Answer:
8p^6q^4
6qp-7
Step-by-step explanation:
on the grid,draw the line with the equation x=-2
Answer: up and down line at -2
Step-by-step explanation: Desmos
Write the equation of the line that is perpendicular to the line below and passes through the point (4,-6) write your equation in point-slope form.
The required equation of the line is given as y = -4/3x - 2/3.
Given that,
The equation of the line that is perpendicular to the line below and passes through the point (4,-6).
A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
Here,
The slope of the given line = 3/4
So the slope of the perpendicular line = -4/3
Now,
The perpendicular line passes from (4, -6)
The standard form of the equation,
y - y₁ = m [ x - x₁]
Substitute the value in the above expression,
y + 6 = -4/3[x - 4]
y = -4/3x + 16/3 - 6
y = -4/3x - 2/3
Thus, The required equation of the line is given as y = -4/3x - 2/3.
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A Question 1 (4 points) Retake question
What is the equation of the line that has a slope of 4 and a y-intercept of -7?
A) y = -7x + 4
OB) y = -7/4x
OC) 4x + 7y= 0
D) y = 4x - 7
Required equation of line in slope intercept form
y = 4x - 7
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Slope of the line = 4
y - intercept of the line = -7
The line passes through (0. -7)
Equation of the required line
y - (-7) = 4(x - 0)
y + 7 = 4x
y = 4x - 7
Option D is correct
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a) find x and y.
b) find x and y
c) find x and y
Using the proportionality theorem, to find the values of x and y, we have:
a. x = 1.25; y = 1.75
b. x = 15; y = 4
c. x = 3; y = 2
What is the Proportionality Theorem?According to the proportionality theorem, the side lengths of similar triangles have the same ratio, or are proportional to each other.
Using the proportionality theorem, we can find the following missing values of x and y.
a. (5 + x)/5 = 10/8 [proportionality theorem]
Cross multiply
8(5 + x) = (5)(10)
40 + 8x = 50
8x = 50 - 40
8x = 10
x = 10/8
x = 1.25
5/x = 7/y
Plug in the value of x
5/1.25 = 7/y
5y = 8.75
y = 1.75
b. x/5 = 18/6 [proportionality theorem]
6x = 90
x = 90/6
x = 15
12/y = 18/6
Cross multiply
18y = 72
y = 72/18
y = 4
c. x/6 = 1.5/3 [proportionality theorem]
3x = 9
x = 9/3
x = 3
y/4 = 1.5/3
Cross multiply
3y = 6
y = 6/3
y = 2
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Answer:
a. x = 1.25; y = 1.75
b. x = 15; y = 4
c. x = 3; y = 2
Step-by-step explanation:
How many 9 in. × 9 in. tiles would be needed to cover a floor that is 288 square feet?
The number of tiles that would be required to cover a floor that is 288 square feet is 512.
According to the question,
We have the following information:
Area of the tile = 9*9 square inches
Area of the tile = 81 square inches
Area of the floor = 288 square feet
So, we will convert the area of the floor from square feet to square inches.
We know that 1 feet = 12 inches.
So, we have the following expression:
Area of the floor = (288*12*12) square inches
Area of the floor = 41,472 square inches
Number of tiles required to cover the floor = area of the floor/area of the tile
Number of tiles required to cover the floor = 41,472/81
Number of tiles required to cover the floor = 512
Hence, the number of tiles that would be required to cover a floor that is 288 square feet is 512.
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A man pulled a cart filled with stones that had a total mass of 60 kg.
He increased the amount of force used to pull the cart from 60 N to 90 N, what is the new
acceleration of the cart?
The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²
What is Force ?The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.
Formula of force,
F = ma
Given that,
A man pulled a cart filled with stones that had a total mass of 60 kg
He increased the amount of force used to pull the cart from 60 N to 90 N
New acceleration of cart = ?
