Answers
Answer:
7. x=11/3
8. no solutions
Step-by-step explanation:
7.
[tex]2*\sqrt{3x-2} =6[/tex]
Divide both sides by two
[tex]\sqrt{3x-2}=3[/tex]
Square both sides
[tex]3x-2=9[/tex]
Simplify
[tex]x=\frac{11}{3}[/tex]
8.
[tex]\sqrt{43-x}+10=1[/tex]
Subtract 10 both sides
[tex]\sqrt{43-x}=-9[/tex]
Impossible to have a negative answer when square rooting, no solutions
Related Questions
Just answer it, dont have to show work, will mark brainly
Answers
The system of equations with the same solution set as the system of equations given is presented as follows:
5x + 3y = 10.x - 2y = -1.How to obtain the system of equations with the same solution set?The system of equations for this problem is presented as follows:
5x + 3y = 10.2x - 4y = -2.Another system of equations will have the same solution set as the system given when it's equations are multiples of the equations in this problem.
This holds true for the first option, as:
The first equation is the same for both systems, 5x + 3y = 10.The second equation on the first option is x - 2y = -1, meaning that it was the second equation of the given system divided by 2.More can be learned about a system of equations at https://brainly.com/question/24342899
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April took out a $600 loan from the bank. At the end of 5 years, she pays back the principal, plus $60 simple interest.
What was the annual interest rate?
Answers
April took out a $600 loan from the bank. At the end of 5 years, she pays back the principal, plus $60 simple interest. the annual interest rate is 2%
How to find annual interest rateSimple interest is calculated using the simple interest formula
The formula is stated as
Simple interest = Principal * time * rate / 100
In the problem the give data include
principal = $600
rate= ?
time = 5 years
simple interest = 60
plugging in the values
Simple interest = Principal * time * rate / 100
60 = 600 * 5 * r / 100
60 * 100 = 3000r
r = 6000 / 3000
r = 2%
The annual interest rate is 2%
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In the graph below, which value is the dependent variable: Total Cost or Days?
Days
Total cost
Answers
The dependent variable represented on the graph is the Total Cost
How to determine the dependent variable?From the question, we have the following parameters that can be used in our computation:
x-axis = Daysy-axis = Total CostAs a general rule:
The variable represented on the y-axis is the dependent variable
From the given parameters, we have
x-axis = Daysy-axis = Total CostThis means that
y-axis = Dependent variable
This can also be expressed as
Dependent variable = Total Cost
This means that the dependent variable is Total Cost
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Help please !!!???!!!!
Answers
Answer:
the lenth of the court is 78 feet
A circle has a diameter of 100 inches. Which expression could be used to find the area of the circle?
100² × π
50² X π
2 × 50² × π
2× 10² x π
Please help if possible
Answers
The correct expression for the area of the circle will be;
⇒ 50² × π
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
A circle has a diameter of 100 inches.
Now,
Since, A circle has a diameter of 100 inches.
Hence, A circle has a radius = 100/2 = 50 inches.
We know that;
The area of circle = πr²
Where, 'r' is radius of the circle.
Substitute all the values, we get;
⇒ The area of circle = πr²
⇒ The area of circle = 50² × π
Thus, The correct expression is,
⇒ 50² × π
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You are given a function f(x) that is continuous on the closed interval [2,10] and differentiable on the open interval (2,10). If f(2)=5 and the average rate of change is bounded between -1 and 3, that is: -1≤f'(x)≤3, what is the smallest possible value for f(10)?
Answers
Answer: -3
Step-by-step explanation:
[tex]-1 \leq f'(x) \leq 3\\\\-\int^{10}_{2} dx \leq \int^{10}_{2} f'(x) \text{ }dx \leq 3\int^{10}_{2} dx\\\\-8 \leq f(10)-f(2) \leq 24\\\\-8 \leq f(10)-5 \leq 24\\\\-3 \leq f(10) \leq 29[/tex]
Booker T. Washington Middle School found two companies that would deliver healthy snacks to school. The tables below show the price charged by each company. How many more times does Company B charge per snack than Company A?
