Answer:
q=10, r=8
Step-by-step explanation:
You have to first cancel one of the variables.
8q-15r=-40
4q+2r=56
To do this, multiply the second equation by -2.
8q-15r=-40
-2(4q+2r)=(56)(-2)
Multiply it out.
8q-15r=-40
-8q-4r=-112
Combine like terms.
-19r = -152
Divide by -19 to get the value of r.
r=8
Substitute r back into one of the equations, it does not matter which one. I'll do both.
8q-15(8)=-40
8q-120=-40
8q=80
q=10
4q+2(8)=56
4q+16=56
4q=40
q=10
You should get the same value for q for both.
In the instance where the variables are x and y, which they usually are, you would write your answer as an ordered pair, (x, y).
(10, 8)
Answer:
q=10 and r=8
Step-by-step explanation:
8q-15r=-40 ...........equation(i)
4q+2r=56................eqn(ii)
Now,
Multiplying eqn (ii) by 2 then we get,
8q+4r=112..........eqn(iii)
Here, Subtracting eqn (i) and (iii)
8q-15r=-40
8q+4r=112
(-) (-) (-)
---------------------
-19r=-152
r= -152/-19
r= 8
Again, Putting the value of r in eqn (ii)
4q+2r=56
4q+2×8=56
4q=56-16
q=40/4
q=10
Row a in a certain section in a football stadium has 10 seats. each row behind row a is labeled alphabetically (b, c, d, and so on) and has 6 more seats than the row immediately in front of it.how many seats are in row g of this section of the stadium?
The total number of seats in row g is 224.
Number of seats in a row a = 10
Number of seats in row b = 16
Number of seats in row c = 22
The common difference is d.
d = (22-16) = 6
The first term is a.
a = 10
The total number of rows is n.
n = 7
[tex]a _{n} = a + (n - 1)d[/tex]
[tex]a _{n} = 10 + (7 - 1)6[/tex]
= 46
The total number of seats in row g is,
[tex]S _{n} = \frac{n}{2} (a + a _{n})[/tex]
[tex]S _{n} = \frac{8}{2} (10 + 46)[/tex]
= 224
Therefore, the total number of seats in row g is 224.
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f(x)=10 x-10 . Find each value.
(f ⁰ f⁻¹)(d)
Function composition exists a mathematical procedure where two functions, f and g, are taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)).
If the function be f(x) = 10x - 10 then the value of (f ⁰ f⁻¹)(d) is 99.
What is meant by composition?Function composition exists a mathematical procedure where two functions, f and g, exists taken and a function, h = g ⁰ f, exists produced such that h(x) = g(f(x)). The function g is used in this operation on the outcome of applying the function f to x.
Let the function be f(x) = 10x -10
We want to find (f ⁰ f⁻¹)(d)
To differentiate with respect to X, then we get
[tex]F^{-1}[/tex](x) = 10
To find the value of (f ⁰ f⁻¹)(d)
F([tex]f^{-1}[/tex](x)) = F(10)
F([tex]f^{-1}[/tex](x)) = 10x - 10
substituting the values in the above equation, then
F([tex]f^{-1}[/tex](x)) = 10(10) - 10
simplifying the above equation, we get
F([tex]f^{-1}[/tex](x)) = 100 -10
F([tex]f^{-1}[/tex](x)) = 99
Therefore, the value of (f ⁰ f⁻¹)(d) = 99
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Point D(−1, 5) is reflected across the x-axis. Which statements about D′ are true? Select each correct answer. Responses The y-coordinate is 5. The , y, -coordinate is 5. The y-coordinate is −5. The , y, -coordinate is , negative 5, . The x-coordinate is −1. The , x, -coordinate is , negative 1, . The x-coordinate is 1.
The correct option is (A) The y-coordinate is -5. If point D(-1, 5) is reflected across the x-axis then the coordinates of D’ are (-1, -5).
What does it mean to reflect coordinates?Geometry. The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
Determine the location of the mirror line before reflecting an object on a coordinate plane. Simply multiply the coordinate of the point by -1 to reflect over the axis. Use the symbols. Simply multiply the coordinate of the point by -1 to reflect over the axis.
Given coordinates of D= (-1, 5)
While reflecting any points across the x-axis with coordinates as (x, y) becomes, (x, -y). i.e sign of y-coordinate changes.
The rule is: (x, y) arrow (x, -y)
Applying so, after reflecting point D, its reflection D' will have coordinates as (-1, -5)
Therefore, the y-coordinate is -5.
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The midpoint of \overline{\text{AB}} AB is M(-4, -3)M(−4,−3). If the coordinates of AA are (-1, -2)(−1,−2), what are the coordinates of BB?
The midpoint of AB is M(-4, -3). If the coordinates of A are (−1,−2), then B has coordinates of (-2, -7/3)
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
Line AB has a midpoint, M.
