Step-by-step explanation:
first collect the like terms together that is all the coefficient of y and the numbers
i.e 5y-3y=8+12
then now you can solve
2y=20
and y=10
Answer: y=10
Step-by-step explanation:
Given the graph of the function f below, estimate the intervals in which fis
increasing.
Answer:
(-∞, -5/2) ∪ (1, ∞)
Step-by-step explanation:
"Increasing" means the graph goes up to the right. It is increasing from the left up to the local maximum--the peak at left.
It is increasing again from the local minimum on the right to the right side of the graph.
The two sections where the graph is increasing are ...
(-∞, -5/2) ∪ (1, ∞)
__
The graph is decreasing between the maximum on the left and the minimum on the right.
On her way home from the school board meeting, Kelly fills up her car. She likes the idea of using gasoline with ethanol, but thinks her car can only handle 50% ethanol. At the gas station, she can use regular gas with 15% ethanol or E78 fuel with 78% ethanol. How many gallons of each type of fuel should Kelly use if she wants to fill up her car with 9 gallons of fuel containing 50% ethanol?
Answer:
4 gallons of 15% ethanol
5 gallons of 78% ethanol
Step-by-step explanation:
Given that:
Two types of gases:
1st gas with 15% ethanol
2nd gas with 78% ethanol
The gases are to be mixed in such a way that the mixture of gases comes out to be with 50% ethanol with volume of 9 gallons.
Let amount of gas with 15% ethanol used = [tex]x[/tex] gallons
Now, we are given that total volume is 9 gallons, then
amount of gas with 78% ethanol used = 9 - [tex]x[/tex] gallons
As per the question statement:
[tex]x\times 15\% + (9-x)\times 78\%=9\times 50\%\\\Rightarrow x\times 15 + (9-x)\times 78=9\times 50\\\Rightarrow 9\times 78-9\times 50=63x\\\Rightarrow 9\times 28=63x\\\Rightarrow \bold{x = 4\ gallons}[/tex]
Therefore, the answers are:
4 gallons of 15% ethanol
9 - 4 = 5 gallons of 78% ethanol
The number of gallons required of both kind would be as follows:
4 gallons having 15% ethanol
5 gallons having 78% ethanol
Given that,
The 2 kinds of gases are:
One with 15% ethanol
Other with 78% ethanol
Given that,
The gases(ethanol and gasoline) are diluted in a such a manner that it involves a total of only 50% ethanol.
Number of gallons she wants to use = 9
This shows that only 50% of 9 gallons i.e. 4.5 gallons of ethanol can be used.
Assuming x being the gasoline's measure that is diluted with 15% ethanol.
Now,
The gasoline's measure that is diluted with 78% ethanol would be = 9 - x gallons
Therefore,
x × 15% + (9-x) × 78% = 4.5
On solving, we get
x = 4 gallons
Thus,
The measure of gallons having 15% ethanol = 4
The measure of gallons having 78% ethanol = (9 - x)
= (9 - 4)
= 5 gallons
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89, 74, 100, 86, 74, 67, 86, 72, 60, 93, 83, 86 what is the median?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{84.5}}}}}[/tex]
Step-by-step explanation:
Given data :
89 , 74 , 100 , 86 , 74 , 67 , 86 , 72 , 60 , 93 , 83 , 86
Arranging the data in ascending order, we have,
60 , 67 , 72 , 74 , 74 ,83 , 86 , 86 , 86 , 89 , 93 , 100
Here, n ( total no.of observation ) = 12
Now, finding the position of media :
[tex] \boxed{ \sf{position \: of \: median = ( \frac{n + 1}{2} ) ^{th} \: item}}[/tex]
⇒[tex] \sf{ (\frac{12 + 1}{2} ) ^{th} item}[/tex]
⇒[tex] \sf{( \frac{13}{2} ) ^{th} item}[/tex]
⇒[tex] \sf{ {6.5}^{th} item}[/tex]
6.5 th item is the average of 6 th and 7 th items.
Again,
[tex] \sf{median = \frac{ {6}^{th \: item} + {7}^{th} item}{2} }[/tex]
⇒[tex] \sf{ \frac{83 + 86}{2} }[/tex]
⇒[tex] \sf{ \frac{169}{2} }[/tex]
⇒[tex] \sf{84.5}[/tex]
Hope I helped!
Best regards!!
