Answer:
see explanation
Step-by-step explanation:
Check the value of the discriminant
Δ = b² - 4ac
• If b² - 4ac > 0 then roots are real
• If b² - 4ac = 0 roots are real and equal
• If b² - 4ac < 0 then roots are not real
given (x - a)(x - b) = k² ( expand factors )
x² - bx - ax - k² = 0 ( in standard form )
x² + x(- a - b) - k² = 0
with a = 1, b = (- a - b), c = -k²
b² - 4ac = (- a - b)² + 4k²
For a, b, k ∈ R then (- a - b)² ≥ 0 and 4k² ≥ 0
Hence roots of the equation are always real for a, b, k ∈ R
what is a mathematical statement consisting of a hypothesis and conclusion that has to be proven true
help please having trouble SUPER EASY!
Answer:
48
because 4 * 12 is 48
Answer:
48
Step-by-step explanation:
12 x 0.25 = 48
Regal Cinemas is selling tickets for the movie “Ghostbusters”. Tomorrow night , there are 73 tickets left to sell. If all the tickets are sold for the same price , the movie theater will make $438. Which of the following students have enough money to buy a ticket?
a. Amanda has $4.50.
b. Bernie has $7.00.
c. Chrissy has $6.50.
d. Dina has $6.00.
e. Evan has $5.00.
f. Frank has $14.00.
Who has enough money to go to the movie? ( write names below )
Answer:
Bernie, Chrissy, Dina and Frank
Step-by-step explanation:
if all 73 tickers are sold, the theatre makes $438 so each ticket is worth $438/73
this equals to $6.00 for one ticket
this means that Bernie, Chrissy, Dina and Frank have enough money to see the movie
Answer:
Bernie, Chrissy, Dina, and Frank are able to go.
Step-by-step explanation:
The question is not entirely clear. I take it that 73 tickets will bring in 438 dollars. If that is so, each ticket is selling for the solution of this proportion.
x / 1 = 438/73 Just do the division on the right
x = 6.00 dollars.
So Amanda will not be able to go.
Even will not be able to go.
Everyone else can.
This is the section 2 test yourself test if u know the whole thing then plz tell me
Answer: D
Step-by-step explanation:
To create a perpendicular bisector:
open the compass more than half-way between points A and Buse that width and place the compass on point A and draw an arc above and below line AB use the same width and place the compass on point B and draw an arc above and below line ABDraw a line from the intersection of the arcs above and the intersection of the arcs below line ABCongrats! You just constructed a perpendicular bisector!
simplify (-6a5b4c3)(5a3b2c)
[tex]\text{Use:}\\\\a^n\cdot a^m=a^{n+m}\\\\(-6a^5b^4c^3)(5a^3b^2c)\\\\=(-6\cdot5)(a^5a^3)(b^4b^2)(c^3c^1)\\\\=-30a^{5+3}b^{4+2}c^{3+1}\\\\=\boxed{-30a^8b^6c^4}[/tex]
x times x^n
Simplify it please and thank you!
Answer:
[tex]x^{n+1}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
note that x = [tex]x^{1}[/tex], hence
x × [tex]x^{n}[/tex] = [tex]x^{n+1}[/tex]
At a restaurant, four people ordered fried crab cakes and four people ordered a cup of gumbo, with a total of $31. If only two people had ordered the crab cakes and one person ordered the gumbo, the bill would have been $12.25. How much are each order of fried crab cakes and each cup of gumbo? (Can you please show the steps?) Thank you.
Answer:
Fried crab cakes = $4.50
Cup of gumbo = $3.25
Step-by-step explanation:
Let's make the price of fried crab cakes = x and the price of a cup of gumbo = y. Set up two equations for x and y and solve for each variable.
Setting up the equations:4 people ordered x and 4 people ordered y for a total of 31 dollars, so this equation would look like: 4x + 4y = 31
2 people ordered x and 1 person ordered y for a total of $12.25, so this equation would look like: 2x + y = 12.25
Substitution method:Now you have your two equations-- solve for a variable in one of the equations and substitute that value into the other equation.
