Answer:
The intersection point is (2, 3)
Step-by-step explanation:
The given (linear) equations for the point of intersection is required are;
y = x + 1...(1)
3·y + 2·x = 13...(2)
To find the point of intersection without using graph, we note that the point of intersection is the point at which the values of both equations are equal
We find the values of 'x' and y-coordinates at the point of intersection as follows;
Making 'y' the subject of equation (2) gives;
y = (13 - 2·x)/3
When both lines intersect, the 'x' and y-values are the same;
y = x + 1 for the first line, and y = (13 - 2·x)/3 for the second line, therefore, at the intersection point, we have;
y = y
x + 1 = (13 - 2·x)/3
3·(x + 1) = 13 - 2·x
3·x + 3 = 13 - 2·x
3·x + 2·x = 13 - 3
3·x + 2·x = 5·x = 13 - 3 = 10
∴ 5·x = 10
Therefore, at the point of intersection, x = 10/5 = 2
x = 2
'y' is given in equation (1) by y = x + 1, therefore, at the point of intersection, 'x = 2', we get;
y = x + 1
∴ The value of 'y' at the point of intersection is y = 2 + 1 = 3
y = 3
Therefore, the (x, y) coordinate at the point of intersection is (2, 3) which can be written as follows;
The point of intersection = (2, 3).
How many in five days?
Answer:
d
Step-by-step explanation:
Answer:
I think it is B
Step-by-step explanation:
How do I solve this?
Answer:
3p³ + 2p² – 3p – 11
Step-by-step explanation:
From the question given above, the following data were obtained:
Side 1 (S₁) = –1(p + 5)
Side 2 (S₂) = 2(p² – 3)
Side 3 (S₃) = 3p³ – 2p
Perimeter (P) =?
The perimeter of the triangle can be obtained as follow
P = S₁ + S₂ + S₃
P = –1(p + 5) + 2(p² – 3) + 3p³ – 2p
Clear bracket
P = –p – 5 + 2p² – 6 + 3p³ – 2p
Rearrange
P = 3p³ + 2p² – 2p – p – 6 – 5
P = 3p³ + 2p² – 3p – 11
Therefore, the perimeter of the triangle is 3p³ + 2p² – 3p – 11
Which of the following is a point-slope equation for a line with the point (-2, 4) and a slope of 3? O A. y - 4 = 3(x+2) B. y - 2 = 3(x-4) C. y + 2 = 3(x-4) O D. y - 4 = 3(x - 2)
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]A)\text{ } y-4=3(x+2)[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Point-Slope Form Is...}}\\\\y-y_1=m(x-x_1)\\------------\\m - \text{slope}\\\\(x_1,y_1)- \text{point}[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{\underline{Information Given:}}}\\\\\rightarrow \text{The point of } (-2,4)\\\\\rightarrow \text{The slope of 3}\\\\\\\text{\underline{This means the following:}}\\\\\rightarrow m = 3\\\\\rightarrow(x_1,y_1) = (-2,4)[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Replace the variables with the respective values:}}\\\\y-y_1=m(x-x_1)\\\\------------\\\rightarrow y-4=3(x-(-2))\\\\\rightarrow \boxed{y-4=3(x+2)}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Solve for the value of x in the diagram: Show your work and explain the steps you used to solve.
Answer:
x = 20
Step-by-step explanation:
The triangles are similar
3 (3+5)
----- = ----------
12 (12+x)
Using cross products
3(12+x) = 12*(3+5)
3(12+x) = 12*8
3(12+x) = 96
Divide by 3
3(12+x)/3 = 96/3
12+x = 32
Subtract 12
12+x-12 =32-12
x = 32-12
x =20
25 [tex]\sqrt{x}[/tex] 64 +187
Answer:
x = 17/4 = 4.250
x = 11/2 = 5.500
Step-by-step explanation:
Which term is defined as a fee charged for the use of money?
a interest
b. down payment
C. principal
d. default
Please select the best answer from the choices provided
A
B
C
D
Which term is defined as a fee charged for the use of money?
[tex]\sf\purple{a.\:interest}[/tex] ✔
b. down payment
C. principal
d. default
Explanation:
Interest is defined as a fee charge for the use of money.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35\:ヅ}}}}}[/tex]
The following table shows the salary of 7 people in an office last year.
Name
Income
Andy
£13500
Bevan
£27500
Cheryl
£13750
Deva
£79000
Elliott
£19250
Frankie
£29000
Grace
£15000
a) Work out the mean income to 2 DP.
b) Deva was given a large bonus for 30 years service..
Excluding Deva's income, what was the mean income for the remaining 6 workers to 2 DP?
Answer:
23 poudsfgghhhhhhhxcvbnmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
anyone know the answer?
Martin collected data from students about whether they played a musical instrument. The table shows his results. Instrument No Instrument TOTAL Boys 32 60 92 Girls 38 68 TOTAL 70 90 160 What is the relative frequency of a boy playing an instrument? Write the answer as a decimal, rounded to the nearest hundredth.
