In order to solve this system of equations, we can add both equations, this way we can find the value of y and then the value of x:
[tex]\begin{gathered} \begin{cases}7x-9y=12 \\ -7x-7y=-28\end{cases} \\ 7x-9y-7x-7y=12-28 \\ -16y=-16 \\ y=\frac{-16}{-16}=1 \\ \\ 7x-9=12 \\ 7x=21 \\ x=\frac{21}{7} \\ x=3 \end{gathered}[/tex]So the solution to this system is (3, 1).
Show all steps. Let a= -1, b = 2, x = -5, y = 4, and w = -10.
5. Given
[tex]a^2-bw[/tex]You know that:
a=-1
b=2
w=-10
Replace these values into the expression:
[tex](-1)^2-2\cdot(-10)[/tex]Following the order of operations, first, you have to solve the exponent and the multiplication:
[tex]1-(-20)[/tex]Both minus signs form a "double negative" when this happens, the signs cancel each other and turn into a plus sign, so that:
[tex]1+20[/tex]Next, solve the addition
[tex]1+20=21[/tex]The result of this operation is 21.
help me with the last question pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
Mrs. Escalate was riding a bicycle on a bike path. After riding 2/3 of a mile, she discovered that she still needed to travel 3/4 of a mile to reach the end of the path. How long is the bike path?
Answer:
17/12
1 5/12
Step-by-step explanation:
If we make the fractions have common denominators, this problem is a piece of cake.
First, since the closest multiple of 3 and 4 is 12, put 12 instead of the 3 and 4.
Since 3x4=12, multiply 2x4.
2x4=8.
So the first fraction would be 8/12
Next, since the 4 turned into a 12, multiply 3 by 3.
3x3=9
So the second fraction would be 9/12.
Now, add 9/12 and 8/12 together.
9/12+8/12=
17/12
1 5/12
Julia received an 88, 90, 94, 89 on her first four English quizzes. What must she get on her fifth in order to have a 92 average?
Answer:
99
Step-by-step explanation:
You can set up a proportion, and solve for the variable (missing grade in this case):
[tex]\frac{88+90+94+89+x}{5} =92[/tex]
Each grade is already in the database, so it can serve as the constant, and five is the denominator because to get a mean average, you must divide all the values by the number of values that exist. So, in this case, it would be 5, 4 including the missing grade, making it 5. Set the equation equal to 92, because that's her desired average, then just solve for x.
Multiply the 5 on both sides.
-> 5 cancels on left, and 5 multiplies with 92 to get 460.
[tex](5)\frac{88+90+94+89+x}{5} = 92(5)[/tex]
Add all constants on the left side of the equation.
-> 88+90+94+89=361
[tex]361+x = 460[/tex]
Subtract that new constant (361) from the 460, and you get x=92.
-> 460-361=99
[tex]x=99[/tex]
Hope this helped. :)
Kuta Software - Infinite Algebra 2 Factoring By Grouping Factor ench completely. 1) 12a-9a? +40 - 3 Name Sarn on the ears Date : 120, 37443 4ac3a ²+1)-3(3u341) ta 2373 (403) 2) 2p'+ 5p² +6p+ 15 apstept sport 2plpa
Factor the expression.
[tex]\begin{gathered} 90au-36av-150yu+60yv=90au-150yu+60yv-36av \\ =30u(3a-5y)-12v(3a-5y) \\ =(3a-5y)(30u-12v) \\ =(3a-5y)(6\cdot5u-6\cdot2v) \\ =6(3a-5y)(5u-2v) \end{gathered}[/tex]So answer is,
[tex]6(3a-5y)(5u-2v)[/tex]Find the equation for the line that passes through the points (-2,-6) and (6,5). Give your answer in point-slope form. You do not need to simplify
The point-slope form of the equation of a line is given by the following expression:
y - y1 = m(x - x1)
Where m is the slope of the line and (x1, y1) is a point where the line passes through.
The slope of the line can be determined with the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1, y1) and (x2, y2) are two points where the line passes through. In this case we are told that the line passes through the points (-2,-6) and (6,5). By replacing the x and y coordinates of these points into the formula of the slope, taking x1 as -2, x2 as 6, y1 as -6 and y2 as 5, we get:
[tex]m=\frac{5-(-6)}{6-(-2)}=\frac{5+6}{6+2}=\frac{11}{8}[/tex]Then, the slope of the line equals 11/8, by replacing 11/8 for m into the slope-point form, we get:
y - y1 = 11/8(x - x1)
By taking one of the points, for example (-2,-6), we replace the x and y-coordinates that appear in the equation of the line, to get:
y - (-6) = 11/8(x - (-2))
y + 6 = 11/8 (x + 2)
Then, the equation of the line in slope-point form is y + 6 = 11/8 (x + 2)
The chart shows the distances Steve ran during the week. According to the chart above, how much farther did Steve run on Wednesday than Monday?
