Answer:
we have x=1, y=0 and x=-3, y=4
Step-by-step explanation:
We need to solve the equations: [tex]y=x^2+x-2 \ and \ y=-x+1[/tex]
Let:
[tex]y=x^2+x-2--eq(1)\\ y=-x+1---eq(2)[/tex]
Putting value of eq(2) into eq(1)
[tex]-x+1=x^2+x-2\\Solving:\\x^2+x-2+x-1=0\\x^2+2x-3=0\\Factorising:\\x^2+3x-x-3=0\\x(x+3)-1(x+3)=0\\(x-1)(x+3)=0\\x-1=0 \ or \ x+3=0\\x=1 \ or \ x=-3[/tex]
Now finding values of y for x=1 and x=-3
[tex]For \ x=1, \\y=-x+1 \\y=-1+1 \\y=0\\For \ x=-3\\ y=-x+1\\y=-(-3)+1 \\y=3+1\\y=4[/tex]
So, we have x=1, y=0 and x=-3, y=4
-5+22=r-4+3r+5
I need help please and thank u
Answer:
r = 4
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
-5 + 22 = r - 4 + 3r + 5
Step 2: Solve for r
Combine like terms: 17 = 4r + 1Subtract 1 on both sides: 16 = 4rDivide 4 on both sides: 4 = rRewrite: r = 4Step 3: Check
Plug in r to verify it's a solution.
Substitute: -5 + 22 = 4 - 4 + 3(4) + 5Add/Subtract: 17 = 3(4) + 5Multiply: 17 = 12 + 5Add: 17 = 17Can anyone help me with this?
Answer:
-37z
Step-by-step explanation:
Hey i need help finding the orthocenter for the following points, please show the steps you used. thanks
(-3, 0.5)
(3,3)
(2,-1)
9514 1404 393
Answer:
(81/43, -31/43) ≈ (1.884, -0.7209)
Step-by-step explanation:
The orthocenter is the intersection point of the altitudes of the triangle. Since this is not a right triangle, you need to find the equations of the altitude lines, then find where those intersect.
If we call the points A, B, C in the order given, the attached figure shows the altitude lines from B perpendicular to AC, and from C perpendicular to AB.
We can find the equation of the perpendicular line using the form ...
∆x·x +∆y·y = c
where ∆x and ∆y are the differences in coordinates between the points on the "side" and the value of constant 'c' is determined by evaluating the expression using x and y as the coordinates of the opposite vertex.
__
For line AC, we have ...
(∆x, ∆y) = C - A = (2, -1) -(-3, 0.5) = (2+3, -1-0.5) = (5, -1.5)
Then the equation of the first altitude line is ...
5x -1.5y = 6(3) -1.5(3) = 10.5
Multiplying by 2 puts this in standard form:
10x -3y = 21
__
For line AB, we have ...
(∆x, ∆y) = B - A = (3, 3) -(-3, 0.5) = (3+3, 3-0.5) = (6, 2.5)
Then the equation of the second altitude line is ...
6x +2.5y = 6(2) +2.5(-1) = 9.5
Multiplying by 2 puts this in standard form:
12x +5y = 19
__
Then the orthocenter is the solution to the system of equations ...
10x -3y -21 = 0
12x +5y -19 = 0
This set of equations can be solved a number of ways. One is the "cross-multiplication" method.
1/(10·5 -12·(-3)) = x/(-3·(-19) -5·(-21)) = y/(-21(12) -(-19)(10))
x = 162/86 = 81/43
y = -62/86 = -31/43
The orthocenter is (81/43, -31/43) ≈ (1.884, -0.7209).
_____
Additional comment
The "cross multiply method" is based on cross products when the equations are written in standard form:
ax +by +c = 0
dx +ey +g = 0
Usually, the coefficients are written in two rows of four, with the first column repeated at the end:
a b c a
d e g d
Then cross products are formed, where diagonal down is positive and diagonal up is subtracted from that:
p1 = (ae -db), p2 = (bg -ec), p3 = (cd -ga)
These give the solution to the equations when put in the form ...