Answer:
Step-by-step explanation:
For the data collected by Martin from students about whether they played a musical instrument, the relative frequency of a boy playing an instrument is 0.348.
What is relative frequency?Relative frequency of an event is the measure of something happens relative to the total outcomes of that event.
The relative frequency can be given as,
[tex]f_r=\dfrac{f}{n}[/tex]
Here, (f) is the frequency of the number of times data occurred in an event and (n) is the total number of outcomes.
The relative frequency can also be defined as, it is the ratio of subgroup frequency to the total frequency of any event.
Martin collected data from students about whether they played a musical instrument.
The table shows his results.
Instrument No Instrument TOTAL Boys 32 60 92 Girls 38 68 TOTAL 70 90 160Here, the total number of boys are 92 and the total number of boys who play instrument is 32. Thus, the relative frequency is,
[tex]f_r=\dfrac{32}{92}\\f_r=0.348[/tex]
Thus, for the data collected by Martin from students about whether they played a musical instrument, the relative frequency of a boy playing an instrument is 0.348.
Learn more about the relative frequency here;
https://brainly.com/question/3857836
#SPJ2
I think of a number, double it, then subtract 13 , I get 73 . Evaluate the number I thought of.
Answer: 43
Step-by-step explanation:
Lets start with the result. First add the number you subtracted with 73
= 73+13=86
Now they had doubled it, now we instead divide it as it was multiplied. Division is the opposite of Multiplication.
86/2= 43
Hence the Answer or the First Number was 43
HOPE IT HELPS AND PLS MARK BRAINLIEST
I swear there are never tutors
Answer:
5-2y (the last option)
hope this helps!
please give brainiest<3
Answer:
2y-5
Step-by-step explanation:
Chris carved three times as many jack-o lanterns as his friend Thomas. if Thomas carved 3 jack o lanterns how many did Chris carve
Answer:
9
Step-by-step explanation:
3 times 3 is 9
hope that helps bby<3
Mark's average after 9 exams was 60. After 10 exams it had decreased to 50. How many marks did he score in his 10th exam?
Answer:
hey how much mark he scored in 9th exam give proper data or how many subject there
Find the missing side and angle measures in triangle ABC. Round your answers to the nearest tenth.
The measure of angle B is approximately
__.
The measure of angle C is approximately
__.
The length of side AB is approximately
___units.
Answer:
[tex]m\angle B\approx 80.27^\circ\text{ and } m\angle C\approx 59.73^\circ[/tex]
Side AB measures approximately 20.15 units.
Step-by-step explanation:
We can use the Law of Sines, given by:
[tex]\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}[/tex]
Since we already know ∠A and a, we can use it to determine our other measures.
We know that b is 23. Substitute:
[tex]\displaystyle \frac{\sin 40^\circ}{15}=\frac{\sin B}{23}[/tex]
Solve for ∠B:
[tex]\displaystyle \sin B=\frac{23\sin 40^\circ}{15}[/tex]
We can take the inverse sine of both sides:
[tex]\displaystyle m\angle B=\sin^{-1}\frac{23\sin 40^\circ}{15}[/tex]
Use a calculator (make sure you're in Degrees mode!):
[tex]m\angle B\approx 80.27^\circ[/tex]
The interior angles of a triangle must total 180°. Hence:
[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]
Substitute in known values:
[tex](40^\circ)+(80.27^\circ)+m\angle C=180^\circ[/tex]
Therefore:
[tex]m\angle C\approx 59.73^\circ[/tex]
Lastly, to find AB or c, we can use the Law of Cosines:
[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]
a = 15, b = 23, and to prevent rounding errors, we will use the exact value for C. Recall that we know that:
[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]
Using the exact value for ∠B, we acquire:
[tex]40^\circ+\displaystyle \sin^{-1}\frac{23\sin40^\circ}{15}+m\angle C=180^\circ[/tex]
Therefore:
[tex]\displaystyle m\angle C=\left(140-\sin^{-1}\frac{23\sin40}{15}\right)^\circ[/tex]
Substitute:
[tex]\displaystyle c^2=(15)^2+(23)^2-2(15)(23)\cos\left(140-\sin^{-1}\frac{23\sin40^\circ}{15}\right)[/tex]
Simplify and take the square root of both sides.
[tex]\displaystyle c=\sqrt{754-690\cos\left(140-\sin^{-1}\frac{23\sin40^\circ}{15}\right)}[/tex]
And use a calculator:
[tex]c\approx 20.15[/tex]
Answer:
Hi! The person above is actually correct, just that it needed to be rounded to the nearest tenth. Check the picture for confirmation. Hope this helped <3
Step-by-step explanation:
The measure of angle B is approximately
80.3
The measure of angle C is approximately
59.7
The length of side AB is approximately
20.2
I got it correct on Edmentum/Plato
y = x2
-2
What is the Domain:
Answer:
all real numbers
Step-by-step explanation:
The domain is the values that x can take
x can be any real number
Convert this radical form to exponential form.
Answer:
I think it's 7.93725
I'm not sure if I did this correctly
help i give many points
Answer:
Step-by-step explanation:
The pic doesnt wrk comment question and ill answer
When a cup of coffee at 100 degree Celsius cools down ,it loses 12%of its current temperature
per minute. What will the temperature be after 10 minutes.
Answer:
Temperature after 10 minute = 27.9 degree Celsius
Step-by-step explanation:
Current temperature, P = 100 degree Celsius
% rate in temperature loses = 12% per minute = 0.12
Time, t = 10 minutes
Temperature after t minutes ,
[tex]= P ( 1 - r )^t\\\\=100( 1 - 0.12)^10\\\\=100(0.278500976)\\\\=27.85[/tex]
= 27.9 degree Celsius
The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
Step-by-step explanation:
Feel free to ask for more help. I love Linear Algebra
A line contains the points (2,-7) and (-4,2). Which statement is not true?
A) The line has y-intercept - 4
B) The line contains
(1,-)
2
C) The line is parallel to 3x - 2y=6 D) The line is perpendicular to y=x+4
E) No portion of the graph of the line lies in the first quadrant
Answer:
a is the answer because I just did that question and got 100 percent.
Please help me with this
Answer:
O = 29
P = 61
Step-by-step explanation:
90 = (x+3) + (2x+9)
90 = 3x + 12
90 - 12 = 3x
78 = 3x
x = 26
26 + 3 = O = 29
(26 * 2) + 9 = P = 61
61 + 29 = 90 = Complementary Angles
the grid below is made up of squares with sides of 1cm draw a rectangle with an area of 12 cm squared
Answer:
6 is length and 2 is width.
Nolan plots the y-intercept of a line at (0, 3) on the y-axis. He uses a slope of 2 to graph another point. He draws a line through the two points. Which equation represents Nolan’s line?
y = 2x + 1
y = 2x + 3
y = 3x + 2
y = 3x + 5
Answer:
B
Step-by-step explanation:
The equation of Nolan's line is
The slope-intercept form of a line is given by:
Here
m is the slope of the line
and b is the y-intercept.
Given
y-intercept = b = 3
slope = m = 2
The values of m and b can be put into the equation to find the line's equation
So,
Putting the value
Hence,
The equation of Nolan's line is
What is the slope that passes through the points (-8, -7) and (-5, 2)?
Answer:
3
Step-by-step explanation:
The equation for finding a slope is (y2-y1)/(x2-x1), where (x1, y1) is a set and (x2,
y2) is another set. (2-(-7))/(-5-(-8) = (2+7)/(-5+8) = 9/3 = 3. Hope this makes sense and helps!
Answer:
3
Step-by-step explanation:
To find the slope given two points, we use the slope formula
m = ( y2-y1)/(x2-x1)
m = ( 2 - -7)/(-5 - -8)
= (2+7)/( -5+8)
9/3
3
.y is inversely proportional to (x + 3) ?.
When x = 2, y = 8.
Find y when x = 7.
A 100
B. 4
C. 2.
D. 16
OA
Answer:
B
Step-by-step explanation:
y = k/(x + 3)
Let x = 2
Let y = 8
k = ?
8 = k/(2 + 3) Combine the terms on the right
8 = k/(5) Multiply both sides by 5
8*5 = k
k = 40
Let x = 7
y = 40/(7 + 3)
y = 40/10
y = 4
Coraline was training for cross country season an app to track 24 laps around the track that measures 110 m what was the total distance Coraline ran in kilometers
Answer:
2.64 km
Step-by-step explanation:
The first step is to calculate the distance in meters
= 24×110
= 2640 meters
1km= 1000 meter
2640 meters to kilometer
= 2640/1000
= 2.64 kilometers
Hence the distance is 2.64 km
Chloe wants to make a scrapbook with old family photos. An online scrapbooking company charges $45 plus $1 per page. Meanwhile, a family friend is willing to make a scrapbook for $9 plus $4 per page. For a certain number of pages, the prices would be equal. How many pages would that be? How much would Chloe be charged?
Answer:
The prices are equal when it's 12 pages. For 12 pages, she'd be charged $57
Step-by-step explanation:
x = PER page
y = total
Online scrapbooking equation:
y = 45 + x
Family friend equation:
y = 9 + 4x
Where prices (y) would be equal:
y = 45 + x (Multiply this by -4)
y = 9 + 4x
y = 9 + 4x
-4y = -180 - 4x
-3y = -171
y = 57
y = 45 + x
-y = -9 - 4x
0 = 36 - 3x
3x = 36
x = 12
b) Find x and y.
x = 10-6
Answer:
to find y you have to do trigonometry
What is the value of x?
sin 49° = COS X
Enter your answer in the box.
X =
Answer:
x = 41°
Step-by-step explanation:
Using the cofunction identity
sinx = cos(90 - x) , then
sin49° = cos(90 - 49)° = cos49°
with x = 41°
1. Tyler's hourly salary is $14. If Tyler works
hours a day, then how much will be earned in a
day?
Answer:
????
Step-by-step explanation:
The number of hours he works is missing???
