Answer: y = -5x - 22
Step-by-step explanation:
Use the Point-Slope formula: y - y₁ = m(x - x₁)
m = -5 (parallel means it has the same slope)(x₁, y₁) = (-4, -2)y - (-2) = -5(x - (-4))
y + 2 = -5(x + 4)
y + 2 = -5x - 20
y = -5x - 22
[PLEASE HELP] The area of Bethany's garden will be 48 square feet once she expands it. She is not going to change the measurement on one side, but the other side will be 8 feet longer than before. The equation that models this situation and can be used to determine the possible dimensions of Bethany's garden is x^2 +8x -48. Factor to determine the possible dimensions of Bethany's new garden.
Final answer:
To find Bethany's expanded garden dimensions, we factored the quadratic equation x² + 8x - 48 = 0 to find that the original dimension is 4 feet, resulting in the new dimensions of 4 feet by 12 feet.
Explanation:
The student is tasked with finding the possible dimensions of Bethany's expanded garden, which will have an area of 48 square feet. The side lengths of the new garden are related by the fact that one side will be 8 feet longer than the other. We can use the given quadratic equation x² + 8x - 48 = 0 to model this situation.
Step-by-Step Factoring
First, we identify the coefficients in the equation, which are A=1 (coefficient of x²), B=8 (coefficient of x), and C=-48 (constant term).
To factor the quadratic equation, we look for two numbers whose product is A*C (-48) and whose sum is B (8). These numbers are 12 and -4.
Rewrite the middle term (8x) using the numbers found: x² + 12x - 4x - 48 = 0.
Factor by grouping: (x² + 12x) - (4x + 48) = 0 becomes x(x + 12) - 4(x + 12) = 0.
Factor out the common factor: (x - 4)(x + 12) = 0.
Solve for x: x = 4 or x = -12. Since a garden's dimensions must be positive, we disregard the negative solution. This leaves us with x = 4 feet as the original dimension and x + 8 = 12 feet as the expanded dimension.
Thus, the dimensions of Bethany's new garden are 4 feet by 12 feet.
Which function is equivalent to f(x)=-4(x+7)^2-6
Answer:
f(x) = - 4x² - 56x - 202
Step-by-step explanation:
We can simplify this quadratic function given in vertex form into standard form by simplifying the exponents and adding like terms.
f(x) = -4(x+7)^2 - 6
f(x) = -4(x^2 + 14x + 49) - 6
f(x) = -4x² - 56x - 196 - 6
f(x) = -4x² - 56x - 202
Answer: b
Step-by-step explanation: just took the quiz on egde.
Find the total surface area.
Thanks!
Answer:
Your answer would be 326.72
Step-by-step explanation:
2(pie) x 4 x 9= (roughly) 326.72
What is 17.043956 in decimal form
Answer:
17.043956
Step-by-step explanation:
Answer:
Step-by-step explanation:
17.043956 in decimal form
This is already in decimal form
A rose garden is circular. The diameter of the garden is 18 feet. Which is
closest to the total area of the garden? Use 3.14 for p.*
Answer: 254 ft
Step-by-step explanation:
Hi, to answer this we have to apply the formula for the area of a circle when we know the diameter.
Area of a circle (A)= (π/4) x D^2
Where D is the diameter
Replacing with the values given:
A = (π/4) x 18^2 = (3.14/4) x 324 =254.34 feet.
Feel free to ask for more if needed or if you did not understand something.
Final answer:
To calculate the area of a circular rose garden with a diameter of 18 feet using π as 3.14, the radius is found to be 9 feet. Using the formula πr², the area is calculated as 254.34 square feet, rounded to 254 square feet.
Explanation:
The question asks, “A rose garden is circular. The diameter of the garden is 18 feet. Which is closest to the total area of the garden? Use 3.14 for π.” To find the area of a circle, the formula is πr², where π (Pi) is approximately 3.14, and ‘r’ represents the radius of the circle. Given the diameter is 18 feet, the radius (half of the diameter) is 9 feet.
