Solve the following simultaneous equation using elimination or substitution method
Answers
Answer:
(15, 10) and (10, 15)
Explanation:
The given system of equation is
x + y = 25
xy = 150
To solve the equation, we will use the subtitution method, so first, we need to solve the first equation for y
x + y = 25
x + y - x = 25 - x
x y= 25 - yx
Then, substitute y = 25 - x on the second equation, we get
xy = 150
x(25 - x) = 150
x(25) - x(x) = 150
25x - x² = 150
Now, we can rewrite the equation as
25x = 15 + x²
0 = 150 + x² - 25x
0 = x² - 25x + 150
Therefore, we need to find the values of x that satisfies
x² - 25x + 150 = 0
Now, we need to factorize this equation, so two numbers that multiply to 150 and add to -25 are -15 and -10. Then
(x - 15)(x - 10) = 0
So, the solutions are
x - 15 = 0
x = 15
or
x 10 = 0
x = 10
Then, the values of y are
If x = 15
y = 25 - x
y = 25 - 15
y = 10
If x = 10
y = 25 - x
y = 25 - 10
y = 15
Therefore, the solutions are (15, 10) and (10, 15)
I
Related Questions
Write an expression in simplest for the volume of the new cube in terms of a.
Answers
After decreasing the sidelength to 20% of the original size, the new sidelength is:
[tex]0.20a[/tex]The volume of a cube is given by the product of 3 of its sidelengths, it means, that the volume of the cube is the sidelength raised to 3:
[tex]V=(0.20a)^3=0.008a^3[/tex]Show how to use place value to add 354 + 271.
Answers
Answer:
Step-by-step explanation:
300+50+4+200+70+1
=500+120+5
=625
Pls help fast it is due in a few minutes
Answers
The day in which Chloe would have more money than Kenzi is after 15 days.
When would Chloe have more money?The equation that represents the amount left after the purchase of Frutti Tutti and lunch is:
Amount left = amount she began with - (amount spent x number of days)
Amount that Chloe has left : $75 - $3x
Amount that Kenzi has left : $90 - $4x
The inequality that can be used to represent when Kenzi would have less money than Chloe is:
$75 - $3x > $90 - $4x
$4x - 3x > $90 - $75
x > 15
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The way too do it and maybe the answer tbh
Answers
Concept
To find the remainder, use the repeated division method.
Step 1: Divide the term with degree 3 with x. Then multiply the result with x - 5, and then subtract
Final answer
Remainder = 240
take the square root of both sides of the equation from part B ( n↑2−c↑2=0 ) and write the resulting equation. how can this equation be true, and what does this show about the relationship between the two triangles?
Answers
SOLUTION
From the question and the instructions given,
Since
[tex]\begin{gathered} n^2-c^2=0 \\ square\text{ rooting both sides } \\ \sqrt{n^2}-\sqrt{c^2}=\sqrt{0} \\ square\text{ cancels square root, we have} \\ n-c=0 \end{gathered}[/tex]Thus, the triangles have all sides congruent, since the triangles are congruent.
Hence, this means that triangle 1 is a right triangle.
☆ Request edit access Show All Work 1) In 2005 the number of seniors at Juarez decreased by 63 students over the 9 month school year. If the decrease was the same over the entire 9 months, write the monthly decrease as a quotient of integers and find the monthly decrease.
Answers
The seniors decreased in 63 in 9 months. if the rate is the same for all the months, to know the monthly decrease we have to divide 63 by 9 and we get that
[tex]\frac{63}{9}=7[/tex]so the monthly decrease is 7
Jerry tries to exercise each day of the week. He burns 850 calories when he runs and 200 calories when he lifts weights. Last week he exercised for a total of 6.5 hours and burn 2,925 total calories. How long does he spend on each exercise? Which augmented matrix can be used to represent the system of equations used to solve the problem above?
Answers
SOLUTION:
Case: Augmented Matrix
Given:
In linear algebra, an augmented matrix is a matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices.
