Q2 - With decimals
Work these simultaneous equations out
on paper and write down your answers.
The cost of 8 CDs and 7 DVDs is
$113.50.
The cost of 12 CDs and 8 DVDs is
$153.
a =
10a + 3b = 31
15a + 4b = 45
b =
m =
4m + 10n = 83
9m + 6 = 96
n =
p =
8p + 59 = 27
12p + 40 = 51
All the CDs are the same price and
all the DVDs are the same price.
q=
Find the cost of one of each.
6S + 7t = 42
S =
1 CD is $
8s + 3t = -1
t =
[8]
[4]
1 DVD is $
Answers
Answer:
Simplify the following algebraic expressions.
- 6x + 5 + 12x -6
2(x - 9) + 6(-x + 2) + 4x
3x2 + 12 + 9x - 20 + 6x2 - x
(x + 2)(x + 4) + (x + 5)(-x - 1)
1.2(x - 9) - 2.3(x + 4)
(x2y)(xy2)
(-x2y2)(xy2)
Solution
Group like terms and simplify.
- 6x + 5 + 12x -6 = (- 6x + 12x) + (5 - by
Solution
Use rules of exponential to simplify the numerator first.
(a b2)(a3 b) / (a2 b3) = (a4 b3) / (a2 b3)
Rewrite as follows.
(a4 / a2) (b3 / b3)
Use rule of quotient of exponentials to simplify.
= a2
Rewrite as follows.
(21 x5) / (3 x4) = (21 / 3)(x5 / x4)
Simplify.
= 7 x
(6 x4)(4 y2) / [ (3 x2)(16 y) ]
Multiply terms in numerator and denominator and simplify.
(6 x4)(4 y2) / [ (3 x2)(16 y) ] = (24 x4 y2) / (48 x2 y)
Rewrite as follows.
= (24 / 48)(x4 / x2)(y2 / y)
Simplify.
= (1 / 2) x2 y
Factor 4 out in the numerator.
(4x - 12) / 4 = 4(x - 3) / 4
Simplify.
= x - 3
Factor -5 out in the numerator.
(-5x - 10) / (x + 2) = - 5 (x + 2) / (x + 2)
Simplify.
= - 5
Factor numerator and denominator as follows.
(x2 - 4x - 12) / (x2 - 2x - 24) = [(x - 6)(x + 2)] / [(x - 6)(x + 4)]
Simplify.
= (x + 2) / (x + 4) , for all x not equal to 6
Solve for x the following linear equations.
2x = 6
6x - 8 = 4x + 4
4(x - 2) = 2(x + 3) + 7
0.1 x - 1.6 = 0.2 x + 2.3
- x / 5 = 2
(x - 4) / (- 6) = 3
(-3x + 1) / (x - 2) = -3
x / 5 + (x - 1) / 3 = 1/5
Solution
Divide both sides of the equation by 2 and simplify.
2x / 2 = 6 / 2
x = 3
Add 8 to both sides and group like terms.
6x - 8 + 8 = 4x + 4 + 8
6x = 4x + 12
Add - 4x to both sides and group like terms.
6x - 4x = 4x + 12 - 4x
2x = 12
Divide both sides by 2 and simplify.
x = 6
Expand brackets.
4x - 8 = 2x + 6 + 7
Add 8 to both sides and group like terms.
4x - 8 + 8 = 2x + 6 + 7 + 8
4x = 2x + 21
Add - 2x to both sides and group like terms.
4x - 2x = 2x + 21 - 2x
2x = 21
Divide both sides by 2.
x = 21 / 2
Add 1.6 to both sides and simplify.
0.1 x - 1.6 = 0.2 x + 2.3
0.1 x - 1.6 + 1.6 = 0.2 x + 2.3 + 1.6
0.1 x = 0.2 x + 3.9
Add - 0.2 x to both sides and simplify.
