Answer:
slope of parallel line and perpendicular line are 5 and -1/5 espectively
equation of parallel and perpendicular line are y = 5x + 22 [tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex] respectively
Step-by-step explanation:
y = 5x - 4 is in the form
y = mx + c
where m is the slope of the line and c is the y intercept of thr line
therefore slope of the line = 5 and y intercept = -4
when an another line is parallel to the given line then the slope of both the lines are equal
therefore the slope the parallel line = 5
equation of a line passing through a given point [tex](x_{1} ,y_{1})[/tex] with slope m is given by [tex]y-y_{1} = m(x-x_{1} )[/tex]
given [tex](x_{1} ,y_{1})[/tex]= (-4,2)
therefore equation of line y-2 = 5(x+4)
therefore y = 2+ 5x+20
y = 5x + 22is the eqaution of required line.
when two lines are perpendiculer then
[tex]m_{1} m_{2}=-1[/tex]
where [tex]m_{1} and m_{2}[/tex] are slope of the lines therefore
m×5=-1
therefore m= [tex]\frac{-1}{5}[/tex]
therefore eqaution of line passing through (-4,2) and with slope m= [tex]\frac{-1}{5}[/tex] is given by [tex]y - 2= \frac{-1}{5} (x+4)[/tex]
[tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex]
We can see here that the line perpendicular to the given line, passing through (-4, 2), is (0, -6).
How we arrived at the solution?Let's first verify the given information and then find the point on the line perpendicular to the given line passing through (-4, 2).
Given line: y = 0.5x - 4
Slope of a line parallel to the given line:
The slope of the given line is 0.5. Parallel lines have the same slope. Therefore, the slope of a line parallel to the given line is also 0.5.
A point on the line parallel to the given line, passing through (-4, 2):
Since the slope of the parallel line is 0.5, and we know a point (-4, 2) that lies on it, we can find the equation of the parallel line using the point-slope form of a line.
Point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.
Substitute the values: y - 2 = 0.5(x + 4)
Now, let's find a point on the line perpendicular to the given line, passing through (-4, 2):
Slope of a line perpendicular to the given line:
Perpendicular lines have slopes that are negative reciprocals of each other. The slope of the given line is 0.5, so the slope of the line perpendicular to it is -1/0.5 = -2.
A point on the line perpendicular to the given line, passing through (-4, 2):
Using the point-slope form again, we can find the equation of the perpendicular line passing through (-4, 2).
Point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.
Substitute the values: y - 2 = -2(x + 4)
Now, we can find another point on the perpendicular line by setting x = 0:
y - 2 = -2(0 + 4)
y - 2 = -8
y = -6
So, another point on the line perpendicular to the given line, passing through (-4, 2), is (0, -6).
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Solve the following system of equations.
3x + 2y - 5 = 0
x = y + 10
Make sure there are NO SPACES in your answer. Include a comma in your answer.
ANSWER: {(
)}
Answer:
The solution is the point (5,-5)
Step-by-step explanation:
we have
[tex]3x + 2y - 5 = 0[/tex] -----> equation A
[tex]x = y + 10[/tex] -----> equation B
Solve the system by substitution
substitute equation B in equation A
[tex]3(y+10) + 2y - 5 = 0[/tex]
solve for y
[tex]3y+30 + 2y - 5 = 0[/tex]
[tex]5y=-25[/tex]
[tex]y=-5[/tex]
Find the value of x
[tex]x=5+ 10[/tex]
[tex]x=5[/tex]
therefore
The solution is the point (5,-5)
Find the product
(-3)(8)
Answer:
-24
Step-by-step explanation:
This is a simple multiplication problem. 8 times 3 is 24, and since one of the numbers is negative, the product (answer in multiplication) will be negative.
In multiplication and division of integers (positive and negative numbers), if the numbers have the same signs, the answer is ALWAYS positive, and if the numbers have different signs, the answer is ALWAYS negative.
