Answer:
y = (x+ 3)^2 - 10.
Step-by-step explanation:
Vertex form is
y = a(x - b)^2 + c
Here b = -3 and c = -10 so we have
y = a(x + 3)^2 - 10 where a is some constant.
The y intercept is (0, -1) so substituting:
-1 = a * 3^2 - 10
-1 + 10 = 9a
9a = 9
a = 1
So the required parabola is (x+ 3)^2 - 10.
Brainliest + points
Please show your work why is C correct!
I'd really appreciate it so I can understand
Answer:
Look below
Step-by-step explanation:
SOH CAH TOA
We are using sine
sin(75) = x/150
x=sin(75)*150
x=0.9659258263*150
x=144.8888739
Check the picture below.
make sure your calculator is in Degree mode.
Solve the equation 2 = -6 – 20x for x.
A. -5/2
B. -2/5
C. 2/5
D. 5/2
Answer: - 2/5
Step-by-step explanation: Isolate the vcariable by divding each side by factors that don't contain the variable.
Exact Form: x = - 2/5
Deciaml form: x = -0.4
Hope this helps! :) ~Zane
Hello there! B. -2/5.
To solve for x, you want to get x alone and isolate all other terms.
2 = -6 – 20x - Start by adding 6 to both sides of the equation.
2+6 = -6+6 – 20x ⇒ 8 = -20x
8 = -20x - Next, divide both sides of the equation by -20..
8/-20 = -20/-20x ⇒ -8/20 = x
Now, we have -8/20 as our value for x. The last step is to simplify. Since 8 and 20 are both divisible by 4, divide both sides of the fraction by 4.
x = -2/5. This is your final answer. I hope this helps and have a great day! ~ saturns
Edit: Sorry for the typos, i fixed them! You have to press suuuper hard to get the S key on my keyboard to work :)
How do I do this question?
Check the picture below.
now, based on the provided information, we know the hexagon and triangle are regular polygons, equal sides and equal angles, we also know the angle in pink there of E and G are twins inside that irregular trapezoid, and you can see the exterior angles labeled there of 220° and 136°.
now, the trapezoid has twin angles at E and G, that means that the sides of DE and JG are equal and that also means that the other two angles inside that trapezoid are also twins, namely D and J.
if you notice the hexagon on the left-hand-side, a hexagon has interior angles of 120° and if we take a peek at the vertex at D, it has two angles then, one interior or 120° and an exterior of 136°, a full revolution will be 360°, so the remaining angle in green there must be 360° - 120° - 136° = 104°, and her twin at vertex J is also 104°.
Line d is parallel to line c in the figure below Which statements about the figure are true? Select three options
Answer: it is B,C, and D
Step-by-step explanation: I got it correct
Please help me asap
the drop downs for the first four are either 50
100
200
300
And the last two are either
faster than
slower than
the same speed as
Answer:
See explanation
Step-by-step explanation:
Car A: Started at 0 and ended at 300, thus, car A travels 300 miles.
It travels 6 hours, so car A speed is [tex]\frac{300}{6}=50[/tex] mph.
Car B: Started at 100 and ended at 300, thus, car B travels 300-100=200 miles.
It travels 5 hours, so car B speed is [tex]\frac{200}{5}=40[/tex] mph.
Since 50>40, car A traveled faster than car B.
The graph for the car A is steeper than the graph for the car B.
The given line segment has a midpoint at (3, 1).
What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?
y = x
y = x – 2
y = 3x
y = 3x − 8
Answer:
y = 1/3 x.
Step-by-step explanation:
The slope of the given line is
(4 - (-2) / 2 - 4)
= -3.
So the slope of the line perpendicular to it = -1 / (-3) = 1/3.
This line also passes through the point (3, 1) so its equation is ( by the point-slope form):
y - 1 = 1/3(x - 3)
y - 1 = 1/3x - 1
y = 1/3 x (answer).
Answer: The answer is y= x/3
Step-by-step explanation:
Given points =(2,4) and (4,-2) whose mid point is (3,1)
Let the points be named as A(2,4) and B(4,-2) and mid point as C(3,1)
So slope of AB = [tex]\frac{4-(-2)}{2-4}[/tex]
=[tex]\frac{6}{-2}[/tex]
= -3
We know that Product of Slope of perpendicular lines = -1
Now slope of the line perpendicular to AB × slope of AB = -1
-3 × m2 =-1
i.e. m2 =[tex]\frac{1}{3}[/tex]
Now equation of perpendicular bisector of AB passing through C(3,1) is
[tex]y -1 =\frac{1}{3}(x-3)\\[/tex]
[tex]y= 1+\frac{1}{3}x -1[/tex]
[tex]y=\frac{1}{3}x[/tex]
Hence the equation of line is y =x/3
Write a real world situation for the function f(x) = 3(1.06x) + 2. Be sure to identify all key features of the function as what they represent in your situation.
