Answers
x + 7y = 15
multiply second equation by (-8)
-8x - 56y = -120
so now
8x + 4y = 16
-8x - 56y = -120
-----------------add
-52y = -104
y = 2
7(2) = 15 - x
14 = 15 - x
x = 1
answer is C.
(1, 2)
Related Questions
Speed = distance divided by time taken. car 1 travels 10 miles every 5 minutes. car 2 travels 30 miles every 20 minutes. what is the difference of speed between these two cars in mph?
Answers
2 miles............................1 minute
10 miles.........................5 minutes
20 miles.........................10 minutes
40 miles..........................20 minutes
car2
1.5 miles...........................1 minute
15miles.............................10 minutes
30 miles...........................20 minutes
the difference is 0.5 miles per minute
0.5*60=30 miles/hour
How many minutes greater is the software company's median than the bank's median?
Enter your answer in the box.
Answers
The median is calculated by taking all values in a data set, placing them in order from least to greatest, and finding the value that is in the middle of the data set. In this case, the middle number (median) for Bank is 15. The middle number (median) for Software Company is 25. The difference between 25 and 15 is 10. So Software Company is 10 more minutes greater than Bank,
Answer:
the answer is 10
The quotient of a number and 2 is the same as the difference of the number doubled and 3
Answers
Abcd is a parallelogram find the measure of a if b is (7x+13)degrees and d d is (8x-8)degrees brainly
Answers
13=1x-8
21=1x
21=x
what are the solutions to the equion
plz answer right no it is 14
Answers
[tex]x^2 = 169[/tex]
What we must do for this case is to clear the value of x.
To do this, remember that when clearing you have two solutions.
A solution is positive.
A solution is negative.
We have then:
[tex]x = +/- \sqrt{169} x = +/- 13 [/tex]
Therefore, the solutions are:
[tex]x1 = 13 x2 = -13[/tex]
Answer:
the solutions to the equation are:
[tex]x1 = 13 x2 = -13[/tex]
A spinner has three sections. The table shows the results of spinning the arrow on the spinner 80 times. What is the experimental probability of the arrow stopping over Section 3? Section 1: 18 Section 2: 30 Section 3 :32
Answers
Answer: [tex]\dfrac{2}{5}[/tex]
Step-by-step explanation:
From the given table, The number of times arrow stops over Section 3 = 32
The total number of times spinner spins = 80
Now, the experimental probability of the arrow stopping over Section 3 is given by :-
[tex]P(S-3)=\frac{32}{80}\\\\\Rightarrow P(S-3)=\dfrac{2}{5}[/tex]
Hence, the experimental probability of the arrow stopping over Section 3 is [tex]\dfrac{2}{5}[/tex]
I need help to answer this please thank you ?
Answers
A reader of a book wants to estimate the mean word length in the book they are currently reading. they randomly select 19 pages from the book and count the length of 5 words they randomly selected on each of those pages. the table shows the results from the survey. using the sample results estimate the mean word length of any word in the book.
a.5.22 letters
b.5.49 letters
c.5.77 letters
d.5.92 letters
Answers
Answer:
B-5.49
Step-by-step explanation:
A machine is set up to cut metal strips of varying lengths and widths based on the time (t) in minutes. The change in length is given by the function I(t)=t^2-squrt(t),, and the change in width is given by w(t)=t^2-2t^1/2. Which function gives the change in area of the metal strips?
Answers
a. a(t) = t^4 + 2t
b. a(t) = t^4 + 2t + 3t^(5/2)
c. a(t) = t^4 - 3t^(5/2) + 2t`
d. a(t) = t^4 + 2t - 2t^(1/2) + sqrt(t)
The answer is letter c.a(t) = t^4 - 3t^(5/2) + 2t`
Solution:
Area= length times width
Then to get the time, a=a(t), l=l(t), and w=w(t)
So, if Area= l times width
a(t)= l(t) • w(t)
a(t)=[t^2-squrt(t)] • [t^2-2t^1/2]
a(t) = [t^2 - t^(1/2)] • [t^2 - 2t^(1/2)]
=t^4 - 3t^(5/2) + 2t
Answer:
'a(t)=t^4-3t^(5/2)+2t'
PLEASE MATH HELP WILL GIVE BRAINLIEST!!
The center of a circle is located at (-5, 2), and the radius of the circle is 5 units.
What is the equation of the circle in standard form?
