Answer:
x1 = 0.45 and x2 = -1.12
Step-by-step explanation:
To solve the equation 6x2+4x−3=0 using the quadratic formula, we use the following equation:
x = [-b ± √(b2 - 4ac)] / 2a
Where a, b and c are coefficients of the quadratic equantion (in our case, a = 6, b = 4 and c = -3)
So we have that:
x1 = [-4 + √(16 + 72)] / 12 = (-4 + 9.3808) / 12 = 0.4484
x2 = [-4 - √(16 + 72)] / 12 = (-4 - 9.3808) / 12 = -1.1151
Rounding to nearest hundredth, we have x1 = 0.45 and x2 = -1.12
April rewrote a quadratic function in vertex form.
h(x) = 5x2 – 30x + 30
Step 1: h(x) = 5(x2 - 6x+ + 30
Step 2: h(x) = 5(x2 - 6x + 9) + 30 – 45
Step 3: h(x) = 5(x - 3)2 + 15.
April said that the vertex is (3, 15). Is April correct?
April correctly transformed the quadratic function into vertex form, and the resulting vertex is (3, 15), as determined by the completion of the square method.
Explanation:April is indeed correct about the vertex of the function h(x). The vertex form of a quadratic function is h(x) = a(x - h)^2 + k, where the point (h, k) is the vertex of the parabola. April has rewritten the quadratic function h(x) = 5x^2 - 30x + 30 into vertex form as h(x) = 5(x - 3)^2 + 15, indicating that the vertex is at (3, 15). This can be verified through the completion of the square method, where a perfect square trinomial is created by adding and subtracting the appropriate constant term. April added and subtracted 9 inside the parentheses, which is (6/2)^2, to keep the equation equivalent. Finally, she factored out the coefficient of the quadratic term (5) before completing the square, which is correct.
mr williamson bought 4 boxes of chewy granola bars in five boxes of crunchy granola bars. Each box contains the same number of granola bars. He took all 72 granola bars to a class picnic. How many granola bars are in each box?
Answer:
8
Step-by-step explanation:
Total amount of boxes is 9 so divide the total number of boxes into the total granolas. So 72/9=8
Answer:
Step 1: Write an equation.
✔ 4x + 5x = 72
Step 2: Identify and combine like terms.
✔ 9x = 72
Step 3: Use the properties of equality and inverse operations to solve the equation.
✔ x = 8
5x(f-32)divided by 9 for f = 95
Answer:
35x
Step-by-step explanation:
[tex]5x(f - 32) \div 9 \\ = \frac{5x(f - 32)}{9} \\ = \frac{5x(95 - 32)}{9} \\ = \frac{5x \times 63}{9} \\ = 5x \times 7 \\ = 35x[/tex]
What does it mean to divide figures into known shapes
Dividing figures into known shapes in mathematics helps simplify complex shapes and analyze their properties effectively.
Dividing figures into known shapes involves breaking down complex figures into simpler, identifiable shapes such as squares, rectangles, triangles, or circles.
This process is commonly used in geometry to analyze and understand the properties of irregular shapes by partitioning them into known geometric shapes.
By dividing figures into known shapes, mathematicians can apply specific formulas and principles to calculate areas, perimeters, and other geometric attributes accurately.
In how many ways can four people sit in a car for a road trip if only two of them can drive?
Answer:
well lets put it in terms of A B C D
so if A and B are the only ones who can drive then we can figure out this pretty easily
ABCD ABDC ACBD ACDB ADCB ADBC
so that's 6 ways
and if B Drives that gives us another 6
so together thats 12
might be wrong have not been in middle school for a while
Which statement about the function is true? The function is positive for all real values of x where x>-4, . The function is negative for all real values of x where - 6 < x < - 2 . The function is positive for all real values of x where x < - 6 or x > - 3 . The function is negative for all real values of x where x < - 2
Answer:
B. The function is negative for all real values of x where
–6 < x < –2.
Step-by-step explanation:
Just took the test
Answer: B!!
Step-by-step explanation: i did on edge
PLEASE HELP!!
At certain times of the year, about 70% of airline flight delays are caused by bad weather. During those times, about 50% of all flights experience bad weather, and about 25% of all flights are delayed.
Given these percentages, if the weather is good, what is the probability that your flight will be delayed?
About 35%
About 20%
About 15%
Answer:
About 15%
Step-by-step explanation:
Since the weather is good, this means that 500 flights are affected because 50% of the flights experience good weather and 50% of the flights experience bad weather.
there will be 75 flights that are delayed due to causes other than bad weather
if you assume that all of the flights that are not caused by bad weather occur in good weather, then the probability would have to be 75 / 500 = .15 = 15%.
Answer:
I believe is 35%
Step-by-step explanation:
Margo deposited $100 into a savings account earning 4.5% simple annual interest. At the end of each year, she adds $100 to her account. Fill in the table below to figure out how much money was in Margo's account at the end of 3 years.
