Answers
Answer: The solution for the system is (2, -7)
Step-by-step explanation:
Ok, here we have linear relationships.
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case, we have two lines:
ya, that passes through:
(-8, -5) and (-3, -6)
Then the slope is:
a = (-6 - (-5))/(-3 - (-8)) = (-6 + 5)/(-3 + 8) = -1/5
now, knowing one of the points like (-3, - 6) we can find the value of b.
y(x) = (-1/5)*x + b
y(-3) = -6 = (-1/5)*-3 + b
-6 = 3/5 + b
b = -6 - 3/5 = -33/5
then the first line is:
ya = (-1/5)*x -33/5
For the second line, we know that it passes through the points:
(-8, -15) and (-3, -11)
Then the slope is:
a = (-11 - (-15))/(-3 -(-8)) = (-11 + 15)/(-3 + 8) = 4/5
The our line is:
y(x) = (4/5)*x + b
and for b, we do the same as above, using one of the points, for example (-3, -11)
y(-3) = -11 = (4/5)*-3 + b
b = -11 + 12/5 = -(55 + 12)/5 = -43/5
then:
yb = (4/5)*x - 43/5.
Ok, our system of equations is:
ya = (-1/5)*x -33/5
yb = (4/5)*x - 43/5.
To solve this, we suppose ya = yb
then:
(-1/5)*x + -33/5 = (4/5)*x - 43/5.
-33/5 + 43/5 = (4/5)*x + (1/5)*x
10/5 = 2 = (4/5 + 1/5)*x = x
2 = x
now we evaluate x = 2 in one of the lines:
ya = (-1/5)*2 -33/5 = -2/5 - 33/5 = -35/5 = -7
Then the lines intersect at the point (2, - 7), which is the solution for the system.
Related Questions
Solve x*2+5x+6=5x+10
Answers
Answer:
x = -2, 2.
Step-by-step explanation:
x*2 + 5x + 6 = 5x + 10
x^2 + 5x - 5x + 6 - 10 = 0
x^2 - 4 = 0
x^2 = 4
x = -2, 2 ( 2 solutions).
Ms. Canton went to the store to buy grapes. She bought four bunches of purple grapes. Each bunch had the same amount of grapes (x) She also bought two bunches of green grapes.Each bunch of green grapes had the same amount of grapes in them (y). Write an expression that will show how many bunches of grapes Ms. Canton purchased. *
Answers
4x+2y
Explanation:
x represents the purple grapes in one bunch, while y represents the green grapes in one bunch.
Given: 4 bunches of purple grapes (x), 2 bunches of green grapes (y)
Combine to get the expression 4x +2y
Hope this helps
A graph is shown. The x-axis is labeled from 0 to 9 and the y-axis is labeled from 0 to 10. The four points shown on the graph are ordered pairs 0, 0 and 1, 2 and 2, 4 and 3, 6. These points are joined by a line. The label on the x-axis is Bags of candy. The title on the y-axis is Total cost in dollars. What is the constant of proportionality?
Answers
Answer:
Heres the graph:
Step-by-step explanation:
Constant is $2 dollars per bag od candy or just 2.
Answer:
2
Step-by-step explanation:
from (0,0) ⇒ (1,2) ⇒ (2,4) ⇒ (3,6)
∴ 2
Circles
1. RS and ST are tangent lines. Find the value of x.
R
9x - 30
c.
S
3x
T
Answers
Answer:
x = 15
Step-by-step explanation:
9x-30 = 3x (tangent lines are congruent)
- move the variables to one side
9x-3x=30
6x=30
x=5
--------------
9(5)-30=3(15)
45-30=15
15=15
Done!
x = 15
Figure ABCD has verticies A(-3, 2) B(2, 2) C(2, -4) D(-3, -2). What was the area of Figure ABCD.
Answers
Match each number with its place in order from smallest (1st) to largest (6th). 1. 6th -56 2. 4th 90 3. 3rd -84 4. 1st 59 5. 2nd -80 6. 5th 48
Answers
Answer:
Numbers provided:
-56, 90, -84, 59, -80, 48
The smallest number is -84.
The highest number is 90.
