solve the equation by using substitution method X + 2 Y equal to 8 equation first 2 x minus 2 equal to 10 equation second
Answer:
(6, 1)
Step-by-step explanation:
x + 2y = 8
1. subtract 2y to get x alone -- x = -2y + 8
2. insert (-2y + 8) as x
2x - 2 = 10
2(-2y + 8) -2 = 10
3. distribute the 2
-4y + 16 - 2 = 10
4. combine like terms
-4y + 14 = 10
5. subtract 14 from both sides
-4y = -4
6. divide by -4
y = 1
7. plug y into any of the two original equations
x + 2(1) = 8
8. simplify
x + 2 = 8
x = 6
9. check answer with second equation
2(6) - 2 = 10
12 - 2 = 10
Please answer it now in two minutes
Answer:3.2 ft
Step-by-step explanation:
sin 32°=[tex]\frac{yz}{6}[/tex]
cross multiply
sin 32° x 6=yz
0.5299 x 6 =yz
yz=3.1795
≅3.2ft
A sixth-grade class is growing plants for their
science projects. Each student spent $1.00 for a
package of seeds and $2.50 for a container to
plant the seeds in. There are 30 students in the
class. How much money did the sixth-grade class
spend on seeds and containers in all?
Answer:
5.76
Step-by-step explanation:
Answer:
$105
Step-by-step explanation:
Each student buys one package of seeds and one container
s = Amount of students; p = price of seed package; c = price of container
s*(p+c)=30(1.00+2.50)=30(3.5)$105.
Hope This Helps!
Find the value of x if 12x=34^2 - 26^2
Answer:
[tex]\boxed{\sf x =40}[/tex]
Step-by-step explanation:
[tex]\sf 12x=34^2 - 26^2[/tex]
Solve the square.
[tex]\sf 12x=1156-676[/tex]
[tex]\sf 12x=480[/tex]
Divide both sides by 12.
[tex]\displaystyle \sf \frac{12x}{12} =\frac{480}{12}[/tex]
[tex]\sf x =40[/tex]
A rectangular solid has edges whose lengths are in the ratio 1:2:3. If the volume of the solid is 864 cubic units, what are the lengths of the solid's edges?
Answer: 5.24 units, 10.48 units , 15.72 units
Step-by-step explanation:
Volume of a rectangular solid is given by :-
V = lwh, where l = length , w= width and h = height
Given: A rectangular solid has edges whose lengths are in the ratio 1:2:3.
Let lengths of the rectangular solid x , 2 x, 3x.
volume of the solid is 864 cubic units
Then, Volume of rectangle = [tex]x (2x)(3x) =864\ \text{cubic units}[/tex]
[tex]\Rightarrow\ 6x^3 = 864\\\\\Rightarrow\ x^3 =144\\\\\Rightarrow\ x=(144)^{\frac{-1}{3}}\approx5.24[/tex]
Lengths of rectangular solid 5.24 units, 2 (5.24) units , 3(5.24) units
= 5.24 units, 10.48 units , 15.72 units
Kelly is a waitress and her average tip rate is 18%. After taking a sample of her tips from a week, she thinks her tip rate is actually higher. The data below is the tip rate for 15 randomly chosen checks (the numbers represent percentage). Assume that tip rates are normally distributed.
18.5 18.2 20 21.3 17.9 17.9 18.1 17.5 20 18
a) Express the null and alternative hypotheses in symbolic form for this claim.
H0 : Select an answer
Ha: Select an answer
b) What is the test statistic. Round to 2 decimals.
c) What is the p-value. Round to 4 decimals p-value =
Answer:
Step-by-step explanation:
From the given information:
the null and alternative hypotheses in symbolic form for this claim can be computed as:
[tex]H_o:\mu = 18 \\ \\ H_a : \mu > 18[/tex]
Mean = [tex]\dfrac{18.5+18.2+20+21.3+17.9+17.9+18.1+17.5+20+18}{10}[/tex]
Mean = 18.74
Standard deviation [tex]\sigma = \sqrt{\dfrac{\sum(x_i - \mu)^2}{N}}[/tex]
Standard deviation [tex]\sigma = \sqrt{\dfrac{(18.5 - 18.74)^2+(18.2 - 18.74)^2+(20 - 18.74)^2+...+(18 - 18.74)^2}{10}}[/tex]
Standard deviation [tex]\sigma[/tex] = 1.18
The test statistics can be computed as follows:
[tex]Z= \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z= \dfrac{18.6- 18}{\dfrac{1.18}{\sqrt{10}}}[/tex]
[tex]Z= \dfrac{0.6}{\dfrac{1.18}{3.162}}[/tex]
Z = 1.6078
Z = 1.61
Degree of freedom = n -1
Degree of freedom = 10 -1
Degree of freedom = 9
Using t - calculator at Z = 1.6078 and df = 9
The P - value = 0.0712
Select the correct answer.
