What are the solutions of the quadratic equation below ?
x^2-8x+11
Answer:
x = 4 ± [tex]\sqrt{5}[/tex]
Step-by-step explanation:
to find the solutions equate the quadratic to zero
x² - 8x + 11 = 0 ( subtract 11 from both sides )
x² - 8x = - 11
solve using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 4)x + 16 = - 11 + 16
(x - 4)² = 5 ( take square root of both sides )
x - 4 = ± [tex]\sqrt{5}[/tex] ( add 4 to both sides )
x = 4 ± [tex]\sqrt{5}[/tex]
If a cup of coffee is 275 mL, what is the volume of 4 cups of coffee, in milliliters?
Answer:
1100 milliliters.
Step-by-step explanation:
First, separate the numbers 275, it will be 200, 70, and 5.
Second, multiply 4x200, it equals 800
Third, multiply 4x70, it equals 280
Fourth, multiply 4x5, it equals 20.
Fifth, add them all together one by one like 280+20=300, then add 280+800 which is 1100.
Thank you please help me thank you please help me I am stuck on this problem and its really important.
Answer:
the order is 30,60,90,120
Step-by-step explanation:
its ten times 3 then u just keep adding the same amount every ten.
Estimate. Include commas if the answer is made of more than three digits.
56 x 324.
Answer:
19,200
Step-by-step explanation:
round 56 to 60 and round 324 to 320 then multiply the two numbers
A swim team member performs a dive from a 14-foot high springboard. Her path is represented by the equation LaTeX: h\left(t\right)=-0.875t^2+5.25t+14h ( t ) = − 0.875 t 2 + 5.25 t + 14, where t is time in seconds and h is the height above the surface of the water. She needs to finish her flip no later than 5 feet above the surface of the water in order to prepare for the splash. What time does this happen? Round to the nearest tenth of a second.
Answer:
7.4secs
Step-by-step explanation:
If the path of a swim team member is modeled by the equation
h(t) = -0.875t²+5.25t+14
where t is time in seconds and h is the height above the surface of the water
If she need to finish in no later than 5feet above the surface, the expression will become:
-0.875t²+5.25t+14≤5
-0.875t²+5.25t+14-5≤0
-0.875t²+5.25t+9≤0
Rewriting using fraction
-7/8t²+21/9t+9≤0
To get the time that this happens we will need to factorize the resulting expression above;
On factorising
Find the roots of the equation using the formulas
t = 3+3√105/7
t = 3+ 3(10.25)/7
t = 3 + (30.75)/7
t = 3 + 4.393
t = 7.393
t = 7.4secs
Hence this happens at t = 7.4secs
Answer:
The time when the swim team member is 5 feet above the water surface is 7.4 seconds.
Step-by-step explanation:
You want to know when a member of the swim team finished his jump no later than 5 feet above the surface of the water to prepare for the splash, that is, when t is 5 feet above the surface of the water. Substituting h(t) for this value 5 in the equation you obtain:
5= -0.875*t²+5.25*t+14
A quadratic equation has the general form:
a*x² + b*x +c= 0
where a, b and c are known values and a cannot be 0.
Taking the equation 5= -0.875*t²+5.25*t+14 to that form, you get:
-0.875*t²+5.25*t+14-5=0
-0.875*t²+5.25*t+9=0
The roots of a quadratic equation are the values of the unknown that satisfy the equation. And solving a quadratic equation is finding the roots of the equation. For this you use the formula:
[tex]\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}[/tex]
In this case, solving the equation is calculating the values of t, that is, you find the time when the swim team member is 5 feet above the water surface.
