For example;
-5/2, -1/5, 3/1, 4/5 etc are all rational numbers because we can write them as a ratio of two integers.
Since some of this fractions can lead to both negativa and positive integers, hence rational number is a positive or negative whole number including 0.
Hence all the options are correct since rational numbers are are also repeating decimals
We can think of 3÷1/4 as the answer to the question " How many groups of 1/4 are in 3?" The tape diagram represents this situation. What is the answer to the question.A:12B:6C:9D:3
The length of the tape is 3 and it is divided into equal parts or groups. The length of each group is 1/4. This means that the number of groups in 3(the tape) would be
3÷1/4
We can hold 3 and flip the fraction, 1/4. If we flip 1/4, it becomes 4/1 and the division sign becomes multiplication. The expression would be
3 x 4/1 = 12
The correct option is A
What rule represents the translation from the pre image ABCD to the image A’ B’ C’ D’
Answer:
The second one
Step-by-step explanation:
Write your equation:
plsssssss helppppp
Answer:
The equation is y = 50 + 25x. The slope is the additional cost per hour, and the y-intercept is the cost of the service call to appear at the house.
What is the distance between a and b on the number line below?0.550.652.484.85
Determine which function has the greatest rate of change as x approaches infinity.
For the given options, we will find the function that has the greatest rate of change as x approaches infinity
[tex]\begin{gathered} a)f(x)=2x-8 \\ b)g(x)=5x^2-x+7 \\ c)h(x)=4^x-6 \end{gathered}[/tex]The first function is a linear
The second function is quadratic
The third function is exponential
By reviewing the graph of the three functions, we can know that the exponential function has the greatest rate of change as x approaches infinity
So, the answer will be option C) h(x)
If
f(x) = 2x² – 5
and
g(x) = 5x + 7
Find
g(f(x)) = [?]x² + [ ]
⇒g(f(x)) means that in the place of x in the function g you will plug in the function f.
⇒This means that [tex]2x^{2} -5[/tex] will be plugged in the place of x in 5x+7 and the simplify.
⇒[tex]=5(2x^{2} -5)+7\\\\=10x^{2} -25+7\\=10x^{2} -18[/tex]
⇒Now you have the unknowns The coefficient of the variable [tex]x^{2}[/tex] is 10 and the constant number is -18.
Find the area of the sector of the circle.
Answer:
D
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{\frac{5\pi }{8} }{2\pi }[/tex]
= π × 12.8² × ([tex]\frac{5}{8}[/tex] ÷ 2)
= π × 163.84 × [tex]\frac{5}{16}[/tex]
≈ 160.8 cm² ( to the nearest tenth )
I need help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Brian cut 4 1/12 yards of fishing line from a new reel. How much is this in inches? Write your answer as a whole number or a mixed number in simplest form.Include the correct unit in your answer.
Given: Brian cut
[tex]4\frac{1}{12}\text{ yards}[/tex]of fishing line from a new reel.
Required: To find how much Brian cut in inches.
Explanation: Since 1 yard is equivalent to 36 inches. Hence we need to multiply by 36 to convert yards to inches.
Hence Brian cut-
[tex]\begin{gathered} 4\frac{1}{12}\times36=\frac{49}{12}\times36 \\ =147\text{ inches} \end{gathered}[/tex]Final Answer: Brian cut 147 inches of fishing line from a new reel.
A large tank of sterile water holds 200 gallons . It is leaking at an unknown rate. At 8:30 am the tank had 137 gallons and at 11:00 am the tank had 115 gallons. Assuming the tank was full when the leak began , write a function to estimate how much water is in the tank. now find the time at which the tank began leaking and the time at which the tank will be empty.
The time that the tank began leaking water is 12:40am
The time the tank will be empty is 11 : 23 pm.
What is the time the tank began leaking water?The function that would determine the amount of water in the tank is a linear function. A linear function is a function that has a single power that is raised to the power of one. When drawn on a graph, a linear function is a straight line.
The first step is to determine the rate of leakage of the tank.
Rate = (water in the tank at 11am - water in the tank at 8:30am) / change in time
(137 - 115) / (11 - 8:30)
22 / 2:30
22 ÷ 2 1/2 hours = 8.8 gallons per hour
Linear function would have this form:
Water in the tank = water in the tank when full - (rate of leakage x number of hours)
137 = 200 - (8.8xh)
137 = 200 - 8.8h
200 - 137 = 8.8h
63 = 8.8h
h = 63 / 8.8
h = 7.16 hours = 7 4/15 hours
8 - 7 4/15 hours = 12 10/15 hours = 12.40am
When the tank is empty:
0 = 200 - 8.8h
200 - 0 = 8.8h
200 / 8.8 = 22.72 = 22 hours 43 minutes
22 hours 43 minutes + 12 : 40M = 11 : 23 pm
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Helppp
Express 27^1/2 as a power of 3
Express root 2 as a power of 8
Express root 2/16 as a power of 2
FOR THE FURST QUESTION.
[tex] {27}^{ \frac{1}{2} } \\ = (3^{3} )^{ \frac{1}{2} } \\ = {3}^{3 \times \frac{1}{2} } \\ = 3^{ \frac{3}{2} } [/tex]
FOR THE SECOND QUESTION
[tex] \sqrt{2} \\ = ( \sqrt[3]{8} )^{ \frac{1}{2} } \\ = ( {8}^{ \frac{1}{3} } )^{ \frac{1}{2} } \\ = 8^{ \frac{1}{3} \times \frac{1}{2} } ) \\ = 8^{ \frac{1}{6} } [/tex]
FOR THE THIRD ONE
[tex] \frac{ \sqrt{2} }{16} \\ = \frac{ \sqrt{2} }{16} \\ = \frac{ {2}^{ \frac{1}{2} } }{ {2}^{4} } \\ = 2^{ \frac{1}{2} - 4 } \\ = 2^{ - \frac{7}{2} } [/tex]
ATTACHED IS THE SOLUTION
for 1 and 2 draw front side and top views of each stack of unit blocks
1.
2.
3.
In the figure of the second exercise there is one block which is not visible.
4.
We can see that the figure is made with 8 blocks
5.
The maximum length of the figure would be 6. You need 3 blocks to get a heigth of 3 units. Then you can add the other 5 blocks to the one which is in the base to make the figure with a length of 6 units.
11=t/-12. Find the value of T
Answer:
t=-132
Step-by-step explanation:
multiply -12 on both sides.
-12x11=t
t=-132
what is the, in units, between (-5,8) and (4,-4) in the coordinate plane
A rectangle is graphed on a coordinate plane. For two of the vertices of the rectangle are (-5,8) and (-5,-6) what is the distance between the two vertices
A 2units
B 4 units
C 10 units or
D 14 units
Find out the distance between the given vertices
we have that
the two coordinates have the same x-coordinate
that means
the distance between the points is the difference of the y-coordinates
8-(-6)=8+6=14 units
the answer is option DProblem N 2
we have that
between -1 and -2 there are 5 spaces
the value of each space is 1/5=0.20
therefore
point A is -1.60
option C
Root of the equation 3x-8=1 is
Answer:
x= 3
Step-by-step explanation:
Add
8
to both sides
3x-8=1
2
Simplify
Add the numbers
3x=9
3
Divide both sides by the same factor
3x=9
4
Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
Answer:
x = 3
You first add 8 to both sides:
3x - 8 + 8 = 1 + 8
Simplify:
3x = 9
The divide both side by the same factor:
3x/3 = 9/3
9 divided by 3 is 3 so the solution is:
x = 3
Step-by-step explanation:
Hope it helps! =D
Act 3 of the 2003 Leonid meteor shower was expected to last 24 hours. The margin of error for this prediction was
0.7 days. Set up and solve an absolute value equation to find the limits of the range for the length of time that Act 3
could last. Show your work.
