Answers
Answer:
The equation in slope-intercept form is:
[tex]y=\frac{1}{3}x+3[/tex]
So the second option is the correct one.
Step-by-step explanation:
Step 1: Identify the gradient
The perpendicular line's equation is given as:
[tex]y=-3x+4[/tex]
This equation is in the form of:
[tex]y=mx+b[/tex]
Upon comparing the [tex]x[/tex] components of both equations, we get[tex]-3x=mx\\\text{Remove the}~ x~ \text{from both sides:}\\-3=m\\m=-3[/tex]
So, the gradient of this 'reference' equation is -3.
The equation we need to find is perpendicular to this 'reference' equation.
So, its gradient should be the negative reciprocal of the gradient of the 'reference' equation.
The negative reciprocal of -3 is:
[tex]-\frac{1}{(-3)}\\=\frac{1}{3}[/tex]
So, the gradient of our equation is [tex]\frac{1}{3}[/tex].
Step 2: Create the equation:
The equation crosses the x-axis at -9, which means its y-coordinate is 0 (at x-axis, y=0) ,so its coordinate is [tex](-9,0)[/tex].
The formula for an equation is:
[tex]y-y_{1}=m(x-x_{1})[/tex]
The coordinate [tex](x_{1},y_{1})[/tex] is [tex](-9,0)[/tex], and the gradient ([tex]m[/tex]) is [tex]\frac{1}{3}[/tex].
Substitute the values into the equation:
[tex]y-y_{1}=m(x-x_{1})\\y-0=\frac{1}{3}(x-(-9))\\\\\text{Simplify}\\y=\frac{1}{3}(x+9)[/tex]
[tex]\text{Simplify further}\\y=\frac{1}{3}x+3[/tex]
Since, the slope-intercept form is:
[tex]y=mx+b[/tex]
We already have our equation in the slope-intercept form.
Related Questions
A tent pole that is 9 feet tall is secured to the ground with a piece of rope that is 15 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.
Answers
Answer:
12 ft
Step-by-step explanation:
To find the base (b), you would first need to sketch a right triangle using the following:
a = 9
c = 15
Using the Pythagorean theorem [tex]a^{2} +b^{2} =c^{2}[/tex], you would change it to [tex]c^{2} -a^{2} =b^{2}[/tex] to fit the question. Next, you would plug in the numbers to the corresponding letter.
[tex]15^{2} -9^{2} =b^{2}[/tex]
[tex]225-81=144^{2}[/tex]
[tex]\sqrt{144} =b[/tex]
[tex]12=b[/tex]
The horizontal distance from the tent pole to the rope along the ground will be equal to 12 feet.
What is the Pythagoras' Theorem?According to the Pythagoras theorem, if a triangle has a straight angle (90 degrees), the hypotenuse's square is equal to the total of its other two sides' squares.
As per the given in the question,
Height of tent pole, p = 9 feet
Height of rope, h = 15 feet
Let the horizontal distance from pole to rope is b.
Use Pythagoras' theorem,
h² = p² + b²
15² = 9² + b²
b² = 225- 81
b = √144
b = 12 feet.
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Which function matches the graph?
-5
-2
3/
7
A. f(x) =
(x + 3)(x - 5)(x + 7)²(x - 2)²
B. f(x) = (x - 3)²(x + 5)²(x-7)(x + 2)
C. f(x) = (x - 3)(x + 5)(x - 7)²(x + 2)²
D. f(x) = (x - 3)²(x + 5)(x-7)(x + 2)²
E. f(x) = (x + 3)²(x - 5)(x-7)²(x + 2)
Answers
Answer: B
Step-by-step explanation:
The root at [tex]x=-5[/tex] cuts through the x-axis, and has a multiplicity of one. So, it corresponds to a factor of [tex](x+5)[/tex].
The root at [tex]x=-2[/tex] bounces off the x-axis, and has a multiplicity of two. So, it corresponds to a factor of [tex](x+2)^2[/tex].
The root at [tex]x=3[/tex] cuts through the x-axis, and has a multiplicity of one. So, it corresponds to a factor of [tex](x-3)[/tex].
The root at [tex]x=7[/tex] bounces off the x-axis, and has a multiplicity of two. So, it corresponds to a factor of [tex](x-7)^2[/tex].
ASAP PLEASE HELP *20 POINTS*
1.If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, what transformation occurs from f(x) to h(x)?
A.Shift left 3 units
B.Shift right 3 units
C.Shift up 3 units
D.Shift down 3 units
2. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the vertex affected? Select all that apply.
A.The vertex will not change.
B.The vertex will shift right 3 units.