Being a= -0.875, b=5.25 and c= 9, then
[tex]\frac{-5.25+-\sqrt{5.25^{2}-4*(-0.875)*9 } }{2*(-0.875)}[/tex]
[tex]\frac{-5.25+-\sqrt{27.56+31.5 } }{-1.75}[/tex]
[tex]\frac{-5.25+-\sqrt{59.06 } }{-1.75}[/tex]
[tex]\frac{-5.25+-7.685}{-1.75}[/tex]
Then:
[tex]t1=\frac{-5.25+7.685}{-1.75}[/tex] and [tex]t2=\frac{-5.25-7.685}{-1.75}[/tex]
Solving for t1:
[tex]t1=\frac{2.435}{-1.75}[/tex]
t1= -1.39 ≅ -1.4
Solving for t2:
[tex]t2=\frac{-12.935}{-1.75}[/tex]
t2= 7.39 ≅ 7.4
Since time cannot be negative, the time when the swim team member is 5 feet above the water surface is 7.4 seconds.
absolute value negative 4
Answer:
4
Step-by-step explanation:
absolute value, if it's a negative number, will be positive. if it's a positive number, it will stay positive.
Answer:
My guess 4
Step-by-step explanation:
i used to do this stuff but i thinks its 4
to make 1 dinner roll, 1/15 cups of flour is used. How much flour is used to make 48 dinner rolls?
The members of the senior class are planning a dance. They use the equation
to determine the total receipts.
2r +t
2
Write the equation in terms of the following variables.
Answer:
I'm guessing you are saying 2r, t, and 2
If that is the case, then the terms are 2r, t, and 2.
Step-by-step explanation:
Terms are numbers in an equation, like terms is when you combine something that is the same variable.
Use the Triangle Inequality to determine if it is possible to draw a triangle with sides: 16 ft, 17 ft, 20 ft
Answer:
It is possible.
Step-by-step explanation:
Since the shorter two sides (16 and 17 feet) added together are greater than the longest side(20 feet) it meets the triangle inequality theorem
Calculate the area of the shaded sector. PQ = 2.8 in
Answer:A= 21 cm2
= 3.25 in2
= 3 in2
Step-by-step explanation:
2.8 in = 7.112 cm
= 7 cm
A = [tex]\pi[/tex][tex]r^{2}[/tex] * [tex]\frac{49}{360}[/tex]
= 22/7*7*7*49/360
= 20.96
= 21 cm2
16x-24 in equivalent expression
3x - 4y= -2
In standard form
Answer:
[tex]4y = 3x + 2 \\ [/tex]
Step-by-step explanation:
y = mx + c[tex]3x - 4y = - 2 \\ 3x - 4y - 3x = - 2 - 3x \\ - 4y = - 2 - 3x \\ \frac{ - 4y}{ - 1} = \frac{ - 2 - 3x}{ - 1} \\ 4y = 2 + 3x \\ 4y = 3x + 2 \\ [/tex]
Please look at the picture.
Answer:
Blue
Step-by-step explanation:
I graphed it, and got the same thing.
Solve using substitution.
–6x + 7y = –6
6x − 8y = 12
Answer:
Step-by-step explanation:
- 6x + 7y = - 6 ⇒ 6x = 7y + 6 ...... (1)
6x - 8y = 12 ........ (2)
(1) ------> (2)
( 7y + 6 ) - 8y = 12
- y + 6 = 12
y = - 6 ------> (1)
- 6x + 7( - 6 ) = - 6
6x = - 42 + 6
x = - 6
( - 6 , - 6 )
i suck at these so like…
x g(x)
-2 1/36
-1 1/6
0 1
1 6
2 36
~
You are making a canvas frame for a painting using stretcher bars. The rectangular painting will be 10 inches long and 8 inches wide. Using a ruler, how can you be certain that the corners of the frame are 90°
Answer:
make sure it’s acute
Step-by-step explanation:
since when you measure 90° the angle has to be acute
How many outcomes will there be for rolling a six-sided number cube three times?
Answer:
216
Step-by-step explanation:
6 * 6*6 = 216 possible outcomes
The number of outcomes for a rolling of cube three times = 216 outcomes
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
When rolling a six-sided number cube three times, we can calculate the total number of outcomes by considering the number of possible outcomes for each individual roll
Now , For each roll of the number cube, there are six possible outcomes
Since we are rolling the cube three times, we need to multiply the number of outcomes for each roll together:
Number of outcomes = 6 x 6 x 6 = 216
Hence , there will be 216 possible outcomes when rolling a six-sided number cube three times
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what is the value of 30-2(7+2)-1
Answer:
48 :)
Step-by-step explanation:
Answer:
11 I'm pretty sure
Step-by-step explanation:
For each value of w, determine whether it is a solution to w-38<11.
