The point of intersection of the lines given by the equations [tex]\( 11x - 6y = 2 \) and \( -8x + 5y = 3 \) is \( (4, 7) \).[/tex]
To find the points of intersection of the given lines, we need to solve the system of linear equations simultaneously.
The given equations are:
[tex]\[ 11x - 6y = 2 \quad \text{(Equation 1)} \][/tex]
[tex]\[ -8x + 5y = 3 \quad \text{(Equation 2)} \][/tex]
We can solve this system using the method of substitution or elimination. Let's use the elimination method to find the values of [tex]\( x \)[/tex]and [tex]\( y \).[/tex]
First, we will make the coefficients of [tex]\( y \)[/tex] the same in both equations by multiplying Equation 1 by 5 and Equation 2 by 6:
[tex]\[ 5(11x - 6y) = 5(2) \][/tex]
[tex]\[ 6(-8x + 5y) = 6(3) \][/tex]
This gives us:
[tex]\[ 55x - 30y = 10 \quad \text{(Equation 3)} \][/tex]
[tex]\[ -48x + 30y = 18 \quad \text{(Equation 4)} \][/tex]
Now, we add Equation 3 and Equation 4 to eliminate [tex]\( y \):[/tex]
[tex]\[ (55x - 30y) + (-48x + 30y) = 10 + 18 \][/tex]
[tex]\[ 7x = 28 \][/tex]
Dividing both sides by 7, we get:
[tex]\[ x = 4 \][/tex]
Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into either Equation 1 or Equation 2 to find the value of [tex]\( y \)[/tex]. Let's use Equation 1:
[tex]\[ 11(4) - 6y = 2 \][/tex]
[tex]\[ 44 - 6y = 2 \][/tex]
Subtracting 44 from both sides, we get:
[tex]\[ -6y = -42 \][/tex] Dividing both sides by -6, we get:
[tex]\[ y = 7 \][/tex].
1.lA right triangle ABC is shown. What is cos A?
Answer:
cos A = 8/17
Step-by-step explanation:
For a right triangle
cos theta = adj side/ hypotenuse
cos A = 8/17
11.
A school club had a T-shirt sale to raise money.
After the sale, an inventory showed that 108 blue
T-shirts and 96 green T-shirts had been sold. The
sizes of these T-shirts included 60 small, 86
medium, and 58 large. Which table correctly
represents these data?
Answer: It is A.
Step-by-step explanation: It's a because all the numbers are in the chart and matches up with it.
The sum of the blue T-shirt is 108 in table number B. Then the correct table is B.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
A school club had a T-shirt sale to raise money.
After the sale, an inventory showed that 108 blue T-shirts and 96 green T-shirts had been sold.
The sizes of these T-shirts included 60 small, 86 medium, and 58 large.
Then the correct table will be
The sum of the blue T-shirt is 108 in table number B. Then the correct table is B.
More about the statistics link is given below.
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What is 120 decreased by 25%
Answer:
90
Step-by-step explanation:
120 - (25% × 120)
120 - 25% × 120
(1 - 25%) × 120
(100% - 25%) × 120
75% × 120
75 ÷ 100 × 120
75 × 120 ÷ 100
9,000 ÷ 100 = 90
The probability of rolling a 6 on a biased die is 1/5
Work out the probability of rolling exactly one 6
Answer:
if the probability of a 6 is 1/5, the probability of “not six” is 4/5. The probability of a 6 on the first roll and not on the second is 1/5 x 4/5 = 4/25. The six could come on the second roll so that probability must be doubled. The overall probability of exactly one six is 8/25 or 0.32.
Step-by-step explanation:
Match each equation to the situation it represents. Situation Equation An adult and 5 55 children rent skates. It costs $ 4 $4dollar sign, 4 per adult for skates and a total of $ 16 $16dollar sign, 16. It costs Mikael $ 4 $4dollar sign, 4 to make a bike bag, and he sells each for $ 5 $5dollar sign, 5. He has made a profit of $ 16 $16dollar sign, 16 so far. It was 16 ° C 16°C16, degree, start text, C, end text. It began falling 4 ° C 4°C4, degree, start text, C, end text per hour until it reached 5 ° C 5°C5, degree, start text, C, end text. 16 − 4 x = 5 16−4x=516, minus, 4, x, equals, 5 ( 5 − 4 ) x = 16 (5−4)x=16left parenthesis, 5, minus, 4, right parenthesis, x, equals, 16 4 + 5 x = 16 4+5x=164, plus, 5, x, equals, 16
Answer:
1. C.
2. B.
3. A.
Step-by-step explanation:
First situation given:
An adult and 5 children rent skates. It costs $ 4 per adult for skates and a total of $ 16.
