Solve the square of this equation with explanation as I don’t understand please
Answers
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Explanation:
Cut the x coefficient (10) in half to get 10/2 = 5. Then square this to get 5^2 = 25.
We'll add 1 to both sides so that the "24" turns into "25", thereby completing the square
x^2 + 10x + 24 = 0
x^2 + 10x + 24+1 = 0+1
x^2 + 10x + 25 = 1
Notice on the left hand side we have something of the form A^2+2AB+B^2 where A = x and B = 5. We can factor this into (A+B)^2, which is the whole reason why we completed the square. You can use the FOIL rule to see how (A+B)^2 expands out into A^2+2AB+B^2. Factoring reverses this process.
This means x^2+10x+25 factors to (x+5)^2 and we now have these steps
(x+5)^2 = 1
x+5 = sqrt(1) or x+5 = -sqrt(1)
x+5 = 1 or x+5 = -1
x = 1-5 or x = -1-5
x = -4 or x = -6 are the two solutions
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Let's check x = -4 to see if it works or not
x^2 + 10x + 24 = 0
(-4)^2 + 10(-4) + 24 = 0
16 - 40 + 24 = 0
-24 + 24 = 0
0 = 0
We get a true equation. That confirms x = -4 is a solution.
If we tried x = -6, then,
x^2 + 10x + 24 = 0
(-6)^2 + 10(-6) + 24 = 0
36 - 60 + 24 = 0
-24 + 24 = 0
0 = 0
That x value is confirmed as well.
Related Questions
Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).
Answers
Answer:
Ax + By = C is standard form.
y + 1 = (2/3)(x - 8)
distribute the (2/3)
y + 1 = (2/3)x - (16/3)
Multiply each term by 3 to clear the fractions.
3y + 3 = 2x - 16
Subtract 2x from both sides.
-2x + 3y + 3 = - 16
Subtract 3 from both sides.
-2x + 3y = - 19
Correct form typically has the leading coefficient as a positive number so multiply each term by - 1.
2x - 3y = 19
Step-by-step explanation:
Answer:
The answer is 2x + -3y = 19
Step-by-step explanation:
got it right on edge
I’m horrible at math and I need to study for the TSI. Help? 4/5+1/10+5/6
Answers
Answer:
4 ÷ 5 + 1 ÷ 10 + 5 ÷ 6 = 1.733
Step-by-step explanation:
One thing you can do is make the denominator equal.
4/5(2/2) + 1/10 = 8/10+1/10 = 9/10
9/10 +5/6
Or you could cross multiply, by multiplying the denominator with the opposite numerator (this is the numerator) then multiply the denominator ( this is the denominator)
(6(9)+5(10))/6(10) = 104/60 then simplify to 26/15
Find AC, given that line AD is the perpendicular bisector of BC
Answers
Answer:
wouldn’t it just be 21? because both are the same but mirrored
Three events A, B and C are defined over a sample space, S. Events A and B are independent. Events A and C are mutually exclusive. Given that P(A)= 0.04, P(B)=0.25, P(C)=0.20 and P(B/C)=0.15. Find for P(C/B)
Answers
Answer:
[(b/c)=0.15)]
Step-by-step explanation:
===================================================
Work Shown:
P(B/C) = P(B and C)/P(C) ... conditional probability formula
P(B and C) = P(C)*P(B/C)
P(B and C) = 0.20*0.15
P(B and C) = 0.03
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P(C/B) = P(C and B)/P(B) .... note the swap of B and C
P(C/B) = P(B and C)/P(B)
P(C/B) = (0.03)/(0.25)
P(C/B) = 0.12
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Extra notes:
The fact that events A and B are independent is not relevant.The fact A and C are mutually exclusive isn't used here either.This problem can be solved through Bayes' Theorem.Another alternative you can do is to set up a 3 by 3 contingency table to help solve this problem.A rectangle is twice as long as it is wide. Its width is 51⁄2 cm. Find the area of the rectangle.
Answers
Step-by-step explanation:
The are of rectangle is 1300.5cm2
Solve the proportion.
