3x-5y=8 2x+5y=22
Solve second equation for x; first subtract 5y from each side.
2x=-5y+22 (Divide by 2)
x=-5/2y+11 (Substitute into x into the first equation)
3 (-5/2y+11)-5y=8 (Simplify )
-15/2y +33-5y=8 (Combine like terms)
-25/2y+ 33=8 -25/2y=-25 (Divide each side by -25)
1/2y=1 y=2 Therefore 3x-5(2)=8 3x-10=8 3x=18 x=6
x=6, y=2
- Hope this helps!
Danielle xo
what is 5/9 of 243??
Answer:
135
Step-by-step explanation:
[tex]\frac{5}{9}\times243=\frac{5\times243}{9}=
\frac{1250}{9}=\boxed{135}
[/tex]
Select all equations that have infinitely many solutions.
A)4+4x-9=8x+4(x-9)
B)9(3x-5)+7=-3(7-8x)
C)8x+4=2(4x+2)
D)4(x-3)+7=x-(5-3x)
Answer:
The answer is C
Explanation:
8x + 4 = 8x + 4
x = x
At a festival 2/7 of the number of girls was equal to 3/5 of the number of boys. There were 165 fewer boys than girls, how many children were at the festival in all?
Answer:
Boys = 150
Girls = 315
Total Boys and Girls 465
Step-by-step explanation:
We call x the number of boys and we call y the number of girls.
So we have to find the total number of children
We know that
[tex]\frac{2}{7}y = \frac{3}{5}x[/tex]
[tex]x =y-165[/tex]
Now we substitute the second equation in the first and solve for y.
[tex]\frac{2}{7}y = \frac{3}{5}(y-165)[/tex]
[tex]\frac{2}{7}y = \frac{3}{5}y-99\\\\99 = \frac{3}{5}y-\frac{2}{7}y\\\\\frac{11}{35}y=99\\\\y = 315\\[/tex]
Now we find x.
[tex]x = 315-165 = 150\\\\x = 150[/tex]
Finally we have that:
Boys = 150
Girls = 315
Total Boys and Girls 465
HELP PLEASE
Use elimination to solve the system of equations
2x + 3y = 9
x + 5y = 8
Answer:
y=5/7 x=31/7
Step-by-step explanation:
Make the x values the opposite of each other:
-2(x+5y=8)
-2x-10y=-16
2x+3y=9
Combine like terms and solve for y:
-7y=-5
y=5/7
Plug y in to find x.
x+5(5/7)=8
x+25/7=8
56/7-25/7=x
x=31/7
Simplify (9/100)^3/2 in rational form.
27\1000 is your rational form.
To simplify (9/100)^3/2, cube 9/100 to get 729/1000000 and then take the square root, which simplifies to 3/100 in rational form.
Explanation:To simplify (9/100)^3/2 in rational form, we first understand that the exponent 3/2 can be broken down into two steps: first cubing the number, then taking the square root. Cubing 9/100 gives us (9^3)/(100^3), or 729/1000000. Then, taking the square root of this result and multiplying by the convenient factor of 1 in the form of 100/100, we simplify to 3/100, which is the result in rational form.
express 7 million in scientific notation
Answer:
Step-by-step explanation:
10^9 x 0.007
Isabella has 2 1/4 oranges. Colleen has 3 1/4 oranges. How many all together?
Answer:
There are 5 1/2 oranges altogether.
Step-by-step explanation:
The 2 and 3 in front of each fraction indicate that there are a total of 5 whole oranges altogether. Now we have to settle these fractions. the 1/4 and the 1/4 both have a common denominator so there is no need to find one. When the common denominator is found, we simply have to add the numberators on the top of the fraction. 1+1 is 2, and, since the denominator stays the same, we should get a total of 2/4. I am unsure as to whether you were asked to simplify your answer (if you weren't you could keep your answer like this), but if you were to simplify the answer, both the numerator and denominator of our total can be divided by 2, so when that is done, we have a simplified total of 1/2. Take that 1/2 of an orange and add it to our 5 whole oranges, and we should get our answer of 5 1/2 oranges in total.