1/p1 = x/p2 = y/p3 ⇒ x = p2/p1 and y = p3/p1
If you look at videos of this "cross multiply method," they will put the 1/p1 at the end of the string of equalities, and they will use the coefficients in the order starting with b instead of a. I find the arrangement here easier to remember, so less likely to get confused.
Further comment
You can, of course, find the slopes of the lines, and their opposite reciprocals, then use a point-slope form or some other method for writing the equations of the altitude lines. The solution to the equations can proceed by substitution or elimination. No doubt these methods are somewhat familiar. The method used here tries to get to the answer much more quickly with a lot less writing. (Unfortunately, it takes a bit of writing to explain it all.)
Will Give brainliest 40 POINTS
In the figure above, lines l and m are parallel. What is the value of x?
Select one:
A. 55
B. 57
C. 61
D. 63
Answer:
55
Step-by-step explanation:
Please let me know if you need an explanation.
Will mark Brianliest !!!!!!!!!!!!!! Answer correctly please !!!!
Answer:
54 degrees
Step-by-step explanation:
Since we know that the angles are supplementary, we can set them to be equal to 180 degrees when combined.
(7x+14) + (5x-26)=180
Drop the parentheses.
7x+14+5x-26=180
Combine like terms.
12x-12=180
Add 12 to both sides.
12x=192
Divide both sides by 12.
x=16
Since the question asks for the measure of angle B, we need to plug x back into that expression to find its measure.
5(16)-26
80-26
54
Angle B has a measure of 54 degrees.
HTH :)
Write the equation of a line perpendicular to y = -2x +8 that passes through the point ( -4, 1)
Answer:
y=1/2x+3
Step-by-step explanation:
let a(-a -b) b(-a -b) distance between two points
fast
Answer:
A(-a,-b)and B(-a,-b) be
distance between AB= square root(x2-x1)^2+(y2-y1)2
AB= square root (-a)-(-a)^2+(-b)-(-b)^2
AB= squareroot (-a+a)^2+(-b+b)^2
AB= square root (0)^2+(0)^2
AB=square root 0+0
AB= square root 0
AB=0 answer
this may help you !!!!!
help! which one is it?
Answer:
quadratics and absolute value
Step-by-step explanation:
they both go up but Quadratic is U and absolute value is V
Rectangle ABCD with coordinates A(1, 1), B(4, 1), C(4, 2), and D(1, 2) dilates with respect to the origin to give rectangle A'B'C'D'. If = 6, what is the scale factor of the dilation? A. 6 B. 3 C. 2 D. E. 4
Answer:
A.
Step-by-step explanation:
Answer:
Answer is C. (2)
for PLATO
Step-by-step explanation:
A'B' = 2 * AB
Therefore, the dilation factor is 2.
A recipe calls for 1 1/2 teaspoons of cinnamon to make 2 dozen oatmeal cookies. How many teaspoons of cinnamon are needed to make 60 oatmeal cookies?
Answer:
3 3/4 teaspoons of cinnamon
Step-by-step explanation:
Proportions
Proportional relationships between two variables imply their ratios are constant.
It means that one variable is always a constant value times the other.
We are told that 1 1/2 (1.5) teaspoons of cinnamon are good to make 2 dozen oatmeal cookies. Two dozen is equivalent to 24, thus the ratio between oatmeal cookies and teaspoons of cinnamon is 24 / 1.5 = 16.
It means for each teaspoon of cinnamon you can make 16 oatmeal cookies.
If we wanted to make 60 oatmeal cookies, we need 60/16 = 3.75 teaspoons of cinnamon.
The number 3.75 is equivalent to
3+0.75 = 3 + 3/4, or 3 3/4 teaspoons of cinnamon
Esmeralda works in the snack bar at the movie theater. She serves popcorn in two sizes, small and giant. The dimensions of the small box of popcorn are similar to the dimensions of the giant box of popcorn 15 in. 4 in 6 in 10 in. Small Popcom Giant Popcorn What is x when the width of the small box is 4 inches? Round your answer to the nearest tenth?
