Answer:
Write its y-intercept as zero:
[tex]y=m\,x[/tex]
Step-by-step explanation:
If the line is given in slope-intercept form:
[tex]y=m\,x+b[/tex]
make sure that you keep the value of the slope (m) as it is (because you want a line parallel to this one so it has to have the same slope "m", and change the value of "b" to zero, leaving the line with the following form:
[tex]y=m\,x+0\\y=m\,x[/tex]
This forces the line to have its y-intercept at the value zero (origin of coordinates)
James washes cars to earn money. He charges $7.00 per compact car, $10.00 per mid -sized car, and $15.00 per SUV. On Saturday, he washed 3 compact cars, 4 mid-sized cars, and 2 SUVs. How much money did he earn?
Answer:
$91.00
Step-by-step explanation:
From the above question, we obtained the following information.
James charges:
1 compact car = $7.00
1 mid sized car = $10.00
1 SUV = $15.00
On Saturday, he washed:
a) 3 compact cars
1 compact car = $7.00
3 compact cars = ?
= $7.00 × 3
= $21.00
b) 4 mid-sized cars
1 mid- sized car = $10.00
4 mid-sized cars = ?
= $10.00 × 4
= $40.00
c) 2 SUVs.
1 SUV = $15.00
2 SUVs = ?
= $15.00 × 2
= $30.00
How much money did he earn?
$21.00 + $40.00 + $30.00
= $91.00
Therefore, James earned $91.00
I'm confused on simplifying radicals.
Answer: 4 or [tex]\sqrt{4 * 4}[/tex]
To find the square root of a number, remember that there will be two factors that are the same that will give you the product.
Lets start from 1:
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
As you can see, 4 x 4 is 16. To make sure I'm correct, remember that a square roots consists two identical factors.
4 and 4 are the same numbers.
Therefore, [tex]\sqrt{16}[/tex] = 4
It can also be written as [tex]\sqrt{4 * 4}[/tex]
Answer:
the answer is 4
Step-by-step explanation:
I use a calulator but if you dont have one then the way to do square roots is find a number say 4 and put it to the 2 power and it equaks 16 (4^2)=16. I cant really explain much more
The length of a side of a square field is 48m.Find the cost of ploughing the field at the rate of rs 25/m and cost of fencing the field at the rate of rs 18/m
Answer: rs 4800, rs 3456
Step-by-step explanation:j
given data:
length of a sid = 48m
cost of ploughing the field = rs 25/m
cost of fencing the field = rs 18/m
solution:
we know a square has four equal sides. so total length of the field is
= m ( 48 + 48 +48 + 48 )
= 192m
cost of ploughing the field
= 192m * rs 25
= rs 4800
cos of fencing the field
= 192m * rs 18
= rs 3456
2²•1/2⁵•2⁵•1/2²??????
Please help
Answer: 1
Step-by-step explanation:
You just simplify each number by the square and then you multiply all of them!!
In 2003, the population of an African country was about 19.5 million people, which is 2 million more than 5 times the population in 1950. Enter and solve an equation to find the approximate population p (in millions) in 1950.
Answer:
[tex]P = 3.5\ million[/tex]
Step-by-step explanation:
Given
Represent 1950 Population with P and 2003 Population with Q
[tex]Q = 19.5\ million[/tex]
Required
Determine the value of P
From the question; we have that
[tex]Q = 2\ million + 5 * P[/tex]
Substitute 19.5 million for Q
[tex]19.5\ million = 2\ million + 5 * P[/tex]
Subtract 2 million from both sides
[tex]19.5\ million - 2\ million= 2\ million - 2\ million + 5 * P[/tex]
[tex]19.5\ million - 2\ million= 5 * P[/tex]
[tex]17.5\ million = 5 * P[/tex]
Divide both sides by 5
[tex]\frac{17.5\ million}{5} = \frac{5 * P}{5}[/tex]
[tex]\frac{17.5\ million}{5} = P[/tex]
[tex]3.5\ million = P[/tex]
[tex]P = 3.5\ million[/tex]
Hence, the 1950 population is 3.5 million
A plant measures 6cm two weeks into an experiment and then measures 12cm four weeks after that. Write the equation of the line describe this situation if x=weeks and y=centimeters
Answer:
y = 3x
Step-by-step explanation:
Use rise over run (y2 - y1) / (x2 - x1) to find the slope
(12 - 6) / (4 - 2)
6/2
= 3
The plant will be 0 cm at 0 weeks, since 3(0) = 0
So, the equation will be y = 3x
6.14 - (9 + 802 =
!!!
