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[tex] \sqrt{x + 9} = x - 3[/tex]
Sides gets power 2
[tex] ({ \sqrt{x + 9} })^{2} = ( {x - 3})^{2} [/tex]
[tex] |x + 9| = {x}^{2} - 6x + 9 [/tex]
_________________________________
[tex]x + 9 = {x}^{2} - 6x + 9[/tex]
Subtract sides 9
[tex]x + 9 - 9 = {x}^{2} - 6x + 9 - 9[/tex]
[tex]x = {x}^{2} - 6x[/tex]
Subtract sides x
[tex]x - x = {x}^{2} - 6x - x[/tex]
[tex] {x}^{2} - 7x = 0[/tex]
[tex]x(x - 7) = 0[/tex]
[tex]x = 0[/tex]
OR
[tex]x - 7 = 0[/tex]
[tex] x = 7[/tex]
_________________________________
[tex]x + 9 = - ( {x}^{2} - 6x + 9)[/tex]
[tex]x + 9 = - {x}^{2} + 6x - 9[/tex]
Subtract sides 9
[tex]x + 9 - 9 = - {x}^{2} + 6x - 9 - 9 \\ [/tex]
[tex]x = - {x}^{2} + 6x - 18 [/tex]
Subtract sides x
[tex]x - x = - {x}^{2} + 6x - 18 - x [/tex]
[tex] - {x}^{2} + 5x - 18 = 0[/tex]
Multiply sides by -1
[tex] {x}^{2} - 5x + 18 = 0 [/tex]
[tex]x = No \: \: solution[/tex]
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CHECK the roots :
[tex]x = 0[/tex]
[tex] \sqrt{0 + 9} ≠0 - 3[/tex]
[tex] \sqrt{9} ≠ - 3[/tex]
[tex]3≠ - 3[/tex]
Thus (( x = 0 )) is unacceptable.
+++++++++++++++++++++++++++++++++++++++
[tex]x = 7[/tex]
[tex] \sqrt{7 + 9} = 7 - 3[/tex]
[tex] \sqrt{16} = 4[/tex]
[tex]4 = 4[/tex]
Thus (( x = 7 )) is the only solution for x.
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Done...
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In exercise teacher wants each student in her class to have at least 48 ft.² of space on the floor. What is the largest number of student she will allow in a classroom with a student exercise area of this size?
Answer: D. 50 students
pls give me brainliest.
Step-by-step explanation: First we find the area of the classroom which is worked out below and it is the shape of a rectangle;
Area of a rectangle = Length * Breadth
= 60 ft * 40 ft
= 2400 ft²
Now to find the number of students that she will allow in the classroom, we have to divide the area of the classroom which is 2400 ft²by the amount of space allocated to each student which will be;
=
= 50
This means she will allow 50 students into her class.
Identify the domain of the relation (-5, 10), (-2, 11), (1, 4), (5, 10) *
Answer:
-5,-2,1,and 5
Step-by-step explanation:
A bag had 7 orange rocks , 6 green rock , 1 white rock ,7 black rocks , and 2 yellow you randomly pull a rock from the bag ,keep it out , and then pull out another one .
What is the probability of getting a yellow rock and then a n orange rock ?
Answer:
[tex]Probability = \frac{7}{253}[/tex]
Step-by-step explanation:
Given
[tex]Orange = 7[/tex]
[tex]Green = 6[/tex]
[tex]White = 1[/tex]
[tex]Black = 7[/tex]
[tex]Yellow = 2[/tex]
Required
Probability of selecting a yellow then orange rock
From the question, we understand that the probability is that of without replacement.
Since the yellow, is first picked.
We need to determine the probability of picking a yellow rock, first.
[tex]P(Yellow) = \frac{n(Yellow)}{Total}[/tex]
[tex]P(Yellow) = \frac{2}{7 + 6 + 1 + 7 + 2}[/tex]
[tex]P(Yellow) = \frac{2}{23}[/tex]
The rock has reduced by 1;
Next is to determine the probability of picking an orange rock
[tex]P(Orange) = \frac{n(Orange)}{Total - 1}[/tex]
[tex]P(Orange) = \frac{7}{7 + 6 + 1 + 7 + 2- 1}[/tex]
[tex]P(Orange) = \frac{7}{22}[/tex]
The required probability is calculated as thus:
[tex]Probability = P(Yellow) * P(Orange)[/tex]
[tex]Probability = \frac{2}{23} * \frac{7}{22}[/tex]
[tex]Probability = \frac{14}{506}[/tex]
[tex]Probability = \frac{7}{253}[/tex]
write the following ratio in their simplest form 25:75
Answer:
1/3 :)
Step-by-step explanation:
4х – 8y = 2
6x - 12y = 3
Answer:
1. Slope=
2.000
1.000
=0.500
x−intercept=
2
1
=0.50000
y−intercept=
−4
1
=−0.25000
2. Slope=
2.000
1.000
=0.500
x−intercept=
2
1
=0.50000
y−intercept=
−4
1
=−0.25000
Hope this helps!
find the product and enter your answer in the space provided 316 x 10
Answer:
The answer to this is: 3160 and can i have brainliest?? please
Step-by-step explanation:
Rational number
between 2 and 3?
