Step-by-step explanation:
the solutions for a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = -4
c = k
x = (4 ± sqrt(16 - 4k))/2 = 2 ± sqrt(4 - k)
x1 = 2 + sqrt(4 - k)
x2 = 2 - sqrt (4 - k)
x1 = 2 + x2
2 + sqrt(4 - k) = 2 + 2 - sqrt(4 - k)
2×sqrt(4 - k) = 2
sqrt(4 - k) = 1
4 - k = 1
k = 4 - 1 = 3
x1 = 3
x2 = 1
Answer:
The roots are 1 and 3.
k = 3.
Step- by-step explanation:
We use the facts that if α and β are the roots of ax^2 + bx + c = o then α+ β = -b/a and α β = c/a.
The roots are written as α and α+2, then:
α + α + 2 = -(-4)
2α + 2 = 4
α + 1 = 2
α = 1
also
α (α + 2) = k
Substituting for α:
1(1 + 2) = k
k = 3.
The roots are 1 and 1 + 2 = 3.
Write the inequality represented by the graph below.
Answer:
y > -x + 3
Step-by-step explanation:
find the slope and y-intercept so you can create a linear equation:
y = mx + b ; m = slope and b = y-intercept
slope (m) = (3-0) / (0-3)
m = 3/-3 or -1
we can see the y-intercept by looking at the graph, it is 3
y > -x + 3
simplify an expression for the perimeter of the rectangle
The expression for the Perimeter of rectangle is 16w-4.
What is perimeter of rectangle?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Perimeter of the rectangle = 2(length+width)
Given the paramters are;
length = 5w-2
width = 3w
Perimeter of the rectangle = 2(length+width)
Perimeter = 3w+3w+(5w-2)+(5w-2)
= 6w+10w-4
= 16w-4
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yesterday 5% of the 120 sixth graders at school were late. How many sixth graders were late?
Answer:
6
Step-by-step explanation:
5% of 120 were late
= [tex]\frac{5}{100}[/tex] × 120
= 0.05 × 120
= 6
Carson rides his bike for 30 mins each day he rides a total of 12 miles every 3 days how many days will it take to ride a total of 80 miles
Answer:
20 days
Step-by-step explanation:
If he rides 12 miles every 3 days, then he rides 4 miles in one day. Divide 80 / 4 and you get 20 days.
Gerry purchases 12 hamburgers at a fast food restaurant for $2.25 each. For half the amount of money, he could purchase 5 buffalo chicken sandwiches. How much does 12 burgers cost?
Write an equation in slope-intercept form for the line with slope 5 and y-intercept -2.
Solve 4,200 ÷ 70 = ________. Rewrite as a fraction to help you.
Please help question in pic
Answer:
7,3
Step-by-step explanation:
for every 5 it goes right it goes 4 up. 2,1+5,4=7,3
Evaluate the expression. 5 x (-6 / -1 + -10)
Answer:
-20
Step-by-step explanation:
[tex]5 * (-6 / -1+ -10)[/tex]
According to PEMDAS, we need to do the math in the parentheses first.
[tex]-6 / -1 + -10[/tex]
Applying PEMDAS to the inside of the parentheses, then we have to divide -6 by -1, where we would get 6.
[tex]6 + -10[/tex]
Adding a negative is the same as subtracting, so adding negative 10 is the same as subtracting 10.
[tex]6 - 10[/tex]
Subtracting, we get 6 - 10 = -4 and we're left with:
[tex]5 * (-4)[/tex]
Multiplying, our final answer is -20.
Hope this helps!
Kim's scores in the diving competition were 7.2, 6.975, 8.0, and 6.96. What is her total score?
Tria had one each of five different-shaped number solids having 4, 6, 8, 12, and 20 sides. She rolled two at a time and found probabilities for the sum of the numbers that came up. She recorded the probabilities in the first column of the table. When it came time to fill in the second column, she had forgotten which number solids she had used. Figure out which number solids she must have used and explain your thinking. The first one has been done.
She found out that the probability of 4 is lesser than 5, which combinations did she use?
