Answer:
EQUATION: [tex]x^2-16x+48=0[/tex]
METHOD: Factorization.
The sellings prices are:
$4
$12
Step-by-step explanation:
You need to find the selling price or prices that would generate $50 in daily profit, then you need to substityte[tex]y=50[/tex] into the quadratic function:
[tex]50=-10x^2+160x-430[/tex]
Make the equation equal to zero:
[tex]-10x^2+160x-430-50=0\\-10x^2+160x-480=0[/tex]
Simplify by dividing by -10, then you obtain the equation:
[tex]x^2-16x+48=0[/tex]
You can solve it with Factorization.
Choose two numbers whose sum is -16 and whose product is 48.
These would by -12 and -4.
Then:
[tex](x-12)(x-4)=0\\x_1=12\\x_2=4[/tex]
Answer:
Replace y in the equation with 50: (50 = -10x2 +160x - 430) Use factoring to solve the equation. After writing the equation in standard form and dividing each side by -10, it is easy to factor as 0 = (x - 4)(x - 12).
How many committees or three people are possible from a group of 12
I thinks its 4 if that's one of your answers. It says of 3 people from a group of 12. And a 3 and 4 are both factors of 12. 3 x 4 = 12.
The number of possible committees of three people from a group of 12 can be found by using combinations, resulting in 220 possible committees.
The number of committees of three people possible from a group of 12 can be calculated using combinations.
To choose 3 people out of 12, you use the combination formula: C(12,3) = 220.
Therefore, there are 220 possible committees of three people from a group of 12.
Which inequality represents the statement A final grade of at least 90? A. x < 90 B. x > 90 C. x ≤ 90 D. x ≥ 90
Answer:
D
Step-by-step explanation:
Since it is at least 90, it literally means that the lowest possible value is 90. Therefore the number can only be greater than or equal to 90. So, the answer is D.
Answer:
C. X is less than or equal to 90
Step-by-step explanation:
because as you can see that the last sentence it says. A final grade of at LEAST 90?
Use a half-angle identity to find the exact solution of cos 3 pi / 8
Answer:
-[tex]\sqrt{\frac{2-\sqrt{2}}{4}[/tex]
Step-by-step explanation:
The cosine half-angle formula is
[tex]cos\frac{\pi }{2}[/tex]=±[tex]\sqrt{\frac{1+cosx}{2} }[/tex]
we can write
[tex]cos \frac{3\pi }{8}[/tex]
as
[tex]cos\frac{\frac{3\pi }{4} }{2}[/tex]
=-[tex]\sqrt{\frac{1+cos\frac{3\pi}{4} }{2}[/tex]
=-[tex]\sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}[/tex]
=-[tex]\sqrt{\frac{2-\sqrt{2}}{4}[/tex]
(cosine is negative is in second quadrant)
Using the half angle identity, the exact value of cos 3 pi / 8 is (√2 - 1) / 2√2.
Given a trigonometric expression,
cos 3π/8
We have to find the exact value of this using the half angle identity.
The half angle identity in terms of cosine function is,
cos (x/2) = ± √[(1 + cos x) / 2]
Here the angle is 3π/8.
This can be written as,
3π/8 = 3π/4 / 2
Substituting to the formula,
cos (3π/4/2) = √[(1 + cos 3π/4) / 2]
Now,
cos 3π/4 = cos (π - π/4)
= -cos(π/4)
= - 1/√2
Substituting to the formula,
cos (3π/4/2) = √[(1 - 1/√2) / 2]
= (√2 - 1) / 2√2
Hence the value is (√2 - 1) / 2√2.
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if the following segment is reflected across the y-axis what are the new coordinates of the new endpoints? A.)(1,6) and (3,2) B.) (-6,1) and (-2,3) C.) (-1,-6) and (-3,-2) D.) (6,-1) and (2,-3)
Answer:
A.) (1, 6) and (3, 2)Step-by-step explanation:
Look at the picture.
[tex]\begin{array}{c|c|}&(x,\ y)\\S_{OX}&(x,\ -y)\\S_{OY}&(-x,\ y)\\S_{(0,0)}&(-x,\ -y)\end{array}[/tex]
Alice took out a $15,000 loan for college. She is borrowing money from two banks. Bank A charges an interest rate of 6%, and Bank B charges an interest rate of 7%. After one year, Alice owes $960 in interest. How much money did she borrow from Bank A?
Answer:
Final answer is $9000.
Step-by-step explanation:
Given that Alice took out a $15,000 loan for college. She is borrowing money from two banks. Bank A charges an interest rate of 6%, and Bank B charges an interest rate of 7%. After one year, Alice owes $960 in interest.
Now we need to find out about how much money did she borrow from Bank A.
