Answer:
2/5
Step-by-step explanation:
Good luck!
X
5x – 3y = -20
4x + 5y = -2
Answer:
x=-106/37
y=70/37
Step-by-step explanation:
I chose to set up the problem as a matrix to solve here.
(Another way to do this would be to isolate one variable in one of the equations, substitute it into the other equation, solve for that, and then plug it back in to get the final variable.)
My work is in the attachment. Lmk if you have any questions.
Answer:
[tex]\huge\boxed{\left\{\begin{array}{ccc}x=-\dfrac{106}{37}\\y=\dfrac{70}{37}\end{array}\right}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}5x-3y=-20&\text{multiply both sides by 5}\\4x+5y=-2&\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}25x-15y=-100\\12x+15y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad37x=-106\qquad\text{divide both sides by 37}\\.\qquad\boxed{x=-\dfrac{106}{37}}[/tex]
[tex]\text{Substitute it to the first equation}\\\\5\left(-\dfrac{106}{37}\right)-3y=-20\\\\-\dfrac{530}{37}-3y=-20\qquad\text{multiply both sides by (-37)}\\\\(-37\!\!\!\!\!\diagup)\left(-\dfrac{530}{37\!\!\!\!\!\diagup}\right)-(-37)(3y)=(-37)(-20)\\\\530+111y=740\qquad\text{subtract 530 from both sides}\\\\111y=210\qquad\text{divide both sides by 111}\\\\y=\dfrac{210}{111}\\\\y=\dfrac{210:3}{111:3}\\\\\boxed{y=\dfrac{70}{37}}[/tex]
The formula for the remaining volume of fuel in a car's tank is I-E\cdot DI−E⋅DI, minus, E, dot, D, where III is the initial volume of fuel, EEE is the fuel efficiency, and DDD is the distance traveled. Carson drove a distance of 120120120 kilometers. He initially had 303030 liters of fuel, and his car's fuel efficiency is 100100100 cubic centimeters per kilometer. What calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters? Choose 1 answer: Choose 1 answer: (Choice A) A 30-\dfrac{100}{1000}\cdot 12030− 1000 100 ⋅12030, minus, start fraction, 100, divided by, 1000, end fraction, dot, 120 (Choice B) B 30\cdot 1000-100\cdot 12030⋅1000−100⋅12030, dot, 1000, minus, 100, dot, 120 (Choice C) C \dfrac{30}{1000}-100\cdot 120 1000 30 −100⋅120start fraction, 30, divided by, 1000, end fraction, minus, 100, dot, 120 (Choice D) D 30-100\cdot 1000\cdot 12030−100⋅1000⋅120
Answer:
30-100/1000*120
Step-by-step explanation:
Source: Khan Academy
Answer:
30 - 100/1000 x 120
Step-by-step explanation:
x^{2m+n} * x^{n-m} / x^{m+2n}
Answer:
=x
Step-by-step explanation:
Answer:
[tex]\boxed{1}[/tex]
Step-by-step explanation:
[tex]x^{2m+n} * x^{n-m} / x^{m+2n}[/tex]
When bases are same for exponents in division, subtract exponents.
[tex]x^{2m+n} * x^{n-m-(m+2n)}[/tex]
[tex]x^{2m+n} * x^{n-m-m-2n}[/tex]
[tex]x^{2m+n} * x^{-n-2m}[/tex]
When bases are same for exponents in multiplication, add exponents.
[tex]x^{2m+n+-n-2m}[/tex]
[tex]x^{2m+0-2m}[/tex]
[tex]x^0[/tex]
Any base with power or exponent of 0 is 1.
[tex]x^{0}=1[/tex]
What is the correct answer!
Answer:
The answer is B.
Step-by-step explanation:
Please let me know if you want an explanation for why this is the answer (comment on this). A lot of people don't actually read the explanations, so I wouldn't want to waste my time. However, if you would like it I would be more than happy to type one out for you. Thanks!
Express 2.99 x 108 m/s (the speed of light) in decimal notation (i.e., express the number without using scientific notation).
options:
2,990,000,000
299,000,000
Answer:
Step-by-step explanation:
I think you mean 2.99×10^8, not 2.99×108.
