Y=-3|x+2|+8 Slope of the rays
Answers
The slopes of the rays of the absolute value function, y = -3·|x + 2| + 8 are 3 and -3
What is an absolute value function?In an absolute value function, an algebraic expression is contained within an absolute value symbol.
The given absolute value function is; y = -3·|x + 2| + 8
The slope of the rays are found as follows;
The general form of the absolute value function is; f(x) = a·|x - h| + k
The vertex of the function is the point (h, k)
The slope of the function is a
Comparing the specified function, y = -3·|x + 2| + 8, to the general function, we get;
The vertex of the function is (h, k) = (-2, 8)
The slope of the rays of the function are; a = 3
Slope of the ray 1 = (8 - (-19))/(-2 - (-11)) = 3
Slope of ray 1 is therefore; 3
Slope of ray 2 = (8 - (-19))/(-2 - 7) = -3
The slope of the ray 2 is therefore; -3
The slope of the rays are; 3 and -3
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Related Questions
question provided in picture only need assistance with part b
Answers
PART B
The probability is 1/2
STEP - BY - STEP EXPLANATION
What to find?
The probability of identical twins given that the twins consists of two boys.
Let A be the event of identical twins.
Let B be the event of having two boys as twins.
From the table given;
P(A) = 2/38
P(B)= 2/38
Recall the formula for a condititional probabibility
[tex]P(A\text{ \backslash{}B)=}\frac{P(A\text{ n }B)}{P(B)}[/tex]Note that:
P(A n B) =1/38
[tex]P(A\text{ \backslash B) =}\frac{\frac{1}{38}}{\frac{2}{38}}[/tex][tex]=\frac{1}{38}\times\frac{38}{2}[/tex][tex]=\frac{1}{2}[/tex]Therefore, the probability of identical twins given that the twins consists of two boys is 1/2
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State all integer values of x in the interval -4 ≤ x ≤ 3 that satisfy the following inequality:
-5x - 3 > 8
Answers
Answer:
[tex]-4 \leq x < -2.2[/tex]
Step-by-step explanation:
-5x - 3 > 8
-5x > 11
x < -11/5
We know that -4 ≤ x ≤ 3 and x < -11/5 (-2.2)
-4 <= x < -2.2
Jenny’s rectangular bedroom has one wall that is 5 feet long. The distance from one corner of the bedroom to the other corner is 13 feet. How long is the other wall?
Answers
The other wall is 12 feet long can be evaluated using Pythagoras theorem.
What is Pythagoras theorem?
The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.
Here given in the question that one side of the wall 5 feet
So as it is a rectangular bedroom it can be split into 2 right-angled triangles.
So the hypotenuse of the triangle is 13 feet
Now using the Pythagoras theorem we can find out the length of the other wall
b²=h²-p²
b²=13²-5²
b²=169-25=144
b=√144
b=12 feet
Hence the other wall is 12 feet long.
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Match the Parallel line of y=-1/2x-2
Answers
The family of all linear equations that are parallel to y=-1/2x-2 is defined as:
y = (-1/2)*x + b
Such that b ≠ -2.
Which lines are parallel to the given one?We know that a general linear equation is written in the slope-intercept form as:
y = m*x + b
Where m is the slope and b is the y-intercept.
We know that two linear equations are parallel if and only if the lines have the same slope and a different y-intercept.
So the family of lines parallel to:
y = (-1/2)*x - 2
Are of the form:
y = (-1/2)*x + b
Where b ≠ -2.
All these lines are parallel to the given ones.
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Write the fractions in order from greatest to least 1/4 3/6 1/8
Answers
3/6, 1/4, 1/8
Step-by-step explanation:
All three fractions have a common denominator of 24.
