The solution of the system of equations are x = -2 and y = 15, the factor is 2 and 4 for the 1st and 2nd equation respectively.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a system of equations:
1st Equation: 4x + y = 7
2nd Equation: 2x + y = 11
Subtract equation 2nd from 1st
(4x + y) - (2x + y) = 7 - 11
2x = -4
x = -2
Now in equation 1st multiply by 2 and in equation 2nd multiply by 4
8x + 2y = 14
8x + 4y = 44
Subtract:
-2y = -30
y = 15
The factor is 2 and 4 for the 1st and 2nd equation respectively.
Thus, the solution of the system of equations are x = -2 and y = 15, the factor is 2 and 4 for the 1st and 2nd equation respectively.
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Please help!!!!!!!!!!!!!!!!!1
Answer:
f(x)=(x+4)(x+2)
Step-by-step explanation:
Factor x^2−6x+8 using the AC method.
Can someone help me?
Answer:
A. 7 and 3D. 1 and 5Three friends go to a store to rent games and movies. Calvin rents 3 movies and 2 video games and spends a total of $25. Samantha rents 2 movies and 1 video game and spends a total of $14.75.
If the rental fee for each game is the same and the rental fee for each movie is the same, determine how much their friend, Keith, will spend at the rental store to rent 1 movie and 2 video games. Explain your answer.
The Keith will spend $16 to rent 1 movie and 2 video games from the store.
How to solve the equation of two variable?Let's assume the rental fee for each movie is "m" and the rental fee for each game is "g".
From the given information, we can form the following system of equations:
3m + 2g = 25 (Calvin's rental)
2m + g = 14.75 (Samantha's rental)
We can solve for "m" and "g" by using elimination or substitution method. Here, we will use substitution method.
From the second equation, we can solve for "g" in terms of "m":
g = 14.75 - 2m
Substituting this into the first equation, we get:
3m + 2(14.75 - 2m) = 25
Simplifying this, we get:
3m + 29.5 - 4m = 25
-m + 29.5 = 25
-m = -4.5
m = 4.5
Now that we know the rental fee for each movie is $4.50, we can find the rental fee for each game by substituting "m" into either of the original equations:
2(4.5) + g = 14.75
g = 14.75 - 9 = 5.75
So the rental fee for each game is $5.75.
To find how much Keith will spend to rent 1 movie and 2 video games, we can simply add up the rental fees:
1(4.5) + 2(5.75) = 16
Therefore, Keith will spend $16 to rent 1 movie and 2 video games from the store.
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Claire and jane did an examination together. jane scored 9 more marks than claire and her marks were 60% of the sum of their scores. what are the scores of each student?
The score of Jane is 27 and the score of Claire is 18.
A linear equation is an equation where highest degree of variables is 1.
Let the score of Jane's mark is x
Given, that score Jane is 9 more than the score of Claire.
So, the score of Claire= x-9
Given, the score of Jane is 60% of the sum of their scores.
the sum of their scores is = x+x-9= 2x-9
from the above it is clear that
the linear equation will be
x=60%(2x-9)
⇒x=0.6(2x-9)
⇒x= 1.2x -5.4
⇒1.2x-x= 5.4
⇒0.2x= 5.4
⇒x= 5.4/0.2
⇒x= 27
So the score of Jane is 27.
As score Jane is 9 more than the score of Claire.
the score of Claire is = x-9= 27-9=18
Therefore the score of Jane is 27 and the score of Claire is 18.
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FIND THE EQUATION FOR THE LINE SHOWN
Answer:
y = 2x - 1
Step-by-step explanation:
gradient is defined as rise over run.
we need coordinates that are both whole numbers. from looking at the graph, I have (0, -1) and (1, 1)
for the run, 1 - 0 = 1
for the rise, 1 - -1 = 2
2 / 1 = 2
it crosses the y-axis at -1
therefore in the form y = mx + b, the equation is y = 2x - 1
Given the following formula, solve for a.
