Answer:[tex] \huge{ \boxed{ \bold{ \tt{ x = - 2}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - 6x + 13 = - 5(7 + 6x) }[/tex]
Distribute -5 through the parentheses
[tex]\longrightarrow{ \sf{ - 6x + 13 = - 5 \times 7 + ( - 5 )\times 6x}}[/tex]
[tex]\longrightarrow{ \sf{ - 6x + 13 = - 35 + ( - 30x)}}[/tex]
[tex] \text{Remember} : \sf{( + ) \times ( - ) = ( - )}[/tex]
[tex]\longrightarrow{ \sf{ - 6x + 13 = - 35 - 30x}}[/tex]
Move 30x to left hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 6x + 30x + 13 = - 35}}[/tex]
Move 13 to R.H.S ( Right Hand Side ) and change it's sign[tex] \longrightarrow{ \sf{ - 6x + 30x= - 35 - 13}}[/tex]
Combine like terms
[tex] \longrightarrow{ \sf{24x = - 35 - 13}}[/tex]
The negative integers are always added but posses the negative ( - ) sign.[tex] \longrightarrow{ \sf{24x = - 48 }}[/tex]
Divide both sides by 24
[tex] \longrightarrow{ \sf{ \frac{24x}{24} = \frac{ - 48}{24}}} [/tex]
Dividing a negative integer by a positive integers gives a negative integer.
[tex]\longrightarrow{\sf{x = -2 }}[/tex]
-----------------------------------------------------
Verification:L.H.S = -6x + 13
Plug the value of x and simplify
[tex] \longrightarrow{ \sf{ - 6 \times ( - 2) + 13}}[/tex]
Multiplying negative integers by a negative integer gives a positive integer.
[tex] \longrightarrow{ \sf{ 12 + 13}}[/tex]
Add the numbers : 12 and 13
[tex] \longrightarrow{ \sf{25}}[/tex]
R.H.S = -5 ( 7 + 6x )
plug the value of x and simplify
[tex] \longrightarrow{ \sf{ - 5(7 + 6 \times ( - 2)}})[/tex]
Multiplying a positive integer by any negative integer gives a negative integer.
[tex] \longrightarrow{ \sf - 5(7 + ( - 12)}[/tex]
[tex]\longrightarrow{\sf{-5(7 - 12)}}[/tex]
Subtract 12 from 7
[tex] \longrightarrow{ \sf{ - 5 \times ( - 5)}}[/tex]
[tex]\longrightarrow{\sf{25}}[/tex]
L.H.S = R.H.S
The value of x is -2 .
Hope I helped!
Best regards!
~TheAnimeGirl
10. How many linear feet of cove molding are needed to trim the ceiling of a
12-foot by 16-foot family room?
Answer:
24 look it up on Google and your welcome I hope I'm right good day
PLEASE HELP ME
15 POINTS
Gabriela is weighing quarters on a scale. She weighs various numbers of quarters, n, and
records their total weight, w, in grams. Find the ratio of the weight of the quarters to the
number of quarters for all three columns of the table. Express your answer using decimals.
Number of quarters, n 4,10,24
Tirol weight, w 22,55,132
The ratio of the weight of the quarters to the number of quarters will be 11: 2
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b Remember that the ratio should always be taken of quantities with the same unit of measurement. Also, the ratio is a unitless(no units) quantity.
We have been given that Gabriela is weighing quarters on a scale. They weigh various numbers of quarters, n, and record their total weight, w, in grams.
Number of quarters, n; 4,10,24
Tirol weight, w; 22,55,132
The ratio of the weight of the quarters to the number of quarters will be;
w: n
22 : 4 = 11 : 2
Also, 55: 10
11: 2
Again,
132: 4
11: 2
Hence, The ratio of the weight of the quarters to the number of quarters will be 11: 2
Learn more about ratios here:
brainly.com/question/186659
#SPJ1
Please Help Asap thank you soo much god bless you
1) x ≤ 30
2) 5x + 2x ≥ 14
3) xy ≤ 4
4) y - 5 < 20
Step-by-step explanation:
please mark me as brainlest
4(3x + 2) = 4(2x + 3) + 4x
Answer:
x = -4
Step-by-step explanation:
4(3x + 2) = 4(2x + 3) + 4x (distribute the 4's on both sides)
12x + 8 = 8x + 12 + 4x (collect like terms)
12x + 8 = 13x + 12 (subtract 12x on both sides)
8 = x + 12 (subtract 12 on both sides)
-4 = x
Hope this helps ya!
Which of the following pairs of functions are inverses of each other?
Answer:
The answer is (B).