Correct equation: C
4 + 5 x = 16
Second situation given:
It costs Mikael $ 4 to make a bike bag, and he sells each for $ 5. He has made a profit of $ 16, so far.
Correct equation: B
( 5 − 4 ) x = 16
Third situation given:
It was 16°C. It began falling 4°C per hour until it reached 5°C.
Correct equation: A
16 − 4 x = 5
Equations are matched to situations based on the context provided: the adult and children renting skates is described by 4 + 5x = 16, Mikael's profit from selling bike bags fits the equation (5 - 4)x = 16, and the temperature dropping over time corresponds to 16 - 4x = 5.
To match each equation to its corresponding situation, let us consider each situation and then associate the relevant equation.
Adult and children renting skates: An adult rents skates at $4, and the total cost including 5 children is $16. The equation representing the total cost is the adult's cost plus 5 times the children's cost equals $16, which is: 4 + 5x = 16.
Mikael making a profit from bike bags: Mikael spends $4 to make a bike bag, sells it for $5, and has made a profit of $16. To determine how many bags he sold (x), we can use the equation that accounts for profit, which is the selling price minus the cost of making the bag, multiplied by the number of bags, equals the profit: (5 - 4)x = 16.
Temperature drop: The temperature started at 16°C and dropped at a rate of 4°C per hour until it reached 5°C. To find the number of hours (x) it took for the temperature to drop, we can use the equation that links the initial temperature, minus the drop per hour times the number of hours, equals the final temperature: 16 - 4x = 5.
Now, we can clearly match the equations to their situations:
The situation where an adult and children rent skates corresponds to the equation 4 + 5x = 16.
Mikael making a profit from selling bike bags is represented by the equation (5 - 4)x = 16.
The decrease in temperature over time until it reached 5°C is described by the equation 16 - 4x = 5.
Find the common difference: 1, 201, 401, 601, ... A
The common difference of the arithmetic sequence 1, 201, 401, 601, ... is 200, which is the difference between successive pairs of terms.
Explanation:In Mathematics, the common difference in an arithmetic sequence is the amount by which successive terms increase. In the given series: 1, 201, 401, 601, ..., the common difference can be found by subtracting a term from the term after it. For instance, if we subtract 1 (the first term) from 201 (the second term), we get 200. If we do the same for 201 and 401 (the second and third terms), we also get 200. This means that the common difference for this arithmetic sequence is 200.
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Identify the vertex and axis of symmetry of the function f(x) = -(x + 1)^2 + 2 *
x = -1; (-1, 2)
x = 1; (1, 2)
x = -2; (2, -1)
x = 2; (2, 1)
Answer:
x = -1; (-1, 2)
Step-by-step explanation:
f(x) = -(x + 1)^2 + 2
This is in vertex form
y = a(x-h)^2 +k where the vertex is (h,k) and the axis of symmetry is x=h
f(x) = -(x - -1)^2 + 2
Axis of symmetry is x=-1
Vertex is (-1,2)
Solve the following linear system by graphing
4x+5y=10
3x-3y=21
Answer:
y = 2
x = 5
Step-by-step explanation:
4x + 5y = 10 | ×3 |
3x - 3y = 21 | ×4 |
12x + 15y = 30
12x - 12y = 84
____________--
27y = -54
y = -54/27
y = 2
4x + 5y = 10 | ×3 |
3x - 3y = 21 | ×5 |
12x + 15y = 30
15x - 15y = 105
____________+
27x = 135
x = 135/27
x = 5
Describe the translation that maps ABCD onto A’B’C’D’
A. Left 6, up 5
B. Left 6 down 5
C. Right 6, up 5
D. Right 6, down 5
Pls don’t do this just for the points.
Answer:
D
Step-by-step explanation:
The translation that maps ABCD onto A’B’C’D’ is Right 6, down 5.
What is the translation of coordinates?Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape.
In fact, during translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.
The translation that maps ABCD onto A’B’C’D’ is;
Shift ABCD to the right side by 6 units then shifted down by 5 units to get A'B'C'D'.
ABCD moved ( 6 units ) times to the ( right), and ( 5 units ) times to the ( bottom) to convert into A'B'C'D'.