So let's assume that money borrowed from bank A = x
then money borrowed from bank B = 15000-x
Interest from bank A = 6% of x = 0.06x
Interest from bank B = 7% of (15000-x) = 0.07(15000-x)
Given total interest is $960. So we can write equation:
0.06x+0.07(15000-x)=960
0.06x+1050-0.07x=960
1050-0.01x=960
-0.01x=960-1050
-0.01x=-90
[tex]x=\frac{-90}{-0.01}[/tex]
x=9000
Hence final answer is $9000.
Answer:
The amount borrowed from bank A = $9000
Step-by-step explanation:
Formula:
I = PNR/100
P - Principle amount
N - Number of years
R - Rate of interest
It is given that,Alice took out a $15,000 loan for college. Bank A charges an interest rate of 6%, and Bank B charges an interest rate of 7%. After one year, Alice owes $960 in interest.
Let 'x' be the amount borrowed from Bank A
Then the amount borrowed from Bank B = 15000 - x
To find the value of x
I = PNR/100
Here I = $960
(x*1*6)/100 + (15000 - x)*1*7/100 = 960
6x/100 + (15000*7)/100 - 7x/100 = 960
1050 - x/100 = 960
x/100 = 1050 - 960 = 90
x = 90 * 100 = 9000
Therefore the amount borrowed from bank A = $9000
An item regularly priced at $80 is on sale for 20% off. There is 3% sales tax. What is the sales price before sales tax?
Answer:
Price before tax is $64
Step-by-step explanation:
It asks for price before sales tax, so ignore sales tax %.
P=original-[original•(20/100)]
=80-80•0.2
=80-16
P=64
Answer:
$64
Step-by-step explanation:
We have been given that an item regularly priced at $80 is on sale for 20% off. There is 3% sales tax. We are asked to find the sales price before sales tax.
The sales price would be 80 minus 20% of 80.
[tex]\text{Sales price}=80-\frac{20}{100}\times 80[/tex]
[tex]\text{Sales price}=80-\frac{1600}{100}[/tex]
[tex]\text{Sales price}=80-16[/tex]
[tex]\text{Sales price}=64[/tex]
Therefore, the sales price before sales tax would be $64.
What is the number????
Step-by-step explanation:
[tex]n-a\ number\\\\3.145<n<3.146\Rightarrow 3.1450<n<3.1460\\\\n\in\{3.1451,3.1452,\ 3.1453,\ 3.1454,\ ...,3.1459\}[/tex]
A store is having a Back To School Sale.The total for a skirt,a pair of shoes,and a pair of socks is $34.95 before tax.The pair of socks costs $3.75.The original prices of the skirt and shoes were the same.What was the sales price of the skirt
Final answer:
The sales price of the skirt was $15.60.
Explanation:
In this problem, we are given that the total cost of the skirt, pair of shoes, and pair of socks is $34.95 before tax. We are also given that the pair of socks costs $3.75. Since the original prices of the skirt and shoes were the same, we can assume they each cost x dollars.
Therefore, the equation we can set up is: x + x + 3.75 = 34.95.
We can solve this equation to find the value of x, which represents the original price of the skirt. Subtracting 3.75 from both sides, we get: 2x = 31.20. Dividing both sides by 2, we find that x = 15.60. Therefore, the sales price of the skirt was $15.60.
How many yards long is John's new surfboard if it is 7 feet long
A) 2 1/3
B) 2 2/3
C) 4 yards
D) 21 yards
Answer:
A)
Step-by-step explanation:
need help asap!!! plzz
What is 75% of 240?
(A)150
(B)60
(C)165
(D)180
Answer:
D) 180
Step-by-step explanation:
Keep in mind to properly use a percent you must set it to a decimal.
To do so simply move the . in 75. over to the left 2 times. Which will go to .75!
Now time to multiply 240 by .45.
240 x .45 =180
Answer:
D 180
Step-by-step explanation:
75/100*240=180
What is 19.55 rounded off to the nearest whole number
Answer:
20
Step-by-step explanation:
19.55 can be either 19 and 20, but it is closer to 20!
Answer: The answer is 20.
Step-by-step explanation: So anytime you are rounded if the number is 5 or over 5 it will round up. If it is under 5 it will round down and in this case it is over half or 5 so it would round up to 20 since 20 is a whole number.
50 POINTS!! HELP ME PLEASE HURRY IM RUNNING OUT OF TIME!!!
Find the volume of each figure to the nearest tenth.