Answer: -24
Step-by-step explanation: To multiply (-3)(8), it is important to understand that a negative times a positive is a negative so (-3)(8) is -24.
The number of students enrolled at a college is 12,000 and grows 4% each year. Complete parts (a) through (e).
a) The initial amount a is
.
Answer:
48000
Step-by-step explanation:
12000 students
4%
1 =annually
12×4×1= 48000
Answer:12,000
Step-by-step explanation:can’t give you one cuz I’m doing this in mathxl :p
Solve the system of equations using any method.
6x + 4y = −8
4x − 2y = 2
A) (11/7, 2/7)
B) (2/7, 11/7)
C) (-2/7, 11/7)
D) (-2/7, -11/7)
PLEASE HELP!!!!
Answer:
My answer what I came up with is B And B
A man gained rs. 3000 by selling a mobile set allowing 15 % discount on the marked price the loss would be rs. 8000. Find the marked price and cost price of a mobile set
Answer:
Marked price is Rs. 53333.33 and the cost price is Rs. 42333.33.
Step-by-step explanation:
Let Rs. x and Rs. y are the cost price and marked price of the mobile set respectively.
Now, the man has a loss of Rs. 8000 after giving a 15% discount on the marked price.
Therefore, 15% of y is 8000 i.e. [tex]8000 = \frac{y\times 15}{100}[/tex]
⇒ y = Rs. 53333.33
Now, the man gained Rs. 3000 by selling the mobile set allowing 15% discount on the marked price.
Therefore, the mobile set has the cost price = x = Rs. [(53333.33 - 8000) - 3000] = Rs. 42333.33 (Answer)
A cat is running away from a dog. After 5 seconds it is 16 feet away from the dog and after 11 seconds
it is 28 feet away from the dog. Let x represent the time in seconds that have passed and y represent the
distance in feet that the cat is away from the dog.
Answer:
18 feet
Step-by-step explanation:
Given:
A cat is running away from a dog.
After 5 seconds it is 16 feet away from the dog
After 11 seconds it is 28 feet away from the dog.
Let x represent the time in seconds that have passed and y represent the
distance in feet, so there are two points are formed such as (5, 16) and (11,28).
We will find the distance between dog and cat. by using distance formula of the two points.
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Now we substitute the given value in above equation.
[tex]d=\sqrt{(11-5)^{2}+(28-11)^{2} }[/tex]
[tex]d=\sqrt{(6)^{2}+(17)^{2} }[/tex]
[tex]d=\sqrt{36+289}[/tex]
[tex]d=\sqrt{325}[/tex]
[tex]d=18.08\ feet[/tex]
18.08 ≅ 18
So [tex]d=18\ feet[/tex]
Therefore the distance between dog and cat is 18 feet.
To find the linear equation for the distance between the cat and the dog, we calculate the slope with the given points and use it with one of the points to establish the equation y = 2x + 6. A graph can be drawn with the points (5, 16) and (11, 28) to visualize the cat's path.
The linear equation describing the distance the cat is from the dog in relation to time can be determined using the two given points: (5, 16) and (11, 28), where 'x' is the time in seconds and 'y' is the distance in feet.
We first find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values we get:
m = (28 - 16) / (11 - 5) = 12 / 6 = 2
This means for each second that passes, the cat is 2 feet further away from the dog. Next, we use one of the points and the slope to write the equation in point-slope form. Using the point (5, 16) we have:
y - 16 = 2(x - 5)
Expanding and simplifying this equation gives us:
y = 2x + 6
This is the linear equation that describes the distance of the cat from the dog over time. To draw a graph, we plot the two points given and draw the line that passes through them, which will represent the cat's path. The slope of 2 indicates that for every 1 second, the distance increases by 2 feet.
a certain triangle has two 45 degree angles what type of triangle is it
Answer:
most likely isosceles
Step-by-step explanation:
due to the fact that two angles are congruent and the other angle is probably not it would make it all isosceles triangle
A triangle with two 45-degree angles is a special type of triangle known as an isosceles triangle.
