Answer:
C. x = 2
Step-by-step explanation:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
Since you have square roots, you need to separate the square roots and square both sides.
[tex] \sqrt{9x + 7} = 7 - \sqrt{2x} [/tex]
Now that one square root is on each side of the equal sign, we square both sides.
[tex] (\sqrt{9x + 7})^2 = (7 - \sqrt{2x})^2 [/tex]
[tex] 9x + 7 = 49 - 14\sqrt{2x} + 2x [/tex]
Now we isolate the square root and square both sides again.
[tex] 7x - 42 = -14\sqrt{2x} [/tex]
Every coefficient is a multiple of 7, so to work with smaller numbers, we divide both sides by 7.
[tex] x - 6 = -2\sqrt{2x} [/tex]
Square both sides.
[tex] (x - 6)^2 = (-2\sqrt{2x})^2 [/tex]
[tex] x^2 - 12x + 36 = 4(2x) [/tex]
[tex] x^2 - 20x + 36 = 0 [/tex]
We need to try to factor the left side.
-2 * (-18) = 36 & -2 + (-18) = -20, so we use -2 and -18.
[tex] (x - 2)(x - 18) = 0 [/tex]
[tex] x = 2 [/tex] or [tex] x = 18 [/tex]
Since solving this equation involved the method of squaring both sides, we much check for extraneous solutions by testing our two solutions in the original equation.
Test x = 2:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(2) + 7} + \sqrt{2(2)} = 7 [/tex]
[tex] \sqrt{25} + \sqrt{4} = 7 [/tex]
[tex] 5 + 2 = 7 [/tex]
[tex] 5 = 5 [/tex]
We have a true equation, so x = 2 is a true solution of the original equation.
Now we test x = 18.
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(18) + 7} + \sqrt{2(18)} = 7 [/tex]
[tex] \sqrt{162 + 7} + \sqrt{36} = 7 [/tex]
[tex] \sqrt{169} + 6 = 7 [/tex]
[tex] 13 + 6 = 7 [/tex]
[tex] 19 = 7 [/tex]
Since 19 = 7 is a false equation, x = 18 is not a true solution of the original equation and is discarded as an extraneous solution.
Answer: C. x = 2
Chloe needs to rent a car while on vacation . The rental company charges $17.95 , plus 18 cents for each mile driven. If Chloe only has $40 to spend on the car rental, what is the maximum number of miles she can drive ?
Answer:
17.95+18x <= 40
Step-by-step explanation
<= less than or equal to0
Answer:
The maximum number of miles than Chloe can drive are:
122.5
Step-by-step explanation:
$1 = 100¢
18¢ = 18/100 = $0.18
17.95 + 0.18m = 40
m = maximum number of miles than can drive
0.18m = 40 - 17.95
0.18m = 22.05
m = 22.05/0.18
m = 122.5
94. A tin of peas & carrots and two mangoes weighing 300 grams each are placed on one
side of a scale. To balance the scale, 4 tins of condensed milk each weighing 250g are
placed on the other side. Determine the mass of the peas & carrots.
Answer:
400 g
Step-by-step explanation:
Let p represent the mass of the peas & carrots. The scale is balanced when the mass on one side is equal to the mass on the other side.
p + 2(300 g) = 4(250 g)
p = 1000 g -600 g . . . . . subtract 600 g
p = 400 g
The mass of the peas & carrots is 400 grams.
Fine the value of x in the triangle. Then classify the triangle as acute, right,
or obtuse.
47* 45* x
Answer:
x = 88
Step-by-step explanation:
The sum of the angles in a triangle add to 180
47+45 +x = 180
Combine like terms
92+x = 180
Subtract 92 from each side
92+x-92= 180-92
x =88
Iris has 120 songs on her playlist. each week, she downloads 4 new songs
Answer:
120 + 4w
Step-by-step explanation:
I am indeed doing it aswell
According to the National Health Statistics Reports, the standard deviation of the weights of all one-year-old baby boys born in the U.S. is 5.3 pounds. A random sample of 360 one-year-old baby boys born in the U.S. had a mean weight of 25.5 pounds.
a) Construct a 90% confidence interval for the mean weight of all one-year-old baby boys in the U.S. Write a sentence that interprets this interval.
b) Should this confidence interval be used to estimate the mean weights of all one-year-old babies in the U.S.? Explain.