Answers
Two more times company B charge per snack than company A
What is meant by ratio?A ratio in mathematics displays the multiplicative relationship between two numbers. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the proportion of oranges to the overall amount of fruit is 8:14, and that of lemons to oranges is 6:8 (or 3:4). (or 4:7).
A ratio can have any number of numbers as its components, including counts of people or things, weights, lengths, and times, among other values.
From the two tables,
0.5/0.25=2
1/0.5=2
1.5/0.75=2
2/1=2
Therefore, 2 more times company B charge per snack than company A
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A restaurant manager can spend at most $600 a day for operating costs and payroll. It costs $100 each day to operate the bank and $50 a day for each employee. Use the following inequality to determine how many employees the manager can afford for the day, at most:
50x + 100 ≤ 600
Answers
One week, Jayden earned $87.50 at his job when he worked for 5 hours. If he is paid
the same hourly wage, how many hours would he have to work the next week to earn
$105.00?
Answers
Answer:
Here answer
Step-by-step explanation:
To find the number of hours Jayden would have to work to earn $105.00, we need to first find his hourly wage. We can do this by dividing his total earnings by the number of hours he worked:
hourly wage = total earnings / number of hours worked
= $87.50 / 5 hours
= $17.50/hour
Now that we know Jayden's hourly wage, we can use it to find the number of hours he would have to work to earn $105.00. We can do this by dividing the total amount he wants to earn by his hourly wage:
number of hours = total earnings / hourly wage
= $105.00 / $17.50/hour
= 6 hours
Therefore, Jayden would have to work for 6 hours to earn $105.00 at his job.
an airplane begins its descent with an average speed of 240 at an angle of depression of . how much altitude will the plane lose in ? round to the nearest tenth of a mile.
Answers
At an average speed of 240 mph and an angle of depression of 45 degrees, the plane will lose 1.1 miles of altitude.
1. Convert the average speed of 240 mph into feet per second: 240 mph x 1.467 = 352 feet per second
2. Calculate the total distance traveled by the plane in one second: 352 x 1 = 352 feet
3. Calculate the total vertical distance traveled by the plane in one second: 352 x sin45 = 250 feet
4. Calculate the total altitude lost by the plane in 1 second: 250 x 1 = 250 feet
5. Calculate the total altitude lost by the plane in 1 minute: 250 x 60 = 15,000 feet
6. Convert the total altitude lost in feet to miles: 15,000 feet / 5,280 = 2.84 miles
7. Round to the nearest tenth of a mile: 2.84 miles = 1.1 miles
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Write Expressions Word Problems 1.
You run a small business and would like to print some business cards.
Staples offers color business cards for a small fee.
The cost is $.75 per card.
A) Write an expression for the total cost (in dollars) if you print b business cards. B) How much does it cost you to print 50 business cards?
Answers
Step-by-step explanation:
cost of business card - $.75 ( per card )
I want to print 50
So we will multiply 75 × 50
75
×50
00
355×
=375
$.375 will be the cost of the same
A shopper needs 24 sandwich rolls the store sells identical rolls and two differently sized packages the store sells a six-pack for $5.28 and four-packs for $3.40 should the shopper buy four six-packs or four 4-packs?
Answers
The shopper must buy six 4-packs sandwiches.
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,
Number of sandwiches to buy = 24
Cost of six-pack sandwiches = $5.28
Cost of four-pack sandwiches = $3.40
Cost of 24 sandwiches from the six-pack.
= 4 x 5.28
= $21.12
Cost of 24 sandwiches from the four-pack.
= 6 x 3.40
= $20.4
Thus,
Six four-pack sandwiches are cheaper than four six-pack sandwiches.
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Which method is best for root finding?
Answers
Answer:
on the value of the root may produce a value of the polynomial at the approximate root that is of the order of. For avoiding these problems, methods have been elaborated, which compute all roots simultaneously, to any desired accuracy. Presently the most efficient method is Aberth method.
The table below represents a linear function.
\def\arraystretch{1.5} \begin{array}{|c|c|c|c|c|} \hline n & -3 & 1 & 5 & 9 \\ \hline f(n) & -3 & 5 & 13 & 21 \\ \hline \end{array}
n
f(n)
−3
−3
1
5
5
13
9
21
What is the slope?