14
y +9
-
10
15
y = [?]
Answers
Answer:
y=12
Step-by-step explanation:
14 10
----- = --------
y+9 15
Using cross products
14*15 = 10 (y+9)
210 = 10(y+9)
Divide by 10
210/10 = 10(y+9)/10
21 = y+9
Subtract 9
21-9 = y
12 =y
To make a disinfecting solution, Alana mixes 2 cups of bleach with 5 cups of
water. What is the ratio of water to the total amount of disinfecting solution?
Answers
Answer:
Step-by-step explanation:
Ok
write an equation of the circle with center (-2,-9) and radius 10
Answers
Answer:
[tex](x+2)^{2}[/tex] + [tex](y+9)^{2}[/tex] = 100
Step-by-step explanation:
Standard Equation of a Circle
[tex](x-h)^{2}[/tex] + [tex](y-k)^{2}[/tex] = [tex]r^{2}[/tex]
(h,k) = center of circle
r = radius of circle
Substitute in given. Watch the negatives.
Identify the range of the function shown in the graph.
Answers
Answer: The answer is all real numbers
Step-by-step explanation:
This is the answer because the line goes on infinitely and will pass through all of the numbers (negative, positive). Its not y [tex]\geq \\[/tex] 0 because it passes through 0 when the line goes through x (side to side) axis.
Which of the following is the inverse relation of the set?
Answers
Answer:
{(1,3),(2,4)(3,5)(4,6)}
Step-by-step explanation:
The input becomes the output and the output becomes the input
{(1,3),(2,4)(3,5)(4,6)}
There are 5 brown horses and 4 tan horses in a barn. Sonia will randomly select two horses to ride with her friend. What is the probability that
the first horse selected is tan and the second horse selected is brown?
20/81
5/18
2/9
1/20
Answers
Answer:
5/18
Step-by-step explanation:
The total number of horses present is 9
The probability that the first selected horse is tan is 4/9
So , now for the second choice , we are left with 8 total horses of which 5 is brown
The probability is 5/8
So the joint probability is the product of this two
That will be;
5/8 * 4/9 = 5/18
please help me asap (geometry)
Answers
Answer:
x = 20
Step-by-step explanation:
Angle 2 and Angle 5 are corresponding angles
Corresponding angles are congruent
If angle 2 = 3x - 20 and angle 5 = x + 20
Then 3x - 20 must equal x + 20 ( because corresponding angles are congruent )
Notice that weve just created an equation that we can use to solve for x
We now solve for x using the equation we created
3x - 20 = x + 20
Step 1 add 20 to both sides
3x = x + 40
Step 2 Subtract x from both sides
2x = 40
Step 3 divide both sides by 2
x = 20
If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initially. When will the amount left be 2 grams? Round to the nearest tenth of a day.
Answers
Answer: [tex]26.4\ \text{days}[/tex]
Step-by-step explanation:
Given
Half life of radioactive substance is [tex]T_{\frac{1}{2}}=20\ \text{days}[/tex]
Initial amount [tex]A_o=2\ \text{days}[/tex]
Amount left at any time is given by
[tex]\Rightarrow A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}\\\\\Rightarrow 2=52^{\dfrac{-t}{20}}\\\\\Rightarrow 0.4=2^{\dfrac{-t}{20}}\\\\\Rightarrow 2^{\dfrac{t}{20}}=2.5\\\\\Rightarrow \dfrac{t}{20}\ln 2=\ln (2.5)\\\\\Rightarrow t=\dfrac{20\ln (2.5)}{\ln 2}\\\\\Rightarrow t=26.4\ \text{days}[/tex]
It takes 26.4 days to reach 2 gm.
What number is 22 ten-thousandths more than 1 1/2?
Answers
Answer:
1.50000
.00022
1.50022
Step-by-step explanation:
The number 22 ten thousandths more than [tex]1\frac{1}{2}[/tex] is 1.5022.
Given that, 22 ten-thousandths and [tex]1\frac{1}{2} =\frac{3}{2}[/tex].
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let x be the unknown number.