Answer: A) At 90% confidence interval estimate of the population mean
is,( 25.0405 , 25.9595 )
B) YES
Step-by-step explanation:
Given that,
Point estimate = sample mean Ж = 25.5
Population standard deviation α = 5.3
Sample size = n =360
At 90% confidence level the z is ,
∝ = 1 - 90% = 1 - 0.90 = 0.1
∝ / 2 = 0.1 / 2 = 0.05
Z∝/2 = Z0.05 = 1.645 ( WHEN WE USE THE Z TABLE )
Margin of error E = Z∝/2 * ( α/√n)
E = 1.645 * (5.3 / √360 ) = 0.4595
At 90% confidence interval estimate of the population mean
is
Ж - E < ц < Ж + E
25.5 - 0.4595 < ц < 25.5 + 0.4595
25.0405 < ц < 25.9595
( 25.0405 , 25.9595 )
At 90% confidence interval estimate of the population mean
is,( 25.0405 , 25.9595 )
B) This confidence interval can be used to estimate the mean weight of all one - year old babies in the US since the mean value of 25.5 falls within the confidence values, we have sufficient evidence to
conclude that the mean weight of all one-year-old boys is 25.5
In year 3 it is expected that the total value of clothing sales will reach 32 million if the total value of ASCO sells Remains the Same as year 2what percentage of sales clothing account for in year three
Answer:
The sales account for year 3 is [tex][\frac{32\ \text{mn}-x\ \text{mn}}{x\ \text{mn}}\times 100\%][/tex].
Step-by-step explanation:
As the sales for year 2 is not provided, assume it is x million.
The total sales in year 3 is, 32 million.
Compute the sales account for year 3 as follows:
[tex]\text{Percentage of sales for year 3}=\frac{\text{Total Sales in year 3}-\text{Total Sales in year 2}}{\text{Total Sales in year 2}}\times 100\%[/tex]
[tex]=\frac{32\ \text{mn}-x\ \text{mn}}{x\ \text{mn}}\times 100\%[/tex]
What is a3 if an=64(12)n−1
Answer:
[tex]\huge\boxed{a_3=9,216}[/tex]
Step-by-step explanation:
[tex]a_n=64(12)^{n-1}\\\\\text{substitute}\ n=3:\\\\a_3=64(12)^{3-1}=64(12)^2=64(144)=9,216[/tex]
What does the symbol in the image on number 39 mean
Answer:
It means direct sum.
Step-by-step explanation:
A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses. How many courses worth 3 credits did the student complete?
Answer:
They completed 13, 3 credit classes
Step-by-step explanation:
1. Make 2 formulas. In this case: x+y=18
and 3x+4y=59
2. Then multiply x+y=18 by 3 and subtract the two equations.
Find y which is 5 and input into the equations. Then find your answer.
If there are 736 students in a school, prove that at least three students have a birthday on the same day of the year.
Step-by-step explanation:
736 / 365 = 2R6
So even if the first 365 students all have different birthdays, and the next 365 students also all have different birthdays, then there are 2 students for every birthday. The last 6 students therefore share a birthday with at least 2 other students. So there are at least 3 students who share a birthday.
Yes, we can prove that at least three students have a birthday on the same day of the year.
What is algebra?
Algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas.
We have,
Total number of students = 736
So,
In a year there are 365 days.
And we have 736 students,
So,
Two students have birthday on same day = 365 × 2 = 730
NOw,
Students left = 736 - 730 = 6
So,
These 6 Students share birthday with othe 6 Students .
So, yes there are at least three students who have a birthday on the same day of the year
To learn more about algebra click here,
https://brainly.com/question/953809
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Find the axis of symmetry and vertex for the parabola y=−5x2+30x+7.
