The solution to this given system of equations is (x,y) = (0.4,15).
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
y - 13 = 5x
y - 5x = 12
Now,
To do this, we can add both equations together to eliminate x:
(y - 13) + (y - 5x) = 5x + 12 2y - 13 - 5x = 17 2y = 30 y = 15
Now that we have found y, we can substitute it into either equation to find x. For example:
15 - 13 = 5x 2 = 5x x = 0.4
Therefore, by the given system of equations the answer will be (x,y) = (0.4,15).
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Mr. Mikie hired 3 students to deliver advertising fliers. He paid each student the same amount. Let x be the total amount the students earned. Write an expression that tells how much 1 student earned.
Answer:
$x/3
Step-by-step explanation:
I need help bro pleaseeee
Answer
20/7=2 6/7
Step-by-step explanation:
soory no explanation
Jada keeps 175 beads in a storage box. She chooses a bead without looking what
color it is, and returns it to the box. She does this severaltimes. The table shows results
Pink - 7
Green - 8
Red - 10
How many pink beads are in Jadas storage box
There will be 49 pink beads in Jada's storage container.
What is the anticipated outcome?The weighted sum is applied to the expected value in parameter estimation. Informally, the expected value is the simple average of a large number of outcomes that were chosen at random and were calculated independently.
A bundle from Jada holds 175 hair beads. Without even glancing at the beads, she chooses one, notes the color, and puts it back in the box. She speaks more than once in the same way. The table below displays the results. Jada's cousin desires to have pink beads placed in her hair.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
The table is given below.
Color Frequency
Pink 7
Green 8
Red 10
Total 25
The probability of getting pink will be given as,
p = 7/25
p = 0.28
Then the expected value of pink will be given as.
E(pink) = 175 x 0.28
E(pink) = 49
Thus, the number of pink beads in Jada's storage box will be 49.
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Consider the following function. g ( x ) = x 3 − 6 A) Find its average rate of change over the interval [ − 2 , 2 ] . B) Compare this rate with the instantaneous rates of change at the endpoints of the interval.
A- The average rate of change of g(x) over the interval [-2, 2] is 4, B- the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
A) To find the average rate of change of the function g(x) over the interval [-2, 2], we need to compute the difference quotient:
average rate of change = [g(2) - g(-2)] / [2 - (-2)]
First, we find the values of the function at the endpoints of the interval:
g(-2) = \(-2^{3}\) - 6 = -14
g(2) = \(2^{3}\) - 6 = 2
Substituting these values into the
average rate of change = (2 - (-14)) / (2 - (-2)) = 16 / 4 = 4
Therefore, the average rate of change of g(x) over the interval [-2, 2] is 4.
B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivatives of the function at x=-2 and x=2 using the power rule of differentiation:
g'(x) = 3\(x^{2}\)
g'(-2) = 3\(-2^{2}\) = 12
g'(2) = 12
The instantaneous rate of change at x=-2 is 12, and the instantaneous rate of change at x=2 is also 12. These values are equal to the average rate of change over the interval [-2, 2], which is 4.
This means that the function g(x) is not a linear function over the interval [-2, 2], and the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.
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I don't remember how this kind of question works. If it helps, this is module 10.04 Geometry. 98 points
Answer choices
7
20
19
6
Answer:
A. 7-----------------------------------
To solve this you need the intersecting secants theorem, which states:
If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.Apply this to the given lengths to get:
IK*IJ = IH*IGSubstitute values to get equation:
(x + 2)(x + 2 + 11) = 10*(10 + 8)(x + 2)(x + 13) = 10*18x² + 15x + 26 = 180x² + 15x - 154 = 0Solve the quadratic equation to get roots:
x = 7 and x = - 22The first root is the answer and the second root is not considered a solution as it is negative.
The matching choice is A.
Which equation is true when k = -15?
a) 4k - 11 = -34
b) -53 + 4k = 7
c) k/3 + 17 = 12
d) k/5 + 2.5 = 0.5
Answer:
c) k/3 + 17 = 12
#JUST A TEXT
Tamara needs tiles to make a border for her bathroom wall. The border will be 9 feet long and 1/3 foot wide. Each tile measures 1/3 by 1/3 foot. Each box of tiles contains 6 tiles. How many boxes of tiles does Tamara need? Write two equations that can be used to solve the problem.
