y = -x - 1 is the equation of the line that passes through (2,-3) and is perpendicular to y = x - 5
Solution:
Given that we have to write the equation of the line that passes through (2,-3) and is perpendicular to y = x - 5
The equation of line in slope intercept form is given as:
y = mx + c ------ eqn 1
Where, "m" is the slope of line and "c" is the y intercept
Given equation of line is:
y = x - 5
On comparing the above equation with eqn 1,
m = 1
We know that,
Product of slope of line and slope of line perpendicular to given line is equal to -1
Therefore,
[tex]1 \times \text{ slope of line perpendicular to given line } = -1\\[/tex]
Slope of line perpendicular to given line = -1
Now we have to find the equation of line with slope -1 and passing through (2, -3)
Substitute m = -1 and (x, y) = (2, -3) in eqn 1
-3 = -1(2) + c
-3 = -2 + c
c = -3 + 2
c = -1
Substitute m = -1 and c = - 1 in eqn 1
y = -x - 1
Thus the equation of line is found
The sum of 7 and the product of a number x and 12
Answer:
-7/12
Step-by-step explanation:
An equation can be made out of this problem.
Sum means adding, so in this problem, you are adding 7 to the product of x and 12.
Product means multiplying, so you are multiplying x by twelve to get 12x.
Since you are adding all of this to 7, you get the equation 7 + 12x = 0.
Now, you just need to solve for x by subtracting the 7 over, giving you 12x = -7.
Now, to isolate x, divide both sides by 12. The twelves on the left cancel each other out, leaving you with -7/12.
A test is worth 50 points. Multiple-choice are worth 1 point and short answer questions are worth 3 points. If a test has 20 questions how many multiple choice questions are there
Answer:
5 multiple choice questions
Step-by-step explanation:
Write equations to represent the situation.
let "x" be the number of multiple choice questions
let "y" be the number of short answer questions
Equation for the total number of questions:
x + y = 20 # of multiple choice questions + # of short answer questions
Equation for the total points: (Multiply the type of question with how many points you get.)
x + 3y = 50 You don't need to write '1' beside 'x' for multiplying by 1.
The system of equations we need to solve is:
x + y = 20 and x + 3y = 50
We can solve using the substitution method.
Rearrange x + y = 20 to isolate one variable.
Isolate 'y'.
x + y = 20
x - x + y = 20 - x Subtract 'x' from both sides
y = 20 - x
Take the other equation x + 3y = 50. You can replace 'y' with the equation that equals 'y' that we got when rearranging.
Substitute y for 20 - x
x + 3y = 50
x + 3(20 - x) = 50 Use distributive property. Multiply the 3 outside the bracket by each number inside the bracket.
x + 60 - 3x = 50 Combine like terms. 'x' and '-3x' are alike because they both have 'x'.
60 - 2x = 50 Start isolating 'x'.
60 - 60 - 2x = 50 - 60 Subtract 60 from both sides.
-2x = 50 - 60 60-60 cancels out on the left side.
-2x = -10
-2x/-2 = -10/-2 Divide both sides by -2 to isolate 'x'.
x = -10/-2 -2x/-2 becomes 'x'. -2/-2 cancels out.
x = 5 Number of multiple choice questions
Therefore there are 5 multiple choice questions.
If you needed the number of short answer questions too, you would substitute x for 5 in any of the other equations.
Write an equivalent expression for -3t+4q+5t-7q
Answer:
The equivalent expression can be given as:
⇒ [tex]2t-3q[/tex]
Step-by-step explanation:
Given expression:
[tex]-3t+4q+5t-7q[/tex]
To write an equivalent expression:
Solution:
In order to write an equivalent expression, we will combine the like terms. By like terms, we mean the terms with the same variable constant.
For example : [tex]5x[/tex] and [tex]-3x[/tex] are like terms.
We have:
[tex]-3t+4q+5t-7q[/tex]
Combining like terms :
⇒ [tex]-3t+5t+4q-7q[/tex]
⇒ [tex]2t-3q[/tex]
Thus, the equivalent expression can be given as:
⇒ [tex]2t-3q[/tex]
select the correct answer
Answer:
???