Jada wanted to construct a line perpendicular to line e
through point C. The diagram shows her construction.
What was her mistake?
Answer:
Here the mistake is that she drew a circle from the point A to intersect the line rather the drawing arcs from the point C
The next another circle was drawn from the point of the intersection of the first circle and the intersection of both circles was used to draw the perpendicular at the midpoint of the intersection of both circles.
Step-by-step explanation:
To construct a line perpendicular to another line through a point the following steps are required
1) From the point, with the compass, C draw to intersect the line at points A and B
2) From A and B with the compass made wider, draw arcs above and below the line to intersect each other
3) With the straight edge Draw a line passing through the intersections of the arcs drawn from A and B and extend the line to pass through the point C
The line constructed above is the perpendicular to the line l passing through the point C.
A sports tournament has b teams. Each team has 15 players. Using b, write an expression for the total number of players in the tournament.
Answer:
b x 15
Step-by-step explanation:
b x 15
b = total number of teams
15 is how many players on each team
rewrite without parentheses and simplify
(6v-5x)^2
Answer:
36v² - 60xv + 25x²
Step-by-step explanation:
Step 1: Write out expression
(6v - 5x)²
Step 2: Expand
(6v - 5x)(6v - 5x)
Step 3: FOIL
36v² - 30xv - 30xv + 25x²
Step 4: Combine like terms
36v² - 60xv + 25x²
Find the solutions of the quadratic equation 2x2 + 6x - 2 = 0.
Sorry didn't know how to write the answer so I just took a screen shot of my answer for you!
Which graph shows the linear inequality y < 2x – 4?
Answer:
Graph the line
y = 2 x − 4
After you have plotted the line, shade in the area to right of the line.
To help you to graph the line, two points are
( 0 , − 4 ) and ( 2, 0 )
Remember to make it a dashed line to indicate that it is not included.
Here is a how it should look:
Fill in the missing work and justification for step 3 when solving 2(x + 1) = 10
Answer:
Below.
Step-by-step explanation:
2x + 2 - 2 = 10 - 2 Subtraction property of equality.
solve for x 9 ( x + 1 ) = 25 + x
Answer: x=2
Step-by-step explanation:
Given
9(x+1)=25+x
Distributive property
9x+9=25+x
Subtract x on both sides
9x+9-x=25+x-x
8x+9=25
Subtract 9 on both sides
8x+9-9=25-9
8x=16
Divide 8 on both sides
8/8 x=16/8
x=2
Hope this helps!! :)
Please let me know if you have any question
Answer:
x = 2
Step-by-step explanation:
big brain/took test
The triangle ABC is isosceles (AB = AC)
DE parallel to BC
You need to prove: The ADE triangle is isosceles
Answer:
ΔADE is isosceles
Step-by-step explanation:
Δ ABC is isosceles
AB ≅ AC
∠B ≅ ∠C
If DE parallel to BC
AD ≅ AE
∠D ≅ ∠E
ΔADE is isosceles
The isosceles triangle is a polygon with three sides, two being equal and the other unequal.
The angles D and E will also be equal and the A other different.
Solve forn in the literal equation a (n -5)+6=bn.
Answer: n = 5a-6 / a-b
Step-by-step explanation: Move all of your terms to the left side of the equation and then set the equal to 0. Then, set each of your factors equal to 0, as well.
I hope this helps you out.
(5x²-2)*(5x²+2)
Thank you
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{25 {x}^{4} - 4}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{(5 {x}^{2} - 2)(5 {x}^{2} + 2)}[/tex]
Use the distributive property to multiply each term of the first binomial by each term of the second binomial.
[tex] \dashrightarrow{ \sf{5 {x}^{2} (5 {x}^{2} + 2) - 2(5 {x}^{2} + 2)}}[/tex]
[tex] \dashrightarrow{ \sf{25 {x}^{4} + 10 {x}^{2} - 10 {x}^{2} - 4}}[/tex]
Since two opposites add up to zero , remove them from the expression
[tex] \dashrightarrow{ \sf{25 {x}^{4} - 4}}[/tex]
Hope I helped!