13x-7+7x-13=180 whats the answer?
Answer:
x=10
Step-by-step explanation:
13x-7+7x-13=180
Combine like terms
20x-20 = 180
Add 20 to each side
20x -20+20 = 180+20
20x=200
Divide by 20
20x/20 = 200/20
x = 10
Answer:x=10
Step-by-step explanation:
1.add the number
2.add the same term to bothe sides of the equation
3.simplify
4.divide bothe side of the equation by the same term
5.simplify
Evaluate each expression if a =2, b = -3 and c = -1 and d =4. 5bc
Answer:
15
Step-by-step explanation:
5bc = 5(-3)(-1) = -15(-1) = 15
Find the area of the triangle ABC A(-6,2) B(3,2) c(-2,6) D (-2,2)
Answer:
18 square units.
Step-by-step explanation:
Area of the triangle = ½*AB*CD
First of all, find the length of AB and CD using the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
A(-6, 2) => (x1, y1)
B(3, 2) => (x2, y2)
[tex] AB = \sqrt{(3 -(-6))^2 + (2 - 2)^2} [/tex]
[tex] AB = \sqrt{(9)^2 + (0)^2} = \sqrt{81} = 9 [/tex]
[tex] CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
C(-2, 6) => (x1, y1)
D(-2, 2) => (x2, y2)
[tex] CD = \sqrt{(-2 -(-2))^2 + (2 - 6)^2} [/tex]
[tex] CD = \sqrt{(0)^2 + (-4)^2} = \sqrt{16} = 4 [/tex]
AB = 9
CD = 4
Area of rectangle = ½*AB*CD = ½*9*4 = 9*2 = 18 square units.
Answer:
18
Step-by-step explanation:
Two lines extend from point S to create a right angle. The vertical line extends from point S through point R. The horizontal line extends right from point S through point T. A third line extends right and up from point S through point U. Which is the endpoint of a ray? point R point S point T point U
Answer:
Option R
Step-by-step explanation:
The point S is the end point of ray.
What is line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.
According to the given information,
A ray's endpoint is a single point that denotes the conclusion of a line segment. In this instance, only one of the three lines that extend from point S contains a ray's terminus.
We must comprehend a ray's qualities in order to establish which location is the endpoint of a ray.
A ray originates at a single place and travels in one direction indefinitely. The beginning of the line segment is the endpoint of a ray.
We can see from the provided lines that the vertical line runs from point S via point R. Since it doesn't go on forever in one direction, this is not a ray example.
Similar to the vertical line,
The horizontal line also extends from point S through point T,
But it does not go on forever.
The third line is a ray because it is infinitely long in one direction and extends right and up from point S via point U.
Therefore, point S, the beginning of the line, is the endpoint of this ray.
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Please solve, m +5=-m-2-5m+7?
Answer:
[tex]\Huge \boxed{m=0}[/tex]
Step-by-step explanation:
[tex]m +5=-m-2-5m+7[/tex]
Adding m and 5m to both sides of the equation.
[tex]m +5+m+5m= -m-2-5m+7+m+5m[/tex]
Subtracting 5 from both sides of the equation.
[tex]m +5+m+5m-5=-2+7-5[/tex]
Combining like terms and simplifying.
[tex]7m=0[/tex]
Dividing both sides of the equation by 7.
[tex]m=0[/tex]
Answer:
m = 0
Step-by-step explanation:
m + 5 = - m - 2 -5m + 7
m + 5 = -m - 5m - 2 + 7
m + 5 = -6m + 5 (combine like terms)
m = 0
please help me!!!!!