Hence, the translation that maps ABCD onto A’B’C’D’ is Right 6, down 5.
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What is the equation for ⊙A?
Answer:
Circumference = 3.14 diameter C = 3.14(6) Answer: 18.84
Step-by-step explanation:
The equation for circle at A is (x+4)²+(y+2)²=9 whose radius is 3 units.
The equation of the circle is (x-h)²+(y-k)²=r²
Where h and k are the coordinates of centre of circle and r is radius of the circle.
From the given figure (h, k) is (-4, -2) and r is 3 units
Plug in these values in the equation of circle.
(x-(-4))²+(y-(-2))²=3²
(x+4)²+(y+2)²=9
Hence, the equation for circle at centre A is (x+4)²+(y+2)²=9 whose radius is 3 units.
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Answer correctly, will mark brainliest answer !!!
Answer:
x-6
Step-by-step explanation:
The formula for the area of a rectangle is (l)(w)
x-5(w)=x²-11x+30
To solve, you need to put the quadratic equation into standard form
x-5(w)=(x-5)(x-6)
Divide both sides of the equation by x-5 to isolate the width(basically strike out x-5 on both sides)
the width is x-6
I pretty sure that's the right answer since (x-5)(x-6)=x²-11x+30, but I'm in geometry right now, and I had to go back and re-learn.
2. Eric had $197 in his savings account before he was paid his weekly salary. His current
savings balance is $429. If Eric deposits all of his earnings, then how much money does he
earn each week? Justify your answer.
a. 197 + 429 = n
b. 197 + n = 429
c. 197n = 429
d. None of the above.
Answer:
I think its b.
Step-by-step explanation: If he already has 197 then he would need to add an amount of money in this case n=232 so if you do 197 plus 232 you would get 429. Hope this helps
What is the surface area of a cylinder that is 5 centimeters high and has a diameter of 1.5 centimeters?
A) 7.5π cm²
B) 8.625π cm²
C) 10.5 π cm²
D) 19.55π cm²
The surface area of the cylinder is 16.125π cm², which is closest to option D) 19.55π cm².
To find the surface area of a cylinder, we need to calculate the sum of the areas of its two bases and its lateral surface.
The formula for the lateral surface area of a cylinder is given by:
[tex]\[ LSA = 2 \pi r h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylinder.
Given that the diameter of the cylinder is 1.5 centimeters, the radius [tex]\( r \)[/tex] is half of that, which is [tex]\( \frac{1.5}{2} = 0.75 \)[/tex] centimeters.
The height of the cylinder is given as 5 centimeters.
Substituting these values into the formula for the lateral surface area:
[tex]\[ LSA = 2 \pi (0.75) (5) \][/tex]
[tex]\[ LSA = 15 \pi \][/tex]
Now, we need to find the area of the two bases of the cylinder. Since the cylinder has two circular bases, we can find their combined area using the formula for the area of a circle:
[tex]\[ A_{\text{base}} = \pi r^2 \][/tex]
[tex]\[ A_{\text{base}} = \pi r^2 \][/tex]
[tex]\[ A_{\text{base}} = \pi (0.75)^2 \][/tex]
[tex]\[ A_{\text{base}} = \pi (0.5625) \][/tex]
[tex]\[ A_{\text{base}} = 0.5625 \pi \][/tex]
The total surface area is the sum of the lateral surface area and the areas of the two bases:
[tex]\[ \text{Total Surface Area} = LSA + 2A_{\text{base}} \][/tex]
[tex]\[ \text{Total Surface Area} = 15 \pi + 2(0.5625 \pi) \][/tex]
[tex]\[ \text{Total Surface Area} = 15 \pi + 1.125 \pi \][/tex]
[tex]\[ \text{Total Surface Area} = 16.125 \pi \][/tex]
[tex]\[ \text{Total Surface Area} = 16.125 \pi \][/tex]
Therefore, the surface area of the cylinder is 16.125π cm².
The closest option is D) 19.55π cm².
The sales tax on a $56.00 is 48. that rate, what would be the sales tax on 60.00 worth -
Answer:
51.43
Step-by-step explanation:
im not sure if you typed it correctly but using the above information and setting up the ratio, this is the outcome
A card is randomly draw from a shuffled
deck of cards and NOT REPLACED. A
second card is drawn from the remaining
shuffled cards. What is the approximate
probability that both cards are FACE
cards?
A. 5%
B. 6%
C. 23%
D. 25%
Answer:5%
Step-by-step explanation:
There are 12 face cards in a deck the chance you draw one are 3/13 and the chance you draw the second card is 4.978%
What is the value of b in the equation below?
StartFraction 5 Superscript 6 Over 5 squared EndFraction = a Superscript b
3
4
5
8
Answer:
I think it is 4
Step-by-step explanation:
Answer:
y = 6|x|
Step-by-step explanation:
y = |x|
When we scale vertically, we multiply by a constant
y = a f(x)
We are multiplying by 6
y = 6|x|
Aidan has $65 in his bank account. His brother Michael also has a bank account. They want to calculate the amount of money in both accounts combined. What variable is needed to calculate their combined total?
A.
d, the difference between the amounts in Aidan's and Michael's account
B.
a, the amount of money in Aidan's bank account
C.
m, the amount of money in Michael's bank account
D.
l, the amount of money in Michael's account last month
Answer:
C because they won't know unless they know what Michael has
Step-by-step explanation:
What is the area of the triangle image above^ ASAP
What is the probability of a die landing on an even number on the first toss, and then an odd number on the second toss?
Dice- 6 sides
Please help
Answer:
i dotn know sorry
Step-by-step explanation:
and this is why brainly is bad
Answer:
1/4 chance
Step-by-step explanation:
Number of even numbers on a die-3
Number of odd numbers on a die-3
a die has 6 sides,
therefore
1/2 of the numbers on a die are even and 1/2 are odd
so a 3/6 chance (1/2 chance (simplify)) of landing on an even number on the first roll
And a 3/6 chance (1/2 chance (simplify)) of landing on an odd number on the second roll
Multiply the two together and a 9/36 chance of this event or simplified to a 1/4 chance of this event
you roll a fair 6-sided die . what is the probability of rolling a 2 .
Answer:
P = 1/6
Step-by-step explanation:
Answer:
1/6
Step-by-step explanation:
6 sides means 1 in 6 chance for each side
find the value of y when x=3: y= 2x +1
Answer: 7
Step-by-step explanation:
x=3 y=2x+1
Y= 2(3)+1
Answer:
y=7
Step-by-step explanation:
We want to find y when x equals 3, so we can substitute 3 in for x
y=2x+1
y=2(3)+1
Multiply
y=6+1
Add
y=7
If a = -3 find the value of 2a
Answer:
2a= -6
Step-by-step explanation:
a= - 3
2a= 2(-3)= -6
Answer:
-6
Step-by-step explanation:
-3×2=-6
DUE TODAY NEED HELP ASAP! WILL MARK BRAINLIEST TO THE FIRST PERSON WHO ANSWERS
Answer:
1 I would use the news and newspaper maybe
2. I would not use social media like T.T and Inst
That is all I could help with sorry And i could not put real names it would not let me sorry
Step-by-step explanation:
1/2(2n+4)+6=-9+4(2n+1)
Answer:
13/7 =n
Step-by-step explanation:
1/2(2n+4)+6=-9+4(2n+1)
Distribute
n +2 +6 = -9 + 8n +4
Combine like terms
n +8 = 8n -5
Subtract n from each side
n+8-n = 8n-n-5
8 = 7n-5
Add 5 to each side
8+5 = 7n-5+5
13 =7n
Divide each side by 7
13/7 = 7n/7
13/7 =n
Answer: n = 13/7 = 1.857
( I hope this is right )
Step-by-step explanation:
Ted and Meg have each drawn a line on the scatter plot shown below:
Which line best represents the line of best fit?
Line P, because it is closest to most data points
Line P, because it shows a positive association
Line R, because it is closest to most data points
Line R, because it shows a negative association
Answer:
A.)Line P, because it is closest to most data points
Step-by-step explanation:
The line of best fit is a line which best represents the data and the data points are closely related to it.
It is also known as a trend line.
The line of best fit may pass through, some , none or all of the data points.
Also if the scatter plot does not pass through all the data point then the magnitude of positive residual must be approximately equal to the magnitude of negative residual of the data points.
Hence, by looking at the scatter plot we see that all the data points lie above Line R.
Hence, the Line R will not be a line of best fit.
But all the data points lie close to the line P , hence it act as a line of best fit.