Best regards! :D
What is the mean medium and mode of $0.99,$0.99,$1.49,$1.49,$1.49,$1.99,$1.99,and$2.49
Mean: $1.615
Median: $1.49
Mode: $1.49
Simplify the expression: -7w - 5 - 7w + 9
Answer:
-14w + 4
Step-by-step explanation:
-7w - 5 - 7w + 9
-7w - 7w + 4
-14w + 4
Derrick got a pizza for lunch. He gave his friend 1/4 of the pizza and his sister 3/8 of the pizza. How many pizza he will have left
Answer: 3/8
Step-by-step explanation: 1/4 x 2 = 2/8 + 3/8 = 5/8 pizza gone. 1 - 5/8 = 3/8
ANSWER: 3/8
let's assume that Derrick is a nice guy and his pizza is an integer of 1
first he gave his friend a quarter so we subtract [tex]\frac{1}{4}[/tex] from 1
[tex]1-\frac{1}{4}[/tex]
now we rewrite 1 as a fraction with a denominator of 4 so that we're able to subtract: [tex]\frac{4}{4}-\frac{1}{4} =\frac{3}{4}[/tex]
now that Derrick still has [tex]\frac{3}{4}[/tex] of his pizza he's gonna give [tex]\frac{3}{8}[/tex] to his sister as well
meaning that we subtract again: [tex]\frac{3}{4} -\frac{3}{8}[/tex]
in order to be able to subtract different fractions, they got to have the same denominator, so we're going to multiply [tex]\frac{3}{4}[/tex] both numerator and denominator by 2: [tex]\frac{2*3}{2*4} -\frac{3}{8} = \frac{6}{8} -\frac{3}{8} = \frac{3}{8}[/tex]
we can now conclude that Derrick is left with only [tex]\frac{3}{8}[/tex] of his pizza.
11(n-1)+35=3n what is the answer
Answer:
n = -3
Step-by-step explanation:
Original Equation:
11 (n-1) + 35 = 3n
Distributive Property:
11n + 24 = 3n
Subtract 24 from both sides:
11n + 24 - 24 = 3n - 24
Simplify:
11n = 3n - 24
Subtract 3n from both sides:
11n - 3n = 3n - 24 - 3n
Simplify:
8n = -24
Divide both sides by 8:
[tex] \frac{8n}{8} = \frac{ - 24}{8} [/tex]
Simplify:
n = -3
Answer:
n=-3
Step-by-step explanation:
evaluate when x=5 x x²-3x+4
Answer:
14
Step-by-step explanation:
To evaluate, substitute x = 5 into the expression, that is
5² - 3(5) + 4 = 25 - 15 + 4 = 14
1. 5 x 6 – 12 ÷ 3 order of operations
Answer:
26
Step-by-step explanation:
First, using PEMDAS, do Multiplication, and division. (30 - 4)
Next, suptract to get your answer.
Answer:
26
Step-by-step explanation:
No P(emdas)
No e(Pemdas)
Multiplication (5 x 6)
5x6=30
Division (12/3)
12/3=4
No addition
Subtraction (30)-(4)
30-4=26
if one side of a square measures (3x-8) find the area of the square
Answer:−21x−8
Step-by-step explanation: All sides have the same measure in a square, therefore all sides are 3x-8. Area is equal to 3x-8 times 3x-8 which is −21x−8
If the side of the square is (3x - 8), the area of the square is 9x² -48x + 64
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side².
We have,
Square:
Side = (3x - 8)
The area of a square.
= Side²
= (3x - 8)²
Factorize using [(a + b)² = a² + 2ab + b²].
Now,
(3x - 8)²
= 9x² + 8² - 48x
= 9x² -48x + 64
Thus,
The area of the square is 9x² -48x + 64.
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1. What is the solution to the system of linear equations? Write you answer as a coordinate. 2x − y = 4 5x + 2y = 10
Answer:
The solution of the system of equation in coordinate form is (2, 0)
Step-by-step explanation:
The given equation are;
2·x - y = 4....................(1)
5·x + 2·y = 10..............(2)
Multiplying equation (1) by 2 and subtract it from equation (2) gives;
5·x + 2·y - 2 × (2·x - y) = 10 - 2×4
5·x - 4·x + 2·y - 2·y = 2
x = 2
From equation (1), we have 2·x - y = 4, when x = 2, we get;
2×2 - y = 4
y = 2×2 -4 = 0
y = 0
Therefore;
The solution of the system of equation in coordinate form is (2, 0).