Please help!!!!!!! I am stuck and don't understand
Given that f(x)=x^2-x and g(x)=3x+9, Find
(A) (f+g)(-2)=
(B) (f-g)(-2)=
(C) (fg)(-2)=
(D) (f/g)(-2)=
The value of the following composite function is as follows:
(f + g)(-2) = 5(f - g)(-2) = - 5(fg)(-2) = 18(f/g)(-2) = 2How to solve composite function?The composite functions can be solved as follows:
Therefore, the given function are:
f(x) = x² - x
g(x) = 3x + 9
Hence,
a.
(f + g)(-2) = f(-2) + g(-2)
f(-2) + g(-2) = (2)² - 2 + 3(-2) + 9
f(-2) + g(-2) = 4 - 2 - 6 + 9
f(-2) + g(-2) = 5
Therefore, the function (f + g)(-2) = 5
b.
(f - g)(-2) = f(-2) - g(-2)
f(-2) - g(-2) = (2)² - 2 - (3(-2) + 9)
f(-2) - g(-2) = 4 - 2 - 3
f(-2) - g(-2) = -5
Therefore, the function (f - g)(-2) = - 5
c.
(fg)(-2)= f(-2) × g(-2)
f(-2) × g(-2) = (-2)² - (-2) × 3(-2) + 9
f(-2) × g(-2) = 4 + 2 × 3
f(-2) × g(-2) = 6 × 3
f(-2) × g(-2) = 18
Therefore, the function (fg)(-2) = 18
d.
(f/g)(-2) = f(-2) / g(-2)
f(-2) / g(-2) = -2² - -2 / 3(-2) + 9
f(-2) / g(-2) = 6 / 3
f(-2) / g(-2) = 2
Therefore, the function (f/g)(-2) = 2
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I will give Brainiest
Answer:
The answer is -2.93333 or -44/15
Answer:
See below
Step-by-step explanation:
(1.6 )( 2 1/6 -4)
1.6 ( -1 5/6) =-2.93333 or -2 14/15
Consider the system of equations.
2x+y=1−3x+4y=15
How can the system of equations be solved using Cramer's rule?
Drag a value or determinant expression into each box to correctly solve the system using Cramer's rule.
The solutions are x = -1 and y = 3 of the given system of equations 2x+y=1, −3x+4y=15 which is determined by Cramer's rule.
We put the tiles in the right order and entered the final result for each x and y.
The main principle is to split determinants as shown by the vertical bars (these are not absolute value bars).
The determinant of the matrix [tex]\begin{bmatrix}2 & 1 \\-3 & 4 \\\end{bmatrix}[/tex], which are the coefficients of the left-hand side of each original equation supplied to you, is in each denominator.
This matrix's numerators are somewhat different. The x determinant requires you to replace the first column with 1 and 15 to produce [tex]\begin{bmatrix}1 & 1 \\15 & 4 \\\end{bmatrix}[/tex], which aids in determining the x solution. The y solution is similar, except we replace the y column rather than the x column. This explains the [tex]\begin{bmatrix}2 & 1 \\-3 & 15 \\\end{bmatrix}[/tex].
You just evaluate each determinant using the formula once you have the right determinants in place and then simplify the outcomes.
Thus, the solutions are x = -1 and y = 3 of the given system of equations 2x+y=1, −3x+4y=15 which is determined by Cramer's rule.
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(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
write an equation of the line that passes through the points in the table x=0,1,2,3 y=10,7,4,1
Equation of the line that passes through the points in the table:
x=0,1,2,3
y=10,7,4,1
is y = -3x + 10
What is Equation of the Line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Key Concept. Y = mx + c is the equation for a straight line with a gradient of m and an intercept of c on the y-axis.
Since, The Equation of the line:
y = mx + b
where m is the slope
For finding slope passing through (0,10) and (1, 7)
m = (y2 - y1)/(x2 - x1)
m = (7 - 10) / (1 - 0)
m = -3/1
m = -3
Therefore, the slope of the line is −3.
