Answer:
q=35
Step-by-step explanation:
x2 - 12x + q = 0
Let the two roots be r and r+2.
Factor the quadratic expression:
(x - r)[x - (r + 2)] = 0
Expand, simplify, group like terms, and get
x2 - 2(r + 1)x + r(r + 2) = 0
Compare to
x2 - 12x + q = 0
and set equal the coefficients of like terms:
Coefficient of x:
-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5
(Then the other root is r + 2 = 5 + 2 = 7)
Constant term:
r(r + 2) = q ⇒ 5(5 + 2) = q
q = 35
Test the solution:
(x - 5)(x - 7) = x2 - 12x + 35
With two roots differing by 2, you get an equation of the form
x2 - 12x + q = 0
with q = 35.
In the diagram, DG I EF
What additional information would prove that DEFG is an
isosceles trapezoid?
y
5
D-22) G 1.2)
O DE GF
O DE DG
O EF DG
O EF = GF
E(-4,-3)
F(3-3)
5
Answer:
a) DE ≅ GF
Step-by-step explanation:
In the picture attached, the diagram is shown.
An isosceles trapezoid is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. In this case, the left and right side lengths are DE and GF, respectively; then they are congruent.
Multiply 1 and 3/4 × 4/5.One and three-fourths written as an improper fraction is .
The product written as an improper fraction in lowest terms is .
The answer written as a mixed number is .
Answer:
Multiplication:
1 x (3/4 x4/5)
= 3/5
Answer:
7/5 (improper fraction), or 1 2/5 (mixed number)
Step-by-step explanation:
One and three-fourths written as an improper fraction is 7/4.
Now we multiply 4/5 by 7/4. The '4' in each fraction cancels out the '4' in the other fraction, so that we are left with (1/5)(7/1), or 7/5 (improper fraction), or 1 2/5 (mixed number)
he price of a pair of headphones is $39.99 before tax. Dalton bought the headphones for 30% off. He then paid 6% sales tax on the discounted price. Part A: How much did Dalton pay in sales tax? Show all work and steps in your solution. (5 points) Part B: What is the total amount that Dalton paid for the headphones? Show all work and steps in your solution
Answer: I think it’s $1.80
Step-by-step explanation:
Sorry if I’m wrong
Answer:
Firstly, divide the tax rate by 100: 6/100 = 0.06 (tax rate as a decimal). Note: to easily divide by 100, just move the decimal point two spaces to the left.
Now, find the tax value by multiplying tax rate by the before tax price:
tax = 39.99 × 0.06
tax = 2.4 (tax value rouded to 2 decimals)
Add tax to the before tax price to get the final price:
The final price including tax = 39.99 + 2.4 = 42.39
Step-by-step explanation:
using the general equation, f(x)=[x/1.50] how many songs can be purchased with a $35 gift card?
Answer:
23
Step-by-step explanation:
[tex] \because \: f(x) = \bigg [ \frac{x}{1.50} \bigg] \\ \\ \therefore \: f(35) = \bigg [ \frac{35}{1.50} \bigg] \\ \\ \therefore \: f(35) =23.33 \\ \\ \therefore \: f(35) \approx 23 \\ [/tex]
Hence, 23 songs can be purchased with a $35 gift card.
What is the slope of the line?
Answer: 3/4
Step-by-step explanation:
Following the rise over run rule it goes 4 on the x axis and then 3 on the y axis
geometry! please help
Answer: 5.2
Step-by-step explanation:
This is known as the heart beat method. Search it up for a better explinations.
Basically you putting 3/x = x/9 and simplifying to get sqrt27.
Search this up and watch the video for a better explination
heartbeat method geometry
awarding branliest for first correct answer!! HELP
Answer:
(3x - (3x - 5y))(3x + (3x - 5y))
Step-by-step explanation:
We use difference of squares to help factor.
Coach kunal stacks all of the tennis balls in a square pyramid. The number of tennis balls, P(n), in n layers of the square pyramid is given by P(n) = P(n - 1) + n^2. Which could not be the number of tennis balls Coach Kunal has? A. 30 B. 5 C. 14 D. 9
Answer:
D. 9
Step-by-step explanation:
We are told in the question that: The number of tennis balls represented by P(n), in n layers of the square pyramid is given as
P(n) = P(n - 1) + n²
Let's take the first layer
n = 1
P(1) = P(1 - 1) + 1²
P(1) = 1 tennis ball.
It is important to note that the first layers we have one tennis ball.