Now, x-22/10000 = 3/2
⇒ x-0.0022=1.5
⇒ x=1.5+0.0022
⇒ x=1.5022
Therefore, the number 22 ten thousandths more than [tex]1\frac{1}{2}[/tex] is 1.5022.
To learn more about an equation visit:
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1 by 8 of the passenger of a train where children is there where 40 children traveling in the train on a Saturday how many Abbott were there in that that day?
Answers
Answer:
200 adults
Step-by-step explanation:
1/8 of the passengers (children) is 40
Total passengers in the train is 8/8
Therefore to get the total number of passengers is given by
(8/8) × 40 × (8/1)
= 240 passengers
Adults in the train = Passengers - Children
= 240 - 40
= 200 adults
what is 8^100 / 8^50 is 8^50?
Answers
Answer:
8^50
Step-by-step explanation:
8^100 / 8^50
We know that a^b / a^c = a^(b-c)
8^(100-50)
8^50
A ball is thrown into the air with an upward velocity of 36 ft/s. It’s height h in feet after t seconds is given by the function h = -16t^2 + 36t + 9. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the balls maximum height ?
Answers
Answer:
Time taken for the ball to hit the ground back = 3.08 s
Step-by-step explanation:
h(t)= -16t² + 48t + 4
when will rhe object come back to hit rhe ground?
When the ball is at the level.of the ground, h(t) = 0.
0 = -16t² + 48t + 4
-16t² + 48t + 4 = 0
Solving the quadratic equation
t = 3.08 s or t = -0.08 s
Since the time cannot be negative,
Time taken for the ball to hit the ground back = 3.08 s
Hope this Helps!!!
Step-by-step explanation:
Which of the following are perfect squares? Check All that apply.
A.36
B.51
C.100
D.19
E.25
F.10
Answers
Answer:
A, C and E.
Step-by-step explanation:
36 = 6^2
100 = 10^2
25 = 5^2.
A diver begins at 140 feet below sea level. She descends at a steady rate of 7 feet per minute for 4.5 minutes. Then, she ascends 112.2 feet. What is her current depth?
Negative 549.3 feet
Negative 59.3 feet
59.3 feet
549.3 feet
Answers
Answer:
Step-by-step explanation:
starting point: 140 feet below sea level.=-140
she then decends= 7(4.5)=31.5
-140-31.5=-171.5
finally she ascends 112.2 feet
-171.5+112.2=-59.3 feet or 59.3 feet below sea level
Answer:
It's B
Step-by-step explanation:
S is the centroid of the triangle. Find IT if ST= 9
Answers
Answer:
IT = 13.5
Step-by-step explanation:
Recall: According to the Centroid theorem the Centroid of is ⅔ of the distance of the vertex of the triangle to the midpoint of the opposite side.
This means that:
ST = ⅔(IT)
ST = 9 (given)
Substitute
9 = ⅔(IT)
Multiply both sides by 3
3*9 = 2(IT)
27 = 2(IT)
Divide both sides by 2
27/2 = IT
IT = 13.5
c) A businessman deposited Rs 60,000 in a Commercial Bank at 4.5% p.a. How long should he deposit the sum to receive an amount of 61,350?
Answers
Answer:
It would take 5 months long to receive an amount of 61,350.
Step-by-step explanation:
P = Rs 60,000
R = 4.5%
T = ?
A = Rs 61,350
so
I = A-P
or, I = Rs 61,350 - Rs 60,000
so, I = Rs 1,350
so
T = (I×100)/P×R
T = (1350×100)/(60,000×4.5)
or, T = 135000/270000
so, T = 0.5 years = 5 months
is the equation below a function? explain
d) y2 = x2 + 5
Answers
Answer:
No
Step-by-step explanation:
y^2 = x^2 + 5
Rewriting
y^2 - x^2 = 5
This is a hyperbola
We can use the vertical line test to show that it is not a function since a vertical line passes through more than one point.
Grade improvement and study motivation
Answers
Answer:
yes you are write because when our results come with good marks and grade the we are motivate .