Now use the slope and either of the two points to find the y-intercept.
y=mx+b
10 = (-3)(0) + b
10 = b
Write the equation in slope intercept form as:
y=mx+b
y = -3x + 10
Hence, the equation of the line is y = -3x + 10
Now, for other two points (2, 4) and (3, 1)
For finding slope passing through (2, 4) and (3, 1)
m = (y2 - y1)/(x2 - x1)
m = (1 - 4) / (3 - 2)
m = -3/1
m = -3
Therefore, the slope of the line is −3.
Now use the slope and either of the two points to find the y-intercept.
y=mx+b
4 = (-3)(2) + b
4 = -6 + b
4+6 = b
b = 10
Write the equation in slope intercept form as:
y=mx+b
y = -3x + 10
Hence, the equation of the line is y = -3x + 10
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Devaughn is 8 years older than Sydney. The sum of their ages is 84. What is Sydney's age?
Answer:
Sydney should be 25 years old
Step-by-step explanation:
Answer:
Sydney is 38 years old.
Step-by-step explanation:
Devaughn is 46 years old, so 46 + 38 = 84.
Subtract 38 from 46.
46 - 38 = 8.
This concludes that Sydney is 38 years old.
Brainliest would mean a lot to me! Thanks!
What is the midpoint of line segment MN with endpoints M(2.7, –1.2) and N(4.1, 7.2)?
(–0.7, –4.2)
(0.75, 5.65)
(3.4, 3)
(3.9, 3.1)
Answer:
(3.4,3)
Step-by-step explanation:
(2.7+4.1÷2, -1.2+7.2÷2)
=(6.8÷2, 6÷2)
=(3.4,3)
2(x-5)+7=x+8
What’s x equal?
Answer: x = 11
Step-by-step explanation:
We can solve for x by isolating the variable with inverse operations.
Given:
2(x - 5) + 7 = x + 8
Distirbute:
2x - 10 + 7 = x + 8
Combine like terms:
2x - 3 = x + 8
Add 3 and subtract x from both sides of the equation:
x = 11
Solve the equation. Write your answer as a decimal.
−4.8f+6.4=−8.48
I need help with this practice problem solving The subject, I believe, is complex numbers and vectors
Given:
Given that
[tex]r=\frac{5}{3\sin\theta-\cos\theta}[/tex]Required: Convert to rectangular form.
Explanation:
The given equation in polar can be written as
[tex]\begin{gathered} r(3\sin\theta-\cos\theta)=5 \\ 3r\sin\theta-r\cos\theta=5 \end{gathered}[/tex]Substitute
[tex]x=r\cos\theta,y=r\sin\theta[/tex]Then the equation becomes 3y - x = 5.
Solve for y.
[tex]\begin{gathered} 3y=x+5 \\ y=\frac{1}{3}x+\frac{5}{3} \end{gathered}[/tex]Final Answer:
[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]Lincoln high wants to estimate the number of students who drive to school. Answer the following
GIVEN:
We are told that a school wants to estimate the number of students who drive to school.
Required:
To determine which survey would best represent the entire student population..
Step-by-sep solution;
Taking a sample of 11th graders would not correctly represent the entire student population. The result from this survey would at best represent the preference of 11th grade students and not other grades. The same thing applies to a survey of the science club. The science club cannot accurately represent all students (including other clubs).
However, a survey of 25 students from the school would best represent the entire student population since there is a probability of every category of student being represented.
Therefore,
25 students are randomly selected from the school; 4 drive to school.
Part (B):
There are 1750 students at Lincoln High. Use the answer above to estimate the number of students who drive to school.
If the sample of 25 students has 4 students who drive to school, then to estimate the entire population based on this;
[tex]\begin{gathered} Sample\text{ }proportion=\frac{4}{25} \\ \\ Population\text{ }proportion=\frac{4}{25}\times1750 \\ \\ Population\text{ }proportion=280 \end{gathered}[/tex]Therefore, we now have;
ANSWER:
[tex]\begin{gathered} (a)\text{ 25 students are randomly selected from the school; 4 drive to school.} \\ \\ (b)\text{ }280\text{ }students \end{gathered}[/tex]
Write the correct equation for the following statement.
You decide to rent a limo for prom. The rate is $175 plus $5 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
If you travel 45 miles what will be your total bill at the end
of the evening?