Step-by-step explanation:
Where's the problem/question?
True or False: In a correlation coefficient, a weak correlation means that the line does not fit the data well.
True).
False).
Answer:
True
Step-by-step explanation:
Write 15/45 as unit rate
Answer:
Step-by-step explanation:
15/45 = 1/3 {giving by 15th table}
= 0.33
Match each picture to its name.
Answer:
line PQline PQ+ lineQR= line PRPQ moves in opposite directions point PP and Q moves in the same directionData;
PQMatching the Line or Points1) Line P to Q can be represented as
[tex]--\\PQ[/tex]
2)
The Line P, Q and R will be represented as
[tex]PQ + QR = PR[/tex]
3)
The point P and Q will be represented as
[tex]< \to \\PQ[/tex]
With the sign above it's head
4)
point P will be represented as
[tex].P[/tex]
5)
The point PQ moving towards in the right hand side can be represented as
[tex]\to\\PQ[/tex]
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Toms garden is 8 acres. Two fifths is corn. Of that, three tenths is early corn and one tenth is late corn. How many acres of early corn does he have ?
Answer:
He have 0.96 acres of early corn.
Step-by-step explanation:
Given:
Toms garden is 8 acres. Two fifths is corn.
Of that, three tenths is early corn and one tenth is late corn.
Now, to find the acres of early corn.
Total garden = 8 acres.
Total Corn in garden = [tex]\frac{2}{5}\ of\ 8=\frac{2}{5} \times 8=\frac{16}{5}[/tex] acres.
As, given of the total corn in garden, three tenths is early corn.
Now, to get the early corn he have:
= [tex]\frac{3}{10} of \frac{16}{5}[/tex]
= [tex]\frac{3}{10} \times \frac{16}{5}[/tex]
= [tex]\frac{48}{50}[/tex]
= [tex]0.96\ acres.[/tex]
Therefore, he have 0.96 acres of early corn.
Pls help me with this question no. 14 asap. will mark brainliest
============================================================================
Work Shown for part (i)
One base of triangle PQR is QR = 4
If the base is QR, then the height is PL = 5, which is perpendicular to QR.
area of triangle PQR = (1/2)*base*height
area of triangle PQR = (1/2)*QR*PL
area of triangle PQR = (1/2)*4*5
area of triangle PQR = 10
---------------------------------
Work Shown for part (ii)
Another base for triangle PQR is PR = 8
Imagine rotating triangle PQR so that PR is completely horizontal and flat.
Note: the diagram implies that MR = 8, but instead it's actually PR = 8
For the base PR, the perpendicular height is QM, which we'll label as x for now
area of triangle PQR = (1/2)*base*height
area of triangle PQR = (1/2)*PR*QM
area of triangle PQR = (1/2)*8*x
area of triangle PQR = 4*x
From part (i), we can set 4x equal to 10 since we know the triangle PQR has area 10 square cm.
4x = 10
4x/4 = 10/4
x = 10/4
x = (5*2)/(2*2)
x = 5/2
x = 2.5
a piggy bank has $6.95 and contain only nickels and dimes. If there are a total of 91 coins, how many nickels are there
There are 43 nickels in the piggy bank.
Step-by-step explanation:
Given,
Amount in piggy bank = $6.95 = 6.95*100 = 695 cents
Total coins = 91
One nickel = 5 cents
One dime = 10 cents
Let,
x be the number of nickels
y be the number of dimes
According to given statement;
x+y=91 Eqn 1
5x+10y=695 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=91)\\10x+10y=910\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](10x+10y)-(5x+10y)=910-695\\10x+10y-5x-10y=215\\5x=215[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{215}{5}\\x=43[/tex]
There are 43 nickels in the piggy bank.
Keywords: linear equation, elimination method
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Final answer:
To find the number of nickels in the piggy bank, you can set up a system of equations. By solving the system, it is determined that there are 43 nickels.
Explanation:
To find the number of nickels in the piggy bank, we need to set up a system of equations. Let's assume that the number of nickels is 'x' and the number of dimes is 'y'.
