Answer:
y = x + 6
x = 1
y = ¼(x - 5) + 3
Step-by-step explanation:
Vetices are;
A(1,5), B(5,3) and C(-3, -2)
Thus;
Median of AB is; D = (1 + 5)/2, (5 + 3)/2
D = (3, 4)
Median of BC is; E = (5 + (-3))/2, (3 + (-2))/2
E = (1, 0.5)
Median of AC is; F ; (-3 + 1)/2, (-2 + 5)/2
F = (-1, 1.5)
Thus, the median lines will be;
CD, AE & BF.
Thus;
Equation of CD is;
(y - (-3))/(x - (-2)) = (-2 - 4))/(-3 - 3)
(y + 4)/(x + 2) = -6/-6
y - 4 = 1(x + 2)
y = 4 + x + 2
y = x + 6
Equation of AE;
(y - 5)/(x - 1) = (0.5 - 5)/(1 - 1)
(y - 5)/(x - 1) = -4.5/0
Cross multiply to get;
0(y - 5) = -4.5(x - 1)
-4.5x = -4.5
x = 1
Equation of BF;
(y - 3)/(x - 5) = (1.5 - 3)/(-1 - 5)
(y - 3)/(x - 5) = -1.5/-6
(y - 3)/(x - 5) = 1/4
y - 3 = ¼(x - 5)
y = ¼(x - 5) + 3
According to the synthetic division below, which of the following statements are true? Check all that apply
The true statements are A , B , E
What is division?It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.
Here, In the synthetic calculation we use the coefficient of the dividend
with the factors of the function
∴ 2 , -2 , -12 are the coefficient of the dividend 2x² - 2x - 12
∵ The divisor is 3
∴ x = 3 is a root of F(x) = 2x² - 2x - 12
∵ x = 3 is the root of F(x) = 2x² - 2x - 12
- Subtract the two sides by 3
∴ x - 3 = 0
∴ (x - 3) is a factor of the dividend F(x) = 2x² - 2x - 12
- The quotient is the last line of the synthetic division
∴ The coefficients of quotient are 2 , 4
- The quotient is 1 degree less than the dividend
∵ The degree of the dividend is 2
∴ The degree of the quotient is 1
∴ The quotient is 2x + 4
* Lets check the answers to chose the write statements
A. The number 3 is a root of F(x) = 2x² - 2x - 12 ⇒ true
B. (x - 3) is a factor of 2x² - 2x - 12 ⇒ true
E. (2x² - 2x - 12) ÷ (x - 3) = 2x + 4 ⇒ true
Thus, the true statements are A , B , E.
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Can anyone help since im struggling with finding the answer!
==========================================================
Explanation:
You'll need the chain rule for this one.
[tex]y = 3x^3 + 4x\\\\\frac{d}{dt}(y) = \frac{d}{dt}\left(3x^3 + 4x\right)\\\\\frac{dy}{dt} = \frac{d}{dt}\left(3x^3\right) + \frac{d}{dt}\left(4x\right)\\\\\frac{dy}{dt} = 3\frac{d}{dt}\left(x^3\right) + 4\frac{d}{dt}\left(x\right)\\\\\frac{dy}{dt} = 3*3\left(x^2\right)*\frac{dx}{dt} + 4\frac{dx}{dt}\\\\\frac{dy}{dt} = 9x^2\frac{dx}{dt} + 4\frac{dx}{dt}\\\\\frac{dy}{dt} = (9x^2+4)\frac{dx}{dt}\\\\[/tex]
Now apply substitution
[tex]\frac{dy}{dt} = (9x^2+4)\frac{dx}{dt}\\\\\frac{dy}{dt} = (9*4^2+4)*2\\\\\frac{dy}{dt} = 296\\\\[/tex]
Answer:
296
Step-by-step explanation:
I just did the math and I also got 296.