Answer:
A. a = 2s - b -c
Step-by-step explanation:
Rearrange the equation in a way that you have only a on one side. When solving equations you can add, subtract, multiply or divide by the same number/variable/expression on the both sides.
[tex]s = \frac{a + b + c}{2}[/tex]
Multiply by 2 to get rid of the fraction.
[tex]s \cdot 2 = \frac{a + b + c}{2} \cdot 2[/tex]
On the right side the 2 cancels out:
[tex]s \cdot 2 = a + b + c[/tex]
On the right side next to a are still b and c. But we want a alone. Subtract b.
[tex]s \cdot 2 - b = a + b + c - b[/tex]
b - b on right side gives 0.
[tex]s \cdot 2 - b = a + c + 0[/tex]
The step above is usually skipped, because number + 0 = number.
[tex]s \cdot 2 - b = a + c[/tex]
Next to a there is still c. Subtract c.
[tex]s \cdot 2 - b - c = a + c - c[/tex]
c - c on the left is 0.
[tex]s \cdot 2 - b - c = a[/tex]
So our answer is:
[tex]s \cdot 2 - b - c = a[/tex]
It can be rewritten to (change sides):
[tex]a = s \cdot 2 - b - c[/tex]
And s · 2 can be rewritten to 2s:
[tex]a = 2s - b - c[/tex]
What is the period of the function y=tan (4/pi (x-pi/3))
O 3 units
O4 units
O 6 units
O 8 units
Answer:
Period = 4 units
Step-by-step explanation:
Standard form of a tangent function:
[tex]f(x)=\sf A \tan(B(x+C))+D[/tex]
A = vertical stretchπ / |B| = period (distance between any two consecutive vertical asymptotes)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftThe tangent function has a vertical asymptote whenever cos(x) = 0
The tangent function does not have an amplitude because it has no maximum or minimum value.
Given function:
[tex]y=\tan \left(\dfrac{\pi}{4}\left(x-\dfrac{\pi}{3}\right)\right)[/tex]
Therefore:
Vertical stretch (A) = none[tex]\textsf{Period}=\dfrac{\pi}{\left|\dfrac{\pi}{4}\right|}=4[/tex]Phase shift (C) = π/3 to the rightVertical shift = noneAnswer: 4 units
Step-by-step explanation:
please be quick im being timed
Answer:
this one
Step-by-step explanation:
Oil tank contains 220.2 gallons of oil. Whenever that amount of oil drops below 90 gallons an alarm sound if 145.3 gallons are pumped into a delivery truck how many gallons must be pumped in back into the tank in order to shut off the alarm
Answer:
15.1 gallons are needed to shut off the alarm.
Which is the graph of the system of inequalities y 2x-and y ≤ 2x + 6
4x
2
ANVA
-6-4-22 26
-6-4-
-6-4
2
246
O
246
2
O
x
246
Answer: Option 1
Step-by-step explanation:
The second and third options do not contain the line y = 2x+6, so they can be eliminated.
Between the first and fourth options, only the first option shows the line y=2x+6 being shaded below, so it is the answer.
The graph of the inequality is graph A
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y ≥ ( 1/5 ) ( 4x - 1 ) be equation (1)
y ≤ 2x + 6 be equation (2)
Now , To graph the system of inequalities, we can start by graphing the boundary lines for each inequality and then determine which region of the coordinate plane satisfies both inequalities.
For the first inequality, y >= (1/5)(4x-1), we can start by graphing the line y = (1/5)(4x-1), which has a y-intercept of -1/5 and a slope of 4/5. We can draw this line as a solid line, since the inequality includes the "or equal to" condition:
And , for the second inequality, y <= 2x+6, we can graph the line y = 2x+6, which has a y-intercept of 6 and a slope of 2. We can also draw this line as a solid line, since the inequality includes the "or equal to" condition:
Hence , the inequality is solved and the solution to the system of inequalities is the shaded region above the line y = (1/5)(4x-1) and below the line y = 2x+6, including the boundary lines.