Only number 14 pleaseee....
Answer:
c
Step-by-step explanation:
There are 6 red and 2 black balls.
The total number of balls = 2 + 6 = 8
The probability of drawing a black ball first is 2/8 = 1/4
The probability of drawing a red ball second is 6/7
P(black, red)=1/4 * 6/7 = 6/28 = 3/14
C
if point (-1,0) is on the line whose equation is y=2x+b what is the value of b? show your work and explain) A. 1 B. 2 C. 3 D. 0
[tex]\bf y=2x+b~~\hspace{8em} (\stackrel{x}{-1},\stackrel{y}{0})~\hspace{8em} 0=2(-1)+b \\\\\\ 0=-2+b\implies 2=b[/tex]
To find the value of b plug in the point (-1,0) into the known part of the equation ( y = 2x + b ) and solve for b
0 = 2(-1) + b
0 = -2 + b
To isolate b add 2 to both sides (addition of 2 will make -2 zero and cancel it from the right side and bring it to the left)
0 + 2 = (-2 + 2) + b
2 = 0 + b
2 = b <------------------------B. 2
Hope this helped!
which equation has the solutions x=5+-2(sqrt)7/3
Answer:
the solution is the last one.
Step-by-step explanation:
We know that for a second grade equation of the type:
ax^2 + bx + c = 0
The solution will be given by the quadratic formula, which states that:
x1 = [-b + sqrt(b^2 - 4ac)]/2a
x2 = [-b - sqrt(b^2 - 4ac)]/2a
So, according to the solution, we have:
x1 = [-5 + 2sqrt(7)]/3
Then:
2a = 3
-b = 5
b^2 - 4ac = 28
Solving each equation:
a = 2/3
b= -5
c = 9/8
None of the alternatives equals the values obtained before. So we can say that the expression is simplified.
Now we knoe what the first and second equation are wrong because b is not equal to -5.
So we have the other two alternatives, where b=-10. This gives us an idea that maybe, the equation is simplified by two. If that's the case:
then:
2a = 6
b= -10
b^2 - 4ac = 112
Then b=-10, a = 3 and c=-1
So the solution is the last one.
Final answer:
The correct quadratic equation with the solutions x = 5 ± 2√7 / 3 is 3x² - 10x - 1 = 0, determined by matching the given solution to the quadratic formula.
Explanation:
The student is asking which of the given quadratic equations has the solutions x = 5 ± 2√7 / 3. The correct equation that yields these solutions must be in the form ax² + bx + c = 0, where a, b, and c are constants.
To determine the right equation, we can work backwards from the given solutions using the quadratic formula:
x = ∛( -b ± √(b² - 4ac) ) / 2a
Comparing the solutions to the standard form obtained by the quadratic formula, we need to match the coefficients such that:
a equals the denominator (3) after the ± symbol,b is opposite in sign to the middle term (5),The discriminant b² - 4ac results in 4×7.After testing each equation, we find that:
33x² - 5x + 7 = 0 (Incorrect)3x² - 5x - 1 = 0 (Incorrect)3x² - 10x + 6 = 0 (Incorrect)3x² - 10x - 1 = 0 (Correct)The discriminant for the last equation is (10)² - 4×3×(-1) = 100 + 12 = 112, which is 4×7, confirming that x = 5 ± 2√7 / 3 are indeed the solutions.
On the track and field team,
3
8
of the members do the hurdles.
Of the members who do the hurdles,
4
5
also do the long jump.
If there are 40 members on the track team, how many do both the hurdles and the long jump? I really need help...
Answer:
It could be anywhere from eight to 15 members.
Step-by-step explanation:
Answer:
A. Count the members on each team
Hurdles = ⅜ × 40 = 3 × 5 = 15
Long jump = ⅘ × 40 = 4 × 8 = 32
Let's look at the two extremes.