0.1 x - 0.2 x = 0.2 x + 3.9 - 0.2 x
- 0.1 x = 3.9
Divide both sides by - 0.1 and simplify.
x = - 39
Multiply both sides by - 5 and simplify.
- 5(- x / 5) = - 5(2
What is the y intercept of the line - 4 x + 6 y = - 12?
Solution
Set x = 0 in the equation and solve for y.
- 4 (0) + 6 y = - 12
6 y = - 12
y = - 2
y intercept: (0 , - 2)
What is the x intercept of the line - 3 x + y = 3?
Solution
Set y = 0 in the equation and solve for x.
- 3 x + 0 = 3
x = -1
x intercept: (-1 , 0)
What is point of intersection of the lines x - y = 3 and - 5 x - 2 y = - 22?
Solution
A point of intersection of two lines is solution to the equations of both lines. To find the point of intersection of the two lines, we need to solve the system of equations x - y = 3 and -5 x - 2 y = -22 simultaneously. Equation x - y = 3 can be solved for x to give
x = 3 + y
Substitute x by 3 + y in the equation - 5 x - 2 y = -22 and solve for y
-5 (3 + y) - 2 y = - 22
-15 - 5 y - 2 y = - 22
-7 y = - 22 + 15
-7 y = - 7
y = 1
Substitute x by 3 + y in the equation -5 x - 2 y = - 22 and solve for y
x = 3 + y = 3 + 1 = 4
Point of intersection: (4 , 1)
For what value of the constant k does the line - 4 x + k y = 2 pass through the point (2,-3)?
Solution
For the line to pass through the point (2,-3), the ordered pair (2,-3) must be a solution to the equation of the line. We substitute x by 2 abd y by - 3 in the equation.
- 4(2) + k(-3) = 2
Solve the for k to obtain
k = - 10 / 3
What is the slope of the line with equation y - 4 = 10?
Solution
Write the given equation in slope intercept form y = m x + b and identify the slope m.
y = 14
It is a horizontal line and therefore the slope is equal to 0.
What is the slope of the line with equation 2 x = -8?
Solution
The above equation may be written as
x = - 4
It is a vertical line and therefore the slope is undefined.
Find the x and y intercepts of the line with equation x = - 3?
Solution
The above is a vertical line with x intercept only given by
(-3 , 0)
Find the x and y intercepts of the line with equation 3 y - 6 = 3?
Solution
The given equation may be written as
y = 3
The above is a horizontal line with y intercept only given by
(0 , 3)
What is the slope of a line parallel to the x axis?
Solution
A line parallel to the x axis is a horizontal line and its slope is equal to 0.
What is the slope of a line perpendicular to the x axis?
Solution
A line perpendicular to the x axis is a vertical line and its slope is undefined
Step-by-step explanation:
y = -22 and solve for y
-5 (3 + y) - 2 y = - 22
-15 - 5 y - 2 y = - 22
-7 y = - 22 + 15
-7 y = - 7
y = 1
Related Questions
I have asked so many times and no one will answer. :(
1. Simplify each expression using the laws of exponents. Use the least number of bases possible and only positive exponents. When appropriate, express answers without parentheses or as equal to 1. All letters denote numbers. (1/2)⁷
2. Simplify each expression using the laws of exponents. Use the least number of bases possible and only positive exponents. When appropriate, express answers without parentheses or as equal to 1. All letters denote numbers. (1/11)⁻⁷
Answers
Answer:
1) [tex]\frac{1}{2^7}[/tex] ; 2) [tex]11^7[/tex]
Step-by-step explanation:
1) Using the Power of a Fraction Rule [tex](\frac{a}{b} )^x = (\frac{a^x}{b^x} )[/tex],
[tex](\frac{1}{2} )^7 = (\frac{1^7}{2^7} )[/tex], which can just be simplified to [tex]\frac{1}{2^7}[/tex].
