Answer:
(1 [tex]\frac{1}{3}[/tex], 2 [tex]\frac{1}{3}[/tex] )
Step-by-step explanation:
Given the 2 equations
7x - y = 7 → (1)
x + 2y = 6 → (2)
Multiplying (1) by 2 and adding to (2) will eliminate the y- term
14x - 2y = 14 → (3)
Add (2) and (3) term by term to eliminate y
15x = 20 ( divide both sides by 15 )
x = [tex]\frac{20}{15}[/tex] = [tex]\frac{4}{3}[/tex] = 1 [tex]\frac{1}{3}[/tex]
Substitute this value of x into either of the 2 equations and solve for y
Substituting in (2)
[tex]\frac{4}{3}[/tex] + 2y = 6
2y = 6 - [tex]\frac{4}{3}[/tex] = [tex]\frac{14}{3}[/tex] ( divide both sides by 2 )
y = [tex]\frac{7}{3}[/tex] = 2 [tex]\frac{1}{3}[/tex]
what is the slope of the line below? If necessary, enter your answer as a fraction in lowest terms, using the slash as the fraction bar. Do not enter your answer as a decimal number or an equation. (-2, - 3) (-4, - 9)
Answer:
The slope is 3
Step-by-step explanation:
The slope is 3 because when you set up the equation (-2,-3) is labeled as x1 and y1 and (-4,-9) is labeled as x2 and y2. When you set up the equation you get -9--3 / -4--2, which becomes -6/ -2, which then becomes -3/-3, which is really just 3. :)
The slope of the line given is 3.
What is a slope of a line?Slope is the 'steepness' of the line, also commonly known as rise over run. We can calculate slope by dividing the change in the y-value between two points over the change in the x-value.
Given is a line passing through points (-2, -3) (-4, -9), we need to find its slope,
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:-
y₂-y₁ / x₂-x₁
Here, (x₁, y₁) and (x₂, y₂) are (-2, -3) (-4, -9)
So, the slope is = -9+3 / -4+2 = -6 / -2 = 3
Hence, the slope of the line given is 3.
Learn more about slopes, click;
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The amount of money 'y' made at a laundromat after 'x' months can be represented by the linear function: y = 8.50x - 5. After 2 months, the laundromat made 20 dollars, but the linear function predicted they would make 12 dollars. What is the residual value for this data?
Answer:
[tex] \hat y = 8.5*2 -5 = 12[/tex]
And the residual is defined as:
[tex] e_ i = y_i -\hat y_i [/tex]
And replacing we got:
[tex] e_i = 20-12 = 8[/tex]
Step-by-step explanation:
For this case we know that the amount of money 'y' made at a laundromat after 'x' months can be represented by the linear function:
[tex] y = 8.50 x -5[/tex]
And fter two months we know that the laundromat made 20 dollars. And if we use the linear function we got:
[tex] \hat y = 8.5*2 -5 = 12[/tex]
And the residual is defined as:
[tex] e_ i = y_i -\hat y_i [/tex]
And replacing we got:
[tex] e_i = 20-12 = 8[/tex]
whats the product for (2z-3)^3
Answer:
8z^3-36z^2+54z-27
Step-by-step explanation:
(2z-3)^3
(2z)^3*(2z)^2*3+3*2z*3^2-3^3
8z^3-3*4z^2*3+3*2z*9-27
8z^3-36z^2+54z-27
Answer:
[tex]8z^3-36z^2+54z-27[/tex]
Step-by-step explanation:
[tex](2z-3)^3\\(2z-3)(4z^2-12z+9)\\2z(4z^2-12z+9)-3(4z^2-12z+9)\\8z^3-24z^2+18z-12z^2+36z-27\\8z^3-36z^2+54z-27[/tex]
The simplified form of 3root45 - root 125 + root 500
Answer:
the answer and explanation is in the picture
please like and Mark as brainliest
hope this helps
Which function is the result of vertically shrinking ƒ(x) = (x + 1)2 by a factor of 1∕6?
Question 6 options:
A) ƒ(x) = (6x + 1)2
B) ƒ(x) = (1∕6x + 1)2
C) ƒ(x) = 6(x + 1)2
D) ƒ(x) = 1∕6 (x + 1)2
Answer:
[tex]y=\frac{1}{6}(x+1)^2[/tex] is the result of vertically shrinking
Step-by-step explanation:
Vertical stretch or shrink
[tex]y=c \cdot f(x)[/tex]
a stretch by a factor of c if c>1
a shrink by a factor of c if c<1
c is the factor
We are given that factor = 1/6 <1
So, Vertical shrink
So, [tex]y = \frac{1}{6} \cdot f(x)[/tex]
We are given that [tex]f(x) = (x + 1)^2[/tex]
So,[tex]y=\frac{1}{6}(x+1)^2[/tex]
Option D is true
Hence [tex]y=\frac{1}{6}(x+1)^2[/tex] is the result of vertically shrinking
Answer:
ƒ(x) = (1∕6x + 1)^2
Step-by-step explanation:
V2 is equal to + 2 a s derive
What is the area of sector GPH?