The most appropriate choice for equation and linear equation will be given by-
c = 175 + 5m is the equation for calculation of total cost (c) at the end of
the evening for a given number of miles (m).
For travelling 45 miles, total cost at the end of the evening is $400
What is equation and linear equation?
A statement that shows the equality between two mathematical expressions by connecting the two mathematical expression with an equal to (=) sign is called equation.
A one degree equation is known as linear equation.
Here,
Let the number of miles be m
Fixed cost for renting a limo for prom = $175
For travelling one mile by limo, amount charged = $5
For travelling m miles by limo, amount charged = $5m
Total cost for renting a limo for pron = $(175 + 5m)
By the problem,
c = 175 + 5m
This is the equation for calculation of total cost (c) at the end of
the evening for a given number of miles (m).
Now,
Putting m = 45 in the above equation,
[tex]c = 175 + 5 \times 45\\c = 175 + 225[/tex]
[tex]c =[/tex] $[tex]400[/tex]
For travelling 45 miles, total cost at the end of the evening is $400
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Greg the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 5 clients who did Plan A and 3 who did Plan B. On Thursday there were 2 clients who did Plan A and 12 who did Plan B. Greg trained his Wednesday clients for a total of 9 hours and his Thursday clients for a total of 9 hours. How long does each of the workout plans last?
The workout plan A lasts 1 hour and 30 mins and the workout plans B last around 30 mins only, solved through elimination method.
What is elimination method?The equations are either added or subtracted to create an equation in one variable when using the elimination method. When two variables' coefficients are in opposition to one another, you add the equations to eliminate that variable, and when they are equal, you subtract the equations to do the same.
Let the time taken for plan A be x
and the time taken for plan B be y
Then the equation forms
Wednesday = 5x + 3y = 9 hours
Thursday = 2x + 12y = 9 hours
Lets solve this with elimination method
5(2x + 12y = 9 hours)
-2(5x + 3y = 9 hours)
⇒ 10x + 60y = 45 hours
-(10x + 6y = 18 hours)
0 + 54y = 27 hours
⇒ y = 27/54 hours
y = 1/2 hours
y = 30 mins
Substituting the value of y in 2x + 12y = 9 hours,
2x + 12(0.5)= 9 hours
2x + 6 = 9 hours
2x = 3 hours
x = 3/2 hours
x = 1 hour 30 mins
Thus, the workout plan A lasts 1 hour and 30 mins and the workout plans B last around 30 mins only.
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equation [tex] - 3 - 4x \leqslant 21.[/tex]solve..........
In the las t image you can see that when you multiply both sides of the inequality for ( - 1 ) the symbol less than or equal changes to greater than or equal
if x - 7/10=y and y=2 what is the value of x
Answer:
x=27/10
Step-by-step explanation:
move all the terms not containing x to the right side of the equation
Help me please ghhyffhbhvhbhbhbh
Answer:
H or 1 7/12
Step-by-step explanation:
because 1/3,3/4,1/2 can all multiply to get 12 as the denominator or 3x4=12
2x6=12 4x3=12 so _/12 then on 1/3 you multiplied 3x4 so you multiply 1x4 to get 4 so 4/12 then 3/4 x3=9/12 last 1/2 x 6=6/12
4/12+9/12+6/12=1 7/12
[tex] \frac{1}{3} + \frac{3}{4} + \frac{1}{2} [/tex]
Question above
[tex] \frac{4 + 9 + 6}{12} [/tex]
Transform the expression
[tex] \frac{19}{12} [/tex]
Answer
[tex]1 \frac{7}{12} [/tex]
Alternative form
Thus, H is the answerHope it helps you...Mark as brainliest answer.
Which number can you add to 14 to get a sum of 0?
Inverse operation
14 + (-14) =0
Answer:
The number is -14.
Step-by-step explanation:
Up to now, you've been working with whole numbers. These are the positive numbers, those numbers you usually count with your fingers (1, 2, 3, ...), and 0. You've been working with these numbers ever since elementary school, where you would do computation with them, like adding, subtracting, and multiplying them. And, on a number line, they go from left to right, starting at 0.
But what happens when you go to the left on the number line? That is, what's before 0? We actually find negative numbers. The normal numbers that we usually work with, that being the positive numbers, now look like this:
(-1, -2, -3, ...)
A good thing to come from this is that now, we can define an additive inverse. An additive inverse is the negative, or opposite, of a whole number. The sum of a number and its additive inverse is 0.