Answer:
No
Yes
No
Yes
Step-by-step explanation:
52-38<11
53-38<11
Both of these are no because they are greater than 11
Answer:
No
Yes
No
Yes
Step-by-step explanation:
put in the values instead of w and check if it is correct
[tex]52-38=14[/tex] which is not less than 11 so no
[tex]44-38=6[/tex] which is less than 11 so yes
[tex]53-38=15[/tex] which is not less than 11 so no
[tex]48-38=10[/tex] which is less than 11 so yes
What is the percentage tax charged if a calculator which cost $4000 is sold for $5000 after tax ?
Answer:
25%
Step-by-step explanation:
find the differences between original price $4000 and the altered price $5000.
$5000 - $4000 = $1000
to find the tax percent charged, take the difference price, divide by the original price and multiply with 100, ( to find percentage, it is a must to multiply with 100 ).
1000/4000 x 100
= 25%
so you will get 25 %
Write an expression the represents the statement "Add 9 and 3, then multiply by 6"
PLEASE ANSWERRRR
15 point
Answer:
6(9+3)
Explanation:
Add 9 and 3 which is 9 + 3
THEN multiply by 6 which is 6(9 + 3)
I put parentheses because it's sayings to add first and then multiply!
The value of B is __
The value of a
Answer:
The value of B is 11 times the value of a.
Step-by-step explanation:
a =| 2 | 4 | 7 | 10 |
b =| 22 | 44 | 77 | 110 |
22 44 77 110
÷2 ÷4 ÷7 ÷10
--------- -------- ------- ---------
11 11 11 11
I hope this helps!
Answer:
see explanation
Step-by-step explanation:
from the table we can see that
the value of b is 11 times the value of a
Which set of angles are complementary in this diagram?
Answer:
ECF and BCF (option 3)
Step-by-step explanation:
Complementary angles are angles that have degrees that add up to 90. From the picture, you can see that angle ECF and BCF put together form a right, or 90 degree angle, so that is your answer.
Hopefully this helps - let me know if you have any questions!
Help me solve this problem, will give brainliest
Answer:
c
Step-by-step explanation:
If a number is a perfect square, then it has only 3 factors.
TRUE OR FALSE
Answer:
False.
Step-by-step explanation:
Think of the number 12 which is 2 * 2 * 3.
Now square 12 to 144.
144 is a perfect square since it is the square of 12.
144 = 2 * 2 * 2 * 2 * 3 * 3
What are the factors of 144?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
That is a lot more than 3 factors.
Jamal plans to attend a 4-year private university. He will receive $8,200 in scholarships and grants each year, and he will earn $1,900 each year through a work study program.
Including his financial aid, what is Jamal’s estimated cost per year? $
Jamal’s family will contribute $21,000 each year. How much will Jamal need to contribute? $
Jamal has one year to save enough for his first year’s contributions. Complete each statement to show how much Jamal will need to save each month based on his current savings.
If Jamal currently has $0 in savings, he will need to save $
each month.
If Jamal currently has $1,000 in savings, he will need to save $
each month.
If Jamal currently has $2,000 in savings, he will need to save $
each month
Based on the scholarships and grants that Jamal will receive, his estimated cost per year is $25,050.
If his family contributes $21,000, he will have to contribute $4,050.
If Jamal has $0 in savings, the amount to save each month is $337.50.
If Jamal has $1,000 in savings, the amount to save each month is $254.17.
If Jamal has $2,000 in savings, the amount to save each month is $170.83.
What is Jamal's estimated cost?= Cost per year of private university - Scholarships - Work study program
= (25,100 + 8,000 + 1,300 + 750) - 8,200 - 1,900
= 35,150 - 8,200 - 1,900
= $25,050
What amount will he contribute if his family contributes?= Estimated cost - family contribution
= 25,050 - 21,000
= $4,050
What amount should Jamal save?The amount that Jamal should save monthly can be found as:
= (Amount to contribute - Amount already saved ) / Number of months in year
If Jamal has $0, he should save:
= (4,050 - 0) / 12
= $337.50
If Jamal has $1,000:
= (4,050 - 1,000) / 12
= $254.17
If Jamal has $2,000:
= (4,050 - 2,000) / 12
= $170.83
Find out more on the cost of college at https://brainly.com/question/9299811.