Answer:
Area of GPH = pi x 15^2 x 40/360 = 78.54 (yd2)
Hope this helps!
Answer:
78.5 yards²
Step-by-step explanation:
Area of a sector:
Theta/360 × pi × r²
40/360 × 3.14 × 15²
78.5 yd²
Solve the right triangle. Round decimal answers to the nearest tenth.
С
12
B
9
A
AB=
m
M
I need help
Answer:
15
Step-by-step explanation:
Use the Pytago theorem.
AB^2=AC^2+BC^2
AB^2= 9^2 + 12^2
= 225
AB = [tex]\sqrt225}[/tex]
= 15
Write and solve an inequality to calculate the swimming rate of a manatee swims for 15 miles in 3 hours
Step-by-step explanation:
D= rt
Where D is distance r is rate and t is time
15 < r3
15/3 < r
5< r
The inequality is Rate > 15 / 3. And the swimming rate of a manatee swims for 15 miles in 3 hours will be 5 miles per hour.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The swimming rate of a manatee swims for 15 miles in 3 hours is given as,
Rate > 15 / 3
Rate > 5 miles per hour
The inequality is Rate > 15 / 3. And the swimming rate of a manatee swims for 15 miles in 3 hours will be 5 miles per hour.
More about the rate link is given below.
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A recipe calls for 2 3/4 cups on milk. If the recipe is tripled, how much milk is needed?
8 1/4 should be the answer
Answer:
8 1/4
Step-by-step explanation:
33/4 simplified is 8 1/4
13th term of 2, 10, 18, 26
Answer:
192
Step-by-step explanation:
Add 8 started from 2 and keep going till you hit 192.
Answer:
a1 = 2 d = 8
n = 13
an = a1 + d(n-1)
a(13) = 2 + 8(13-1)
2 + 8(12)
2 + 96 = 98
Step-by-step explanation:
1. identify the terms
2. write down the arithmetic sequence formula and then replace the letters with their values.
3. do parenthesis first, then multiply by d.
4. add them together to get the 13th term
Mr. Blackburn is buying new carpet for his family room and hallway. The floor plan is shown below.
Pls help me ASAP
Answer:
Step-by-step explanation:
3.2 times 1.5 plus 6 times4.2= 30 meters of carpet.
Answer:
He needs 23.7 of carpet
Step-by-step explanation:
multiply 4.2 and 6 which is 25.2. Then subtract 1.5 from 25.2 which is 23.7.
− 5/6 x=−10/3 solve for X
Answer:
X = 4
Step-by-step explanation:
-5/6x = -10/3
x = -10/3 * -6/5
x = 60/15
x = 4
Answer:
The result for this equation is [tex]x =4[/tex] .
Step-by-step explanation:
Solve the equation for [tex]x[/tex] :
[tex]-\frac{5}{6}x =-\frac{10}{3}[/tex]
[tex]\frac{-\frac{5}{6}x }{-\frac{5}{6} } =\frac{-\frac{10}{3} }{-\frac{5}{6} }[/tex]
[tex]x = 4[/tex]
So, the answer for this equation is [tex]x =4[/tex] .
A rectangular field on a farm is to be fenced in using the wall of the barn for one side and 200 meters of fencing for the other three sides. The area A(x) in square meters of the field is a function of the length x in meters of each of the sides perpendicular to the barn wall
Answer:
Rectangular area as a function of x : A(x) = 200*x + 2*x²
A(max) = 5000 m²
Dimensions:
x = 50 m
l = 100 m
Step-by-step explanation:
"x" is the length of the perpendicular side to the wall of the rectangular area to be fenced, and we call "l" the other side (parallel to the wall of the barn) then:
A(r) = x* l and the perimeter of the rectangular shape is
P = 2*x + 2*l but we won´t use any fencing material along the wll of the barn therefore
P = 2*x + l ⇒ 200 = 2*x + l ⇒ l = 200 - 2*x (1)
And the rectangular area as a function of x is:
A(x) = x * ( 200 - 2*x) ⇒ A(x) = 200*x + 2*x²
Taking derivatives on both sides of the equation we get:
A´(x) = 200 - 4*x ⇒ A´= 0
Then 200 - 4*x = 0 ⇒ 4*x = 200 ⇒ x = 50 m
We find the l value, plugging the value of x in equation (1)
l = 200 - 2*x ⇒ l = 200 - 2*50 ⇒ l = 100 m
A(max) = 100*50
A(max) = 5000 m²
Answer:
Sorry man i dont know they answer
Step-by-step explanation:
Unit 5. 4) Please help. Marcie purchases a helium tank that contains 7.9 cubic feet of helium. Marcie is making a balloon display that contains 15 spherical balloons with a one-foot diameter. Will the helium tank provide enough helium for the display? Why or why not?