Let's take the second layer
n = 2
P(2) = P(2 - 1) + 2²
P(2) = P(1) + 2²
Note that: P(1) above = 1
P(2) = 1 + 2²
P(2) = 5 tennis balls
It is important to note that the second layer we have five tennis balls
Let's take the third layer
n = 3
P(3) = P(3 - 1) + 3²
P(3) = P(3 - 1) + 3²
P(3) = P(2) + 3²
Note that: P(2) above = 5
P(3) = 5 + 3²
P(3) = 14 tennis balls
It is important to note that the second layer we have fourteen tennis balls
Let's take the fourth layer
n = 4
P(4) = P(4 - 1) + 4²
P(3) = P(4 - 1) + 4²
P(3) = P(3) + 4²
Note that: P(3) above = 14
P(3) = 14 + 4²
P(3) = 30 tennis balls
It is important to note that the fourth layer we have thirty tennis balls
Hence, the number of tennis balls from the first four layers will be: 1, 5, 14, 30,
So, the number of tennis balls that Coach Kunal could not have is 9.
im gon be posting a lot so helppp
Answer:
It's Rational. Hopes this helps you!
Step-by-step explanation:
Put this into slope form x/2 + 2y= 6
Answer:
y=-1/4x +3
Step-by-step explanation:
x/2 + 2y = 6
Subtract x/2 from both sides
2y=-x/2 +6
Simplify by dividing by 2
y=-1/4x +3
plzzzzzzzzzzzzzz answer this!!
Answer:
≈ 9.4 cm
Step-by-step explanation:
P(-4, -2), Q(4,3)
d= √(x2-x1)²+(y2-y1)²=√ (4+4)²+(3+2)²= √64+25 = √89 ≈ 9.4 cm
Answer:
9.4
Step-by-step explanation:
Hello! To solve this problem, you need to know the distance between two points formula. That is [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 } \\[/tex]. Now, just plug in the numbers from the equation. [tex]x_{2}[/tex] is -4, [tex]x_{1}[/tex] is 4, [tex]y_{2}[/tex] is -2, and [tex]y_{1}[/tex] is 3. So, then you have [tex]\sqrt{(-4-4)^2+(-2-3)^2}[/tex], which is equal to [tex]\sqrt{89[/tex]. [tex]\sqrt{89[/tex] rounded to one decimal place is 9.4. I believe that is the right answer, please let me know if it helped.
PLEASE HELP simplify the expression: 2/3÷(-4)-[ 1/6-8/6] A. 1 B. 29/24. C. -24/17. D. 23/24
Answer:
A. 1
Step-by-step explanation:
2/3 ÷ (-4) - (1/6-8/6)
Solve for brackets.
2/3 ÷ (-4) - (-7/6)
2/3 ÷ (-4) + 7/6
-2/12 + 7/6
Make denominators equal.
-2/12 + 14/12
12/12
= 1
Which expression is equal to 6/√5? 6√5/25 30/√5 36/√30 6√5/5
Answer:
6√5/25 = 6√5/(√5)^4 = 6/(√5)^3 (invalid)
30/√5 = 6*(√5)^2/(√5) = 6√5 (invalid)
36/√30 = 6*(√6)^2/(√5*√6) = 6√6/√5 (invalid)
6√5/5 = 6√5/(√5)^2 = 6/√5 (valid)
Answer:
[tex]$\frac{6\sqrt{5} }{5} $[/tex]
Step-by-step explanation:
Which expression is equal to [tex]$\frac{6}{\sqrt{5} } $[/tex]?
Rationalizing denominator:
[tex]$\frac{6}{\sqrt{5} }\cdot \frac{\sqrt{5} }{\sqrt{5} }=\frac{6\sqrt{5} }{5} $[/tex]
1. Write your answer using only
positive exponents.
(3ab^3c^-1)^3
Answer:
[tex](\frac{{3ab^{3}}}{c^{1}} )^{3}[/tex]
Step-by-step explanation:
[tex](3ab^{3} c^{-1} )^{3} =(\frac{{3ab^{3}}}{c^{1}} )^{3}[/tex]
WILL MARK BRAINIEST IF CORRECT.
Which of the following statements are true about the solution set? There is more than one correct answer choice. Select all that apply. 1) −7 is not a solution. 2) Any value greater than −7 is a solution. 3) Any value less than −7 is a solution. 4) There are a limited number of solutions. 5) There are infinite solutions. 6) There are no solutions less than −7.
Answer:
1, 2, 5 and 6 are the answers.
Step-by-step explanation:
2 is correct because the arrow shows that the number line continues till infinity. 5 is correct because any fraction is possible as no restriction of integer value is placed. Any number less than 7 is not included. There are some confusions with 1 as it's not a solid color, So, I assume -7 is not included.
