If we know the quadratic formula, the quadratic formula is
x = [-b ± √(b²- 4ac)] / 2a
Gosh! So overwhelming! But let's look at the composition of a quadratic equation:
ax² + bx + c = 0
And we have 6x² - 3x = 1. So, what do we do? We need to put this quadratic equation into an easy form to find the value of a, b, and c to plug in to the equation.
We can just minus one on both sides to get this:
6x² - 3x - 1 = 0
Is it in the form of ax² + bx + c? Yes! a = 6, b = -3, and c = -1. Now, all we have to do is plug it into the quadratic formula.
x = [-b ± √(b²- 4ac)] / 2a
x = [-(-3) ± √((-3)²- 4(6)(-1))] / 2(6)
[3 ± √(9- 4(6)(-1))] / 12
[3 ± √(9 + 24)] / 12
[3 ± √(33)] / 12
At this point, we should just use a calculator, and recognize we have two answers because of the plus-or-minus sign! (or this sign: ±)
[3 ± √(33)] / 12
1) [3 + √(33)] / 12 = 0.73 approximately
2) [3 - √(33)] / 12 = -0.23 approximately
So, x=0.73 and x= -0.23.
A local ice cream shop wants to see if they should promote a new swizzleberry swirl or creamsicle flavored drink. In order to determine which one to promote, they took a sample of 80 patrons and asked them to choose which they preferred. The one that is significantly preferred over the other (at a .05 level of significance) will be promoted. It is expected that an equal number of patrons will choose each flavor. Based on the observed frequencies given below, what is the decision for this test
Danielle sells 3 donuts for $9. Write an equation to represent the relationship between the number of donuts sold and the earning
Halp
Help please I’ll mark you brainliest!!
Answer:
35 ft
Step-by-step explanation:
Sorry this took me so long, I am 99% sure it is right though
I hope this helps :)
Nick has an album that holds 700 compact discs. Each page of the album holds 7 compact discs. If 69% of the album is empty, how many pages are filled with compact discs?
Answer:
41
Step-by-step explanation:
each page holds 7 discs. the alb holds 700 discs. that means there are 100 pages. 69% of the pages are empty so therefore 41 pages are filled.
What are the formulas for a 90, 180, 270, and 360 rotation?
Difference between 3/5 of Raman's present age and his age 4 years ago is zero. What will be his age after 5 years?
Answer: 15 years
Step-by-step explanation:
Given
Difference between [tex]\frac{3}{5}[/tex] Raman's present age and his age 4 years ago is 0
Suppose Raman's present age is [tex]x[/tex]
So, we can write
[tex]\Rightarrow \dfrac{3x}{5}-(x-4)=0\\\Rightarrow \dfrac{3x-5x}{5}+4=0\\\Rightarrow \dfrac{-2x}{5}+4=0\\\Rightarrow x=\dfrac{20}{2}=10[/tex]
His age after 5 years is [tex]x+5=15\ yr[/tex]
A t-shirt company spent 28% of its annual budget developing a new heat-press machine. What fraction of the company's budget was spent developing the new machine?
Answer:
7/25
Step-by-step explanation:
ayo can yall help me plzzz
Answer:
D, Impossible
Step-by-step explanation:
Answer:impossible
Step-by-step explanation:
there aren’t any green folders
Can u guys pls help me if u are correct I will give brainliest i swear!
[tex]5 \times 10 + \frac{7 + 10}{2} \times 4 = 50 + 17 \times 2 = 50 + 34 = 84[/tex]
Answer:
i believe the area is 92
Step-by-step explanation:
,,,,,,,,,,,,,,,,,,,,,,,
Answer:
I think the answer is D, 15 Square Inches
Sal buys y pens and some pencils. He buys 10 more pencils than pens. How many pens and pencils does he buy
altogether?
Answer:
20
Step-by-step explanation:
Which transformation shows a translation of 3 units to the right?
A)
А
B)
B
0)
С
D)
D
Answer:
B
Step-by-step explanation:
It shows the P moving to the right three units without flipping it.
Find the surface area of the figure below. Leave answers in terms of 7 for answers that contain T. Round to the nearest hundredthin
necessary
5.4 ft
4 ft
4ft
82.7 ft
Oь
59.2 ft2
Oc
35.5 ft
Od
44 ft
Answer:
Hello! 59.2 is our answer
This is because for all the triangles we do 5.4 x 4 = 21.6 then I divide by 2 cause thats the formula when doing triangles so I get 10.8 and sense all the triangle sides our the same I do 10.8 x 4 and get 43.2 then for the bottom side I just have to do 4 x 4 cause thats the formula and get 16 then I add these up so 43.2 + 16 = 59.2 and We get our answer 59.2 Hope this helps!
Find the missing measurements in triangle ABC. Round your answer to the nearest tenth if necessary.