We know that there are a total of 91 coins, so we can write the equation: x + y = 91.
We also know that the value of the nickels is 5 cents and the value of the dimes is 10 cents. The total value of the coins is $6.95, so we can write the equation: 5x + 10y = 695.
Solving this system of equations will give us the number of nickels.
First, let's multiply the first equation by 5 to eliminate 'x'.
5x + 5y = 455
Next, subtract this new equation from the second equation.
(5x + 10y) - (5x + 5y) = 695 - 455
5y = 240
y = 48
Finally, substitute the value of 'y' back into the first equation to find 'x'.
x + 48 = 91
x = 43
Therefore, there are 43 nickels in the piggy bank.
Department A occupies 10,000 square feet, Department B occupies 6,000 square feet, and Department C occupies 4,000 square feet. What percent of the total overhead expense should be allocated to Department B?
60 percent
40 percent
30 percent
10 percent
Answer:
The correct answer is C. 30 percent
Step-by-step explanation:
What percent of the total overhead expense should be allocated to Department B?
For answering this question, we should make the following calculations this way:
Company's footprint = Department A + Department B + Department C
Company's footprint = 10,000 + 6,000 + 4,000
Company's footprint = 20,000 square feet
Overhead expense allocated to Department B = Department B footprint/Company's footprint
Overhead expense allocated to Department B = 6,000/20,000
Overhead expense allocated to Department B = 0.3 = 30%
The correct answer is C. 30 percent
KKrutika, Alex and Gordon share £49 in a ratio 3:3:1. How much money does each person get?
Answer:
Krutika get 21
Alex get 21
Gordon get 7
Step-by-step explanation:
Given: Total amount= 49
Ratio= 3:3:1
Now, finding the amount received by Krutika, Alex and Gordon.
First, lets find the sum of ratio
Sum of ratio= [tex]3+3+1= 7[/tex]
We know now that amount will be distributed in the following fraction:
Krutika= [tex]\frac{3}{7}[/tex]
Alex= [tex]\frac{3}{7}[/tex]
Gordon= [tex]\frac{1}{7}[/tex]
∴ Amount received by Krutika= [tex]\frac{3}{7}\times 49= 21[/tex]
Alex,
Amount received by Alex= [tex]\frac{3}{7}\times 49= 21[/tex]
Gordon,
Amount received by Gordon= [tex]\frac{1}{7}\times 49= 7[/tex]
Hence, they get 21,21 and 7 respectively out of 49.
KKrutika and Alex each get £21, and Gordon gets £7.
Explanation:To find out how much money each person gets, you need to divide the total amount of money (£49) in the ratio of 3:3:1.
First, add up the parts of the ratio to find the total number of parts: 3 + 3 + 1 = 7.
Next, divide the total amount of money (£49) by the total number of parts (7) to find the value of one part: £49 ÷ 7 = £7.
Finally, multiply the value of one part (£7) by each part of the ratio to find out how much money each person gets: KKrutika and Alex each get £7 × 3 = £21, and Gordon gets £7 × 1 = £7.
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Rectangular prism has base area 522 square millimeters and height 31 millimeters. Find volume in cubic millimeter
Answer:
The volume in cubic millimeter is 16182.
Step-by-step explanation:
Given:
Rectangular prism has base area 522 square millimeters and height 31 millimeters.
Now, to find the volume in cubic millimeter.
Base area = 522 square millimeters.
Height = 31 millimeters.
Now, to get the volume we put formula:
[tex]Volume=base\ area\times height[/tex]
[tex]Volume=522\times 31[/tex]
[tex]Volume=16182\ cubic\ millimeter.[/tex]
Therefore, the volume in cubic millimeter is 16182.
one fourth of the students in Mrs. Bennett's class have blue eyes. Two eighths of the students have green eyes. Does the class have an equal number of students with blue and green eyes.
Yes
No
Answer:
Yes
Step-by-step explanation: 2/8 is eq equivalent to 1/4 when reduced to the lowest term(i.e form)
Yes, this is because 2/8 is equivalent to one fourth, this is because eighths are fourths cut in half, so, you only need two of them to make a one right.