Answers
Answer:
2
Step-by-step explanation:
if you do change in y/change in x it would be 8/4 with simplifies down to 2
Find the coordinates of Triangle KLM after a translation to the right by 8 units, then a reflection across the x-axis. Show your work or explain what steps you take to find your answer.
Answers
The new coordinates of triangle KLM after the given translation is;
M'(6, 1)
L'(1, 4)
K'(4, 8)
How to find the coordinates of translation?In transformations, there are different types such as reflection, dilation, translation e.t.c
Now, translation is what we are dealing with here and translation is a rigid transformation which means that it does not alter the dimensions of the figure after transformation. Translation is just moving the object from one point to another.
In translation, the size, the shape and the orientation of the image remain the same as that of the original object. Thus, the same orientation means that the object and image are facing the same direction.
The given coordinates of the triangle are;
M(-2, 1)
L(-7, 4)
K(-4, 8)
Now, If you move horizontally 8 units to the right, it means that 8 is added to the x-coordinate of each of the vertices. Thus, the transformation rule here is;
(x, y) → (x + 8), y
Therefore the new coordinates of triangle KLM are;
M'(-2 + 8, 1) = M'(6, 1)
L'(-7 + 8, 4) = L'(1, 4)
K'(-4 + 8, 8) = K'(4, 8)
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Find the equation of a parabola with its vertex at the origin and directrix x = 3.
Answers
The equation of a parabola is y²+12x=0.
In mathematics, what is a parabola?A parabola is a U-shaped plane curve in which any point is an equal distance from both a fixed point (known as the focus) and a fixed straight line (known as the directrix).
What exactly are the three parabola equations?Parabola functions are classified into three types: standard form, vertex form, and intercept form (also known as factored).
as per the given question:
We have a vertex at (0,0) and the directrix is x = 3, a line parallel to the y-axis, it must have a focus at (3,0).
The parabola equation represents the locus of a point (x, y) that moves so that its distance from x=3 and (3,0) is equal. As a result, the parabola equation is, An equation of the parabola represents the locus of a point (x, y), which moves so that its distance from x=3 and (−3,0) are equal. Hence, the equation of a parabola is
(x−(−3))² + (y−0)² = (x−3)²
or (x+3)² + y² = (x−3)²
or x² + 6x + 9 + y² = x² − 6x + 9
or y² + 12x =0
Hence, The equation of a parabola is y²+12x=0.
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a square room has a floor area of 64 square meters. the height of the room is 9 meters. what is the area of all 4 walls?
Answers
Answer:
288 m^2
Step-by-step explanation:
each side of the room is 8 m ( 8x8 = 64)
So you have FOUR walls of widht 8 and height 9
area = FOUR * ( 9 *8) = 288 m^2
In a classroom 1/5 student get grade A; 3/10 got grade B and rest get grade C in math. Total number of students in the class is 50. Find how many students got grade C
Answers
Answer:
25
Step-by-step explanation:
make 1/5 and 3/10 with equivalent denominator which will give us 2/10 and 3/10 now add them and we get 5/10 5 is the half of ten so we will divide 50 over 2 and we will get 25
A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo paperclips weighs 2 pounds and an order of packing tape weighs 3 pounds. If x is the number of orders of paperclips and y is the number of orders of packing tape, which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (3, 0). Everything below and to the left of the line is shaded.
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (3, 0). Everything above and to the right of the line is shaded.
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the right of the line is shaded.
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the left of the line is shaded.
Answers
The first graph shows how many of each order could fit into a bag that was hanging from a hook. First, a detailed explanation: * Let's discuss the issue's solution.
Find graph?The quantity of orders of paperclips is x, and the weight of the order of jumbo paperclips is 2 pounds. The order of paperclips weighs 2 x = 2 x, the order of packing tape weighs 3 lbs., and the quantity of orders of packing tape is y. The weight of the tape order is 3 y = 3 y, the weight of the entire order is 2 x + 3 y, and the hook can only support a maximum weight of 6 y. 2x + 3y ≤ 6
The graph that depicts this inequality, Any line's equation is y = mx + c, where m represents its slope.