What is the exact solution to the system of equations shown on the graph?
Answer:
Option (B)
Step-by-step explanation:
There are two lines on the graph representing the system of equations.
First line passes through two points (-3, 1) and (-2, 3).
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{3-1}{-2+3}[/tex]
m = 2
Equation of the line passing through (x', y') and slope = m is,
y - y' = m(x - x')
Equation of the line passing through (-3, 1) and slope = 2 will be,
y - 1 = 2(x + 3)
y = 2x + 7 ----------(1)
Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.
Let the equation of this line is,
y = mx + b
Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{4-1}{-1-0}[/tex]
= -3
Here 'b' = 1
Therefore, equation of the line will be,
y = -3x + 1 ---------(2)
From equation (1) and (2),
2x + 7 = -3x + 1
5x = -6
x = [tex]-\frac{6}{5}[/tex]
x = [tex]-1\frac{1}{5}[/tex]
From equation (1),
y = 2x + 7
y = [tex]-\frac{12}{5}+7[/tex]
= [tex]\frac{-12+35}{5}[/tex]
= [tex]\frac{23}{5}[/tex]
= [tex]4\frac{3}{5}[/tex]
Therefore, exact solution of the system of equations is [tex](-1\frac{1}{5},4\frac{3}{5})[/tex].
Option (B) will be the answer.
Answer:
B. (-1 1/5, 4 3/5)
Step-by-step explanation:
A ball is dropped from a window 24 m high. How long will it take to reach the ground? Acceleration is 9.8 m/s^2 because of gravity. PLS SHOW WORK
Answer:
0.638 seconds
Step-by-step explanation:
Since the ball is being dropped from a height of 24 meters, the equation will look like this:
24=9.8/s^2.
This is asking for how much seconds it will take for the ball to fall 24 meters to the ground.
Solve the equation:
24(s^2)=9.8
(s^2)=0.408
s^2=0.408
root the number:
0.638
you can round it to the nearest whatever it's asking you to round it to
Im not an expert, so please excuse me if it's not done correctly
PLEASE PLEASE PLEASE HELPPPP ASAPPPP!!!! best answer I’ll give brainliest :) HELP ASAP!
Step-by-step explanation:
2The perimer of a traingle is the saum of its sides
P = 2(3x+7) + 2(2x+2)
3P= 2(3x+7) + 2*(2x+2) multiply (3x+7) and (2x+2) by 2 P= 6x+14+4x+4 add the khown values together P=6x+4x+18 add the terms with the variable xP= 10x+18the legnth of rectangular sheet decreases by 34.5 cm its width decreases proportionally that is by the same percentage. if the sheets original width was half of the legnth and the new (smaller) area was 1.2 m^2 what was original sheet's width
Answer:
The original width was 94.71 cm
Step-by-step explanation:
Given:
new smaller area = 1.2m^2
Decrease in length of the rectangular sheet = 34.5cm
Therefore:
1. the final width of the sheet is given as
2X^2 = 1.2 m^2
X^2 - 0.6 m^2
X^2 = 10000 * 0.6 cm
X = 77.46 cm (this is the width)
2. The length of the sheet
= 2 * 77.46
= 154.92 cm.
3. Initial length of the sheet
= 154.92 + 34.5
= 189.42 cm.
4. Initial width of the sheet ( original ).
= 189.42 / 2
= 94.71 cm.