C.The vertex will shift left 3 units.
D.The vertex will shift up 3 units.
E.The vertex will shift down 3 units.
F.The vertex will not move up or down.
G.The vertex will not move right or left.
3. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the range affected?
A.The range will not change.
B.The range will be all real numbers.
C.The range will change from y ≥ 0 to y ≥ -3.
D.The range will change from x ≥ 0 to x ≥ -3.
Answers
if the parent function f(x) = |x| is transformed to h(x) = |x| - 3,
1. The transformation occurs from f(x) to h(x) is D. Shift down 3 units
2. The vertex is affected by:
E. The vertex will shift down 3 unitsG. The vertex will not move right or left3. The range will C. change from y ≥ 0 to y ≥ -3.
What is transformation?This is an ordered movement of image or object as seen in geometry. The instance here the movement is done by the graph f(x) and h(x) as described.
The type of movement described is called translation.
What is the range?The range refers to the output of the graph and is typically the y direction.
The range here changed from the origin which is the initial vertex and included point y ≥ -3
It should be noted that the origin of the graph refers to the point y ≥ 0
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22 Olivia has $700 in her bank account at the beginning of the
summer. She wants to have at least $150 in her account at the
end of the summer. Each week she withdraws $40 for food
and entertainment.
a. Write an inequality for this situation. Let x represent
the number of weeks she withdraws money from her
account.
b. What is the maximum whole number of weeks
that Olivia can withdraw money from her account?
Explain how you know your answer is correct.
Answers
a. The amount remaining in the account after x week is 700 - 40x
b. Olivia can withdraw can withdraw money from her account money for approx. 13 weeks.
Let x represent the number of weeks. Then the amount of withdrawal in this time is 40x
So, the amount remaining in the account after x weeks is 700 - 40x
Since he needs 150$ in the account for safety net, we must have
700 – 40x ≥ 150
So,
700 - 150 ≥ 40x
550 ≥ 40x
550/40 ≥ x
x ≤ 13.75
Hence, he can withdraw money for approx. 13 weeks.
What is withdraw?Withdrawal involves removing money from a bank account, savings plan, pension or trust. In some cases, conditions must be met for funds to be withdrawn without penalty, and an early withdrawal penalty usually occurs when a condition of the investment agreement is violated. Withdraw money from account: With this account you can withdraw a maximum of $500 per day. withdraw money/money/savings With the financial crisis, people had to withdraw their savings.
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The radius of a circle can be approximated using the expression sqrt(((A)/(3))) where A represents the area . A circular kiddie swimming pool has an area of about 28 square feet . An inflatable full-size circular pool has an area of about 113 square feet , how much greater is the radius of the full-size pool than the radius of kiddie pool? Round to the nearest whole number .
Answers
The radius of the full-size pool is 2 times greater than the radius of kiddie pool
How to determine the ratioThe formula for determining the area of a circle is expressed mathematically as;
Area = πr²
Where;
r is the radius of the circleπ has a value of 3.142From the information given, we have that;
Radius = √A/3
Where;
A is the radius of the circle
For the circular kiddie, we have;
Radius = √28/3
Find the ratio
Radius = √9. 3
Find the square root
Radius = 3 feet
For the circular pool
Radius = √ 113/3
Find the ratio
Radius = √37. 66
Find the square root
Radius = 6 feet
We then have;
Radius of the pool/radius of the kiddie pool
6/3
Find the quotient
2
Hence, the value is 2
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In a given year, residents of a country spent approximately $52.9 billion on their pets. Of this amount, $17.3 billion was for veterinarian bills. What percent of the total was spent on veterinary cave?About ...% of the total was spent on veterinary care.
Answers
32.7 %
Explanation
we can easily solve this by using a rule of three
Step 1
Let x represents the percent of the total that was spent on veterinary
[tex]\begin{gathered} \text{ \$ 52.9 billions}\rightarrow100\text{ percent} \\ \text{ \$ 17.3 billons}\rightarrow x\text{ percent} \end{gathered}[/tex]
the ratios are equal , so we have a proportion
[tex]\frac{52.9}{100}=\frac{17.3}{x}[/tex]Step 2
solve the equation
[tex]\begin{gathered} \frac{52.9}{100}=\frac{17.3}{x} \\ \text{cross multiply} \\ 52.9x\cdot17.3\cdot100 \\ 52.9x=1730 \\ \text{divide both sides by 52.9} \\ \frac{52.9x}{52.9}=\frac{1730}{52.9}=32.7 \\ x=32.7 \\ \\ \end{gathered}[/tex]so, the answer is
About 32.7% of the total was spent on veterinary care.