The y-intercept indicates to replace x in the equation by 0; the x-intercept indicates to replace y in the equation by 0; 2x - 3y 6 is the inequality. 2x + 3y = 6 is the equation for the line.
- Subtract 2x from both sides: 3y = 6 - 2x; - Divide both sides by 3: y = 6/3 - 2/3 x; - Locate the y-intercept: x = 0; y = 2;
The line crosses the y-axis at position (0 , 2)
– Locate the x-intercept.
∵ y = 0
∴ 0 = 2 - 2/3 x
- Adjust both sides by 2/3x.
∴ 2/3 x = 2
Increase both sides by 3.
Divide all sides by 2 to get the answer.
∴ x = 3
The line crosses the x-axis at position (3 , 0)
First and second from the figure.
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Dwight is packing for a vacation. He is deciding which books to bring. He wants to bring one book from each
genre. Given he has 3 science fiction, 8 business ethics, and 7 beet farming books, how many unique
combinations of books could be bring with him?
Answers
The number of unique combinations of books Dwight could bring with him is 168
How to determine the number of unique combinations?From the question, we have the following parameters that can be used in our computation:
Science fiction = 3
Business ethics = 8
Beet farming = 7
The number of unique combination of books is then calculated as
Number of unique combinations = Science fiction * Business ethics * Beet farming
Substitute the known values in the above equation, so, we have the following representation
Number of unique combinations = 3 * 8 * 7
Evaluate the products
Number of unique combinations = 168
Hence, the number of unique combinations is 168
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Question 1-1
Look at the geometric sequence.
8, 64, 512, 4,096, ..
What is the seventh term in the sequence?
O 32,768
O262, 144
O2,097, 152
o 134, 217, 728
Answers
The 7th term of the geometry sequence is 2,097, 152. Hence option C is the correct option.
What is a term of a sequence?
A phrase is used to describe each number in the series. The first term in the order 1, 3, 5, 7, 9,... is 1, the second is 3, the third is 5, and so on.
A geometric sequence is sequence such that the pervious term is multiplied by a constant number to get next term. The constant number is known as common ratio.
Given pattern is 8, 64, 512, 4,096, ..
The common ratio is 64/8 = 512/64 = 4096/512 = 8.
The first term of the sequence is 8.
The nth term of geometric sequence is ar^(n-1), where a is the first term, r is the common ratio.
The 7th term of the sequence is 8(8)⁷⁻¹ = 8(8)⁶ = 2,097, 152.
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During a single day at radio station WMZH, the probability that a particular song is played is 0.23. What is the probability that this song will be played on exactly 0 days out of 7 days? Round your answer to the nearest thousandth.
Answers
The probability that this song will be played on exactly 0 days out of 7 days, if The probability that a particular song is played is 0.23 is 0.008.
What is the combination?A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.
Given:
The probability that a particular song is played is 0.23,
As can be seen that the problem is of combination, so we have to choose 5 out of 7,
Calculate the combination as shown below,
⁷C₅ = 7! / (5! × 2!) = 7 × 6 / 2
⁷C₅ = 7 × 6 / 2
⁷C₅ = 21
Calculate the probability as shown below,
P = ⁷C₅ × (0.23)⁵ × (0.77)²
P = 0.008
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Evaluate each function.
g(n)=-n+ 5; Find g(1)
B) 4
D) -3
A) 6
C) 15
Answers
-(1)+5
Solution
Option B (4)
3. Solve each equation. Show your work.
a. 2x = 27 - x
Answers
Answer:
2x=27-x - given
3x=27 - add x to both sides
x=9 - divide both sides by 3
Step-by-step explanation:
[tex]2x=27-x[/tex]
Simplify:
[tex]2x=-x+27[/tex]
Add x to both sides:
[tex]2x+x=-x+27+x[/tex]
[tex]3x=27[/tex]
Divide both sides by 3:
[tex]\dfrac{3x}{3} =\dfrac{27}{3}[/tex]
[tex]\fbox{x = 9}[/tex]
What is the probability that the students will have a pop quiz on a randomly selected day? a. 0.25 b. 0.52 c. 0.77 d. 0.90
Answers
The probability that the students will have a pop quiz on a randomly selected day will be A. 0.25.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
From the information, the probability that students will not have a quiz is 75%. The probability that the students will have a pop quiz on a randomly selected day will be:
= 1 - 75%
= 0.25
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Complete question
The probability that students will not have a quiz is 75%. What is the probability that the students will have a pop quiz on a randomly selected day? a. 0.25 b. 0.52 c. 0.77 d. 0.90
Lin says she has memorized the lengths of a few right triangles, for example, 3, 4, and 5. She is trying to compile a list of several right triangles but needs your help.