Answer: see proof below
Step-by-step explanation:
Use the Sum & Difference Identity: tan (A - B) = (tanA - tanB)/(1 + tanA tanB)
Use the Half-Angle Identity: tan (A/2) = (1 - cosA)/(sinA)
Use the Unit Circle to evaluate tan (π/4) = 1
Use Pythagorean Identity: cos²A + sin²A = 1
Proof LHS → RHS
[tex]\text{Given:}\qquad \qquad \qquad\dfrac{2\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}{1+\tan^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}[/tex]
[tex]\text{Difference Identity:}\qquad \dfrac{2 \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)^2}[/tex]
[tex]\text{Substitute:}\qquad \qquad \dfrac{2 \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)^2}[/tex]
[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{1-\tan^2\frac{A}{2}}{1+\tan^2\frac{A}{2}}[/tex]
[tex]\text{Half-Angle Identity:}\qquad \quad \dfrac{1-(\frac{1-\cos A}{\sin A})^2}{1+(\frac{1-\cos A}{\sin A})^2}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{\sin^2 A-1+2\cos A-\cos^2 A}{\sin^2 A+1-2\cos A+\cos^2 A}[/tex]
[tex]\text{Pythagorean Identity:}\qquad \qquad \dfrac{1-\cos^2 A-1+2\cos A}{2-2\cos A}[/tex]
[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{2\cos A-2\cos^2 A}{2(1-\cos A)}\\\\.\qquad \qquad \qquad \qquad =\dfrac{2\cos A(1-\cos A)}{2(1-\cos A)}[/tex]
= cos A
LHS = RHS: cos A = cos A [tex]\checkmark[/tex]
The number of points scored by a basketball player in the first eight games of a season are shown below. 15, 35, 18, 30, 25, 21, 32, 16 What would happen to the data distribution if she scored 24, 22, 27, and 28 points in her next four games?
Answer:
im not sure how the data should be interpreted but here is the distribution. It goes up by .416
Step-by-step explanation:
the average of the first 8 games is 24
the average of the 12 games is 24.416
The mean of the data of the given basketball player will increase if she scored 24, 22, 27, and 28 points in her next four games.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
Given that the number of points scored by a basketball player in the first eight games is 15, 35, 18, 30, 25, 21, 32, and 16. Therefore, the mean of the first 8 games is,
Mean = (15 + 35 + 18 +30 + 25 + 21 + 32 + 16)/8
= 176/8
= 22
Now, the player scored 24, 22, 27, and 28 points in her next four games. Therefore, the mean will be,
New Mean = (15 + 35 + 18 +30 + 25 + 21 + 32 + 16 + 24 + 22 + 27 + 28)/12
= 277 / 12
= 23.0833
Hence, the mean of the data of the given basketball player will increase if she scored 24, 22, 27, and 28 points in her next four games.
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If 2^x=5, what is 2^3x-4
Answer:
121
Step-by-step explanation:
2^3x - 4 = (2^x )^3 - 4 = 125 - 4 = 121
[tex]\implies\tt 2^x = 5 [/tex]
[tex]\implies\tt \Big( 2^x \Big)^3 - 4 [/tex]
[tex]\implies\tt 125 - 4 [/tex]
[tex]\huge\implies\tt 121 [/tex]
Can someone please help solve this and show me the formula of how to do it?
Answer:
f=2.93cm
Step-by-step explanation:
SOH CAH TOA [the length you are finding is adjacent to the angle and opposite to right angle is the hypotenuse, therefore use cosine]
cos(43°)=f/4
[times 4x on both sides it cancels on the left]
4cos(43°)=f
2.93=f
! 25 points ! a) 68 is what percent of 80? b) 88.83 is 423% of what? c) 36.8% of what number is 28.52? d) What number is 95% of 40? Thankyou!
Step-by-step explanation:
Let the number to be found be x
a).68 is what percent of 80 is written as
[tex] \frac{x}{100} \times 80 = 68[/tex]
Multiply both sides by 100
We have
80x = 6800
Divide both sides by 80
we have the answer as
x = 85
Therefore the percentage is 85%b).Let the number be x
88.83 is 423% of what is written as
[tex] \frac{423}{100} x = 88.83[/tex]
Multiply through by 100
We have
423x = 8883
Divide both sides by 423
We have the answer as
x = 21
The number is 21c).Let the number be x
36.8% of what number is 28.52 is written as
[tex] \frac{36.8}{100} x = 28.52[/tex]
Multiply through 100
We have
36.8x = 2852
Divide both sides by 36.8
We have the answer as
x = 77.5
The number is 77.5d).What number is 95% of 40 is written as
[tex] \frac{95}{100} \times 40[/tex]
We have the final answer as
38Hope this helps you
If n denotes a number to the left of 0 on the number line such that the square of n is less than \small \frac{1}{100}, then the reciprocal of n must be
Answer:
The reciprocal of n must be less than 10.
Step-by-step explanation:
It can be inferred from the question given that n is not a negative number.
But,
[tex](n)^{2}[/tex] < [tex]\frac{1}{100}[/tex]
Find the square root of both sides,
n < [tex]\sqrt{\frac{1}{100} }[/tex]
⇒ n < [tex]\frac{1}{10}[/tex]
n < 0.1
The reciprocal of n can be estimated as;
[tex](n)^{-1}[/tex] < [tex](\frac{1}{10}) ^{-1}[/tex]
[tex]\frac{1}{n}[/tex] < 10
The reciprocal of n is less than 10.
please help me will mark as brainlist
Answer:
17.3825
Step-by-step explanation:
First I figured out the area of the square which is 18×18=324
Then I found out the are of the circle which is 254.47, so 324 - 254.47 = 69.53
Then there are 4 times the shaded are so divided by 4, so 69.53 ÷ 4 = 17.3825
PLEASE GIVE BRAINLIEST!
Answer:
shaded area = 17.38 cm²
Step-by-step explanation:
given:
diameter of circle = 18 cm and = side of square
π = 3.142
shaded area = ( Area of square - Area of circle ) x 1 / 4
Area of square = s² = 18² = 324 ²cm
Area of circle = π d² / 4
= 3.142 (18²) / 4
= 254.5 cm²
therefore, shaded area = ( 324 cm² - 254.5 cm² ) * 1/4
= 17.38 cm²
the lcd for fractions 1/3 3/4 and 8/9 is
Answer:
the answer is /36
Step-by-step explanation:
3 goes into 36
4 goes into 36
9 goes into 36
A fountain was marked up 170% from an original cost of $1000. Last Friday ,Bernie bought the fountain and paid and additional 13% in sales tax.what was his total cost?
Answer:
$ 3051
Step-by-step explanation:
Original cost = $ 1000
Marked up Price = Original cost + 170% of 1000
= 1000 + 1.7 * 1000
= 1000 + 1700
= $ 2700
Sales tax = 13% of 2700
= 0.13 * 2700
= 351
Total cost paid by Bernie = 2700 + 351 = $ 3051
(4x + 2y]³ -(4x-2y)³
Answer:
answer is attached
Round 548.8 to the nearest thousand.
Answer:
The answer is 1,000
**50 Points Possible** I NEED URGENT HELP
please provide a graph
Answer:
See below.
Step-by-step explanation:
1)
For Ben's social media post, we are told that it was initially shared to only 2 people. However, each of those shares it with 3 people. In other words, Ben's post triples every day. This means that the rate of growth is 3. Thus, Ben's post as an exponential function is:
[tex]f(x)=2(3)^x[/tex]
The 2 represents the initial amount at day 0, and the 3 represents the rate at which the post grows each day.
2)
Similarly, Carter's post was originally sent to 10 people. However, each of the 10 shares it with two others. Therefore, it doubles each day. Thus, the rate is 2. So, Carter's exponential function is:
[tex]f(x)=10(2)^x[/tex]
The 10 represents the initial amount while the 2 represents the rate.
3)
I've use Desmos to graph the functions. Refer to the picture attached. Red is Amber, blue is Ben, and green is Carter.
4)
To find out the number of shares each student's post will receive on day 3 and day 10, simply plug the numbers into the functions. Therefore:
For Amber:
Day 3:
[tex]f(3)=3(4)^3=192[/tex]
Day 10:
[tex]f(10)=3(4)^{10}=3,145,728[/tex]
For Ben:
Day 3:
[tex]f(3)=2(3)^3=54[/tex]
Day 10:
[tex]f(10)=2(3)^{10}=118,098[/tex]
And for Carter:
Day 3:
[tex]f(3)=10(2)^3=80[/tex]
Day 10:
[tex]f(10)=10(2)^{10}=10,240[/tex]
5)
Amber's new graph of:
[tex]f(x)=3(4)^x+45[/tex]
will be a shifted version of her original graph. The new graph will be shifted upwards by 45 units. However, since the 45 is not affected by the x in any way, the change will be minuscule. For instance, her number of shares on day 10 of the old graph is 3,145,728. Even with the additional 45, it will just be: 3,145,773. With enough days, the additional number becomes trivial.
6)
On the 10th day, Amber's post was shared almost 3 million times, while Ben's was shared "only" 118,098 times and Carter's with 10,240. Undoubtedly, Amber's post was the fastest.
7)
If you want to most shares as possible, choose Amber with fewer friends initially but more shares. This is because the exponential potential of a number even just a bit higher is insane. For instance, 3^10 (Ben's rate at 10th day) is only 59,049 while Amber's rate will be 4^10 which is 1,048,576. Amber's number is almost 18 times higher than Ben's. Even if Ben's initial number was say 1,000 or even 1,000,000, Amber would catch up rather quickly. Therefore, the rate is the quintessential part of an exponential growth function.