Step-by-step explanation:
thanks mark me brainlist
Two runners started to run in the same direction at the same time. The speed of the first runner is 8 mph, and the speed of the second runner is 9.6 mph. What is the distance between them after 5 hours?
Answers
Answer:
8 miles
Step-by-step explanation:
9.6-8=1.6
1.6 times 5 equals 8 miles
It should be noted that after 5 hours, the distance between the two runners will be 8 miles.
How to calculate the distanceDistance = Speed × Time
For the first runner:
Distance covered by the first runner = Speed of the first runner × Time
= 8 mph × 5 hours
= 40 miles
For the second runner:
Distance covered by the second runner = Speed of the second runner × Time
= 9.6 mph × 5 hours
= 48 miles
Since both runners are running in the same direction, we subtract the distance covered by the first runner from the distance covered by the second runner to find the distance between them:
Distance between the runners after 5 hours = Distance covered by the second runner - Distance covered by the first runner
= 48 miles - 40 miles
= 8 miles
Learn more about distance
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The equation $y=-4.9t^2+3.5t+5$ describes the height (in meters) of a ball thrown upward at $3.5$ meters per second from $5$ meters above the ground, where $t$ is the time in seconds. In how many seconds will the ball hit the ground? Express your answer as a common fraction.
Answers
Answer:
Step-by-step explanation:
The position function is
[tex]s(t)=-4.9t^2+3.5t+5[/tex] and if we are looking for the time t it takes for the ball to hit the ground, we are looking for the height of the ball when it is on the ground. Of course the height of anything on the ground is 0, so if we set s(t) = 0 and solve for t, we will find our answer.
[tex]0=-4.9t^2+3.5t+5[/tex] and factor that however you are currently factoring in class to get that
t = -.71428 seconds or
t = 1.42857 seconds (neither one of those is rational so they can't be expressed as fractions).
We all know that time will never be a negative value, so the time it takes this ball to hit the ground is
1.42857 seconds (round how you need to).
Can someone help me like Fr like please
Answers
Answer:
Line goes other way through (2,3)
Step-by-step explanation:
The negative slope only applies once.
Your line goes down 3 AND back 3.
It should go down 3 and right 4. Or up 3 and back 4.
**back = left (sorry for inconsistency)
Answer: Draw a line through (2,3) and (6,0)
See the graph below
=====================================================
Explanation:
Start with the point (2,3)
Then move down 3 units (aka rise) and move to the right 4 units (aka run). You should arrive at (6,0).
As you can probably guess, the rise and run are drawn directly from the slope of -3/4.
slope = rise/run = -3/4
rise = -3 and run = 4
So this line goes through (2,3) and (6,0)
find the missing length indicated.
Answers
Answer:
The answer is 192 bestie btw im a freshmen
Step-by-step explanation:
Which of the following models the Additive Inverse Property?
061-1) = 6
06+0 -0+ 6
06+0 - 6
6+(-6) = 0
Answers
Given:
The different models in the options.
To find:
The model that represent the Additive Inverse Property.
Solution:
Additive inverse property: The sum of a number and its additive inverse is always 0.
If [tex]a[/tex] is a number, then [tex](-a)[/tex] is the additive inverse because
[tex]a+(-a)=0[/tex]
If the number is 6, then the additive inverse is (-6) because
[tex]6+(-6)=0[/tex]
Therefore, the correct option is D.
If you roll a standard number cube 42 times, how many times do you expect the cube to show a five?
Round your answer to the nearest whole number if needed.
Answers
Answer:
5
Step-by-step explanation:
this is probability
probability of 5 occuring once is = 5/42=0.119
therefore, probability of 5 occuring in 42 times is;
42 x 0.119=4.998
approximately 5
Second time posting this. Please help!! :)
Answers
Answer:
Step-by-step explanation:
[tex]\frac{480+24(x-40)}{x}[/tex]
The numerator of the rational expression the money he earned for 'x' hours
The rate at which William is paid for each hour in excess of 40 hours 24.
x = 50 hours = (40 + 10 ) hours
The amount paid for excess 10 hours = 24 *10 = 240
Total amount earned for the week = 480 + 240 = 720