Answer:
it would be 7 and 8
Step-by-step explanation:
Answer:
rational numbers lie between 2 and 3 are infinite there are infintie numbers of rational number which lie between 2 and 3
Write the next three terms of the sequence:
1, 4, 16, 64,
Answer:
256, 1024, 4096
Step-by-step explanation:
Here, we can see that each term can be represented by [tex]2^{2n}[/tex] where n starts at 0. We can then plug in n=4, 5, and 6 for the next three terms respectively to get the answer above.
How do you write 31 billon in scientific notation
Answer:
3.10E+10 (3.10 x 10 10)
Step-by-step explanation:
The mean and standard deviation for number of battery crimes in the U.S. from 1985 to 2000 are X = 326,845 and sx = 27,569. The mean and standard deviation for number of property crimes in the U.S. for the same time period are y = 634,235 and Sy = 42,268. The correlation coefficient is r = 0.92. Find the equation for the least- squares regression line for number of property crimes compared with number of battery crimes.
A: y = 1.41 + 173,214.37x
B: y = 173,214.37 + 1.41x
C: y = 421,052.69 + 0.65x
D: y = 0.65 + 421,052.69x
E: Unable to determine the equation
Answer:
The correct answer is: A
Step-by-step explanation:
The value of the slope and intercept is:
=0.92(42268/27569)
=1.410518
a=y-bx
=634235-1.410518×326845
=173214.3716
The eququation for the least-square regression line is:
y=173214.3716 + 1.4105518x
Round to the 2 decimal place:
=173,214.37 +1.41x
The equation for the least squares regression line for number of property crimes compared with number of battery crimes is (b) y = 141x + 173214.37
How to determine the least square regression equation?The given parameters are:
Mean x, μ = 326,845 Standard deviation of x, σ = 27,569Mean y, μ = 634,235 Standard deviation of y, σ = 42,268Correlation coefficient, r = 0.92Calculate the slope (m) using:
m = r * Sy/Sx
This gives
m = 0.92 * 42268/27569
Evaluate
m =1.41051761036
Approximate
m = 1.41
The y-intercept (c) is calculated using:
c = μy -m * μx
So, we have:
c = 634235 - 1.41051761036 * 326845
Evaluate
c = 173214.371642
Approximate
c =173214.37
The least-square regression line equation is represented as:
y = mx + c
So, we have:
y = 141x + 173214.37
Hence, the equation for the least squares regression line for number of property crimes compared with number of battery crimes is (b) y = 141x + 173214.37
Read more about least squares regression at:
https://brainly.com/question/14563186
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Traeq pays 35.34 for 3.1 pounds of salmon. What is the price per pound of salmon
if KM = 32 units, KL = 3x+6 and LM= 11 units, what is the value of x?
Answer:
x = 5Step-by-step explanation:
|<------------------- 32 units ---------------->|
K-----------------------L-------------------------M
3x + 6 11
KL + LM = KM
3x + 6 + 11 = 32
3x = 32 - 11 - 6
x = 15 / 3
x = 5 units
The formula for the volume of a rectangular prism is v=Iwh which is the equivalent equation solved for h
Answer:
6x^3+39x^2+59x
Step-by-step explanation:
ANSWER BRIEFLY AND FAST FOR GUARANTEED BRAINLY AND POINTS!
• commutative property
• addition property of equality
• 2x=8
• distributive property
• division property of equality
• x=4
• multiplication property of equality
• subtraction property of equality
Answer:
See below
Step-by-step explanation:
[tex]2(x+5)-3 =15[/tex]
Using the distributive property in the LHS we get
[tex]2x+10-3 =15[/tex]
[tex]2x+7=15[/tex]
Now add -7 both sides. So we have the subtraction property of equality.
[tex]2x+7+(-7)=15+(-7) \text{ This is what I meant for add}[/tex]
[tex]2x+7-7=15-7[/tex]
[tex]2x=8[/tex]
Now divide both sides by 2. So we have the division property of equality
[tex]\dfrac{2x}{2} =\dfrac{8}{2}[/tex]
[tex]x=4[/tex]
-6x+15=33 what is the first best step in solving for x?