A is (-1, -2)
B is unknown, M is(−4,−3)
Let's assume straight line of the form y=mx+b, where m is the slope.
Rise = (-3-(-2))= -1
Run = (-4-(-1)) = -3
Slope = (Rise/Run) = (1/3)
The line becomes y=(1/3)x+b
Calculate b, the y-intercept (the value of y when x is 0)
y=(1/3)x+b
-2 = (1/3)(-1)+b
b = -2 + (1/3)
b = -5/3
The equation becomes:
y=(1/3)x - -5/3
Find the value of y for x=-2:
y=(1/3)x - -5/3
y=(1/3)(-2) - 5/3
y= -7/3
B has coordinates of (-2, -7/3)
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Motorcycle A can reach a top speed of 140 miles per hour motorcycle B can reach a top speed of 200 feet per second which motorcycle has a greater top speed
Motorcycle A has a greater top speed.
What unit conversion?A unit conversion expresses the same property as a different unit of measurement.
given:
Motorcycle A can reach a top speed of 140 miles per hour.
Motorcycle B can reach a top speed of 200 feet per second
Now,
1 miles/h = 1.46667 feet/sec
140 miles/h = 140*
= 205.333 feet/sec
So, Motorcycle A can reach a top speed of 205.333 feet/sec.
Hence, Motorcycle A has a greater top speed
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Can some one help me it’s too difficult
Please help me calculate the value of y with steps
The value of y in the triangle is 7.5
How to calculate the value of y?The given parameter is the triangle
On the triangle, we have the following equivalent ratio
y : 8 = y + 15 : 20
Express as fraction
y/8 = y + 15/20
Cross multiply
20y = 8y + 90
Collect the like terms
20y - 8y = 90
Evaluate
12y = 90
Divide by 12
y = 7.5
Hence, the value of y in the triangle is 7.5
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2(3) 3 as an exponent + 5
Answer: 13
Step-by-step explanation:
Iggy bought the refrigerator on a payment plan.He paid $150 when he bought it and he agreed to pay $28.50 each month for the next 24 months.
Answer:834$
Step-by-step:150+28.24=834$
MODELING REAL LIFE Bowling alley A charges $3.75 to rent shoes and $4 per game. Bowling alley B charges $2.50 to
rent shoes and $4.50 per game.
a. For what numbers of games is the total cost, including a pair of rental shoes, less at bowling alley A? at bowling alley B?
Bowling alley A:
Bowling alley B:
or more games
or
games
b. Bowling alley A increases the cost per game by $0.50. How does this affect your answer in part (a)? Explain.o
Using linear functions, it is found that:
a) The cheaper costs are given as follows:
Bowling alley A: 3 or more games.Bowling alley B: 1 or 2 games.b) Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The cost to rent shoes is the intercept.The cost per game is the slope.Hence the cost functions are given as follows:
A(x) = 3.75 + 4x.B(x) = 2.5 + 4.5x.The costs are equal when:
A(x) = B(x)
3.75 + 4x = 2.5 + 4.5x
0.5x = 1.25
x = 1.25/0.5
x = 2.5.
Hence the cheaper costs are given as follows:
Bowling alley A: 3 or more games.Bowling alley B: 1 or 2 games.Alley B has the lower initial cost due to the lower cost for the pair of shoes.
For item b, if we increase the cost per game by $0.50 for alley A, we have that:
A(x) = 4.5x + 3.75.
Hence:
Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.
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(2x)²y; x = 4, y = 8
[Mathematical Problem]
[tex](2x)^2y; x=4,y=8[/tex]
Solution:
Substitute the value of the variable into the expression, then simplify.
[tex](2(4))^2[/tex] × [tex]8[/tex]
↓
[tex](8)^2[/tex]
↓
[tex](8)^2[/tex] × [tex]8[/tex]
↓
[tex]64[/tex]
↓
[tex]64[/tex] × [tex]8[/tex] = 512
Hence, our solution is 512.
Hope this helps! It's been a while since I've done this, but this should be correct. Lmk if it helps! Thanks and good luck!
Which of the following vertices would minimize the objective function N = 7x + 2y?
A. (4,0)
B. (6,3)
C. (3,9)
D. (0,12)
Check the picture below.
In ΔJKL, m ∠ L=71°, j=11 m , and m ∠ K=46° . Find k .
Step-by-step explanation:
first : the sum of all angles in a triangle is always 180°.
second : the law of sine
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides, A, B, C are the the corresponding opposite angles.
therefore,
angle J = 180 - 71 - 46 = 63°
j/sin(J) = k/sin(K)
11/sin(63) = k/sin(46)
k = 11×sin(46)/sin(63) = 8.880673249... m
Doy muchos puntos pls ayuda
Answer:
5. 18%
6. 5.25% o 5.3 o 5
7. 33.33%
8. 2005-2010
8x = 2
Write down the value of x.