1/4=6/24
3/6=12/34
1/8=3/24
Lastly, order them from greatest to least, hence 3/6, 1/4, and 1/8
While digging in his garden Will pushes a shiv into the ground with a force of 585 newtons at an angle of 80° with the ground
Answers
Force, F = 585 N
Angle, θ = 80°
The diagram that shows the resolution of the force into its rectangular component is drawn below
The magnitude of the horizontal component is:
[tex]\begin{gathered} F_x=585\sin 80 \\ F_x=585(0.9848) \\ F_x=576N \end{gathered}[/tex]The magnitude of the vertical component is:
[tex]\begin{gathered} F_y=585\cos 80 \\ F_y=585(0.174) \\ F_y=102N \end{gathered}[/tex]Therefore, the magnitudes of the horizontal and vertical components of the force are (576, 102)
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answers
Answer:
x = 1 , x = 13
Step-by-step explanation:
(x - 7)² = 36 ( take square root of both sides )
x - 7 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 7 to both sides )
x = 7 ± 6
then
x = 7 - 6 = 1
x = 7 + 6 = 13
A tennis star was hired to sign autographs at a convention. She was paid 3000 plus 2% of all admission fees collected at the door. The total amount she received for the day was 3540. Find the total amount collected at the door
Answers
Let x be the total amount collected at the door. Then, we can write
[tex]3000+(0.02\times x)=3540[/tex]where the 0.02 denotes the comission of 2%. From this equation, we can find x.
Then, by moving 3000 to the right hand side, we have
[tex]\begin{gathered} 0.02x=3540-3000 \\ \end{gathered}[/tex]which gives
[tex]0.02x=540[/tex]Now, by moving 0.02 to the right hand side, we get
[tex]x=\frac{540}{0.02}[/tex]then, x is given by
[tex]x=27000[/tex]Therefore, the total amount collected at the door is $ 27 000.
Please help me with this and make it quick because it due 6:00
Answers
• x(5-2)=4x-x
distributive property:
5x -2x = 4x -x
3x =3x
Infinite solutions
• 14x - 17 -8x + 2 = 12x +3 -x - 10
Combine like terms:
14x -8x -12x +x = 3 - 10 + 17 - 2
-5x= 8
x = -8/5
Unique solution
• 6(x-2)=6x-12
Apply distributive property:
6(x) + 6(-2) = 6x-12
6x - 12 = 6x - 12
Since both sides are equal:
Infinite solutions
• 2/3x - 7/4 = 4/3x - 2/3 (x+5)
Apply distributive property:
2/3x-7/4 = 4/3x - 2/3(x) - 2/3(5)
2/3x-7/4= 4/3x-2/3x - 10/3
Combine like terms
2/3x + 2/3x - 4/3x = -10/3 + 7/4
0 = -19/12
Since 0 is not equal to -19/12
No solution
what do we do with 3 1/3 in the problem and also i need the answer to all of it
Answers
The answer after solving the expression 12x - 3y / 4x - z with x = 3,y=1/3 and z = 5 is 5.
Given:
x = 3 , y = 1/3 and z = 5 and expression 12x - 3y / 4x - z.
substitute the x,y,z values in expression.
= 12(3)-3(1/3) / 4(3)-5
= 36 - 3/3 / 12 - 5
= 36 - 1 / 7
= 35/7
= 5.
Therefore the answer after solving the expression 12x - 3y / 4x - z with x = 3,y=1/3 and z = 5 is 5.
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write the line, in slope-intercept form,that is (a) parallel and and (b) perpendicular to the line 4x +2y=6 that passes through the point (2,6).
Answers
We have the following equation given:
[tex]4x+2y=6[/tex]If we solve in the form y=mx+b we got:
[tex]y=-2x+3[/tex]Part a
S
what tip of function line exponential or quadratic best models in each table
Answers
This makes the correct answer to be exponential function
The weights of the melons harvested from a patch are distributed normally. The mean weight is 6 pounds; the standard deviation is 0.25 pounds. Which is closest to the percent of melons that weigh 6.25 pounds or less?A) 34B) 68C) 84D) 98
Answers
As it is normally distributed, we can use Z to find the result.
Procedure
0. Finding the value of ,Z
[tex]Z=\frac{x-\mu}{\sigma}[/tex]1.2. Replacing the values given in the problem:
[tex]Z=\frac{6.25-6}{0.25}[/tex][tex]Z=\frac{0.25}{0.25}=1[/tex]2. As it is normally distributed:
[tex]P(x\le6.25)=P(Z\le1)[/tex]3. Using the normal standard table, we can conclude:
[tex]P(Z<1)=0.8413[/tex]As it is asking for a percentage, we multiply by 100.
