Answer:
x = -34 , y = 31
Step-by-step explanation suing Gaussian elimination:
Solve the following system:
{2 x + 3 y = 25
3 x + 4 y = 22
Express the system in matrix form:
(2 | 3
3 | 4)(x
y) = (25
22)
Write the system in augmented matrix form and use Gaussian elimination:
(2 | 3 | 25
3 | 4 | 22)
Swap row 1 with row 2:
(3 | 4 | 22
2 | 3 | 25)
Subtract 2/3 × (row 1) from row 2:
(3 | 4 | 22
0 | 1/3 | 31/3)
Multiply row 2 by 3:
(3 | 4 | 22
0 | 1 | 31)
Subtract 4 × (row 2) from row 1:
(3 | 0 | -102
0 | 1 | 31)
Divide row 1 by 3:
(1 | 0 | -34
0 | 1 | 31)
Collect results:
Answer: {x = -34 , y = 31
Translate and solve: 518% of what number is 3885?
Answer:The answer is 750
Step-by-step explanation:3885 of 750 can be written as:
3885/ 750
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
3885/750 × 100/100= (3885 × 100) over 750) × 1 over 100= 518/100
Therefore, the answer is 518%
If you are using a calculator, simply enter 3885÷750×100 which will give you 518 as the answer.
PLEASE HELP ME !!!! What is the value of |-25| ?
Answer: 25
Step-by-step explanation: The absolute value is the distance between a number and zero. The distance between − 25 and 0 is 25
Answer:
[tex]\Huge \boxed{25}[/tex]
Step-by-step explanation:
[tex]|-25|[/tex]
The absolute value of a number is the distance of that number from zero.
Applying absolute value rule : [tex]|-a|=a[/tex]
[tex]|-25|=25[/tex]
2+2995442974346496329869631467646547624672463777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777
Answer:
2.9954429743464962e+168
Step-by-step explanation:
solve for x : 8 (2-x) +3x= -4
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
So we have the equation:
[tex]8(2-x)+3x=-4[/tex]
Distribute the first term:
[tex]16-8x+3x=-14[/tex]
Combine like terms:
[tex]16-5x=-4[/tex]
Subtract 16 from both sides:
[tex]-5x=-20[/tex]
Divide both sides by -5:
[tex]x=4[/tex]
So, the value of x is 4 :)
Parabola,,Could you help me please??
Answer:
[tex]\large \boxed{\sf \bf \sqrt{\dfrac{10}{3}}}[/tex]
Dimension of the rectangle is
[tex]2\times\sqrt{\dfrac{10}{3}}\\ \\10-\dfrac{10}{3}=\dfrac{20}{3}[/tex]
Step-by-step explanation:
Hello,
[tex]\text{The area is }2x(1-x^2) \\ \\\text{The derivative is }2(10-x^2)+2x(-2x)=2(10-3x^2)\\\\\text{The derivative is }0\text{ for} 10-3x^2=0 \\\text{so for } x=\sqrt{\dfrac{10}{3}}[/tex]
Thanks
A circle is defined by x^2+y^2+2gx+2fy-15=0. The gradient of the tangent to the circle at the point (3,2) is -1/2. Find the value of g and f
Answer:
(g, f) = (-1, 2)
Step-by-step explanation:
The equation can be put into standard form:
(x^2 +2gx) +(y^2 +2fy) = 15
(x^2 +2gx +g^2) +(y^2 +2fy +f^2) = 15 +g^2 +f^2
(x +g)^2 +(y +f)^2 = 15 +g^2 +f^2 . . . . equation in standard form
The point (3, 2) is on the circle, so one of the equations we have is ...
(3+g)^2 +(2 +f)^2 = 15 +g^2 +f^2
9 +6g +g^2 +4 +4f +f^2 = 15 +g^2 +f^2
6g +4f = 2 . . . . . . . subtract g^2 +f^2 +13
3g +2f = 1 . . . . . . . divide by 2
__
A line through the center of the circle is perpendicular to the tangent at the point of tangency. That line will have a slope that is the negative reciprocal of the tangent's slope: m = -1/(-1/2) = 2. Then in point-slope form the equation of the line through the center is ...
y -2 = 2(x -3)
2x -y = 4 . . . . rearrange to standard form
The point at the center of the circle, (-g, -f), satisfies this equation, so we have another relation for f and g:
2(-g) -(-f) = 4
2g -f = -4 . . . . . . multiply by -1
Adding twice this equation to the one above, we have ...
