What are the roots of the equation?
x^2+24=−11x
Enter your answers in the boxes.
Answers
x=-3 and x=-8.
Explanation:
We can first write this in standard form, ax²+bx+c=0. To do this, we will add 11x to both sides:
x²+24+11x=-11x+11x
x²+11x+24=0.
Now we can factor this. Look for factors of c, 24, that sum to b, 11. Factors of 24 are:
1 and 24 (sum 25)
2 and 12 (sum 14)
3 and 8 (sum 11)
4 and 6 (sum 10).
The factors we need are 3 and 8, since they sum to 11. This gives us factored form:
(x+3)(x+8)=0.
Using the zero product property, we know that in order to have a product of 0, one or both of the factors must be 0. This means we have:
x+3=0 or x+8=0.
Solving the first equation:
x+3-3=0-3
x=-3.
Solving the second equation:
x+8-8=0-8
x=-8.
Answer:
[tex]x_1 = -8[/tex]
[tex]x_2 = -3[/tex]
Step-by-step explanation:
Given the equation:
[tex]x^2+24 = -11x[/tex]
Add 11x to both sides we have;
[tex]x^2+11x+24 = 0[/tex]
Split the middle terms we have;
⇒[tex]x^2+8x+3x+24 = 0[/tex]
⇒[tex]x(x+8)+3(x+8)= 0[/tex]
⇒[tex](x+8)(x+3)= 0[/tex]
By zero product property we have;
x+8 = 0 and x+3= 0
⇒x = -8 and x = -3
Therefore, the roots of the given equations are:
[tex]x_1 = -8[/tex]
[tex]x_2 = -3[/tex]
Related Questions
The manager of a store selling tea plans to mix a more expensive tea that cost $7 per pound with a less expensive tea that cost $4 per pound to create a hundred forty pound blend that will sell for $6.10 per pound. How many pounds of each type of tea are required?
Answers
x = expensive tea
y = less expensive tea
We write the system of equations:
7x + 4y = 6.10 * (140) = 854
x + y = 140
The system of equations is:
7x + 4y = 854
x + y = 140
Resolving we have:
x = 98
y = 42
Note: see attached image for the solution.
Answer:
They are required:
expensive tea = 98 pounds
less expensive tea = 42 pounds
HELP ASAP PLS Solve and check c-4/c-2=c-2/c+2-1/2-c the solution is c = ? How many extraneous solutions are there?
Answers
Answer : the solution of c is 14.
Explanation :
Since we have given that
[tex]\frac{c-4}{c-2}=\frac{c-2}{c+2}-\frac{1}{2-c}\\\\\frac{c-4}{c-2}=\frac{c-2}{c+2}+\frac{1}{c-2}\\\\\frac{c-4}{c-2}=\frac{(c-2)^2+c+2}{(c+2)(c-2)}\\\\\frac{c-4}{c-2}=\frac{c^2+4-4c+c+2}{(c+2)(c-2)}\\\\(c-4)(c+2)=c^2+6-3c\\\\c^2-8-2c=c^2+6-3c\\\\-2c+3c=6+8\\\\c=14[/tex]
So, c = 14
So, the solution of c is 14.
There is no extraneous solution as if we put the value of c i.e. 14 in the equation it does not make the equation not defined . so by putting the value of c we get a defined value,
Hence , there is no extraneous solution.
Answer: The solution is C = 14
And there is zero extraneous solutions
Step-by-step explanation: Because I said so :-)
Consider the diagram shown where a ladder is leaning against the side of a building. The base of the ladder is 12 ft from the building. How far is the top of the ladder from the ground?(to the nearest ft)
Answers
tan A = CBAC
tan 70° = CB12
2.7475(12) = 32.97 ftThe correct answer is 33 ft.
Find the volume of the figure. A) 33 in3 B) 150 in3 C) 233 in3 D) 425 in3
Answers
The Volume of Figure is 233 inch³.
What is Volume?Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill. Volume is a three-dimensional quantity used to calculate the capacity of a container.