Answer:The probability of a 3 is 2/80 or 1/40
The probability of a 4 is less than the probability of a 5
Step-by-step explanation:
"flower, heart, circle." what is The 35th shape is
Answer:
heart
Step-by-step explanation:
Answer:
heart
Step-by-step explanation:
The 36th shape will be the last shape in the 12th repeat of the sequence.
The 35th shape is next-to-last: heart.
If Delta FGH sim Delta KJH find FH .
Answer:
39
Step-by-step explanation:
Two triangles are similar so we can use the similarity ratio to calculate the value of x this way we can find the length of FH
(x+8)/32 = (4x-25)/52 cross multiply expressions
52x + 416 = 128x - 800 export like terms to the same side of equation
416 + 800 = 128x - 52x
1216 = 76x divide both sides by 76
16 = x then the length of FH
4*16 - 25 = 39
On September 1, you own 12.5 shares of stock that are worth $149.87. On
December 1, the shares are worth $94.87. What was the change in the price per
share of stock?
The required change in the price of the share of stock is $4.4.
Given that,
On September 1, you own 12.5 shares of stock that are worth $149.87. On December 1, the shares are worth $94.87, and the change in the price per share of stock is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Initial total cost shares of stock = $149.87
A total number of shares = 12.5
The initial cost of single share = 149.87/ 12.5 = $11.98
Now final cost of the total share = $94.87
The final cost of the single share is = 94.87 / 12.5 = $7.58
Change in price of shares of stock = 11.98 - 7.58 = $4.4
Thus, the required change in the price of the share of stock is $4.4.
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PLZ HELP!!!!!!!!
Function 1 is defined by the equation y=-1/4r-5 Function 2 is defined by line p.shown on the following graph. Which function has a more negative slope?
A. Function 1
B. Function 2
C. The functions have the same slope.
Answer:
Function 1
Step-by-step explanation:
I got it correct on khan academy
The function defined on the graph by the equation y = (-1/4)r -5 and line p has slope which is represented by option C. The functions have same slope.
Let the two coordinate on the line p of the function 2 on the graph.
( x₁ , y₁ ) = (-4, -6)
(x₂ , y₂ ) = ( 4 ,-8 )
Slope of the line = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substitute the value in the formula we get,
Slope of line p = ( -8 + 6 ) / ( 4 + 4 )
= -2/8
= -1/4
Slope of the function 1
y = -(1/4)r -5
When r = 8 ⇒ y = -7
r = -8 ⇒ y = -3
( x₁ , y₁ ) = (8, -7)
(x₂ , y₂ ) = ( -8 ,-3 )
Slope of the function 1 = ( -3 + 7 ) / ( -8 - 8 )
= 4/ -16
= -1/4
Therefore, slope of the both the function 1 and function 2 represented by line p are given by option C. the functions have same slope.
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Help please and thank you.
Answer:
b
Step-by-step explanation:
Which correlation coefficient best matches the graph?
Answer:
Which graph?
Step-by-step explanation:
Answer:
where is the graph
Step-by-step explanation:
umm i dont know how to answer
A laptop is 30% off the regular price of 920$ If a 6% sales tax is added to the cost what is total cost of the laptop
Answer
If we had a sale price of 30% off of $1,050then the sale price is 70% of $1,050 or 0.7(1050) Then we add 7% sales tax to that making thefinal price paid 107% of [0.7(1050)] ... 1.07[0.7(1050)] = $786.45
The ratio of cats to dogs seen at CyFair Animal Hospital is 2 to 5. If Dr. Blue, Dr. Ross, and Dr. Lavigne see 40 dogs altogether, how many cats AND dogs did they see in all? Explain your answer.
Please
The number of cats and dogs the doctor saw is 56.
Ratio expresses the relationship between two values. It shows the frequency that one value is contained another value. The sign of ratio is :.
The equation that can be used to determine the total number of dogs that the doctor saw is:
(ratio of dog / total number of dogs and cats) x total number of animals = number of dogs
5/7 x a = 40
Where a is the total number of dogs and cats
In order to determine the value of a, divide both sides of the equation by 7/5.