Question 1 options:
(x−5)2 + ( y+2)2 = 10
(x+ 5)2 + (y−2)2 = 25
(x+5)2 + (y−2)2 = 10
(x−5)2 + (y+2)2 = 25
Answers
Answer B
(x-(-5))²+(y-2)²=5²
(x+5)²+(y-2)²=25
If 5x^2 + y^4 = −9 then evaluate d^2y/dx^2 when x = 2 and y = 1. Round your answer to two decimal places.
Answers
.. 10x +4y^3*dy/dx = 0
.. dy/dx = -5x/(2y^3)
Then
.. d^2y/dx^2 = d(dy/dx)/dx = (-5/2)(y^-3 -3xy^-4*dy/dx)
Evaluated at x=2, y=1
.. dy/dx = -5(2)/(2*1^3) = -5
.. d^2y/dx^2 = (-5/2)*(1^-3 -3*2*1^-4*(-5))
.. = (-5/2)(1 +30)
.. = -155/2 = -77.50
d^2y/dx^2 = -77.50 at the specified point.
A car dealership has seven cars in the lot. Unfortunately, the keys to the cars have been mixed up. The manager randomly grabs a key and tries to start a car salesman also randomly picks a different key and tries to start another car. What is the probability that both cars start?
Answers
Please help asap!!!!!!!!!!18 points
Answers
what is the vertex of the parabola
Answers
Let's consider the equation of parabola, y = a·(x - α)·(x - β)
where α, β are the x-intercepts.
From the given graph, the y-intercept is (0, -3).
From the given graph, the x-intercept are (-1, 0) and (3, 0) i.e. α = -1, β = 3.
So the equation of parabola would be now, y = a·(x + 1)·(x - 3)
We can plug the y-intercept (0, -3) in the equation to find value of 'a'.
-3 = a·(0+1)·(0-3)
-3 = -3a
a = 1
So the equation of parabola would be now, y = (x + 1)·(x - 3) = x² - 2x - 3
Comparing it with y = ax² + bx + c
The x-coordinate of vertex would be, [tex] x = \frac{-b}{2a} = \frac{-(-2)}{2(1)} =\frac{2}{2} = 1 [/tex]
the y-coordinate of vertex would be, y = (1)² - 2(1) - 3 = -4.
Hence, vertex would be (1, -4).
What is the value of x in the proportion StartFraction 6 x plus 1 over 7 EndFraction equals StartFraction 18 x minus 2 over 14 EndFraction?
A. 0
B. 3
C. two-thirds
D. one-fourteenth
Answers
____________________________________________________
" x = " [tex] \frac{2}{3} [/tex] " ; which is: " two-thirds " .
____________________________________________________
Explanation:
____________________________________________________
Given: " [tex] \frac{6x + 1}{7} = \frac{18x-2}{14} [/tex] " ; Solve for "x" ;
____________________________________________________
First, multiply the first fraction by "[tex] \frac{2}{2} [/tex]" ;
{ since: "[tex] \frac{2}{2} [/tex] = 1" ; and since any value, multiplied by "1" results in that exact same value. By multiplying the first fraction by: "[tex] \frac{2}{2} [/tex]" , we can get the "denominator" in the first fraction equal to the "denominator" of the second fraction.
→ [tex] \frac{2}{2}*( \frac{6x + 1}{7})=\frac{2(6x+1)}{2(7)} =
"\frac{2(6x+1)}{14} [/tex]" .
___________________________________________________________
Note the "distributive property of multiplication" :
_______________________________________________________
a(b + c) = ab + ac ;
a(b – c) = ab – ac .
_______________________________________________________
As such, take the "numerator" ; which is:
" 2(6x + 1) " ; and expand:
→ = (2*6x) + (2*1) = " 12x + 2 " ;
Now, we can rewrite the entire expression:
________________________________________
"[tex] \frac{12x+2}{14} [/tex]" ; and we can rewrite the entire equation:
________________________________________
→ " [tex] \frac{12x+2}{14} [/tex] = \frac{18x-2}{14} [/tex] " ;
Let us simplify this: " 12x + 2 = 18x – 2 " ; Solve for "x" ;
_____________________________________________________
→ 18x – 2 = 12x + 2 ;
→ Subtract "12x" from each side of the equation; and subtract "2" from each side of the equation:
→ 18x – 2 – 12x – 2 = 12x + 2 – 12x – 2 ;
to get:
→ 6x – 4 = 0 ;
Add "4" to each side of the equation:
→ 6x – 4 + 4 = 0 + 4 ;
to get:
→ 6x = 4 ;
Divide each side of the equation by "6" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ 6x / 6 = 4 / 6 ;
→ x = 4/6 ; → "4/6" = "(4÷2)/(6÷2)" = "2/3" .