2(2g -f) +(3g +2f) = 2(-4) +(1)
7g = -7 . . . . . . . . . simplify
g = -1 . . . . . . . . . . divide by 7
f = 2g +4 = 2(-1) +4 = 2 . . . find the corresponding value of f
The values of f and g are: f = 2 and g = -1.
Please help me out thank you
Answer:
(-0.0008)^0 =11291^1 =1(1/3)^0 = 1Step-by-step explanation:
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^0=1,\:\\\\(-0.0008)^0 = 1\\\\1291^0 =1\\\\-(-3141)^0 = -1\\\\-(\frac{5}{8} )^0 =-1\\\\0^1 = 0\\\\(\frac{1}{3} )^0 = 1\\[/tex]
Triangle△ABC is rotated -120 about point P to create △ABC
Calculate the average rate of change for the given function, from x = -1 to x = 2.
Answer:
it moved 3 spots
Step-by-step explanation:
Find the area of the triangle below. Be sure to include the correct unit in your answer.
Answer:
54cm²
Step-by-step explanation:
Area=1/2bh
=1/2(18)(6)
=54cm²
8(−5d−9)−3(−6d+10) in simplest terms?
Answer:
-22d+42
Step-by-step explanation:
-40d+72+18d-30=-22d+42
A bag contains 3 red apples and 6 yellow apples. 3 apples are selected at random. Find the probability of selecting 1 red apple and 2 yellow apple.
Step-by-step explanation:
[tex]number \: of \: ways \: to \: select \: 3 \: out \: of \: 9 = {C}^{9}_3 = 84[/tex]
[tex]ways \: to \: select \: 1red \: and \: 2yellow \: apples \: = {C}^{3}_1 \times {C}^{6}_2 = 3 \times 15 = 45[/tex]
Probability of selecting 1 red and 2 yellow apples = 45 / 84 = 0.53
Solve the equation below.
6(-2w - 3) = -4(3w + 7) + 10
Answer: all real numbers
Explanation:
Let's solve your equation step-by-step.
6(−2w−3)=−4(3w+7)+10
Step 1: Simplify both sides of the equation.
6(−2w−3)=−4(3w+7)+10
(6)(−2w)+(6)(−3)=(−4)(3w)+(−4)(7)+10(Distribute)
−12w+−18=−12w+−28+10
−12w−18=(−12w)+(−28+10)(Combine Like Terms)
−12w−18=−12w+−18
−12w−18=−12w−18
Step 2: Add 12w to both sides.
−12w−18+12w=−12w−18+12w
−18=−18
Step 3: Add 18 to both sides.
−18+18=−18+18
0=0
Amanda has a recipe that requires 3 1/2 cups of milk. If she is only making 2/3 of the recipe, how many cups of milk will she need?
Answer:
2 1/3
Step-by-step explanation:
She will need 2/3 of 3 1/2:
(2/3)(3 1/2) = (2/3)(3) +(2/3)(1/2) = 2 + 1/3
Amanda will need 2 1/3 cups of milk.
The angles in a triangle are such that one angle is 85∘ more than the smallest angle, while the third angle is 3 times as large as the smallest angle. Find the measures of all three angles.
Answer:
Step-by-step explanation:
x + x + 85 + 3x = 180
5x + 85 = 180
5x = 95
x = 19°
3(19)= 57°
x + 85 = 19 + 85 = 104°
The angles in a triangle are such that one angle is 85° more than the smallest angle, while the third angle is 3 times as large as the smallest angle. On solving the linear equation, the measures of all three angles are 17°, 51° and 102°.
Linear equation in one variable is an equation with an equals to sign with expressions on either side of it being equal. There must only be one variable. Also, the degree of each term must be one.