F = ma
Old acceleration,
60 = 60a
a = 1 m/s²
New acceleration,
90 = 60a
a = 90/60
a = 3/2
a = 1.5 m/s²
Hence, the new acceleration is 1.5 m/s²
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Find the surface area of a cylinder pls
The total surface area of the cylinder is 157 square feet.
Given the radius of the cylinder = 4 inches
height of the cylinder = 9 inches
Total surface area is calculated by the formula:
A = 2πr² + 2πh
A = 2 × 3.14 × 4² + 2 × 3.14 × 9
or, A = 157 square feet.
Therefore the total surface area of the cylinder is 157 square feet.
The surface area of a solid item is a measurement of the total volume that the surface of the thing occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more complicated than the definition of arc length for one-dimensional curves.
The definition of surface area for polyhedral (i.e., particles with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces. When smooth surfaces, like spheres, are represented as parametric surfaces, their surface area can be calculated.
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how can I change eight days into hours
Answer:
8 days = 192 hours
Step-by-step explanation:
Formula we use,
→ 1 day = 24 hours
Conversion of 8 days into hours,
→ n days × 24 hours
→ 8 × 24
→ 192 hours
Hence, there are 192 hours.
17p5
Exponent:
Variable:
tify the term, coefficient, and the variable.
Term:
Coefficient:
For the given expression, the variable is p, coefficient is 17 and the exponent is 5.
Expression:
Expression refer the algebraic expression that consists of variables, numbers and math operators.
Given,
Here we have the expression 17p⁵
Now, we have to find the exponent, coefficient and variable.
As per the definition of exponent, the term exponent refers the power value of the expression.
So, the exponent is 5.
And the definition of coefficient is an integer that is written along with a variable or it is multiplied by the variable.
So, the coefficient is 17.
And the variable of this expression is p.
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4. Four years ago, Melody was one fourth as old as her sister was then, In six years, Melody will be half as old as het sister will be then. Find their ages now.
5. The sum of the digits of a two-digit number is 12 . The value of the number is 6 less than 5 times the units digit. Find the number.
6. Hannah likes to spend her free time hanging out at the airport. She likes to run on the walkways. While running with the walkway, she can cover 48 feet in 3 seconds. While running against the walkway, she can cover 24 feet in 2 seconds. Find Hannah's rate (in feet per second) if the walkway stopped moving.
Answer:
4) Melody is 9 and her sister is 24
5) The numbers are 3 and 9
6) 14 feet per second
Step-by-step explanation:
Questions 4
There is a lot going on here. This is probably hard to follow. If it is, it is me and not you.
Let m = Melody and s = sister
m - 4 = 1/4(s-4) m + 6 = 1/2(s + 6) Clear the fractions
4m - 16 = s -4 2m -s = -6
Multiple the second equation by -1 and add together
4m - s = 12
-2m + s = 6
2m = 18 Divide both sides by 2
m = 9 Substitute this in to find the sister's age
2m + 12 = s + 6
2(9) +12 + s + 6
18 + 12 = s + 6
30 = s + 6 Subtract 6 from both sides
24 = s
Questions 5
x + y = 12 x = 5y - 6
Plug in 5y - 6 in the first equation for x
5y - 6 + y = 12 Combine like terms
6y - 6 = 12 Add 6 to both sides
6y = 18 Divide both sides by 6
y = 3
x + y = 12
3 + y = 12 Subtract 3 from both sides
y = 9
I am little confused by this because it says, "The value of the number..." What number are they referring to?
Question 6
To find the rate taking into consideration the walkway rate:
[tex]\frac{48}{3}[/tex] - w Which is equivalent to 16 - w
[tex]\frac{24}{2}[/tex] + w Which is equivalent to 12 + w
Set these expression equal to each other and find the rate of the walkway
16 - w = 12 + w Add w to both sides
16 = 12 + 2w Subtract 12 from both sides
4 = 2w Divide both sides by 2
2 = w
The rate of the walkway is 2 feet per second. Subtract that from 16 or add is to the 12 to get 14 steps per second.
what is.25 times .26
Answer:
25 x 26 = 650
0.25 x 0.26 = 0.065
Step-by-step explanation:
17 + 2.6b = 30
2.6b=30-17=
2.6b=13
b=13/2.6
2.6b/2.6=13/2.6
2.6b/2.6=5
b=5
How do I check this equation to see if it is correct?