→ x = 2/3 ; → x = " [tex] \frac{2}{3} [/tex] " ; which is "two-thirds" ;
→ which is: Answer choice: [C]: " two-thirds" .
__________________________________________________________
The correct value of x is [tex]\frac{2}{3}[/tex].
To find the value of x in the proportion [tex]\frac{6x+1}{7} = \frac{18x-2}{14}[/tex], follow these steps:
Cross-multiply to eliminate the fractions. Multiply 7 by (18x - 2) and 14 by (6x + 1):
7(18x - 2) = 14(6x + 1)
Expand both sides:
126x - 14 = 84x + 14
Move all terms involving x to one side and constant terms to the other side:
126x - 84x = 14 + 14
Simplify the equation:
42x = 28
Divide both sides by 42 to solve for x:
x = 28 ÷ 42 = [tex]\frac{2}{3}[/tex]
Therefore, the value of x is [tex]\frac{2}{3}[/tex] and the correct answer is option C.
Complete question: What is the value of x in the proportion [tex]\frac{6x+1}{7} = \frac{18x-2}{14}[/tex]?
A. 0
B. 3
C. [tex]\frac{2}{3}[/tex]
D. [tex]\frac{1}{14}[/tex]
I️ need to find the answer
Answers
(b) m∠QPR = m(arc QR) = 74° . . . . . an arc has the same measure as its central angle
Please help! I'm very confused. 20 points.
Answers
.. 3(6x) -3(5) -7(3x) -7(10) = 0
.. 18x -15 -21x -70 = 0 . . . . . . finish multiplying terms
.. -3x -85 = 0 . . . . . . . . . . . . . collect like terms
.. -85 = 3x . . . . . . . . . . . . . . . .add 3x
.. -85/3 = x . . . . . . . . . . . . . . .divide by 3
.. -28 1/3 = x . . . . . . . . . . . . . write as mixed number
2) 5 -(6 +9x) = 9 -(4x -1)
.. 5 -6 -9x = 9 -4x +1 . . . . . eliminate parentheses using the distributive property
.. -1 -9x = 10 -4x . . . . . . . . . collect like terms
.. -1 = 10 +5x . . . . . . . . . . . . add 9x
.. -11 = 5x . . . . . . . . . . . . . . . subtract 10
.. -11/5 = x . . . . . . . . . . . . . . divide by 5
.. -2 1/5 = x . . . . . . . . . . . . . write as mixed number
please help asap! match equation to the graph
Answers
Answer:
B) -7x + 7y= -49
Step-by-step explanation:
Using the general equation for a line
y=mx+b
where m is the slope (positive if the line goes up from left to right and negative is it goes down from left to right)
and b is the point where the line crosses the y-axis
By th graph we can see that the line goes up from left to right, so the slope is positive, and that it crosses the y axis in -7, b= -7 and x is positive.
Solving for y in all the options
A) y = -x
B) y = x - 7
C) y = -x +7
D) y= x+7
the option that describes the line in the graph is B) -7x + 7y= -49 since when clearing for y we get y = x - 7 wich has a positive slope, and has an interception b = -7.
The vertex of this parabola is at (3, -2). When the x-value is 4, the y-value is 3. What is the coefficient of the squared expression in the parabola's equation?
Answers
in this case, h=3, k=-2, so y=a(x-3)-2
plug (4,3) in the equation: 3=a(4-3)²-2, a=5
so the coefficient of the squared expression is 5.
Answer:[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]
Step-by-step explanation:
Given
Vertex of Parabola is [tex]\left ( 3,-2\right )[/tex]
and parabola passes through [tex]\left ( 4,3\right )[/tex]
Let us take a parabola of the form
[tex]\left ( y-y_0\right )^2=4a\left ( x-x_0\right )[/tex]
And here [tex]\left ( x_0,y_0\right ) is \left ( 3,-2\right )[/tex]
therefore
[tex]\left ( y+2\right )^2=4a\left ( x-3\right )[/tex]
Now put [tex]\left ( 4,3\right)[/tex] as it lies on parabola
[tex]\left ( 3+2\right )^2=4a\left ( 4-3\right )[/tex]
[tex]a=\frac{25}{4}[/tex]
Thus Equation of parabola is
[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]
Find the image of z(1,1) after two reflections first across L1 and then across L2
L1: y=2 L2: x-axis
L1: x=3 L2: y=2
Answers
A contractor purchases 7 dozen pairs of padded work gloves for $94.92. He incorrectly calculates the unit price as $13.56 per pair for the expense report. What is the correct unit price? What is the error?