5. Initial area of the sheet
= 94.71 * 189.92
= 17939.9 cm^2
New area of the sheet
= 79.46 * 154.92
= 12000.1 cm^2
Difference between the initial and new area
= 17939.9 - 12000.1
= 5939.86 cm^2
Percentage of area decrease
= 5939.86 ' 17939.9
= 33.1%
can someone help me
Answer:
Step-by-step explanation:
The length of side length VY is 4z+2
The same as side length WX
what is the lengthy of side s of the square below
Answer:
D. 4√2
Step-by-step explanation:
A triangle with 45°, 45°, and 90° is a special right triangle.
hypotenuse = √2 · leg
1. Set up the equation
8 = √2 · x
2. Divide by √2 and solve
x = [tex]\frac{8}{\sqrt{2} }[/tex] · [tex]\frac{\sqrt{2} }{\sqrt{2}}[/tex] = [tex]\frac{8\sqrt{2} }{2}[/tex] = 4√2
help again plz.......
Please help WILL GET REPORTED IF ANSWERS NONSENSE FOR POINTS I am really struggling and need help It is a lot of points so try answering as much
Answer:
301.59
Step-by-step explanation:
your answer was almost right you just forgot to multiply by 9
Starting from an airport, an airplane flies 290 miles east and then 290 miles northwest. How far, in miles, from the airport is the plane? (Round your answer to the nearest mile.)
Answer:
The airplane is 222 miles far from the airport.
Step-by-step explanation:
After a careful reading of the statement, distances can be described in a vectorial way. A vector is represented by a magnitude and direction. That is:
Airplane flies 290 miles (east) (290 km with an angle of 0º)
[tex]\vec r_{A} = (290\,mi)\cdot i[/tex]
Airplane flies 290 miles (northwest) (290 km with and angle of 135º)
[tex]\vec r_{B} = [(290\,mi)\cdot \cos 135^{\circ}]\cdot i + [(290\,mi)\cdot \sin 135^{\circ}]\cdot j[/tex]
The resultant vector is equal to the sum of the two vectors:
[tex]\vec r_{C} = \vec r_{A} + \vec r_{B}[/tex]
[tex]\vec r_{C} = \{(290\,mi) + \left[(290\,mi)\cdot \cos 135^{\circ}\right]\}\cdot i + \left[(290\,mi)\cdot \sin 135^{\circ}\right]\cdot j[/tex]
[tex]\vec r_{C} = (84.939\,mi)\cdot i + (205.061\,mi)\cdot j[/tex]
The magnitude of the final distance of the airplane from the airport is obtained by the Pythagorean Theorem:
[tex]\|\vec r_{C}\|=\sqrt{(84.939\,mi)^{2}+(205.061\,mi)^{2}}[/tex]
[tex]\|\vec r_{C}\| = 221.956\,mi[/tex]
The airplane is 222 miles far from the airport.
Please find out the answer and I will mark your answer as the brain test with a five-star rating and a thank you. But only if the answer will be proper and neat...
Answer:
Below
Step-by-step explanation:
Let x be that missing number
One third of it is x/3
One-ninth of it is x/9
Multiply x/3 and x/9
● (x/3)*(x/9) = (x^2/27)
● (x^2/27) = 108
Multiply both sides by 27
● (x^2/27)*27 = 108*27
● x^2 = 2916
● x = √(2,916) or x = -√(2,916)
● x = 54 or x = -54
So there are two possibilities 54 and -54.
a1/3×1/9=!08
if you multiply you should get 1/27a=108
in order to let a alone multiply both sides by 27
and now your a which is unknown will equal 2916.
Find the slope of the line that contains (6, 2) and (6,-3).
Find the slope of the line through the points (-4,-7) and (4, 3).
Answer:
A. Undefined slope (no slope)
B. [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
A slope is rise over run.
The points (6, 2) and (6, -3) are located on the same x coordinate, therefore they have an undefined slope.
However, the points (-4, -7) and (4, 3) do have a slope. The rise is 10 ( | -7+ 3 | ) and the run is 8 ( | -4 + 4 | ). 10/8 is equivalent to 5/4.
Hope this helped!
What is the image of N for a 300° counterclockwise rotation about the center of the regular hexagon? Will give brainiest only if answered correctly with explanation
Answer:
H
Step-by-step explanation:
here, the question says that the given regular hexagon needs to be rotated counter clockwise 300°, considering the edges labels, each movement from one edge to other is 60° as 360/6 =60.
focus on N and move on anti clockwise.