Answer:
axis of symmetry x=3
vertex (3, 52)
Step-by-step explanation:
y = -5x² + 30x + 7
x = -b/2a = -30/2(-5) = -30/-10 = 3
y = -5(3)² + 30(3) + 7
y = -45 + 90 + 7
y = 52
3) The chance that a salmon jumps up the waterfall to upstream successfully 35%. We have a group of 9 salmon. What is the chance that none of them jump up successfully? What is the chance that all of them reach up-stream? What is the chance that at least 2 of them reach up-stream? What is the chance that at most 1 of them reaches up-stream? Is “at least 1” complement of the event “at most 1”?
Answer:
(a) P(0,9) = 0.0207
(b) P(2-9,9) = 0.1004
(c) P(0-1,9) = 0.1211
(d) "at least 1" and "at most 1" are not complements of each other because there is an overlap of "1" in both cases.
Step-by-step explanation:
With appropriate assumptions, this can be solved using the binomial distribution.
Probability of success for each trial, p = 35%
Number of trials, n = 9
using formula for x successes out of n trials, each with probability p
P(x,n) = C(n,x) p^x (1-p)^(n-x)
where C(n,x) = n!/(x!(n-x)!)
(a) zero success
n=9
p=0.35
x = 0
P(0,9) = 9!/(0!9!) 0.35^0 * 0.65^9
= 1*1* 0.0207
= 0.0207
(b) 2 or more successes
We need the sum of probabilities of 2,3,4,5,6,7,8,9 successes, which is easier calculated by (1-P(0,9)-P(1,9))
P(1,9) = C(9,1) * p^1 * p^8
= 9 * 0.35 * 0.65^8
= 9 * 0.35 * 0.3186
= 0.1004
Therefore
P(2 to 8, 9)
= 1 - P(0,9) - P(1,9)
= 1 - 0.0207 - 0.1004
= 0.8789
(c) at most 1 success
P(0,9) + P(1,9)
= 0.0207 + 0.1004
= 0.1211
Mary wants to make brownies to make brownies she needs 7/12 of a cup of flour per batch of brownies if Mary has 7 cups of flour then how many batches of brownies can mary make?
━━━━━━━☆☆━━━━━━━
▹ Answer
12
▹ Step-by-Step Explanation
[tex]7/\frac{7}{12} \\\\= 7 * \frac{12}{7} \\\\= \frac{84}{7} \\\\= 12[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Help with 18 - 22
18 4 x 1 =
— —
7 2
A. 8
—
7
B. 4
—
14
C. 28
—
2
19. 15 X 2 =
— —
2 20
A. 4
—
300
B. 30
—
40
C. 30
—
4
20. 3 x 7 =
— —
6 8
A. 18
—
56
B. 24
—
42
C. 21
—
48
21. 9 x 1 =
— —
10 2
A. 9
—
20
B. 18
—
10
C. 8
—
18
22. 3 x 2 =
— —
6 4
A. 6
—
24
B. 18
—
8
C. 8
—
18
Answer:
18. b. 4/14
19. b. 30/40
20. c. 21/48
21. a. 9/20
22. a. 6/24
Step-by-step explanation:
So in these questions all we do is multiply the fractions.
18)
[tex]\frac{4}{7} * \frac{1}{2}[/tex]
4*1 = 4
7*2 = 14
b. 4/14
19)
[tex]\frac{15}{2}*\frac{2}{20}[/tex]
15*2 = 30
2*20 = 40
b. 30/40
20)
[tex]\frac{3}{6}*\frac{7}{8}[/tex]
3*7 = 21
6*8 = 48
c. 21/48
21)
[tex]\frac{9}{10}*\frac{1}{2}[/tex]
9*1 = 9
10*2 = 20
a. 9/20
22)
[tex]\frac{3}{6}*\frac{2}{4}[/tex]
3*2 = 6
6*4=24
a. 6/24
Hope this helps :)
Let y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that x and y are related by the equation =y+115025x. Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
Answer:
Change in the cost of each book printed = $25
Cost to get started = $1150
Step-by-step explanation:
Equation representing the relation between number of copies of the books (x) and total cost of publishing a book (y) is,
y = 1150 + 25x
This equation is in the form of a linear equation,
y = mx + b
Where m represents the change in cost of printing each book and y-intercept of the line 'b' represents the cost before any book is printed.