Answer:
principal interest total money in account
at the end of year
Year one $100 $4.5 $104.5
year two $200 $ 9 +$4.5 $ 213.5
year three $300 $ 9 +$4.5 + $13.5 $ 327
Step-by-step explanation:
Simple interest for any principal is given by
I = p* r* t/100
I = interest rate accrued on principle amount
p is the amount deposited
r is the rate of interest
t is the time period of saving
_______________________________________________
For year one
p = $100
r = 4.5%
t=1
I = 100*4.5*1/100 = 4.5
_______________________________________________
For year two $100 more is added to already existing $100 in account.
p = 100 +100 = $200
r = 4.5%
t=1
I = 200*4.5*1/100 = 9
_______________________________________________
For year two $100 more is added to already existing $200 in account after two years.
p = 100 +100 +100 = $300
r = 4.5%
t=1
I = 300*4.5*1/100 = 13.5
_______________________________________________
There fore total money in Margo account is
$300 saving deposited by her
$4.5 + $9 + $13.5 = $27 (interest accrued in three time)
Formulating the results in tabular form
principal interest total money in account
at the end of year
Year one 100 4.5 104.5
year two 200 9 +4.5 213.5
year three 300 9 +4.5 + 13.5 327
x−1.27=4.09
What is x
Every Wednesday, Carla runs 2.5 miles. How many feet did she run?
Answer:
13,200 feet
Step-by-step explanation:
There are 5280 feet in a mile, so multiply 5280 by 2.5
5280*2.5=13,200
So, every Wednesday, she runs 13,200 feet
Hope this helps! :)
plz see the attachment
The fish population of Lake Collins is decreasing at a rate of 5% per year. In 2001 there were about 1,200 fish. Write an exponential decay function to model this situation. Then find the population in 2006.
The student's question involves creating an exponential decay function to determine the fish population in Lake Collins after five years, given a starting population in 2001 and a 5% annual decrease. The function is N(t) = 1200e^-rt, with r being 0.05 and t being 5. The estimated fish population for the year 2006 is approximately 935.
The student is asking for an exponential decay function to model the decrease in the fish population at Lake Collins. We are given that in 2001, there were about 1,200 fish, and the fish population is decreasing at a rate of 5% per year. To model this situation, we use the exponential decay formula:
N(t) = N0e-rt
Where:
N(t) is the fish population at time tN0 is the initial fish populationr is the decay rate (as a decimal)t is the time in years since the initial countFor this problem, the initial population N0 is 1,200, the decay rate r is 0.05 (since 5% is 0.05 as a decimal), and the time t we are interested in is 2006 - 2001 = 5 years. Plugging these values into the formula, we get:
N(5) = 1200e-0.05 * 5
Calculating N(5), the fish population in 2006, using the above formula:
N(5) = 1200e-0.25 ≈ 1200 * 0.7788 ≈ 935
Therefore, the estimated fish population in Lake Collins in 2006 would be approximately 935 fish.
i need help please !!!!!
Answer:
1. No.
2. No.
3. No.
4. Yes.
Step-by-step explanation:
You just need to sub in the numbers for x and y. For the first one, it is -21 - 8 > 18 which is equal to -29 > 18, so the answer is no. For the second one, it is -21 > 18, so the answer is no. For the third one, it is -14 + 32 > 18 which is equal to 18 > 18, so the answer is no. For the fourth one, it is 56 - 36 > 18 which is equal to 20, so the answer is yes. I hope this helps, please mark me brainliest!
A gardener is planting two types of trees:
Type A is 8 feet tall and grows at a rate of 6 inches per year.
Type B is 10 feet tall and grows at a rate of 4 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
12 years
Step-by-step explanation:
8 feet = 96 inches
10 feet = 120 inches
96 + 6t = 120 + 4t
2t = 24
t = 12
Amber is on a family cell phone plan with the other 3 members of her family. The family gets 840 shared cell phone minutes a month, and each family member is limited to his or her equal share of the minutes. The only free calls are calls between family members.
How many minutes per day can Amber talk on her cell phone with her friends during a 30-day month, without going over her share of the minutes?
Answer:
this confuses me
Step-by-step explanation:
A set of points that form a line are called..??
Answer:
collinear points
Step-by-step explanation:
A set of points that form a linear are called collinear points
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. What is the volume of the rectangular prism?
A rectangular prism has a length of 10.4 millimeters, a width of 5 millimeters, and a height of 8 millimeters.
Please answer ASAP! I've been stuck on this problem for hours.
Answer:
[tex]V=416\ mm^3[/tex]
Step-by-step explanation:
we know that
The volume of a rectangular prism is given by the formula
[tex]V=LWH[/tex]
we have
[tex]L=10.4\ mm\\W=5\ mm\\H=8\ mm[/tex]
substitute in the formula
[tex]V=(10.4)(5)(8)=416\ mm^3[/tex]
The volume of the rectangular prism is [tex]416\ mm^3[/tex]
Calculation of the volume of the rectangular prism:Since A rectangular prism has a length of 10.4 millimeters, a width of 5 millimeters, and a height of 8 millimeters.