When N rotates anti clockwise about center from original to position G, is 60°,
when N moves on anti clockwise about center from original to position A is 120°.
similarly, to X is 180°, to E is 240° and to H is 300°.
so, the new position of N when rotated anti clockwise about origin of the hexagon will be at H.
Point A is at (-6,6) and point C is at (-6,-2). Find the coordinates of point B on Ac such that AB =3/4AC
Answer:
B(-6, 0)
Step-by-step explanation:
You want to find B such that ...
(B -A) = (3/4)(C -A) . . . . the required distance relation
4(B -A) = 3(C -A) . . . . . . multiply by 4
4B = 3C +A . . . . . . . . . . add 4A, simplify
Now, we can solve for B and substitute the given coordinates:
B = (3C +A)/4 = (3(-6, -2) +(-6, 6))/4 = (-24, 0)/4 = (-6, 0)
The coordinates of point B are (-6, 0).
Answer:
the answer your looking for is (-3,-3)
Step-by-step explanation:
The quadrilateral shown is a (blank) x= (blank)
Answer:
The quadrilateral shown is a kite, because it has two non-congruent pairs of congruent sides
x = 3
Step-by-step explanation:
The vertex angles in a kite are bisected by the diagonals. Thus, 11x = 9x + 6.
11x=9x+6
2x=6
x=3
Hope it helps <3
) 5 is subtracted from one-fourth part of the product of 12 and 3 and multiplied
by 2.
e) 7 is subtracted from the quotient of 48 divided by the sum of 5 and difference
Step-by-step explanation:
the first answer is 72 as it is it
Answer:
The answer is 8.
Step-by-step explanation:
The product of 12 and 3 is 36. One-fourth of 36 is 9. 5 subtracted from 9 is 4.
1) In rectangle ABCD, AE is perpendicular on diagonal BD, BE=3DE and AC∩BD={O}.
1. DE/EO=?
2. If BD=8√2 inches, find out the lenght of AE
3. Calculate the measure of angle AOD.
2) In rectangle MNPQ, MA⊥NQ, A∈NQ, MA∩PQ={B}. If AN measures 12 inches, AQ=27 inches, calculate the lenght of MA and MB.
Please help me with these. Or at least with one of them.
Answer:
to be honest I'm not sure how to do
Harry needs 21 square meters of fabric for every 6 wizard cloaks he makes. How many square meters could he make with 4 cloaks of fabric
Answer:
14 square meters of fabricStep-by-step explanation:
[tex]21\: square\:meters = 6 \:wizard \:cloak\\x\:square\:meters\:\:=4 \:wizard\:cloaks\\\\Cross\:Multiply\\6x = 84\\\frac{6x}{6} =\frac{84}{6} \\\\x = 14 \:square\:meters[/tex]
Answer:
14.0 square meters
Step-by-step explanation:
plssssssss helppp 3x – 5 = 1
Answer:
x = 2
Step-by-step explanation:
Add 5 to both sides to get the 5 to the right side since we are trying to isolate the variable x:
3x – 5 + 5 = 1 + 5
Simplify: 3x=6
Divide each side by 3 to isolate and solve for x:
3x/3=6/3
Simplify: x=2
A newspaper article claimed: "The average cost of weekly groceries is $124.50." What
statistical measurement are they most likely claiming?
O A. median
B. mean
C. range
D. mode
The average cost of weekly groceries is $124.50." The statistical measurement are they most likely claiming is Mean
The correct option is (B)
what is Mean?The arithmetic mean of a given data is the sum of all observations divided by the number of observations.
For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:
Mean = Sum of all observations/Number of observations
MedianThe value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.
For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = middle value i.e. 4.
ModeThe value which appears most often in the given data i.e. the observation with the highest frequency is called a mode of data.
As per the situation we have given average cost of groceries.
The mean is also the average sum of data divided by total number of data.
Hence, The statistical measurement is Mean.
Learn more about mean here:
https://brainly.com/question/15323584
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Una compañía sabe que si produce "x" unidades mensuales su utilidad "u" se podría calcular con la expresión: u(x)=-0.04x^2+44x-4000 donde "u" se expresa en dólares. Determine la razón del cambio promedio de la utilidad cuando el nivel de producción cambia de 600 a 620 unidades mensuales. Recuerde que la pendiente de la recta secante a la gráfica de la función representa a la razón de cambio promedio.