Given in the question:
Let the smallest angle be x°
the second angle = (x+85)°
the third angle = 3x°
Sum of all interior angle of a triangle = 180°
The linear equation becomes:
x + (x+85) + 3x = 180
5x + 85 = 180
5x = 95
x = 17°
x + 85 = 17 + 85 = 102°
3x = 17 * 3 = 51°
Learn more about linear equation here
https://brainly.com/question/32634451
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Suppose that the height s of a ball (in feet) at time t (in seconds) is given by the formula s(t) = 64 - 16(t - 1)^2. This function is graphed below on the interval 0 ≤ t ≤ 3. Which labeled point (A-G) corresponds to the release of the ball? How high (in feet) was the ball when it was released? Which labeled point corresponds to the highest point of the ball? When (in seconds after being released) did the ball reach its highest point? Which labeled point corresponds to the ball hitting the ground? How long (in seconds) after being released did the ball hit the ground?
Answer:
Kindly check explanation
Step-by-step explanation:
Suppose that the height s of a ball (in feet) at time t (in seconds) is given by the formula
s(t) = 64 - 16(t - 1)^2
t interval = 0 ≤ t ≤ 3
1) point A (from the graph)
11) Height of ball when it was released
Ball was released at t = 0
s(0) = 64 - 16(0 - 1)^2
= 64 - 16(-1)^2
= 64 - 16(1)
= 64 - 16
= 48 feets
111) point C ( from the graph)
IV) highest point of the ball is 64
Hence,
s(t) = 64 - 16(t - 1)^2
64= 64 - 16(t - 1)^2
16(t - 1)^2 = 64 - 64
16(t - 1)^2 = 0
16t^2 - 32t + 16 = 0
t^2 - 2t + 1 = 0
(t-1) = 0 (t-1) = 0
t = 1
V) Point G (from graph)
V1)
height = 0
s(t) = 64 - 16(t - 1)^2
0 = 64 - 16(t - 1)^2
16(t - 1)^2 = 64
(t - 1)^2 = 64/16
(t - 1)^2 = 4
(t - 1)² = 2²
t - 1 = 2
t = 2 + 1
t = 3
Twenty points :) plz help. The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. Show your work. Convert your answer into scientific notation if necessary: Earth-151.13 Neptune- 4.4764
Answer:
53357.1428571 hours
Step-by-step explanation:
1.494 billion km from Saturn to earth, divided by 28,000
Question
The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. Show your work. Convert your answer into scientific notation if necessary: Earth-151.13 Neptune- 4.4764
Answer
53357.1428571 hours
( 4a + 1 )( 7a 2 - 3a - 5 ) simplified
Answer:
28a³ - 5a² - 23a - 5
Step-by-step explanation:
FOIL and Distribute Parenthesis
Step 1: Write out expression
(4a + 1)(7a² - 3a - 5)
Step 2: Distribute 4a
28a³ - 12a² - 20a
Step 3: Distribute 1
7a² - 3a - 5
Step 4: Combine
28a³ - 12a² - 20a + 7a² - 3a - 5
Step 5: Combine like terms
28a³ - 5a² - 23a - 5
Simplify the expression (4x^3y^-5)^4
Answer:
64x^12 / y^20
Step-by-step explanation:
(4x^3y^-5)^4
Distribute the exponential value of 4 to all terms in the parentheses.
4^4 * x^(3*4) * y^(-5*4)
Multiply each exponent.
64x^12 * y^-20
Make the negative exponent positive by making it a fraction.
64x^12 / y^20
NEED HELP FAST!! A group of students performed an experiment to prove the law of conservation of energy. In the experiment, a flask containing water at room temperature was shaken vigorously for a few minutes. The table shows a partial record of the temperature of the water before and after shaking. Experimental Record Temperature Before Shaking 20 °C After Shaking Unknown What best predicts the unknown temperature? A- Less than 20 °C because the total energy of the system after shaking is lower B- Greater than 20 °C because the total energy of the system after shaking is higher C- Less than 20 °C, because the mechanical energy from shaking transforms to thermal energy D -Greater than 20 °C, because the mechanical energy from shaking transforms to thermal energy
Answer:
I think option D is the answer.
Answer:
D
Step-by-step explanation:
true answer ;)
Write an equation to solve for x, then solve for x. The whole question is in the picture.