The easiest way to start would be to solve for y in the second equation by subtracting 2x from both sides.
y = 12.25 - 2x
Substitute this value into the first equation.
4x + 4(12.25 - 2x) = 31
Now solve for x-- start by distributing 4 inside the parentheses.
4x + (49 - 8x) = 31
Combine like terms.
-4x + 49 = 31
Subtract 49 from both sides.
-4x = -18
Divide both sides by -4.
x = 4.5
Substitute this value of x into our starting equation for which we solved for y.
2(4.5) + y = 12.25
Multiply 2 and 4.5 together.
9 + y = 12.25
Subtract 9 from both sides.
y = 3.25
Each order of fried crab cakes is worth the x-value [$4.50] and each cup of gumbo is worth the y-value [$3.25].
In this system of linear equations, by denoting the cost of the fried crab cakes as x dollars, and the cost of a cup of gumbo as y dollars, we find that each order of fried crab cakes is $4.50 and each cup of gumbo is $3.25.
Explanation:The subject of this problem is linear algebra, and it can be solved using a system of linear equations. Let's denote the cost of the fried crab cakes as x dollars, and the cost of a cup of gumbo as y dollars.
From the information given in the problem, we can create the following two equations:
4x + 4y = 31 (This is from the information that four people ordered fried crab cakes and four people ordered a cup of gumbo, with a total of $31.)2x + y = 12.25 (This is from the information that if only two people had ordered the crab cakes and one person ordered the gumbo, the bill would have been $12.25.)Now, we can solve this system of equations. Divide the first equation by 2, which will give us:
2x + 2y = 15.5
Then subtract the second equation from the result, which will give us:
y = 3.25
Substitute y = 3.25 into the second equation:
2x + 3.25 = 12.25
Finally, solve for x:
x = 4.5
So, each order of fried crab cakes is $4.50 and each cup of gumbo is $3.25.
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Please answer this correctly
Answer:
$13.66
Step-by-step explanation:
Multiply the amount of Dijon mustard and mustard by its price, then add them together.
3 * 3.69 = 11.07
.5 * 5.18 = 2.59
Add these sums together.
11.07 + 2.59 = 13.66
a) 2/3 divided by 1/4 b) 7/5 multiply by 8 c) 2/5-1/3 d)3/10+2 7/12
[tex]a)\\\dfrac{2}{3}\div\dfrac{1}{4}=\dfrac{2}{3}\cdot\dfrac{4}{1}=\dfrac{8}{3}=2\dfrac{2}{3}\\\\b)\\\dfrac{7}{5}\cdot8=\dfrac{56}{5}=11\dfrac{1}{5}\\\\c)\\\dfrac{2}{5}-\dfrac{1}{3}\\\text{common denominator is (5)(3) = 15}\\\\\dfrac{2\cdot3}{5\cdot3}-\dfrac{1\cdot5}{3\cdot5}=\dfrac{6}{15}-\dfrac{5}{15}=\dfrac{1}{15}\\\\d)\\\dfrac{3}{10}+2\dfrac{7}{12}\\\text{common denominator is 60}\\\\\dfrac{3\cdot6}{10\cdot6}+2\dfrac{7\cdot5}{12\cdot5}=\dfrac{18}{60}+2\dfrac{35}{60}=2\dfrac{53}{60}[/tex]
does 1/6, -3, √7, -6/5, or 4.5 comes first when the numbers are listed from least to greatest
The arrangement is as follows:
-3<-1.2<1/6<√7<4.5
What is ascending and descending order?Ascending means smallest to largest, 0 to 9, and/or A to Z and Descending means largest to smallest, 9 to 0, and/or Z to A.
Given:
1/6= 0.16667
√7= 2.645
-6/5= -1.2
So, the least number is -3 and greatest number is 4.5.