1st: -84
2nd: -80
3rd: -56
4th: 48
5th: 59
6th: 90
Fill in the blank with a constant, so that the resulting quadratic expression is the square of a binomial. $\[x^2 + 22x + \underline{~~~~}.\]$
Answers
Answer:
[tex]$\[x^2 + 22x + 121\]$[/tex]
Step-by-step explanation:
Given
[tex]$\[x^2 + 22x + \underline{~~~~}.\]$[/tex]
Required
Fill in the gap
Represent the blank with k
[tex]$\[x^2 + 22x + k\]$[/tex]
Solving for k...
To do this, we start by getting the coefficient of x
Coefficient of x = 22
Divide the coefficient by 2
[tex]Result = 22/2[/tex]
[tex]Result = 11[/tex]
Take the square of this result, to give k
[tex]k= 11^2[/tex]
[tex]k= 121[/tex]
Substitute 121 for k
[tex]$\[x^2 + 22x + 121\]$[/tex]
The expression can be factorized as follows;
[tex]x^2 + 11x + 11x + 121[/tex]
[tex]x(x + 11)+11(x+11)[/tex]
[tex](x+11)(x+11)[/tex]
[tex](x+11)^2[/tex]
Hence, the quadratic expression is [tex]$\[x^2 + 22x + 121\]$[/tex]
what number would you subtract from each side of inquality to solve y+3/8>16
Answers
Explanation:
y + 3/8 > 16
y > 16 - 3/8 (subtract 3/8 from both side)
y > 128/8 - 3/8
y > 125/8
Answer:
[tex]y > 125[/tex]
Step-by-step explanation:
[tex]y + \frac{3}{8} > 16 \\ y > 16 - \frac{3}{8} [/tex]
[tex]y > (16 \times 8) - ( \frac{3}{8} \times 8) [/tex]
[tex]y > 128 - 3[/tex]
[tex]y > 125[/tex]
What is the value of x that makes L1 || L2? please help!! A. 18 B. 12 C. 10 D. 6
Answers
Answer:
x = 18
Step-by-step explanation:
Because the 2 lines are parallel we can use same side interior theorem to find x
This would mean the equation is 6x + 30 + 2x + 6 = 180
When you solve that this would be 18
Answer:
x = 18
Step-by-step explanation:
→ Utilise the fact that interior angles add up to 180
6x + 30 + 2x + 6 = 180
→ Simplify
8x + 36 = 180
→ Minus 36 from both sides to isolate 8x
8x = 144
→ Divide both sides by 8 to isolate x
x = 18
Estimate the difference to the nearest tenth.
0.612 – 0.185
Answers
Answer:
I can’t understand that
Step-by-step explanation:
Find the measure of the remote exterior angle. m∠x=(4n−18)°m∠y=(n+9)°m∠z=(151−5n)° A. 71 B. 16 C. 100 D. 46
Answers
Answer: A.71
Step-by-step explanation: 1.set up the equation
2. 4n-18+n+9=151-5n
3.combine like terms -> 5n-9=151-5n
4.solve for n
5.10n=160
n=16
now you have to plug 16 in for n in order to get the remote exterior angle.
151-5(16)
151-80
71°
The sum of any two interior angle is equal to the third exterior angle. The value of n will be 16°. Then the correct option is B.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The triangle having the interior angle x and y, and z is the exterior angle of triangle.
m∠x = (4n − 18)°, m∠y = (n + 9)°, and m∠z = (151 − 5n)°
Then the value of n will be
We know that the sum of any two interior angle is equal to the third exterior angle. Then we have
∠x + ∠y = ∠z
4n - 18 + n + 9 = 151 - 5n
10n = 160
n = 16°
Then the correct option is B.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ2
Question 8(Multiple Choice Worth 1 points)
(06.05 MC)
A paper cup is dropped and its landing position is recorded. The cup can land on the side, on the open end, or on the closed end. The results of 20 trials are shown in the table below:
Paper Cup Experiment
# of times occurred
Open
HT III
Closed
Side
HT III
Based on the table, which of the following best compares the experimental probability of the cup landing on its open end with the experimental probability of the cup landing on its closed end?