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if the exterior angles of a pentagon are x° 2x° (x+30)°,(x-10)° and (x+40)° find x
a) 30
b) 50
c) 60
d) 80
Answer:
[tex]\fbox {b) 50}[/tex]
Step-by-step explanation:
The sum of the exterior angles of any polygon (including a pentagon) is equal to 360 degrees.
Then :
⇒ x + 2x + x + 30 + x - 10 + x + 40 = 360
⇒ 6x + 60 = 360
⇒ 6x = 300
⇒ x = 50
Answer:
[tex]\huge\boxed{\sf x = 50}[/tex]
Step-by-step explanation:
Statement:The exterior angles of a pentagon add up 360 degrees.Given angles:x°2x°(x+30)°(x-10)°(x+40)°Solution:x + 2x + x + 30 + x - 10 + x + 40 = 360
6x + 60 = 360
Subtract 60 to both sides
6x = 360 - 60
6x = 300
Divide 6 to both sides
x = 300/6
x = 50
[tex]\rule[225]{225}{2}[/tex]
What is the measure of
the number of cows in the field minus 12...
Answer:
maybe minus 12 there was no number of cows
Answer:
x - 12
Step-by-step explanation:
x represents the number of cows since we do not know the number
then "minus 12"
bada bing bada boom
after this i will only have 4 questions please and ty!
Answer:D
Step-by-step explanation:
this expression gives the original price reduce by 15%. The second term adds the tax to the price after the sale has been applied
y=5+3x for x
Show work
Answer:
[tex]x = \frac{y - 5}{3}[/tex]
Step-by-step explanation:
Hello!
To solve for x, we have to first isolate the variable.
Solve for x[tex]y = 5 + 3x[/tex][tex]y - 5 = 3x[/tex][tex]y - 5 = 3(x)[/tex][tex]\frac{y - 5}{3} = x[/tex]The value of x is [tex]\frac{y - 5}{3}[/tex].
Work out m and c for the line:
y = 2 − 3 x
Answer:
m = -3
c = 2
Step-by-step explanation:
This equation is given in slope-intercept form. The general structure of these equations is:
y = mx + c
In this form, "m" represents the slope and "c" represents the y-intercept. As you have been given the entire equation, the only thing you have to do is rearrange the equation to find which values correspond with the variables.
y = 2 - 3x -----> y = -3x + 2
Therefore,
m = -3
c = 2
A person paid by the hour works 22 hours a week and makes $359. How much would they make if they work
37 hours?
Round your answer to 2 decimal places.
Answer:
$ 603.77
Step-by-step explanation:
Find unit rate of dollars per hour : 359/22
now multiply by hours : 359/22 * 37 = 603.77
Answer:
$603.77
Step-by-step explanation:
if they work 22 hours a week
and once a week they make $359
therefore divide to get the hourly rate
359/22 = 16.3181818182
they make 16.3181818182 per hour
then we have to multiply the hourly by the hours worked
16.3181818182 * 37 = 603.772727273
since this is in dollars ($) we round to the second decimal place (hundredths)
meaning we cut off the numbers after it
603.77║2727273
then, determine if the thousandths place is equal to or greater than five or less than five
since it is a 2 then the 7 stays the same
if it were a 5 or greater we would round up, making the 7 in the hundredth place turn into an 8.
therefore your answer is $603.77
hope this helps:)
How many solutions are there to the system of equations graphed below if
the lines are parallel?
O A. Zero
O B. Two
C. Infinitely many
O D. One
(c) The result of a number, when increased by 40%, is 2.1. Find the number. ( c ) The result of a number , when increased by 40 % , is 2.1 . Find the number .
Answer:
1.5 is the number.
Explanation:
Let the number be 'n', this is 100% - original number.
When increased by 40%, 100% + 40% = 140%.
140% × n = 2.1
1.4n = 2.1
n = 2.1/1.4
n = 1.5
Hence, the original number is 1.5.