Please help!!!
Answer:
Putting money in a bank and earning interest
Step-by-step explanation:
This problem can be used in real life to describe when you put money in a bank, in this case, it could be two dollars, and leave it there for x amount of years, then taking it out after an amount of years and checking what you have. Since this is a linear equation, your money doesn't go up exponentially. It'll keep going up the same rate for the whole time until you decide to take it out. Here's an example of what it'll look like, if it helps:
Before interest: You put in $2First year: You have $5.18 in the bankSecond year: $8.36Third year: $11.54Your money keeps going up. Hope this helps!
Final answer:
A real world situation for the function f(x) = 3(1.06x) + 2 could be a situation where a person is investing money in a savings account. The function represents the balance in the account after a certain amount of time (x years) with an interest rate of 6%.
Explanation:
A real world situation for the function f(x) = 3(1.06x) + 2 could be a situation where a person is investing money in a savings account. Let's say the initial amount of money deposited in the account is $2. The function represents the balance in the account after a certain amount of time (x years) with an interest rate of 6%. The key features of the function are:
3: This represents the multiplier of the initial investment, indicating that the account balance increases by three times the amount of the initial investment.
1.06: This represents the growth factor due to the 6% interest rate. It is multiplied by the current balance each year.
2: This represents the $2 initial deposit in the account.
You need 2 3/4 cups of flour for one batch of rolls. Find how much flour you would need for three batches of rolls.
The answer is 8 1/4 hope this helps
To find out how much flour is needed for three batches of rolls, you multiply 2 3/4 cups by three, resulting in 8 1/4 cups of flour.
Finding the Amount of Flour for Multiple Batches of Rolls
To calculate the amount of flour needed for three batches of rolls, we simply multiply the amount needed for one batch by three. The recipe states that you need 2 3/4 cups of flour for one batch. Thus, the mathematically formal way to find the amount for three batches is:
2 3/4 cups of flour × 3 = (2 × 3) + (3/4 × 3)
Now, solve the equation step by step:
Multiply the whole number: 2 × 3 = 6 cups of flour.
Multiply the fraction: 3/4 × 3 = 9/4, which can be simplified to 2 1/4 cups of flour by dividing 9 by 4.
Add the results from step 1 and step 2 together: 6 cups + 2 1/4 cups = 8 1/4 cups of flour.
Therefore, you would need 8 1/4 cups of flour to make three batches of rolls.
Find the value of x that makes a ll b
Answer:
x = 15
Step-by-step explanation:
∠2 and ∠4 are same side interior angles and are supplementary, thus
2x + 10 + 4x + 80 = 180
6x + 90 = 180 ( subtract 90 from both sides )
6x = 90 ( divide both sides by 6 )
x = 15
Help pleaaaaaaaseeeeeeeee
For this case we must factor the following expression:
[tex]-13m-m ^ 2 = 0[/tex]
We have a common factor "m" because it is the common term, so we have:[tex]m (-13-m) = 0[/tex]
Finally, the factorized expression of [tex]-13m-m ^ 2 = 0[/tex] is:[tex]m (-13-m) = 0[/tex]
ANswer:
[tex]m (-13-m) = 0[/tex]
Option B
one number is less than a second number. twice the secind number is less 16 less than 4 times the first. find the smaller of two numbers
Answer:
The smaller number is 11
Step-by-step explanation:
The question is
One number is 3 less than a second number. Twice the second number is 16 less than 4 times the first. Find the smaller of two numbers
Let
x and y the numbers
x=y-3 ----> equation A
2y=4x-16 ----> equation B
Substitute equation A in equation B and solve for y
2y=4(y-3)-16
2y=4y-12-16
4y-2y=12+16
2y=28
y=14
x=14-3=11
Read the following paragraph. Select each of the ways Ramiro was financially responsible.
Ramiro was going to buy a car, so he shopped around on the Internet for the best price for car insurance. Then he read some consumer Web sites about reviews on the types of cars he was thinking about buying. He also plugged a few payments into his budget to see how much he could afford. When he decided on a car, he shopped around for a loan with a good APR.