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Answer:
Line P, because it is closest to most data points
Step-by-step explanation:
solve the equation by completing the sqaure. if necessary round to the nearest hundreth x^2+4x=1
Answer:
x = ± √ 5 − 2
Step-by-step explanation:
triangle ABC is isosceles a= 56 degrees work out three possible values of angle B
def: -in an isosceles triangle two of its angles measure the same
- the sum of all angles in a triangle is 180°
case1: if angle a measures the same with another angle in the triangle
=>angle1=56
angle2=180-2*56=180-112=68°
from this case we extract 2 posibilities:
B=56° or B=68°
case2: if the other 2 angles beside a measure the same
angle1=angle2=(180-56)/2=62°
from this case we e extract one posibility:
B=62°
Final answer:
In an isosceles triangle ABC with angle A equal to 56 degrees, three possible values for angle B are 68 degrees if it is the vertex angle, and 56 degrees or 62 degrees if it is one of the base angles.
Explanation:
If triangle ABC is an isosceles triangle with angle A (a) equal to 56 degrees, we can work out three possible values of angle B using the properties of an isosceles triangle and the fact that the sum of angles in any triangle is 180 degrees.
Since triangle ABC is isosceles, two of its angles are equal. If angle A is one of the two equal angles, then angle B (which is the vertex angle) is given by:
B = 180° - 2AIf angle B is one of the two equal angles, then we have two cases:
B = A (the two base angles are equal)B = (180° - A) / 2 (the vertex angle is different)In the first case where angle B equals angle A (56 degrees), then the other base angle (angle C) must also be 56 degrees, and the remaining vertex angle B would be 180° - 56° - 56°, which is 68 degrees.
In the second case, where B is the vertex angle:
B = 180° - 2AB = 180° - 2(56°)B = 180° - 112°B = 68 degreesThis gives us the same value for angle B as in the first case since both result in the same configuration.
Finally, if angle B is one of the two base angles and equal to angle C, then B would be (180° - A) / 2:
B = (180° - 56°) / 2B = 124° / 2B = 62 degreesSo, three possible values for angle B are 68 degrees, 56 degrees (if B is one of the base angles), and 62 degrees (again, if B is a base angle).
In △ABC, angle C is a right angle and BC > AC. Select all the statements that are true.
A. m∠B > m∠A
B. sin A > sin B
C. sin A < sin B
D. cos A > cos B
E. cos A < cos B
△ABC right angle C, leg BC > leg AC. So angle A > angle B.
a=BC, b=AC, c=AB
a > b
sin A= cos B = a/c
sin B = cos A = b/c
a = c sin A = c cos B
b = c sin B = c cos A
a > b
c sin A > c sin B
sin A > sin B
c cos B > c cos A
cos B > cos A
Answer: B, E
Final answer:
In a right-angled triangle △ABC with BC > AC, it is true that m∠B > m∠A, sin A < sin B, and cos A > cos B. These correspond to choices A, C, and D.
Explanation:
In the context of triangle △ABC where angle C is a right angle and BC > AC, we can assess the truth of various statements regarding the angles and their sine and cosine values:
m∠B > m∠A: This statement is true because in a right-angled triangle the side opposite the right angle is the hypotenuse and is the largest side. Therefore, the angle opposite the longest side (BC) must be the largest acute angle, hence m∠B > m∠A.
sin A > sin B: This statement is false. Since m∠B > m∠A and sine of an angle increases with the angle's magnitude (for acute angles), it must be that sin A < sin B.
sin A < sin B: This statement is true based on the relationship of the sides and angles mentioned earlier.
cos A > cos B: This statement is true. Since m∠B > m∠A and cosine of an angle decreases as the angle's magnitude increases (for acute angles), it must be that cos A > cos B.
cos A < cos B: This statement is false for the same reason that cos A > cos B is true.
The correct statements are therefore A, C, and D.
The area of a parallelogram is 74, with the base measuring triple the height. If the unknown variable represents the height of the parallelogram, what does each variable in the model represent?
A parallelogram with height h and base b.
h =
b =
Answer:
The answer is A. 88.8 cm2
Work:
74 x 2 = 148
14.8 = 29.6
Add them = 177.6
Step-by-step explanation:
Answer:
h=x
b=3x
Step-by-step explanation:
Just got it right on Edge.
i need the answer
PLEASE HELP :) :(
So the answer is 6 km.
Look at the attached picture⤴
Hope it will help u...:)
Answer:
it will be 6km
i just go by 2 like 10, 8, then 6
-Hops