Select all the lengths of triangles that are right.
1.) 8, 9, 64
2.) 2,4,6
3.) 1, 1, V2
4.) 7,19,22
5.) 5, 12, 13
Answers
How many 3/4-cup servings are in 5/12 cups of yogurt?
Answers
A box in the shape of a rectangular prism has the dimensions shown. What is the length of the interior diagonal of the box? Round to the nearest tenth. Enter your answer in the box. A rectangular prism 60 centimeters wide, 80 centimeters long, and 100 centimeters tall. A diagonal d is drawn from the upper right rear corner to the lowest left front corner.
Answers
It is to be noted that the length of the interior diagonal of the box whose dimensions are Height 100cm, Lenght, 80 cm, and width 60 cm, is 140.4cm.
What is the formula for the length of a right rectangular prism?
Recall that the formula for the diagonal length of a right rectangular prism is calculated as √(l² + w² + h²) units. So, the formula for the length of a right rectangular prism's diagonal is √(l²+w²+h²), where l is the length, b is the breadth, and h is the height.
Plugging in the values we have:
d² = 60² + 80² + 100²
Solving for d, we get:
d = √(660² + 80² + 100²)
= √(3600 + 6400 + 10000)
= √(20000)
= 140.4 cm
Thus, the length of the interior diagonal of the box is 140.4 cm.
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A food scientist studies the relationship between mass and calories in different types of
burritos. the scatter plot shows the data for 15 types of burritos. based on a line of best fit
for the data,
Answers
The number of calories for 180-gram burrito is 392
How to determine the number of calories for 180-gram burritoFrom the question, we have the following parameters that can be used in our computation:
The scatter plot
From the line of the best fit on the scatter plot, we have the following points
(0, 250) and (190, 400)
A linear function is modelled by:
y = mx + b
In which:
m is the slope, which is the rate of change
b is the y-intercept, which is the value of y when x = 0
Using the above points, we have
b = 250
This means that
y = mx + 250
From the point (190, 400), we have
400 = 190m + 250
So, we have
190m = 150
And, this gives
m = 15/19
So, the equation is
y = 15/19x + 250
For a 180-gram burrito, we have
y = 15/19 x 180 + 250
Evaluate
y = 392
Hence, the number of calories is 392
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Could someone pls explain on how to find the 5 number summary, Recall that the 5-number summary is the minimum, lower quartile, median, upper quartile, and maximum.
The numbers are 1 1 1 1 3 3 3 4 4 4 5 5 5 5 6 6 6 13 13 16 16 16 21 22 24 28 28
Answers
Maximum = 28, Minimum = 1, Lower Quartile = 3, Median = 5, and Upper Quartile = 16
The Five Number Summary is what?The minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum make up the five-number summary. The median is the middle value; Q1 is the median of the first half of the data, and Q3 is the median of the second half. The lowest is the smallest number, the maximum is the highest, the median is the intermediate value.
The 5 digit summary definition
minimal is a smaller number.
lower quartile: First-half median of the data.
median
upper quartile :Median of the second half of data
greatest number is maximum
The numbers are 1 1 1 1 3 3 3 4 4 4 5 5 5 5 6 6 6 13 13 16 16 16 21 22 24 28 28
minimum = smallest number = 1
lower quartile = Median of the first half of data = 1 1 1 1 3 3 3 4 4 4 5 5 5 = 3
median = median( middle value) = 5
upper quartile = Median of the second half of data = 6 6 6 13 13 16 16 16 21 22 24 28 28 = 16
maximum = largest number = 28
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