A has a budget
B sets goals
C considers important factors when he shops for a car loan
D uses strategies to minimize risks
E shops around for car insurance
F spends wisely
Answer:
The answer is A,C and F
Step-by-step explanation:
A because he said the best price on internet
C because he read some consumer website about review
F. plugged a few payment into his budgets
Ramiro was financially responsible because he has a budget, considers important factors when he shops for a car loan, uses strategies to minimize risks, shops around for car insurance, and spends wisely.
What does financially responsible mean?Financially responsible means the careful spending of money after analyzing alternatives and choosing the right path in saving money for the future.
We can find how Ramiro was responsible as follows:The paragraph is given.
Now we must read and understand the graph and choose the correct answers from the given options.
Option A is true because he has a budget.
Option B is not fully true, as he has no goals for the future yet.
Option C is true as he considers important factors when he shops for a car loan.
Option D is true as he uses strategies to minimize risks.
Option E is true because he has shopped around for car insurance.
Option F is true because he spends wisely.
Therefore, we have found that Ramiro was financially responsible because he has a budget, considers important factors when he shops for a car loan, uses strategies to minimize risks, shops around for car insurance, and spends wisely.
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:)
If the radius of a sphere is doubled, how does this affect the volume?
A)
It will be one-half as large.
It will be two times larger.
It will be four times larger.
It will be eight times larger.
source of answer
Answer:
D is the right answer
Step-by-step explanation:
A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100. Using the eight‐part symmetry of the area under a normal curve, what is the probability that a randomly chosen exam score is less than 200 or greater than 800?
The probability is__?
Final answer:
The combined probability of scoring less than 200 or greater than 800 on a normally distributed college-entrance exam with mean 500 and standard deviation 100 is approximately 0.3%.
Explanation:
The probability that a randomly chosen exam score is less than 200 or greater than 800 in a normally distributed college-entrance exam can be found by using the properties of the normal distribution. Since the mean score is 500 and the standard deviation is 100, scores below 200 are three standard deviations below the mean, and scores above 800 are three standard deviations above the mean. Given the symmetry and the empirical rule of normal distribution, approximately 99.7% of values lie within three standard deviations from the mean, leaving roughly 0.3% of the values outside this range. Therefore, since both tails (below 200 and above 800) are considered, we need to split this percentage, which gives us approximately 0.15% (or 0.0015 in probability terms) for each tail. Thus, the combined probability of scoring less than 200 or greater than 800 is approximately 0.3% (or 0.003 in probability terms).
what is 518/20 as a decimal
Answer:
25.9
Step-by-step explanation:
That is:
25.9
Hope this helped!
Find the volume and explain please ASAP.
Answer:
1395in^3
Step-by-step explanation:
First find the volume of the cuboid, 15in x 9in x 7in = 945in^3
Then find the volume of the rectangular pyramid using the formula V=lwh/3, the total height is 17in so subtract the height of the cuboid from the total height, giving you 10in.
V=(15in)(9in)(10in)/3 = 450in^3
450in^3 + 945in^3 = 1395in^3
Choose the best graph to fit the inequality. x^2 + y^2 is less than 16.
Answer:
The graph in the attached figure
Step-by-step explanation:
we know that
[tex]x^{2}+y^{2}=4^{2}[/tex]
Is the equation of a circle with center at the origin and radius 4 units
so
the inequality
[tex]x^{2}+y^{2}< 4^{2}[/tex]
[tex]x^{2}+y^{2}< 16[/tex]
The solution is the shaded area inside the dashed line of the circle
using a graphing tool
see the attached figure
Which expression is equivalent to 7^5/7^2
Answer:
You are correct my good sir! 7^5/7^2 expanded is (7x7x7x7x7)/(7x7)! another awesome thing to know for future reference is when dividing exponents with the same base you can simply subtract the exponents from each other! for example, 7^5/7^2=7^3! :D Hope This Helps!
Step-by-step explanation:
Answer:
Option D is the answer.
Step-by-step explanation:
The given expression is [tex]\frac{7^{5}}{7^{2}}[/tex]
We know [tex]7^{5}[/tex] = 7×7×7×7×7
and [tex]7^{2}[/tex] = 7×7
Therefore, we can rewrite the expression as [tex]\frac{7\times 7\times 7\times7 \times 7}{7\times 7}[/tex] which maches with option D.
If you buy five of the XYZ bonds with $8 commission for each how much will it cost?