In a triangle, if two angles are congruent, then the opposite sides of those angles are also congruent. In an isosceles triangle, two sides are equal in length, and the angles opposite those sides are congruent. Since two angles of the triangle are 45 degrees each, their opposite sides are also equal in length, making it an isosceles triangle.
To the nearest tenth, what is the distance between the point (10, -11) and (-1, -5)
Answer:
≈ 12.5 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (10, - 11) and (x₂, y₂ ) = (- 1, - 5)
d = [tex]\sqrt{(-1-10)^2+(-5+11)^2}[/tex]
= [tex]\sqrt{(-11)^2+6^2}[/tex]
= [tex]\sqrt{121+36}[/tex]
= [tex]\sqrt{157}[/tex] ≈ 12.5 ( to the nearest tenth )
The following proof shows an equivalent system of equations created from another system of equations. Fill in the missing reason in the proof.
Statements Reasons
2x + 2y = 14
−x + y = 5 Given
2x + 2y = 14
y = x + 5 ?
Answer:
As addition property of equality clearly states that if we add the same number to both sides of an equation, the sides remain equal.
Step-by-step explanation:
[tex]2x + 2y = 14[/tex]
[tex]-x + y = 5[/tex] Add x in both sides (Addition Property of Equality)
[tex]2x + 2y = 14[/tex]
[tex]y = x + 5[/tex] Multiply both sides by 2
[tex]2x + 2y = 14[/tex]
[tex]2y = 2x + 10[/tex] Subtract 2x in both sides
[tex]+\left \{ {{2x + 2y=14} \atop {-2x + 2y=10}} \right.[/tex] ∵adding both equation
[tex]4y = 24[/tex] divide both sides by 4
[tex]y = 6[/tex]
Put the value of y = 6 to the equation [tex]-x + y = 5[/tex]
[tex]-x + 6 = 5[/tex] Subtract 6 from both sides
[tex]-x = -1[/tex] Change the sign
[tex]x = 1[/tex]
Keywords: Addition property of equality, reason, proof
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Select the correct answer from each drop-down menu.
A 4
7
15
B 15
4
7
C 15
7
4
Answer: The correct answer is: [C]: " [tex]15^{(7/4)}[/tex] " .
____________________________________
Step-by-step explanation:
____________________________________
Note the property for square roots in exponential form:
_____________________________________
→ [tex]\sqrt[a]{(b)^ c}[/tex] ; ↔ b[tex]b^{(c/a)}[/tex] ;
{ [tex]a\neq 0[/tex] ; [tex][a^{(b/c)}]\neq 0[/tex] ; [tex]c\neq 0[/tex] .}.
_____________________________________
As such, given:
→ [tex]\sqrt[4]{(15^7)}[/tex] ;
a = 15, b = 7, c = 4 .
→ [tex]\sqrt[4]{(15^7)}[/tex] ; ↔ [tex]15^{(7/4)}[/tex] ;
→ which corresponds to:
_____________________________________
Answer choice: [C]: " [tex]15^{(7/4)}[/tex] " .
_____________________________________
Hope this helps!
Wishing you well in your academic endeavors!
_____________________________________
-3x+7y=5x+2y−3x+7y=5x+2yminus, 3, x, plus, 7, y, equals, 5, x, plus, 2, y
Complete the missing value in the solution to the equation.
(-5,(−5,left parenthesis, minus, 5, comma
))
Answer:
The complete missing value in the solution to the equation is (-5,-8).
Step-by-step explanation:
Consider the provided equation.
[tex]-3x+7y=5x+2y[/tex]
We need to find the missing value of the coordinate; (-5__)
To find the missing value substitute x = -5 in above equation.