Answer:
The ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.
Step-by-step explanation:
The question is:
A company knows that if it produces "x" monthly units its utility "u" could be calculated with the expression: u (x) = - 0.04x ^ 2 + 44x-4000 where "u" is expressed in dollars. Determine the ratio of the average change in profit when the level of production changes from 600 to 620 units per month. Remember that the slope of the secant line to the graph of the function represents the average rate of change.
Solution:
The expression for the utility is:
[tex]u (x) = - 0.04x ^ {2} + 44x-4000[/tex]
It is provided that the slope of the secant line to the graph of the function represents the average rate of change.
Then the ratio of the average change in profit when the level of production changes is:
[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]
Compute the values of u (x₁) and u (x₂) as follows:
x₁ = 600
[tex]u (x_{1}) = - 0.04x_{1} ^ {2} + 44x_{1}-4000[/tex]
[tex]= - 0.04(600) ^ {2} + 44(600)-4000\\=-14400+26400-4000\\=8000[/tex]
x₂ = 620
[tex]u (x_{2}) = - 0.04x_{2} ^ {2} + 44x_{2}-4000[/tex]
[tex]= - 0.04(620) ^ {2} + 44(620)-4000\\=-15376+27280-4000\\=7904[/tex]
Compute the average rate of change as follows:
[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]
[tex]=\frac{7904-800}{620-600}\\\\=\frac{-96}{20}\\\\=-\frac{24}{5}\\\\=-24:5[/tex]
Thus, the ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.
Rewrite 4 - 5 using the addictive inverse and display the expression on a number line
Answer:
d. (4) + (-5)
Step-by-step explanation:
We know that 4 is the positive value and 5 is the negative value, therefore if to be able to rewrite in it we will almost make a sum of these values without changing the meaning of each one of the values, therefore:
(+4) + (-5)
Which means that the correct option is the last option, that is, d. (4) + (-5). Furthermore, the representation is correct because the resulting arrow is the one corresponding to -1.
11/10= x+2/5 Please Explain
Answer:
x=7/10
Step-by-step explanation:
2/5=4/10
11/10=x+4/10
11/10-4/10=x
7/10=x
Answer:
x=7/10 or 0.7
Step-by-step explanation:
I turned the fractions into decimals
so
1.1=x+0.4
subtract 0.4 from 1.1 to get 0.7
Turn it into a fraction which is 7/10
Simplify the expression (3-4i)(1+5i)-(2-i). Please show your work
Answer:
21 + 12i
Step-by-step explanation:
Given
(3 - 4i)(1 + 5i) - (2 - i) ← expand the product of factors using FOIL
= 3 + 11i - 20i² - 2 + i ( note i² = - 1 )
= 3 + 11i + 20 - 2 + i ← collect like terms
= 21 + 12i
Answer:
The answer is
21 + 12iStep-by-step explanation:
(3-4i)(1+5i)-(2-i)
Expand the terms in the bracket first
That's
3 + 15i - 4i - 20i² - ( 2 - i)
Remove the bracket
3 + 15i - 4i - 20i² - 2 + i
But i² = - 1Group like terms
- 20(-1) + 15i - 4i + i + 3 - 2
15i - 4i + i + 20 + 3 - 2
Simplify
We have the final answer as
21 + 12iHope this helps you
PLEASE HELP
Jina received a $70 gift cards for a coffee store. She used it in buying some coffee that cost $8.64 per pound. After buying the coffee, she had $26.80 left on her card. How many pounds of coffee did she buy?
Answer:
If I'm correct she bought 5 pounds of coffee.
Step-by-step explanation:
$70 (gift card)
-$26.80 (remainder on g.c.)
= $43.20 ($ spent on money)
$43.20/ $8.64 = 5
(remainder)/ cost per lb. = lbs of coffee bought
Answer: She bought 5 pounds of coffee
Step-by-step explanation:
This situation can be represent by the equation
70 - 8.64 x = 26.80 where x is the number of coffee she bought. solve for x
-70 -70
-8.64x = -43.20
x = 5