Question Write an equation of the line that passes through (4,−1) and is parallel to the line y=3x+7
Answer:
y=3x-13
Step-by-step explanation:
Since the parallel equations have equal slope.
The equation of line parallel to y=3x+7 will be y=3x+k.
(4,-1) lies in the line so it satisfies the equation amd we get the value of k as -13 and finally we substitute the value of k in the eqn and we finally get the equation as 3x-y-13=0 or you can also write it as y=3x-13
A spinner has 8 evenly spaced different colored sections. You spun the spinner 10 times and landed on yellow 2 times. How many times can you expect to land on yellow if you spin the spinner 100 times?
20 times can you expect to land on yellow if you spin the spinner 100 times.
Given:
A spinner has 8 evenly spaced different colored sections. You spun the spinner 10 times and landed on yellow 2 times.
10 times spinning = landed on yellow 2 times.
divide by 10 on both sides
1 time spinning = landed on yellow 2/10 times
1 time = 1/5 times
multiply by 100 on both sides
1 time * 100 = 1/5*100 landed on yellow
100 times spinning = 20 times landed on yellow.
Therefore 20 times can you expect to land on yellow if you spin the spinner 100 times.
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a bag contains 10 red marbles, 5 white marbles, and 6 blue marbles. you draw 5 marbles out at random, without replacement. what is the probability that exactly two marbles are red?
The probability that exactly two marbles are red, is 0.365.
In the given question we have to find the probability that exactly two marbles are red.
A bag contains 10 red marbles, 5 white marbles, and 6 blue marbles.
Total marbles is
10+5+6=21
We draw 5 marbles out at random, without replacement.
Marbles taken out =5
Total possibility of taking 5 marbles out of 21 marbles is [tex]^{21}C_{5}[/tex].
Using [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
So [tex]^{21}C_{5}=\frac{21!}{5!(21-5)!}[/tex]
[tex]^{21}C_{5}=\frac{21!}{5!16!}[/tex]
[tex]^{21}C_{5}=\frac{21\times20\times19\times18\times17\times16!}{5\times4\times3\times2\times1\times16!}[/tex]
Simplifying
[tex]^{21}C_{5}[/tex] =7×19×9×17
[tex]^{21}C_{5}[/tex] = 20,349
Probability of exactly two marbles are red is
Possible out comes of exactly two red marbles equal to 2 red and other color marble 3.
Total red marbles are 10. So [tex]^{10}C_{2}[/tex]
The remaining marble except red marble is 11. So [tex]^{11}C_{3}[/tex]
[tex]=^{10}C_{2}\times^{11}C_{3}[/tex]
Simplifying
[tex]=\frac{10!}{2!(10-2)!}\times\frac{11!}{3!(11-3)!}[/tex]
[tex]=\frac{10!}{2!8!}\times\frac{11!}{3!8!}[/tex]
[tex]=\frac{10\times9\times8!}{2\times1\times8!}\times\frac{11\times10\times9\times8!}{3\times2\times1\times8!}[/tex]
=5×9×11×5×3
=7,425
So the probability that exactly two marbles are red
P(R)=7,425/20,349
P(R)=0.365
Hence, the probability that exactly two marbles are red, is 0.365.
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Ralph hit a softball into the air with an initial upward velocity of 48 feet per
second. The height h in feet of the ball above the ground can be modeled by
h = -16t² +48t + 3, where t is the time in seconds after Ralph hit th
softball.
What is the realistic domain for this function?
Answer:
domain: [0, (6+√39)/4] ≈ [0, 3.06125]
Step-by-step explanation:
You want the realistic domain of a height function h = -16t² +48t + 3.
DomainThe given polynomial is defined for all values of t. Since it represents height above the ground, and after the ball is thrown, only function values in the first quadrant are of interest: h ≥ 0, t ≥ 0.
The height becomes zero at t = (6+√39)/4 ≈ 3.061 seconds after the ball is hit. Hence the realistic domain is [0, (6+√39)/4], the interval in which the ball is above ground.