Measure of Angle B=
AB=
AC=
Answer:
m∡B = 55°
AB = 5.2
AC = 7.4
Step-by-step explanation:
m∡B = 180-(90+35)
use Law of Sines to find AB and AC:
sin 90° / 9 = sin 35°/AB
AB = .57(9) = 5.2
sin 90° / 9 = sin 55°/AC
AC = .82(9) = 7.4
The solution is,
m∡B = 55°
AB = 5.2
AC = 7.4
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
from the given figure, we get,
m∡B = 180-(90+35)
=55
use Law of Sines to find AB and AC:
sin 90° / 9
= sin 35°/AB
AB = .57(9)
= 5.2
sin 90° / 9 = sin 55°/AC
AC = .82(9
= 7.4.
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help me pls :) i put a lot of points
if a_1=3 and a_n=(a_n-1)^2-5 then find the value of a_3
Answer:the value would be 6-10
Step-by-step explanation:
The sum of 2 and the quantity 20 divided by n.
Answer:
[tex] \dfrac{2 + 20}{n} [/tex]
Step-by-step explanation:
[tex] \dfrac{2 + 20}{n} [/tex]
Answer:
I think your answer is 10
Step-by-step explanation:
An 18 kg weight is lifted up to 12 m in height and then released in free fall. What are the potential energy, kinetic energy and total energy at: The highest point? 3 m above the ground? At the ground?
Answer:
1) at the highest Point
KE= 0 PE=2116.8 N
2) 3 m above the ground
PE= 529.2 N KE=1587.6 N
3) at the ground
KE= 2116.8 N and PE=0
Step-by-step explanation:
The potential energy is given by
PE= mgh where m is the mass , g is the acceleration due to gravity which is equal to 9.8 m/s² and h is the height.
The kinetic energy is given by KE= 1/2 mv² where m is the mass of the body and v is the velocity.
1) at the highest Point
Now at the highest point the velocity is zero
KE= 1/2 mv²
KE= 0
PE = mgh
PE= 18 *9.8* 12= 2116.8 N
Total Energy = KE + PE= 0 + 2116.8 N= 2116.8 N
2) 3 m above the ground
At 3 m above the ground
PE= mgh
PE= 18 *9.8* 3= 529.2 N
According to law of conservation of energy the total energy ( sum of KE and PE) remains the same at every point.
Total Energy = KE + PE
2116.8 N-529.2N= 1587.6N
KE=1587.6 N
3) at the ground
at the ground the height will be zero
PE= mgh
PE= 18 *9.8* 0= 0 N
According to law of conservation of energy the total energy ( sum of KE and PE) remains the same at every point.
Total Energy = KE + PE
2116.8 N=2116.8 N + 0
KE= 2116.8 N
or
KE= 1/2 mv²
KE = 1/2* 18 *(15.36)²= 2116.8
jason is closing on a $430,000 home. he made a 10% down payment and is borrowing the rest. closing costs are 3.5 percent of the mortgage.
a. what is the down payment?
b. what is the amount of the mortgage?
c. what are the closing costs?
d. what is the total amount of the mortgage if they finance the closing costs with the mortgage
The total Amount of the mortgage is $400,545 if the closing costs are financed with the mortgage.
a) The down payment of Jason is 10% of $430,000 =$43,000b) The amount of the mortgage is the difference between the home value and the down payment.
Mathematically, $430,000 - $43,000 = $387,000.c) The closing costs are 3.5% of the mortgage. So, 3.5% of $387,000 is: 0.035 × $387,000 = $13,545.
Hence, the closing costs are $13,545. d) The total amount of the mortgage if they finance the closing costs with the mortgage is the sum of the amount of mortgage and the closing cost.
So, the total amount of the mortgage is: $387,000 + $13,545 = $400,545.Solution:a) Jason's down payment is 10% of the cost of the house, which is given as $430,000.
To calculate the down payment, multiply the cost of the house by 10%.Down payment = $430,000 x 10% = $43,000
Therefore, Jason's down payment is $43,000.b)
The amount of the mortgage is the difference between the total cost of the house and the down payment. The cost of the house is given as $430,000.
Thus, we have:Mortgage amount = Total cost - Down paymentMortgage amount = $430,000 - $43,000Mortgage amount = $387,000
Therefore, the amount of the mortgage is $387,000.c) The closing costs are 3.5% of the mortgage.
Using the mortgage amount calculated in part b), we can compute the closing costs as follows:Closing costs = 3.5% x Mortgage amountClosing costs = 3.5% x $387,000
Closing costs = $13,545
Therefore, the closing costs are $13,545.
d) If the closing costs are financed with the mortgage, we simply need to add the closing costs to the mortgage amount calculated in part b):Total amount of the mortgage = Mortgage amount + Closing costsTotal amount of the mortgage = $387,000 + $13,545
Total amount of the mortgage = $400,545
Therefore, the total amount of the mortgage is $400,545 if the closing costs are financed with the mortgage.
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A school is holding its annual book fair. The line plot below shows the amount of books students have bought
What is the experimental probability that a student will buy 3 books?