Answer:
6.7
Step-by-step explanation:
For the pair of shapes below, decide whether or not it appears that the two shapes are congruent.
Answer:
I do not see the shapes copy and paste them here
please help with this work sheet
Answer:
Grade ano po
Step-by-step explanation:
Para maidentify ko po
1. In order to increase sales the price of a Concorde airliner is reduced from
$30,000,000 to 28,400,000, what percentage reduction is this?
Answer:
5.33%
Step-by-step explanation:
(28,400,000÷30,000,000 ) × 100%
= 94.67%
the reduced amount = 100 - 94.67
= 5.33%
Answer:
5.333333333333334%
Step-by-step explanation:
5.333333333333334% of 30,000,000 = 1,600,000
Tip: Don't get scared by numbers, percentage don't change by how many zeros, i found this just by figuring out by: 1.6 is what percentage of 30?
You could find it on a "Percentage calculator"
Hope this helps!
Ace Carlos
Find the slope of the line that passes through (7,5) and (5, 8).
Simplify your answer and write it as a proper fraction, improper fraction, or integer
Answer:
slope is -3/2
Step-by-step explanation:
Use the slope formula
y2-y1/x2-x1=m (rise over run)
(7,5) (5,8)
x1 y1 x2 y2
8-5/5-7=m
-(3/2)=m
10
44:25
The monthly mean salaries and standard deviations of four college students are given below.
Standard Deviation
12.53
Student
Clarissa
Abi
Kaila
Shenika
Mean
$345
$598
$812
$208
8.99
15.29
7.67
Which statement must be true?
O The monthly salary of Shenika is less spread out than the monthly salary of Clarissa,
O The monthly salary of Kaila is less spread out than the monthly salary of Abi.
O The monthly salary of Abi is less spread out than the monthly salary of Shenika.
O The monthly salary of Clarissa is less spread out than the monthly salary of Abi.
Save and Exit
Next
Submit
Mark this and return
Answer: The monthly salary of Shenika is less spread out than the monthly salary of Clarissa.
Step-by-step explanation:
Standard deviation measures the spread around the mean of the different variables.
Shenika's monthly salary has a standard deviation of 7.67 while Clarissa has a standard deviation of 12.53. This means that Shenika's monthly salary is less spread out than the monthly salary of Clarissa.
four times a number is greater then 48. what are the possible values for the number?
Any number that is 13 to Infinity
Any number greater then 12
Assume;
Given number = a
So,
Four times a number;
4 × a
4a
Greater then 48
So,
4a > 48
By solving inequality
a > 12
So,
Any number greater then 12 is the possible value
Learn more:
https://brainly.com/question/1301963?referrer=searchResults
To calculate the length of the hypotenuse in this triangle, the formula we would use is:
A.
[tex] {w}^{2} = {x}^{2} + {y}^{2} [/tex]
B.
[tex] {x}^{2} = {w}^{2} + {y}^{2} [/tex]
C.
[tex] {x}^{2} = {y}^{2} - {w}^{2} [/tex]
D.
[tex] {y}^{2} = {x}^{2} - {w}^{2} [/tex]
Answer:
it is b !!
Step-by-step explanation:
a^2 + b^2 = c^2 :)
In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find
the probability that she did not hit a boundary.
Answer: She has not hit the boundary 4/5 of the time.
Step-by-step explanation: 6/30 is 1/5. Subtract 1 - 1/5.
[tex] {16}^{ - 2x} = 32[/tex]
find x
Answer: x=−0.208333
Step-by-step explanation:
hope that helps enjoy
Simplify 4/8 pls need help
Answer:
1/2
Step-by-step explanation:
4 and 8 are both divisible by four so divide four by four and divide and by four and you get 1/2
Choose the word that correctly completes the statement. Triangle A B C is shown. Angle A C B is 45 degrees, angle C B A is 75 degrees, and angle B A C is 60 degrees. Since angle B is the largest angle, Line segment A C is the ________ side. adjacent included longest shortest
Answer:
longest
Step-by-step explanation:
was Answer Expert Verified on a different question :)
Answer:
Longest
Step-by-step explanation:
Edgen 2021
What is the equation, in slope-intercept form, of the line that passes through the points (−24, 5) and (16, −20)?