__
Additional comment
We can solve this using the "completing the square" method.
t^2 -3t = 3/16 . . . . . . divide by -16, add 3/16
(t -3/2)^2 = 3/16 +9/4 . . . . . add 9/4 to complete the square
t = 3/2 ± √(39/16) = (6 ± √39)/4 . . . . . . take the square root, add 3/2
Only the positive value of the solution is applicable to this problem. That value is ...
h = 0 at t = (6 +√39)/4 ≈ 3.061249
Hello a girl out pls
Answer:
D
Step-by-step explanation:
Translate this phrase into an algebraic expression.
Eight less than the product of 21 of goran’s score.
Use the variable g to represent Goran’s score.
Answer:
21g-8
Step-by-step explanation:
The product of Goran's score and 21 = 21g, then subtract 8 from that.
Answer:
lo siento no se mucho de este ap
expand and simplify (x+5)(x-3)
The simplified expression is x² + 2x - 15.
We are given a mathematical expression. The expression has two terms. The first term is (x + 5) and the second term is (x - 3). The terms are multiplied by each other to obtain the final expression. Let the resulting expression be represented by the variable "E". The expression has been solved below.
E = (x + 5)(x - 3)
We will use the distributive property.
E = x*(x - 3) + 5*(x - 3)
E = x*x - x*3 + 5*x - 5*3
E = x² - 3x + 5x - 15
E = x² + 2x - 15
Hence, the expanded and simplified form of the given expression is x² + 2x - 15.
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A, B & C lie on a straight line. G, B & F lie on a different straight line. D, E & F lie on a straight line parallel to AC. DEB = 104°. GBA = 24°. Work out EBF.
The measure of angle EBF is 80° .
In the question ,
it is given that ,
point A, B and C lie on a straight line .
and G , B and F lie on a different straight line .
angle GBA = 24° so ,
GBA + GBC = 180° ...because linear pair
So , GBC = 180 - 24 = 156°
angle CBF = 24° ......because vertically opposite angles are equal .
from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,
156° = ABE + EBF .....(1)
Since the line AC and DF are parallel and BE is the transversal
So , angle DEB + angle ABE = 180°
104° + ABE = 180°
ABE = 180-104
ABE = 76°
Substituting ABE = 76° in the equation (1) ,
we get ,
156 = 76+ EBF
EBF = 156 - 76
EBF = 80°
Therefore , The measure of angle EBF is 80° .
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Find all real numbers x such that
3x - 4 > 5 or -8x - 19 > 21
Click on the correct answer.
Answer:
Option B
Step-by-step explanation:
3x - 4 > 5
3x > 9
x > 3
-8x - 19 > 21
-8x > 40
x < -5
This means that we can eliminate the first option, since it includes all real numbers. We can also eliminate the last option since it doesn't include any real numbers.
The middle option is the only graph that includes numbers from -∞ to -5, and 3 to ∞
Write down the factors of 28 Then,write down the prme factors of 28
the factors of 28 are : 1, 2, 4, 7, 14, and 28.
the prime factors of 28 are : 2, 2, and 7.
Solve :
22r^2+1144r-7656=0
1. 6:N=2:5
2. 5:3=N:6
3. N:20=5:10
4. 1:4=2:N
Question 12 (10 points)
If AWXY is equilateral and AWZY is isosceles, find each missing measure. Answers may be used more than once!
angle 1 =
angle 2 =
angle 3 =
angle 4 =
angle 5 =
The measure of all the angles is given below :
angle 1 = angle 2 = angle 3 = angle 4 = angle 5 = 60°
Given, ΔWXY is an equilateral triangle and ΔWZY is an isosceles triangle.
We have to find the measure of all the angles,
As, ΔWXY is an equilateral triangle
so, ∠WXY = ∠XYW = ∠YWX = 60°
Now, let ∠WZY = ∠WYZ = x and ∠ZWY = y
so, on applying angle sum property, we get
2x + y =180°
so, y = 60°
and 2x = 120°
x = 60°
Hence, angle 1 = angle 2 = angle 3 = angle 4 = angle 5 = 60°
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Complete the equation describing how
and y are related.
XOL2345
911 13 15
1
y
7
17
y = [? ]x + [ ]
Enter the answer that
belongs in [?].
