Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 10}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ \frac{5}{6} = \frac{x - 10}{3x + 6} }[/tex]
Apply cross product property
⇒[tex] \sf{5(3x + 6) = 6( x - 10)}[/tex]
Distribute 5 through the parentheses
⇒[tex] \sf{15x + 30 = 6( x - 10)}[/tex]
Distribute 6 through the parentheses
⇒[tex] \sf{15x + 30 = 6x - 60}[/tex]
Move 6x to left hand side and change it's sign
⇒[tex] \sf{15x - 6x + 30 = - 60}[/tex]
Collect like terms
⇒[tex] \sf{9x + 30 = - 60}[/tex]
Move 30 to right hand side and change it's sign
⇒[tex] \sf{9x = - 60 - 30}[/tex]
Calculate
⇒[tex] \sf{9x = - 90}[/tex]
Divide both sides of the equation by 9
⇒[tex] \sf{ \frac{9x}{9} = \frac{ - 90}{9} }[/tex]
Calculate
⇒[tex] \sf{x = - 10}[/tex]
Hope I helped!
Best regards!!
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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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
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.
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).
Solve for x. Round your answer to 2 decimal places. A right triangle is shown with the hypotenuse labeled x. One angle has a measure of 32 degrees, and the opposite leg has a length of 7.
Answer:
x would be 58°
Step-by-step explanation:
Answer:
13.21
Step-by-step explanation:
Sin(32)=7/x
x=7/sin(32)= 13.21
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!
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
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°
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
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.
1588 nearest thousand answer me fast ♥️
Answer:
2,000
Step-by-step explanation:
Look at the hundreds place. It has a 5 in its place. The rule for rounding is that if the number directly to the right of the place you are rounding is 4 or below, you round down. If it's 5 or above, you round up. It has a 5 in its place, so we round up. The 5 becomes a 0, and the 1 in the thousands place becomes a 2. All other places are 0 because the rounding up affects all other places.I hope this helps!
Write the equation in standard form for the ellipse with center at the origin, vertex (-8, 0), and co-vertex (0,4).
Answer: [tex]\dfrac{x^2}{64}+\dfrac{y^2}{16}=1[/tex]
Step-by-step explanation:
The standard form for an ellipse is: [tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex] where
(h, k) is the centera is the radius on the x-axisb is the radius on the y-axisGiven: (h, k) = (0, 0)
a = 8 (distance on x-axis from origin to -8)
b = 4 (distance on y-axis from origin to 4)
Input h = 0, k = 0, a = 8, b = 4 into the standard form for an ellipse:
[tex]\dfrac{(x-0)^2}{8^2}+\dfrac{(y-0)^2}{4^2}=1[/tex]
[tex]=\dfrac{x^2}{64}+\dfrac{y^2}{16}=1[/tex]
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
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.
Solise is planting 24 bushes and 16 trees in equal rows. She wants all the rows to be exactly the same with no plants left over. What is the greatest number of rows Solise can plant?
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Since Solise want to plant both trees and bushes in the same number of rows, you need to find the common factor.
Since the question is asking what the greatest number of rows she can plant, you have to find the greatest common factor.
The greatest common factor of 24 and 16 is 8.
You can plant 24 bushes in 8 rows (meaning you can divide it by 8), and 16 trees in 8 rows (meaning you can divide it by 8). Since the greatest number you can divide them both by is 8, the GCF of 24 and 16 is 8.
So the greatest number of rows Solise can plant is 8 rows.
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
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!
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.
Evan's family took a road trip to Niagrara Falls. Evan fell asleep 5% of the way through the trip. If Evan fell asleep after they had travelled 30 miles, what was the total length of the trip?
Answer:
The length of the trip is 1.5
Step-by-step explanation:
5÷100×30=1.5
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.
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.
Learn more about squares here:
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Find the distance between (3,5)
and (7,-3). **(round to the nearest tenth.)
Answer:
The answer is
8.9 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(3,5)and (7,-3)
The distance between them is
[tex]d = \sqrt{( {3 - 7})^{2} + ({5 + 3})^{2} } \\ = \sqrt{ ({ - 4})^{2} + {8}^{2} } \\ = \sqrt{16 + 64} \\ = \sqrt{80} \\ =4 \sqrt{5} \\ \: \: \: \: = 8.9442[/tex]We have the final answer as
8.9 units to the nearest tenthHope this helps you
Step-by-step explanation:
√(7-3)^2+(-8)^2
√16+64
√80
8.94
Over the summer, Kelly read 19 books. Elyse read 6 more
books than Kelly did. How many books did Elyse read over
the summer?
Answer:
25
Step-by-step explanation:
Answer:
25 books
Step-by-step explanation:
So, we know that Kelly read 19 books.
Elyse read 6 more books than 19.
Therefore, to find the amount of books Elyse read, add 6 to 19:
[tex]6+19[/tex]
Add:
[tex]=25[/tex]
So, Elyse read 25 books.
Simplify the expression: -7w - 5 - 7w + 9
Answer:
-14w + 4
Step-by-step explanation:
-7w - 5 - 7w + 9
-7w - 7w + 4
-14w + 4
please help me answer number 3 !!!
Answer:
Prime factorization method.(Table method)Step-by-step explanation:
Answer& Step-by-step explanation:
To multiply powers of the same base, add their exponents.
5d³ / 3f
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
Name the Property Shown: 16=16 Question 1 options: Transitive Property Reflexive Property Symmetric Property Distributive Property
7а — За +2а — а = 16
Answer:
(7a-3a)+(2a-a)=16
4a+a or 1a =16
5a=16
5a/5=16/5
a =16/5 or a=3.2
Step-by-step explanation:
solving like terms or substract are same
you only have to find value of uknown value which was "a" question
Round 48.1 to the nearest whole number
Answer:
48
Step-by-step explanation:
48.1
for decimals:
0-4 keep the number the same
5-9 rounds up