The expression y2 – 10y + 24 has a factor of y – 4. What is another factor of y2 – 10y + 24?
y – 20
y – 14
y – 8
y – 6
Answer:
Step-by-step explanation:
If we divide 24 by 6, we get 4, which is the other factor of 24 when given the one factor of 6. Same goes here. In order to find out what the other factor of [tex]y^2-10y+24=0[/tex] is when given one factor of y - 4, we simply divide the second degree polynomial by y - 4 to get the quotient. The quotient, then, is the other factor. Synthetic division is the easiest way to do this.
If y - 4 is the factor, then by the Zero Product Property, y - 4 = 0 and y = 4. Setting up synthetic division:
4| 1 -10 24
____________
The rule is to start by bringing down the first term, multiplying it by the number outside, then putting that product up under the next term in line:
4| 1 -10 24
4
1
Then add the column, multiply the sum by the number outside, and put that product up under the next term in line:
4| 1 -10 24
4 -24
1 -6
And add the last column and that is the remainder. We get a 0 remainder. That means that y - 4 goes evenly into the polynomial and the other factor we are looking for is found in the numbers under the addition line. These numbers are the leading coefficients of the depressed polynomial, the polynomial that serves as the other factor: 1y - 6.
Therefore, the 2 factors that multiply together to give us [tex]y^2-10y+24=0[/tex] are (y - 4)(y - 6) and we can check ourselves by multiplying this out by FOILing to see if the result is the polynomial we started with. It is, so we're all done!
Answer:
its ( y-6 )
Step-by-step explanation:
well if you use the FOIL method you will get that answer. also i took the test and got a 100 so there u go.
A man sold a ratet for Rs 252 at 5% pofi't percent is the profit?
Answer:
Step-by-step explanation:
Selling price (SP) = Rs. 252
Profit% = 5%
[tex]CP=\frac{100}{100+profit}*SP\\\\\ = \frac{100}{105}*252\\\\[/tex]
CP = Rs. 240
Profit = 252 - 240 = Rs. 12
the distance between the points (tan a, 1) , (0,2)
Answer:
Answer
Step-by-step explanation:
please like and mark me brainlist
Holly invited her friends to her pool party. She decided to add trail mix to the snack menu. In the trail mix, the ratio of cups of peanuts to cups of raisins is 6:4. How many cups of raisins would be needed for a mix that included 9 cups of peanuts
Answer:my dog is cute
Step-by-step explanation:because
please help,
all i have is 16 x 33 = 528cm2 ?!!!
Answer:
732 m^2
Step-by-step explanation:
Find the area of the full rectangle
33*24 =792
Find the area of the triangle
24-16 = 8
33 -18 =15
The area of the triangle is
A = 1/2 bh = 1/2 ( 15)(8) = 60
Subtract the triangle from the rectangle
792 - 70=732 m^2
Answer:
732 [tex]m^2[/tex]
Step-by-step explanation:
First we can find the area of the shape if the triangle wasn't there. That would be:
24×33=792.
Then, we can find the area of the triangle to subtract that from the total.
The formula for the area of a triangle is [tex]A=\frac{1}{2} bh[/tex].
So [tex]A=\frac{1}{2} (8)(15)[/tex]
I found the base of the triangle by subtracting 16 from 24.
I found the height of the triangle by subtracting 18 from 33.
Now, solve the equation.
[tex]A=\frac{1}{2}( 120)[/tex]
A=60
Then finally, Subtract 60 from 792.
You get 732.
I hope this helps!
Find DC, given that line AD is the angle bisector of
Answer:
2
Step-by-step explanation:
because line a d divided the triangle ABC is into equal parts therefore line BD is equal to line DC which is equal to 2
A shopkeeper buys TVs for Nu 15000 and marks them up 15% to sell them. What is the mark up amount? *
[tex] \\ \sf \longmapsto \: 15000 \times 15\% \\ \\ \sf \longmapsto \: 15000 \times \frac{15}{100} \\ \\ \sf \longmapsto \: 150 \times 15 \\ \\ \sf \longmapsto \: 2250[/tex]
Markup amount is 2250Nu
There is a sales tax of $9 on an item that costs $120 before tax. The sales tax on a second item is $19.05. How much does the second item cost before tax?