Answer: C) 84%
Explain step by step how to complete -0.7 = 9.1
Answers
Answer:
9.1.4 -0.7=9.1
Step-by-step explanation:
Step 1: Determine the Assessment Unit ID (AUID) of the waterbody of interest.
Step 2: Express the quadratic equation in standard form
(13.9 x 108) - (2 x 102
Answers
Answer
Answer = (6.95 × 10⁻¹⁰)
Explanation
We are asked to solve (13.9 × 10⁻⁸) ÷ (2 × 10²)
To solve this, we will have
[tex]\begin{gathered} \frac{13.9\times10^{-8}}{2\times10^2}=\frac{13.9}{2}\times\frac{10^{-8}}{10^2}=6.95\times10^{-8-2} \\ =6.95\times10^{-10} \end{gathered}[/tex]Hope this Helps!!!
write 10x10x10x10x10 with an exponet explain how you decided what exponet to write
Answers
Answer:
10^5
Step-by-step explanation:
10 is multiplied by itself 5 times so you use 5 as the exponent
10 is the number you're multiplying so it the bottom number
10^5
D
If the conditional statement "If I use my cell phone too much, my bill will be expensive," is true, which other statement must also be true?
If I do not use my cell phone too much, my bill will not be expensive.
O None must be true.
Of my bill is expensive, I used iny cell phone too much.
If my bill is not expensive. I did not use my cell phone too much
4
Answers
Answer: "If my bill is not expensive. I did not use my cell phone too much"
Reason:
The original statement is of the form "If P, then Q"
P = "I use my cell phone too much"
Q = "my bill will be expensive"
An equivalent form to the original condition is known as the contrapositive of the form "If not Q, then not P". We swap the positions of P and Q. We also negate each part. You can use a logical truth table to verify that the conditional and contrapositive have equivalent truth values, which means they are effectively equivalent statements.
Answer:
If my bill is not expensive. I did not use my cell phone too much
Step-by-step explanation:
Function A represents the amount of money in a jar based on the number of quarters in the jar. Function B represents your distance from home over time. Compare the domains.
Answers
The domains of each function are classified as follows:
Function A: Discrete domain.Function B: Continuous domain.What is the domain of a function?
The domain of a function is the set composed by all the input values that are assumed by the function.
For each function in this problem, the inputs are given as follows:
Function A: number of quarters in the jar.Function B: time.Hence, the domain of function A is a discrete domain, as the number of quarters in the jar can assume countable values such as 0, 1, 2, ..., it does not assume decimal values.
For function B, the domain is a continuous domain, as measures of time can assume decimal values, for example, 10.5 minutes.
These differences discussed represent the comparison of the domains of each function.
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The point (3,-1)( 3 , − 1 ) is a solution to this system of equations:
Answers
The system of equations we have is:
[tex]\begin{gathered} -3x-2y=-7 \\ x+4y=1 \end{gathered}[/tex]And we need to check if the point (3,-1) is a solution.
Step 1. Identify the values of x and y from the point.
In a point, the first number represents the x-value, and the second number represents the y-value. So in point (3,-1) 3 is the x-value, and -1 is the y-value:
[tex]\begin{gathered} x=3 \\ y=-1 \end{gathered}[/tex]Step 2. Substitute the x and y-value into the first equation and check that the result is equal to -7.
The first equation is:
[tex]-3x-2y=-7[/tex]Substituting x=3 and y=-1:
[tex]-3(3)-2(-1)=[/tex]Solve the operations:
[tex]-9+2=-7[/tex]Since we get -7 as the result, (3,-1) is a solution for the first equation. But we still need to check if the point is a solution for the second equation.
Step 3. Substitute the x and y values into the second equation and check that the result is 1.
The second equation of the system is:
[tex]x+4y=1[/tex]Substituting x=3 and y=-1:
[tex]3+4(-1)=[/tex]Solving the operations:
[tex]3-4=-1[/tex]The result we get is -1, not 1. Thus, since the point (3,-1) is not a solution for the second equation, it is also not a solution to the system of equation.