Answers
13.56-1.13=12.43 absolute error
The correct unit price for the work gloves is $1.13 per pair, and the error in the reported unit price is $12.43 per pair, as the contractor incorrectly reported it as $13.56 per pair.
The question is asking to calculate the correct unit price for the padded work gloves purchased by the contractor and to identify the error in the calculation provided in the expense report.
Firstly, let's determine the total number of pairs of gloves. Since 1 dozen represents 12 items, 7 dozen pairs of gloves will be [tex]7 \times 12 = 84[/tex] pairs of gloves.
Now, to find the correct unit price, we divide the total cost by the total number of pairs:
Unit Price = Total Cost / Total Number of Pairs
Unit Price = $94.92 / 84 pairs
Unit Price = $1.13 per pair
The incorrect unit price was calculated as $13.56 per pair. Therefore, the error in the calculation is:
Error = Incorrect Unit Price - Correct Unit Price
Error = $13.56 - $1.13
Error = $12.43 per pair
The contractor overestimated the unit price by $12.43 per pair.
Crop researchers plant 15 plots with a new variety of corn. The yields in bushels per acre are: 138.0 139.1 113.0 132.5 140.7 109.7 118.9 134.8 109.6 127.3 115.6 130.4 130.2 111.7 105.5 Assume that bushels per acre. a) Find the 90% confidence interval for the mean yield for this variety of corn. b) Find the 95% confidence interval. c) Find the 99% confidence interval. d) How do the margins of error in (a), (b), and (c) change as the confidence level increases?
Answers
[tex]\theta=\overline{x} \pm \frac{z\sigma}{\sqrt{n}}[/tex]
Where [tex]\overline{x}[/tex] is the mean, [tex]\sigma[/tex] is standard deviation, and n is number of data points.
Every confidence interval has associated z value. This can be found online.
We need to find the standard deviation first:
[tex]\sigma=\sqrt{\frac{\sum(x-\overline{x})^2}{n}[/tex]
When we do all the calculations we find that:
[tex]\overline{x}=123.8\\
\sigma=11.84[/tex]
Now we can find confidence intervals:
[tex]($90\%,z=1.645): \theta=123.8 \pm \frac{1.645\cdot 11.84}{\sqrt{15}}=123.8 \pm5.0\\($95\%,z=1.960): \theta=123.8 \pm \frac{1.960\cdot 11.84}{\sqrt{15}}=123.8 \pm 5.99\\ ($99\%,z=2.576): \theta=123.8 \pm \frac{2.576\cdot 11.84}{\sqrt{15}}=123.8 \pm 7.87\\[/tex]
We can see that as confidence interval increases so does the error margin. Z values accociated with each confidence intreval also get bigger as confidence interval increases.
Here is the link to the spreadsheet with standard deviation calculation:
https://docs.google.com/spreadsheets/d/1pnsJIrM_lmQKAGRJvduiHzjg9mYvLgpsCqCoGYvR5Us/edit?usp=sharing
a) For a 90% confidence interval: (117.838, 130.056)
b) For a 95% confidence interval: (117.543, 130.352)
c) For a 99% confidence interval: (113.816, 134.078)
d) As the confidence level increases, the margins of error also increase, resulting in wider confidence intervals, indicating greater certainty in the estimation of the true population mean yield.
To find the confidence intervals, we first calculate the sample mean and standard deviation of the yields. Then, we use the t-distribution with degrees of freedom (n-1) to determine the critical values for the given confidence levels. Finally, we use these critical values along with the sample mean and standard deviation to calculate the margins of error and construct the confidence intervals.
a) For a 90% confidence interval:
Sample mean = 123.947
Sample standard deviation = 11.669
Margin of error = t * [tex](s / sqrt(n)) = 1.761 * (11.669 / sqrt(15)) ≈ 6.109[/tex]
90% confidence interval: (123.947 - 6.109, 123.947 + 6.109) ≈ (117.838, 130.056)
b) For a 95% confidence interval:
Margin of error = [tex]2.145 * (11.669 / sqrt(15)) ≈ 7.404[/tex]
95% confidence interval: (117.543, 130.352)
c) For a 99% confidence interval:
Margin of error = [tex]2.947 * (11.669 / sqrt(15)) ≈ 10.131[/tex]
99% confidence interval: (113.816, 134.078)
d) As the confidence level increases, the margin of error also increases because the critical value from the t-distribution becomes larger, resulting in wider confidence intervals. This reflects the increased certainty associated with higher confidence levels.