Plugging the values into the formula gives: A = πr² = 3.14 × (9 feet)². This equates to 3.14 × 81 feet² = 254.34 square feet. Therefore, the area of the rose garden is closest to 254 square feet.
What is the length of AC on the number line
According to the given question, the length of AC on the number line is 5 units
The length of AC on the number line can be determined by subtracting the coordinate of point A from the coordinate of point C. Let's say point A is located at coordinate 2 and point C is located at coordinate 7. To find the length of AC, we subtract the coordinate of A from the coordinate of C: 7 - 2 = 5
Therefore, the length of AC on the number line is 5 units. Another way to think about this is by considering the distance between the two points. In this case, the distance between point A and point C is the same as the length of AC. If you have any further questions, please, let me know.
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please help me with this math problem!!
Answer:
y=3
Step-by-step explanation:
This is an isosceles triangle because the two angles at the bottom are equal.
This means the two sides are equal
5y-2 = 13
Add 2 to each side
5y-2+2 =13+2
5y = 15
Divide each side by 5
5y/5 = 15/5
y =3
Find the unit vector e which is collinear to vector a = (6,8) , and has the same direction.
the unit vector e which is collinear to vector a = (6,8) , and has the same direction is [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex] .
Step-by-step explanation:
Here we have , vector a = (6,8) . We need to find the unit vector e which is collinear to vector a = (6,8) , and has the same direction. Let's find out:
We know that for a vector [tex]a = (x,y)[/tex] the unit vector is given by :
⇒ [tex](\frac{x}{|a|} ,\frac{y}{|a|} )[/tex] , where |a| is modulus of vector a . So , Modulus of vector a is :
⇒ [tex]|a| = \sqrt{x^2+y^2}[/tex]
⇒ [tex]|a| = \sqrt{6^2+8^2}[/tex]
⇒ [tex]|a| = \sqrt{36+64}[/tex]
⇒ [tex]|a| = \sqrt{100}[/tex]
⇒ [tex]|a| =10[/tex]
Hence , unit vector is given by [tex](\frac{6}{10} ,\frac{8}{10})[/tex] or , [tex](\frac{3}{5} ,\frac{4}{5})[/tex] . Vector is already collinear as it's in same direction of original vector as :
⇒ [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex]
Therefore , the unit vector e which is collinear to vector a = (6,8) , and has the same direction is [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex] .
For every 8 shots barry made,he missed 5.Barry missed 20 shots in all how many did he make?
Answer:
he made 12 shots
Step-by-step explanation:
since he missed 5/8 shots and 20 divided by is 4, you multiply (8-5) which is 3 by 4 and you get 12
Answer:
He made 32 shots
Step-by-step explanation:
8/5=?/20
put them together and make them as equal as possible.
What is the value of x?
Answer:
Answer is 71 degree
Step-by-step explanation:
AS we can see it is an isosceles triangle so base angles are equal
x + x + 38 = 180 ( sum of angles of triangle )
2x = 180 - 38
2x = 142
x = 142 / 2
Therefore x = 71 degree
Hope it helps :)
Three tanks, A, B and C are used to store oil.
Tank A contains n litres of oil. Tank B contains (n + 150) litres of oil.
Tank C is empty.
Oil is pumped from tank A and from tank B into tank C so that
all three tanks contain the same amount of oil.
500 litres of oil are pumped from tank A into tank C.
Work out the value of n.
Final answer:
To solve this problem, we set up a system of equations representing the amount of oil in each tank. Using the fact that all three tanks end up with the same amount of oil, we determine that Tank A must have started with 1000 litres of oil.
Explanation:
You need to find the value of n which represents the amount of oil initially in Tank A, given that 500 litres are pumped from Tank A to Tank C, and that Tanks A, B, and C eventually contain the same amount of oil.
After transferring 500 litres from Tank A to Tank C, Tank A will have n - 500 litres left. Since tank C was empty and now has 500 litres, Tank B must also transfer enough oil to Tank C such that both B and C have the same amount of oil. Tank B started with n + 150 litres and must end up with the same amount as tank C, which we will refer to as x.