Given:
He burns 850 calories when he runs.
he burns 200 calories when he lifts weight
he exercised for a total of 6.5 hours
he burns 2,925 total calories
Method:
First, we make a linear equation:
Assumption: Let the number of hours he runs be r. The number of hours he lifts weights be w.
The equation therefore is:
Hours:
r + w = 6.5
Calories:
850x + 200y = 2925
Final answer:
Augmented Matrix
[tex]\begin{bmatrix}{1} & {1} & {|6.5} \\ {850} & {200} & {|2925} \\ {} & {} & {}\end{bmatrix}[/tex]3. On the map 1/3 cm represents 5 kilometers. How many centimeters on map represent 200 kilometers?A. 1/5B. 1 2/3C.13 1/3D. 40E. 66 2/3
Answers
Answer:
C.13 1/3 cm
Explanation:
On the map, 5km is represented by 1/3 cm.
Therefore:
[tex]1\operatorname{km}\text{ is represented by }\frac{1}{3}\div5=\frac{1}{15}cm[/tex]We can then conclude that:
[tex]\begin{gathered} 200\operatorname{km}\text{ is represented by }\frac{1}{15}\times200\text{ cm} \\ \frac{1}{15}\times200=13\frac{1}{3}cm \end{gathered}[/tex]The correct choice is C.
a car loses value at a rate of $2,500 per year (slope) you purchase a car for $21,000 which equation can be used to find y its value in dollars, x years after it was purchased
Answers
The value decreases at the rate of 2500 means slope of equation is -2500 and present value is 21000 so y intercept for the line is 21000.
Determine the equation for the car value after x years.
[tex]y=-2500x+21000[/tex]So answer is -2500x + 21000.
A store owner buys sweatshirts for $16 and marks them up 20% to make a profit. The sales tax where his store is located is 7.5%. A customer considers buying one or two sweatshirts from the store. Select all the statements that apply.
A One sweatshirt before tax costs $19.20.
B One sweatshirt before tax costs $12.80.
C The sales tax for two sweatshirts is $1.92.
D The sales tax for two sweatshirts is $2.88.
E Total cost for two sweatshirts is $41.28
F Total cost for two sweatshirts is $27.52.
(you can only choose up to three btw)
Answers
The correct statement are;
⇒ One sweatshirt before tax costs $19.20.
Option A is true.
What is Percentage?
A relative value indicating hundredth part of any quantity is called percentage.
Given that;
Cost of sweatshirts for a store owner = $16
Profit percent = 20%
Sales tax = 7.5%
Now,
Profit price for a sweatshirts = 20% of $16
= 20/100 × 16
= 320 / 100
= $3.20
And, The sales tax price = 7.5% of 16
= 7.5 / 100 × 16
= 120 / 100
= $1.20
So, The cost of one sweatshirt before tax costs = $16 + $3.20
= $19.20
And, Sales tax for one sweatshirt = $1.20
So, Cost of sales tax for two sweatshirt = 2 × 1.20
= $2.40
And, Total cost of a sweatshirt = $16 + $3.20 + $1.20
= $20.4
So, Total cost of two sweatshirt = 2 × $20.4
= $40.8
Thus, The correct statement are;
⇒ One sweatshirt before tax costs $19.20.
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pleae help me and show work you will be braineist
Answers
The equation of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]where (x1,y1) is a point on the line and m is the slope. To find the slope of a line we use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, we have:
[tex]m=\frac{4-3}{5-(-2)}=\frac{1}{5+2}=\frac{1}{7}[/tex]Then, the equation of the line is:
[tex]\begin{gathered} y-4=\frac{1}{7}(x-5) \\ 7y-28=x-5 \\ x-7y=-23 \end{gathered}[/tex]Therefore:
[tex]x-7y=-23[/tex]Which is a description of the vertical shift of the function f(t)=3sec(t-pi/4)-2
Answers
The vertical shift of the given function is -2 or down 2. (Option D)
Here's why:
The function is given in a form of:
[tex]f(t)=a\sec (bx-c)+d[/tex]where d is the vertical shift. Since -2 is the value of d in the given function, then, -2 is the vertical shift.
An animal shelter currently only has 19 dogs and 13 cats. What is the ratio of cats to animals?