So, for example, the additive inverse of 1 is -1, and 1 + (-1) = 0.
So clearly, we can see that the additive inverse of 14 is -14, since
14 + (-14) = 0.
(In case you wanted to know, the additive inverse of 0 is 0 because 0 is neither negative nor positive. So, 0 + 0 = 0.)
what is the lowest common denominator of 3/4, 1/8, 7/16, and 3/32
Answer: im pretty sure its 4 from 3/4
Step-by-step explanation:
∠A=6x−18 ∘ start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 18, degrees, end color #11accd \qquad \green{\angle B} = \green{14x +38^\circ}∠B=14x+38 ∘ start color #28ae7b, angle, B, end color #28ae7b, equals, start color #28ae7b, 14, x, plus, 38, degrees, end color #28ae7b Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd:
Using the properties of alternate angles, the value of x = 8 and ∠ A = 30
What are Alternate Angles?A transversal that crosses two parallel lines produces alternate exterior angles. They form two pairs (four total angles) of alternate outside angles since they are situated "outside" the two parallel lines but on different sides of the transversal.
For the given question,
∠A=6x−18
∠B=14x+38
As, both parallel lines are intersected by a transversal,
the value of angle ∠A and ∠180 - B is same as they are alternate angles,
⇒ 6x−18 = 180 - 14x - 38
⇒ 6x + 14x = 142 + 18
⇒ 20x = 160
⇒ x = 8
∠A = 6x−18
⇒ ∠ A = 30
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Correct question -
Han made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa.
How many tablespoons of cocoa per cup of milk is that?
tbsps
How many cups of milk per tablespoon of cocoa is that?
cups
In one cup of milk there is 1.5 tablespoons of cocoa and one tablespoon of cocoa is mixed in 0.67 cups of milk.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the value of single unit according to the needs.
Given is Han who made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa.
There are 6 tablespoons of cocoa in 4 cups of milk.
Then, in one cup of milk there will be (6/4) tablespoons of cocoa or 1.5 tablespoons of cocoa.
Similarly, 6 tablespoons of cocoa are mixed in 4 cups of milk.
1 tablespoon of cocoa will be mixed in (4/6) cups of milk or 0.67 cups of milk.
So, in one cup of milk there is 1.5 tablespoons of cocoa and one tablespoon of cocoa is mixed in 0.67 cups of milk.
Therefore, in one cup of milk there is 1.5 tablespoons of cocoa and one tablespoon of cocoa is mixed in 0.67 cups of milk.
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What in the equation of part (d) makes its graph different?(PART D IS THE LOOP ONE)a.) y = 2x + 7, b.) y = 3/5x + 1, c.) 3x + 2y = 6, and of course d (the last one), y = x (to the power of 2)
Given:
The equations are:
a.) y = 2x + 7, b.) y = 3/5x + 1, c.) 3x + 2y = 6, d.) y = x^2
To determine what in the equation of part (d) makes its different, we first note that the graph for part (d) is a parabola, which is a curve with an upward opening. In addition, we also note that the power of x in the equation of part (d) is 2, while the other three graphs have a power of 1.
Therefore, the answer is:
The power of x in the equation of part (d) makes its graph different.
gure 727 particles) are being deflected by yold market ere plete the following: Find the intercepts and domain and perform the symmetry test on each of the following hyperbolas, (c) 25x2 - 4y2 = 100 e) --- + y2 = 1 g) - 9x2 + raph the vertices, foci, endpoints of the conjugate axis, fundamental rectangle, and asymptotes, en draw the hyperbola for each equation in problem 1. is a chord of the partial hyperbola with equation f(x)=b Jax? - G? les for a, b, A (x, y) and B (x, y) from: 16y2 = 144 (a) 9x2 (b) 9x² - y2 = 9 (d) 25x2 - 36y2 = 900 -25x² + 4y2 = 100 (h) x2 + 4y = 16 Find the lenoth ne Dino
Find the intercepts and domain and perform the symmetry test on each of the following hyperbola
9x² - 16y² = 144
Domain (-inf, -4] and [4, inf)
Symetry around y-axis
There is no y intercepts
X-intercepts at x = -4 and x = 4
Focus at (-4, 0) and (4, 0)
Write a quadratic function in standard form containing the point (5,-6) and
x-intercepts -1 and 4.
Answer:
28th 5577e535r5ytt
Step-by-step explanation:
so h just Aliquippa well all am to PIZ well keep.