[tex]-3(-5)+7y=5(-5)+2y[/tex]
[tex]15+7y=-25+2y[/tex]
[tex]7y-2y=-25-15[/tex]
[tex]5y=-40[/tex]
[tex]y=-8[/tex]
Hence, the missing value is -8.
Thus, the complete missing value in the solution to the equation is (-5,-8).
Answer:
Step-by-step explanation:
-5, -8
Write the quadratic equation whose roots are 3 and 4, and whose leading coefficient is 2.
(Use the letter x to represent the variable.)
Step-by-step explanation:
equation-
(x-3) (x-4) =
[tex] {x }^{2} - 3x - 4x + 12 = {x}^{2} - 7x + 12[/tex]
Given the roots 3 and 4 of a quadratic equation, and the leading coefficient 2, the quadratic equation can be derived as 2x^2 - 14x + 24.
Explanation:To find a quadratic equation given its roots and leading coefficient, you use the factored form of a quadratic equation, x = (x - root1)(x - root2).
Given that the roots are 3 and 4, the equation takes the form of x = (x - 3)(x - 4). When you multiply this out, you get x^2 - 7x + 12.
The problem also states that the leading coefficient is 2, so we multiply our obtained equation by 2 to get: 2x^2 - 14x + 24.
So, the requested quadratic equation is 2x^2 - 14x + 24.
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I need help with algebra 2a
Answer:
31
Step-by-step explanation:
[tex]\bf \displaystyle\sum\limits_{j=1}^{10}~2j+7\implies \displaystyle\sum\limits_{j=1}^{10}~2j+\displaystyle\sum\limits_{j=1}^{10}~7\implies 2\displaystyle\sum\limits_{j=1}^{10}~j+\displaystyle\sum\limits_{j=1}^{10}~7 \\\\\\ 2\cdot \cfrac{10(10+1)}{2}~~+~~(10)(7)\implies 2\cdot 55+70\implies 110+70\implies 180[/tex]
when a positive number is multiplied by itself, the result is equal to 3 more than twice the original amount. What is the value of that number?
Hope it helps u..........
what number is 10 times as great as 7962
To find a number that is 10 times greater than 7962, we can multiply.
7,962 * 10 = 79,620
79,620 is 10 times greater than 7,962.
Best of Luck!
Answer:
79,620
Step-by-step explanation:
7,962 (10) = 79,620
Prove that ABCD is a square if a A(1,3) B(2,0) C(5,1) and D(4,4)
[tex]AB=BC=CD=AD = \sqrt{10}[/tex]
As all the sides have same length, ABCD is a square
Step-by-step explanation:
To prove ABCD a square we have to find the lengths of each side
So,
the distance formula will be used to find the lengths
The distance formula is:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now,
[tex]AB = \sqrt{(2-1)^2+(0-3)^2}\\= \sqrt{(1)^2+(-3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]
[tex]BC = \sqrt{(5-2)^2+(1-0)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]
[tex]CD = \sqrt{(4-5)^2+(4-1)^2}\\= \sqrt{(-1)^2+(3)^2}\\=\sqrt{1+9}\\=\sqrt{10}[/tex]
[tex]AD = \sqrt{(4-1)^2+(4-3)^2}\\= \sqrt{(3)^2+(1)^2}\\=\sqrt{9+1}\\=\sqrt{10}[/tex]
we can see that
[tex]AB=BC=CD=AD = \sqrt{10}[/tex]
As all the sides have same length, ABCD is a square
Keywords: Distance formula, square
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how can you use functions to solve real world problems ??