Answer:
B) 5065
Step-by-step explanation:
100.5 times 5 = 502.5
502.5 times 100
+ 8 times 5 (commission)
The question asks for the total commission fee when buying five XYZ bonds. Each bond has $8 commission. Therefore, 5 bonds * $8 = $40.
Explanation:To determine the total cost of purchasing five XYZ bonds with a commission fee of $8 each, you have to multiply the number of bonds by the commission fee. So, the calculation will be:
Identify the number of bonds: 5 bonds.Identify the commission fee per bond: $8.Multiply the number of bonds by the commission fee: 5 bonds * $8 = $40.This means the total cost just for purchasing (not including the face value of the bonds themselves) is $40.
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which point best approximates the square root of 45?
Since
[tex]6^2 = 36,\quad 7^2 = 49[/tex]
Then we have
[tex]6 = \sqrt{36}<\sqrt{45}<\sqrt{49}=7[/tex]
So, the square root of 45 is somewhere between 6 and 7.
Answer:
C
Step-by-step explanation:
Note that
[tex]\sqrt{36}[/tex] < [tex]\sqrt{45}[/tex] < [tex]\sqrt{49}[/tex], that is
6 < [tex]\sqrt{45}[/tex] < 7
The square root lies between 6 and 7 → point C
Sail with the equation by completing the square x^2+8x=-3
Answer:
The solutions are [tex]x=-4(+/-)\sqrt{13}[/tex]
Step-by-step explanation:
we have
[tex]x^{2} +8x=-3[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]x^{2} +8x+16=-3+16[/tex]
[tex]x^{2} +8x+16=13[/tex]
Rewrite as perfect squares
[tex](x+4)^{2}=13[/tex]
square root both sides
[tex]x+4=(+/-)\sqrt{13}[/tex]
[tex]x=-4(+/-)\sqrt{13}[/tex]
∠1 and ∠2 are a linear pair, and ∠2 and ∠3 are vertical angles. m∠2=(5+4y)∘ and m∠3=(6y−25)∘
.
What is m∠1
?
65°
85°
95°
115°
Answer:
The measure of angle 1 is 115°
Step-by-step explanation:
we know that
If ∠1 and ∠2 are a linear pair
then
∠1 +∠2 =180° -----> supplementary angles
If ∠2 and ∠3 are vertical angles
then
∠2 =∠3
step 1
Find the value of y
we know that
∠2 =∠3
substitute values
(5+4y)°=(6y-25)°
6y-4y=(5+25)°
2y=(30)°
y=15°
step 2
Find the measure of angle 2
∠2=(5+4y)°
substitute the value of y
∠2=(5+4(15))°
∠2=65°
step 3
Find the measure of angle 1
we know that
∠1 +∠2 =180°
we have
∠2=65°
substitute
∠1 +65°=180°
∠1 =180°-65°=115°
I don’t get this problem
Answer:
Line B
Step-by-step explanation:
It is the line that most of the dots surround
Answer:
Line b
Step-by-step explanation:
Line b has the most black dots positioned close to it, and therefore is the best fit line.
Suppose that F(x) =x^3 and G(x) =-5x^3. Which statement best compares the graph of g(x) with the graph of f(x)?
The statement that best compares the graph of g(x) = -5x³ with the graph of f(x) = x³ is that the graph of g(x) is a reflection of the graph of f(x) across the x-axis and is vertically stretched by a factor of 5."
Option D is the correct answer.
We have,
Reflection across the x-axis:
The negative coefficient of -5 in g(x) reflects the graph across the x-axis compared to f(x).
This means that the points on the graph of g(x) will have the same
x-coordinates as the corresponding points on the graph of f(x) but will have opposite y-coordinates.
Vertical stretching by a factor of 5:
The absolute value of the coefficient (-5) in g(x) indicates that the graph is vertically stretched by a factor of 5 compared to f(x).
This means that for any given x-value, the corresponding y-value on the graph of g(x) will be five times larger (or smaller, depending on the sign) than the corresponding y-value on the graph of f(x).
Thus,
The graph of g(x) is a reflection of the graph of f(x) across the x-axis and is vertically stretched by a factor of 5."
Learn more about reflections here:
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Solve this question using simultaneous equations.
To cover a distance of 10 km, Jacob runs some of the way at 15 km/h, and walks the rest of the way at 5 km/h. His total journey time is 1 hour. How far did Jacob run?