I hope this helps you
a and b agree to try to meet between 12 and 1pm for lunch. assuming that the arrival times and of a and b are uniform between 12 and 1pm, independently. if whoever comes first waits 15 minutes and then leaves, what is the probability that they actually meet for lunch?
Answers
. of the 27 tasks available, 3 will pay $1000, 5 will pay $500, 10 will pay $200, and 9 will pay $100. you are assigned two tasks. what is the probability that you will make at least $1300?
Answers
The probability that you will make at least $1300 is 2/39 or 0.0513.
Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.
probability = desired outcome / total outcomes
Using combinations, if there are 27 tasks available, then there are 351 combinations of two tasks assigned.
27C2 = 351
Also, count how many ways you could make at least $1300.
# ways = 2 of $1000 each or 1 of $1000 and 1 of $500
# ways = (3C2) + (3 x 5)
# ways = 3 + 15
# ways = 18
Solve for the probability by dividing the number of the desired outcomes by the number of total possible outcomes.
probability = desired outcome / total outcomes
probability = 18 / 351
probability = 2/39 or 0.0513
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What is x in this equation -7(x+-2)=-63
Answers
The given equation is [tex]\fbox{-7(x+(-2))=-63}[/tex]
Multiplying -7 with x and -2
=> -7x+14 = -63
Transposing 14 to right hand side with change in sign,
=> -7x = -63-14
=> -7x = -77
Canceling ‘-‘ on both sides ,
=> 7x = 77
=> x=[tex]\frac{77}{7}[/tex]
=> x = 11
Hence the required value of x is [tex]\fbox{x= 11}[/tex].
I inserted a picture because it was too much to type but please, if you answer try and do it fast. It's homework.
Answers
Jaleel and Angela purchased a bag of sugar and used it evenly so the amount of flour that they each need, based on their brownie recipes are:
Angela - 5 cups of flour Jaleel - 6 ²/₃ cups of flourHow to find the amount of flour needed?Jaleel and Angela purchased a 20-cup bag of sugar and divided it evenly which means that they each get 10 cups of sugar.
The number of cups of sugar needed per cup of flour is:
= Change in sugar / Change in flour
= (3 - 1.5) / (2 - 1)
= 1.5 cups of sugar
The amount of flour needed would be:
= Number of cups of sugar / Cups of sugar per cup of flour
= 10 / 1.5
= 6 ²/₃ cups of flour
Angela's recipe shows that the cups of sugar needed per cup of flour is:
= (2 - 0) / (1 - 0)
= 2 cups of sugar
This means that with 10 cups of sugar, the amount of flour needed is:
= 10 x 1/2
= 5 cups of flour
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PLS HELP WILL MARK BRAINLIEST
Answers
Answer:
did not understand waht should we do
Which of the following statements is a valid polynomial identity?
Statement 1: x3 + 27 = (x + 3)(x2 − 3x + 9)
Statement 2: x3 + 27 = (x − 3)(x2 + 3x + 9)
a
Only statement 1 is valid.
b
Only statement 2 is valid.
c
Statement 1 and statement 2 are valid.
d
Statement 1 and statement 2 are invalid.
Answers
Answer:
the answer is C :) good luck
Beau spends €15000 buying computer
materials for his office. Each year the
material depreciates by 12%.
a Find the value of the material after three
years.
b Find how many years it takes for the
materials to be worth €5 000.
Answers
Answer:
First, you must specify if the depreciation is simple or compound
subtract (17x^2-6x+12) from (21x^2+13x-9)
Answers
we will solve as follows:
[tex](21x^2+13x-9)-(17x^2-6x+12)=4x^2+19x-21[/tex]Find the area of thisirregular figure.9 ft8 ft15 ft26 ft
Answers
The area of the irregular figure will be equal to the sum of area of triangle and the area of the rectangle.
The required area can be determined as,
[tex]\begin{gathered} A=A_t+A_r \\ =(\frac{1}{2}\times8\text{ ft}\times9\text{ ft)+(15 ft}\times26\text{ ft)} \\ =36ft^2+390ft^2 \\ =426ft^2 \end{gathered}[/tex]Thus, the required area of the irregular figure is 426 square feet.
Need help on this asap
Answers
Answer:
K=0 N=3 and I=-2
it's
3+-20= -17
Let o be the point of intersection of the diagonals of a quadrilateral abcd. prove that abcd could be a trapezoid (that is, it has one pair of opposite sides parallel) if aaod=aboc
Answers
Given the details above, the sequence of steps below shows that ABCD is a Trapezoid.