Anything helps! :)
Answer:
254
Step-by-step explanation:
Divide 9 by 120, to get 0.075
Divide 19.05 by 0.075
Jalil and Victoria are each asked to solve the equation ax – c = bx + d for x. Jalil says it is not possible to isolate x because each x has a different unknown coefficient. Victoria believes there is a solution, and shows Jalil her work:
ax – c = bx + d
ax – bx = d + c
x (a – b) = d + c
x = x equals StartFraction d plus c Over a minus b EndFraction.
How can Victoria justify Step 3 of her work?
Answer:
A: Rewrite the expression on the left using the distributive property.
!!ASAP!!
1.
25
40
75
2.
40
75
140
Answer:
C= 40
D= 75
Alternate interior angle
○●○●○●○●○
Hope it helps...
Have a great day!!!
What is this equation rewritten in logarithmic form?
9X = 3
A. log 3 = x
B. log, 3 = 9
C. log3 9 = x
D. log3 x = 9
Answer:
A. log9 3=x
Step-by-step explanation:
The logarithmic form with base 9 is log₉ 3 = x.
The correct option is A.
The equation 9ˣ = 3 can be rewritten in logarithmic form by identifying the base and the result of the exponential operation. In this case, the base is 9, the result is 3, and the exponent is x.
The logarithmic form with base 9 is log₉ 3 = x.
Option A, log₉ 3 = x, is the correct representation of the equation in logarithmic form.
The logarithmic form states that the logarithm of a number (3 in this case) to a specific base (9 in this case) is equal to the exponent (x in this case).
In the equation, 9ˣ = 3, the logarithmic form log₉ 3 = x indicates that the logarithm of 3 with base 9 is equal to x. This means that 3 is the result of raising 9 to the power of x.
Therefore, option A, log₉ 3 = x, is the correct answer representing the equation 9ˣ = 3 in logarithmic form.
To learn more about the logarithms;
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Use proportional reasoning to solve for the missing value in each of the following scenarios. Enter a numerical answer only.
1.) If a business jet burns 300 gallons of gasoline per hour, it burns____gallons of gasoline in a three hour flight.
2.) On average, one gallon of gasoline weights approximately six pounds. Fifty gallons of gasoline weighs____pounds.
3.) For every one yard, there are thirty-six inches. 2,124 inches =_______ yards
4.) A person who weighs 240 pounds burns 180 calories per mile of running.A person who weighs_____ pounds, burns thirty-six calories while running one mile.
5.) A rice casserole recipe serves four people and requires two tablespoons of butter. A rice casserole that requires six (6) tablespoons of butter serves____ people.
Answer:
1.) 900
2.) 300
3.) 59
4.) 48
5.) 12
Step-by-step explanation:
1.) 300 x 3 = 900
2.) 50 x 6 = 300
3.) 2,124 / 36 = 59
4.) 180 / 36 = 5 | 240 / 5 = 48
5.) 6 / 2 = 3 | 4 x 3 = 12
Hope this helps.
If there is something wrong, please let me know.
Proportional reasoning refers to the ability to compare and analyze relationships between two or more quantities that change in a consistent way. It involves understanding the concept of proportionality and applying it to solve problems.
1.) If a business jet burns 300 gallons of gasoline per hour, it burns 900 gallons of gasoline in a three-hour flight. This can be calculated by multiplying the burn rate of 300 gallons per hour by the duration of the flight, which is three hours.
2.) On average, one gallon of gasoline weighs approximately six pounds. Therefore, fifty gallons of gasoline weighs 300 pounds. This can be calculated by multiplying the weight of one gallon (six pounds) by the quantity of fifty gallons.
3.) For every one yard, there are thirty-six inches. To find the number of yards in 2,124 inches, we divide 2,124 by 36. The result is 59 yards. This can be calculated by dividing the total number of inches by the conversion factor of thirty-six inches per yard.
4.) A person who weighs 240 pounds burns 180 calories per mile of running. A person who weighs 48 pounds, burns thirty-six calories while running one mile. To find the number of pounds for which the person burns thirty-six calories while running one mile, we can set up a proportion. If we let x represent the weight in pounds, the proportion would be: 240 pounds / 180 calories = x pounds / 36 calories. Solving for x gives us x = 48 pounds.
5.) A rice casserole recipe serves four people and requires two tablespoons of butter. If a rice casserole requires six tablespoons of butter, it serves twelve people. This can be determined by setting up a proportion: 4 people / 2 tablespoons = 12 people / 6 tablespoons. Solving for the unknown number of people gives us 12 people.
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Which situation would be represented by zero?
A) a $3 loss and à $4 profit
B) a $3 loss
C) a $4 loss and a $4 profit
D) a $4 profit
Pls help me I’m timed, I’ll give brainliest
Answer:
C) a $4 profit and $4 loss is the correct answer.
The formula for centripetal acceleration, a, is given by this formula, where v is the velocity of the object and r is the object's distance from the center of the circular path: . Solve the formula for r.
Answer:
v = √ar
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION;
The formula for centripetal acceleration, a, is given below, where v is the velocity of the object and r is the object's distance from the center of the circular path. Solve the formula for the velocity. the formula is a= v^2/ r
the given formula is (a= v^2/ r) .....eqn(1)
Where
a=centripetal acceleration
r = object's distance
We were told to find velocity (v)
From eqn(1) we can cross multiply, then we have
a.r=v^2 ...................eqn(2)
Then we can make (v^2) the subject of the formula, we have
(v^2) = ar
We can make "v" subject of the formula, then we have
v = √ a*r
Answer:
r = v^2/a
Step-by-step explanation:
1. Which of the following expressions are equivalent to? Select all that apply. A. 31 . 36 B. 31 . 35 C. 3-2 . 3-4 D. 32 . 3-8 E. 3 • 3-6 F.3-1 . 3-5
Answer: A and C
Step-by-step explanation:
UR SO COOL IF UOU ANSWERRR PLEASE ANSWERRRR
Answer:
1/6 is less than 1/2
Step-by-step explanation:
1/6 is close to 0
8/9 is close to 1
1/6 is less than 1/2
triangles help pls!!
Answer:
x = 60
Step-by-step explanation:
The single dashed line represents congruent side lengths.
If every side of a triangle has a single dashed line then all of the sides are congruent meaning that the triangle is an equilateral
Equilateral triangles have all congruent side lengths and angles
In an equilateral triangle each angle has a measure of 60 degrees
So x = 60
Answer:
Step-by-step explanation:
A parallelogram is divided into two triangles, both triangles having equal sides.
So triangles are equilateral..In equilateral triangles, the angles are also equal..the interior angles of a triangle are 180 degrees..
180 ÷ 3 = 60 degree---> x:60°
Can someone help me with this math homework please!
Step-by-step explanation:
the answer is
the Value of b to 2
Can someone help me by please
=============================================================
Explanation:
10% in decimal form is 0.10
25% in decimal form is 0.25
The jump from 0.10 to 0.25 is "times 2.5" since (0.25)/(0.10) = 2.5
This means that we have 2.5 times as many apples compared to oranges.
If we have 2 oranges, as mentioned in every answer choice, then we must have 2*2.5 = 5 apples.
Based on this, the answer is either A or B.
----------------
65% turns into 0.65
The jump from 0.10 to 0.65 is 6.5 since (0.65)/(0.10) = 6.5
So we have 6.5 times as many pears as oranges.
If we had 2 oranges, then we have 2*6.5 = 13 pears
----------------
To summarize, we have:
2 oranges, 5 apples, 13 pears.
The answer is therefore choice A
Which of the following contains a variable?
A. He scored a 95 on the test.
B. The bug crawled 15 inches per second.
C. The area is 56 square centimeters.
D. Ana is 3 years older than Mark.
Answer:
D. Ana is 3 years older than Mark.
Step-by-step explanation:
We do not know how old Mark is. That is the variable
Can someone help me with this math homework please!
Answer:
[tex][-2.5,-2][/tex]
[tex][-2,-1.5][/tex]
[tex][1.5,2][/tex]
[tex][2,2.5][/tex]
------------------------
Hope it helps...
Answer:
B, D, E
Step-by-step explanation:
The values in the answer choices are x-values, meaning on the x-axis.
B: [-2, -1.5]
From -2 to -1.5, the graph goes down from left to right, so it's decreasing.
D: [1.5, 2]
From 1.5 to 2, the graph goes down from left to right, so it's decreasing.
E: [2, 2.5]
From 2 to 2.5, the graph does down from left to right, so it's decreasing.
Hope that helps (●'◡'●)
i don't know just curious do you guys still got school?
yes i do got school
and what about you
Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.
Which choice represents the sample space, S, for this event?
S = {PQR}
S = {PQR, PRQ, QPR, QRP, RPQ, RQP}
S = {PQ, PR, QR}
S = {PQ, QP, PR, RP, QR, RQ}
Answer:
S = {PQ, QP, PR, RP, QR, RQ}
Step-by-step explanation:
We have 3 friends:
Patty (who we can represent with the letter P)
Quinlan (who we can represent with the letter Q)
Rashad (who we can represent with the letter R)
There are two positions, that can be represented as:
First-Second.
Where "first" refers to the student whose name is chosen first, this student will be the president.
"second" refers to the student whose name is chosen second, this student will be the vice president.
For example:
PQ
refers for the case where Patty is the president and Quinlan is the vice-president.
Notice that PQ is different than QP.
The sample space will be the set of all the possible combinations of the elements (P, Q, and R) of the form First-Second, which are just the permutations:
PQ, QP, PR, RP, QR, RQ
Then the sample space is:
S = {PQ, QP, PR, RP, QR, RQ}
The correct option is the last one.
Answer:
D. S = {PQ, QP, PR, RP, QR, RQ}
Which angles are adjacent to each other?
• Angle KGD and Angle AEB
• Angle BEC and Angle AEB
• Angle AEB and Angle ECU
• Angle JCI and Angle KGD
Answer:
Step-by-step explanation:
adjacent angles have a common vertex and a common ray
∠BEC and ∠AEB (common vertex E common ray EB)
Solve the equation for x: (4x+38) + (2x-18)=180
Answer:
80/3
Step-by-step explanation:
try mathw4y it helps alot.
Answer:
x = 80/3
Step-by-step explanation:
(4x+38) + (2x-18)=180
Combine like terms
6x +20 = 180
Subtract 20 from each side
6x+20 -20 = 180-20
6x = 160
Divide by 6
6x/6 = 160/6
x = 80/3
Mrs. Bajracharya sold a 'Palpali Dhaka Topi' for Rs 870 and made a profit of 16%. Find her buying price of the 'Dhaka Topi'. And how much is her actual profit?
Answer:
Buying price = x = Rs 750
Profit = Rs 120
Step-by-step explanation:
Buying price = x
Selling price = Rs 870
Profit = 16% of x
Profit = selling price - cost price
16% of x = 870 - x
0.16 * x = 870 - x
0.16x = 870 - x
0.16x + x = 870
1.16x = 870
x = 870 / 1.16
x = 750
Buying price = x = Rs 750
Profit = 16% of x
= 0.16 * Rs 750
= Rs 120
Profit = Rs 120
Help me out hhhhhhhjjnjnfd
since its the same you will have to multiple it all to get the answer
help please i’ve been in here for hours looking for answers
Answer:the 2nd row, x=0, f(x)=2
Step-by-step explanation:
When x=0, the line touches the y-axis because the f(x) has a value. therefore when x=0, y=2
you'll understand better if you sketch it out