Answer:ioj;i;
hStep-by-step explanation:
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Given the following diagram, if m ∠ COF = 150°, then m ∠ BOC = AD ⊥ BF
150 °
90 °
45 °
30 °
Answer:
[tex]m\angle BOC=30^o[/tex]
Step-by-step explanation:
step 1
Find the measure of angle COD
we know that
[tex]m\angle COF=m\angle COD+m\angle DOF[/tex] ---> by addition angle postulate
we have
[tex]m\angle COF=150^o[/tex] ----> given problem
[tex]m\angle DOF=90^o[/tex] ----> because AD is perpendicular to BF
substitute the given values
[tex]150^o=m\angle COD+90^o[/tex]
[tex]m\angle COD=150^o-90^o[/tex]
[tex]m\angle COD=60^o[/tex]
step 2
Find the measure of angle BOC
we know that
[tex]m\angle BOC+m\angle COD=90^o[/tex] ---> by complementary angles
we have
[tex]m\angle COD=60^o[/tex]
substitute
[tex]m\angle BOC+60^o=90^o[/tex]
[tex]m\angle BOC=90^o-60^o[/tex]
[tex]m\angle BOC=30^o[/tex]
short answer: 30 degrees :)
Which equation has both -3 and 3 as possible values of y?
A
y^2=6
B
y^2=8
C
y^2=9
D
y^2=64
Answer:
C. [tex]y^2=9[/tex]
Step-by-step explanation:
1. [tex]y^2 = 9[/tex]
2. [tex]y = \frac{+}{}\sqrt{9}[/tex]
3. Equation solutions:
[tex]y_{1} = 3\\y_{2} = -3[/tex]
Write the equation of the line that passes through (-1, 8) and is parallel to the line that passes through (5, -1) and (2, -5).
Answer:
[tex]\large\boxed{y=-\dfrac{3}{4}x+\dfrac{29}{4}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\=================================[/tex]
[tex]\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\text{Calculate the slops:}\\\\(5,\ -1),\ (2,\ -5)\\\\m_1=\dfrac{-5-(-1)}{2-5}=\dfrac{-5+1}{-3}=\dfrac{-4}{-3}=\dfrac{4}{3}\\\\\text{Therefore}\\\\m_2=-\dfrac{1}{\frac{4}{3}}=-1\left(\dfrac{3}{4}\right)=-\dfrac{3}{4}\\\\\text{Put the value of slope and coordinates of the given point (-1, 8) }\\\text{to the equation of a line:}\\\\8=-\dfrac{3}{4}(-1)+b\\\\8=\dfrac{3}{4}+b\qquad\text{subtract}\ \dfrac{3}{4}\ \text{from both sides}\\\\7\dfrac{1}{4}=b\to b=\dfrac{29}{4}\\\\\text{Finally:}\\\\y=-\dfrac{3}{4}x+\dfrac{29}{4}[/tex]
A student spends 2200 dollars during one semester of college. They spend 325 on books. What percentage was spent on books
Answer:
Step-by-step explanation:
percentage spent on books = (325/2200) * 100
= 325/22 = 14.77%
Evaluate f(1) using substitution:
f(x) =2x^3 -3x^2-18x+8
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Substitute 1 in everywhere you see 'x'
2(1)^3 - 3(1)^2 - 18(1) + 8
Solve:
f(1) = -11
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Final answer:
To evaluate the function f [tex](x) = 2x^3 - 3x^2 - 18x + 8[/tex] at x=1, substitute 1 for every instance of x in the function and simplify to get f(1) = -11.
Explanation:
The question appears to be a math problem where the student is asked to evaluate a function at a specific input. Specifically, the function given is [tex]f(x) = 2x^3 - 3x^2 - 18x + 8[/tex] and the student has been asked to evaluate this function when x is equal to 1. To find f(1), we replace every instance of x in the function with 1.
So, f(1) = [tex]2(1)^3 - 3(1)^2 - 18(1) + 8[/tex]= 2(1) - 3(1) - 18 + 8 = 2 - 3 - 18 + 8 = -11.
Thus, f(1) evaluates to -11.
The diameter of a circle is 4 cm. Which equation can be used to find its circumference?
OC = T2
OC= Tx4
4
Answer: OC = πx4
Step-by-step explanation:
This question is incomplete, the correct question is
The diameter of a circle is 4 cm. Which equation can be used to find its circumference?