Volume of sphere = 4/3 x PI x r^3
= 4/3 x 3.14 x 6^3
= 904.3 cubic meters
Volume of cone = PI x r^2 x h/3
h = √13^2-5^2 = 12
= 3.14 x 5^2 x 12/3
= 314 cubic meters
Which expression gives the measure of ACE in the diagram below
Answer:
B
Step-by-step explanation:
There are 2 secant lines intersecting a circle. We can use far arc - near arc formula to find this.
Let far arc be arc AE, and near arc be arc BD. So the theorem tells us:
Measure of Angle C = half of the difference of far arc - near arc
so we can say:
∠ACE = half of (arc AE - arc BD)
or
∠ACE = [tex]\frac{1}{2}(172-58)[/tex]
Option B is right.
Answer:b
Step-by-step explanation:
Let P represent the statement "Mary works at the water park." Let Q represent the statement "Mary takes college classes."
Which symbolic notation represents the statement "Mary works at the water park or takes college classes." ?
A. P ∨ Q
B. P ∧ Q
C. P → Q
D. P ↔ Q
b is the correct answer
Step-by-step explanation:
The symbolic notation that represents the statement 'Mary works at the water park or takes college classes' is P ∨ Q.
Explanation:The symbolic notation that represents the statement 'Mary works at the water park or takes college classes' is P ∨ Q.
The '∨' symbol represents the logical operator 'or', which indicates that either statement P or statement Q (or both) can be true for the overall statement to be true.
In this case, Mary can work at the water park, take college classes, or do both.
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Triangle ABC is shown below :
Answer:
try the answer C
Step-by-step explanation:
You must show all steps and provide any evidence needed in your solution to receive full credit.
4. The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made one eight of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?
5. Using the information from #4, answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.
Answer:
4) Volume model = 1723 ft³
5) The percentage of the original tank is 51200% of the mock-up
Step-by-step explanation:
4) ∵ The volume of the main tank is 882,158 ft³
∵ The dimension of the scale model is 1/8 of the original model
∵ V model/v original = (dimension model/dimension original)³
∴ Volume model/882,158 = (1/8)³
∴ Volume model = (1/512) × 882,158 = 1722.965 = 1723 ft³
5) The percentage of the original tank is
(882158/1722.965) × 100% = 51200%
Final answer:
The volume of the scale model tank is 1/512 of the original tank's volume, which is approximately 0.1953125%. The original tank's volume is 51200% of the scale model's volume.
Explanation:
Step-by-Step Solution for Volume of Scale Model Tank
Let's denote the original dimensions of the theater's main show tank as length L, width W, and height H. Therefore, the original volume V of the tank is V = L \times W \times H.
For the scale model, each linear dimension is scaled down to one eighth of the original. Thus, the dimensions of the model will be L/8, W/8, and H/8.
Now, the volume of the scale model V_{model} can be calculated as:
The volume of the scale model is 1/512 or about 0.1953125% of the original tank's volume.
Percentage Volume of Original Tank to Mock-up Tank
To find out what percentage the original volume is of the mock-up tank, we can set up a proportion.
The original volume is 51200% of the mock-up of the tank.
What is the domain of f(x)= 3x/x-1
Answer:
The answer is C on edge (all real numbers except 1)
Step-by-step explanation:
Given the points (3,0) and (-1,-3) which of the statements below is true
What are the statements?
Final answer:
The given statements about the points (3,0) and (-1,-3) are not true. One cannot determine if they are parallel to x-axis or mutually perpendicular without more information or a third point/vector.
Explanation:
The question describes two points, (3,0) and (-1,-3), and asks which statements are true regarding their position. To determine the relationship between these points, we can visualize them on a coordinate system. Point (3,0) lies on the x-axis, while point (-1,-3) does not. The statements provided suggest a scenario where the points either form parallel lines along the x-axis or are mutually perpendicular to each other.
Neither of the given statements is correct since one point lies on the x-axis, and the other does not, which means they cannot be parallel along the x-axis. Additionally, without a third point to form a triangle or a clear reference for perpendicular vectors, we cannot assert that they are mutually perpendicular. Therefore, we need additional information, such as the context for these points or the third reference point/vector, to make a proper determination.
Regarding the information about vectors and coordinates, remember that vectors can be used to define directions and magnitudes from one point to another. In this case, however, we are only given two points without clear instruction on how to interpret them as vectors.
For the statement 'Clearly, the three directions are mutually perpendicular to each other,' note that this applies to three-dimensional coordinate axes or where three vectors are given, which are specifically defined as perpendicular. This situation described with two points does not satisfy the conditions of that statement.
can someone help me.
Answer:
[tex]\large\boxed{x=\pm\sqrt{10}}[/tex]
Step-by-step explanation:
[tex]x^2=10\Rightarrow x=\pm\sqrt{10}\\\\\text{because}\ (-\sqrt{10})^2=10\ \text{and}\ (\sqrt{10})^2=10.\\\\\text{used}\ (\sqrt{a})^2=a[/tex]
which of the following has two bases?