A.4/15
B.3/15
C.4/3
D.4/9
HELP ASAAAPPPPPPP PLEASEEEEE
Answer:
I say it is A.
Step-by-step explanation:
It is the one that makes the most sense.
Hope this helps.
State if the two triangles are congruent. If they are, state how you know
A) SSS
C) ASA
B) Not congruent
D) SAS
Answer:
C) ASA
Step-by-step explanation:
angles are indicated equal and they share the common diagonal between those angles, so ASA
The given two triangles are congruent due to the ASA postulate, which is the correct answer that would be an option (C).
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
The given triangles are given in the figure.
We can see that there are two angles that are the same and one side is the same.
According to ASA, two triangles are congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.
So, we conclude that the given two triangles are congruent.
Hence, the given two triangles are congruent due to the ASA postulate.
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what is the simplified fractional equivalent of the terminating decimal 0.78?
Answer: 39/50
Step-by-step explanation: the answer is 39/50
Answer:
the answer is 39/50
Step-by-step explanation:
thank you
Please third time asking I’ll mark brainliest
Answer: A≈440.44
Step-by-step explanation:
Answer:
1,536
Step-by-step explanation:
i calculated it
thisssss??????????????
Answer:
Part A = 91.125in²
Part B = 8 boxes
Step-by-step explanation:
Work is underlined
Normal text = explanation
Hey There!
What we want to do to find how many supply boxes can fit inside of the larger box is find the volume of the larger box and divide that by the volume of the supply boxes.
To find the volume of the supply boxes:
We are told that the supply box is in the shape of a cube.
That being said we can find the volume by using this simple formula
[tex]V=s^3[/tex]
where s = side length
The supply box has a side length of 4.5 so we just plug in 4.5 into the formula
[tex]V=4.5^3\\4.5*4.5*4.5=91.125[/tex]
So we can conclude that the volume of the supply box is 91.125 square inches.
Now to find the volume of the larger box.
The larger box is in the shape of a rectangular prism.
The volume of a rectangular prism can be found by multiply the width by the length by the height.
The box has the following dimensions:
width = 18 in
height = 4.5 in
length = 9 in
This means that the volume = 9 * 4.5 * 18
9 * 4.5 = 40.5
40.5 * 18 = 729.
so the volume of the larger box is 729 square inches.
Now we want to find how many little boxes can fit inside the larger box.
Like stated before this can be done by dividing the volume of the little boxes by the volume of the larger box
so # of supply boxes that can fit inside of the larger box = [tex]\frac{729}{91.125}[/tex]
Using a calculator: [tex]\frac{729}{91.125} =8[/tex]
Hence, 8 smaller boxes can fit inside of the larger box
Marcus wants to earn an "A" in math for the 4th quarter. His teacher is averaging 4 test grades. His grades on the first three tests are 85, 95, and 88. What grade does he need to earn on his 4th test to end up with an average of 90?
Answer:
87
Step-by-step explanation:
0.33333333×3.14×8×8×18
Answer:
1205.75999
Step-by-step explanation:
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease y=330(1.06)^x
=======================================================
Explanation:
The general form of an exponential function is
y = a*b^x
where 'a' is the initial starting amount and b helps determine if we have exponential decay or exponential growth, and how much of it.
We have a = 330 as the initial amount. Since b = 1.06 is larger than 1, this means we have exponential growth. If 0 < b < 1, then we would have exponential decay.
Solving 1+r = 1.06 leads to r = 0.06 = 6%, showing we have a growth rate of 6%
This means that if we started with say 100 people, and the population grew by 6%, then at the end of the time unit (say 1 year), then we'd have 106 people.
why life on Earth depends on matter
Answer:
because matter is everything, everything around us is made of matter even people
have a good day :)
Step-by-step explanation:
-19 2/9 -4 1/9-(-3 4/9) = ?
Answer:
I think its -19.9
Step-by-step explanation:
just break it down :)
On Sarah's shelf are 6 mystery books,5 science books,4 history books, and 3 adventure books. What is the probability of NOT selecting a mystery book?
Answer:
Probability of Sarah NOT selecting a mystery book = 0.67
Step-by-step explanation:
Probability helps to show how likely an event will occur;
The probability an event will not occur can be obtained by subtracting the probability that the event will occur from 1.
We can take this route to solve this problem
The probability of picking an option from a broad list of alternatives can be calculated using the formula:
Probability = number of expected outcomes/ total number of options
For our problem, there are only 6 mystery books on the shelf. Hence, the number of expected outcomes is = 6. Sarah cannot pick any more than 6 mystery books, and any mystery book she picks will be from that lot.
The total number of options refers to the total number of books available to pick from; whether mystery, science history, and adventure.
We can get this by adding 6 + 5 + 4 + 3 = 18
Probability of Sarah selecting a mystery book = 6/18
Probability of Sarah NOT selecting a mystery book = 1 - (6/18) = 0.67