Use 3.14 for π in your calculations. Round your answer to the nearest tenth if necessary.
Answer:
The correct answer is option c.
Graph the equation of the line y=3x+4 and use it for your reference to find: Quadrants in which this graph is in. (Use the numbers 1−4)
Answer:
Quadrants: 1, 3, 4. (See explanation for further details)
Step-by-step explanation:
The graphic of the linear function is included below as attachment. The line covers the following quadrants: 1, 3, 4
Answer:
1, 2, 3
Step-by-step explanation:
The dimensions of a chocolate box are: height=x + 2 inches, length=2x+5 inches, and width=4x-1 inches. If the volume of the chocolate box is 605 cubic inches, what is the value of x?
I hope this helps you
Answer:
To begin to answer your question you would need to know that the formula for the volume of a rectangular prism is the following: [tex]V=lwh[/tex]. Now its just a manner of substitutions.
Step-by-step explanation:
[tex]V=605 \text{in}^3[/tex]
Then one can also state the following:
[tex]V=(x+2)(4x-1)(2x+5)[/tex]
Following up with this substitution:
[tex]605=(x+2)(4x-1)(2x+5)[/tex]
Proceeding with a FOIL procedure:
[tex]605=(4x^2+8x-x-2)(2x+5)[/tex]
[tex]605=8x^{3}+34x^{2}+31x-10[/tex]
[tex]0=8x^{3}+34x^{2}+31x-615[/tex]
Using PRZs:
[tex]PRZs=\frac{\text{Factors of Constant Term}}{\text{Factors of Highest Power}}=\frac{\pm 1,\pm 3, \pm 5, \pm 41, \pm 615}{\pm 1, \pm 2, \pm 4, \pm 8}[/tex]
By graphing it one can identify that 3 is a solution so plugging it in and using synthetic division.
[tex]\begin{array}{ccccc}3|& 8 & 34 & 31 & -615\\ \ \ |& & 24 & 174 & 615 \\ & 8 & 58 & 205 &0 \end{array}\\[/tex]
Giving the following the polynomial:
[tex]0=(x-3)(8x^2+58x+205)[/tex]
Now one can evaluate the discriminant of that quadratic:
[tex]58^2-4(8)(205)=-3196[/tex]
Because it is negative one knows that it produces imaginary solutions. Therefore the only real solution is [tex]x=3[/tex]. Therefore the dimension of the box is the following: [tex]5\text{in},11\text{in}, 11\text{in}[/tex]
PLEASE ANSWER THIS ASAP
Answer:
i really dont know
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The slope (rate of change) are 2/5 or .4 for both of them
1
2
3..
4
5
6
8
9
10
Which set of data does not contain any outliers?
113, 115, 103, 154, 109, 111, 119
141, 151, 111, 142, 149, 140, 150
99, 103, 91, 104, 109, 107, 97
131, 135, 131, 99, 138, 136, 140
Answer:
99, 103, 91, 104, 109, 107, 97
Step-by-step explanation:
The bold is the outlier
113, 115, 103, 154, 109, 111, 119
141, 151, 111, 142, 149, 140, 150
131, 135, 131, 99, 138, 136, 140
can someone helpme please
Answer: the first box is 1/5 since one of 5 squares are shaded.
The next box the answer is “there are 4 groups 1/5.
The next answer is 4/5
The last answer is 4/5
Step-by-step explanation:
1. Find the volume of the rectangular prism.
4 ft
6 ft
8 ft
Answer:
192[tex]feet^3[/tex]
Step-by-step explanation:
The formula for the area of a rectangle is : [tex]length*width[/tex]
In order to work out the volume you would first need to work out the area. You can do this by multiplying the length of 6 by the height of 4, this gives you 24.
To workout the volume you would need to multiply the area of 24 by the width of 8, this gives you 192.
1) Multiply 6 by 4.
[tex]6*4=24[/tex]
2) Multiply 24 by 8.
[tex]24*8=192 feet^3[/tex]
Find the value of the variable in each pair of similar figures. Round the answers to the nearest tenth. please help!!!!
Answer:
x = 18 units
w = 20 units
n = 6.9 units
Step-by-step explanation:
Given: Similar figures
To find: value of the variable in each pair of similar figures
Solution:
Figures are said to be similar if they have same shape and not necessarily same size.
Corresponding sides of similar figures are always proportional.
[tex]ABCD\sim JKLM\\\frac{AB}{JK}=\frac{AD}{JM}\\\frac{12}{x}=\frac{6}{9}\\x=\frac{12\times 3}{6}=18\,\,units[/tex]
[tex]\Delta NOP\sim \Delta XYZ\\\frac{XZ}{NP}=\frac{YZ}{OP}\\\frac{12}{3}=\frac{w}{5}\\w=\frac{12\times 5}{3}=20\,\,units[/tex]
[tex]\Delta GHI\sim \Delta PQR\\\frac{GI}{PR}=\frac{GH}{PQ}\\\frac{3}{n}=\frac{7}{16}\\n=\frac{3\times 16}{7}=\frac{48}{7}=6.9\,\,units[/tex]
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Answer:
D
Step-by-step explanation:
see attachment
HELP ASAP!
Point A is located at (1, 4), and D is located at (-3, 6). Find the coordinates of the point that lies halfway between A and D. (5 points)
(3, 4)
(-3, 4)
(1, 5)
(-1, 5)
Answer:
I believe the answer is (-1,5)
Step-by-step explanation: because when you draw it out on a coordinate plain (-1,5) lies right in the middle of these two points.
The area of a garden is 30 square feet. The perimeter is 26 feet. What are the measurements of each side?
Please help this question is fustrating
Answer: 3 feet by 10 feet rectangle
===========================================================
Explanation:
Assuming this garden is a rectangle, it has dimensions L and W which are the length and width respectively.
perimeter of rectangle = 2*(length+width)
P = 2*(L+W)
26 = 2(L+W) ... plug in given perimeter
26/2 = L+W .... divide both sides by 2
13 = L+W
13-W = L .... isolate L by subtracting W from both sides
L = 13-W
------
Area of rectangle = Length*Width
A = L*W
A = (13-W)W .... replace L with 13-W
A = W(13-W)
A = 13W - W^2 ..... distribution
30 = 13W - W^2 .... plug in given area A = 30
W^2 - 13W + 30 = 0 ... get everything to one side
(W - 10)(W - 3) = 0 ...... factor
W-10 = 0 or W-3 = 0 ...... zero product property
W = 10 or W = 3
----------
If the width is W = 10, then
L = 13-W
L = 13-10
L = 3 is the length
Or if the width is W = 3, then
L = 13-W
L = 13-3
L = 10 is the length
Either way, this is a 3 ft by 10 ft rectangle
--------
Check:
Area = length*width = 10*3 = 30 square feet
perimeter = 2(length+width) = 2*(10+3) = 2*13 = 26 feet
or you could say
perimeter = L+W+L+W = 10+3+10+3 = 13+13 = 26 feet
we get the correct area and perimeter, so this confirms our answer.
Question 2 of 10
2 Points
What is the location of the point on the number line that is of the way from
A = 37 to B = 13?
A 19
B. 28
C. 31
D. 25
Answer:
31
Step-by-step explanation:
9. What is the volume of the given prism? Round the answer to the nearest tenth of a centimeter.
The figure is not drawn to scale.
8.8 cm
/
4.7 cm
13.1 cm
313.3 cm3
436.4 cm
541.8 cm3
681.5 cm3
Answer:
The answer is 541.8 cm³
Step-by-step explanation:
you just have to multiply the measures of each side:
(8.8)(4.7)(13.1) = 541.8
The graph shows the relationship between mass and volume for pure silver. Use the graph to determine the density of pure silver to the nearest tenth and complete the explanation of how do you find the density
The density is equal to the
A. Run
B. Rise
C. Slope
D. Degree
The density of sliver is approximately __ g/cm cube
Answer:
C. Slope and [tex]10.49 g/cm^3[/tex]
Step-by-step explanation:
We're missing the graph itself, but I can make an educated guess:
- Assuming x = volume and y = mass:
[tex]p = \frac{m}{v}[/tex]
density = mass/volume
x = volume = run
y = mass = rise
mass/volume = rise/run = slope
The slope of the line (assuming the graph is purely linear) represents mass/volume, which is the formula for density.
I had to Google the density of silver itself. Do the math from the graph for a more appropriate answer, as the graph may be less scientifically precise.
cAnswer:
Step-by-step explanation:
Help me out!!!! What is it
Answer:
92
Step-by-step explanation:
180-88=92
Supplementary angles equal 180 degrees
Answer:
92 degrees
Step-by-step explanation:
180-88=92
15. Find the largest number which divides 70
and 125 leaving remainders 5 and 8,
respectively
Answer:
13
Step-by-step explanation:
70 - 5 = 65
125 - 8 = 117
Find the Greatest Common Divisor of 65 & 117
65 = 5 * 13
117 = 3 * 3 * 13
GCD = 13
13 is the largest number that divides 70 & 125 and leaves remainders 5 and 8 respectively