Hope this helps, if not, comment below please!!!
In a triangle the length of two sides are 1.9m and 0.7m. What is the length of the third side, if you know that it should be a whole number?
Answer:
their sum: 2.8m
their difference: 1.2m
the third side's length should be smaller than their sum, larger than their difference
it could be: 1.3-1.4-1.5-1.6-1.7-1.8-1.9-2-2.1-2.2-2.3-2.4-2.5-2.6-2.7 but since it has to be a whole number, 2m is the only eligible answer.
Using the Pythagorean theorem, we can calculate the third side of the triangle considering both positions for the side: as the hypotenuse and one of the two remaining sides. In both cases, the result is rounded to a whole number due to the constraints of the question.
Explanation:In this case, we need to calculate the third side of the triangle based on the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, which can be written as: a² + b² = c². To find the possible lengths of the third side, we need to consider that it should be a whole number, and use both possible positions: once as a hypotenuse and once as the other side of the triangle.
If the third side is the longest (hypotenuse), then based on the Pythagorean theorem: (1.9m)² + (0.7m)² = c². The answer should be rounded to a whole number.
If the third side is not the longest one, then we could subtract the square of the shorter side from the square of the longer one: (1.9m)² - (0.7m)² = (c)². Again, the answer should be rounded to a whole number.
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At a track meet 2/7of the 756 competing athletes are sophomores. How many of the competing
athletes are sophomores? Round to the nearest athlete if necessary.
A. 204 athletes
B. 2,646 athletes
C. 108 athletes
D. 216 athletes
Answer:
D
Step-by-step explanation:
700/7= 100
100*2= 200
200+ (756-700)= 256
256 closest to 216 than to 204 or any other answer.
Answer:216.
Step-by-step explanation:
if ur doing the scantron so am i i hate it as much as you do
Expand the following expression.
5.9(21 - 3.54x)
A.
123.9x - 20.886
B.
26.9 - 9.44x
C.
20.886 + 123.9x
D.
123.9 - 20.886x
Answer:
D. 123.9 - 20.886x
Step-by-step explanation:
Using the distributive property, we find the expansion to be ...
5.9(21) +5.9(-3.54x) = 123.9 -20.886x
_____
The distributive property tells you ...
a(b+c) = ab +ac
The factor outside parentheses multiplies each of the individual terms inside parentheses.
An adult and five children rent skates. It costs $4 per adult for skates and a total of $16. What would be the equation?
Final answer:
The equation representing the total cost for an adult and five children renting skates, with the adult's rental at $4 and the total at $16, is 4 + 5x = 16.
Explanation:
The question is asking for an equation that represents the total cost for an adult and five children renting skates where the adult's rental costs $4 and the total cost is $16. To write this equation, we let x be the cost for renting skates for a child. Since there are five children, the cost for the children's skates is 5x. Adding the adult's cost, we have the total cost expressed as 4 + 5x = 16.
Explanation: We know that the cost for one adult is $4, so that's a fixed amount. Since we don't know the individual cost for a child's skate rental, that's our variable x. We have five children, so we multiply x by 5. Adding up the adult's cost and the children's cost gives us the total cost, which is $16, and thus we arrive at our final answer, 4 + 5x = 16.
Delia is hosting a BBQ. She buys a total of 50 burgers and Hot Dogs for $90. Delia pays $2 per burger and $1.50 per Hot Dog. Write a system of linear equations to find the number x of burgers and the number y of Hot Dogs Delia buys. Solve the linear system by substitution. Please help-
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
False
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b
where m is the slope and c the y- intercept
What is 16 2/3% of 96 lamps
Answer:
16 lamps
Step-by-step explanation:
we know that
96 lamps represent the 100%
so
using proportion
Find out how many lamps represent 16 2/3%
but first convert to an improper fraction
[tex]16\frac{2}{3}\%=\frac{16*3+2}{3}=\frac{50}{3}\%[/tex]
Apply proportion
[tex]\frac{96}{100\%}=\frac{x}{\frac{50}{3}\%} \\\\x= (\frac{50}{3})(96)/100\\\\x=16[/tex]
Answer:
16 lamps
Step-by-step explanation:
At time t = 0, a football player kicks a ball from the point A with position vector (2i + j) m on a horizontal football field. The motion of the ball is modelled as that of a particle moving horizontally with constant velocity (5i + 8j) m s–1.
Find
(a) the speed of the ball,
(b) the position vector of the ball after t seconds.
The point B on the field has position vector (10i + 7j) m.
(c) Find the time when the ball is due north of B.
At time t = 0, another player starts running due north from B and moves with constant speed v m s–1. Given that he intercepts the ball,
(d) find the value of v.
(e) State one physical factor, other than air resistance, which would be needed in a refinement of the model of the ball’s motion to make the model more realistic.
Final answer:
To solve these physics problems, we used vector mathematics to find the speed of the ball, its position after a certain time, the time it aligns with a certain point, and the speed of a player to intercept it. Additionally, we considered gravity as a factor for a more realistic model of the ball's motion.
Explanation:
Speed of the ball: To find the speed of the ball, we calculate the magnitude of the velocity vector (5i + 8j) m/s using the Pythagorean theorem, which results in \(\sqrt{5^2 + 8^2} = \sqrt{89}\) m/s.
Position vector after t seconds: We calculate the position vector at time t by using the initial position vector (2i + j) m and adding the product of the velocity vector and time t. This yields the formula (2i + j) + t(5i + 8j).
Time when the ball is due north of B: For the ball to be due north of B, their i-components must be equal. Given B's position vector is (10i + 7j), we set the i-component equal to 10 and solve for t, getting t = (10 - 2)/5 = 1.6 seconds.
Value of v for the running player: Since the player intercepts the ball after 1.6 seconds, and the ball's j-component of the velocity is 8 m/s, the player's velocity v must be the distance covered in the j direction divided by time, which is (8j - 7j)/1.6 = 0.625 m/s.
Physical factor for a more realistic model: One physical factor to make the model more realistic could be the effect of gravity on the ball's trajectory, which would cause the ball to follow a parabolic path rather than a straight line.
Find x.
pleaaaaase help
Answer:
x = 12
Step-by-step explanation:
1. Set up a proportion:
32 (32 + x)
------ = ------------
24 (24 + 9)
2. Cross-multiply & solve for x:
32*(24 + 9) = 24*(32 + x)
1056 = 768 + 24x
288 = 24x
12 = x
x = 12
For each linear system,tell whether you would multiply the terms in the first or second equation in order to eliminate one of the variables.Give the number by which you could multiply.
X+3y=-14, 2x + y =-3
We can multiply first equation x + 3y = -14 by 2 to get rid of varibale "x"
Solution:
Given that, the system of equations are:
x + 3y = -14 ----- eqn 1
2x + y = -3 --------- eqn 2
We can solve by elimination method
For doing elimination, we have to make the any one of coefficient of variable same
Here, in eqn 1 we have 1 as coefficient for "x"
In eqn 2, we have 2 as coeficient for "x"
So, we can multiply eqn 1 by 2, to get rid of "x"
2(x + 3y = -14)
2x + 6y = -28 ------- eqn 3
If we subtract eqn 2 from eqn 3, we will get the solution
2x + 6y = -28
2x + y = -3
( - ) ----------------
5y = -25
y = -5Substitute y = -5 in eqn 1
x + 3(-5) = -14
x -15 = -14
x = 1Thus the solution is x = 1 and y = -5. So we have multiplied equation 1 by 2 to get of varibale "x" and solved the equations
John is driving around town. When he reaches the gas station, he notes that he has traveled 20 miles. He reaches home 2 hours later and notes that he has traveled 30 miles.
If d represents the distance and t represents the time, in hours, John has traveled since the gas station, which of the following equations can be used to model this situation?
Answer:
[tex]d=5t+20[/tex]
Step-by-step explanation:
The equation that will model this situation will be of the form
[tex]d=mt+b[/tex]
where [tex]t[/tex] is the time in hours john has traveled since the gas station, and [tex]d[/tex] is the distance.