Answer:
You insert 5 back into the equation
Step-by-step explanation:
17 +2.6b=30
17 +2.6(5)=30
17 +13=30
30% of the animals in a wildlife park are lemurs, 40% are ring tailed lemurs. What percentage of the animals in the wildlife park are ring tailed lemurs?
12% of total animals are ring-tailed lemurs.
What is percentage?A percentage is a fraction of an amount expressed as a particular number of hundredths of that amount.
Given that, 30% of the animals in a wildlife park are lemurs, 40% are ring-tailed lemurs.
Let total animals be 100.
30% of 100 = 30
40% of 30 = 12
12/100*100 = 12%
Hence, 12% of total animals are ring-tailed lemurs.
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1. Find extrema and intervals of increasing and decreasing the function
[tex]y = \frac{ {e }^ { - (x + 2)} }{x + 2} [/tex]
2. Find inflection points and intervals of concavity and convexity of the function:
[tex]y = \frac{2x - 1}{(x - 1) ^{2} } [/tex]
The function y = (e⁻⁽ˣ⁺²⁾) / x + 2 increases along intervals of (-∞, 3) and decreases along (-3, -2), (-2, ∞) and the function y = 2x - 1 / (x - 1)² has no inflection points but concave downwards along (-∞, 1) ∪ (1 ,∞)
Extrema and Intervals of a FunctionAn extremum (or extreme value) of a function is a point at which a maximum or minimum value of the function is obtained in some interval. A local extremum (or relative extremum) of a function is the point at which a maximum or minimum value of the function in some open interval containing the point is obtained.
The function given;
y = (e⁻⁽ˣ⁺²⁾) / x + 2
The extrema and intervals of increase or decrease of this function are
(-1, 1.63) and it increases along (-∞, 3) and decreases along (-3, -2), (-2, ∞)
2. The inflection points and intervals of concavity and convexity of the function
y = 2x - 1 / (x - 1)² are
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Question 3
0.5 pts
Jim wants to buy a computer. The total cost is $947. If he can save $60 a month, how
long will it take for him to save up for the computer? Round UP to the next whole
number of months!!
Question 4
1 pts
Justin wants to borrow $18,091 to buy a used car. He examined his budget and
decided that he can afford a payment of $400 per month. If his bank offers him an
SHA
The graph of y=f(x) is graphed below. What is the end behavior of f(x)? Please need help, need by TONIGHT!!!
Step-by-step explanation:
if x→+∞, then y→-∞ [increasing];
if x→-∞, then y→+∞ [decreasing].
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.
q^2+5/6q
The perfect square trinomial and binomial of the expression [tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] are [tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] + [tex]\frac{25}{144}[/tex] and [tex](q + \frac{5}{12}) ^{2}[/tex]
What is a perfect square expression?Perfect squares are numbers or expressions that are the product of a number or expression multiplied to itself. 7 times 7 is 49, so 49 is a perfect square. x squared times x squared equals x to the fourth, so x to the fourth is a perfect square.
[tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] expression can be made into a perfect square by adding the square of half the coefficient of q
coefficient of q = [tex]\frac{5}{6}[/tex]
Half of [tex]\frac{5}{6}[/tex] = [tex]\frac{5}{12}[/tex]
square [tex]\frac{5}{12}[/tex] we have [tex](\frac{5}{12}) ^{2}[/tex] which becomes [tex]\frac{25}{144}[/tex]
so the perfect square trinomial = [tex]q^{2}[/tex] + [tex]\frac{5}{6}q[/tex] + [tex]\frac{25}{144}[/tex]
the binomial is [tex](q + \frac{5}{12}) ^{2}[/tex]
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a(5-4) i need the full answer pls
Answer:
1a (or) a
Step-by-step explanation:
Given expression,
→ a(5 - 4)
Let's simplify the expression,
→ a(5 - 4)
→ a(1)
→ a × 1
→ 1a (or) a
Therefore, the answer is 1a.