Given:
Top Cuboid:
length = 12 inch
width = 3 inch
Height = 3 inch
Bottom Cube:
Edge = 5 inch
So, the Volume of Figure
= Volume of Top Cuboid + Volume of Cube
= 12 x 3 x 3 + 5 x 5 x 5
= 72 + 125
= 233 inch³
Learn more about Volume here:
https://brainly.com/question/13338592
#SPJ3
the product of twice a number and two is the same as the difference of three times the number and 8/3. find the number
Answers
[tex]let \: the \: required \: no. \: be \: \: x \\ \\ acc. \: to \: the \: question \: \: , \\ \\ 2 \times 2x \: \: = |3x - \frac{8}{3} | \\ 4x = |3x - \frac{8}{3} | \\ \\ case \: 1 - \: \\ 4x = 3x - \frac{8}{3} \\ \\ 4x - 3x = - \frac{8}{3} \\ \\ x = - \frac{8}{3} \: \: \: \: ans.\\ \\ \\ case \: 2 \: - \\ 4x = - (3x - \frac{8}{3} ) \\ 4x = - 3x + \frac{8}{3} \\ 7x = \frac{8}{3} \\ \\ x = \frac{8}{21} \: \: \: \: ans.[/tex]
The perimeter of a rectangle is 44 ft. the length is 6 ft longer than the width. find the dimensions. write a system of linear equations and solve the resulting system. let x be the length and y be the width.
Answers
y= width
P= perimeter
P= 2x + 2y
44= 2(y+6) + 2y
44= 2y + 12 + 2y
44= 4y + 12
subtract 12 from both sides
32= 4y
divide both sides by 4
8 ft= y
Substitute y=8 to find x
44= 2x + 2y
44= 2x + 2(8)
44= 2x + 16
subtract 16 from both sides
28= 2x
divide both sides by 2
14 ft= x
ANSWER: Length is 14 feet and width is 8 feet.
Hope this helps! :)
EXPERTS/ACE/GENIUSES HELP PLZ!!:)
Answers
so 4 x 3 = 12
Q would be at (12,0)
Answer is B
Find the values of x,y, and z. The diagram is not to scale.
A. x = 86, y = 94, z = 75
B. x = 86, y = 75, z = 94
C. x = 75, y = 94, z = 86
D. x = 75, y = 86, z = 94
Answers
180 = 59 + 35 + x
180 = 94 + x
86 = x
Supplementary angles x and z add to 180
180 = x + z
180 = 86 + z
94 = z
Now the last triangle is with angles 11, z, and y
they must add to 180 so...
180 = 11 + z + y
180 = 11 + 94 + y
180 = 105 + y
75 = y
The answer is B.)
Hope this helps!
Answer:
b) x=86,y=75,z=94
Step-by-step explanation:
130.8996939 rounded to the nearest hundredth
Answers
hope i helped :)
In a certain class of students, there are 10 boys from wilmette, 5 girls from kenilworth, 10 girls from wilmette, 7 boys from glencoe, 5 boys from kenilworth and 6 girls from glencoe. if the teacher calls upon a student to answer a question, what is the probability that the student will be from kenilworth?
Answers
what's the square root of 89
Answers
But if you need it rounded then its 9.43
Write an expression that is equivalent to 3x3x3x3x3x3x3 ?!?!?!
Answers
The expression 3x3x3x3x3x3x3 is equivalent to 3⁷.
Given that an expression 3x3x3x3x3x3x3, we need to write an equivalent expression to it,
The expression that is equivalent to 3x3x3x3x3x3x3 can be simplified using the exponentiation operation.
In mathematics, when you have a number or variable multiplied by itself multiple times, you can represent it using exponentiation.
In this case, we have the number 3 multiplied by itself 7 times. Using exponentiation, we can rewrite this expression as 3⁷.
The exponent 7 indicates that the base number, which is 3, should be multiplied by itself 7 times. So, 3⁷ means 3 multiplied by itself 7 times.
When we calculate 3⁷, we get the result 2187.
Therefore, the expression 3x3x3x3x3x3x3 is equivalent to 3⁷.
Learn more about equivalent expression click;
https://brainly.com/question/27911936
#SPJ6
Yvonne put $4000 in a savings account. At the end of three years, the account had earned $960 in simple interest. A. How much does she have in her own account at the end of three years? B. What annual simple interest rate did the account grow? Show your work. C. How many more dollars would she have in her account if the interest rate were 1% greater? Show your work.
Answers
[tex]A=P(1+rt)[/tex]
where
[tex]A[/tex] is the final amount after [tex]t[/tex] years
[tex]P[/tex] is the initial amount
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is the time in years
A. We now form our problem that her initial savings were $4000. Since she earned $960 in interest after 3 years, her final amount will be his initial savings plus the interest hat she earned:
[tex]A=4000+960[/tex]
[tex]A=4960[/tex]
We can conclude that she will have $4960 in her account at the end of three years.
B. We know for our problem that [tex]P=4000[/tex], and [tex]t=3[/tex]. We also know that the account earned $960 in interest, so [tex]A=4000+960=4960[/tex]. Let [tex]x[/tex] represent the interest rate; since the interest rate should be in decimal form, [tex]r= \frac{x}{100} =0.01x[/tex]. Lets replace all the values in our formula to find [tex]x[/tex]:
[tex]4960=4000[1+(0.01x)(3)][/tex]
[tex]4960=4000(1+0.03x)[/tex]
[tex]4960=4000+120x[/tex]
[tex]120x=960[/tex]
[tex]x= \frac{960}{120} [/tex]
[tex]x=8[/tex]
We can conclude that the account growth by an annual simple interest rate of 8%
C. if the interest rate were 1% greater, our new [tex]r[/tex] is going to be [tex]r=8+9[/tex]. But remember that the interest rate should by in decimal form, so we are going to divide 9% by 100%:
[tex]r= \frac{9}{100} [/tex]
[tex]r=0.09[/tex]
We also know that the conditions are the same as before, so [tex]P=4000[/tex] and [tex]t=3[/tex]. Lets replace all our values in our formula to find [tex]A[/tex]:
[tex]A=4000[1+(0.09)(3)][/tex]
[tex]A=4000(1+0.27)[/tex]
[tex]A=4000(1.27)[/tex]
[tex]A=5080[/tex]
We can conclude that she will have [tex]5080-4960=120[/tex] $ more in her account if the interest rate were 1% greater.
What is 21/16 simplified
Answers
1) 21 ÷ 6 = 1 and remainder = 5 =>
2) 1 [tex]1 \frac{5}{16} [/tex] (as a mixed fraction)
3) 1.3125
when you divide a whole number by a fraction with a numerator of 1, explain how you can find the quotient
Answers
just multiply The number you started with be the denominator of the fraction.
4 * 255 = 1020
The reason why is that though I didn't say so you are actually multiply both top and bottom by 255
4 * 255
==
1 * 255
--
255
The bottom 255s cancel. and you are left with 4 * 255 on the top.
Short cut you want. Short cut you get.
Thanks for posting.
What are the direction indices for a vector that passes from point 34 1 12 to point 14 12 1 in a cubic unit cell? please indicate negative directions by a "-" sign before the integer and omit spaces between numbers?
Answers
P = (34, 1, 12)
Q = (14, 12, 1)
From P to Q, we have:
PQ = Q-P
PQ = (14, 12, 1) - (34, 1, 12)
PQ = (14-34, 12-1, 1-12)
PQ = (-20, 11, -11)
Rewriting:
PQ = -20i + 11j -11k
Answer:
The direction indices for the vector are:
PQ = -20i + 11j -11k
The direction indices for a vector passing from point (34, 1, 12) to point (14, 12, 1) are calculated by subtracting the coordinates of the starting point from the ending point, resulting in the indices [-20 11 -11].
Explanation:The student asked for the direction indices of a vector passing from point (34, 1, 12) to point (14, 12, 1) in a cubic unit cell. To determine the direction indices, we need to subtract the coordinates of the initial point from the coordinates of the final point. The resulting vector ∆r will have components ∆x, ∆y, and ∆z as follows:
∆x = 14 - 34 = -20∆y = 12 - 1 = 11∆z = 1 - 12 = -11Therefore, the direction indices for the vector are written without spaces and with negative signs for negative directions. In this case, the direction indices would be [-20 11 -11].
Learn more about direction indices here:https://brainly.com/question/1420586
#SPJ3
A picture contains 2/3 quart of lemonade If an equal amount of lemonade is poured into each of six classes how much lemonade will each class contain
Answers
however, 2/3 divided in 6 equal pieces is just
[tex]\bf \cfrac{2}{3}\div 6\implies \cfrac{2}{3}\div \cfrac{6}{1}\implies \cfrac{2}{3}\cdot \cfrac{1}{6}\implies \cfrac{1}{3}\cdot \cfrac{1}{3}\implies \cfrac{1}{9}[/tex]
The area of a rectangle is 56 cm.the length is 2 cm more than x and the width is 5 cm less than twice x.solve for x
Answers
Answer:
x = 6 cm
Step-by-step explanation:
The area is the product of length (x +2) and width (2x -5). It is 56 cm², so for all dimensions in cm, we can write ...
(x +2)(2x -5) = 56
2x² -x -66 = 0 . . . . . subtract 56 to put into standard form
(x -6)(2x +11) = 0 . . . . factor
Solutions to the equation are values of x that make the factors zero:
x = 6, x = -11/2
The negative solution is extraneous, so the solution of interest is ...
x = 6 cm
Lin has 13 coins in her pocket that equal 40 cents. All the coins are dimes, d, and pennies, p. Which combination of coins does Lin have? Use the table to answer the question.
Answers
I used a guess and check strategy starting with 2 dimes.
The combination of coins are:
3 dimes and 10 pennies.
Step-by-step explanation:Let there are d number of dines and p number of pennies.
Now as there are a total of 13 coins this means that:
d+p=13------(1)
and also the total value of the coins is 40 cents.
1 dime=10 cents
Hence, d dime= 10 d cents
Also, 1 penny= 1 cent
Hence p penny= p cents
Hence, we get:
10d+p=40------(2)
On subtracting equation (1) from (2) we get:
9 d=27
on dividing both side by 9 we get:
d=3
On putting the value of d in equation (1) we get:
3+p=13
i.e. p=13-3
i.e. p=10
The combination is:
3 dimes and 10 pennies
SUSAN NEEDS EXACTLY 4 PLATES ON EACH TABLE FOR THE BANQUET,AND 5 PLATES AT THE MAIN TABLE.IF SHE HAS 417 PLATES,HOW MANY TABLES IS SHE ABLE TO PREPARE?INCLUDE THE MAIN TABLE IN COUNT
Answers
4+5=9 plates
the sets of 9 plates in the total of 417 plates are:
417/9=139/3
thus the total number of tables will be:
139/3*2
=92.6667~93 tables
What is the difference between sin and cosine
Answers
What is the decimal value of the 2 in the hexadecimal number f42ac16?
Answers
we know that
to convert hex to decimal
Multiply every digit with 16 power of digit location
the digit location of number 2 is--------> 5
then
2*16^5=2097152
the answer is 2097152
The decimal value of the 2 in the hexadecimal number f42ac16 is 2.
Explanation:The hexadecimal number f42ac16 can be split into individual digits, where each digit represents a power of 16. Starting from the rightmost digit, the 2 represents the digit in the 16^0 (1) place, which is simply 2. Therefore, the decimal value of the 2 in the hexadecimal number f42ac16 is 2.
Learn more about Hexadecimal Numbers here:https://brainly.com/question/36345940
#SPJ11
Brent conducted a survey in his school regarding whether students ride their bikes to school each day. he surveyed a random sample of 150 students and 40 said they rode their bikes to school each day. there are 450 students who attended school. based on the results of Brents survey, about how many students in the school ride their bikes to school each day
Answers
Fabian harvests 10 pounds of tomatoes from his garden he needs 2 2/5 pound to make a batch of soup. If he sets aside 2.8 pounds of tomatoes to make spaghetti sauce, how many batches of soup can He make
Answers
Starting with 10 pounds of tomatoes and taking out the number of pounds he sets aside for spaghetti sauce, 2.8, we have:
10-2.8 = 7.2 pounds left.
0.2 is read as "two tenths," so 7.2 = 7 2/10
We divide this remaining number of pounds by 2 2/5 for each batch of soup:
7 2/10 ÷ 2 2/5
Convert each to an improper fraction:
72/10 ÷ 12/5
Multiply by the reciprocal:
72/10 × 5/12 = 360/120 = 3
With 7.2 pounds of tomatoes, Fabian can make 3 batches of soup since each batch requires 2.4 pounds of tomatoes.
Explanation:First, let's understand the total quantity of tomatoes Fabian has to make soup. He harvested a total of 10 pounds and set aside 2.8 pounds for spaghetti sauce. So, he has 7.2 pounds of tomatoes left to make soup. Every batch of soup needs 2 2/5 pounds of tomatoes which is equivalent to 2.4 pounds. To find out how many batches of soup he can make, divide the total weight of tomatoes he has for the soup by the weight each batch needs. Therefore, 7.2 divided by 2.4 gives 3 batches of soup.
Learn more about Quantity division here:https://brainly.com/question/32833997
#SPJ3
What must be true of the discriminant the soulution to a quadratic equation is a set of 2 different real numbers?