A. Y = -8/5x + 10
B. Y = -8/5x - 10
C. Y = -5/8x - 10
D. Y = -5/8x + 10
Answer:
C (Y = -5/8x - 10)
Step-by-step explanation:
first find the slope (y₂ - y₁) ÷ (x₂ - x₁)
(5 - (-20)) ÷ (-24 - 16)
-5/8 = slope (m)
now that we know the slope is -5/8 we can rule out A and B
now to find the y intercept just substitute a point in for x and y
5 = (-5/8)(-24) + b
multiply
5 = 15 + b
subtract 15 from both sides tp isolate b
-10 = b
Find All real square roots of 16 If there is more then one answer separate them with commas if there are none, click on “None”
Answer:
4,-4
Step-by-step explanation:
[tex]\sqrt16=4\\\sqrt16=-4.\\[/tex]
Both are possible. Hope this helps and if you can, hit the crown ;D
Factor the trinomial 3x^2+14x+15
Answer:
(3x+5)(x+3)
Step-by-step explanation:
3x^2+14x+15
SIMPLIFY INTO COMMON FACTOR
3x^2+9x+5x+15
FACTOR OUT DISTRIBUTION
3x(x+3)+5(x+3)
(3x+5)(x+3)
what is the effect on the graph of the function f x is equal to the square root of x - 2
Answer:
g(x) = (x-3)^2 - 3
Step-by-step explanation:
to move up or down just add or subtract the constant equal to the units moved
so just to move it DOWN 3 would give us
g(x) = x^2 - 3
to move horizontally replace each x with (x ± c)
if you move it to the right, you need x - c
if you move it to the left , you need x + c
so , since we are moving 3 units to the right, we replace the x with x-3
g(x) = (x-3)^2 - 3
sorry if I get it wrong.
18. George invests $5000 for 14 years at a rate of 2% per year compound interest. Calculate the interest he
receives. Give your answer correct to the nearest dollar.
Answer:
He will receive $1, 400 for interest
&
A total amount of $6, 400
Step-by-step explanation:
To find the interest, we must apply the following formula:
I = P × R × T
I represents interest
R represents rate
T represents time
P represents principle
Steps:
1. Change the rate, which is 2%, into a decimal.
2. Multiply the principle, which is 5,000, by the rate, which is 0.02.
3. Multiply the product of the principle and rate, which is 100, by the time, which is 14 years.
So he will receive $1, 400 interest.
To find the total amount he recieved, we must:
Add the principle, which is 5,000, and the current interest, which is 1, 400.
5,000 + 1,400= 6,400
He will receive a total of $6, 400
I hope this helps! I'm sorry if it's wrong.
Three friends each have some ribbon. Carol has 54 inches of ribbon, Tino has 10.5 feet of ribbon, and
Baxter has 45 yards of ribbon. Express the total length of ribbon the three friends have in inches, feet, and
yards
Answer:
1800 inches, 150 feet, and 50 yards
Step-by-step explanation:
First, lets start in inches. multiply 45 by 3, to get 135 feet, and add that with 10.5 to get 145.5 feet. multiply that by 12 to get 1746 inches, and add 54 to that to get 1800 inches. divided that by 12 to get 150, and divided 150 by 3 to get 50.
PLEASE HELP MEEEE!! With the following question below.
Answer:
5
Step-by-step explanation:
Answer:
a. which is the best way to get the information to the police to be able to help you with the information you need to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport to get to the airport by your flight number at your airport to get the car in and you have been advised by our insurance broker to let you all
The function n(t) = 825(1.12)t models the number of bacteria, n(t), after t weeks. What does 825 represent?
Answer: it represents “n” which is the number of bacteria
Step-by-step explanation: