Answer:
x=9, y=-4
C (9,-4)
Step-by-step explanation:
−4y − 3x = −11
x − 2y = 17
WE are using substitution, so solve the second equation for x
Add 2y to each side
x -2y+2y = 17+2y
x = 17+2y
Substitute this into the first equation
-4y -3x = -11
-4y -3(17+2y) = -11
Distribute the 3
-4y -3*17 -3*2y = -11
-4y -51 -6y = -11
Combine like terms
-10y-51=-11
Add 51 to each side
-10y-51+51=-11+51
-10y = 40
Divide by -10
-10y/-10 = 40/-10
y = -4
Now we need to find x
x= 17+2y
x = 17+ 2(-4)
x =17-8
x=9
By solving the second equation for x, substituting into the first equation, and simplifying, we find the solution to the system is (9, -4), which corresponds to Option C.
In order to find the solution of the system using substitution, we first solve one of the equations for x or y. Looking at the second equation x - 2y = 17, we can solve for x to get x = 2y + 17. Now we substitute this expression for x into the first equation - 4y - 3x = - 11, which gives us:
- 4y - 3(2y + 17) = - 11
Simplifying this equation, we obtain:
- 4y - 6y - 51 = - 11
Combine like terms:
- 10y - 51 = - 11
Add 51 to both sides:
- 10y = 40
Now, divide both sides by - 10 to find y:
y = - 4
After obtaining the value for y, we substitute it back into the equation we derived for x (x = 2y + 17):
x = 2( - 4) + 17
Which simplifies to:
x = - 8 + 17
Finally, we get x = 9.
The solution for the system is therefore (9, - 4), which corresponds to Option C.
A 24 ounce can of Fanta cost $1.75.How many does it cost per ounce round to the nearest cent
If 24 ounce can of Fanta cost $1.75 then it cost 13.71 per ounce.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that a 24 ounce can of Fanta cost $1.75.
We need to find the how many does it cost per ounce.
To find this we need to divide twenty four by one point seven five.
Cost per ounce is twenty four by one point seven five
Cost = 24/1.75
Cost per ounce=13.71
So a 24 ounce can of Fanta cost $1.75 can cost 13.71 per ounce.
Hence, if 24 ounce can of Fanta cost $1.75 then it cost 13.71 per ounce.
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fill in the missing reasons for the proof below.
what would the identity be?
[tex] \frac{2}{3} ( \frac{3}{2} ) = 1[/tex]
Answer:
Since both sides equal, there are infinitely many solutions
Step-by-step explanation:
Simplify brackets
2/3×3/1=1
Use this rule: a/b×c/d=ac/bd
Simplify 2×3 to 6
6/3×2=1
Simplify 3×2 to 6
6/6=1
cancel 6
1=1
Since both sides equal, there are infinitely many solutions
Mrs.Maxwell is buying pencils for her students. She has 3 classes of 28 students each. For Valentine’s Day, she wants to give each of her students 4 pencils. She can purchase packs of 18 pencils for $2.52. How many packs of pencils will Mrs. Maxwell need to purchase? Justify your answer.
Answer:
the answer might be 336 sorry if i am not right
Step-by-step explanation:
Answer:
I think the answer is approximately 5 packs of pencils.Hooe this helps :)
Step-by-step explanation: what I did was I multiplied 3 and 28 then divide that number by 12 and rounded my answer up.
Please answer number 3.
I can't exactly SHOW you where to put the numbers, but I can teach you the process of how you'd do it.
First off, label your number line from 0-15, as it is the simplest. (You'd be counting by 1 per each line). Then, follow this process:
1) Look at the first digit of your value. Place your number according to your first digit. (So, you'd put 0.365 at the 0 line and 3.521 at the 3 line)
2) Look at the second digit of your value. Imagine that between the two main lines (0-1 and 3-4) that there is 10 smaller lines. Then, you can place your number according to your second digit. (So, you'd put 0.365 at the 0.3 line and 3.521 at the 3.5 line).