B. Most people will compete in only one event
Then the teams will overlap by seven members (Figure 1).
C. All those in Hurdles compete in the Long Jump
Then 15 members will compete in both Hurdles and Long Jump (Figure 2).
Answer:
12 do both hurdles and long jump
Step-by-step explanation:
3/8 of the team does hurdles, so that number is 3/8·40 = 15.
Of those 15, 4/5 do long jump, so there are ...
4/5·15 = 12 . . . hurdlers who do long jump
Which graph represents the equation y = 1/4 x^2 ?
Answer:
Answer in attachment
Step-by-step explanation:
To solve the sustem of equations below, kira isolated variable y in the first equation then sybstituted it into the second equation.what was the resulting equation? 3y=12x, x^2+y^2=81
The resulting equation after substituting [tex]\( y = 4x \)[/tex] into [tex]\( x^2 + y^2 = 81 \)[/tex] is [tex]\( x^2 = \frac{81}{17} \)[/tex]
Let's isolate the variable [tex]\( y \)[/tex] in the first equation [tex]\( 3y = 12x \)[/tex]:
Divide both sides by 3 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = 4x \][/tex]
Now that we have an expression for [tex]\( y \)[/tex], substitute it into the second equation [tex]\( x^2 + y^2 = 81 \)[/tex]:
[tex]\[ x^2 + (4x)^2 = 81 \][/tex]
Now simplify the equation:
[tex]\[ x^2 + 16x^2 = 81 \][/tex]
Combine like terms:
[tex]\[ 17x^2 = 81 \][/tex]
Divide both sides by 17 to solve for [tex]\( x^2 \)[/tex]:
[tex]\[ x^2 = \frac{81}{17} \][/tex]
So, the resulting equation after substituting [tex]\( y = 4x \)[/tex] into [tex]\( x^2 + y^2 = 81 \)[/tex] is [tex]\( x^2 = \frac{81}{17} \)[/tex].
20 points!!! plz help asap
Suppose 10% of the flights arriving at an airport arrive early, 60% arrive on time, and 30%
arrive late. Valerie used the random-number table to find the experimental probability that of 5
flights, at least 2 will arrive late. The digit 0 represents flights arriving early. The digits 1,2,3,
4, 5, and 6 represent flights arriving on time. The digits 7, 8, and 9 represent flights arriving
late. Find the experimental probability that of 5 flights at least 2 will arrive late.
A: 3/10
B:2/5
C: 9/20
D: 11/20
Answer:
D. 11/20
Step-by-step explanation:
7, 8, and 9 represent late flights. We want to count how many of the 20 trials have at least two of these digits. Counting, we find that 11 of the 20 have at least two of these digits.
D. 11/20
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
A hiker recorded the temperature at different altitudes on a mountain trail. The results are shown in the table.
1,500 2,800 3,500 4,500 5,000 6,000 8,000 8,500 9,000 9,500
Altitude
(feet)
Temperature
(°F)
75
73
72
70
66
63
60
60
57
55
Calculate the approximate correlation coefficient for the data, and interpret the value to describe the correlation
0.986
-0.025
strong postive
linear correlation
weak negative
linear correlation
weak positive
linear correlation
strong negative
linear correlation
-0.986
0.025
correlation coefficient
of the data
interpretation of the
correlation coefficient
Answer:
Step-by-step explanation:
Given is table as follows
1500 75
2800 73
3500 72
4500 70
5000 66
6000 63
8000 60
8500 60
9000 57
9500 55
r -0.98649651
We get correlation coefficient is negative and near -1
Hence there is a strong negative correlation.
Whenever x increases y decreases with almost constant slope.
Answer:
correlation coefficient of the data ---->strong negative linear correlation
interpretation of the correlation coefficient ----> -0.986
Step-by-step explanation:
Simplify the following expression (3x^2y)^3
Answer:
[tex]\large\boxed{\left(3x^2y\right)^3=27x^6y^3}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\\left(3x^2y\right)^3=3^3(x^2)^3y^3=27x^6y^3[/tex]
How many solutions does the system have?
A. Exactly one solution
B. No solution
C. Infinitely many solutions
Answer:
B. No solution
Step-by-step explanation:
y = 3x+9
y = 3x-7
Set the two equations equal since they are both equal to y
3x+9 = 3x-7
Subtract 3x from each side
3x+9-3x = 3x-7-3x
9 = -7
This is never true, so there are no solutions
Answer: on edge its one and then after that 0,-3
Step-by-step explanation:
You have $20dollar to spend on taxi fare. The ride costs $5dollar plus$2.50 dollar per kilometer. Write an inequality to determine the distance in kilometers, d, you can ride for $20.
Answer: ($2.50k) + $5
The distance you can ride is 6 kilometers.
($2.50 x 6) + $5 = $20
Answer:
[tex]2.50d+5\leq 20[/tex]
Step-by-step explanation:
Let d represent distance in kilometers.
We have been given that a taxi ride costs $2.50 per kilometer, so the cost of d kilometers would be [tex]2.50d[/tex] dollars.
We are also told that ride costs a fixed charge of $5, so total cost of d kilometers would be [tex]2.50d+5[/tex] dollars.
You have $20 to spend on taxi fare, so the total cost of riding d kilometers should be less than or equal to 20.
We can represent this information in an inequality as:
[tex]2.50d+5\leq 20[/tex]
Therefore, our required inequality would be [tex]2.50d+5\leq 20[/tex].
Consider the diagram shown where a tree that is 100 feet tall cast a shadow 120 feet long find the angle of elevation of the sun
It’s -125 and you welcome
What the mass of an encyclopedia grams or kilograms?
Answer:
kilograms
Step-by-step explanation:
Which side of DEF is longest?
Answer:
A. DE
Step-by-step explanation:
The side opposite the angle with the largest measure is the longest
<F has a measure of 72, so it is the largest angle and DE is opposite <F
Side DE is the longest
Which represents the imverse of the function f(x) = 4x?
For this case we must find the inverse of the following function:[tex]f (x) = 4x[/tex]
We follow the steps below:
We change f(x) to y:
[tex]y = 4x[/tex]
We exchange the variables:
[tex]x = 4y[/tex]
We solve for and:
[tex]4y = x[/tex]
We divide between 4 on both sides of the equation:
[tex]y = \frac {x} {4}[/tex]
then y by [tex]f ^ {-1} (x):[/tex]
[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]
ANswer:
[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]
how do you find the surface area of a rectangular prism ?
The official formula is 2B+ Ph
where B is the area of a base of the prism, P is the perimeter of a base, and h is the height of the prism (distance between the two bases)
However, length x width x height can also be used
PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A pizza shop has 27 adult customers every hour. It has 12 younger customers every hour. It is open from 12 p.m. to 10 p.m. each day.
Write an expression for the total number of customers it would have in 3 days.
A. 27×10×3+12×10
B. (27+12)×10×3
C. (27+10)×12×3
D. 27+10×12×3
How many customers would it have in 3 days?
A. 387 customers
B. 930 customers
C. 1,170 customers
D.1,332 customers
387 customers or 930 customers
(27+12)x10x3 and 1,170
please help
Marcy plays a game with a spinner and a 6-sided number cube. The spinner is divided into 4 equal sections numbered 1 to 4. Marcy spins the spinner and rolls the number cube. She records both numbers. What is the probability that at least one of the numbers is a 4? Write out the sample space to help you
Answer:
9/24 or 3/8
Step-by-step explanation:
Spinner gives a 4.
Suppose the 4 shows up on the spinner.
There is a 1/4 chance of that happening.
Suppose the cube does not have a 4 on the top face. There is a 5/6 chance of that happening
Together the probability is 1/4 * 5/6 = 5/24
The cube gives a 4
The cube gives a four 1/6 of the time.
The spinner cannot give a 4, which happens 3/4 of the time.
Together the probability is 1/6 * 3/4 = 3/24
Both Cube and Spinner give a 4
The cube will give a four 1/6 of the time
The spinner gives a four 1/4 of the time.
1/6*1/4 = 1/24
Total
1/24 + 3/24 + 5/24 = 9/24 = 3/8
What happens to the rest?
The answer is neither gives a four.
Spinner 3/4
Die: 5/6
Combined amount = 3/4 * 5/6 = 15/24
There is a quick way to do this.
1 - no fours =
1 - 15/24 = 9/24
The image below is a triangle drawn inside a circle with center O:
A triangle is shown inscribed inside a circle. The leg of the triangle labeled 6 inches passes through the center of the circle, O. The other two legs are labeled as 4 inches and 3 inches.
Which of the following expressions shows the area, in square inches, of the circle?
(π = 3.14)
3 ⋅ 3.14 ⋅ 22
3.14 ⋅ 32
3.14 ⋅ 22
3.14 ⋅ 3
3.14 • 3 I think I hope this is right and helps
The area of circle in inches be: 3.14* [tex](3)^{2}[/tex]
What is Area of circle?The area of a circle is pi times the radius squared (A = π r²).
As it is known that the triangle in inscribed under the circle.
The diameter of the circle will be = 6 inches (hypotenuse of triangle)
radius = 3 inches
So, Area of circle= π[tex]r^{2}[/tex]
= 3.14* 3 * 3
= 3.14* [tex](3)^{2}[/tex]
So, the area of circle is : 3.14* [tex](3)^{2}[/tex]
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Approximate area of the triangle below?
Answer:
Step-by-step Answer:
This question expects a choice out of the four answers.
We can reason it as follows:
If the angles had been 90-45-45, then the triangle would be isosceles with each leg equal to 14, and the area would be 14*14/2 = 192/2 = 96.
Now one of the base angles has been reduced from 45 to 35 (still assuming a right triangle), the other leg can only diminish, and therefore the area is LESS than 96.
We also realize that changing from 90 to 95 degrees will not change the area by a whole lot, so we are looking for a number LESS than 96, the only of which is 72.8.
The exact value, by solving the triangle,
the opposite side of 35 degrees is 10.483 (using sine rule), and
the area is 73.378 (using A=(1/2)a*b*sin(C), not far from 72.8, if we are looking for the exact value.
9 km and 597 m is equal to which of the following? (Please show the work tysm
e 95,970 l dont know any work just looked it up sorry
What is the maximum value that the graph of y=cos x assumes?
Answer: 1
Step-by-step explanation: the cosine function oscillates between the values -1 to 1
The amplitude of this particular function is understood to be 1
The maximum value that a graph of y = cos(x) assumes is y = 1.
What is the cosine function?In a triangle, the cos function (or cosine function) is the ratio of the base side to the hypotenuse.
What are some important values of cosine function?cos(0°) = 1
cos(30°) = √3/2
cos(45°) = 1/√2
cos(60°) = 1/2
cos(90°) = 0
Cosine function is a periodic function and the value repeat themselves at an interval of 2π. The maximum value the cosine function achieves is y=1. The graph of the function is shown below:
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Cathy pays $25 a month plus $0.05 per text message. She models this with the function C = 0.05x + 25. If the text messaging fee increases to $0.10, what is her new function?
A) C = 10x + 25
B) C = 0.10x + 25
C) C = 0.10x + 0.05
D) C = 0.05x + 0.10
I think the answer is b) C=.10x+25
Answer: B. C = .10x + 25
Step-by-step explanation: If the original equation uses .05, and that equation is .05x + 25 = C, then increasing it to .10 would mean that the new equation is .10x + 25.