Which expression is equivalent to
b^m/b^n
Answer:
b^ (m-n)
Step-by-step explanation:
When the bases are the same, when dividing, we subtract the exponents
b^m/b^n
b^ (m-n)
The balance on Taylor's credit card is $2000. It has an interest rate of 12.5%. She wants to compare the difference between paying $75 and $100 of the monthly balance. How much does she save in interest and fees if she pays $100 instead of $75? Round to the nearest dollar. Enter your answer as a total in dollars, such as $134.
Answer: kindly check Explanation
Step-by-step explanation:
The balance on card = $2000
Interest rate = 12.5%
Therefore, monthly rate = 12.5% / 12 = 0.0104167
Paying $75 of monthly balance :
Interest amount on 2000 = 0.0104167 × 2000 = $20.83
Therefore,
Principal amount payed = 75 - 20.83 = 54.17
Balance = ($2000 + $20.83) - $75 = 1945.83
Interest on balance = 0.0104167 × 1945.83 = $20.2691
Paying $100 of monthly balance :
Interest amount on 2000 = 0.0104167 × 2000 = $20.83
Therefore,
Repayment = 100 - 20. 83 = $79.17
Balance = ($2000 + $20.83) - $100 = 1920.83
Interest on balance = 0.0104167 × 1920.83 = $20.0087
Interest saved by paying $100 instead of $75
$20.27 - $20.00 = $0.27 = 27 cent
Answer:
$101
Step-by-step explanation:
Check link answer.
Plzz help, I will mark brainliest m Answer needed fast.
Answer:
A=bh=21·13=273
Step-by-step explanation:
using this formula A=bh
place base in b, and the height or hypotenuse in A
Answer: A~267.96
Step-by-step explanation: Draw a height down from the top of the arrow to the base. USE the formula for the Area of a parallelogram A=bh (base x heght) find height using trig 13sin79 . Then multiply 21 x 12.76
awarding branliest for first correct answer
Answer:
(x - 3)(x + 3)(x² + 9)
Step-by-step explanation:
Step 1: Difference of Squares
(x² - 9)(x² + 9)
Step 2: Difference of Squares within Difference of Squares
(x - 3)(x + 3)(x² + 9)
*You can't factor x² + 9 because it has no real roots. You can factor it to have complex roots (imaginary number i).
Answer:
(x+3)(x+3)(x²-9)
How many 4-digit numbers divisible by 5, all of the digits of which are even, are there? WILL MARK BRAINLIEST NEEED ASAP
Answer:
4*5*5*2=200 numbers
Step-by-step explanation:
this is because 2,4,6,8 can be the first digit.
2,4,6,8,0 can be the second same for the third.
2 digits can be divisible by 5 which are 5, 0. If it has a 0 at the end it is divisible by 10 which means it is divisible by 5.
Answer:
100 numbers
Step-by-step explanation:
Since there are four digits, the answer will be the product of four numbers. The first digit has to be either 2,4,6, or 8 because it is a four digit number with all even digits. Same for the next two numbers, but zero is also a possibility. The question asks for a number divisible by 5, so the last digit must be a 0 in order to qualify as an even number. So the answer would be 4*5*5*1 (number of possible digits) which is 100.
What is 4•4•4•4•4 in exponential form? And need the answer ASAP
Answer:
It is [tex]4^{5}[/tex]
Step-by-step explanation:
the four is multiplied 5 times
Answer:
it will be 4^5
Step-by-step explanation:
add the # of 4s and u will get ur exponent
ASAP!!!!!!! The graph represents the money collected at the movie theater on Saturday. Find the domain when the maximum number of people allowed in the movie theater is 30 people. graph of y equals 2 times x plus 40 with x axis labeled Number of People and y axis labeled Amount of Money 0 ≤ y ≤ 30 40 ≤ x ≤ 100 0 ≤ x ≤ 30 40 ≤ y ≤ 100
Answer:
40 ≤ y ≤ 100
Step-by-step explanation:
Answer: Domain must include the x value. With a maximum of 30 people allowed in the theater, the domain is between 0 and 30, or 0<x>30
Step-by-step explanation:
IfA=(-2,-4) and B=(-8,4), what is the length of AB?
Answer:
10 unitssolution,
A(-2,-4)--->(X1,y1)
B(-8,4)----->(x2,y2)
now,
[tex]ab = \sqrt{(x2 - x1) ^{2} + {(y2 - y1)}^{2} } \\ \: \: \: \: = \sqrt{ (- 8 - ( - 2)) ^{2} + (4 - ( - 4)) ^{2} } \\ \: \: \: = \sqrt{( - 8 + 2) ^{2} + {(4 + 4)}^{2} } \\ \: \: \: = \sqrt{( - 6) ^{2} + {(8)}^{2} } \\ \: \: = \sqrt{36 + 64} \\ \: \: \: = \sqrt{100} \\ \: \: \: = \sqrt{ {(10)}^{2} } \\ \: \: \: \: = 10 \: units[/tex]
Hope this helps..