Therefore, we need to solve the following system of equations:
Tank A: n - 500 = x
Tank B: n + 150 - x = x
Tank C: 500 = x
From Tank C's equation, we know that x = 500. Substituting this into the equations for Tanks A and B gives us:
Tank A: n - 500 = 500
Tank B: n + 150 - 500 = 500
From Tank A's equation, we see that n = 1000 litres.
Jason walks 1/2 of a mile in 1/3 of an hour. If he walks at the same rate, how many miles does Jason walk each hour
Answer:
He would walk 1 1/2 a mile. Hope that helps
Step-by-step explanation:
During summer, when the snow melts, the water level of the Yukon River increases. If the water level of the river increased by 72 centimeters in 8 days, what is the water level increase rate in centimeters per day?
A. 9 centimeters per day
B. 12 centimeters per day
C. 11 centimeters per day
D. 8 centimeters per day
Answer:
A) 9cm/day
Step-by-step explanation:
72/8=9
You randomly choose a marble from a jar. The jar contains 3 red marbles, 10
blue marbles, 8 green marbles, and 4 yellow marbles. Find the probability
of choosing a blue marble. *
The probability of choosing a blue marble is 2/5 or 0.4.
It is given that the jar contains 3 red marbles, 10 blue marbles, 8 green marbles, and 4 yellow marbles.
It is required to find the probability of choosing a blue marble.
What is probability?
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
We have:
Number of total marbles = 3+10+8+4 ⇒25
Number of blue marble = 10
From the definition of the probability:
[tex]\rm Probability = \frac{Favourable \ outcomes}{Total \ outcomes}[/tex]
[tex]\rm Probability = \frac{10}{25}[/tex]
[tex]\rm Probability = \frac{2}{5 } \Rightarrow 0.4[/tex]
Thus, the probability of choosing a blue marble is 2/5 or 0.4.
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4. In how many ways can six different books, four of which are math books, be arranged on a shelf if the math
books must be placed next to each other?
Answer:
3
Step-by-step explanation:
The math books can all be in the middle with the other two on the sides, or the math books can be on the left side with the other books at the right side. Also, the math books can be on the right side with the other books at the left side.
The diameter of the wheel is 22 inches what is the circumference of the world use 3.14 for pie
Answer:
69.08 inches
Step-by-step explanation:
Circumference of the wheel
= 2 pi r
Given
Pi = 3.14
Radius r = diameter/2 = 22/2
= 11
Therefore
Circumference = 2 x 3.14 x 11
= 69.08 inches
I need help with my homework plis
Box Plots
Which function rule represents the data in the table below? Input (x) 1 2 3 4 5 Output (y) 9 15 21 27 33 • y = 4 + 5x • y = 3 + 6x • y = 5 + 4x • y = 6 + 3x
By substituting the input values into each of the provided function rule options, it becomes clear that only the function rule y = 4 + 5x correctly represents the data in the given table.
Explanation:The question is asking which function rule represents the data in the given input and output table.
Let's test each option:
y = 4 + 5x: Replacing x by 1, we get y = 4+5*1 = 9 (It matches with the output table), Therefore this option seems to be the correct one, but let's check the other ones for confirmation. y = 3 + 6x: Replacing x by 1, we get y = 3+6*1 = 9 (But for x = 2, y becomes 15, which is not similar with the output table), therefore this isn't the correct function. y = 5 + 4x: Replacing x by 1, we get y = 5+4*1 = 9 (But again for x = 2, y becomes 13 which does not match with the output in the table), hence, not the correct function. y = 6 + 3x: Replacing x by 1, we get y = 6+3*1 = 9 (Once again, for x = 2, y becomes 12 which is not in the table), so it also isn't correct.
As a result, only the function rule y = 4 + 5x matches the pattern in the given table correctly.