The margins of error increase as the confidence level increases, indicating wider confidence intervals and greater certainty in the estimation of the true population mean yield.
Amys class is selling books to raise money for a field trip. If each book sells for $7, how many books will they need to sell to raise $125?
Answers
7x=125 where x is equal to the number of books sold
x=17.9
Since you cannot sell .9 of a book, this must be rounded up to 18.
Therefore, Amy must sell 18 books.
When calculating the successive discounts of 15% and 10% on a $100 item, _____. a. take 10% of $85 b. take 10% of $90 c. take 15% of $85 d. take 25% of $100
Answers
Answrer
Option (a) is correct .
i.e take 10% of $85
Reason
As given
15% and 10% on a $100 item i.e first applied 15 % discount on $ 100 and than apply 10% discount .
15 % is written in the decimal form
[tex]= \frac{15}{100}[/tex]
= 0.15
Amount becomes when 15 % discount on$100 = 100 - 0.15 × 100
= 100 - 15
= $ 85
Now apply 10 % discount on $ 85.
10 % is written in the decimal form
[tex]= \frac{10}{100}[/tex]
= 0.1
Amount becomes when 15 % discount on$100 = 85- 0.1 × 85
= 85 - 8.5
= $ 76.5
Therefore the option (a) is correct about the successive discounts of 15% and 10% on a $100 item is $76.5 .
The area of a triangle is 40sq inches. If the base of the triangle is 10 inches what is it’s height?
Answers
substitute
40=1/2*10*x
40=5x
x=8
the height is 8 inches
Answer:
Step-by-step explanation: 8 inches
Michael takes a multiple-choice test with 5 answer choices for each question. If he randomly answers every question what is his expected score
Answers
An airplane takes off from the ground and reaches a height of 500 feet after flying 2 miles. given the formula h = d tan θ, where h is the height of the plane and d is the distance (along the ground) the plane has flown, find the angle of ascent θ at which the plane took off.
Answers
1 mile = 5280 feet
So, we have:
h = 500 feet
d = 2 (5280) = 10560 feet
Substituting in the given formula we have:
h = d tan θ
500 = 10560tan θ
tan θ = 500/10560
θ = Atan (500/10560)
θ = 2.71 degrees.
Answer:
the angle of ascent θ at which the plane took off is:
θ = 2.71 degrees.
Or an angle θ with the point (−20, −21) on its terminating side, what is the value of cosine?
Answers
.. = -20/-√841 . . . . . . . . . . . . . . . . . θ is a 4th-quadrant angle, so cos(θ) > 0
.. = 20/29
The value of the cosine is 20/29.
Answer:
The value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].
Step-by-step explanation:
It is given that an angle θ with the point (−20, −21) on its terminating side.
It means the right angle triangle is formed in third quadrant where length of the perpendicular is 21 and the base is 20.
According to the Pythagoras theorem,
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
[tex]hypotenuse^2=(20)^2+(21)^2[/tex]
[tex]hypotenuse^2=400+441[/tex]
[tex]hypotenuse^2=841[/tex]
Taking square root both the sides.
[tex]hypotenuse=\sqrt{841}[/tex]
[tex]hypotenuse=29[/tex]
In a right angled triangle,
[tex]\cos \theta=\frac{base}{hypotenuse}[/tex]
[tex]\cos \theta=\frac{20}{29}[/tex]
θ lie in the third quadrant and cosine is negative in third quadrant.
[tex]\cos \theta=-\frac{20}{29}[/tex]
Therefore the value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].
If you flip three fair coins, what is the probability that you'll get all three tails?
Answers
pr(3 Tail) = 1/2 × 1/2 × 1/2
= 1/8
Let H be the event that head occurs and let T be the event that tail.
Then the complete Sample Space,S for the experiment given in the question is:
S={ HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
As we can see the total number of elements in the sample space is 8. Let us represent this by the letter N.
Therefore, N=8
Now, the event of interest to us is TTT and it's occurrence is once. Let represent this by the letter E.
Therefore, E=1
Thus, the probability of the event E occurring is given as:
[tex] P(E)=\frac{E}{N}=\frac{1}{8} [/tex]
[tex] \frac{1}{8} [/tex] is the required answer. This can be represented in percentage too as:
[tex] \frac{1}{8}\times 100=12.5 [/tex]%
f(x) = (x − 3)(x + 3)[x − (2 − i)][x − (2 + i)] The function has real roots and imaginary roots.
Answers
Imaginary roots:-
x - (2 - i) = 0
x = 2 -i is one imaginary root and the other is 2 + i
Answer:
The function has
2 real roots and
2 imaginary roots.