The limits of the range for the length of time that Act 3 could last is 33.6
What is limit ?The values that a function approaches for the specified input values are known as limits in mathematics. Limits are essential to calculus and mathematical analysis because they help define concepts like integrals, derivatives, and continuity. It's employed in the analysis process and always has to do with how the function behaves at a specific moment. In the idea of the limit of a topological net, the limit of a sequence is further generalized and connected to the limit and direct limit in the theory category. In general, integrals are divided into two categories: definite integrals and indefinite integrals.
A 24-hour period was predicted for Act 3 of the 2003 Leonid meteor shower. This prediction had a 0.7-day error window. How long could Act 3 potentially last, in the range
Lower Limit: 24-0.7(24) = 0.3(24) = 7.2 hrs
Upper Limit: 24+0.7(24) = 40.8 hrs
Range = Upper Limit - Lower Limit
= 40.8 - 7.2
=33.6
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What is the solution to x-8=-8 hint is not zero
IT HAS TO BE X=0 BECAUSE YOU ADD 8 TO X-8 THAT REMOVES THAT 8 THEN THE ADD 8 TO THE OTHERSIDE OF THE EQUAL SIGN
What’s the correct number and label for the
denominator of the ratio.
Answer:
see explanation
Step-by-step explanation:
ratio required is houses : turbines
let x be the number of turbines required for 26 houses , then
[tex]\frac{6houses}{18turbines}[/tex] = [tex]\frac{26houses}{x}[/tex] ( cross- multiply )
6x = 26 × 18 = 468 ( divide both sides by 6 )
x = 78
78 turbines are required for 26 houses
Raina runs 6 miles in 55 minutes. At the same rate, how many miles would she run in 44 minutes?
raina runs 6 miles in 55 minutes
so it speed is 6/55 miles per minute
that means in one minute he runs 6/55 miles
so in 44 minutes
[tex]\begin{gathered} =\frac{6}{55}\times44 \\ =\frac{6\times4}{5}=\frac{24}{5} \end{gathered}[/tex]in 44 minutes he will run 24/5 miles or 4.8 miles
How many days will it take the crew to lay all the track? L(d)=189-7d
Answer:
HIH
Step-by-step explanation:
HOW ARE
Answer:
d = 189/L+7unless you are looking for L, then it's
L = 189/d-7
Benji has four -0.5 cards. what is his total score
Benji's total score is -2.
What is the total of negative numbers?If two numbers are negative, their sum will also be negative. When two negative numbers are added together, their value is further diminished, hence the sum of the two negative numbers is always negative.
Given:
Benji has four -0.5 cards.
According to the question, we have to determine his total score which will be equal to adding scores on all four cards.
As we are adding negative scores, upon adding them place a negative sign in front of the sum.
The total score of Benji = (-0.5) + (-0.5) + (-0.5) + (-0.5)
= -2
Therefore, his total score is -2.
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Discuss the transformation of g(x)=2 (x−3)2 + 4 compared to the original function f(x)=x2. Select all that apply.
Group of answer choices
The graph is shifted right 4 units.
The graph has a horizontal stretch by a factor of 2.
The graph is shifted right 3 units.
The graph has a vertical stretch by a factor of 2.
The graph is shifted left 3 units.
The graph is shifted up 4 units.
The graph is shifted down 3 units.
The graph is shifted down 4 units.
The graph has a horizontal compression by a factor of 1/2.
The graph is shifted right to 3 units, then the graph has a horizontal stretch by a factor of 2 and the graph is shifted up 4 units.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The function is:
f(x) = x²
First transformation:
x → (x- 3)
The graph is shifted right to 3 units.
F(x) = (x- 3)²
Second transformation:
F(x) → 2F(x)
The graph has a horizontal stretch by a factor of 2.
h(x) = 2(x- 3)²
Third transformation:
h(x) → h(x) + 4
The graph is shifted up 4 units.
g(x) = 2(x- 3)² + 4
Thus, the graph is shifted right to 3 units, then the graph has a horizontal stretch by a factor of 2 and the graph is shifted up 4 units.
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Can someone help me step by step to the answer please? thank you!
Help me solve this please
(a) 291/2020
Divide the total for the 10-14 year column by the total.
(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years
(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.
(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.
(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.
(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.
(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.
(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.