Answers
Answer:
13:32
Step-by-step explanation:
You have 10 gallons of lemonade to sell. [tex](1gal = 378 {cm}^{2})[/tex] Each customer uses 1 paper cup. The cups are sold in packages of 50. How many packages should you buy?
Answers
The volume of a cilinder (like the cup) is given by:
[tex]V=\pi r^2h[/tex]Then, each cups can hold:
[tex]V=\pi(8)^2(11)=2211.68[/tex]Now, since each gallon is equivalent to 3785.41 cubic cm then we have a total of 10 times 3785.41=37854.1 cubic cm of lemonade.
Therefore we need:
[tex]\frac{37854.1}{2211.68}=17.11[/tex]Hence, we need 18 cups of lemonade and we only have to buy one package.
A linear function that models a relationship where the x-values increases by 4 units for every 2 units the y-value increases. The value of the function at x=0 is -2.
Answers
The most appropriate choice for equation of line in slope intercept form will be given by
x -2y = 4 is the required linear function.
What is equation of line in slope intercept form?
Equation of line in slope intercept form is given by y = mx + c
Where, m is the slope of the line and c is the y intercept of the line
The distance from the origin to the point where the line cuts the x axis is called x intercept
The distance from the origin to the point where the line cuts the y axis is called y intercept
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by [tex]tan \theta[/tex]
If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex])
slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here,
Increase in x value = 4 units
Increase in y value = 2 units
Slope = [tex]\frac{2}{4}[/tex]
Slope = [tex]\frac{1}{2}[/tex]
Let the equation of line be [tex]y = \frac{1}{2}x + c[/tex]
When x = 0, y = -2
[tex]-2 = \frac{1}{2}\times 0+c[/tex]
c = -2
Equation of line
[tex]y = \frac{1}{2} x - 2\\2y = x - 4\\x - 2y = 4[/tex]
This is the required linear function.
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Kylie wants to ride her bicycle 27.5 miles this week. She has already ridden 9 miles. If she rides for 5 more days, which equation or tape diagram could be used to represent the context if mm represents the average number of miles she would have to ride to meet her goal?
Answers
The equation to represent the context is 9 + 5m = 27.5
How to frame the equation?
Number of miles Kylie wants to ride in a week= 27.5
Number of miles already ridden = 9
Average number of miles to meet her goal = mm
Let average no. of miles in 5 days = 5m
Rewriting as equation,
9 + 5m = 27.5
How to find the average number of miles?
5m = 37.5 -9
5m = 18.5
m = 18.5
[tex]m =\frac{18.5}{5} \\\\m = 3.7 \text{ or } 3\frac{7}{10}[/tex]
Kylie should travel 3.7 miles per day and 18.5 miles in 5 days to meet her goal
What is an equation?
A mathematical statement that has two expressions with equal values separated by the symbol ' = ' is called an equation. The expression on the left and the expression on the right are shown to be equal in reference to one another. The equations are solved to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no equal to sign in the statement and shall be taken into account as an expression.To learn more about equations, refer:
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Determine if the function is an example of exponential growth or exponential decay:A) f(x) = (1/3)^xB)f(x) =8^xC) f(x) =0.3^x
Answers
a) decay
b) growth
c) decay
Explanation:Exponential function is given as:
[tex]y=ab^x[/tex]To determine if the function is an exponential growth or decay:
when a is positive and b is greater than 1, it is a growth
when a is positive and b is less than 1, it is a decay
[tex]\begin{gathered} a)\text{ f(x) = (}\frac{1}{3})^x \\ a\text{ in this case 1 (positive)} \\ b\text{ = 1/3 (it is less than 1)} \\ \text{Hence, it is a decay} \end{gathered}[/tex][tex]\begin{gathered} b)f(x)=8^x \\ a\text{ in this case 1 (positive)} \\ b\text{ = 8 (it is greater than 1)} \\ \text{Hence, it is a growth} \end{gathered}[/tex][tex]\begin{gathered} c)\text{ }f\mleft(x\mright)=0.3^x \\ a\text{ in this case 1(positive)} \\ b\text{ = 0.3 (it is less than 1)} \\ \text{Hence, it is a decay} \end{gathered}[/tex]Question in picture please answer I’ll give bonus points if right
Answers
Answer:
Division Property
Step-by-step explanation:
Step 3: 4x = -24
÷4 ÷4
---------------
Step 4: x = -6
Since -24 is being divided by 4 the division property is being used.
I hope this helps
Given: x-8> -3.
Choose the solution set.
OXIXER, Xx>-5]
OXIXER,X > 14]
OXIXER,X > 5)
OXIXER,X> -9)
Answers
Solution set for x - 8 > -3 will be [ x|x E R, x > 5 ] --(option 3)
We have given rule x - 8 > -3.
Adding 8 on both side of given rule.
∴ x - 8 + 8 > -3 + 8
By Simplification of given rule.
∴ x > 5
Solution set : -The solution set of an inequality is the set of all solutions. An inequality usually has an infinite number of solutions, and the set of solutions can be easily written using interval notation.
A solution set is the set of all variables that makes the equation true.
Here as given solution set will be all the numbers greater that 5 excluding 5.
∴ Solution set will be [ x|x E R, x > 5 ] --(option 3)
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Help mee pleasee!!
thank you <3
Answers
540 people will be employed as medical assistants in the year 2013.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
We have to determine the slope of the line :
m = (y₂ - y₁)/(x₂ -x₁ )
m = (560 - 359)/(10-0)
m = 20.1
This represents new assistants per year
So with your y-intercept of 359, your equation becomes
y = 20.1x + 359
Using this equation to estimate the number of people who will be employed as medical assistants in the year 2013.
Let y be the number of medical assistants (in thousands) employed in the country in the year x, where x = 0 represents 2004.
Substitute the value of x = 9 for the year 2013
y = 20.1(9) + 359
y = 180.90 + 359
y = 539.90 ≈ 540
Hence, 540 people will be employed as medical assistants in the year 2013.
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I need help making a tree diagram
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Please don't close the session, the image its downloading
Solve for r.0.5(r +2.75) = 3
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The given equation is,
[tex]0.5\mleft(r+2.75\mright)=3[/tex]To solve the above equation for r, first divide both sides of the equation by 0.5.
[tex]\begin{gathered} \frac{0.5\mleft(r+2.75\mright)}{0.5}=\frac{3}{0.5} \\ r+2.75=6 \end{gathered}[/tex]Subtract 2.75 from both sides of the above equation.
[tex]\begin{gathered} r+2.75-2.75=6-2.75 \\ r=3.25 \end{gathered}[/tex]Therefore, the value of r is 3.25.
y= 10-4x identity the slope and y-intercept
Answers
Answer:
Step-by-step explanation:
First, graph the expression by making sure it goes through 10 on the y-axis and since it shows -4 that means for every 1 unit to the right the y coordinate moves 4 boxes down. (Your graph should look like a downwards slope)
Now, pick 2 points on your graph, ill pick (0, 10) and (1, 6)
Now, put these in point-slope form and you will get your slope
Point-Slope form
m=y2-y1/x2-x1
m= 10-6/0-1
m= 4/-1
m=-4
Also, you can just see that it's the slope by the graph by using rise over run.
A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1350 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
First car:
Second car:
Answers
Answer:
Follow these steps to find your answer
Assuming that the shapes are similar. Find the values of x,y, and z
Answers
Assuming that both figures have the same shape, we can observe that one is bigger than the other, that means that there is a scale factor that must be found before calculating our values.
We can see that we have one side of both figures have the exact value, we will use these to find the scale factor
[tex]\begin{gathered} X\to\text{scale factor} \\ X=\frac{8}{12} \\ X=\frac{2}{3} \end{gathered}[/tex]Now we are going to multiply each of the sides of the big figure by the scale factor and we are going to match it with the corresponding side of the small figure.
To prove that the scale is correct, we try it with the known side:
[tex]\begin{gathered} 12X=8 \\ 12(\frac{2}{3})=8\to\text{correct } \end{gathered}[/tex]Now we calculate x, y and z
[tex]\begin{gathered} x\cdot(\frac{2}{3})=6 \\ x=\frac{6\cdot3}{2} \\ x=9 \end{gathered}[/tex][tex]\begin{gathered} 6(\frac{2}{3})=y \\ y=4 \end{gathered}[/tex][tex]\begin{gathered} 10(\frac{2}{3})=z \\ \frac{20}{3}=z \\ z=6.66 \end{gathered}[/tex]May I get help? I seem to keep losing connection
Answers
Answer
Option C is correct.
A = 1, B = 1, C = 0, D = -8, and E = 7
Explanation
The equation of a circle with center (h, k) and a radius of r, is given as
(x - h)² + (y - k)² = r²
This can then be expanded to form the general form of the equation,
Ax² + By² + Cx + Dy + E = 0
For this question, where the center of the circle lies on the y-axis, the coordinates of the center of that circle will be (0, p)
where p is the y-coordinate of the center of the circle.
(x - h)² + (y - k)² = r²
(h, k) = (0, p)
h = 0, k = p
r = 3 units
(x - 0)² + (y - p)² = 3²
x² + y² - 2py + p² = 9
x² + y² -2py + p² - 9 = 0
Comparing this with Ax² + By² + Cx + Dy + E = 0
A = 1
B = 1
C = 0
D = -2p
E = p² - 9
We can easily see that only Option C has C = 0 and matches the equation of the circle described in the question.
Hope this Helps!!!
Move values to the line to complete the scentence about P’ Q’ R’
Answers
The first step to solve this problem is to calculate the missing angle that has its vertex on P. The sum of the internal angles on every triangle is equal to 180 degrees, since we have the other two angles we can calculate the missing one as shown below:
[tex]\begin{gathered} 48+35+\measuredangle P=180 \\ 83+\measuredangle P=180 \\ \measuredangle P=180-83 \\ \measuredangle P=97 \end{gathered}[/tex]The angle is equal to 97 degrees. Now we know all the measurements of all the angles and sides of this triangle. When a triangle is rotated its measurements don't change, this means that if a side is equal to 2 before the rotation it should also be equal to 2 after the rotation. With this in mind we can say that:
The length of the side P'Q' is 9 units and the measurement of the angle P' is 97 degrees.
Consider the function f(x)=2x2 + 7x-30What are the zeros of the function?
Answers
We have the following quadratic function:
[tex]f(x)=2x^2+7x-30[/tex]And we need to find its zeros i.e. the solutions to the equation:
[tex]2x^2+7x-30=0[/tex]Given a quadratic equation like the following:
[tex]ax^2+bx+c=0[/tex]Its solutions are given by the quadratic solving formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In our case we have a=2, b=7 and c=-30. Then we get:
[tex]x=\frac{-7\pm\sqrt[]{7^2-4\cdot2\cdot(-30)}}{2\cdot2}=\frac{-7\pm\sqrt[]{49+240}}{4}=\frac{-7\pm\sqrt[]{289}}{4}[/tex]So we continue:
[tex]x=\frac{-7\pm\sqrt[]{289}}{4}=\frac{-7\pm17}{4}[/tex]So we have two solutions:
[tex]\begin{gathered} x_1=\frac{-7+17}{4}=\frac{10}{4}=2.5 \\ x_2=\frac{-7-17}{4}=-\frac{24}{4}=-6 \end{gathered}[/tex]Then the answers are -6 and 2.5.
Evaluate the function at the given values.
H(r) = 8
a. H(3) = |
b. H (8) =
c. H (0)
Answers
Factor these expressions.
x^2 + 7x + 10
Answers
Answer:
[tex](x+2)(x+5)[/tex]
Step-by-step explanation:
Let's factor x2+7x+10
x2+7x+10
The middle number is 7 and the last number is 10.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 7Multiply together to get 10Can you think of the two numbers?
Try 2 and 5:
2+5 = 7
2*5 = 10
Fill in the blanks in
(x+_)(x+_)
with 2 and 5 to get...
(x+2)(x+5)