Fund x+y+z+ shown in the following figure
Answer:
60°, 100° and 120°
Step-by-step explanation:
The angles x, y and z all lie on straight lines adjacent to other angles, thus
x = 180° - 120° = 60°
y = 180° - 80° = 100°
z = 180° - 60° = 120°
Name the Property Shown: 16=16 Question 1 options: Transitive Property Reflexive Property Symmetric Property Distributive Property
Name two lines in the diagram.
B.
S
A
D
E
line A
line B
BC
point a
Answer:
Options (3) and (6)
Step-by-step explanation:
"A straight line is a set of all points between two points and extending beyond these points."
Therefore, from the given diagram,
Arrows connecting set of two points B and C and D and E will be straight lines.
Geometrically we denote them with an arrow over the line.
[tex]\overleftrightarrow {BC}[/tex] and [tex]\overleftrightarrow {DE}[/tex]
Therefore, Options (3) and (6) will be the answer.
Over 7 months, the value of Thus stocks dropped a total of $35, or -$35. What integer value represents the average monthly change in the value of his stocks?
Answer:
7 times 5 is 35 so I think that's the answer
Answer:
Step-by-step explanation: 35- Because 7÷35
area & perimeter help!
Answer:
40ft
Step-by-step explanation:
√100=10
10*4=40ft
Answer:
The correct answer is 40 feet.
Step-by-step explanation:
We know that the area of the square is 100 square feet. We also know that we can find the area of the square using the formula A = s^2, where s represents the side length of the square.
A = s^2
If we plug in the value for the area that we are given, we get:
100 = s^2
To find the side length, we take the square root of both sides.
10 = s
To find the perimeter of a square, we should add up four times the side length (since there are 4 equal sides to a square).
Thus, the perimeter of a square is given by:
P = 4s = 4(10) = 40 feet
Therefore, the correct answer is 40 feet.
Hope this helps!
How many garbage cans should be placed in each campground? Explain how you can use addition or multiplication to find the answer
Answer:
Step-by-step explanation:
Multiplication
Ratio of Tables to garbage = 8:3
Small camp ground:
40 picnic tables and let x be the number of garbage cans
[tex]\frac{8}{3}=\frac{40}{x}\\\\\frac{8*5}{3*5}=\frac{40}{x}\\\\\frac{40}{15}=\frac{40}{x}\\\\[/tex]
x = 15
Small campground with 40 picnic table needs 15 garbage cans
Large picnic ground:
120 picnic tables and let y be the number of garbage cans
[tex]\frac{8}{3}=\frac{120}{y}\\\\\frac{8*15}{3*15}=\frac{120}{y}\\\\\frac{120}{45}=\frac{120}{y}[/tex]
y= 45
Big campground with 120 picnic table needs 45 garbage cans
|3x+1|=-5
How do I do this step by step
3. Is this relation a function? (-1,5) (-3, 6) (-2, 9) (5, 11) (-3, 6) (4, 11) (0, 10)
Answer:
Yes, it is.
Step-by-step explanation:
A function is a relation between two sets of elements, where each valid input can be mapped to exactly one output.
Indeed, the relation in this question is between two sets of elements. Each of these pairs includes exactly two elements: the input and the output.
On the other hand, does this relation maps each valid input to exactly one output? Arrange these pairs by the input in increasing order:
Input: [tex]-3[/tex]; Output: [tex]6[/tex].Input: [tex]-3[/tex]; Output: [tex]6[/tex].Input: [tex]-2[/tex]; Output: [tex]9[/tex].Input: [tex]-1[/tex]; Output: [tex]5[/tex].Input: [tex]0[/tex]; Output: [tex]10[/tex].Input: [tex]4[/tex]; Output: [tex]11[/tex].Input: [tex]5[/tex]; Output: [tex]11[/tex].Indeed, the input [tex]-3[/tex] appeared twice in the list. However, in both occurrence, this input mapped to the same output, [tex]6[/tex]. This relation is still a function.
A grocery clerk changes the display of oranges regularly. If the pattern indicated
below is continued, determine the number of oranges that will be displayed on
the 8th figure. Use a table to find the pattern.
Answer:
36
Step-by-step explanation:
F1 = 1
F2 = 1 + 2
F3 = 1 + 2 + 3
--> The n(th) figure has the number of oranges = the sum of the first n natural numbers, which has the general form:
F(n) = 1 + 2 + 3 + ... + n = n(n+1) / 2
So, 8th figure has:
F(8) = 8.(8+1) / 2 = 8 . 9 / 2 = 36