2) Using the Negative Exponent Rule, [tex]a^{-x} = \frac{1}{a^{x}}[/tex],
[tex](\frac{1}{11} )^{-7} = \frac{1}{\frac{1}{11^7}}[/tex], which can be simplified to [tex]11^7[/tex].
what is the actual length?
Answers
Answer:
Step-by-step explanation:
2ft
PLEASE HELP (don't put fake answers !!)
Answers
Answer:
=33.55 m^2
Step-by-step explanation:
The area of the trapezoid is
A = 1/2 a(b+c) where a is the height and b and c are the bases
A = (1/2 *5.5)(5+7.2)
= 2.75(12.2)
=33.55 m^2
Answer:
i resubmitted my Persuasive Argument: Letter to Gov. Abbott Choice
Step-by-step explanation:
5.) Forty percent of the students at Pinecrest Middle School have a school
sweatshirt. There are 560 students at the school. How many students have
a school sweatshirt? *
PLSS HELP
Answers
224 students have a sweatshirt.
7n +2 –(2n +7) pls help I will give you 15 points
Answers
Answer:
5n -5
Step-by-step explanation:
7n +2 –(2n +7)
7n +2 -2n -7
5n -5
Ann and bill shared £440 in the ratio 9:2 Ann gives bill some of her money Bill now has the same amount as ann
Answers
Answer:
Bill gave Ann £220
Step-by-step explanation:
plz mark brainliest :D
Ann shared £360 and Bill shared £80.
What is ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
Ann and bill shared £440
Ratio = 9:2
Total is = 9+ 2= 11
So, Anna shred
= 9/11 x 440
= 360
and Bill shred
= 2/11 x 440
= 80
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Dane needs to cut 4 strips of border for his rectangular project board. The project board has a length of 12 1/2 inches and a width of 6 1/4 inches. How much border will Dane have left if the border comes in a 60-inch roll?
Answers
One hundred grams of radium are stored in a container. The amount RR (in grams) of radium present after tt years can be modeled by R=100e−0.00043tR=100e−0.00043t. After how many years will only 5 grams of radium be present? Round your answer to the nearest whole year.
Answers
Answer:
6967 years
Step-by-step explanation:
Given the exponential function :
R=100e−0.00043t
Time = t in years
R = final amount
Number of years in which only 5 grams of radium will be present :
R = 5
Plugging into our formula :
5 = 100 * e^−0.00043t
5 / 100 = e^−0.00043t
0.05 = e^−0.00043t
Take the In of both sides
−2.995732 = - 0.00043t
t = −2.995732 / - 0.00043t
t = 6966.819
t = 6966.819 years
t = about 6967 years
Find the quotient and remainder when the first polynomial is divided by the second 3x⁴+16x³+6x²-2x-13; x+5
Answers
Answer:
Quotient : 3x³ + x² + x + 3
Step-by-step explanation:
Give the polynomial :
Dividend : 3x⁴+16x³+6x²-2x-13;
Divisor : x+5
Kindly check attached picture for detailed explanation.
Can someone help me I'm confused
Answers
Answer:
I think its 5 t shirts for 11 dollars?
Step-by-step explanation:
Answer:
When she buys 0 t-shirts, the price is $0.
Step-by-step explanation:
the numerical coefficient in the expression -3×y² is
Answers
The numerical coefficient for the expression how much of the variables, in this case xy^2 there are in number form. There is only one number in this question so it makes it fairly straight forward. The answer is -3.
Which expression is equivalent to (6 * p ) + 3? *
Answers
Answer:
What are the other choices
Step-by-step explanation:
Which statement best describes the area of Triangle ABC shown below?
А
с
00
(5 points)
O It is twice the area of a square of side length 4 units.
O It is one-half the area of a square of side length 4 units.
It is twice the area of a rectangle with sides 4 units x 3 units.
It is one-half the area of a rectangle with sides 4 units x 3 units.
Answers
Answer:
Would be the 3rd one I believe
Step-by-step explanation:
The statement that is true is:
It is one-half the area of a rectangle with sides of 4 units x 3 units is true.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
The area of the triangle.