By comparing these equations,
m = 25
Therefore, change in the cost of each book printed = $25
b = 1150
Which represents the cost to get started = $1150
Need help ASAP! Will give brainliest if you tell me how to do this!
Answer:
A
Step-by-step explanation:
The syntax is binomcdf(trials, probability, value). There are 100 trials, and the probability is 0.5. binomcdf will return the probability that there is at most n successes. So, in this case we want 45 or less successes, so n is 45. So, the answer is binomcdf(100, 0.5, 45).
Hope this makes sense! Please give brainliest!
If x is 6, What is X+4
Answer:
x = 10
Step-by-step explanation:
We know x = 6
asked: x + 4
Plus it in =>
6 + 4
=> 10
A cream is sold in a 34-gram container. The average amount of cream used per application is 1 and two ninths grams. How many applications can be made with the container?
Answer:
Total cream = 34g
One application = 1 8/9 =(9+8)/9 = 17/9
Total applications = total cream/one application = 34/(17/9) = 34*9/17 = 18 applications
Step-by-step explanation:
A man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the constant rate of 45 mph . The man can run at a constant rate in either direction to get off the bridge just in time before the train hits him. How fast can the man run?
Answer:
9mph
Step-by-step explanation:
Given the following :
Speed of train = 45miles per hour
Distance of the man = 2/5
To avoid just about being hit by the train:
The main may run to the start point of the bridge towards the train = 2/5 length of the bridge, this is also when the train gets to the bridge
If the man runs forward away from the train, he has to cover a distance of (1 - 2/5) = 3/5 to avoid being hit, this is also when the train gets to the end of the bridge.
From here it could be inferred that :
The distance 3/5 ran by the man away from the bridge is equivalent to (3/5 - 2/5) =1/5, which seems to be moved by th etrain during the same period.
However, the only explanation for the discrepancy in length or distance is that the train moves faster than the man.
If the train's speed = 45mph
Then the train's speed is 5 times the speed of the man;
Man speed is thus;
(1/5) * 45 = 9mph
Set up a rational equation and then solve the following problems. A positive integer is twice another. The sum of the reciprocals of the two positive integers is 3/14. Find the two integers.
Answer:
7 and 14
Step-by-step explanation:
let one integer = x
other integer = 2x
sum of reciprocal = 1/x + 1/2x
= 3/2x = 3/14
= x = 7
one no. = 7
other no. = 14
Evaluate the expression.
Answer:
work is shown and pictured
The altitude of an airplane is decreasing at a rate of 41 feet per second. What is the change in altitude of the airplane over a period of 32 seconds?
Answer:
1312 feet
Step-by-step explanation:
41 ft=1 sec
how about 32 sec
41 x 32=1312/1=1312
Write a short statement that expresses a possible function between the given variables.(price of a DVD player, demand for DVD player)
Answer:
When the price of DVD player increases, the demand will decrease.
Step-by-step explanation:
The price and demand function have an inverse relationship. When the price of good increases its demand will decrease. This is law of demand. If the price of goods increase to a certain level its demand will start decreasing. The people will start buying lesser good and will consume less. The propensity to consume will decline and less economic goods will be consumed. When the price of DVD player is increased then the demand will decline for DVD players and people will drop the decision to buy the DVD player.
Please answer this correctly without making mistakes
Answer:
1/2
Step-by-step explanation:
There are eight equal pieces. Oliver used four pieces to make toast. Since the total is eight pieces, the fraction he used to make toast is 4/8, which simplifies to 1/2
Answer:
4/8
Step-by-step explanation:
He cut the bread into 8 equal pieces, so the denominator is 8.
He used 4 pieces for making toast.
He saved 4 pieces for later.
Hope this helps ;) ❤❤❤
Really need help on question 10.
Answer:
44 degrees
Step-by-step explanation:
4 multiplied by 7 is 28.
28 + 2 = 30
angle ABC = 30 degrees
3 multiplied by 7 is 21
21 - 7 = 14.
angle CBD = 14 degrees.
30 + 14 = 44.
The answer is ABD = 44 degrees
here are the 2 questions in the 2 pics separated lol
Answer:
60 and 87
Step-by-step explanation:
Question 1: The chance of losing would be 100% - 40% = 60%.
Question 2: Again, we just have to do 100% - 13% = 87%.
Answer:
Below
Step-by-step explanation:
First question:
Jade has a 40% chance of winnig wich could be expressed as 2/5
The chance of losing is the remainning pourcentage from 100%
●100-40 =60%
60% is the chance of losing wich could be expressed as 3/5
The sum of 3/5 and 2/5 is 1 so it's true.
■■■■■■■■■■■■■■■■■■■■■■■■■
Same method for the 2nd question:
The person has a 13 % chance of winning.
The chance of losing is 87%
● 100-13 =87
Find the length of AG
Answer:
[tex]AG=22[/tex]
Step-by-step explanation:
Follow the next steps:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F} =\frac{C-D}{F-G} =\frac{A-C}{A-F} =\frac{B-D}{E-G} =\frac{A-D}{A-G}[/tex]
Let:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F}\\ \\\frac{4}{A-E} =\frac{5}{10x}\\ \\Solving\hspace{3}for\hspace{3}A-E\\\\A-E=8x[/tex]
Now:
[tex]\frac{C-D}{F-G} =\frac{A-C}{A-F} \\\\\frac{2}{F-G} =\frac{9}{18x} \\\\Solving\hspace{3}for\hspace{3}F-G\\\\F-G=4x[/tex]
Hence:
[tex]A-G=(A-E)+(E-F)+(F-G)=22x[/tex]
Finally:
[tex]\frac{B-D}{E-G} =\frac{A-D}{A-G}\\\\\frac{A-D}{B-D} =\frac{A-G}{E-G}\\[/tex]
[tex]\frac{11}{7} =\frac{22x}{14x} \\\\\frac{11x^{2} }{7} -\frac{11}{7} =0\\\\[/tex]
Hence:
[tex]x=1\\x=-1[/tex]
Since it would be absurd for [tex]x=-1[/tex], the real solution is [tex]x=1[/tex]
Therefore:
[tex]AG=22[/tex]
The following table shows the number of innings pitched by each of the Greenbury Goblins' starting pitchers during the Rockbottom Tournament. Pitcher Calvin Thom Shawn Kris Brantley Number of innings pitched 11 1111 12 1212 7 77 3 33 ? ?question mark If the mean of the data set is 8 88 innings, find the number of innings Brantley pitched. innings
Answer:
The number of innings Brantley pitched is 7.
Step-by-step explanation:
We are given that the table shows the number of innings pitched by each of the Greenbury Goblins' starting pitchers during the Rockbottom Tournament below;
Pitcher Number of innings pitched
Calvin 11
Thom 12
Shawn 7
Kris 3
Brantley x
Let the number of innings Brantley pitched be 'x'.
The mean of the following data set is given by the following formula;
Mean = [tex]\frac{\text{Sum of all data values}}{\text{Total number of observations}}[/tex]
[tex]8 = \frac{11+12+7+3+x}{5}[/tex]
[tex]8\times 5 =33+x[/tex]
[tex]40 = 33+x[/tex]
x = 40 - 33 = 7
Hence, the number of innings Brantley pitched is 7.
Answer:
7
Step-by-step explanation:
Khan Academy
and click Submit
By visual inspection, determine the best fitting regression model for the
scatterplot.
O A Quadratic
O B. Linear
OC Exponential
OD. No pattern
Answer:
quadratic
Step-by-step explanation:
This graph has a parabola form wich is a propertie for qaudratic functions
Answer:
A
Step-by-step explanation:
multiply (x-4) (2x+3) using the distributive property. select the answer choice showing the correct distribution
Answer:
2x'2-3x-12
Step-by-step explanation:
(x-4) (2x+3)
2x'2 + 3x-6x-12
2x'2-3x-12
* this " '2 is squared
Answer: If this helps plz mark as brainliest
Step-by-step explanation:
(x−4)(2x+3)
=(x+−4)(2x+3)
=(x)(2x)+(x)(3)+(−4)(2x)+(−4)(3)
=2x2+3x−8x−12
=2x2−5x−12