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What is the axis of symmetry for f(x) = 2x − 8x + 8? (1 point) Select one: a. x = −2 b. x = −3 c. x = 3 d. x = 2
Answer:
x=2
Step-by-step explanation:
F(x) = 2x^2 - 8x +8
Axis of symmetry lies at the x coordinate of vertex
To find x coordinate of vertex use formula
[tex]x=\frac{-b}{2a}[/tex]
from the given f(x) , a= 2 and b = -8
Plug in all the values
[tex]x=\frac{-(-8)}{2(2)}[/tex]
[tex]x=\frac{8}{4}=2[/tex]
x=2
So the axis of symmetry at x=2
the total cost of four boxes of pasta is $14 There are 16 oz of pasta in each box of the same amount what is the maximum number of boxes that can be purchased with $65
Answer:
18.5 but rounded to 19 because you cant have half of a box
Step-by-step explanation:
because each box costs 3.5 dollars because i did 1 4 divided by 4.then you want to get to 65 so i did 3.5 divided by 65 then got 18.5 which was rounded because the decimal was big This was the real decimal 18.5714286. THIS MIGHT BE WRONG
Please help me out and answer!!!!!
Really struggling
Answer:
D
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y) → (- y, x)
A translation of 3 units up → + 3 in the y- direction, that is add 3 to the y- coordinate, hence
(x, y) → (- y, x) → (- y, x+ 3) → D
What is the equation of the line with a slope of -2 that passes through the
point (4, -3)?
y + 3 = 4(x - (-2))
y + 4 = -2(x - 3)
y + 3 = -2(x - 4)
y + 4 = 3(x - (-2))
The point-slope form of the line:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = -2 and the point (4, -3). Substitute:
[tex]y-(-3)=-2(x-4)\\\\\boxed{y+3=-2(x-4)}[/tex]
Seclet the locations on the number line to plot the points -5 2/3 and 5 1/3
Step-by-step explanation:
5 1/3 means 5 and 1/3 more.
So first we count 5 unit on right side of 0. Then for 1/3 we will divide the length between 5 and 6 into three equal parts and select only 1 part
That location will be exact location of the point 5 1/3.
Repeat same process for -5 2/3 on left side of 0 because -5 2/3 is a negative number.
Check the attached graph for correct locations.
Answer:
nagetive-number
negative 3
Step-by-step explanation:
A kite is stuck in a 36-ft tree. If the angle of elevation from the kite and the ground is 12, find the length of the kite.
Answer:
173.15 ft.
Step-by-step explanation:
Please find the attachment.
Let L be the length of kite.
We have been given that a kite is stuck in 36-ft tree. The angle of elevation from the kite and the ground is 12.
We can see from our attachment that kite and tree form a right triangle. height of tree is opposite of angle of elevation and length of kite is hypotenuse.
Since we know that Sine relates the opposite and hypotenuse of a right triangle, so we will use sine to find the length of kite.
[tex]sin(12)=\frac{36}{L}[/tex]
[tex]L=\frac{36}{sin(12)}[/tex]
[tex]L=\frac{36}{0.207911690818}[/tex]
[tex]L=173.1504364105882792\approx 173.15[/tex]
Therefore, the length of kite is 173.15 ft.
Please help me answer both questions if they are correct I’ll give brainliest
Answer:
see explanation
Step-by-step explanation:
(4)
Under a counterclockwise rotation about the origin of 90°
a point (x, y) → (- y, x), hence
C(- 3, 4) → C'(- 4, - 3)
(5)
Under a clockwise rotation about the origin of 180°
a point (x , y) → (-x, - y), hence
A(- 3, 2) → A'(3, - 2)
2x-y=3
SHOW WORKKKKKK
Answer:
Well, y = 2x - 3.
Step 1:
Subtract 2x from both sides.
-y = -2x + 3.
Step 2:
Divide it all by negative 1.
y = 2x - 3.
IF YOU WANT TO SOLVE FOR X:
Well, x = .5y + 3/2
Which equals to:
(y + 3)/2.
Step 1:
Add y to both sides.
2x = y + 3.