Answers
2 The quadratic has 2 different solutions.
3 The x value of the minimum or maximum is 1/2 way between these 2 solutions.
4 The y value of the minimum or maximum is found by substituting the x value into the original quadratic. (You can't really tell this from the discriminate, but it is an inferred property).
which equation are true for x=-2 and x=2 check all that apply
Answers
[tex] {x}^{2} - 4 = 0 \\ {x}^{2} = + 4 \\ x = \sqrt{4} = 2[/tex]
2 it's not true
[tex] {x}^{2} = - 4 [/tex]
3 it's not true
[tex]3 {x}^{2} + 12 = 0 \\ 3 {x}^{2} = - 12 \\ {x}^{2} = \frac{ - 12}{3} = - 4 \\ [/tex]
4 it's true
[tex]4 {x}^{2} = 16 \\ {x}^{2} = \frac{16}{4} = 4 \\ x = \sqrt{4} = 2[/tex]
5- it's true
[tex] {2(x - 2)}^{2} = 0 \\ {(x - 2)}^{2} = 0 \\ x - 2 = 0 \\ x = 2[/tex]
Answer:
A. [tex]x^2-4=0[/tex]
D. [tex]4x^2=16[/tex]
Step-by-step explanation:
To check which of the given equations have solution [tex]x=-2\text{ and }x=2[/tex], we will solve our given equations one by one.
A. [tex]x^2-4=0[/tex]
[tex]x^2-4+4=0+4[/tex]
[tex]x^2=4[/tex]
[tex]\sqrt{x^2}=\pm\sqrt{4}[/tex]
[tex]x=\pm 2[/tex]
[tex]x=-2\text{ or }x=2[/tex]
Therefore, option A is the correct choice.
B. [tex]x^2=-4[/tex]
To solve our given equation, we need to take square root of both sides of equation. Since square root is not defined for negative numbers, therefore, option B is not a correct choice.
C. [tex]3x^2+12=0[/tex]
[tex]3x^2=-12[/tex]
[tex]x^2=-4[/tex]
To solve our given equation, we need to take square root of both sides of equation. Since square root is not defined for negative numbers, therefore, option C is not a correct choice.
D. [tex]4x^2=16[/tex]
[tex]x^2=4[/tex]
[tex]\sqrt{x^2}=\pm\sqrt{4}[/tex]
[tex]x=\pm 2[/tex]
[tex]x=-2\text{ or }x=2[/tex]
Therefore, option D is the correct choice.
E. [tex]2(x-2)^2=0[/tex]
[tex](x-2)^2=0[/tex]
[tex]\sqrt{(x-2)^2}=\sqrt{0}[/tex]
[tex]x-2=0[/tex]
[tex]x=2[/tex]
Therefore, option E is not a correct choice.
One side of a rectangle is five times as long as the other side. If the perimeter is 72 meters, what is the length of the shorter side?
Answers
x----------> length of the long side of rectangle
y---------> length of the short side of rectangle
P----------> perimeter of rectangle
we know that
x=5y-------------> equation 1
P=2x+2y---------> 72=2x+2y---------> equation 2
then
I substitute 1 in 2
72=2*(5y)+2y----------> 72=10y+2y----------> y=72/12---------> y=6
the answer is
the length of the short side of rectangle is 6 m
Evaluate 10x^2y^-1 for x=3 and y=2
Answers
10*9*2^-1
10*9*1/2
9/2
45
Answer:
[tex]10x^{2} y^{-1}[/tex] for x=3 and y=2 is 45.
Step-by-step explanation:
In order to evalue the given expression [tex]10x^{2}y^{-1}[/tex] you have to rewrite it as a fraction, using the property for a negative exponent which says that [tex]y^{-1}[/tex] can be written as [tex]\frac{1}{y}[/tex]
You obtain: [tex]\frac{10x^{2} }{y}[/tex]
Now, you have to replace the given values of x and y in the previous expression:
x=3 and y=2
[tex]\frac{10(3)^{2} }{2}[/tex]
Solving the square:
[tex]\frac{(10)(9)}{2}[/tex]
Solving the multiplication and division:
[tex]\frac{90}{2} = 45[/tex]
The answer is 45
What is the speed of a plane that travels at a rate of 410 mph with a wind of r mph?
Answers
.. 410 mph +r*cos(θ)
where θ is the angle between the plane's heading and the direction the wind is moving toward.
That is, if the plane is moving "with the wind," its speed is (410 +r) mph.
If the plane is moving "against the wind", its speed is (410 -r) mph.
In a recent semester at a local university, 490 students enrolled in both General Chemistry and Calculus I. Of these students, 61 received an A in general chemistry, 63 received an A in calculus, and 25 received an A in both general chemi: and calculus Find the probability that a randomly chosen student received an A in general chemi stry or calculus or both