Answer:
Hi I'm always here to help!!!
______________________________
6x*(1/3)*(1/3) >= 9*(1/3)
(2/3)x >= 3
x >= 4.5
Since x is integer, the smallest integer such that x >= 4.5 is x = 5.
Tamara needs 5 boxes of tiles.
_______________________________
Have a great day!!!!!
Answer:
X is the integer, the smallest integer such that x >= 4.5 is x = 5.
Tamara needs 5 boxes of tiles.
Equation representation:
6x times (1/3) times (1/3) >= 9 times (1/3)
(2/3)x > = 3
x >= 4.5
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
the volume of a cone is 120 cubic centimeters. the height of the cone is 4.5 centimeters. determine the radius of a cone
\(v = 120 \: {cm}^{3} \)
\(h = 4.5 \: cm\)
to find:the radius of the cone.
solution:\(r = \sqrt{3 \frac{v}{\pi \: h} } \)
\(r = \sqrt{3 \times \frac{120}{\pi \times 4.5} } \)
\(r = 5.04627 \: cm\)
\(r = 5.05 \: cm\)
hence, the radius of the given cone is 5.05 centimeters.
help please this is confusing me i only need number 7
Answer:
24.98 units
Step-by-step explanation:
You want the perimeter of triangle ABC with vertices A(-5, 4), B(1, -2), and C(3,6).
Distance formulaThe distance between two vertices can be found using the formula ...
d = √((x2 -x1)² +(y2 -y1)²)
ApplicationThe distance between A and B is ...
d = √((1 -(-5))² +(-2 -4)²) = √(6² +(-6)²) = 6√2 ≈ 8.485
The attached spreadsheet performs the same calculation on all the pairs of points. (The distance from each point to the one below it is listed.)
PerimeterThe perimeter of the triangle is the sum of the segment lengths. That is also shown in the spreadsheet.
P = AB +BC +CA
P = 8.485 +8.246 +8.246 ≈ 24.98
The perimeter of triangle ABC is about 24.98 units.
__
Additional comment
When calculations are repetitive, we like to let a spreadsheet do them.
6 more than 7 times a number
Answer:
See below.
Step-by-step explanation:
6 more than 7 times a number would be represented as 7n+6.
-hope it helps
Answer:
7n+6
Step-by-step explanation:
Im learning this in class and im really good so this is the answer
Pls give brainliest
From a group of 8 women and 6 men, a committee consisting of 3 men and 3 womenis to be formed. How many different committees are possible if 2 of the men refuse toserve together? How many different committees are possible if 1 man and 1 womanrefuse to serve together?
Answer:
a) 896 ways
c) 910 ways
Step-by-step explanation:
The question is a combination problem since it has to do with selection. In combination, if r object is selected from a pool of n objects, this can be done in nCr ways.
nCr = n!/(n-r)!r!
If from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed, we need to first calculate the total committee formed without any condition.
8C3 × 6C3
= 8!/5!3! × 6!/3!3!
= 8×7×6×5!/5!×6 × 6×5×4×3!/3!×6
= 56×20
= 1120ways
Now if;
a) two of the men refuse to serve together.
Since two men refuse to serve together, we will select 1 man from remaining 4 men since two has already been selected then select 3 from 8 women as shown.
4C1×8C3
= 4×56
= 224ways
Number of ways this can be done will be 1120-224 = 896ways
b) 1 man and 1 woman refuse to serve together
We need to choose 2 men from remaining 5 and 2 women from the rest of the men which is 7 as shown:
= (8-1)C(3-1) × (6-1)C(3-1)
= 7C2 × 5C2
= 7!/5!2! × 5!/3!2!
= 7×6×5!/5!×2 × 5×4×3!/3!×2
= 21×10
= 210ways
The number of ways this can be done will be 1120-210 = 910ways
New tablets are on sale for 40% off. They're
normally $149.50. What will I pay for my tablet
when I get 40% off?
Answer:
$89.7
Step-by-step explanation:
First, find the 40% of 149.5, which is 59.8. Then, subtract the percentage (59.8) from 149.5 which equals 89.7.
So it is $89.7 dollars when it is 40% off.
HOPE THIS HELPS!!!!
BEST OF LUCK!!!
The sum of two numbers is 50 and the difference is 4
Step-by-step explanation:
let the 2 numbers be x and x + 4 as their deference is 4.
their sum = 50
now,
→ x + x + 4 = 50
→ 2x + 4 = 50
→ 2x = 50 - 4 = 46
→ x = 46/2 = 23
therefore two numbers are,
x = 23
x + 4 = 23 + 4 = 27
hope this answer helps you dear...take care and may u have a great day ahead!
Step-by-step explanation:
x + y = 50
x - y = 4
x = y + 4
let's use that as substitute in the first equation
y + 4 + y = 50
2y = 46
y = 46/2 = 23
=>
x = y + 4 = 23 + 4 = 27
the 2 numbers are 23 and 27.
Find the missing variables. Round to the nearest tenth if necessary.
The value of a and b are; 4.8 and 10.8 respectively.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We have been given a figure which shows that;
Let x, y z, and u lines are parallel.
Therefore, by using proportion we can say that
a/ 12 = 4/ 10
thus, a = 4/ 10 (12)
a =2(12)/ 5
a = 24/5
a = 4.8
Now, 12/b = 10/8
b = 12 (8/10)
b = 6(8)/ 5
b 54/5
b = 10.8
Hence, tha value of a and b are; 4.8 and 10.8 respectively.
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The sum of two numbers is 12 and the quotient of those numbers is -4.
Answer:
16 and -4
Step-by-step explanation:
16 + (-4) = 12
16 / -4 = -4
9y-7=29
Prove y=4
Solve the problem
9y - 7 = 29
=> 9y = 29 + 7 [Transferring 7 to R.H.S.]
=> 9y = 36
=> y = 36/9 [Transferring 9 to R.H.S.]
=> y = 4
Hence proved.
Answer:
Here
Step-by-step explanation:
A 5oz jar of jam costs $2.50. How much is the unit price per ounce?
The unit price per ounce of the jar of jam is $0.50
How to determine the unit price per ounce for the jam?From the question, the given parameters are
Volume = 5 oz
Cost of jam = $2.50
The unit rate of the jam is calculated as
Unit rate = Cost of jam/Volume
Substitute the known values in the above equation
So, we have the following equation
Unit rate = 2.50/5
Evaluate the quotient
So, we have the following equation
Unit rate = 0.5
Hence, the unit price per ounce is $0.50
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use green's theorem to find the counterclockwise circulation and outward flux for the field f=(7x−4y)i (9y−4x)j and curve c: the square bounded by x=0, x=4, y=0, y=4.
The counterclockwise circulation around c is 12 and the outward flux through c is zero.
Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.
In this case,
we have a field f=(7x−4y)i+(9y−4x)j and
a square curve c bounded by x=0, x=4, y=0, y=4.
To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.
The curl of f is given by (0,0,3), so the line integral evaluates to 12.
To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.
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CAN SOMEONE PLEASE HELP I WILL GIVE YOU GOOD RATING PLS also round to the nearest tenths
A successful lawyer ownsthree vintage cars. The ratio of car is value to 1's value is 3:4. The ratio of car 2's value tocar 3's is 8:5. d the total value of three cars is $1115900, fins the value of each car
Answer: Let's represent the value of car 1 as x. Then, the value of car 2 is 3/4 of x, and the value of car 3 is 4/5 of the value of car 2.
So, we can write the following equations:
x = (3/4) * y
y = (4/5) * z
Where y is the value of car 2, and z is the value of car 3.
Adding all the values, we have:
x + y + z = 1115900
We can substitute the values of y and z in terms of x:
x + (3/4) * x + (4/5) * (3/4) * x = 1115900
Simplifying the expression on the left side, we get:
7/4 * x = 1115900
Finally, dividing both sides by 7/4, we get:
x = 359900
So, the value of car 1 is $359900, the value of car 2 is (3/4) * x = (3/4) * 359900 = 269925, and the value of car 3 is (4/5) * (3/4) * x = (4/5) * (3/4) * 359900 = 213140.
Step-by-step explanation:
Answer: the value of car 1 is $467125, the value of car 2 is $623033.33, and the value of car 3 is $350937.5.
Step-by-step explanation:
Let's call the value of car 1 "x".
From the first ratio, we know that the value of car 2 is 4/3 times greater than the value of car 1, and the value of car 3 is 3/4 times greater than the value of car 1.
So, the value of car 2 is 4/3 * x, and the value of car 3 is 3/4 * x.
From the second ratio, we know that the value of car 2 is 8/5 times greater than the value of car 3.
So, the value of car 2 is 8/5 * (3/4 * x) = 6/5 * x.
The total value of all three cars is $1115900, so we can set up an equation to solve for x:
x + 4/3 * x + 3/4 * x = 1115900
Expanding and simplifying the right side:
x + 4/3 * x + 3/4 * x = 1115900
8/3 * x = 1115900
x = 1115900 * 3 / 8
x = 467125
So, the value of car 1 is $467125, the value of car 2 is $623033.33, and the value of car 3 is $350937.5.
Write a polynomial function that has four possible rational zeros but no actual rational zeros.
This polynomial function has four possible rational zeros (2, 3, 5, and 7) but no actual rational zeros since these values are all prime numbers.
To write a polynomial function that has four possible rational zeros but no actual rational zeros,
we can use the Rational Root Theorem.
The theorem states that if a polynomial has a rational root (zero), it must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
Since we want four possible rational zeros but no actual rational zeros, we can use a constant term that is not divisible by any integers and a leading coefficient that is not divisible by any integers except
1. For example, we can use the constant term of 150 and the leading coefficient of 1.
The polynomial function that satisfies these conditions is:
f(x) = (x - p1)(x - p2)(x - p3)(x - p4)
Where p1, p2, p3, and p4 are four distinct prime numbers.
By using distinct prime numbers as the possible zeros, we ensure that there are no actual rational zeros.
For example, let's use p1 = 2, p2 = 3, p3 = 5, and p4 = 7:
f(x) = (x - 2)(x - 3)(x - 5)(x - 7)
This polynomial function has four possible rational zeros (2, 3, 5, and 7) but no actual rational zeros since these values are all prime numbers.
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Solve the quadratic by factoring. 3x^{2}+7=-8x+3 3x 2 +7=−8x+3
The roots of the given quadratic equation are x = -2/3 and x = -2.
What is a quadratic equation?A quadratic equation is a equation that is of the form -
y = f{x} = ax² + bx + c
Given is a quadratic equation as follows -
3x² + 7 = - 8x + 3
The given quadratic equations are -
3x² + 7 = - 8x + 3
3x² + 8x = 3 - 7
3x² + 8x + 4 = 0
(x + 2/3)(x + 2) = 0
(x + 2/3) = 0 and (x + 2) = 0
x = -2/3 and x = -2
Therefore, the roots of the given quadratic equation are x = -2/3 and x = -2.
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which measure of center best represents this set of data: red, blue, red, yellow, red, green, black, red, white, red, red. a) Mean. b) Mode. c) Median.
The mode best represents the set of data: red, blue, red, yellow, red, green, black, red, white, red. The mode is a statistical measure that represents the most frequently occurring value or values in a dataset.
The mode is the measure of center that represents the most frequently occurring value in a dataset. In this case, the color "red" appears most frequently, occurring 6 times out of the 11 data points. Therefore, the mode of the dataset is "red."
The mean, on the other hand, calculates the average value by summing all the data points and dividing by the total number of data points. The mean can be influenced by extreme values or outliers, which may not accurately represent the overall data.
The median is the middle value when the data is arranged in ascending or descending order. In this case, since there are 11 data points, the median would be the sixth value. However, there is no clear middle value as there are multiple occurrences of "red" in the dataset.
Hence, the mode, representing the most frequently occurring value, is the measure of center that best represents this set of data.
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I have to get to 80% but I’m stuck on this question
The supplementary angles are ∠GDF and ∠EDG, ∠CED and ∠BEC. The correct options are C and D.
What are supplementary angles?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. The sum of complementary angles is 90 degrees.
The sum of the two angles ∠GDF and ∠EDG is equal to 180°. So these angles are supplementary to each other.
The sum of the two angles ∠CED and ∠BEC is equal to 180°. So these angles are supplementary to each other.
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14. A box of mineral water contains 24 bottles from a given factory. A woman bought 135 boxes from the company. If each bottle of water has a mass of 728g, find the total mass in kilograms of all the 135 boxes of water, correct to 1 decimal place.
The total mass of the 135 boxes that the woman bought is 2358.7 kg
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
Each bottle of water has a mass of 728g. A box of mineral water contains 24 bottles from a given factory, hence:
Mass of each box = 24 bottles * 728 g per bottle = 17472 g
The woman bought 135 boxes, therefore:
Total mass of boxes = 135 boxes * 17472 g per box = 2358720 g
But 1 kg = 1000 g
2358720 g = 2358720 g * 1 kg per 1000 g = 2358.7 kg
The total mass is 2358.7 kg
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A baseball stadium has 15,002 seats. The lower level has 50 fewer than three times as many seats as the upper level. The middle level has 40 more than twice as many seats as the upper level. You solved for x and found that the upper level has 2,502 seats.
How many seats are in the lower level?
How many seats are in the middle level?
Answer:
There are 7456 seats on the lower level and there are 5044 seats on the middle level.
Step-by-step explanation:
Let 'X" be the number of seats on the upper level. Then we can find how many seats are on the lower level by solving the following equation...
# of seats on the lower level = 3x - 50
# of seats on the lower level = 3(2502) - 50
# of seats on the lower level = 7456
Now we just make the equation for the number of seats on the middle level, and so we get...
# of seats on the middle level = 2x + 40
# of seats on the middle level = 2(2502) + 40
# of seats on the middle level = 5044
Answer:
There are 7456 seats on the lower level and there are 5044 seats on the middle level.
Step-by-step explanation:
this is correct on edge 2021
slope of 2,1 and 7,1
Answer:
0
Step-by-step explanation:
Answer:
0
I hope this helps!
solve the separable differential equation dy / dx = − 0.6 y , and find the particular solution satisfying the initial condition y (0) = − 9 . y(x) =___
The particular solution is: y(x) = -9e^(-0.6x) To solve the separable differential equation dy/dx = -0.6y, we need to separate the variables by dividing both sides by y and dx:
1/y dy = -0.6 dx
Then, we integrate both sides:
ln|y| = -0.6x + C
where C is the constant of integration. To find the particular solution satisfying the initial condition y(0) = -9, we substitute x = 0 and y = -9 into the above equation:
ln|-9| = -0.6(0) + C
ln 9 = C
Therefore, the particular solution is:
ln|y| = -0.6x + ln 9
|y| = e^(ln 9) e^(-0.6x)
|y| = 9 e^(-0.6x)
Since y(0) = -9, we take the negative sign for the absolute value of y:
y(x) = -9 e^(-0.6x)
Therefore, the particular solution satisfying the initial condition y(0) = -9 is y(x) = -9 e^(-0.6x).
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A lawn 46m by 34m has a path of uniform width around it. If the area of the
path is 425m², find its width.
The width of the path is 24 meters.
How to calculate the widthLet's call the width of the path "x".
The dimensions of the inner rectangle (the lawn without the path) are 46m by 34m. The dimensions of the outer rectangle (the lawn with the path) are (46+2x) by (34+2x).
Area of path = Area of outer rectangle - Area of inner rectangle
425m² = (46+2x)(34+2x) - (46)(34)
Simplifying and solving for x:
425m² = (2x+46)(2x+34)
425m² = 4x² + 80x + 1564
4x² + 80x - 1161 = 0
We only want the positive value for x, so:
x = (-80 + 272) / 8
x = 24m
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pls answer will mark brainliest
Which expression is equivalent to 9x - (x - 8)(x + 1) + 10x?
a. -x^2+19x+8
b. -x^2+26x+8
c. 8x^2+10x+8
d. 8x^2+26x+8
Answer:
x^2+12x-8
Step-by-step explanation:
(x-8)(x+1) = x^2-7x-8
x^2+9x-7x+10x-8
simplify:
x^2+12x-8
Answer: -x^2+26x-8
Step-by-step explanation:
1. Multiply
9x-(x-8)(x+1)+10x
9x-x^2-x+8x-8+10x
2. Combine Like Terms
-x^2+26x-8
Answer: -x^2+26x-8