= 1/2 x base x height
Now,
Base = 4 units
Heights = 3 units
So,
Area = 1/2 x 4 x 3 = 6 units²
Now,
It is twice the area of a square of the side length of 4 units.
6 units² < 16 units²
This is not true.
It is one-half the area of a square of side length 4 units.
1/2 x 16 units² = 6 units²
8 units² = 6 units²
This is not true.
It is twice the area of a rectangle with sides 4 units x 3 units.
2 x 12 units² = 6 units²
24 units² = 6 units²
This is not true.
It is one-half the area of a rectangle with sides 4 units x 3 units.
1/2 x (4 x 3) units² = 6 units²
6 units² = 6 units²
This is true.
Thus,
It is one-half the area of a rectangle with sides of 4 units x 3 units is true.
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1.) Eric is twice as tall as Kevin. Kevin is also three feet shorter than Eric.
a. Use mathematical sentences to represent all of the information in this problem.
b. Find each boy's height. HINT: Can you represent both boys with ONE variable?
Answers
What is the answer?
Is it A B C or D
Answers
Answer:
D
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
square the 3 and times 4 and 2
In which diagram do <1 and <2 appear to be vertical angles?
Answers
pq=3-a√x
make x the subject
Answers
Step-by-step explanation:
pq = 3 - a√x
Making x subject
a√x = 3 - pq
√x = (3 - pq) / a
x = [ (3 - pq) /a ]²
Hope it will help :)
Fwam answered 142 questions correctly on his multiple choice science final that had
a total of 200 problems. What percentage of questions did Fwam answer correctly on
the final exam?
Answers
Answer:
71%
Step-by-step explanation:
Percentage Chart
X is what percent of 200?142 is71% of 200143.26 is71.63% of 200144.64 is72.32% of 200146.02 is73.01% of 200
The volleyball team needs new uniforms. The students plan to sell plush toy eagles (the school mascot) for $5 each. The students find three companies on-line that sell stuffed mascots. Company A sells 12 eagles for $34.56. Company B sells 15 eagles for $42.90. Company C charges $51.30 for 18 eagles. Which company has the best buy?
Answers
Answer:
Step-by-step explanation:
A=34.56/12=$2.88 each
B=42.90/15=$2.86 each
C=51.30/18=$2.85 each
So C is the cheapest.
Graph the line with the equation y=
- 1/5x + 4
Answers
Step-by-step explanation:
look at the attachment
.....
The graph of the linear equation is plotted and y = ( -1/5 )x + 4
Given data ,
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
On simplifying , we get
y = ( -1/5 )x + 4
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = -1/5
And , the y-intercept of the graph of the line is when x = 0
So , when x = 0
y = ( -1/5 ) ( 0 ) + 4
y = 4
Hence , the equation of line is y = ( -1/5 )x + 4
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need help im dum (not really but i dont get it)
i will give brainliest
Answers
Answer:
20
Step-by-step explanation:
to do % you have to multiply your number (50) by the % which is 40%
but you have to turn your number into a decimal (.40) then multiply
you'll get 20 and there is your answer!
hope this helps!
Destiny spent $12.00 of the $20.00 in her wallet.Write a decimal and percent that represents the fraction of the $20.00 that denstiny spent
Answers
Answer:
40% and 0.4
Step-by-step explanation:
What is the value of x in the equation 2.5(6x - 4) = 10 + 4(1.5 +0.5 x)?
3
이를
02
0 13
Answers
Answer:
Step-by-step explanation:
15x - 10 = 10 + 6 + 2x
15x - 10 = 16 + 2x
Bringing like terms on one side
15x - 2x = 16 + 10
13x = 26
x = 26/13
x = 2
The value of x in the equation is 2.
Option C is the correct answer.
What is an equation?An equation is a mathematical statement that shows that two expressions are equal.