The probabilities are equal.
The probability of landing on the open end is greater.
The probability of landing on the closed end is greater.
O No conclusion can be made.
Answers
Table Given in the question :
Open = HT 111 = 8
Side = 1111 = 4
Side = HT 111 = 8
Answer:
The probability of landing on the open end is greater.
Step-by-step explanation:
Given the experimental probability distribution :
Open = HT 111 = 8
Side = 1111 = 4
Side = HT 111 = 8
The experimental probability is the ratio of the number of times an event occurs and the total number of trials.
P(A) = number of times A occurs / total number of trials
Where A is defined event.
COMPARING the probabilities of open and closed events
P(open) = 8 / 20 = 2 / 5
P(closed) = 4 / 20 = 1/5
2/5 > 1/5
P(open) > P(closed)
Find RS. A. 5 B. 10 C. 9 D. 12
Answers
Answer:
x=9
Step-by-step explanation:
PQ + QR + RS = PS
2x-6 + 1 + x-4 = 18
Combine like terms
3x -9 = 18
Add 9 to each side
3x-9+9= 18-9
3x = 27
Divide by 3
3x/3 = 27/3
x = 9
Answer:
RS=5
Step-by-step explanation:
solve for x:
2x-6+1+x-4 = 18
combine like terms
3x-9=18
subtract both sides to make x isolated
3x=27
divide by 3 to get x
x=9
RS=x-4
RS=9-4
RS=5
find the value of a answers: a:15 b:14 c:19 d:16
Answers
Answer:
6a+10= 3a+55
6a-3a= 55-10
3a= 45
a= 45/3
a= 15
The answer is (A) 15
Hope this helps^°^
Answer:
A. 15
Step-by-step explanation:
The angles are vertical angles, therefore they are congruent. We can set the two measures equal to each other.
[tex]6a+10=3a+55[/tex]
Now, solve for a. We must get a by itself on one side of the equation.
First, subtract 3a from both sides of the equation.
[tex]6a-3a+10=3a-3a+55[/tex]
[tex](6a-3a)+10=55[/tex]
[tex]3a+10=55[/tex]
Next, subtraction 10 to both sides of the equation. We subtract because 10 is being added to 3a. The inverse of addition is subtraction.
[tex]3a+10-10=55-10[/tex]
[tex]3a=55-10[/tex]
[tex]3a=45[/tex]
3 and a are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 3
[tex]3a/3=45/3[/tex]
[tex]a=45/3[/tex]
[tex]a=15[/tex]
The value of a is 15 and choice A is correct.
if
[tex] \sqrt{5} x = \sqrt{3} x + \sqrt{7} [/tex]
find the value of x in the form
[tex] \sqrt{ \frac{a}{b} } [/tex]
Answers
Answer:
[tex]$x=\sqrt{\frac{7(4+\sqrt{15})}{2}} $[/tex]
Step-by-step explanation:
From the way it is written, the [tex]x[/tex] is outside the square root. I will rewrite it as:
[tex]x\sqrt{5} =x\sqrt{3} +\sqrt{7}[/tex]
[tex]x\sqrt{5}-x\sqrt{3}=\sqrt{7}[/tex]
[tex]x(\sqrt{5} - \sqrt{3} )=\sqrt{7}[/tex]
[tex]$x= \frac{\sqrt{7} }{\sqrt{5} - \sqrt{3}} \implies \frac{\sqrt{7}(\sqrt{5} + \sqrt{3}) }{2} $[/tex]
[tex]$x=\frac{1}{2} \sqrt{7} (\sqrt{5} + \sqrt{3} )$[/tex]
[tex]$x=\frac{\sqrt{35}}{2} +\frac{ \sqrt{21}}{2} $[/tex]
[tex]$x=\frac{\sqrt{35}+\sqrt{21}}{2} $[/tex]
Multiply denominator and numerator by 3
[tex]$x=\frac{3\sqrt{35}+3 \sqrt{21}}{6} $[/tex]
Factor [tex]\sqrt{3}[/tex]
[tex]\sqrt{3} (\sqrt{105}+3 \sqrt{7})[/tex]
[tex]$x=\frac{\sqrt{3} (\sqrt{105}+3 \sqrt{7})}{6} $[/tex]
Divide denominator and numerator by [tex]\sqrt{3}[/tex]
[tex]$x=\frac{\sqrt{105}+3 \sqrt{7}}{2\sqrt{3} } $[/tex]
Let's rewrite it again
[tex]$x=\frac{\sqrt{ (\sqrt{105}+3 \sqrt{7})^2}}{\sqrt{12} } $[/tex]