2.99×10⁸ meters per second = 299,000,000 meters per second
The slope of two lines are - 3/2 and 18/a. Determine the value of α that will make the lines:
a) parallel
b) perpendicular
Answer:
a) a=-12
b) a=27
Step-by-step explanation:
a) parallel lines have = slopes SO
-3/2 = -3/2
-3/2 = 18/a
-3a/2 = 18
-3a = 18 * 2 = 36
a = -12
b) perpendicular lines have negative inverse slopes SO
- 3/2 ---> 2/3
2/3 = 18/a
2a/3 = 18
2a = 18 * 3 = 54
a = 54/2 = 27
What is the perimeter of a square with side length (2x-3)?
Answer:
Perimeter = 8x - 12
Step-by-step explanation:
The perimeter of a square is:
p = 4(side length)
on this case:
p = 4(2x-3)
p = 4*2x + 4*-3
p = 8x - 12
Evaluate the expression for x= 3 and y= 6.
51x² + y + 3
Answer:
468
Step-by-step explanation:
The equation is: 51x² + y + 3
Let's first find x. It says x= 3, so let's subsitute that in.
51(3)² + y + 3
3² is 9 because 3 times 3 is 9, which means:
51(9) + y + 3.
It is 51 times 9 and not 519 because x was supposed to be squared by itself and 51 was next to it. When a number is close to another number, especially with parentheses, it wants you to multiply the two together.
For example: 3(3) is 9 and 4(5) is 20.
Now that we found x, let's get y. The problem states that y= 6...let's subsitute that in.
51(9) + 6 + 3.
Now that we got all the variables out of the way, we can simplify!
51 times 9= 459
459+6+3 is the same thing as 459+9, since 6+3= 9.
459+15= 468 :)
Use the rule "add 2" to create a sequence of 5 numbers starting with 8.
Answer:
8 10 12 14 16
Step-by-step explanation:
8+2=10, 10+2=12, 12+2=14, 14+2=16
write each number in scientific notation.
1,050,200
The number between 1 and 10:
The power of 10:
The number in scientific notation:
34,600
The number between 1 and 10:
The power of 10:
The number in scientific notation:
what is an equivalent expression for 3a + 5 ?
Answer:
Equivalent expression:
6a + 10
or
9a + 15
Use the discriminant to determine the number of real solutions to the equation,
10n^2 = 10 - 8n
Answer:
2 real solutions
Step-by-step explanation:
Get all the terms to one side
10n^2 = 10 - 8n
10n^2 +8n -10 =0
ax^2 +bx+c =0
The discriminant is
b^2 -4ac
8^2 - 4(10)(-10)
64 +400
464
If the discriminant is greater than 0 we have 2 real solutions
If BC = 15, BE = 6, DC = 12, and AD = 8,
then segment DE is parallel to segment
AB.
If the square of the hypotenuse of an isosceles right triangle is 98cm2 find the length of each side
Answer:
7
Step-by-step explanation:
Let the each leg be x so,
√(x²+x²)=√98
or, √(2x²)=√98
or, x√2=7√2
or, x=7
A person is standing exactly 36 ft from a telephone pole. There is a 30° angle of elevation from the ground to the top of the pole. A person is standing 36 feet from the base of a telephone pole. A line is drawn from the top of the telephone pole to the person to form a right triangle. The angle at the person is 30 degrees. What is the height of the pole? 12 ft 12 StartRoot 3 EndRoot ft 18 ft 18 StartRoot 2 EndRoot ft
Answer:
20.78feet
Step-by-step explanation:
The question made us to understand that the man is standing and also there is angle of elevation, then we need to draw a right triangle having a base equal to 36 feet with an angle from the base to the top of the pole which is 30 degrees.