3) Look at the third digit of your value. Imagine that between the two smaller lines (0.3-0.4 and 3.5-3.6) that there is 10 smaller lines. Then, you can place your number according to your third digit. (So, you'd put 0.365 at the 0.36 line and 3.521 at the 3.52 line).
4) Look at the fourth digit of your value. Imagine that between the two even smaller lines (0.36-0.37 and 3.52-3.53) that there is 10 smaller lines. Then, you can place your number according to your fourth digit. (So you'd place 0.365 at the 0.365 line and 3.521 at the 3.521 line)
Given 3X=-15
Prove X =-5
Answer:
X = -5
Step-by-step explanation:
3X=-15
Lets solve the equation for x. We will isolate x by dividing each side by 3
3X/3 = -15/3
X = -5
Method 1:
Solve the equation
3x = -15 divide both sides by 3
3x : 3 = -15 : 3
x = -5
Method 2:
Put the value of x to the equation:
L = 3(-5) = -15
R = -15
L = R CORRECT
A=1+Prt solve for p
[tex]A=1+Prt\\\\Prt=A-1\\\\P=\dfrac{A-1}{rt}[/tex]
Which characteristics describe the scatterplot? Check all that apply.
1.Negative Correlation
2.Positive Correlation
3.Strong Correlation
4.Weak Correlation
5.Linear
6.Nonlinear
A. Negative Association
C. Strong Association
E. Linear
Answer:
1. Negative Correlation
3. Strong Correlation
5. Linear
Step-by-step explanation:
We have been given a scatter-plot. We are asked to choose the characteristics of the given scatter-plot.
Upon looking at our given scatter-plot, we can see that as the values of x are increasing values of y are decreasing.
We know that the relationship between two variables in which one variable increases as the other decreases is known as negative correlation. Therefore, the given scatter-plot represents negative correlation and 1st option is a correct choice.
We can also see that the slope of the line connecting all data points is approximately [tex]-1[/tex], which represents a strong negative correlation, therefore, 3rd option is correct as well.
If we draw a line on our given scatter-plot, it will connect all the data points. Therefore, the given scatter-plot has a linear correlation and 5th option is correct as well.
The two rectangles shown have equal areas. Find the value of x
Answer:
x=18
Step-by-step explanation:
We need to find the areas of the rectangles
1st rectangle
A= l*w
A = (2x+4)*9
= 18x+36
2nd rectangle
A = l*w
= 15*(3x-30)
= 45x-450
Since the area of the rectangles are equal, we set these two equations equal
18x+36 = 45x-450
Subtract 18x from each side
18x-18x+36 = 45x-18x-450
36 = 27x-450
Add 450 to each side
36+450 =27x
486 = 27x
Divide by 27 on each side
486/27 = 27x/27
18=x
If your starting salary is $40,000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars, you will earn over the first 16 years that you work?
Round your answer to the nearest whole dollar, and express your answer without using commas.
Answer:
SEE BELOW PLEASE GIVE BRAINLIEST
Step-by-step explanation:
YEAR 1: 40000 X .03 = 1200 40,000 + 1200 = 41200
YEAR 2: 41,200 X .03 = 1236 41,200 + 1236 = 42436
YEAR 3: 42436 X .03 = 1273.08 42436 + 1273.08 = 43709.08
YEAR 4: 43709.08 x .03 = 1311.27 43709.08 + 1311.27 = 45020.35
YEAR 5: 45020.35 X .03 = 1350.61 45020.35 + 1350.61 = 46370.96
YEAR 6: 46370.96 X .03 = 1391.13 46370.96 + 1391.13 = 47762.09
YEAR 7: 47762.09 X .03 = 1432.86 47762.09 + 1432.86 = 49194.95
YEAR 8: 49194.95 X .03 = 1475.85 49194.95 + 1475.85 = 50670.80
YEAR 9: 50670.80 X .03 = 1520.12 50670.80 + 1520.12 = 52190.92
YEAR 10: 52190.92 X .03 = 1565.73 52190.92 + 1565.73 = 53756.65
YEAR 11: 53756.65 X .03 = 1612.70 53756.65 + 1612.70 = 55369.35
YEAR 12: 55369.35 X .03 = 1661.08 55369.35 + 1661.08 = 57030.43
YEAR 13: 57030.43 X .03 = 1710.91 57030.43 + 1710.91 = 58741.34
YEAR 14: 58741.34 X .03 = 1762.24 58741.34 + 1762.24 = 60503.58
YEAR 15: 60503.58 X .03 = 1815.11 60503.58 + 1815.11 = 62318.69
YEAR 16: 62318.69 X .03 = 1869.56 62318.69 + 1869.56 = $64,188.25 = $64188
$806275, hope this helps!
Hello! I kinda need a little help with this...
Lines m contains (6,8) and (-1,2). Lines n contains (-1,5) and (5,y). What is the value of y if line m is perpendicular to line n?
Can someone please help? The Maths is not something I'm too good at. :D
I honestly don't know or I would have replied. Sorry :(
Answer: y = -2
========================================
Explanation:
Find the slope of line m using the slope formula
slopeM = (y2-y1)/(x2-x1)
slopeM = (2-8)/(-1-6)
slopeM = -6/(-7)
slopeM = 6/7
The slope of line m is 6/7. The perpendicular slope is -7/6. We flip the fraction (aka reciprocal) and flip the sign (from positive to negative). The phrase "flip the fraction and flip the sign" is a handy way to think of "negative reciprocal", at least in my opinion. Note how the two slopes 6/7 and -7/6 multiply to -1 to prove they are perpendicular slopes
We'll use the slope formula again to set up the slope for line n. We don't know y, but we can set the fraction equal to -7/6 and solve for it.
slopeN = (y2-y1)/(x2-x1)
slopeN = (y-5)/(5-(-1))
slopeN = (y-5)/(6)
-7/6 = (y-5)/6
-7*6 = 6(y-5)
-42 = 6y-30
6y-30 = -42
6y = -42+30
6y = -12
y = -2
So in short, if y = -2, then line n goes through (-1,5) and (5,y) = (5,-2). The slope of line N is computed to be...
slopeN = (y2-y1)/(x2-x1)
slopeN = (-2-5)/(5-(-1))
slopeN = (-2-5)/(5+1)
slopeN = -7/6
which is the proper slope value we want.
If the current exchange rate is 1.35261 US dollars for each Euro, how many dollars would be exchanged for 285 Euro?
Answer:
$385.49
Step-by-step explanation:
285x1.35261=385.49385
round to the nearest cent and you get $385.49
To exchange 285 Euros for US dollars at an exchange rate of 1.35261, you would receive 385.80785 US dollars.
Current exchange rate = 1.35261 US dollars
To calculate how many dollars would be exchanged for 285 Euros at an exchange rate of 1.35261 US dollars per Euro:
Set up a simple multiplication problem: 285 Euros multiplied by 1.35261 US dollars per Euro.
Multiply the two numbers to get the total amount in US dollars.
So, 285 Euros x 1.35261 = 385.80785 US dollars would be exchanged for 285 Euros.
You've baked 26 cookies, which is two-thirds of all the cookies you planned to bake. How many cookies did you plan to make?
Equation:
Solution:
Answer,
(26/2) * 3
= 39
Explanation,
26 cookies is only 2/3 of 3/3. So, we divide 26 by 2 to see how many cookies are in 1/3. We then can find out that when you make 1/3 of the cookies there are 13. Since that is only 1/3 and we want to find out 3/3. We multiply 13 by 3 and get 39 which is all the cookies she planned to make.
Hope this helps :-)
Triangle ABC is reflected over the y-axis. The coordinates of Point A are (–3, –1). What are the coordinates of Point A', the reflected image, using an algebraic representation?
Answer:
A'(3, - 1)
Step-by-step explanation:
Under a reflection in the y-axis
a point (x, y) → (- x, y), hence
A (- 3, - 1) → A'(3, - 1)
The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)
what is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates.