Step-by-step explanation:
A). y = f(x) = 6(x - 2) + 3 ⇔ y = 6x - 12 + 3 ⇔ 6x = y + 9 ⇔ x = [tex]\frac{y+9}{6}[/tex]
g(x) = [tex]\frac{x+9}{6}[/tex] is inverse function of f(x) and ≠ [tex]\frac{x+2}{6}[/tex] - 3
B). y = f(x) = [tex]\frac{5x}{4}[/tex] - 3 ⇔ 4y = 5x - 12 ⇔ x = [tex]\frac{4y+12}{5}[/tex]
g(x) = [tex]\frac{4(x + 3)}{5}[/tex] is inverse of f(x)
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PLZ HELP!!!! Explain 72. Determine the value of r so that a line through the points with the coordinates (r, 4) and (-2,3) has
slope 1/4
a. 4.5
b. 6
c. -2
d. 2
9514 1404 393
Answer:
d. 2
Step-by-step explanation:
The point-slope form of the equation for the line can make use of the given slope and point:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y -3 = 1/4(x +2) . . . . line with slope 1/4 through point (-2, 3)
Filling in the unknown point values, we have ...
4 -3 = 1/4(r +2)
4 = r + 2
2 = r
_____
Alternate solution
The way the question is worded, you seem to be expected to use the slope formula.
m = (y2 -y1)/(x2 -x1)
For the given points and slope, you have ...
1/4 = (3 -4)/(-2 -r)
-2 -r = 4(-1) . . . cross multiply
2 = r . . . . . . . . add r+4 to both sides
Is h = 11 a solution to the inequality below? 22 over h > 11
Answer:
no because if you insert 11 as h you get the inequality 2>11 wich isnt true
Step-by-step explanation:
Find the value of the expression when b= 9 c= 5 and d=10 ............ ½d + c² - b
Answer:
1/2d+c^2-b = 21
Step-by-st ep explanation:
= 1/2(10) + 5^2 -9
= 5 + 25 - 9
= 30 - 9
= 21
When Brandon went bowling, it cost $4.95 per game, plus a one-time fee to rent the shoes. Brandon played 5
games and paid $32. Write and solve a linear equation to find the cost to rent the shoes.
Help please! Due today
Solve: |x|-7<15
Answer:
No Solution
Step-by-step explanation:
Answer:
pretty sure its
0.466666
Step-by-step explanation:
The plumber added an extra $35 to her bill
Answer:
you just add 35 to her bill
2.Larry's car travels 230 miles on 10 gallons of fuel. What is the ratio of miles to
gallons for Larry's car?
A 10 Miles to 1 Gallon
B 10 Gallons to 1 Mile
<
23 Miles to 1 Gallon
D 23 Gallons to 1 Mile
Answer:
D
Step-by-step explanation:
If he travels 230 miles on 10gallons of fuel, then he will travel 23 miles on 1 gallon of fuel. So it is 230 gallons to one mile.
Anna is x years old, her sister Jane is y years younger. What will the sum of there ages be in 3 years. SORRY IM DUMB
You are not dumb. No one is dumb. Einstein failed math in high school.
Anna is x years old.
Jane is y years younger.
This means the Jane is x - y years old.
In three years, Anna will be x + 3 years old.
In three years, Jane will be (x - y) + 3 years old.
Let S = the sum of their ages in 3 years.
S = x + 3 + (x - y) + 3
S = 2x + 6 - y
Got it?
3. Use the given information about the polynomial graph to write out the equation.
Degree 5, Roots of multiplicity 2 at x = 3 and x = -2 and a root of multiplicity 1 at x = 4,
y-intercept at (0,12).
Answer:
[tex]f(x)=-\frac{1}{12}(x-3)^2(x+2)^2(x-4)[/tex]
Step-by-step explanation:
The standard form for a polynomial equation in its factored form is:
[tex]f(x)=a(x-p)(x-q)...[/tex]
Where p and q are the zeros and a is the leading coefficient.
We know that the degree of the polynomial is 5.
We are also given roots at x=3 and x=-2. Hence, our factors are (x-3) and (x+2).
These have a multiplicity of two, so we will square them.
We also know that there is a root at x=4. Hence, the factor is (x-4). This has a multiplicity of 1.
Therefore, our polynomial is now:
[tex]f(x)=a(x-3)^2(x+2)^2(x-4)[/tex]
We know that the y-intercept is 12. Therefore, if we substitute in 0 for x, we should get 12 for y. Here, we are solving for our a. Therefore:
[tex]12=a(0-3)^2(0+2)^2(0-4)[/tex]
Evaluate:
[tex]12=a(9)(4)(-4)[/tex]
Evaluate:
[tex]-144a=12[/tex]
Divide both sides by -144:
[tex]a=-1/12[/tex]
Hence, our entire polynomial is:
[tex]f(x)=-\frac{1}{12}(x-3)^2(x+2)^2(x-4)[/tex]
A gas tank holds 16 1/2 gallons of fuel. If you used 7 1/4 gallons of fuel yesterday and 3 1/2 gallons of fuel today, how many gallons of fuel are left in the tank?