A. prism
B. pyramid
C. line
D. plane
A. Prism
A prism has two bases
PLEZ HELP ME ASAP 21.66÷5.7
Answer: 3.8
Step-by-step explanation: See the attached file!
Solve the triangle. A = 46°, a = 34, b = 27
Find the length of the hypotenuse
34^2 + 27^2 = c^2
1156 + 729 = 1885
c^2 = 1885
sqrt(1885)
c = 43.42
Answer:
All sides of the triangle are a = 34, b = 27 and c = 46.7
and angles are A = 46°, B = 34.83° and C = 99.17°
Step-by-step explanation:
In a given triangle A = 46°, a = 34 units and b = 27 units
Then we have to find all angles and measure of the side left.
By sine rule,
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
[tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex]
[tex]\frac{34}{sin46}=\frac{27}{sinB}[/tex]
sinB = [tex]\frac{27\times sin46}{34}[/tex]
sinB = 0.5712
B = [tex]sin^{-1}(0.5712)[/tex]
B = 34.83°
Since in a triangle,
∠A + ∠B + ∠C = 180°
46°+ 34.83° + ∠C = 180°
80.83° + ∠C = 180°
∠C = 180 - 80.83 = 99.17°
[tex]\frac{b}{sinB}=\frac{c}{sinC}[/tex]
[tex]\frac{27}{sin34.83}=\frac{c}{sin99.17}[/tex]
[tex]\frac{27}{0.5711}=\frac{c}{0.9872}[/tex]
c = [tex]\frac{27\times 0.9872}{0.5711}=46.67[/tex]
Therefore, all sides of the triangle are a = 34, b = 27 and c = 46.7
and angles are A = 46°, B = 34.83° and C = 99.17°
A living room has a circular rug with a diameter of 8 feet. What is the rug's area? Use 3.14 for .
Answer:
Step-by-step explanation: 50.27 is the area
Final answer:
The area of a circular rug with an 8 feet diameter, using the formula A = π[tex]r^2[/tex] and π approximated as 3.14, is 50.24 square feet.
Explanation:
The question seeks to determine the area of a circular rug with a diameter of 8 feet. To calculate the area of a circle, the formula used is A = π[tex]r^2[/tex], where A is the area and r is the radius of the circle. Since the diameter is twice the radius, we have a radius of 4 feet (8 feet divided by 2).
Using 3.14 for π, the calculation is:
First square the radius: 4² = 16.
Multiply this by π (approximated as 3.14): A = 3.14 × 16.
Complete the multiplication to find the area: A = 3.14 × 16 = 50.24 square feet.
Therefore, the area of the rug is 50.24 square feet.
PLZ HELP
Robert makes a monthly budget. His monthly
allowance is $40. He makes $25 each month from
mowing the neighbor’s yard. Robert’s monthly
expenses are $75. How much does he need to earn
from babysitting to balance his budget?
A $75
B $10
C $50
D $35
Please help me with 26
Answer:
Step-by-step explanation:
3x3=9 For the second week
9x3=27 For the Third week
27x3=81 For the Forth week so
3 Min first week
9 Min second week
27 Min third week
81 Min forth week
How long does it take to get to space
Answer:
At 3,500 MPH, the shuttle is traveling approximately one mile per second. That means it only takes 32 seconds more to reach an altitude of 62 miles. If you want to take acceleration into account, it is a few seconds less. So it takes approximately 150 seconds for the shuttle to get out of earth's atmosphere.
Step-by-step explanation:
Answer:
That means it only takes 32 seconds more to reach an altitude of 62 miles. If you want to take acceleration into account, it is a few seconds less. So it takes approximately 150 seconds for the shuttle to get out of earth's atmosphere.
Find the seventh term of
Answer:
99
Step-by-step explanation:
Which even number comes right before 29?
Answer:
28
Step-by-step explanation:
0, 2, 4, 6, 8, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 are even numbers.
mark as brainsliest♡
Answer:
28
Step-by-step explanation:
29, 28, 27
28 is before 29 and its even fam
Ian ran a total of 6 miles around his school track. Each lap around the track is 3/4 mile. What math expression can be used to find the number of laps Ian ran? How many laps did he run?
Answer:
The answer is 8
Step-by-step explanation:
Math help pls,, will give brainiest reward! :)
Answer
16
Step by step
The triangles,PRS and PQT are similar.
PS:ST=15:3
=5:1
let PQ=x
PR:RQ
x+4:4
using the PS:ST ratio,
5:1=x+4:4
4×5=1(x+4)
20=x+4
collecting like terms
20-4=x
x=16.