Given here: The coordinate of a Triangle A as (-3,-1)
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Thus The vertex of the triangle (-3,-1) it changes to (3,-1)
The algebraic representation for the transformation is given by '
(x,y)⇒(-1×x,1×y)
⇒(-x, y)
Hence, The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)
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Mother has purchased 75 yards of green fabric and 125 yards of white fabric to make green and white curtains. What is the largest number of curtains she can make if she wants all the curtains to be exactly the same length, and to have no fabric left over? How many yards of each kind of fabric would be used for each curtain?
The mother can make 3 green curtains and 5 white curtains, using the greatest common divisor of 75 and 125 yards which is 25. Each curtain would thus be 25 yards.
Explanation:This question can be solved using the concept of Greatest Common Divisor (GCD), which finds the largest possible length that can divide two given lengths without leaving any remainder. In this case, the lengths are 75 yards and 125 yards, which are the quantities of green and white fabric respectively. The GCD of 75 and 125 is 25.
Therefore, the largest number of curtains that can be made is based on this length, which means the mother can make 75/25=3 green curtains and 125/25=5 white curtains. Each curtain would be 25 yards.
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find the slope of the line through each pair of points.
A quadratic equation is shown below:
9x^2 - 16x + 60 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work
Part B: Solve 4x^2 + 8x - 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you choose the method used.
the solutions to a general quadratic equation is
X=-b±√b²-4ac/2a ,, When ax²+bx+c=0
the discriminant is the expression under the radical b²−4ac
Part A:
discriminant is (-16)² - 4(9)(60) = -1904
there are two complex solutions
Part B:
4x² + 8x − 5 = 0
4x² + 10x -2x - 5=0
2x ( 2x + 5) - 1(2 x + 5) =0
(2x + 5)(2x-1) = 0
/ \
/ \
2x+5 = 0 2x-1 =0
x = -5/2 x = 1/2
Change each improper fraction into an equal mixed number.
a. 15⁄4
b. 41⁄9
c. 67⁄8
d. 135⁄11
e. 107⁄20
f. 493⁄174
Answer:
A. 3 3/4
B. 4 5/9
C. 8 3/8
D. 12 3/11
E. 5 7/20
F. 2 145/174
Hope That Helps!
Help me find the slope of the line please
Answer: 3/4
Step-by-step explanation:
Please help me I’m begging someone I really need help !!!!!!! I will mark brainlest!!!!!
Answer:
I can be little confident because if it was just 0.7 then it would be I am not confident at all. This decimal is more than 0 so it would be a little and not a lot.
Step-by-step explanation:
use the quadratic formula to solve -5x^2-12x+8=0
[tex]\text{The quadratic formula:}\\\\ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\--------------------------------\\\text{We have}\ -5x^2-12x+8=0\\\\a=-5,\ b=-12,\ c=8\\\\\text{Substitute:}\\\\b^2-4ac=(-12)^2-4(-5)(8)=144+160=304\\\\\sqrt{b^2-4ac}=\sqrt{304}=\sqrt{16\cdot9}=\sqrt{16}\cdot\sqrt{19}=4\sqrt{19}\\\\x_1=\dfrac{-(-12)-4\sqrt{19}}{2(-5)}=\dfrac{12-4\sqrt{19}}{-10}=\boxed{-\dfrac{6-2\sqrt{19}}{5}}\\\\x_2=\dfrac{-(-12)+4\sqrt{19}}{2(-5)}=\dfrac{12+4\sqrt{19}}{-10}=\boxed{-\dfrac{6+2\sqrt{19}}{5}}[/tex]
Given 4x = a + b/
8c
, rearrange the equation for a, in terms of b, c, and x
Answer:
B) a = 32cx − b
Step-by-step explanation:
i just did it
what is the solution to the system of equations y=x+3, y=3x+1
Substitution method
y = x + 3 (*)
y = 3x + 1 (**)
Substitute (*) to (**):
3x + 1 = x + 3 subtract 1 from both sides
3x = x + 2 subtract x from both sides
2x = 2 divide both sides by 2
x = 1Put the value of x to (*):
y = 1 + 3
y = 4Answer: x = 1 and y = 4 → (1, 4).what is seven decreased by 3 times some number
the answer to the question is 7-3x.