Answer:
Here is the slope:
[tex]y = zy + dsince m = 0c = 9[/tex]
Hope this helps
Simplify: (x^-3/y) (x/y)^-1
Answer:
x(5)/(6)y(1)/(2)
Step-by-step explanation:
Hoped I helped
leave a like or rate.
What is 12/2? Answer for 10 points!!!
Answer:
6
Step-by-step explanation:
12/2=6/1=6
Answer:
6
Step-by-step explanation:
At a local discount theatre, tickets to the film The
Early Bird Gets the Sleepiest cost only $2.50 for
adults and $1 for children. If 19 people attended
the last showing and the theatre sold $40 worth of
tickets:
a.) How many adults attended the showing?
b.) How many children attended the showing?
Answer:
14 adults and 5 children
Step-by-step explanation:
Set up a system of equations, where a is the number of adults and c is the number of children:
2.5a + c = 40
a + c = 19
Multiply the bottom equation by -1 to solve by elimination:
2.5a + c = 40
-a - c = -19
1.5a = 21
a = 14
Now, plug in 14 as a to find the number of children:
a + c = 19
14 + c = 19
c = 5
So, 14 adults and 5 children attended
how do I solve this .... question in the image.
thank you
Answer:
Below
Step-by-step explanation:
● x-20 = y+20 (1)
● 2(y-22) = x+22 (2)
This is a system of simulataneous equations
Let's simplify the expressions first
● x -20 = y + 20 (1)
Add 20 to both sides
● x -20 + 20 = y+20 +20
● x = y + 40 (1)
● 2(y-22) = x+22 (2)
● 2y - 44 = x +22
Substrat 22 from both sides
● 2y-44-22 = x+22-22
● 2y -66 = x (2)
This is the new system:
● x = y+40 (1)
● x = 2y-66 (2)
Substract (2) from (1)
● x-x = y+40-(2y-66)
● y+40-2y+66 = 0
● -y +106 = 0
● y = 106
Replace y with 106 in (1)
● x = y +40
● x = 106+40
● x = 146
So the solutions are (146,106)
Find the standard form of the equation of the parabola with a focus at (0, 4) and a directrix at y = -4. Answer choices: y = 1/16x2 y2 = 16x y2 = 4x y = 1/4x2
Answer:
a) The standard form of the equation
[tex]y=\frac{16}{x^{2} }[/tex]
Step-by-step explanation:
Explanation:-
A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point (not in a line) in the plane
• The Fixed line is called the directrix of the parabola.
• The Fixed point is called the focus of the parabola.
• A line through the focus and perpendicular to the directrix is called the axis of the parabola.
• The point of intersection of parabola with the axis is called the vertex of the parabola.
Given Focus of the parabola S(0,a)= (0,4)
Given Focus is lies on y-axis and the directrix is parallel to x-axis
Given directrix of the parabola y = -4
Directrix y = -a
Standard form of the parabola
x² = 4ay
x² = 4(4)y
x² = 16y
[tex]y=\frac{16}{x^{2} }[/tex]
An expirement consists of rolling two fair number cubes. What is the probability that the sum of the two numbers will be 4? Express your answer aa a fraction in simpleat form.
Answer:
[tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Given:
Two fair number cubes i.e. two dice consisting the numbers 1, 2, 3, 4, 5, 6 on their faces and have equal probability of each number.
The dice are rolled.
To find:
Probability of getting the sum of two numbers as 4.
Solution:
First of all, let us have a look at the total possibilities when two dice are rolled:
([1][1], [1][2], [1][3], [1][4], [1][5], [1][6],
[2][1], [2][2], [2][3], [2][4], [2][5], [2][6],
[3][1], [3][2], [3][3], [3][4], [3][5], [3][6],
[4][1], [4][2], [4][3], [4][4], [4][5], [4][6],
[5][1], [5][2], [5][3], [5][4], [5][5], [5][6],
[6][1], [6][2], [6][3], [6][4], [6][5], [6][6])
These are total 36 possible outcomes.
For getting a sum as 4:
Possible number of favorable cases are 3 (as highlighted in BOLD in above)
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Required probability is:
[tex]\dfrac{3}{36} = \bold{\dfrac{1}{12}}[/tex]