Answer:
12x = 60 x = 5
Step-by-step explanation:
2 (2x + 4x) = 2 (6x) = 12x
the perimeter is 12x and 60 is the perimeters value so you divide 60 by 12 and get 5
what is 3 2/3 as a fraction
Answer:
[tex]\frac{11}{3}[/tex]
Step-by-step explanation:
[tex]3\frac{2}{3}[/tex]
3 * 3 = 9
So we add 9 to the top which is 2
9+2 = 11
ta da
11/3
Hope this helps!!! :)
pls mark brainliest
Answer:
3 2/3= 11/3
Step-by-step explanation:
Work to prove it:
Step 1
Multiply the denominator by the whole number
3 × 3 = 9
Step 2
Add the answer from Step 1 to the numerator
9 + 2 = 11
Step 3
Write answer from Step 2 over the denominator
11/3
If this helps please mark me the brainiest
you are making lemonade to sell at the trck meet. according to the recipe, you need 12 ounces of lemon juice for every 240 ounces of sugar water. You have 16 ounces of lemon juice. How many ounces of sugar water do you need?
What equation do you obtain when you solve the formula A = 1/2bh for h?ASAP PLEASE
Answer:
2Ab=h
Step-by-step explanation:
A=1/2bh
2A=bh
2Ab=h
8. Solve for y. **THINK! a) what type of angles do you have? b) what is their
relationship (add up to 90, add up to 180, or congruent)? c) set up an equation
and solve *
Answer:
a. Linear pair (supplementary)
b. Add up to 180°
c. [tex] y = 20 [/tex]
Step-by-step explanation:
78° and (5y + 2)° are a linear pair. They are supplementary, and add up to 180°.
Therefore, the following equation expresses their relationship:
[tex] 78 + (5y + 2) = 180 [/tex]
Solve for y
[tex] 78 + 5y + 2 = 180 [/tex]
[tex] 78 + 2 + 5y = 180 [/tex]
[tex] 80 + 5y = 180 [/tex]
Subtract 80 from both sides
[tex] 80 + 5y - 80 = 180 - 80 [/tex]
[tex] 5y = 100 [/tex]
Divide both sides by 5
[tex] \frac{5y}{5} = \frac{100}{5} [/tex]
[tex] y = 20 [/tex]
At the farmers market 2 pounds of peaches cost $4.20 how much will 4 pounds cost
Answer:
$8.4
Step-by-step explanation:
2 pounds of peaches cost $4.20
1 pound of peaches costs = 4.20 /2
4 pounds of peaches cost =[tex]\frac{4.20 *4}{2} \\8.4[/tex]
4 pounds of peaches cost $8.4
A health and fitness club surveys 40 randomly selected members and found that the average weight of those questioned is 157 lb. Is this average an example of a statistic or a parameter?
A) Parameter
B) Statistic
Answer:
B. Statistic
Step-by-step explanation:
The average weight of those questioned which is 157 lb. from the survey of 40 randomly selected member of a health and fitness club is an example of a statistic.
It is a calculated numerical value that characterises some aspects of a sample set of data.
Statistic refers to a numerical piece of information that uses quantified models, representations and synopses for a given set of a study. Statistic is used to to estimate the true value of a parameter in a population.
11. Emma has been offered a job that pays $36.950 for working a 52-week year
training software users. What average amount does the job pay per month? per
week?
2.84 per month, 0.71 per week
Step-by-step explanation:
52/4 =13 months
36.95/15=2.84
31.95/52 = 0.71
Which shows all the factors for 36?
1, 2, 3, 4, 6, 9, 12, 18, 36
1, 2, 3, 4, 9, 12, 18, 36
2, 3, 4, 6, 9, 12, 18
1, 2, 3, 4, 8, 12, 18, 36
Answer:
1, 2, 3, 4, 6, 9, 12, 18, 36
Hope it helps.
Please mark it as Brainliest.
Is the value of the 8 in 12.984 the same as the value of the 8 in 7.38? Justify your response.
Answer:
hundredths’ value in 12.984
hundredths’ value in 7.38
My response: In arithmetic, a hundredth is a single part of something that has been divided equally into a hundred parts. For example, a hundredth of 675 is 6.75. In this manner it is used with the prefix "centi" such as in centimeter. A hundredth is the reciprocal of 100.