The equation that describing how x and y are related is y = 2x + 7
From the given table we have to choose two points
The first point = (1, 9)
The second point = (2, 11)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (11-9) / 2 - 1
= 2 / 1
= 2
From the table
At x = 0 the value of y = 7
Therefore the y intercept = 7
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Then,
y = 2x + 7
Hence, the equation that describing how x and y are related is y = 2x + 7
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Find the slope (3,-20),(5,8)
Answer: 14
Explanation:
(3, -20) (5, 8)
x1 y1 x2 y2
[tex]\frac{y2 - y1}{x2 -x1}[/tex]
[tex]\frac{8 - -20}{5-3}[/tex] = [tex]\frac{8+20}{5-3} = \frac{28}{2} = 14[/tex]
Fill in the equation for the missing components of the line through (3, 5) and (8, 10)
"ENTER ANSWER AS A DECIMAL
y-5=__(x-3)
The equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)
The first point = (3, 5)
The second point = (8, 10)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (10-5) / (8-3)
= 5 /5
= 1
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope of the line
Consider the point (3, 5)
Substitute the values in the equation
y-5 = 1(x-3)
Hence, the equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)
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HELP MEEEEEE PLEASEEEEE
unable to see the graph
9) Give the following expression in index form
a) √3
For the given expression √3, its index form is written as ( 3 )¹/² .
As given in the question,
Given expression is equal to :
√3
Standard form of writing expression in index form is given by:
√ ( square root ) will express the value in index form as 1 / 2 in the exponent.
√x = ( x ) ¹/²
Here x = 3 substitute the value of x in the standard way of index form we have:
Index form of the given expression is written as :
√3
= ( 3 )¹/²
Therefore, for the given expression √3, its index form is written as ( 3 )¹/² .
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isaac owns a trucking company. for every truck that goes out, isaac must pay the driver $19 per hour of driving and also has an expense of $1.50 per mile driven for gas and maintenance. on one particular day, the driver drove an average of 30 miles per hour and isaac's total expenses for the driver, gas and truck maintenance were $512. write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. define the variables that you use to write the system.
8 hours the driver worked and 240 miles the truck drove.
Assume that the truck traveled y miles per hour. and that the driver worked x hours per day.
The equations describing the provided issue will be
19x + 1.50 y = 512
y = 30x
y = 19 x + 1.50 y = 30 x + 1.50 y
When we enter the second equation into the first one, we get,
19 x + 1.50 (30 x) = 512
19x+ 45x = 512
64x = 512
x = 8
y = 240
The vehicle traveled 240 miles, and the driver put in eight hours' worth of work.
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Find the area of the circle pictured above.
Round your answer to the nearest tenth
Answer:
153.9 units squared
Step-by-step explanation:
A = pi*r^2
A = pi* 7^2
A = pi* 49
A = 153.9
Write a function for the tranformations described below:
"The cubic function shifts 7 units right and 5 units up."
The function for the transformation "The cubic function shifts 7 units right and 5 units up. is written as f(x) = (x - 7)^3 + 5.
How to write the function for the given transformationLet the cubic function be = f(x) = x^3
The transformation required include shifts 7 units right and 5 units up
shifting 7 units to the right is achieved by subtracting 7 units from x in the function hence f(x) = (x - 7)^3
moving 5 units up is achieved by adding 5 units to the function hence
f(x) = (x - 7)^3 + 5
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What is the value of x?
Enter your answer in the box.
x = ___
Answer:
x=32 degrees
Step-by-step explanation:
Since the triangle is equilateral, each angle is = 60 degrees. This means that 2x-4=60
=) 2x=64
=) x=32
The vertex angle of an isosceles triangle is 5 degrees more than 3 times the measure of one of the
base angles. Determine the measure of each angle of the triangle.
The measure of each angle of the triangle are 35°, 35°, 110°.
What is an isosceles triangle?
An isosceles triangle has two equal sides as well as two equal angles.The Greek words iso (same) and skelos are the source of the name (leg).An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.Let's Base angle =x°
Vertex angle = 5° +3x°
The sum of measure of angles of triangle are supplementary.
i.e., Sum of triangle = 180°
So,
x° + x° + 5° + 3x° =180°
5x° + 5° = 180°
5x° = 175°
x° = 175° /5°
x = 35°
Base angle = 35°
Vertex angle = 5°+ 3x°
= 5° + 3×35°
= 5° +105°
Vertex angle = 110°
Hence, the measure of each angle of the triangle are 35°, 35°, 110°.
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Find the value of the expression (2x − 12) + (xy-10) for x = 8 and y = 2.
-
O-8
O 6
O-10
02
The value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.
According to the question,
We have the following expression:
(2x − 12) + (1/2xy-10)
Now, the values of x and y are given to be 8 and 2 respectively.
So, we will put these values of x and y in the given expression:
(2*8-12)+(1/2*8*2-10)
First, we will use multiplication:
(16-12)+(8-10)
4+(-2)
(Note that when two integers are of different signs then the integers are subtracted but the sign in the result is of the larger integer.)
4-2
2
Hence, the value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.
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At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48. Are the cost, y, in dollars and the amount of yogurt, x, proportional? explain. Write an equation to represent this relationship.
Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.
Given:
At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48.
y varies directly as x :
y = kx
k = constant of proportionality
y = 2.56 and x = 32
y = kx
k = y/x
= 2.56/32
k = 0.08
substitute k we get
y = 0.08x.
so x and y are directly proportional.
Therefore Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.
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(Pleasee hurry) Expand the expression: 1/2 (10x + 8)
5x+4 is the simplified form of expression 1/2(13x+5x-6-8x+14)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is
1/2(13x+5x-6-8x+14)
one by two times of thirteen x plus five times of x minus six minus eight times of x plus fourteen.
In the equation x is the variable
plus, minus and multiply are the operators
1/2(13x+5x-6-8x+14)
1/2(10x+8)
Now apply distributive property
1/2(10x)+1/2(8)
5x+4
Hence 5x+4 is the simplified form of expression 1/2(13x+5x-6-8x+14)
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Please help giving out max points!!
Question: Graph the polygon and its image after a dilation with the given scale factor.
See attached
Given Triangle DGF, with vertices D(- 2, 0), G(2, 0), F(2, - 2),Scale factor r = 1.5.SolutionTriangle DGF is plotted, blue figure.
Find the coordinates of the image using the rule:
(x, y) = (1.5x, 1.5y)D' = (1.5*(-2), 1.5*0) = (-3, 0),G' = (1.5*0, 1.5*2) = (0, 3),F' = (1.5*2, 1.5*(-2)) = (3, - 3).The points added to same plot, red figure.
Answer:
D' = (-3, 0)
G' = (0, 3)
F' = (3, -3)
Step-by-step explanation:
Given vertices of the polygon:
D = (-2, 0)G = (0, 2)F = (2, -2)To dilate a figure by a given scale factor, multiply the coordinates of the vertices of the figure by the scale factor:
D' = (-2 × 1.5, 0 × 1.5) = (-3, 0)G' = (0 × 1.5, 2 × 1.5) = (0, 3)F' = (2 × 1.5, -2 × 1.5) = (3, -3)Therefore, the vertices of the image after dilation are:
D' = (-3, 0)G' = (0, 3)F' = (3, -3)Finn wants to buy a sweater for $29.50 and jeans for $42.50 if the sales tax rate is 8.25% what will be the amount of cell taxes on finn’s purchase
The amount of cell taxes on finn’s purchase is $5.94.
How to calculate the value of the tax?Since Finn wants to buy a sweater for $29.50 and jeans for $42.50, the total cost will be:
= $29.50 + $42.50
= $72
If the sales tax rate is 8.25%, the amount on tax will be:
= Tax rate × Total cost
= 8.25% × $72
= $5.94
The tax is $5.94.
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Warren and Dirk are baking cookies for a charity bake sale. First they bake gingersnaps, which are Warren's favorite cookie. Then they bake 120 chocolate crinkles, which are Dirk's favorite. In all, Warren and Dirk bake 204 cookies. Use an equation to find the number of gingersnaps Warren and Dirk bake. gingersnaps Ver en españ
Answer:
g = 204 - 120
Step-by-step explanation:
T - CC = amount of gingersnaps
204 - 120 = 84
Warren and Dirk baked 84 gingersnaps
Julie made 7 out every 10 baskets she attempted during a basketball game. If she attempted to make 30 baskets, how many did she make?
Answer: 21
Step-by-step explanation:
If she makes 7 out of 10 shots she makes 70% of her shots (7/10 x 100 = 70%)
So if she makes 30 shots, 21 will go in the basket
(30)(0.70) = 21