Answer: Jacob ran for half an hour, and walked for the remaining half an hour. 15 km/hr x 0.5 hr = 7.5 km running, and 5km/ hr x 0.5 hr=2.5 km walking
Step-by-step explanation:
Let x hours be the time Jacob ran, and therefore for 1-x hours he walked.
time x speed= distance
we get, 15x + 5*(1-x)=10
15x+5-5x=10,
10x=5,
x=0.5 hours.
Average speed was 10km/h.
HOPE THIS HELPS.
Jacob ran 7.5 km at a speed of 15 km/h. By setting up a system of simultaneous equations, we found the distances for both running and walking that add up to the total distance of 10 km, while also fulfilling the constraint of a 1-hour total journey time.
To solve this problem with simultaneous equations, let's define two variables for the two different parts of the journey: x for the distance Jacob runs at 15 km/h and y for the distance he walks at 5 km/h. We know that Jacob covers a total distance of 10 km and the total time taken for the journey is 1 hour.
Set up the equations:
Equation for the distance: x + y = 10
Equation for the time: (x/15) + (y/5) = 1 (Since time is distance divided by speed)
Solve these equations simultaneously.
Multiply the second equation by 15 to clear the denominators: x + 3y = 15
Subtract the first equation from this new equation to solve for y: 2y = 5, so y = 2.5 km.
Substitute y back into the first equation to find x: x = 10 - 2.5, so x = 7.5 km.
Jacob ran 7.5 km at 15 km/h.
Check the answer:
Is 7.5 km in 1 hour at 15 km/h reasonable? Yes, because 15 km/h means he would run 15 km in 1 hour, so running for less than an hour for 7.5 km is plausible.
a farmer needs a rectangular garden that is 64 square feet in area. the length varies inversely with the width. You can use l = 64/w. find the length and the width of the garden if it is a square
Answer:
The length and the width of the garden is equal to [tex]l=8\ ft[/tex]
Step-by-step explanation:
Let
l -----> the length
w----> the width
we have
[tex]l=\frac{64}{w}[/tex] ------> equation A
If the garden is a square
then
l=w
substitute in the equation A
[tex]l=\frac{64}{l}[/tex]
[tex]l^{2}=64[/tex]
square root both sides
[tex]l=8\ ft[/tex]
therefore
The length and the width of the garden is equal to [tex]l=8\ ft[/tex]
If h(x)= x-7 and g(x)=x^2, which expression is equivalent to (g•h)(5)
Answer:
[tex]\large\boxed{(g\cdot h)(5)=-10}[/tex]
Step-by-step explanation:
[tex](g\cdot h)(x)=g(x)\cdot h(x)\\\\g(x)=x^2,\ h(x)=x-7\\\\\text{substitute:}\\\\(g\cdot h)(x)=(x^2)(x-7)\qquad\text{use the distributive property}\\\\(g\cdot h)(x)=(x^2)(x)+(x^2)(-7)=x^2-7x^2\\\\(g\cdot h)(5)-\text{put}\ x=5\ \text{in the expression}\\\\(g\cdot h)(5)=5^2-7(5)=25-35=-10[/tex]
i need help on this please
Answer:7.C
8.B
9.A
Step-by-step explanation:
Make me the brainliest
Find the average rate of change between f(-7) and f(-1) in the function f(x)=x^2+2x -8
Answer:
- 6
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ - 7, - 1 ]
f(b) = f(- 1) = (- 1)² + 2(- 1) - 8 = 1 - 2 - 8 = - 9
f(a) = f(- 7) = (- 7)² + 2(- 7) - 8 = 49 - 14 - 8 = 27
Hence
average rate of change = [tex]\frac{-9-27}{-1-(-7)}[/tex] = [tex]\frac{-36}{6}[/tex] = - 6
The tiles on the left contain functions written using function notation. Match each function with its input.
Answer:
1. The input is f
2. The input is g
3. The input is h
Step-by-step explanation:
The value inside the bracket of the function is the input given to the function.
1. g(f) = 2f
The input is f
2. h(g) = -4+g
The input is g
3. f(h) = h - 7
The input is h
Answer:
g(f)=2f⇒ f
h(g)=-4+g ⇒ g
f (h) =h-7 ⇒h
Step-by-step explanation:
Hi, to answer this question we have to understand what is the input of a function.
A function has an input and an output. The input is inside the parentheses, next to the name of the function.
The input is the independent variable.
Now, with this information, we can match each function with its input.
So:
g(f)=2f⇒ f
h(g)=-4+g ⇒ g
f (h) =h-7 ⇒h
Feel free to ask for more if it´s necessary or if you did not understand something