Now we know that John has already traveled 20 miles when he is at the gas station, this means at [tex]t=0[/tex], [tex]d=20[/tex]; or
[tex]20=m(0)+b[/tex]
[tex]\boxed{b=20}[/tex]
Thus we have
[tex]d=mt+20[/tex].
Now we need to figure out [tex]m.[/tex]
When John reaches home 2 hours later he notes that he has traveled 30 miles, which means he has traveled 30 - 20 = 10 miles; thus we have
[tex]m= \frac{\Delta d}{\Delta t} =\frac{10 miles}{2hours} =5[/tex]
[tex]\boxed{m=5}[/tex]
Now we have the full equation:
[tex]\boxed{d=5t+20}[/tex]
Liam wants to buy a car. He has $100. The car that he wants costs $120,000. His parents is willing to give him $1,300. How long will it take him to get enough money to buy the car?
The equation A = x(x-4) describes the area, A, of a rectangular flower garden, where x is the width in feet.
What would be the width in feet of the flower garden if the area is 12 square feet?
A.2
B.6
C.4
D.7
Answer:
The flower garden width would be 6 ft
Step-by-step explanation:
A = 12 ft^2 = x(x + 4) becomes:
x^2 + 4x - 12 = 0, or (by completing the square) x^2 + 4x + 4 - 4 - 12 = 0
Thus, we have (x + 2)^2 - 16 = 0, or (x + 2)^2 = 16
Taking the square root of both sides yields x + 2 = ±4.
In this context only a positive x value makes sense: x = 2 + 4 => x = 6.
The flower garden width would be 6 ft. The other dimension would be 6 - 4, or 2, ft.
To find the width of the flower garden when the area is 12 square feet, the equation A = x(x-4) is used. Solving for x, the width of the flower garden is 6 feet.
To find the width of the flower garden when the area is 12 square feet:
Plug in A=12 into the equation: 12 = x(x-4)
Solve the equation for x by factoring or using the quadratic formula
The possible values for x are 6 and -2, but since width can't be negative, the width of the flower garden is 6 feet (B)
Sarah bought two t-shirts and one sweatshirt. The t-shirts cost $15.22 each. If Sarah spent a total of $67.94,how many dollars did the sweatshirt cost? Express your answer as a decimal to the nearest hundredth.
Answer:
111
Step-by-step explanation:
So firstly, you have two t-shirts, so you do 15.22*2=30.44. Then you use 67.94, and subtract 30.44, which is 37.5
Simple as that!!
Show how to use the distributive property to simplify 4(5+x)
Answer:
20+4x
Step-by-step explanation:
Distributive property is quite easy to learn... its just multiplication in an easier form to visualize once you're used to using it.
To first start this problem you want to use the number 4 in the expression 4(5+x). You then want to multiply 4 by both terms inside of the parentheses. So you would do both 4*5 and 4*x. You would then get 20+4x because 4*5=20 and 4*x is just put together as 4x.
Answer:
[tex]4(5+x)=20+4.x[/tex]
Step-by-step explanation:
Distributive property:-
The distributive property is one of the most frequently used properties in mathematics.
Distributive property
a(b+c) = a.b+a.c ((using multiplication of distributive law)
given
[tex]4(5+x) = 4.5+4.x[/tex]
[tex]4(5+x)=20+4.x[/tex]
5.3x − 8.14 + 3.6x + 9.8
Answer:
5.3x − 8.14 + 3.6x + 9.8
group the numbers on one side and the x's on the other
5.3x + 3.6x - 8.14 + 9.8
solve
8.9x + 1.66
Brainliest pls ;)
The given algebraic expression simplifies to 8.9x + 1.66 by combining like terms.
Explanation:The question you've asked appears to be a linear algebraic expression. Here is how you would simplify it. First, you should group like terms together. So, the equation becomes 5.3x + 3.6x - 8.14 + 9.8. You will add together the x-terms and the constants separately, resulting in 8.9x + 1.66. Therefore, the simplified form of the given algebraic expression is 8.9x + 1.66.
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