40 x 7/5 = 56
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nolan is taking a multiple choice test his grade is given by the equation y=70-2x where y represents his final score and x represents the number of questions he got wrong . waht could the number 70 represents in the equation?
Answer:
70 could represent the total number of points nolan can earn on the test
Step-by-step explanation:
Simplify. Pls help really need help
Answer:
the answer is 5a
Step-by-step explanation:
what is 1/5 of 15? ( algebra)
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Please help me π_π π_π
Lea worked for 3 hours 20 minutes and rested for 30 minutes. The she continued worked for 2 hours till 3.40 pm. What time did she start working?
Answer:
9.50 am
Step-by-step explanation:
3.40pm minus 2 hours = 1.40pm
1.40 minus 30 min = 1.10pm
1.10am minus 3 hours = 10.10am
10.10 am minus 20 min = 9.50 am
start at 9.50 .... works for3hrs and 20 min which ends at 1.10... 30min break which ends at 1.40...works for 2hrs that finally ends at 3.40pm
hope this helps☆☆☆
Translate. Eight less than the difference of a number and five is twelve.
Answer:
(x - 5) - 8 = 12
Step-by-step explanation:
Lets portion each part out:
Eight less than
The difference of a number and five
Is twelve.
First, we must write down the portion with "a number" in it: x - 5. We use subtraction because the sentence states "the difference".
Next, we will write down "eight less than". The problem states that twelve is "eight less than" the difference. This means that we must subtract 8 from out first part: (x - 5) - 8
Finally, the sentence tells us that this equals twelve: (x - 5) - 8 = 12
Lucy works as a tutor for $7 an hour and as a waitress for $12 an hour. This month, she worked a combined total of 86 hours at her two jobs.
Lett be the number of hours Lucy worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.
==========================================================
Explanation:
t = number of hours she worked as a tutor86-t = number of hours she worked as a waitressThe two expressions mentioned add to 86, to indicate the total number of hours for both jobs combined.
7t = amount earned as a tutor12(86-t) = amount earned as a waitressWe multiply the number of hours by the wage per hour to get the amount earned per job.
Lastly, we add those two subtotals to get the grand total earned
7t + 12(86-t)
Optionally you can distribute the 12 through and combine like terms. I'll leave it like this because I think it's more descriptive to show the two amounts earned from each job.
If you wanted to simplify 7t+12(86-t), then you would get 1032-5t or -5t+1032
if you have 55 bad kids in classroom and 25 good kids how many bad have solve the equation
Answer:
none of them bc they're all bad kids
Step-by-step explanation:
An item is regularly priced at $35. It is now priced at a discount of 55% off the regular price. What is the new price?
Enzel goes online to buy a graphing calculator. He finds a site that currently has a promotion of 15% off on all orders over $50. Enzel decides to buy his graphing calculator, with a price tag of $83, at this site because he knows that he will get the 15% discount when he checks out. Enzel pays 4. 5% sales tax on the discounted price and pays a shipping fee of $6. 35. What is the total of Enzel’s online purchase? a. $80. 07 b. $80. 36 c. $86. 74 d. $93. 09 Please select the best answer from the choices provided A B C D.
Based on the cost of the calculator, the discount, the shipping fee, and the tax, the total cost of the purchase was a. $80.07
The cost of the calculator was:
= Cost of calculator x ( 1 - discount)
= 83 x ( 1 - 15%)
= $70.55
The sales tax would be:
= 70.55 x 4.5%
= $3.17
The total cost would be:
= Cost + Sales tax + Shipping fee
= 70.55 + 3.17 + 6.35
= $80.07
In conclusion, the total is $80.07.
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what is the x value of the solution to the system of equations below
x+y+z=8
x+2y=6
y+z=4
Answer:
Let's solve for x.
x+y+z=8
Step 1: Add -y to both sides.
x+y+z+−y=8+−y
x+z=−y+8
Step 2: Add -z to both sides.
x+z+−z=−y+8+−z
x=−y−z+8
Answer:
x=−y−z+8
Please help on both. I’m not sure of my answrs before I submit. Thank u :)