It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. Equations are used to solve problems and find unknown values.
We have,
We are given the equation 2.5(6x - 4) = 10 + 4(1.5 + 0.5x) and we need to find the value of x that satisfies this equation.
First, we can simplify both sides of the equation by using the distributive property of multiplication.
This gives us:
15x - 10 = 10 + 6 + 2x
Next, we can combine like terms on both sides of the equation. Specifically, we can combine the constants on the right-hand side:
15x - 10 = 16 + 2x
Now, we want to isolate the term with x on one side of the equation.
We can do this by subtracting 2x from both sides of the equation:
13x - 10 = 16
Finally, we can solve for x by adding 10 to both sides of the equation and then dividing both sides by 13:
13x = 26
x = 2
Therefore,
The value of x in the equation is 2.
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Anya found the slope of the line that passes through the points (–7, 4) and (2, –3). Her work is shown below.
Let (x2, y2) be (–7, 4) and (x1, y1) be (2, –3).
m = m equals StartFraction x 2 minus x 1 over y 2 minus y 1.
= Equals StartFraction negative 7 minus 2 Over 4 minus negative 3.
= Negative StartFraction 9 Over 7 EndFraction.
The slope is Negative StartFraction 9 Over 7 EndFraction..
What error did she make?
She simplified the denominator incorrectly. The denominator simplifies to –7.
She labeled the points incorrectly. The point (–7, 4) should be (x1, y1).
She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values.
She used an incorrect formula. The formula should be the sum of the x-values with respect to the sum of the y-values.
Answers
Answer:
It is C 100% 2021 on edge
Step-by-step explanation:
Answer:
The answer is C "She used an incorrect formula. The formula should be the change in y-values with respect to the change in the x-values."
Step-by-step explanation:
I just did it and got it right.
Solve for b
Solve for b : -3b+2.5=4
Answers
Answer: -0.5
Step-by-step explanation:
-3b = 4-2.5
-3b = 1.5
(-3b)/-3 = 1.5/-3
b = -0.5
Answer:
should be - 0.5
Step-by-step explanation:
- 3b + 2.5 = 4
1.Turn the equation around
1. -3b = -2.5 + 4.
1. The reason why you turn the 2.5 into a negative is because you basically doing the oppisite if that makes sence.
2. Add -2.5 + 4
2. -2.5 + 4 = 1.5
2. I just added.
3. Plug 1.5 into the equation. Like so
3. -3b = 1.5
3. I just replaced -2.4 + 4 with the answer
4. Divied -3b = 1.5
4. -3b/-3b = 1.5/-3b = -0.5
4. What you do to one side you have to do to the other so -3b/-3b is 0 or it just is not there anymore next you take -3b and divide it by 1.5 and get - 0.5 BAM.
5. Plug -0.5 in for b.
5. -3(-0.5) + 2.5 = 4
Rich bought 5 cupcakes and one pie. He knows his total bill is $13.14 and knows the pie was
$6.89. How much is the cost of one cupcake?
Answers
$6.25
Take the total and subtract the amount of money from the pies to get the amount for cupcakes
Answer fast!!!!!!!!!
Answers
Answer:
$0.52 = 0.52
Step-by-step explanation:
I think so.....
Please answer the correctly in the picture below 8TH GRADE MATHENMATICS?!
Answers
Answer:
B 3.5
Step-by-step explanation:
Hope it Helps!
Hope it helps my freind
9.
In the expression 7g + 12
a. 7 is the constant
b. c. 12 is the coefficient
C. g is the variable
d. if g = 4, the expression equals 30
Answers
Answer:
c. g is the variable
Step-by-step explanation:
Answer:
The only true answer is that g is the variable
C
solve for x and y
-4x + 9y = 9
x - 3y = -6
Answers
Answer:
Solve for x:
[tex]x = \frac{9(y - 1)}{4} [/tex]
Solve for y:
[tex]y = \frac{4x}{9} + 1[/tex]