(It’s not 2/8 or 0.25)
Answer:
1/4
Step-by-step explanation:
Get x by itself by dividing both sides by 8
x = 2/8
Reduce
1/4
Answer:
8x=2
/8 /8
Step-by-step explanation:
it is 0.25
8x=2
/8 /8
x=0.25
How many passes were completed in the NFL for the 2018 season?
Lola went to the hardware store and bought 6 yellow ropes. The total length of the ropes was 8.1 meters. How long was each rope?
The length of each rope is 1.35 meters
How to calculate the length of each rope ?Lola went to the hardware store and bought 6 yellow ropes
The total length of the rope was 8.1 meters
Therefore the length of each rope can be calculated as follows
= 8.1/6
= 1.35
Hence the length of each rope at the hardware store is 1.35 meters
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What is each expression written as a single natural logarithm?
(c) 3 ln x+2 ln y+ln 5
According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.
Therefore, the given expression is [tex]3 ln x+2 ln y = ln5[/tex]
The values get multiplied in addition. Therefore, the above expression can be written as: [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]
Expression = [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]
Using logarithmic definition, we can write:
[tex]ln(x^{3} )+ln(y^{2} )+ln5\\ln(5x^{3} y^{2} )[/tex]
The solution for the given expression is [tex]ln(5x^{3}y^{2} )[/tex]
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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Write as an expression using an negative exponent 1/16
The negative exponent of 1/16 is 2⁻^{4}.
What is an expression?A statement is considered to be an expression if it has a minimum of two numbers or variables as well as at least one mathematical action.
Wha at is negative exponent?The multiplicative inverse of the base raised to the power opposite to the provided power is the definition of a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. For instance, (2/3)-2 may be represented as (3/2)2.
1/16 = 16⁻¹
1/16 = 16⁻¹ = 4⁻²
1/16 = 16⁻¹ = 4⁻² = (2^2)⁻² = 2⁻^{4} .
1/16 = 2⁻^{4} .
Hence, the negative exponent of 1/16 is 2⁻^{4}.
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Solve each equation. Check for extraneous solutions. 4(3 x-3)²/₃=36
The solutions of the equation [tex]4(3x-3)^{\frac{2}{3} } = 36[/tex] are x = 10 and x = - 8.
An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Consider the equation,
[tex]4(3x-3)^{\frac{2}{3} } = 36[/tex]
Now, divide each side of the equation by 4.
[tex]\frac{4(3x-3)^{\frac{2}{3} }}{4}=\frac{36}{4}[/tex]
[tex](3x-3)^{\frac{2}{3} } = 9[/tex]
Cubing the above equation.
[tex]((3x-3)^{\frac{2}{3} })^{3}=(9)^{3}[/tex]
( 3x - 3 )² = 729
3x - 3 = ( √729 )
3x - 3 = ± 27
Now,
3x - 3 = 27
3x = 30
x = 10
and;
3x - 3 = - 27
3x = - 24
x = - 8
Checking for extraneous solutions,
x = 10
[tex]4(3x-3)^{\frac{2}{3} }=36\\4(3(10)-3)^{\frac{2}{3} }=36\\4(27)^{\frac{2}{3} }=36\\27^{\frac{2}{3} }=9\\(3^{3})^{\frac{2}{3} } = 9\\3^{2}=9\\9=9[/tex]
When x = - 8,
[tex]4(3x-3)^{\frac{2}{3} }=36\\4(3(-8)-3)^{\frac{2}{3}}=36\\(-27)^{\frac{2}{3}}=9\\(-27)^{2}=(9)^{3}\\729=729[/tex]
The solutions for the equation are x = 10 and x = - 8.
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EVERY ONE PLEASE GO ON MY PAGE AND HELP ME, PLEASE
Answer:With what?
Step-by-step explanation:there is no page
Answer:
I helped you on your first question, I wasn't too sure about the others because their answer options are mostly inaccurate from what I know.
the table shows a proportional relationship between the millilitres (ml) of red paint and millilitres of yellow paint to make a certain shade of orange.
Factor the expression. 8+27 x³
The factored form of the given expression is (3x+2)(9x²-6x+4).
Given the expression is 27x³+8.
In order to be factor out any polynomial expression, we want to identify firstly the method of factoring to be used in the given expression. We also need to simplify the factors.
We are given the expression 27x³+8.
We want to factor out the given expression.
Applying the sum of two cubes formula x³+y³=(x+y)(x²-xy+y²), we have:
27x³+8=(3x)³+(2)³
27x³+8=(3x+2)(3²x²-3x·2+2²)
27x³+8=(3x+2)(9x²-6x+4)
Hence, the factored form of the given expression 27x³+8 is (3x+2)(9x²-6x+4).
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Simplify each expression. (-8x³)⁻⁴/₃
The solution for the expression ( -8x³) ⁻ ⁴/₃ = 1 / 16x⁴
Given expression is ( -8x³) ⁻ ⁴/₃
= ( -8x³) ⁻ ⁴/₃
It can be written as
We know that 8 = 2³ then
= ((-2x)³) ⁻ ⁴/₃
= ((-2x)³* ⁻ ⁴/₃
On the exponents '3' will be canceled then we get
= (-2x) ⁻ ⁴
We know that x ⁻ ¹ can be written as 1/x, then
= 1/(-2x)⁴
= 1 / 16x⁴
∴ ( -8x³) ⁻ ⁴/₃ = 1 / 16x⁴
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A farmer has 30 boxes of eggs.
6 There are 6 eggs in each box.
Write, as a ratio, the number of eggs in three boxes to the total number of eggs.
Give your answer in its simplest form
Answer: 1:15
Step-by-step explanation:
we know that the total number of eggs is the same as the number of eggs in 30 boxes. Hence the ratio will be 2 : 30, and then divide both sides by 2 to get 1 : 15 as the ratio in its simplest terms.
The ratio of the number of eggs in three boxes to the total number of eggs is 1 : 10.
We have,
To find the ratio of the number of eggs in three boxes to the total number of eggs, first, let's calculate the number of eggs in three boxes:
Number of eggs in three boxes
= 3 boxes * 6 eggs per box
= 18 eggs
Now, the ratio of the number of eggs in three boxes to the total number of eggs is:
18 eggs : 30 boxes x 6 eggs per box
18 eggs : 180 eggs
Cancel out the common factors.
1 egg : 10 eggs
So, the simplified ratio is:
1 egg : 10 boxes
Therefore,
The ratio of the number of eggs in three boxes to the total number of eggs is 1 : 10.
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−4k + 6 − 2k= −3 (4k − 10)?
Sorry, I got perplexed about how I was doing this.
Answer:
k=4
Step-by-step explanation:
−4k+6−2k=−3(4k−10)
−4k+6−2k=−3(4k−10)
−4k+6+−2k=(−3)(4k)+(−3)(−10)
−4k+6+−2k=−12k+30
(−4k+−2k)+(6)=−12k+30
−6k+6=−12k+30
−6k+6=−12k+30
−6k+6+12k=−12k+30+12k
6k+6=30
6k+6−6=30−6
6k=24
6k/6=24/6
k=4
(sorry if this was confusing)
Answer:
-3.5
Step-by-step explanation:
-4k+ 6 - 2k= -3(-6k)
-4k+ 4k= 18k
-4k = 18k-4k
-4k = 14
-4k/-4 = 14/-4
K= -3.5
Your sports drink bottle is 56 full. After practice, the bottle is 38 full. Write the difference of the amounts after practice and before practice. Write your answer as a fraction in simplest form.
The difference of the amounts after practice and before practice is 18 full.
The difference as a fraction in simplest form will be 9/28.
How to calculate the value?The sports drink bottle is 56 full and after practice, the bottle is 38 full, the difference of the amounts after practice and before practice will be:
= 56 - 38
= 18
The difference as a fraction in simplest form will be:
= Difference / Original value
= 18 / 56
= 9 / 28
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The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55.
The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10.
Work out the cost of
a) 1 kg of turnips.
b) 1 kg of mushrooms.
The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.
Let x represent the cost of on kg of mushroom and y represent the cost of one kg of turnips.
The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. Hence:
2x + 2.5y = 8.55 (1)
The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Hence:
3x + 4y = 13.10 (2)
From both equations:
x = 2.9, y = 1.1
The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10
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Jodi wants to visit her extended family in barbados next summer, and the flight costs $450. how much does she need to save each month if she wants to buy the flight in exactly 9 months?
If Jodi wants to visit her extended family in Barbados next summer, and the flight costs $450, then she needs to save 50$ each month if she wants to buy the flight in exactly 9 months.
If the flight costs $450, then the amount of money Jodi needs to save each month can be determined by using division.
Division is one of the four basic operations of arithmetic and involves the separation into equal parts.
By dividing the cost of the flight by the number of months, the money Jodi needs to save each month can be calculated.
Considering x to be money Jodi needs to save each month,
x = flight cost / number of months
x = 450 / 9
x = 50
Hence, the money Jodi needs to save each month if she wants to buy the flight in 9 months is calculated to 50$.
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Please help fast thank you!
Answer:
-3.78= (-1.2y)+(-4.2y)
y= 0.7
Step-by-step explanation:
-3.78= (-1.2y)+(-4.2y)
-3.78= -5.4y
/-5.4 /-5.4
y=0.7