tan= opposite side / adjacent side
Let height of the pole =h
Tan(30)= h/36
But tan 30degree= 1/√3
h= 36 × 1/√3
h= 20.78feet
Therefore, the height of the pole= 20.78feet
CHECK THE ATTACHMENT FOR DETAILED FIGURE
Answer:
B. 12\sqrt{3} ft
Step-by-step explanation:
What is the following product? StartRoot 12 EndRoot times StartRoot 18 EndRoot StartRoot 30 EndRoot
Answer:
[tex] 6\sqrt{6} [/tex]
Step-by-step explanation:
[tex] \sqrt{12}\sqrt{18} = [/tex]
[tex] = \sqrt{12 \cdot 18} [/tex]
[tex] = \sqrt{4 \cdot 3 \cdot 9 \cdot 2} [/tex]
[tex] = \sqrt{36 \cdot 6} [/tex]
[tex] = \sqrt{36}\sqrt{6} [/tex]
[tex] = 6\sqrt{6} [/tex]
Following are the step by step solutions to the given expression:
Given:
[tex]\to \sqrt{12} \times \sqrt{18} \sqrt{30}[/tex]
To find:
solve=?
Solution:
[tex]\to \sqrt{12} \times \sqrt{18} \sqrt{30}[/tex]
[tex]\to \sqrt{2\times 2 \times 3} \times \sqrt{2\times 3 \times 3} \sqrt{2 \times 3 \times 5} \\\\ [/tex]
[tex]\to 2\sqrt{3} \times 3\sqrt{2} \sqrt{2 \times 3 \times 5} \\\\ \to 6\times \sqrt{3} \times \sqrt{2} \sqrt{2\times 3 \times 5} \\\\ \to 6\times \sqrt{3} \times \sqrt{2} \times \sqrt{2}\times \sqrt{3} \times \sqrt{5} \\\\ \to 6 \times 3 \times 2 \times \sqrt{5} \\\\ \to 36 \sqrt{5}[/tex]
Therefore, the final answer is "[tex]36\sqrt{5}[/tex]"
Learn more:
brainly.com/question/24050871
Julio is paid 1.3 times his normal hourly rate for each hour he works over 31 hours in a week. Last week he worked 42 hours and earned $548.13. Enter and solve an equation to find Julio's normal hourly rate, r. Complete the explanation how you know that your answer is reasonable.
Step-by-step explanation:
Answer:
$12.10 / hour
Step-by-step explanation:
42 - 31 =
1.3(11)r + 31r = 548.13
14.3r + 31r = 548.13
45.3r = 548.13
r = 12.1 / hour
help8b2 • 2b3 a) 16b-2 ,b) 16b6 ,c) 16b-4 ,d) 16b5
Answer:
16b^5
Step-by-step explanation:
8b^2×2b^3
= 16b^2+3
= 16b^5
Answer:
D)16b5
Step-by-step explanation:
8b2×2b3
= 16b2+3
= 16b5
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Julie wants to make 800 g of a 15% alcohol solution by mixing a
20% solution and a 4% solution. How many grams of each kind
does she need?
Answer:
x =550
y=250
Step-by-step explanation:
.2x + .04y = 120
x + y = 800
A= 12b1+b2h ; solve for b1
Answer:
b1 = 0, b2 = 0
EXPLICACION
A = 12 b1 + b2 h
A - 12 b1 - b2 h = 0
b2!=0, h = -(12 b1)/b2
What is 7.3482 rounded to 2, 3 and 4 significant figures?
2 figures - 7.3
3 figures - 7.35
4 figures - 7.348
Convert 1.2 radians to an
angle in degrees
Answer:
Below
Step-by-step explanation:
Let x be the measure in degrees
● x/180 = 1.2/Pi
Cross multiply the values
● x*Pi = 180×1.2
● x = 216/Pi
Take Pi = 3.14
● x = 68.78 wich is approximatively 69°
Use the distributive property to write an expression that is equivalent to 1/2 (8y - x - 12).
Answer:
4y - 0.5x - 6
Step-by-step explanation:
1/2 (8y - x - 12)
= (8y * [1/2]) - (x * [1/2]) - (12 * [1/2])
= (8y/2) - (x/2) - (12/2)
= 4y - 0.5x - 6
Tell me if I got it wrong! Hope this helps!
Answer:
4y+1/2x+6
Step-by-step explanation:
uh nvm someone already answered my bad
A5cm x 11 cm rectangle sits inside a circle with radius of 12 cm.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
5 cm
12 cm
11 cm
cm?