Step 2:
Divide it all by 2:
x = .5y + 3/2
Which equals to:
(y + 3)/2.
They are the same.
15. You are buying batteries, a stereo, and some CDs from the I.B. Electronics store. You can buy from this store online or in a physical store. You have a coupon for 10% off that can only be used in the physical store and a $5.00 off coupon that can only be used online. The sales tax of 5% only applies to the physical store. Shipping for the online store is a flat rate of $6.99. You are trying to decide whether to shop at the physical store or the online store. Using the pricing information below, how much would you pay at the physical store after all discounts, taxes, and shipping fees have been applied?
The total amount you would pay at the physical store after all discounts, taxes, and fees have been applied is [tex]{128.36} \)[/tex].
Let's go through the calculations again to find the final cost at the physical store after all discounts, taxes, and fees.
Physical Store Pricing:
- Batteries: 2 packs at $5.99/pack
- Stereo: 1 system at $100.00
- CDs: 3 CDs at $7.95 each
Discounts and Taxes in the Physical Store:
1. 10% Off Coupon: This coupon applies to the total purchase amount before tax.
2. Sales Tax: 5% sales tax applies to the total purchase amount after applying discounts.
Calculation Steps:
Step 1: Calculate the total cost of items before discounts and tax:
- Batteries: 2 packs × $5.99/pack = $11.98
- Stereo: $100.00
- CDs: 3 CDs × $7.95/CD = $23.85
Total before discounts: $11.98 + $100.00 + $23.85 = $135.83
Step 2: Apply the 10% off coupon:
- 10% of $135.83 = $13.583
- Total after 10% off: $135.83 - $13.583 = $122.247
Rounded to two decimal places: $122.25
Step 3: Apply the 5% sales tax:
- 5% sales tax on $122.25:
[tex]\[0.05 \times 122.25 = 6.1125\][/tex]
Rounded to two decimal places: $6.11
Step 4: Calculate the final cost at the physical store:
- Total cost after tax: $122.25 + $6.11 = $128.36
The complete question is
You are buying batteries, a stereo, and some CDs from the I.B. Electronics store. You can buy from this store online or in a physical store. You have a coupon for 10% off that can only be used in the physical store and a $5.00 off coupon that can only be used online. The sales tax of 5% only applies to the physical store. Shipping for the online store is a flat rate of $6.99. You are trying to decide whether to shop at the physical store or the online store. Using the pricing information below, how much would you pay at the physical store after all discounts, taxes, and shipping fees have been applied?
Item Quantity Physical Store Online Store
Batteries 2 packs $5.99/pack $4.99/pack
Stereo 1 system $100.00/system $90.00/system
CDs 3 CDs $7.95/CD $8.95/CD
the regular price of a item is $150 the item was on sale at a discount rate of 30% what is the sales price of the item
Amanda is riding her bicycle. She takes 5 hours to ride 62.5 kilometers. What is her speed?
Answer:
12.5 per kilometers
Step-by-step explanation:
to find speed is going to be distance divided by time so 62.5/5
so her speed is going to be 12.5
Amanda's average speed while riding her bicycle is found by dividing the total distance of 62.5 kilometers by the total time of 5 hours, resulting in an average speed of 12.5 kilometers per hour.
To calculate her speed, we use the formula for speed, which is speed = distance ÷ time. Applying the given values, we have speed = 62.5 kilometers ÷ 5 hours.
Therefore, Amanda's average speed is 12.5 kilometers per hour. This calculation involves dividing the total distance traveled by the total time taken, resulting in the average speed over the journey.
Which of the following choices is the correct translation of the statement: “the length of a rectangle if the length is twice the size of the width increased by one”?
The statement 'the length of a rectangle if the length is twice the size of the width increased by one' translates into the equation l = 2w + 1 in mathematical terms. This equation represents a relationship between the rectangle's length (l) and width (w), with the length being twice the width, increased by one.
Explanation:The correct translation of the statement 'the length of a rectangle if the length is twice the size of the width increased by one' is mathematical in nature. This sentence is describing a relationship between the length and width of a rectangle.
To put it into an equation, start by denoting the width of the rectangle as 'w'. The statement says that the length is twice this width (2w) plus one. So, the length 'l' can be represented as:
l = 2w + 1
This equation shows the relationship between the length and width of a rectangle according to given statement. For practical purposes, you can insert a numerical value for width 'w' and perform the calculation on the right side to find the length 'l'.
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The mathematical expression translating the phrase is 'L = 2W + 1', where 'L' represents length of the rectangle and 'W' represents the width. It indicates that the length is twice the width, and further increased by one.
Explanation:The correct translation of the statement 'the length of a rectangle if the length is twice the size of the width increased by one' would result in a mathematical expression for the length of the rectangle (L). If we denote the width of the rectangle as W, then we could represent the length of the rectangle as follows:
L = 2W + 1
This expression indicates that the length is twice the size of the width, and then increased by one. Depending on the value of W, we plug it into the equation to determine the length of the rectangle.
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I have the data in that picture , I need help answering these questions that continue with that
F: how much money will Jason have in the bank after 9 weeks
G: if Jason has $80 left, how many weeks have passed
This is for question 2 in the picture
Answer:
F $185
G 12 weeks
Step-by-step explanation:
Assuming your equation is correct
y = -35x +500
We want to let x=9
y = -35(9) +500
y = -315+500
y =185
Jason will have $185 after 9 weeks
If he has 80 dollars left we put that in for y and solve for x
80 = -35x +500
Subtract 500 from each side
80-500 = -35x +500-500
-420 = -35x
Divide each side by -35
-420/-35 = -35x/-35
12 = x
After 12 weeks he will have 80 dollars left
On order for two triangles to be similar, all corresponding pairs of angles be
Answer: similar
Step-by-step explanation:
Answer:
Answer is similar
Step-by-step explanation:
an ordinary Fair die is a cube with the number 1 through 6 on the sides (represented by painted spots). imagine that such a die is rolled twice in succession and the face values of the two dice rolls are added together. this sum is recorded as the outcome of a single trial of random experiment.
compute the probability of each of the following events. event A: the sum is greater than 7. B: the sum is an even number
Event A Answer: [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
sum greater than 7 leaves are the following combinations for 8, 9, 10, 11, and 12:
8 = 26, 35, 44, 51, 62 (5 possibilities)
9 = 36, 45, 54, 63 (4 possibilities)
10 = 46, 55, 64 (3 possibilities)
11 = 56, 65 (2 possibilities)
12 = 66 (1 possibility)
This is a total of 15 possibilities out of 36 total: [tex]\frac{15}{36}[/tex] = [tex]\frac{5}{12}[/tex]
***********************************************************************************
Event B Answer: [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
sum is an even number means both dice are odd or both dice are even. That results in the following combinations:
11 13 15
22 24 26
31 33 35
42 44 46
51 53 55
62 64 66
This is a total of 18 possibilities out of 36 total: [tex]\frac{18}{36}[/tex] = [tex]\frac{1}{2}[/tex]
X+3y=5
-X+6y=3
solve the system of equation
A.X=1,Y=2
B.X=2,Y=1
C.X=1, Y=1
D.X=0, Y=2
Answer:
That all the answer hope i helped
Answer:
The answer will be B
Step-by-step explanation:
what is the inverse of the function x + 2y + 3 = 0
The inverse of the function x + 2y + 3 = 0 is found by first expressing the function explicitly as y = -½x - 1½ and then swapping x and y to solve for the new y, yielding the inverse function y = -2x - 3.
Explanation:To find the inverse of a function, we typically swap the roles of x and y, and then solve for y. Given the function x + 2y + 3 = 0, we first write the function explicitly as y in terms of x:
y = -½x - ³2
Now let's find the inverse:
Swap x and y to get x = -½y - ³2.Solve for y. Multiply every term by 2 to get rid of the fraction: 2x = -y - 3.Rearrange the equation to solve for y: y = -2x - 3.This new function y = -2x - 3 is the inverse of the original function.