Good luck on your assignment
-Rounded to the nearest ten, the number is 61 460.
-The number is divisible by 4.
-The digit sum is even.
What is the number
Answer:
61464
Step-by-step explanation:
61464 ~ 61460 to the nearest ten
61464 ÷ 4 = 15366
61464 is an even number
The number is 61464
What is Number system?A number system is defined as a system of writing to express numbers.
When a number is rounded to the nearest ten, the number is 61 460.
61464 ~ 61460 to the nearest ten
When the number is divisible by 4
61464 ÷ 4 = 15366
The digit sum is even
61464 is an even number
Hence, the number is 61464
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ5
Question 19 (4 points)
Saved
2(x + 1) + 2(x - 2) = 3(x-3) + 4
Answer:
x=-3solution,
[tex]2(x + 1) + 2(x - 2) = 3(x - 3) + 4 \\ or \: 2x + 2 + 2x - 4 = 3x - 9 + 4 \\ or \: 2x + 2x + 2 - 4 = 3x - 5 \\ or \: 4x - 2 = 3x - 5 \\ or \: 4x - 3x = - 5 + 2 \\ x = - 3[/tex]
Hope this helps...
good luck on your assignment.
Answer:
x = - 3
Step-by-step explanation:
2(x + 1) + 2(x - 2) = 3(x-3) + 4
2x + 2 + 2x - 4 = 3x - 9 + 4
2x + 2x - 3x = - 9 + 4 - 2 + 4
4x - 3x = - 3
x = - 3
HELP FIRST GET BRAINLLEST Which of the statements below are true? Select all that apply. A) Tom's friends are taller than Sam's friends B) Sam's tallest friend is 72 inches tall C) Sam's friends are taller than Tom's friends. D) Tom's tallest friend is over 70 inches tall
Answer:
Step-by-step explanation:
c
solve the equation [tex]\frac{x}{3} -\frac{3-2x}{6}=\frac{5}{2} x[/tex]
Answer:
x = - [tex]\frac{3}{11}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x}{3}[/tex] - [tex]\frac{3-2x}{6}[/tex] = [tex]\frac{5}{2}[/tex] x
Multiply through by 6 to clear the fractions
2x - (3 - 2x) = 15x ← distribute and simplify left side
2x - 3 + 2x = 15x
4x - 3 = 15x ( subtract 4x from both sides )
- 3 = 11x ( divide both sides by 11 )
- [tex]\frac{3}{11}[/tex] = x
Answer: x=-3/11
Step-by-step explanation:
What is true about the diagonals of
the shapes below? Select all that
apply.
Click the bottom right arrow to go
to the next set. Click the
checkmark (available on the last
set) to submit all your answers.
Parallelograms and Rhombi:
far
Diagonals bisect each other
Diagonals are perpendicular
Diagonals are not congruent
Diagonals bisect the angles
Diagonals are congruent
Answer: B
Step-by-step explanation: it could not be A bc A is 3.4 and 34.8 and its not correct
In 1980, the median age of the U.S. population was 30.0; in 2000, the median age was 35.3.
Create an explicit linear equation to model the change in median age over time. Use t for time (measured in decades since 1980) and a for median age (measured in years).
Answer:
y = 0.265x - 494.7
Step-by-step explanation:
Let median age be represent by 'a' and time be represent by 't'
In 1980, median age is given 30
which means that
a₁ = 30
t₁ = 1980
In 2000, the median age is given 35.3
which means that.
a₂ = 35.3
t₂ = 2000
The slope 'm' of the linear equation can be found by:
m = (a₂ - a₁) /(t₂ - t₁)
m = (35.3 - 30)/(2000-1980)
m = 0.265
General form of linear equation is given by:
y = mx + c
y = 0.265x +c
Substitute point (1980,30) in the equation.
30 = 0.265(1980) + c
c = -494.7
Hence the the linear equation can be written as:
y = mx + c
y = 0.265x - 494.7
(80 pts) Find the probability of selecting two 10's when two cards are drawn (without replacement) from a standard deck of cards.
Answer:
3/663 or 1/221 chance
Step-by-step explanation:
A standard deck of cards contains 52 cards total, 4 suits total. Therefore there are 4 "10"s.
There is a 4/52 (simplified: 1/13) chance to draw a 10 on the first try.
To do it twice there is a 3/51 x 1/13 chance.