Determine the whether the quadratic equation below has a maximum or minimum.
y = 4x² – 3x - 43
Answer:
Minimum
Need to know:
Derivative power rule: d/dx xⁿ = nxⁿ⁻¹
Derivative constant rule: d/dx c = 0
Step-by-step explanation:
A way to determine whether the quadratic equation has a maximum or a minimum is by graphing it.
If we look at the image below, we notice that the graph does not go to the bottom infinitely, but it keeps going up infinitely. This means there is a minimum to this graph.
Another way to determine this is through calculus.
First, we have to find the point of extremum
Find the derivative of the given equation
d/dx 4x² - 3x - 43
You can separate the terms and solve them individually
d/dx 4x² = 4(2)(x²⁻¹) = 8x
d/dx -3x = -3(1)(x¹⁻¹) = -3(1)(1) = -3
d/dx -43 = 0
y' = 8x - 3
Set y' to equal 0
8x - 3 = 0
Add 3 to both sides
8x - 3 = 0
+ 3 + 3
8x = 3
Divide both sides by 8
8x/8 = 3/8
x = 3/8
There is only one point of extremum
Now we have to test whether the equation changes from negative to positive or positive to negative
If it changes from negative to positive, that point is a minimum
If it changes from positive to negative, that point is a maximum
To find this, pick a number less than 3/8 and plug it in the place of x in the derivative equation. We'll use 0.
y' = 8(0) - 3 = -3
Now we will do the same for a number larger than 3/8. We'll use 1
y' = 8(1) - 3 = 5
Since the lesser side of 3/8 is negative and the larger side of 3/8 is positive, that means it changes from negative to positive. This point is a minimum.
4x-6y+3=0
please answer and show work ASAP!!!
Step-by-step explanation:
This question is not complete check well
What is the approximate length of arc qr? round to the nearest tenth of a centimeter. 9.9 centimeters 19.9 centimeters 21.5 centimeters 43.0 centimeters
The length of the arc of the QR which is formed in a circle from center P will be equal to 9.9 cm.
What will be the Arc?The arc of the circle is defined as the product of the angle and the radius of the circle.
[tex]Arc=\theta \times r[/tex]
Now it is given in the question that
circle P, i.e. center is point P.
QS is a diameter with a length of 20 cm so radius =10 cm
Given that RP is the radius with
To find the length of arc QR =?
Now for finding the arc of QR we will find the angle [tex]\angle QPR[/tex] since we have the angle [tex]\angle RPS=123^o[/tex].
[tex]\angle QPR+\angle RPS=180[/tex]
[tex]\angle QPR+123=180[/tex]
[tex]\angle QPR=57^o[/tex]
[tex]\angle QPR=\dfrac{57\times\pi}{180} =0.99\ radian[/tex]
Now the formula for finding the arc will be given by
[tex]Arc \ (QR)=\angle QPR\times r[/tex]
[tex]Arc\ (QR)=0.99\times 10=9.9\ cm[/tex]
Thus the length of the arc of the QR which is formed in a circle from center P will be equal to 9.9 cm.
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Samantha and mia each left julia’s house at the same time. mia walked north at 7 kilometers per hour. samantha ran west at 11 kilometers per hour. how far apart were they after one hour? round the answer to the nearest tenth. a right triangle. a point at the angle with measure 90 degrees is labeled julia's house. a line drawn north is labeled 7 kilometers and a line drawn west is labeled 11 kilometers. 7.7 km 8.4 km 13.0 km 18.0 km
Mia walked 7km/h so after 1 hour, she is 7 km north of the house of Julia
Samantha walked 11km/h so after 1 hour, she is 11 km west of the house of Julia.
The points where Mia and Samantha are after 1 hour , and the house of Julia form a right triangle with sides 7 and 11 km. The distance between the girls, is the hypotenuse of his triangle.
by the pythagorean theorem:
Answer: 13 km
Answer:
C
Step-by-step explanation: