Answer:
Answer: approximately -1.63 and -7.37
Step-by-step explanation:
First of all, let's expand the parenthesis by multiplying x into both of its terms.
[tex]x(x+9)+12 = 0\\x^2+9x+12=0[/tex]
We get the equation:
[tex]x^2+9x+12=0[/tex]
The quadratic formula looks like this
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
where the equation is of the form
[tex]ax^{2}+bx+c=0[/tex]
Comparing this to our equation above,
[tex]x^2+9x+12=0[/tex]
we can see that
[tex]a = 1\\b= 9\\c= 12[/tex]
Let's put these values into the quadratic formula.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-9\pm\sqrt{9^2-4*1*12}}{2*1}\\x=\frac{-9\pm\sqrt{9^2-48}}{2}\\x=\frac{-9\pm\sqrt{81-48}}{2}\\x=\frac{-9\pm\sqrt{33}}{2}\\x=\frac{-9\pm\ 5.744...}{2}\\x=\frac{-9\pm\ 5.744...}{2}\\x_{1}=\frac{-9+5.744...}{2}=\frac{-3.255...}{2}=-1.62771867\\x_{2}=\frac{-9-5.744...}{2}=\frac{-14.744...}{2}=-7.3722813\\[/tex]
Answer: approximately -1.63 and -7.37
You can also choose not to approximate the square root of 33, and you'd receive the answers:
[tex]x_{1}=\frac{-9+\sqrt{33}}{2}\\x_{2}=\frac{-9-\sqrt{33}}{2}[/tex]
find the length of the hypotenuse !!
Answer:
17
Step-by-step explanation:
To find the hypotenuse, you would use the Pythagorean theorem.
[tex]A^{2} +B^{2} =C^{2}[/tex]
We can plug 8 and 15 into A and B\
[tex]8^{2} +15^{2} =C^{2}[/tex]
We can simplify this to
64+225=[tex]C^{2}[/tex]
289 = [tex]C^{2}[/tex]
To get C by itself not squared, we can do the square root of both sides.
[tex]\sqrt{289} =\sqrt{C^{2} }[/tex]
If we simplify, we get
17 = C or C = 17
Therefore the length of the hypotenuse is 17.
Which expression is equivalent to-10w - 15.5? A. -5(2w-15.5) B. -5(2w+3.1) C. -5(5w-15.5) D. -5(5w+10.5).
Answer:
D
Step-by-step explanation:
The required expression that is equivalent to the given expression is -5(w+3.1) . Option D is correct.
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,
The given expression,
= -10w - 15.5
taking 5 commons from both the terms,
= -5(2w + 3.1)
Thus, the required expression that is equivalent to the given expression is -5(w+3.1) . Option D is correct.
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Whitch of the following shows the correct order of the numbers
Answer:
The answer is B
Step-by-step explanation:
What is the first step in solving the equation Two-thirds x + one-third x + 2 = 5? Subtract One-third from each side of the equation. Add 2 to each side of the equation. Combine like terms. Multiply each side of the equation by 5. PLEASE HURRY I WILL MARK BRAINLIEST!
Hey There!! ⚘~
The answer to this is: add 1/2x to both sides.
multiply both sides by 6/7
Hope It Helped!~
〰️~ItsNobody~〰️
Answer:
Combine Like Terms
Step-by-step explanation:
Select the expression that is equal to (9x + 3) – (5z - 7)
Answer:
9x+10-5z
Step-by-step explanation:
(9x + 3) – (5z - 7)
9x+3-5z + 7)
9x+10-5z
The function h is defined as h (x) = 5x² – 3.
Find h(x+1).
Answer:
h(x + 1) = 5x² + 10x + 2
Step-by-step explanation:
Step 1: Write out function
h(x) = 5x² - 3
Step 2: Plug in x + 1 for x
h(x + 1) = 5(x + 1)² - 3
Step 3: Expand
h(x + 1) = 5(x² + 2x + 1) - 3
Step 4: Distribute
h(x + 1) = 5x² + 10x + 5 - 3
Step 5: Combine like terms
h(x + 1) = 5x² + 10x + 2
Which of the following shows as a mixed number and as an improper fraction?
There's no following. You need to post a picture or complete the question.
A book sold 33,700 copies in its first month of release. Suppose this represents 9.3% of the number of copies sold to date. How many copies have been sold to date? Round your answer to the nearest whole number.
Answer: 362,365 copies
Step-by-step explanation: Using proportions, I set it up like 33700/? (total copies)= 9.3/100. I multiplied 33700 and 100 to get 3370000 and divided by 9.3 and rounded.
what's the steps used to solve modeling problems in the correct order
Answer:
see below
Step-by-step explanation:
The first step is to read the problem
Then you need to make a plan
Implement the plan
Then evaluate the answer to see if it makes sense
2. Which of these values is the GREATEST?
63/7
450%
8.99
-22
Geometry and Trigonometry
Answer:
a. 227 cm
b. 495 cm
Step-by-step explanation:
a. Radius of arc = sin(½θ) = 2.10/r
θ = (360-225)/2 = 67.5
Radius of arc = sin(67.5) = 2.10/r
r = 2.10/sin(67.5) = 2.273 m = 227 cm (nearest cm)
b. Length of arc = θ/360*2πr
Take π as 3.14
r = 210 cm
θ = 360 - 225 = 135°
Length of arc = [tex] \frac{135}{360}*2*3.14*210 = 495 cm [/tex] (to nearest cm)
25x + 11(2+2) when X = 6 a.234 b.83 c.194 d.150
Answer:
194
Step-by-step explanation:
(-6+1 1/2+5)^2...I'm getting 1 but when I put it in the calculator I get .25...What am I do wrong?
Answer:
Step-by-step explanation:
your doing the calculation wrong
Rena decides to go to a technical college for 18 months to get a degree in computer networking. There are 6 school quarters in the program with a tuition of $600 each. Books for the entire program cost $2,800. How much will it cost Rena to get his degree?
Answer:
Total Cost 6400
Step-by-step explanation:
Each quarter is 600 dollars
There are 6 quarters. 6 * 600 = 3600
Books 2800
Total 6400
Answer:
6400
Step-by-step explanation:
600*6=3600
3600+2800=6400
Daisy walked two-fifths of a mile in one-fifth of an hour. Walking at the same pace, how far will Daisy walk in 1 hour?
Answer:
2 miles
Step-by-step explanation:
2/5 mile = 1/5 hour
x mile(s) = 1 hour
Cross multiplying.
x · 1/5 = 2/5 · 1
x/5 = 2/5
Multiplying both sides by 5.
x = 10/5
x = 2
Daisy will walk 2 miles in 1 hour.
Answer:
[tex]\Huge \boxed{\mathrm{2 \ miles}}[/tex]
Step-by-step explanation:
2/5 mile = 1/5 hour
x mile(s) = 1 hour
Cross multiplying.
x · 1/5 = 2/5 · 1
x/5 = 2/5
Multiplying both sides by 5.
x = 10/5
x = 2
Daisy will walk 2 miles in 1 hour.
Which list shows all the factors of 18?
1, 2, 3, 4, 6, 9, 18
1, 2, 3, 6, 9, 18
2, 3, 4, 6,9
2, 3, 6, 9
[tex]:\implies\sf\:18=1\times 18[/tex]
[tex]:\implies\sf\:18=2\times 9[/tex]
[tex]:\implies\sf\:18=3\times 6[/tex]
Hence, All the factors of 18 are
[tex]\boxed{\bf{\orange{(1,2,3,6,9,18)}}}[/tex]
Answer:
1, 2, 3, 6, 9, 18 is the answer
Step-by-step explanation:
Steve spent $40 at the grocery store. He bought bottled water, soda, and sandwiches. A bottle of water costs $1.50, a bottle of soda costs $2, and a sandwich costs $3. If he bought 10 bottles of water and 5 bottles of soda, how many sandwiches did he buy?
Answer:
5 sandwiches.
Step-by-step explanation:
$15 for the water, $10 for the soda. So if you add 15 and 10 that's 20. 40-25 = 15 on sandwiches. If each sandwich is $3, then that's 5 sandwiches.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The number of sandwiches bought is 3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Cost of a bottle = $1.50
Cost of a soda = $2
Cost of a sandwich = $3
Number of bottles bought = 10
Number of sodas bought = 5
Number of sandwiches bought = S
Total amount spend = $40
Now,
10 x 1.50 + 5 x 2 + 3S = 40
Simplify.
15 + 10 + 3S = 40
25 + 3S = 40
Subtract 25 on both sides.
3S = 40 - 25
3S = 15
Divide both sides by 3.
S = 15/3
S = 3
Thus,
The number of sandwiches bought is 3.
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Mrs. Robertson is taking a picture of three students-Zach, John, and
Reginald. How many different ways can these three students stand in a line
to have their pictures taken?
Evaluate the expression when x=5 and y= -5
5x-4y=
Answer:
45
Step-by-step explanation:
5x-4y=
Let x=5 and y = -5
5*5 - 4 * (-5)
25 + 20
45
If f is a differentiable function such that f′(x)≥6, find the largest value of ???? so that f(4)≥???? whenever f(2)=10. (Use decimal notation. Give your answer as exact number.)
Answer:
12
Step-by-step explanation:
If the slope of the function were exactly 6 on the interval between 2 and 4, then the increase on that interval from f(2) = 10 would be (4-2)·6 = 12. Since the slope is at least 6, the increase is at least 12, so ???? = 10+12 = 22.
5! The office needs cabinets. The price for the first type of cabinet is $10, it
needs 6 ft2 of floor space, and it has a storage volume of 8 ft. The price
for the second type of cabinet is $20, it needs 8 ft? of floor space, and it
has a storage volume of 12 ft. The company wants to spend no more
than $140 and the office can hold up to 72 ft2 of cabinets. How can the
storage volume be maximized?
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of 6 ft² to be purchased and y represent the number of 8ft² cabinet to e purchased.
x > 0 and y > 0
6 ft² cabinet cost $10 and 8 ft² cabinet cost $20, only $140 is available to spend, therefore the cost equation is:
10 x + 20 y ≤ 140
Also the office can hold only 72 ft², the space equation is:
6x + 8y ≤ 72
The volume equation is:
V = 8x + 12y
From the graph attached, we have to find the point with maximum volume by testing the point (12, 0), (0,7) , (8,3)
For (12, 0): V = 8(12) + 12(0) = 96 ft³
For (0, 7): V = 8(0) + 12(7) = 84 ft³
For (8, 3): V = 8(8) + 12(3) = 100 ft³
The (8,3) point has the maximum volume. That is 8 6 ft² cabinet and 3 8ft² cabinet
A 20 pound mixture of salt water is 5% salt. How many pounds of water must be added to make it 3% salt?
Answer:
5 pounds
Step-by-step explanation:
(.15(20))/(20+w)=.12
3/(20+w)=.12
20+w=25
w=5
So 5 pounds of water must be added to the solution.
Order the numbers in each list from least to greatest.
0,|-14|, 13, -12, |-16|,17
Answer:
-12, 0, 13, [-14], [-16], 17
Step-by-step explanation:
Which of the numbers below is greater than zero? Select all that apply.
A)0.8
B)4.5
C)1/4
D)-2.25
E)-0.5
Answer:
The answers are letters A,B,and C
I need help again, please.
I hope this helps you...
What is the solution to the equation
below?
-5/4 x+ 2/5= -13/30
Answer:
x = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given
- [tex]\frac{5}{4}[/tex] x + [tex]\frac{2}{5}[/tex] = - [tex]\frac{13}{30}[/tex]
Multiply through by 60 ( the lcm of 4, 5 and 30) to clear the fractions
- 75x + 24 = - 26 ( subtract 24 from both sides )
- 75x = - 50 ( divide both sides by - 75 )
x = [tex]\frac{-50}{-75}[/tex] = [tex]\frac{2}{3}[/tex]
Answer:
is it a times before the +?
Step-by-step explanation:
Male children. While it is often assumed that the probabilities of having a boy or a girl are the same, the actual probability of having a boy is slightly higher at 0.51. Suppose a couple plans to have 3 kids. A) Use the binomial model to calculate the probability that two of them will be boys. B) Write out all possible orderings of 3 children, 2 of whom are boys. Use these scenarios to calculate the same probability from part (a) but using the addition rule for disjoint outcomes. Confirm that your answers from parts (a) and (b) match. C) If we wanted to calculate the probability that a couple who plans to have 8 kids will have 3 boys, briefly describe why the approach from part (b) would be more tedious than the approach from part (a). 1) (32)0.512 ∗ 0.49 = 0.3822) BBG,BGB,GBB,GGB,GBG,BGG,GGG,BBBP(2boy) = BBG + GBB + BGBBBG + BGB + GBB + GGB + GBG + BGG + GGG + BBB = 3/8 = 0.375So since boy and girl has slight different probablity, two answer will be different but they are close3) Because using approach, you will have to list all 56 combinations
Answer:
Step-by-step explanation:
Since the actual probability of having a boy child is 0.51, the probability of having a girl child will be (1 - 0.51) = 0.49
A couple plans to have 3 kids; 2 of whom are boys
(A) Using the binomial model, the probability that 2 of the 3 children will be boys is (2/3) × 0.51 = 0.34
(B) The possible orderings of the 3 children are given below:
B1 B2 G / B1 G B2
B2 B1 G / B2 G B1
G B1 B2 / G B2 B1
Where B1 is one male child and B2 is the other male child
(C) If we wanted to calculate the probability that a couple who plans to have 8 kids will have 3 boys, briefly describe why the approach from part (b) would be more tedious than the approach from part (a)
If the probability of 2/3 is 0.34 then the probability of 3/8 will be 0.1912 when you cross multiply
Solve the inequality for x. –2x + 3 < –13
Answer:
x > 8
Step-by-step explanation:
When you divide or multiply both sides of an inequality by a negative number, the equality is switched.
-2x + 3 < -13
(-2x + 3) - 3 < -13 - 3
-2x < -16
-2x/-2 < -16/-2
x > 8
Answer:
x > 8
Step-by-step explanation:
In order to solve the inequality for x, we must get x by itself on one side of the equation.
-2x + 3 < -13
3 is being added to -2x. The inverse of addition is subtraction. Subtract 3 from both sides of the equation.
-2x + (3-3) < (-13-3)
-2x < -13 -3
-2x < -16
x is being multiplied by -2. The inverse of multiplication is division. Divide both sides of the equation by -2.
-2x/-2 < -16/-2
When dividing or multiplying by a negative number, remember to flip the inequality sign.
-2x/-2 > -16/-2
x > -16/-2
x > 8
The solution to the inequality is x>8
Let A = {Dirk, Johan, Frans, Sarie}, B = {Frans, Sarie, Tina, Klaas, Henrika}, C = {Hans, Frans}. Find the number indicated. n(A) + n(B)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \bold{9}}}}}[/tex]
Step-by-step explanation:
Given,
A = { Dirk , Johan , Frans , Sarie }
B = { Frans , Sarie , Tina , Klass , Henrika }
To find : n ( A ) + n ( A )
Now, count the number of member of a set A
n ( A ) = 4
Also, Count the number of members of a set B
n ( B ) = 5
Finding n( A ) + n ( B )
= 4 + 5
= 9
Hope I helped!
Best regards! :D
5x−6=3x+10 PLSPLS HELP
Answer:
x = 8
Step-by-step explanation:
Let's solve your equation step-by-step.
5x−6=3x+10
Step 1: Subtract 3x from both sides.
5x−6−3x=3x+10−3x
2x−6=10
Step 2: Add 6 to both sides.
2x−6+6=10+6
2x=16
Step 3: Divide both sides by 2.
2x /2 = 16/ 2
x=8
Answer:
So x=8 is the answer.
Step-by-step explanation:
5x-6=3x+10
Adding 6 on both sides to find out the value of x
5x-6+6=3x+10+6
5x=3x+16
Subtracting 3x on both sides to find out the value of x
5x-3x=3x-3x+16
2x=16
Dividing 2on both sides
2x/2=16/2
x=8
I hope this will help you :)