Answer:
5 3/4 gallons of fuel left in the tank
Step-by-step explanation
16 1/2 - 7 1/4 = 9 3/4
9 3/4 - 3 1/2 = 5 3/4
Help please!!!!!!!!!!
Answer:
A)Two times the quantity of seven less than a number equals thirty-three
Solve -2(5x – 3) = 41.
Answer:
Divide both sides by the numeric factor on the left side, then solve.
Exact Form:
x=−7/2
Decimal Form:
x=−3.5
Mixed Number Form:
x=−3 1/2
Step-by-step explanation:
Answer:
- 3.5
Step-by-step explanation:
hope this helps :)
An airplane flew 2400 miles in 4 hours if the plane for the same number of miles each hour how many miles it fly in 1 hour
Answer:
600?
Step-by-step explanation:
you do 2400÷4 which would be 600 for each hour
what is 8 divided by 3/5
Answer:
13 1/3. have a great day!! :D
Step-by-step explanation:
To solve the equation, you first need to multiply 8 by 3/5's reciprocal, which is 5/3. Reciprocal basically means to flip the fraction. By multiplying 8 by 5/3 you'll get 40/3, which you can simplify to 13 1/3.
Given q(x)=3x and r(x)=x2.
What is (r∘q)(2)?
a. 36
b. 10
c. 12
d. 24
Answer:
36
Step-by-step explanation:
(r∘q)(2)=
= ((3x)^2(2)
=(3*2)^2
=6^2
=36
Find the value of the variable
[tex] \LARGE{ \underline{\underline{ \tt{Required \: answer:}}}}[/tex]
The above quadrilateral is a square because of the marking shown for the equilaterality of sides.
We have,
Side of the square = 13We need to find:
Variable x and y?Solution:
x is the side of the square and y is the diagonal. Hence,
[tex] \large{ \boxed{ \sf{x = 13}}}[/tex]
And for finding the diagonal which can use the Pythagoras theoram where the leg sides (p and b) are the sides of the triangle. Hence,
➝ y = √13² + 13²
➝ y = √338.
[tex] \large{ \boxed{ \sf{y = 13 \sqrt{2} }}}[/tex]
The correct option is Option (D)
☃️[tex] \large{ \purple{ \bf{FadedElla}}}[/tex]
-4/5 divided by -2
Pls help
Answer:
-2/5 or -0.40
Step-by-step explanation:
Answer:0.4
Step-by-step explanation:
How do the final lines of “A Blessing” emphasize the author’s peaceful tone?
1 The final two lines, in which the speaker states, “I would break into blossom,” indicate that flowers blossom in the spring.
2 The final two lines, in which the speaker states, “I would break into blossom,” indicate the feeling of beauty and growth from contact with the horses.
3 The final two lines, in which the speaker states, “That if I stepped out of my body,” indicate the feeling of excitement when watching horses run.
4 The final two lines, in which the speaker states, “That if I stepped out of my body,” indicate the feeling of death and dying.
Answer:
4
Step-by-step explanation:
how can patterns help me divide multiples of 10?
44. Time to Complete a Task Two machines can complete a task in t hours, where t must satisfy the
equation t/8+t/12 = 1. How long will it take for the two machines to complete the task?
Answer:5 h 48 min
Step-by-step explanation:
t/8+t/12=1
=> 3t+2t =24
5t=24
t=24/5
t=5 and 4/5 h
That equal to 5 h and 8/10 h or 5h and 8*6 min
So the answer is 5 h 48 min
4
Which function family does f(x)=5(x-2)2 + 3 belong to?
Answer:
Quadratic
Step-by-step explanation:
The type of quadratic function in the question is in vertex form.
Carly can paint 6/7 of a picture in 3/14 of an hour how many pictures can they paint in a full hour
Answer:
4 paintings in a full hour
Work:
Carly painted 6/7 of a picture in 3/14 hours:
6/7=3/14
Which means Carly painted 2/7 of a picture in 1/14 hours:
2/7=1/14
We need to find how many paintings she can paint in 1 full hour, or 14/14 of an hour, how do you get from 1/14 to 14/14? You do multiplication:
1/14 x 14 = 14/14
but there is a rule that says what you do to one side of the equation, you need to do it to the other side too so:
2/7 x 14=1/14 x 14
28/7=14/14
28/7=4
(x-5)²+2y³(x-5)+y[tex]{6}[/tex]
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[tex]( {x - 5})^{2} + 2 \times ( x - 5 ) \times ( {y}^{3} ) + ({ {y}^{3} })^{2} = \\ [/tex]
[tex]( \: {(x - 5) + {y}^{3} } \: )^{2} [/tex]
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how could we graphically visualize the relationshio between the age of a used car and the selling price if a used car