Answer:
x= -3
Step-by-step explanation:
1) subtract 15 on both sides
should look like: -6x=18
2) divide the -6 on both sides
3) 18 divided by -6 is -3
The sports store made $564 from selling pool rafts this week (Monday-Friday). Of that amount, it made $132.56 on Monday and $107.38 on Tuesday. IT made an equal amount of money on Wednesday, Thursday, and Friday. How much money did the store make from selling pool rafts on Friday?
Answer:
Amount made from selling pool rafts on Friday is equal to $108.02
Step-by-step explanation:
Total amount made from selling pool rafts = $564
Amount made from selling pool rafts on Monday = $132.56
Amount made from selling pool rafts on Tuesday = $107.38
Let amount made on each of the days - Wednesday, Thursday, and Friday be equal to $x.
Therefore,
[tex]132.56+107.38+x+x+x=564\\239.94+3x=564\\3x=564-239.94\\3x=324.06\\x=\frac{324.06}{3}\\ x=$108.02[/tex]
So,
amount made from selling pool rafts on Friday is equal to $108.02
whats 18+18+= equal to
Answer:
36
Step-by-step explanation:
Answer:
the correct answer is 36
A small submarine starts at - 1.260 feet in relation to sea level. Then it descends 5 feet per minute for 12 minutes What expression represents the new position of the submarine in relation to sea level?
Answer:
The submarine is at -1260 ft.
It descends 5 ft/min for 12 min.
12 min * 5 ft/min = 60 ft.
It descended 60 ft, so you must subtract 60 ft from -1260 ft.
-1260 ft + (-5)(12) ft = -1260 ft - 60 ft = -1320 ft
The error in the last line in the problem is that (-5)(12) = -60, not 60.
The correct line is:
-1260 + (-5)(12) = -1260 - 60 = -1320
Step-by-step explanation:
HELP ASAP!!!!!!!!!!!!!!!!!!
Answer:
I'm pretty sure it would be 1 acre
Step-by-step explanation:
5/2 which is improper for 2 1/2 and 2/5 are multiplicative inverses so 2/5 of 5/2 is 1
What is −15÷3/5?
-25
-9
-1/9
-1/25
Answer:
-25
Step-by-step explanation:
i took the test
How many cupcakes can I make with 16 cups of batter if I pour 2/3 Cup of batter into each cake?
Answer:
Step-by-step explanation:
16×2/3
32/3
104
what is the difference between m∠A and ∠A?
thank you so much!!
Answer:
The measure of an angle is a numerical value. <A just refers to the angle itself.
Step-by-step explanation:
If PQ = 2.1 and QR = 0.8, what is PR?
Answer:
2.9
Step-by-step explanation:
If the order is P, Q, R on the number line, add both segments together.
Given: In the figure, B is the midpoint of AC and AD = EC. Prove: DB = BE.
Match each statement to its corresponding reason in the flow diagram. Drag the items on the left to the correct
location on the right.
Answer:
The PLATO answer...
Mr. Peters uses a phone card to call relatives in France. It costs him 48 cents to talk for 12 minutes. What is the call rate for the phone card?
Answer:
The ratio is 1:4
Step-by-step explanation:
For every minute of talking, it costs him 4 cents, and so on.
A whale is 215 feet below sea level and descends 23 feet then ascends 119 feet. What is the location of the whale?
Answer:
354 feet below sea level
Step-by-step explanation:
Subtract 23 from 215, then add 119
Write an equivalent fraction with the given denominator. 9/19=?/57
Answer:
27
Step-by-step explanation:
Divide the denominators first. 57/19 = 3
That means to get the denominator you had to multiply 3 to 19. What you do to the bottom must be done at the top.
9*3 = ?
27
549 divided by 61. Dont round the answer
Answer:
9
Step-by-step explanation:
Answer: The Answer is 9 i'm really sure this is the answer
how many solutions does the equation 8x+16=8x-16 have?
Answer:
8*x+16-(8*x-16)=0
Step-by-step explanation:
Solve : 32 = 0
This equation has no solution.
A. a non-zero constant never equals zero.
Hope this helps! Please mark Brainliest!
Macy drove her car to visit her uncle. She came part of the way home after her visit. This graph shows the distance Macy was from her home during the course of the day. During which part of the graph is Macy visiting her uncle?
Answer:
part 11
Step-by-step explanation:
B
Step-by-step explanation:
hope that help!