What is a Trapezoid?A trapezoid, also known as a trapezium, is a closed, flat object with four straight sides and one set of parallel sides. A trapezium's parallel sides are known as the bases, while its non-parallel sides are known as the legs.
Given:
The diagonals of the quadrilateral ABCD intersect at o where AO/BO = CO/DO; which also means that
AO/CO = BO/DO the proof is given as follows:
Create line OE || DC in a way that E lies on BC.
In ΔBDC, based on the Basic Proportionality Theory,
BO/OD = BE/EC ............................1
It is also given that:
AO/CO = BO/DO ..........................2
Hence, from Equations 1 and 2,
AO/CO = BE/EC
Thus, we can state that on the basis of the Converse of the Basic Proportionality Theorem,
OE || AB
Since AB || OE || DC, it is correct to state that ABCD is a Trapezoid.
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Please help me on this question need it by today
Answers
it means 3x -15
90 +15 is 105
105 divided by 3 is 35
X=35
triangle are given as (x+ 3)°, (2x - 18)° and
90°.
(X +3) + (2x-18) + 90 = 180
3x+75=180
Subtract 75
3x=105
Divide 3
X=35
PLEASE ANSWER ASAP GIVING CROWN (don't know what its called)
Which point is not included in the solution set for the inequality?
(–2, 1)
(1, 3)
(4, 3)
(5, –1)
Answers
Answer: The answer is B. At least that is what I think the answer would be.
Step-by-step explanation: I hope this helps.
A car that originally valued at $32,000 loses 18% of its value every 3 years. What will be the value of the car after 12 years?
Answers
The value of the car after 12 years is $15,229.50
Here, we want to calculate the value of a car that loses a percentage of its origial value after some years
To do this, we shall need an exponential equation that represents decay or depreciation
We can have this as;
[tex]P=I(1-r)^t[/tex]where;
P is the present value that we want to calculate
I represents the original value of the car which is $32,000
r is the percentage of decrease per year
From the question, there is a decrease of 18% every 3 years
The percentage decrease per year will be 18%/3 = 6%
6% is same as 6/100 = 0.06
t represents the time frame we are considering = 12 years
We proceed to input all these values into the equation above
We have it as;
[tex]\begin{gathered} P=32,000(1-0.06)^{12} \\ \\ P=32,000(0.94)^{12} \\ \\ P\text{ = \$15,229.50} \end{gathered}[/tex]Solve for the single variable in the equation below:
−16+x=−27
Answers
Answer:
x = -11
Step-by-step explanation:
Hello!
This is a one-step equation. To solve for x, you simply have to isolate it.
Since -16 is being added to x, we can add 16 to both sides to cancel out the negative 16.
Solve for x-16 + x = -27-16 + x + 16 = -27 + 16x = -11The value of x is -11.
Please helppp as fast as possible 25 POINTS**
FIND THE DOMAIN & RANGE OF THE FUNCTION
g(x)=|x + 4|
Please helppp as fast as possible
Answers
The domain and the range of the function g(x) = |x + 4| are oo < x < oo and y >= 4
What is domain?The domain of a function are the set of output values, the function can take
What is range?The range of a function are the set of output values, the function can take
How to determine the domain and the range?The definition of the function is given as
g(x) = |x + 4|
From the definition of the above function, we can see that the function is an absolute value function
This means that the function has a domain of all set of real values
This domain is represented as
Domain: -oo < x < oo
For an absolute function represented as
f(x) = |x + k|
The range is
y >= k
This means that the range of g(x) = |x + 4} is y >= 4
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In a quadrilateral, two angles are x°, two angles are (3x+8)°. What is x and the measures of the angles?
Answers
Step-by-step explanation:
the sum of all angles in any quadrilateral is 360°.
so,
x + x + 3x + 8 + 3x + 8 = 360
8x + 16 = 360
8x = 344
x = 344/8 = 43°
3x + 8 = 3×43 + 8 = 129 + 8 = 137°
so, the angles are
43°
137°
43°
137°
The drivers at a warehouse need to deliver 40,000 packages each day. The warehouse has 128 trucks. Each truck has 350 packages. The drivers deliver all the packages on the trucks. Do the warehouse drivers deliver enough packages
Answers
Yes. The warehouse drivers deliver enough packages.
What is an expression?An expression is used to illustrate the information that's given.
In this case, the warehouse has 128 trucks. Each truck has 350 packages. The number of packages that van be delivered will be:
= Number of trucks × Amount in each package
= 128 × 350
= 44800
Since the drivers at a warehouse need to deliver 40,000 packages each day. this means they denied enough packages because 44800 is more than 40000.