So here the volume is
= (10.4) (5) (8)
= [tex]416\ mm^3[/tex]
Here we multiplied all three things to get the volume
hence, The volume of the rectangular prism is [tex]416\ mm^3[/tex]
learn more about volume here: https://brainly.com/question/12497184
How do you factor 6x^2+x+2
Answer:
[tex]6x^{2} +x + 2[/tex] cannot be factored
Step-by-step explanation:
The equation cannot be simplified so you have to use the quadratic formula
and you will get imaginary numbers from the formula
PLZ HELP!!!!!!! WILL GIVE BRAINLIEST!!!
Answer:
Step-by-step explanation:
The hood above the stove in a restaurant kitchen is filled with fans and other ventilation parts.
How much space is there inside the empty hood?
8 feet cubed
12 feet cubed
36 feet cubed
38 feet cubed
Answer:
B.12 feet cubed
Step-by-step explanation:
We are given that
Height of prism,h=4 feet
Base of triangle,b=3 feet
Height of triangle=l=2 feet
Area of triangular base,B=[tex]\frac{1}{2}bl[/tex]
Using the formula
Area of triangular base=[tex]\frac{1}{2}\times 3\times 2=3ft^2[/tex]
Volume of triangular prism=Bh
Using the formula
Volume of triangular prism=[tex]3\times 4=12ft^3[/tex]
There is 12 cubic feet space inside the empty hood.
Option B is true.
Answer:
B. 12 feet cubed is correct!
Step-by-step explanation:
Hope this helps! :)
ankur bought a toy for rs 130 and sold it to his friends for 150 .profit incurred by him is
Answer:
Rs 20
Step-by-step explanation:
Profit = selling price - cost price
= 150 - 130
= Rs 20
The top of the lid to a small container is in the shape of a square with a side length of 6 centimeters, as shown. What is the
area of the top of the lid?
Use the formula for the area of a square, A-s. Where Arepresents the area and s represents the side length
O 12 cm
O 24 cm?
O 36 cm
72 cm
Given:
The top of the lid to a small container is in the shape of a square with a side length of 6 centimeters.
We need to determine the area of the top of the lid.
Area of the top of the lid:
The area of the top of the lid can be determined using the formula,
[tex]A=s^2[/tex]
where s is the side length of the square
Substituting [tex]s=6[/tex] in the above formula, we get;
[tex]A=6^2[/tex]
[tex]A=36[/tex]
Therefore, the area of the top of the lid is 36 cm²
Hence, Option C is the correct answer.
What are the solutions of 3(x – 4)(2x – 3) = 0? Check all that apply
Answer:
x= 3/2 or x=4
Step-by-step explanation:
Let's solve your equation step-by-step.
3(x−4)(2x−3)=0
Step 1: Simplify both sides of the equation.
6x2−33x+36=0
Step 2: Factor left side of equation.
3(2x−3)(x−4)=0
Step 3: Set factors equal to 0.
2x−3=0 or x−4=0
x= 3/2 or x=4
What is the equation of the line?
Answer:
y=(1/4)x-3
Step-by-step explanation:
To find the equation of a line, use the following equation:
y=mx+b where m is the slope (rise/run) and b is the y-intercept.
The slope of the line is 1/4 and the y-intercept is -3. Just fill it into the problem to get the answer y=(1/4)x-3. Hope this helps! :)
Jeremy claims that if a linear function has a slope of the same steepness and the same y-intercept as the linear function in the
graph, then it must be the same function.
Which equation is a counterexample to Jeremy's argument?
Answer:
A
Step-by-step explanation:
240 as a percentage
Answer:
240%
Step-by-step explanation:
240 / 100 Answer: 240%
Answer:
240%
Step-by-step explanation:
Samuel and Sebastian go to the movie theater and purchase refreshments for their friends.
Samuel spends a total of $36.75 on 1 bag of popcorn and 3 drinks.
Sebastian spends a total of $138.00 on 3 bags of popcorn and 12 drinks.
Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink.
Using these equations, determine and state the price of a drink, to the nearest cent.
Answer and Step-by-step explanation:
samuel---> 1pc+3dr=36.75
sebastian--->3pc+12dr=138
1pc+4dr=46
1pc+4dr=46
1pc+3dr=36.75
so 1 dr=46-36.75=$9.25
4dr is 9.25×4=37
so 1 pc=46-37=$9.00
Answer:
$9.25
Step-by-step explanation:
Cost of popcorn: x
Cost of drink: y
x + 3y = 36.75
x = 36.75 - 3y
3x + 12y = 138
x + 4y = 46
36.75 - 3y + 4y = 46
y = 46 - 36.75
y = 9.25
What is the value of y, given x=6 and the equation y= 0.5x + 7
Answer:
10
Step-by-step explanation:
y=(0.5)6+7
y=3+7
y=10
Answer:
the value is 10
Step-by-step explanation:
y = 0.5(6) + 7
y = 3 + 7
y = 10
lines p and q are parallel. what is the measure of angle 3 in degrees?
27°
33°
60°
153°
5x-6>-6
what is the answer?
Hope this will help u....:)