Answer:
( - 1, 1 )
Step-by-step explanation:
Given the 2 equations
3x - y = - 4 → (1)
x + y = 0 → (2)
Subtract y from both sides in (2)
x = - y → (3)
Substitute x = - y into (1)
- 3y - y = - 4, that is
- 4y = - 4 ( divide both sides by - 4 )
y = 1
Substitute y = 1 into (3)
x = - 1
Solution is (- 1, 1 )
The solution to the system of equations 3x - y = -4 and x + y = 0 is found by substitution, resulting in the solution set (x, y) = (-1, 1).
To find the solution to the equations 3x - y = -4 and x + y = 0, you can use the method of substitution or elimination. Since the second equation easily gives us y in terms of x (that is, y = -x), we can substitute this into the first equation.
Substitute y = -x into the first equation: 3x - (-x) = -4.
Simplify: 3x + x = 4x
hence, 4x = -4
Divide both sides by 4 to solve for x: x = -1.
Now substitute x = -1 into y = -x to find y: y = -(-1) = 1.
The solution to the system of equations is (x, y) = (-1, 1).
Greta is 1 1/2 meters tall which of the following is equivalent to 1 1/2 meters
1 1/2 meters is equivalent to 1500 millimeters.
The correct option is (b).
To find out which option is equivalent to 1 1/2 meters, we need to convert 1 1/2 meters to millimeters.
Given:
- Gretta's height is 11/2 meters.
To convert meters to millimeters, we'll use the fact that 1 meter is equal to 1000 millimeters.
So, to convert 1 1/2 meters to millimeters:
[tex]\[ \text{1 1/2 meters} = (1 + 1/2) \times 1000 \text{ millimeters} \][/tex]
[tex]\[ = (1.5) \times 1000 \text{ millimeters} \][/tex]
[tex]\[ = 1500 \text{ millimeters} \][/tex]
So, 1 1/2 meters is equivalent to 1500 millimeters.
Therefore, the correct option is:
b. 1500 millimeters
complete question given below:
Gretta is 11/2 meters tall. Which of the following is equivalent to 1 1/2 meters?
a.150 millimeters
b.1,500 millimeters
c.100 millimeters
d.1,000 millimeters
What is the value of k in the equation 10k-7=7k-15
Answer:
k=-8/3
Step-by-step explanation:
10k-7=7k-15
10k-7k-7=-15
3k-7=-15
3k=-15+7
3k=-8
k=-8/3
The vertices of triangle ABC are A(−5, 1), B(−2.5, 7), and C(0, 1). Find the new coordinates of the vertices after the given translation.
Answer:
A'(-2,0) , B'(0.5,6) and C'(3,0)Step-by-step explanation:
The vertices of triangle ABC are A(−5, 1), B(−2.5, 7), and C(0, 1).
The given translation of vertices,
(x, y) → (x + 3, y − 1)This translation shows shift x-coordinate 3 unit right and y-coordinate 1 unit down.
First translate vertices A(-5,1)[tex]A(-5,1)\rightarrow A'(-5+3,1-1)[/tex]
New vertices A'(-2,0)
Now vertices B(-2.5,7)[tex]B(-2.5,7)\rightarrow B'(-2.5+3,7-1)[/tex]
New vertices B'(0.5,6)
Now vertices C(0,1)[tex]C(0,1)\rightarrow C'(0+3,1-1)[/tex]
New vertices C'(3,0)
Hence, the new coordinate of the vertices are A'(-2,0) , B'(0.5,6) and C'(3,0)
Jeff has 4 red pens and 2 blue pens in his backpack. He also has 1 yellow highlighter and 4 green highlighters in his
backpack. If he reaches into his backpack and grabs one pen and one highlighter without looking, what is the probability
that he will grab a blue pen and a yellow highlighter?
Answer:
[tex]\frac{1}{15}[/tex]
Step-by-step explanation:
In probability,
"AND" means "multiplication"
"OR" means "ADDITION"
We want probability of Blue Pen and Yellow Highlighter. So we find individual probabilities and "MULTIPLY" them.