Answer: False
Mr. Jensen purchased an airline ticket on a web site. The original price of the airline ticket was $473.00. He used a coupon code to receive a 20% discount. A sales tax of 12% was applied after the discount. What was the total purchase price of the airline ticket after the discount, including sales tax?
A $105.92
B $332.99
C $423.81
D $529.76
Answers
The price of the online ticket after discount, including sales tax, is $423.81.
What is percentage?Percentage is a measurement to find the value of a given number out of a hundred.
Given that,
The original price of the airline ticket = $473
Discount after applying coupon code = 20%
The price after applying coupon code = 473x4/5 = 378.4
Since, there is a sales tax of 12%,
So the price of airline ticket after sales tax = 378.4 x 112/100 = 423.808
The price of online ticket after discount and including sales tax is $423.81
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The cat of a play had a party. The drama teacher erved 20 cookie and 40
carrot tick a refrehment. Each cat member ate the ame number of
whole cookie and the ame number of whole carrot tick. Nothing wa left
over. The drama teacher did not eat. How many cat member might have
been at the party? Explain
Answers
Given two quantities (number of cookies and carrot sticks), we find the greatest common divisor (gcd) to know that were 20 cast members at the party. Below is a solution algorithm written in Python.
The Solution Algorithmif __name__ == '__main__':
# Define variablesa = int()
b = int()
x = int()
gcd = int()
# Number of cookies
a = 20
# Number of carrot sticks
b = 40
# Calculate the greatest common divisor (gcd) between the number of cookies and the number of carrot sticksgcd = 1
x = 1
while x<=a:
if a%x==0 and b%x==0:
if x>gcd:
gcd = x
x = x+1
# Displaying resultsprint("Number of cookies: ",a)
print("Number of carrot sticks: ",b)
print("Number of cast members at the party: ",gcd)
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A box of fruit has four times as many oranges as grapefruit. Together there are
60 pieces of fruit. How many pieces of each type of fruit are there?
Answers
The number of mangoes = 48
The number of grapefruit = 12
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A box of fruit has four times as many oranges as grapefruit.
And, Total number of fruit = 60 pieces
Now,
Let number of grapefruit = x
Then, Number of Mangoes = 4x
So, We can formulate;
⇒ x + 4x = 60
Solve for x as;
⇒ 5x = 60
⇒ x = 12
Thus, Number of grapefruit = x
= 12
Then, Number of Mangoes = 4x
= 4 × 12
= 48
Therefore, The number of mangoes = 48
The number of grapefruit = 12
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You are tasked with analyzing a design that has been drawn for a bridge over an existing two-lane road. The arch over the road is in the shape of a half-ellipse that is 40 feet wide at the base of the arch and it is 15 feet tall at the center of the arch. The bridge must have a 13-foot clearance for vehicles on the road. The 22-foot-wide road is centered directly beneath the highest point of the arch. a) the semi-truck will NOT be able to pass under the bridge,so it is time to make an adjustment. You will need to modify the design of the bridge. Keep the arch shape as half an ellipse, and the base as 40 feet wide. You may adjust the bridge’s arch up to 18 feet above the center line of the two-lane road below, but no more than that because of restrictions concerning the road crossing over the bridge. Give a new equation for the ellipse that represents your modified design.
Answers
We are asked to determine the equation of an ellipse that has a base of 40 feet and a height of 18 feet. This can be visualized in the following diagram:
The general form of the equation of an ellipse is:
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]We have set the origin of the coordinate system to be in the middle of the ellipse. The value of "a" is the x-intercept of the ellipse and the value of "b" is the y-intercept of the ellipse. Therefore, the equation is:
[tex]\frac{x^2}{(20)^2}+\frac{y^2}{(9)^2}=1[/tex]Now, we solve the squares:
[tex]\frac{x^2}{400}+\frac{y^2}{81}=1[/tex]And thus we have determined the equation of the ellipse.
What is the value of x?
A) x=15
B) x=22
C) x=12
D) x=20
Answers
Answer: It would be c x=12
Step-by-step explanation:
The radius of a circle is 18 ft. Find its área un terms of pi
Answers
Answer
Area = 324π ft²
Explanation
The area of a circle is given as
Area = πr²
where
π = pi
r = radius of the circle = 18 ft.
Area = πr²
Area = π (18²)
Area = 324π ft²
Hope this Helps!!!
If a_1=6a
1
=6 and a_n=a_{n-1}+3a
n
=a
n−1
+3 then find the value of a_4a
4
.
Answers
The fourth term a₄ of the sequence is 15
How to determine the value of a₄?The definition of the function is given as
a₁= 6
aₙ = aₙ₋₁ + 3
The above definitions imply that we simply add 3 to the previous term to get the current term
using the above as a guide,
so, we have the following representation
a₂ = 6 + 3
a₂ = 9
Also, we have
a₃ = 9 + 3
a₃ = 12
Lastly, we have
a₄ = 12 + 3
Evaluate the equation
a₄ = 15
Hence, the value of a₄ is 15
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In 2.073, in which place is the 7?
Answers
Answer:
Step-by-step explanation:
tents is what place it is <3
PLS SOMEONE HELP ME OUT ASAP
Answers
The results of the transformations carried out are respectively;
1) Preserves only angles but not distance
2) Preserves both angles and distance.
3) Preserves only angles but not distance
How to Interpret Transformation of Objects?
In transformations, there are different types such as dilation, reflection, translation, rotation, e.t.c
1) Dilation of a quadrilateral by a scale factor of 2;
When we dilate by a scale factor of 2, it simply means we are enlarging the side lengths by a scale factor of 2. Thus, the side lengths will increase but angles remain the same.
2) Translation of a rhombus 3 units to the right and then a reflection across the x-axis;
When we translate an object, it means we just move it from one point to the other and this means that the length and angles do not change, Similarly, reflection is just a mirror image and it also means that the length and angles do not change.
3) Translation of a triangle 2 units to the left and then a dilation by a scale factor of 5 about the origin;
This will end up changing the side lengths but not the angles.
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Seven times the quotient of x and 9 added to 2
gives
25. What is x?
Answers
After making and solving an equation, we can say that the value of x is 1.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.Like this: 2x - 4 Equals 2. In the above example, the variable x exists.So, to find the value of x, we will solve the equation:
7(x/9) + 2 = 25/9
Now, solve this equation as follows:
7(x/9) + 2 = 25/9
7x/9 = 25/9 - 2
7x/9 = 7/9
x = 1
Therefore, after making and solving an equation, we can say that the value of x is 1.
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Objective function Z=3x+6yFind the value at each corner of the graph
Answers
Given: An objective function
[tex]z=3x+6y[/tex]with constraints-
[tex]\begin{gathered} \\ \begin{cases}{x\ge0,y\ge0} \\ {2x+y\leq12} \\ {x+y\ge6}\end{cases} \end{gathered}[/tex]Required: To graph the linear inequalities representing the constraints and determine the objective function's value at each corner.
Explanation: The inequalities can be graphed by considering them as equations and then determining the shaded region by less than or greater than symbol.
The equation for the first inequality is-
[tex]2x+y=12[/tex]This represents a straight line passing through points (6,0) and (0,12).
The shaded region will be below this line as the inequality is-
[tex]2x+y\leq12[/tex]Similarly, the inequality-
[tex]x+y\ge6[/tex]Represents a shaded region above the line x+y=6.
The inequalities-
[tex]x\ge0,y\ge0[/tex]Represents the positive values of x and y. Hence we need to determine the graph in the first quadrant.
The graph of the inequalities is-
The graph in blue represents the inequality-
[tex]2x+y\leq12[/tex]While the graph in green represents the inequality-
[tex]x+y\ge6[/tex]The corner points of the common shaded area are A(0,6), B(0,12), and C(6,0).
Now the value of the objective function at these points is-
a) At A(0,6)
[tex]\begin{gathered} z=3(0)+6(6) \\ =36 \end{gathered}[/tex]b) At B(0,12)
[tex]\begin{gathered} z=3(0)+6(12) \\ =72 \end{gathered}[/tex]c) At C(6,0)
[tex]\begin{gathered} z=3(6)+6(0) \\ =18 \end{gathered}[/tex]Final Answer: a) The graph is drawn.
b) 36,72,18