PLS HELP ME FOR 17 POINTS
Answer:
397.16 cm²
Step-by-step explanation:
Area of the circle = πr²
3.14 * 144 = 452.16
452.16 - (11 x 5 ) = area shaded region
452.16 - 55 = 397.16
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
In each of the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also write them with appropriate sign (>,<) between them (a) 530, 503 (b) 370, 307 (c) 98765, 56789 (d) 10023001
D) in the question
1002, 3001
Answer:
a) 503 b) 307 c) 56789 D) 1002
Step-by-step explanation:
Numbering starts from the left hand side and are arranged in ascending order.
A) (530, 503)
503 < 530
503 is lesser than 530 and as such it is encountered first when numbers are written, hence 503 will appear on the left side of the number line when both are written.
B.) (370, 307)
370 > 307
307 comes before 370, therefore it will appear on the left side of 370 when illustrated on a number line.
C.) (98765, 56789)
98765 > 56789
56789 will appear on the leftside of 98765 when both number are illustrated on a number line.
D.) 1002 < 3001
1002 will appear on the leftside of 98765 when both number are illustrated on a number line.
PLEASE HELP I PUT THE PROBLEM AS A PICTURE PLEASE ANSWER WILL GIVE 30 POINTS SHOW WORK
Answer:
[tex]\huge\boxed{9}[/tex]
Step-by-step explanation:
[tex]\sf (2^8 * 3^{-5} * 6^0)^{-2 } (\frac{3^{-2}}{2^3} )^4*2^{28}[/tex]
Rule of exponents [tex]a^0 = 1[/tex] , [tex]1/a^m = a^{-m}[/tex]
=> [tex]\sf 2^{8*-2} * 3 ^{-5*-2} * 3 ^{-2}* 2^{-3*4} * 2^{28}[/tex]
=> [tex]\sf 2 ^ {-16} * 3^{10} * 3^{-8} * 2 ^{-12}* 2^{28}[/tex]
Combining same bases
=> [tex]\sf 2 ^ {-16} * 2 ^{-12}* 2^{28}* 3^{10} * 3^{-8}[/tex]
When bases are same , powers are to be added
=> [tex]\sf 2 ^{-16-12+28} * 3^{10-8}[/tex]
=> [tex]\sf 2^{-28+28} * 3^2[/tex]
=> [tex]\sf 2^0 * 3^2[/tex]
=> [tex]\sf 3^2[/tex]
=> 9
Maria cut four equivalent lengths of ribbon. Each was 5 eighths of a yard long. How many yards of fabric did she cut?
Answer:
2.5 Yards
Step-by-step explanation:
Multiply 5/8 by 4
Shanti is taking a cube-shaped gift to a friend's birthday party. She wants to wrap it but she doesn't have very much paper, so she does not overlap any of the edges. How much paper did it take to cover the gift? cm2\text{cm}^2cm2start text, c, m, end text, squared
Answer:
It will take Shanti 150 square inches of paper to wrap the gifts
Step-by-step explanation:
Shanti wraps the gift she is taking to a friend's birthday party. She doesn't have very much paper, so she does not overlap any of the edges. The side lengths of the cube are all 5in.
How much paper did it take to cover the gift?
Solution
To solve this, you will find the surface area of a cube
Surface area of a cube = 6a^2
Where,
a=side length of the cube
a= 5 in
a^2=a × a
=5 × 5
=25 in^2
a^2=25 in^2
Surface area of a cube = 6a^2
=6 × 25 in^2
=150 in^2
It will take Shanti 150 square inches of paper to wrap the gifts
Answer:
1014
Step-by-step explanation:
I took the test i know
If 3.7 inches of rain fall on Seattle during the first four days of December and the rain continues to fall at this pace for the rest of the month approximately how many feet of rain will fall during December
Answer:
28.675 inches
Step-by-step explanation:
If 3.7 inches of rain has been poured in the four days. Then the rate of rain fallen in one day = 3.7/4 .
For the the amount of rain poured in December.
Simply multiply the rate*days=rain amount poured.
So,
Amount Of Rain In December= (3.7/4)*31 = 28.675 inches.
It is approximately 29inches.
I hope that helps.