Answer:
7 - 3x
Step-by-step explanation:
let "some number" = x
"3 times x" = 3(x)
"seven decreased by" 7 -
Put together the phrases.
"seven decreased by 3 times x" is 7 - 3x
7 - 3x is your answer
~
what is i + 6i? You have to simplify
[tex]i=1i\\\\i+6i=1i+6i=(1+6)i=\boxed{7i}[/tex]
what is the sum 12 1/4+ 5 5/6 reduce to lowest terms
Answer:
is it 2/21 i hope im right cuz i just looked it up
Step-by-step explanation:
To find the sum, convert the fractions to have the same denominator. Add the whole numbers and the fractions separately. The sum of 12 1/4 and 5 5/6 reduced to lowest terms is 17 13/12.
Explanation:To find the sum of 12 1/4 and 5 5/6, we need to convert the fractions to have the same denominator. The common denominator for 4 and 6 is 12. So, we can rewrite 12 1/4 as 12 3/12 and 5 5/6 as 5 10/12. Now we can add the whole numbers, 12 and 5, which gives us 17. Then, we add the fractions, 3/12 and 10/12, which equals 13/12. Therefore, the sum of 12 1/4 and 5 5/6 reduced to lowest terms is 17 13/12.
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The exression below represents Julia's annual salary after t years.
25,000(1.04)t
Interpret the meaning of the expression.
Julie's salary started at $25,000. t is the number of years since her original $25,000 salary started. Each year she gets a 4% raise. The expression gives her salary at year t.
Answer:
b.
Step-by-step explanation:
Interpret the meaning of the expression.
A.
Julia's initial salary is $4,000, and the growth rate is 25% per year.
B.
Julia's initial salary is $25,000, and the growth rate is 4% per year.
C.
Julia's initial salary is $4,000, and the growth rate is 2.5% per year.
D.
Julia's initial salary is $25,000, and the growth rate is 40% per year.
4m of timber costs £33.60 what is the cost of 9m?
Answer:
£ 75.60
Step-by-step explanation:
4 m ↔ £ 33.60
1 m ↔ £ 8.40
9 m ↔ £ 75.60
The cost of one meter of timber is £8.40, calculated by dividing £33.60 by 4. To find the cost of 9 meters, multiply £8.40 by 9, resulting in a total cost of £75.60.
To determine the cost of 9 meters of timber when we know that 4 meters cost £33.60, we can use a unit rate approach. First, we need to calculate the cost of one meter of timber by dividing the total cost by the number of meters. Then, we multiply the cost per meter by 9 to find the cost of 9 meters of timber.
Find the cost per meter: £33.60 / 4 meters = £8.40 per meter.Calculate the cost for 9 meters: £8.40 per meter * 9 meters = £75.60.Therefore, the cost of 9 meters of timber would be £75.60.
A marketing company surveys 100 males and 100 females between the ages of 55 and 70 to determine how many times they text each day. The mean for males is 6 with a range of 4. The mean for the females is 8 with a range of 4. According to the statistics, which statement is TRUE?
A)
On average, females text more than males.
B)
On average, females text less than males.
C)
On average, females and males text about the same .
D)
On average, both males and females text 4 times each day.
Answer: I believe that A is the correct answer.
Answer:
It's A
Step-by-step explanation:
I just did this question
I WILL AWARD BRAINLIEST!
Find the measures of all angles formed by line a parallel to line b with transversal m, if one angle is 25° bigger than another
Answer:
Measures of all angles is either 77.5° or 102.5°
Step-by-step explanation:
See the attached figure.
As shown:
line a parallel to line b with transversal m
So, all the angles are either congruent or supplementary.
Let the supplementary angles x and y and y > x
x + y = 180° ⇒ (1)
one angle is 25° bigger than another
y - x = 25° ⇒ (2)
solving (1) and (2)
∴ x = 77.5° and y = 102.5°