What is the value of f^-1 (-3)
According to the plot of [tex]f(x)[/tex], whose curve passes through the point (-5, -3), we have
[tex]f(-5) = -3 \implies f^{-1}(-3) = \boxed{-5}[/tex]
What is the measure (in radians) of central angle & in the circle below?
O
O
O
옥
26
ㅇ 역
12 cmy
0
14 cm
Answer:
7pi/6
Step-by-step explanation:
Using the formula for arc length in radians, we get:
14pi = 12(theta)theta = 7pi/6 [divide both sides by 12]Keri did jumping jacks for ⅗ of a minute and sit-ups for ½ a minute. How many more seconds did Keri do jumping jacks than sit-ups?
PLS HELP AND HURRY
Answer:
so we need to subtract the situps from the jumping jack so
3/5-1/2
first we need to simplify to the same bottom number
6/10=3/5
5/10=1/2
6/10-5/10=1/10
so 1/10 of 60 is
1/10*60=6
Hope This Helps!!!
pls help!! determine the period! thx
Answer:
T=5
Step-by-step explanation:
is 9x=63,x=7 true or false
Answer:
True
9 * 7 = 63
Therefore when x=7 9x=63
The equation given is true since 7 is the solution.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign.
The two sides of an equation is usually called as left hand side and right hand side.
The given equation is 9x = 63.
There is only one variable here, x.
We have to solve this equation and find whether the solution is 7 or not.
Solution of the equation is the value of x.
9x = 63
Divide both sides of the equation by 9, then, we get,
9x / 9 = 63 / 9
9 gets cancelled in the left hand side and 63/9 = 7.
So we get,
x = 7
So the given statement is true that for 9x = 63, the solution is x = 7.
Hence the given equation is true.
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Given:
p: Angles XYZ and RST are vertical angles.
q: Angles XYZ and RST are congruent.
Which statement is logically equivalent to p → q?
A. If angles XYZ and RST are congruent, then they are vertical angles.
B. If angles XYZ and RST are not vertical angles, then they are not congruent.
C. If angles XYZ and RST are not congruent, then they are not vertical angles.
D. If angles XYZ and RST are vertical angles, then they are not congruent.
Answer:
C
Step-by-step explanation:
The contrapositive is always logically equivalent to the original statement.
Answer:
C
Step-by-step explanation:
Can yall help me Find m/1.
Answer:
mAngle1 = 33°
Step-by-step explanation:
The three angles in a triangle add up to 180°.
31° + 116° + x = 180°
147° + x = 180°
Subtract 147° from both sides.
x = 33°
The measure of Angle1 is 33°
Please answer this thanks
Answer: down below
Step-by-step explanation:
1. How many hay bales did the farmer sell?
To do that, you need to divide the weight of a hay bale by the total weight of the hay bales that the farmer sold.
That will be 24,300 / 75 = 324 bales
2. Divide the new number (26,700) by the same number 75.
26,700 / 75 = 356 hay bales
Subtract the bales from last year to the bales from this year:
356 bales - 324 bales = 32 bales
Mr wong predicted that he would sell 45 automobiles , he actually sold 48
Answer:
well done mr wong lol
Step-by-step explanation:
what's the question is it the percent he beat his prediction?
if it is then its 48 divided by 45 times 100
this equals 106.67%
then take this away from his prediction percent originally which is 100%
106.67-100= 6.67%
Find the reflection of point (50, 25) across the x-axis.
The reflection of any point across the x-axis:
⇒ means that x-coordinate remains the same
⇒ but the y-coordinate is multiplied by '-1'
In this case:
⇒ (50,25) becomes (50,-25)
Answer: (50,-25)
Hope that helps!
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Answer:
(50, -25)
Step-by-step explanation:
When we reflect a point across the x-axis, only the sign of the y-value the changes. In this case, the y-value is 25, so after the reflection it becomes -25. The x-value stays the same. So your resulting point is (50, -25)
Which method is better to solve the following equation?
²-25=0
Your answer:
O Quadratic Formula
O Square Rooting
Clear answer
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