For each problem, use implicit differentiation to find
dy at the given point.
Using implicit differentiation at the given point gives;
a) dy/dx = 4
b) dy/dx = -³/₈
How to carry out implicit differentiation?In implicit differentiation, what we are doing is that we are differentiating each side of an equation with two variables (usually x and y) by treating one of the variables to act as a function of the other. This implies the use of chain rule
13) x² + y³ = 5
Using implicit differentiation gives;
2x + y²(dy/dx) = 0
dy/dx = -2x/(y²)
At (-2, 1), we have;
dy/dx = -2(-2)/(1²)
dy/dx = 4
14) x³ = -4y² + 3
Using implicit differentiation gives;
3x² = -8y(dy/dx) + 0
dy/dx = -³/₈x²/y
At (-1, 1), we have;
dy/dx = -³/₈(-1)²/1
dy/dx = -³/₈
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Gary can order stickers from two companies company A charges a $30 design fee plus $0.80 per sticker company beat charges of $14 design fee plus $1.20 per sticker how many stickers would Garrett have to order for the cost at both companies to be the same. what would the equation be?
To have the same price, 40 stickers will have to be ordered and the equation is 16 = 0.40p.
What is the equivalent equation?
Equivalent equations are algebraic equations with identical solutions or roots. Adding or subtracting the same number or expression from both sides of an equation yields an equivalent equation. An equivalent equation is created by multiplying or dividing both sides of an equation by the same non-zero number.
We have,
for company A :
Design Fee = $30
Costvper sticker = $0.80
for company B :
Design Fee = $14
Cost per sticker = $1.20
Let the number of stickers = p
Total cost of company A = 30 + 0.80p
Total cost of company B = 14 + 1.20p
For the cost to be the same :
Company A = Company B
30 + 0.80p = 14 + 1.20p
Collect like terms :
30 - 14 = 1.20p - 0.80p
16 = 0.40p
p = 16/0.40
p = 40 stickers
Therefore, to have the same price, 40 stickers will have to be ordered and the equation would be 16 = 0.40p.
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Suppose that $2000 is initially invested in an account at a fixed interest rate, compounded continuously. Suppose also that, after four years, the amount of
money in the account is $2411. Find the interest rate per year.
Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2411\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]2411=2000e^{\frac{r}{100}\cdot 4}\implies \cfrac{2411}{2000}= e^{\frac{r}{25}}\implies \log_e\left( \cfrac{2411}{2000} \right)=\log_e\left( e^{\frac{r}{25}} \right) \\\\\\ \log_e\left( \cfrac{2411}{2000} \right)=\cfrac{r}{25}\implies 25\cdot \ln\left( \cfrac{2411}{2000} \right)=r\implies \stackrel{\%}{4.67}\approx r[/tex]
Can someone help me how to get to this answer. What do you do to get to this answer
Answer:
Step-by-step explanation:
1 gallon = $29.95
Nikki needs 12.25 gallons, so,
12.25 gallons= 12.25 × 29.95 = $ 366.8875 = $ 366.89
The McDonald family drove from Halifax to Montreal on a summer vacation. On the way there, they traveled approximately 240 km each day, stopping overnight in many different resorts. They stayed in Montreal for 6 days. On the way back, they drove about twice as far each day before stopping. The total trip was about 2880 km. How many days did the vacation last?
Answer:
18 days
Step-by-step explanation:
this question is actually pretty simple, so all you have to do is take the total km which is 2880 divide it by 240 which is 12 then add 6 to it which makes 18 days
19. Jules and Lauren need to write an equation of a line that is perpendicular to: y - 2 = 1/(x-3). Jules writes the equation: y = -5x + 1 Lauren writes the equation: y = -5x + 7. Explain why both equations are correct.