[tex]$x=\sqrt{ \frac{1}{12} \cdot (\sqrt{105}+3 \sqrt{7})^2}$[/tex]
It is already in the form [tex]$\sqrt{\frac{a}{b} } $[/tex]
Expanding the perfect square, we have
[tex]63+42\sqrt{15}+105[/tex]
[tex]$\frac{63}{12} +\frac{42\sqrt{15}}{12} +\frac{105}{12} $[/tex]
[tex]$\frac{21}{4} +\frac{7\sqrt{15}}{2} +\frac{35}{4} $[/tex]
Factor [tex]$\frac{7}{2} $[/tex]
[tex]$\frac{7}{2} (4+\sqrt{15} )$[/tex]
Therefore,
[tex]$x=\sqrt{\frac{7}{2} \left(4+\sqrt{15} \right)} $[/tex]
[tex]$x=\sqrt{\frac{7(4+\sqrt{15})}{2}} $[/tex]
if all the possible values of x are indicated by the shaded part of the number line above, which number line best shows all possible values of 1/x? (the shaded part in the number line is 0.5 to 1.5, the whole number line segment is from 0 to 3)
Answers
Answer:
can i see a picture of the number line?
Step-by-step explanation:
The graph of f(x) = xx is reflected across the x-axis and then across the y-axis to create the graph of function g(x).
Which statements about the functions f(x) and g(x) are true? Check all that apply.
The functions have the same range.
The functions have the same domains.
The only value that is in the domains of both functions is 0.
There are no values that are in the ranges of both functions.
The domain of g(x) is all values greater than or equal to 0.
The range of g(x) is all values less than or equal to 0.
Answers
Answer:C and F are correct
Step-by-step explanation:
got it right on edge
Please help me! I will give brainly!
Asapppppp
Answers
Answer:
20
Step-by-step explanation:
I believe it's 20 because you multiply 20 . with 60 and 80 and it will give 1200 and 1800.
Answer:
It should be 20
Step-by-step explanation:
The question is asking multiply the serving by __ to find amount of pretzels.
Be careful what is the question is asking.
30*20=600
60*20=1200
90*20=1800
and continue on...
Pls give brainliest
HELPP! QUICKKKK! Lol
Problem:
Last year I attended the Jurassic World Dinosaur Exhibit with my family and my friend and her family. My
family includes 2 adults (including myself) and my child we paid a total of $94. Her family includes 2
adults and 2 children she paid a total of $110. What was the admission price for an adult ticket and how
much was it for the admission price for a child ticket?
Let a represent adult ticket price
Let c represent child ticket price
Answers
Answer:
Child ticket = $16.
Step-by-step explanation:
Let adult tickets = a;
child ticket = c.
2a + c = 94 — eq no. 1,
2a + 2c = 110 — eq no. 2,
then,from eq 1,
c = 94 - 2a. —eq no. 3.
Substitute eq 3 into eq 2,
2a + 2(94 - 2a) = 110
2a - 4a = 110 - 188
-2a /-2 = -78 / -2
a = 39.
Substitute value of a into eq 3,
c = 94 - 2(39)
= 94 - 78
c = 16.
Thus, child ticket = $16.
Because, for the first family 39a+16c= $94 total for that family and just do the math for the other one :)
Two boxes are shown below
What is the difference in the surface areas, in square feet, of the two boxes?
Answers
Answer:
Option (B):3
Step-by-step explanation:
S.A of Box J =57ft^2 ; using formula 2(lb+lh+hb)
S.A of BoxF=54Ft^2;using formula (6a^2)
Differenceof S.A of boxes:57-54=3
Which system of equations has no solution?