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HW 7.4/7.5 backside
Answer:
9. x=10
10. x=8
11. x=9/4=2.25
12. x=28
13. x=14
14. x=35
15. x=66
16. x=77/6
Step-by-step explanation:
9. x/20=18/36
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 18:
x/20=(18/18) / (36/18)
x/20=1/2
Solving for x: Multiplying both sides of the equation by 20:
20(x/20)=20(1/2)
x=10
10. x/12=6/9
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 3:
x/12=(6/3) / (9/3)
x/12=2/3
Solving for x: Multiplying both sides of the equation by 12:
12(x/12)=12(2/3)
x=4(2)
x=8
11. x/3=3/4
Solving for x: Multiplying both sides of the equation by 3:
3(x/3)=3(3/4)
x=9/4=2.25
12. x/42=30/45
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 15:
x/42=(30/15) / (45/15)
x/42=2/3
Solving for x: Multiplying both sides of the equation by 42:
42(x/42)=42(2/3)
x=14(2)
x=28
13. x/12=14/12
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 2:
x/12=(14/2) / (12/2)
x/12=7/6
Solving for x: Multiplying both sides of the equation by 12:
12(x/12)=12(7/6)
x=2(7)
x=14
14. x/25=28/20
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 4:
x/25=(28/4) / (20/4)
x/25=7/5
Solving for x: Multiplying both sides of the equation by 25:
25(x/25)=25(7/5)
x=5(7)
x=35
15. x/110=(160-100)/100
x/110=60/100
Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 20:
x/110=(60/20) / (100/20)
x/110=3/5
Solving for x: Multiplying both sides of the equation by 110:
110(x/110)=110(3/5)
x=22(3)
x=66
16. x/11=(x+7)/17
Solving for x: Cross Multiplication:
17x=11(x+7)
Eliminating the parentheses on the right side of the equation:
17x=11(x)+11(7)
Multiplying:
17x=11x+77
Grouping the x's on the left side of the equation: Subtracting 11x both sides of the equation:
17x-11x=11x+77-11x
Subtracting:
6x=77
Dividing both sides of the equation by 6:
6x/6=77/6
Dividing:
x=77/6
Explain how to determine if the two expressions are equivalent using x = 6 and x = 10.
8x + 40 8(x + 5)
The expressions 8x + 40 and 8(x + 5) are equivalent because both expressions have the same value at x = 6 and x = 10
How to determine the two equivalent expressions?The expressions are given as:
8x + 40 and 8(x + 5)
When x = 6, we have:
8x + 40 = 8 * 6 + 40
8x + 40 = 88
8(x + 5) = 8(6 + 5)
8(x + 5) = 88
When x = 10, we have:
8x + 40 = 8 * 10 + 40
8x + 40 = 120
8(x + 5) = 8(10 + 5)
8(x + 5) = 120
Notice that both expressions have the same value at x = 6 and x = 10
Hence, the expressions 8x + 40 and 8(x + 5) are equivalent
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Answer:
Sample Response: If both expressions have the same value after substituting and simplifying for x = 6 and x = 10, then they are equivalent. Substitute 6 for each variable, x, in both expressions. Use the order of operations to simplify both expressions. The value of both expressions is 88. Now, substitute 10 for each variable, x, in both expressions. Use the order of operations to simplify both expressions. The value of both expressions is 120. Therefore, the expressions are equivalent.
Step-by-step explanation: trust
What is the greatest common factor of the terms in the expression 21x - 18x + 28xy?
Answer:
The terms are already in lowest form. The factors of 21 are 21 and 1, and 3 and 7. The factors of 18 are 1 and 18, 2 and 9, and 3 and 6. The factors of 28 are 1 and 28, 2 and 14, and 7 and 4. None of them match up so it is as low as it can be.
Step-by-step explanation:
the greatest common factor is x. because
21, -18, and 28 do not have any shared factors