I'm assuming your equation was:
[tex]y-2=\dfrac{1}{5}(x-3)[/tex]
Both Jules' line and Lauren's line have a slope of -5 or [tex]-\dfrac{5}{1}[/tex] and those two lines are parallel since they have the same slope.
Perpendicular lines have slopes that are opposite reciprocal values.
The opposite reciprocal of [tex]-\dfrac{5}{1}[/tex] is a positive [tex]\dfrac{1}{5}[/tex], which is why these two lines are perpendicular to the line at the top of my answer.
ITS A SIMPLE 50 POINT QUESTION! PLEASE HELP!
is y = 4 a relation?
Answer:
Y=4 is a function
Step-by-step explanation:
And to me function is relation
Hope i got this right and have a great day :)
Answer: Yes
Step-by-step explanation:
Yes, y = 4, which is often written as f(x) = 4, is a function that means “take any input, and no matter what it is, produce an output of 4”.
An account earning interest at a rate of 4% compounded monthly has a principal of $ 500,000 . If no more deposits or withdrawals are made , how much money will be in the account after five years?
Answer:
$610,498.30
Step-by-step explanation:
P = C (1 + r/n)^nt
4% = 0.04
P = 500 000(1+0.04/12)^(12*5)
P = 500 000 (1.003333)^60
P = 500 000 (1.220997)
P = $610 498.296971
a(b + c) help pls pls help
Answer:
ab + ac
Step-by-step explanation:
Given expression,
→ a(b + c)
Simplifying the expression,
→ a(b + c)
→ (a × b) + (a × c)
→ ab + ac
Hence, answer is ab + ac.
How many solutions does the following equation have?
2(3x + 5) = 2(2x - 3) + 2x
There are infinitely many solutions.
There are no solutions.
There are two solutions.
There is one solution.
Need help dragging the dot on the graph as well
The drag point point is shown on the graph.
What is drag point?
When a single point or the center of a circle is specified numerically, the point can be moved, and the mouse can be used to edit graphs (ex. translation of a parabola).
Consider, the given equation
[tex]g(x) = -\frac{5}{3} x-1[/tex]
We have to find the value of g(x) at x = 3.
So, plug x = 3 in the above equation.
[tex]g(3) = -\frac{5}{3}(3)-1\\ g(3)=-5-1\\g(3) = -6[/tex]
Therefore, the point is (3, -6).
We have to drag the point (3, -6) on the graph.
The drag point graph is attached below.
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please help!
Urgent!
Thank u!
The value of the height of the water at midday is 14 feet.
How to calculate height of the water?Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is used to describe everything that may be measured vertically, high or low.
Similarly, we will determine the height at other times during the day, at midday . we have the value $t=3$, so using the formula, we have
[tex]H(3)=10+4 \sin \left(\frac{\pi}{6} \cdot 3\right)=10+4 \cdot \sin \frac{\pi}{2}[/tex]
Taking into account that
[tex]\sin \frac{\pi}{2}=1[/tex]
we get the following:
H=10+4 [tex]\cdot \sin \frac{\pi}{2}=10+4 \cdot 1=14[/tex]
Thus, the value of the height of the water at midday . is 14 feet.
The value of the height of the water at midday is 14 feet.
How to calculate height of the water?Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is used to describe everything that may be measured vertically, high or low.
Similarly, we will determine the height at other times during the day, at midday. we have the value[tex]$\$ \mathrm{t}=3 \$$[/tex], so using the formula, we have [tex]$H(3)=10+4 \sin \left(\frac{\pi}{6} \cdot 3\right)=10+4 \cdot \sin \frac{\pi}{2}$[/tex]Taking into account that
[tex]$\sin \frac{\pi}{2}=1$[/tex]
we get the following:
[tex]$\mathrm{H}=10+4 \cdot \sin \frac{\pi}{2}=10+4 \cdot 1=14$[/tex]
Thus, the value of the height of the water at midday . is 14 feet.
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