Answers
Answer:
B.
[tex]{ \binom{7x - 2y = 9}{7x - 2y = 13} }[/tex]
A 20% discount on pants, and its price became 48 after the sale, what was its price before
Answers
Answer:
$60
Step-by-step explanation:
Represent the original price by p. Then:
1.00 p = original price
0.20 p = discount
0.80p = price after discount = $48
Solving for p, we divide both sides by 0.80:
$48
p = ---------- = $60
0.80
What is D+26/-17 = - 25
Answers
Answer:
-399/17
Step-by-step explanation:
D+26/-17=-25
D=-25-(-26/17)
D=-25+26/17
D=-425/17+26/17
D=-399/17
The answer is D= -399/17
Halfway through the second quarter, what fructional part of the game is left?
Answers
Answer:
5/8 of the game
Step-by-step explanation:
Half of a quarter is 1/2, and 1 quarter is already done, therefore 1/2, or to simplify it 1/8, plus 2/8, would be 3/8. Now, a quarter is 1/4th of something therefore there must be 4 quarters in a total.so that means that there are 8 halfves in total , so 8-3=5, so the fractional parts of the game left is 5/8.
The part of the game i.e. left should be [tex]5\div 8[/tex]
Calculation of the part of the game:Since the half of the quarter is one-half. And, the one quarter is done so one-half is remaining. That means
[tex]= 1\div 8 + 1\\\= 2\div 8[/tex]
Since one-fourth should be of something also there are total 4 quarters that means there are 8 halves.
So, remaining it should be
= 8 -3
= 5
Hence, The part of the game i.e. left should be [tex]5\div 8[/tex]
Learn more about game here: https://brainly.com/question/1415899
Mathematics, probability and chance Can somebody help me, I always thank and vote
Answers
If h(x) = x2-5x + 7
find: h(-5)
Answers
Answer:
h(-5)=22
Step-by-step explanation:
Replace x with -5.
[tex]h(-5) = (-5)2-5(-5) + 7[/tex]
Simplify.
[tex]h(-5)=-10+25+7[/tex]
Simplify.
[tex]h(-5)=22[/tex]
Tamara walked 3/4 mile in 1/2 hour. Which of the following represents the unit rate that Tamara walked? A. 1/2 mi/h B. 2/3 mi/h C. 3/4 mi/h D. 1 1/2 mi/h Include ALL work please!
Answers
Answer:
1 1/2 miles / hour
Step-by-step explanation:
We want distance / time
3/4 miles
---------------
1/2 hour
3/4 ÷ 1/2
Copy dot flip
3/4 * 2/1
3/2
1 1/2 miles / hour
Answer:
D
Step-by-step explanation:
Multiple (3/4) by 2 to find the information for one hour)
6/4 in one hour
3/2 or 1 + 1/2 mi/h
D is the answer
In which of the following cases would the quantity 'q' decrease proportionally when the quantity 'p' is increased?
a) P = 3 x q
b) p-3=q
c) p=3/q
d) 1/p=3/q
Please give me the correct answer along with the explanation and I shall mark you as the brainliest. Please answer ASAP, it's urgent
Answers
Answer:
c) p = 3/q
Step-by-step explanation:
If 3 is divided by a smaller number "q", then it would result in a larger number "p".
Example:
1. Substitute 3 for "q"
3/3 = 1
q = 3
p = 1
2. Substitute 1 for "q"
3/1 = 3
q = 1
p = 3
When "q" decreased, "p" increased.
Step-by-step explanation:
c) p=3/q
i can confirm after 10.30
I really need help with this
Answers
Answer:
8/5
Step-by-step explanation:
There are 8 jokers combined, and 5 decks, so the mean is 8/5.
Help pls! Will give brainliest to first person who answers correct
Answers
Answer:
a) x greater than or equal to 10
b) x = 9
Step-by-step explanation:
a)
[tex]x + 5 \geqslant 15 \\ x \geqslant 15 - 5 \\ x \geqslant 10[/tex]
b)
[tex]2x < 18 \\ x = \frac{18}{2} \\ x = 9[/tex]