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On one day Fred’s Sports World sold 9 Buffalo Bills jerseys and 3 Miami Dolphin jerseys for a total of $899.40. The next day they sold 12 Bills jerseys and only 2 Dolphins jerseys for a total of $1139.30. How much is the Bills jersey and how much is the Dolphins jersey?
Answers
Given:
Let x be the cost of the Buffalo Bills jersey.
Let y be the cost of the Miami Dolphin jersey.
According to the question, we have
9x+3y=899.40.......(1)
12x+2y=1139.30.....(2)
From (1),
[tex]\begin{gathered} 3y=899.40-9x \\ y=299.8-3x\ldots\ldots(3) \end{gathered}[/tex]Substitute equation (3) in equation (2), we get
[tex]\begin{gathered} 12x+2(299.8-3x)=1139.30 \\ 12x+599.6-6x=1139.30 \\ 6x=539.7 \\ x=89.95 \end{gathered}[/tex]Then the value of y is,
[tex]\begin{gathered} y=299.8-3(89.95) \\ y=29.95 \end{gathered}[/tex]Hence, the cost of the Buffalo Bills jersey is $89.95, and the cost of the Miami Dolphin jersey is $29.95.
Agnes, evangelina, isabela, omar, and yuri each made a tower using wooden blocks. each person used a different number of blocks in their tower, and the mean (average) number of blocks in each tower was 25 . yuri used the most blocks in her tower, and agnes used the fewest blocks in her tower. if yuri used 32 blocks, determine the minimum possible number of blocks that agnes could have used.
Answers
Given a block play problem, the minimum number of blocks Agnes can use to build a tower is 3 or 1.
To calculate the average (mean) of a set of values, first divide by the number of values in the set. Therefore, the sum of the values in the set is equal to their average multiplied by the number of values in the set. The average number of blocks in each tower was 25, and since there were 5 towers, the total number of blocks used was 5 × 25 = 125. Yuri's Tower used 32 blocks, so the remaining towers used a total of 125 minus 32 = 93 blocks.
To find the minimum possible number of blocks for Agne's tower, let the other three towers use as many blocks as possible. Now we know that Yuri's tower used the most blocks and each tower used a different number of blocks. So the other 3 towers can use up to 31, 30 and 29 blocks respectively. The result was an absolute minimum number of blocks that Agnes could use, 93 - 31 - 30 - 29 = 3
By the way, the minimum number of blocks Agnes can use is not 93 - 32 - 32 - 32 = - 3 , but negative value is not possible. so, if everyone could use the same number of blocks. Agnes must have used at least one block, as it is possible to use a negative number of blocks.
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Trigonometry question
Given the following function, choose the graph with the two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees.
1. sin0 = -2/3
2. sec0 = 2/1
3. tan0 = 4/5
4. csc0 = -3/2
5. cos0 = -3/5
Answers
Graph 1 contains the two angles in the domain 0 ≤ θ ≤ 360º that have cosine given by cos(θ) = -3/5.
Where is the cosine of angle negative?The sine and the cosine of an angle are represented in the unit circle, in which:
The x-axis is composed by the cosine of the angle.The y-axis is composed by the sine of the angle.Hence the cosine of the angle is negative when the x-axis is negative, which happens in these following quadrants:
Second quadrant.Third quadrant.The only equation that can be solved in the context of this problem is:
cos(θ) = -3/5.
The solution is composed by two angles, one in the second quadrant and one in the third quadrant, hence Graph 1 shows the correct solution.
The exact angles are found applying the inverse cosine function as follows:
θ = arccos(-3/5) = 126.9º = 233.1º.
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This is algebra 2 (Parabola Transformation) . I have no clue on how to do this and I’m failing because of this missing assignment. Please help me. Please.
Answers
SOLUTION
Step 1 :
We are meant to graph the function,
[tex]\begin{gathered} y=-(x+2)^2\text{ + 7} \\ \text{compared with the parent function,} \\ y=x^2 \end{gathered}[/tex]Step 2 :
The Transformations are Reflection, Vertical Shift and Horizontal Shift.
Step 3 :
The vertex is at ( - 2, 7 ) and it is a maximum.
Solve 2x>8 or 2x< 4.
Answers
The same number of guests are seated at each of 8 large tables. There are 2 guests seated at one small table. Write an equation to represent the total number of guests T and the number of people x at
each large table. If there are 82 guests, how many are seated at each large table?
Answers
Answer:
10
Step-by-step explanation:
Since there are 2 people sitting alone, we can put them aside
then we have 8 large tables, each seat x number of guests
we would have total 8x guests there
so 8x+2=82
then solve
8x=80
x=10