Let P(b) be probability of blue pen
Let P(y) be probability of yellow highlighter
We know probability of event is that event divided by total number of that
So,
There are 4 + 2 = 6 pens
Blue pen = 2
Hence,
P(b) = 2/6 = 1/3
And,
There are 5 highlighters
Yellow highlighter = 1
Hence,
P(y) = 1/5
Now,
P(b and y) = 1/3 * 1/5 = 1/15
Hence,
probability of grabbing blue pen and a yellow highlighter is [tex]\frac{1}{15}[/tex]
Answer:
2/15
Step-by-step explanation:
Please answer ASAP!
The sum of three numbers is -44.84. One of the numbers is 24.6. The other numbers are equal to each other. What is the value of each of the other two numbers?
Answer:
-34.72
Step-by-step explanation:
a + b + c = -44.84
a= 24.6
24.6 + b + c = -44.84
Since b = c (given "the other numbers are equal to each other")
Substitute b into c, we have
24.6 + b + b = -44.84 (b+b is the equivalence of 2 x b)
24.6 + 2b = -44.84 (subtract 24.6 from both sides)
2b = -69.44 (divide 2 from both sides)
b= -34.72
Since b = c (given "the other numbers are equal to each other")
c is also -34.72
math! About 3 percent of Earth's water
is fresh water. Of that 3 percent, about
69 percent is ice. About what percent of
Earth's total water supply is ice?
Help
Answer:
2.07%
Step-by-step explanation:
69 percent of 3 percent = 0.0207 = 2.07%
Answer:2.07%
Step-by-step explanation:
Point Q(-1, 5) is reflected across the line x = -1. What are the coordinates of its image? (5, -1) (1, 5) (-1, -5) (-1, 5)
Answer:
(-1,5)
Step-by-step explanation:
The line x = -1 is a vertical line parallel to the y-axis.
Therefore, if the point Q(-1,5) reflects on line x = -1, then the y-coordinate of the image point will not change.
Again, as the point Q(-1,5) is on the line x = -1, therefore, the image will be the point itself i.e. (-1,5). (Answer)
The horizontal distance from point (-1,5) to the line x = -1 is zero.
Answer:
(-1,5)
Step-by-step explanation:
4x + 9y = 4
9x+4y = 13
5
The tables of ordered pairs represent some points on the graphs of lines q and v.
Line 9
Line v
-9,6-
3
2
| 24410
T 1o| 8
10
| 3
y
0
18
33
Which system of equations is represented by lines q and V?
F
H
21x - y = 9
5x + 6y = 40
21x - y = 9
5x + 6y = 20
G
3x - y =-27
x + 2y = 16
9x - y = -27
x + 2y = 8
Answer:
x=101/65, y=-16/65. (101/65, -16/65).
Step-by-step explanation:
4x+9y=4
9x+4y=13
----------------
9(4x+9y)=9(4)
-4(9x+4y)=-4(13)
------------------------
36x+81y=36
-36x-16y=-52
----------------------
65y=-16
y=-16/65
4x+9(-16/65)=4
4x-144/65=4
4x=4+144/65
4x=404/65
x=(404/65)/4=101/65
x=101/65, y=-16/65.
Marty must pack 4,125 steel ball bearings into 10 boxes. Each box must contain an equal number of bearings. How many bearings does he have left over? (use long division to find the remainder)
A) 3
B) 5
C) 7
D) 9
Answer:
5 are left over
The drawing will help
Answer:
B
Step-by-step explanation:
d. Last year, Mr. Petersen was able to plant 4 rows of carrots with 13 plants in each row. This year, he
plans to plant twice as many rows with twice as many carrot plants in each. How many carrot plants
will he plant this year? Write a multiplication equation to solve. Assess the reasonableness of your
answer.
(2x + 6y = -28
(x+3y=-14
YOU
how do u solve this
Answer:
Infinite Solution
Step-by-step explanation:
Your teacher gave you a tricky one lol
NVM it's right, I doubled checked
Answer:
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRAINLIEST!!
Answer:
Not the commutative property but the fact that absolute value is always positive so the absolute value of x is equal to the absolute value of negative x
Step-by-step explanation:
What is the midpoint of a line segment with endpoints at (3,-1) and (8, -4)?
The midpoint of a line segment with endpoints at (3,-1) and (8, -4) is [tex]\left(\frac{11}{2},-\frac{5}{2}\right)[/tex]
Solution:
We have been given 2 end points of a line which are: (3,-1) and (8, -4)
The midpoint of a line segment is half way from both the ends of the line segment.
The formula for midpoint for the two points [tex]P(x_1, y_1) \text{and} Q(x_2, y_2)[/tex] is given as:
[tex]\text {Midpoint}=(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})[/tex]
Here P(3, -1) and Q(8, -4)
[tex]\text { So } x_{1}=3 ; x_{2}=8 ; y_{1}=-1 ; y_{2}=-4[/tex]
Plugging in values in above formula, we get
[tex]\begin{array}{l}{\text {Midpoint}=(\frac{3+8}{2}, \frac{-1-4}{2}})\\\\ {\text {Midpoint}=(\frac{11}{2}, \frac{-5}{2}})\end{array}[/tex]
Hence, the midpoint of the line segment is [tex]\left(\frac{11}{2},-\frac{5}{2}\right)[/tex]
Mrs. Wadley is tie-dying t-shirts for her AP Stats class. White shirts cost $4 each and black shirts are $5 each. There are 18 students in the class, and she spent $75. How many white shirts did she buy ? how many black shirts?
Mrs. Wadley bought 15 white shirts and 3 black shirts.
Step-by-step explanation:
Cost of one white shirt = $4
Cost of one black shirt = $5
Students in class = 18
Money spent on shirts = $75
Let,
white shirts = x
black shirts = y
According to given statement;
x+y=18 Eqn 1
4x+5y=75 Eqn 2
Multiplying Eqn 1 by 5;
[tex]5(x+y=18)\\5x+5y=90\ \ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3;
[tex](5x+5y)-(4x+5y)=90-75\\5x+5y-4x-5y=15\\x=15[/tex]
Putting x=4 in Eqn 1
[tex]15+y=18\\y=18-15\\y=3[/tex]
Mrs. Wadley bought 15 white shirts and 3 black shirts.
Keywords: linear equation, subtraction
Learn more about linear equations at:
brainly.com/question/5341416brainly.com/question/5340976#LearnwithBrainly
-6x+y=8
5x+y=8
using elimination method
Answer:
x=0, y=8. (0, 8).
Step-by-step explanation:
-6x+y=8
5x+y=8
-----------
-6x+y=8
-(5x+y)=-8
--------------
-6x+y=8
-5x-y=-8
-------------
-11x=0
x=0/-11
x=0
5(0)+y=8
0+y=8
y=8-0
y=8
A metalworker has a metal alloy that is 30% copper and another alloy that is 55% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 50% copper alloy? The metal worker should use (blank) kilograms of the metal alloy that is 30% copper and (blank) kilograms of the metal alloy that is 55% copper. (show your work)
X+Y=100kg
X=100-Y
X*0.3+Y*0.55=100*0.5
(100-Y)*0.3+Y*0.55=50
30-0.3*Y+0.55*Y=50
0.25*Y=20
Y=80 kg
X=100-80
X=20 kg
The metal worker should use 20 kilograms of the metal alloy that is 30% copper and 80 kilograms of the metal alloy that is 55% copper.
Answer:
x=20kg
Step-by-step explanation:
2(4x - 5) - (x - 4) solve please
Answer:
7x-6
Step-by-step explanation:
2(4x-5)-(x-4)
8x-10-x-(-4)
8x-10-x+4
7x-10+4
7x-6
Step-by-step explanation:
2(4x-5) - (x-4)
8x-10 - (x-4)
8x-10 -x+4
7x-6
The price of a pair of shoes is $52. This price is 15% lower than last week.
What was the price of the shoes last week?
Round your answer to the nearest cent.
Enter your answer in the box.
Answer:
60
Step-by-step explanation:
Answer:
$61.18
Step-by-step explanation: the first one is wrong it is $61.18
A water park charges a rental fee plus $1.50 per hour to rent inflatable rafts. The total cost to rent a raft for 6 hours is $15. Assume the relationship is linear. Find and interpret the rate of change and the initial value.
Answer:
C = 6 + 1.5h.
$6 is the fixed fee that the park charges.
And $1.5 is the rate of charge per hour for rent of the raft.
Step-by-step explanation:
The water park charges a rental fee plus $1.5 per hour to rent inflatable rafts.
Let the total charge (C) has a linear relationship with the number of hours (h) spent in the park and it is C = a + bh ......... (1)
Now, b is the rate of charge to rent inflatable rafts and b = $1.5 per hour.
So, C = a + 1.5h ........... (2)
Now, given that the total cost to rent a raft for 6 hours is $15.
So, from equation (2) we get,
15 = a + 1.5 × 6
⇒ a = 6
Therefore, the equation (2) becomes C = 6 + 1.5h.
Here, $6 is the fixed fee that the park charges.
And $1.5 is the rate of charge per hour for rent of the raft. (Answer)
The LCM of 3 and 8 is ______.
Answer: the lowest common multiple of 3 and eight is 24
Step-by-step explanation:
Answer:its 24 :)
Step-by-step explanation:
Divide 100 by 16 and write the answer as mixed number. Reduce the fraction part of the mixed number
Answer:
Step-by-step explanation:
100/16 = 25/4 = 6(whole number )1/4
[hg](x,) if g(x)=x-5 and h(x)=|x|
It looks like you want to multiply the two functions. If so, then,
(h*g)(x) = h(x)*g(x)
(h*g)(x) = (x-5)*|x|
(h*g)(x) = x|x| - 5|x|
142.5 divided by 9.5
Answer:
The answer to your question is 15
Answer: the answer is 15
Hope this helps :)
9.
Given that 4:5:8 is equivalent to 1:n:b. Find the ratio of n:b only.
Step-by-step explanation:
So 4:5:8
= 1:n:b
which means that 4/n= 1
n= 1x4 so n=4
Now we know that 4 is divided by 4 to get 1, so we do the same for the other two values.
5/4= 1.25 and 8/4= 2
So now place the values for n:b
n= 1.25 b=2
So n:b= 1.25:2
To check, multiply each of the values in 1:1.25:2 by 4 and see if the answer you get is the same as 4:5:8.
is -44 a rational or irrational
Answer: Rational
Step-by-step explanation: -44 is an integer and all integers are rational numbers. Therefore, -44 is classified as a rational number.
The set of integers includes the set of whole numbers {0, 1, 2, 3...} and they also include their negative counterparts.
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My nickname - Lovely
please solve with steps how to do this exponets and signed fraction problem
( - 1/4) 2
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
Given
[tex](-1/4)^{2}[/tex]
= - [tex]\frac{1}{4}[/tex] × - [tex]\frac{1}{4}[/tex]
= [tex]\frac{1(1)}{4(4)}[/tex]
= [tex]\frac{1}{16}[/tex]
what is the multiplicative inverse of -5 1/2
Answer:
-2/11
Step-by-step explanation:
-5 1/2=-11/2
-2/11
Find the inverse of f(x) = 3x - 2.
A) f^-1(x) = x+2/3
B) f^-1(x) = x-2/3
C) f^-1(x) = x - 2/3
D) f^-1(x) = x + 2/3
Answer:
x=0.6
Step-by-step explanation:
f(×)=3x-2 , 0=3x-2
Alison saves $29.26 each month. How many months will it take her to save enough money to buy a stereo for $339.12?
A. 10
B. 11
C. 12
D. 13
Answer:
C. 12 months
Step-by-step explanation:
If you do 339.12/29.26 it will equal to 11.589 so that's like 11 months and a half so can't be 11 months has to be 12 months
Solve -9 (t -2) = 4(+ -15
The solution t =
Answer:
8.67
Step-by-step explanation:
-9t+18= -60
60+18=9t
78=9t
t= 78/9
=8.66