OC = πx2
OC= πx4
4
Answer,
Since the diameter is given as 4cm
Also,
The circumference of a circle OC = π x diameter
Therefore, OC = πx4
Please solve number 80
Answer:
option D. 20 cm
Step-by-step explanation:
step 1
Find the volume of the water
The volume of the water is equal to
[tex]V=LWH[/tex]
we have
[tex]L=60\ cm\\W=40\ cm\\H=50\ cm[/tex]
substitute
[tex]V=(60)(40)(50)[/tex]
[tex]V=120,000\ cm^3[/tex] ---> volume of water
step 2
Find the deep of the water, if the tank is returned to its horizontal position
we have
[tex]V=120,000\ cm^3[/tex]
[tex]L=100\ cm\\W=60\ cm\\H=?\ cm[/tex]
where
H is the deep of the water
substitute in the formula of volume
[tex]120,000=(100)(60)(H)[/tex]
solve for H
[tex]120,000=6,000)(H)[/tex]
[tex]H=20\ cm[/tex]
evaluate 81/36 x^2 - y^2/25
Answer:
Step-by-step explanation:
Final answer:
To simplify the given expression involving fractions and variables, multiply, divide, and subtract accordingly to obtain the simplified form. Therefore, the simplified expression is [tex](9/4)x^2 - (1/25)y^2.[/tex]
Explanation:
The given expression is:
[tex]81/36 * x^2 - y^2/25[/tex]
To simplify this expression:
Multiply 81/36 which equals 9/4.
Then, divide [tex]x^2[/tex] by 4, and subtract [tex]y^2[/tex] divided by 25.
Therefore, the simplified expression is [tex](9/4)x^2 - (1/25)y^2.[/tex]
What did Tarzan like to play?
Answer:
Step-by-step explanation:
.The sum of the digits of a two-digit number is one-fifth the value of the
number. The tens digits is one less than the ones digit. What is the two-digit
number? (Hint: Assign a different variable to the value of each digit.)
Here's how I'm assigning a different variable to the value of each digit:
10x + y, where x is the first digit, and y is the second digit (you can test if this equation works)
The sum of the digits is 1/5 the value of the number. Using the information, we can form the equation:
x + y = (1/5)(10x + y)
Simplify
x + y = 2x + (1/5)y
The tens digit is one less than the ones digit. Using this information, we can form the equation:
x = y - 1
Adding both sides by 1 gives
x + 1 = y
Substituting this into the y's the first equation gives:
x + x + 1 = 2x + (1/5)(x + 1)
Distribute and simplify
2x + 1 = 2x + (1/5)x + 1/5
Subtract both sides by 2x
1 = (1/5)x + 1/5
Subtract 1/5 from both sides
4/5 = (1/5)x
Multiply both sides by 5
4 = x
x = 4
Use this to solve for y
x + 1 = y
4 + 1 = y
y = 5
Thus, x = 4 and y = 5. The 2 digit number is XY, which is 45.
Let me know if you need any clarifications; this was a very interesting math problem to solve!
Plz help me this isn’t that hard but I’m struggling so plz I don’t want another detention
Answer:
The length of the total 8 pieces in 0.8 meters = 6.4 meters
How many pieces there are in the remaining 0.4 meter = 6.5
Step-by-step explanation:
0.8 x 8 = 6.4
9 meters - 6.4 meters = the remaining 2.6 meters
2.6 x 0.4 = 6 1/2 pieces of ribbon in 0.4 meters.
Karli and her friend can paint 6/7 of a picture in 3/14 of an hour. How many pictures can they paint in a full hour?
A movie theater sells out 7 times per month. How many times will it sell out in the next 2 years?
1 year = 12 months.
2 years = 12 x 2 = 24 months.
Multiply the number of times it sells out per month by the number of months:
7 x 24 months = 168 times.