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2/3 of a number is -6 find the number
Answer:
-12
Step-by-step explanation:
-6 times 3 is -18 and 2/3 of -18 is -12
[tex] 24{ \times }^{2} + 25 \times - 47 = - 8 \times - 3 - 53 [/tex]
please help
Answer: Multiply both sides of the given equation by ax−2. When you multiply each side by ax−2, you should have:
24x2+25x−47=(−8x−3)(ax−2)−53
You should then multiply (−8x−3) and (ax−2) using FOIL.
24x2+25x−47=−8ax2−3ax+16x+6−53
Then, reduce on the right side of the equation
24x2+25x−47=−8ax2−3ax+16x−47
Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.
so answer is -3
Step-by-step explanation: Hope I helped, Pls mark brainliest. And say thx. But its up to you.
Quiz
Active
TIMER
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Which set has the greatest range?
(10, 14, 8, 19, 22, 13, 44}
(19, 16, 50, 18, 29, 23, 37}
{11, 9, 31, 29, 15, 17, 20,
(12. 6. 24. 20, 44, 15, 29}
Answer:
the answer is D
ILL GIVE YOU BRAINLIEST!! A survey of 500 people was taken regarding their favorite winter outdoor activity.The results are shown in the table below.
In a circle graph,what would be the measure of the central angle for snowmobiling?
A. 200°
B. 144°
C. 72°
D. 56°
E. 40°
Answer:
144°
If you look up 144° it matches exactly how it looks on a pie chart
I hope this helped
Can someone answer this for me also I’m being timed so hat would be great if you were to answer quickly thanks:)
Answer: I haven't done this test but I am good at math and I bilieve the answer is Trapazoid From the looks of it.
Step-by-step explanation: look at the shape your looking at and the one below.
Write 7 3/10 as an improper fraction
Answer:
73/10
Step-by-step explanation:
7*10+3/10=
70+3/10=
73/10
Your answer would be 73/10.
Step-by-step explanation:Think of it this way, each whole number counts as 10/10. So by using that, just do 10 * 7 / 10...
So you would get 70/10.
Then you would add on the left over 3/10 that you had at the beginning.
70/10 + 3/10 = 73/10
This would get your final answer of 73/10.
complete the number line model to find (-5) + 6.
Answer:
Step-by-step explanation:
Answer:
-11
Step-by-step explanation:
I think this is right
Dividing exponents in this equation
Answer:
18x^5y
Step-by-step explanation:
Divide 36 by 2 first : 18
since you are dividing, you subtract the exponents:
x^8 - x^3= x^5
y^4-y^3= y^1 but you usually just write y
Dividing exponents in this equation [tex]\frac{36x^{8}y^{4} }{2x^{3} y^{3} }[/tex] is [tex]18x^{5} y[/tex]
How can the expression be simplified?
A mathematical action called an exponent, sometimes referred to as a power, is the result of repeatedly multiplying a base number by itself. A little number or variable to the right and above the basic number serves as a symbol for it. For instance, in the notation 2^3, the base and exponent are 2 and 3, respectively, denoting three times the product of 2 and itself: 2^3 = 2 x 2 x 2 = 8.
Given that;
[tex]\frac{36x^{8}y^{4} }{2x^{3} y^{3} }[/tex]
Divide 36 by 2 first : 18
[tex]\frac{18x^{8}y^{4} }{x^{3} y^{3} }[/tex]
=[tex]18x^{5} y[/tex]
Brianna’s family spent $100 on 1 adult ticket and 3 youth tickets at an amusement park. Max’s family spent $146 on 3 adult tickets and 2 youth tickets. What is the price of a youth ticket?
A. $34
B. $22
C. $12
D. $55
Answer:
B $22
Step-by-step explanation:
What is y = -3(x – 7)(x + 3) in standard form?
Answer:
y=-3x^2+12x+63
Step-by-step explanation:
y=-3(x-7)(x+3)
y=-3(x^2-4x-21)
y=-3x^2+12x+63
Erica makes 6 sandwiches and cuts
each sandwich into 1/3. How many 1/3
size sandwich pieces does she have ?
Answer:
the answer is 18
Step-by-step explanation:
can u put me as brainliest
Statistical Question
Answer:
c
Step-by-step explanation: