Answers
9514 1404 393
Answer:
x = 2 or x = 9
Step-by-step explanation:
To use the quadratic formula, we first need the equation in standard form for a quadratic. We can get there by multiplying the equation by 3(x -3).
2(3) +4(3(x -3)) = (x +4)(x -3)
6 +12x -36 = x² +x -12
x² -11x +18 = 0
Using the quadratic formula to find the solutions, we have ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-11)\pm\sqrt{(-11)^2-4(1)(18)}}{2(1)}\\\\x=\dfrac{11\pm\sqrt{49}}{2}=\{2,9\}[/tex]
The solutions are x=2 and x=9.
Related Questions
Ken needs a total of $410 to buy a new bicycle. He has $35 saved. He earns $15 each week delivering newspapers. How many weeks will Ken have to deliver papers to have enough money to buy the bicycle?
Thanks so much! :D
Answers
Answer:
25 weeks
Step-by-step explanation:
Since we already know that he has $35 buck-a-roons saved, we can just subtract that from the cost of the bicycle to find the actual price—which would be 375. Then, we know that for every week, he gains $15 bucks. Therefore we know that 15 would be our variable so we can create the following equation:
15x + 35 = 410
15x = 375
15x/15 = 375/15
x = 25
After 25 weeks, Ken will have enough money to buy the bicycle.
In the figure, ∆BAT ≅ ∆CAT. Which statement is not true by CPCTC? ∠BTA ≅ ∠CTA ∠BAT ≅ ∠CAT
Answers
Answer:
The two choices are true by CPCTC. Are there other choices that were not posted?
write 20.99988 as a mixed number
Answers
Answer:
Wouldn't it just be
24997
20 ------------
25000
Step-by-step explanation:
Answer:
20 24997/25000
Step-by-step explanation:
1. Convert 0.99988 into a fraction...99988/100000
2.Simplify with greatest common factor.....99988/4=24997 100000/4=25000
24997/25000
3. Add 20 to 24997/25000......20 24997/25000
1.1.3 what is the the perimeter of a swimming pool if the length is 4,5m and the breadth is 3m? 1.1.4 Define the following concepts :a. Ratio. b. Rate
Answers
The perimeter of the swimming pool is 15m
A swimming pool is rectangular in nature. The perimeter of the rectangular pool is expressed using the formula;
[tex]P=2(L+W)[/tex]
Given that
Length L = 4.5m
Width W = 3m
Get the perimeter
[tex]Perimeter = 2(4.5+3)\\Perimeter = 2(7.5)\\Perimeter = 15m[/tex]
Hence the perimeter of the pool is 15m
1.1.4 Rate is defined as the ratio between two quantities with a different unit. Examples of rates are;
meter per second, miles per hourcalories per serving etcThe ratio is simply defined as the ordered pair between two variables x and y, For instance,
The ratio of x to y is x:y.If there are 5 pencils and 2 pens in a carton, then the ratio of the pencil to pen is 5:2.Learn more on ratio and rate here: https://brainly.com/question/24325733
From a group of 11 people, 4 are randomly selected. What is the probability the 4 oldest people in the group were selected
Answers
The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.
Given that:
Find how many ways the 4 oldest people can be selected from the group.
Since the 4 oldest people are already determined, there is only 1 way to select them.
n = 11 (total number of people in the group) and k = 4 (number of people to be selected).To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:
Number of ways to choose k items from n items :
C(n,k) = n! / (k!(n-k)!)
Calculate the total number of ways to select 4 people from the group:
Plugging n and k value from given data:
C(11,4 )= 11! / (4!(11-4)!)
On simplifications gives:
C(11, 4) = 330.
Calculate the probability:
Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people
Plugging the given data:
Probability = 1 / 330
Probability ≈ 0.00303 or 0.303%.
Therefore, the probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.
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1. Hypothesis Test. Gender bias researchers compared the promotion rate of 412 women in manufacturing management positions to the national average which was known to be 75 months for a mostly male population. They measured the number of months each woman worked in middle management. Given a 0.01 level of significance, the correct statistical conclusion is to reject the null.
A. True
B. False
2. Hypothesis Test. Gender bias researchers compared the promotion rate of 412 women in manufacturing management positions to the national average which was known to be 75 months for a mostly male population. They measured the number of months each woman worked in middle management before being promoted to senior management, and found an average 79 months (s.d. = 19). Researchers want to know if women are promoted more slowly (i.e. after a larger number of months). What is the correct research conclusion?
A. Evidence suggests there is no difference in promotion rates.
B. Evidence suggests a small difference in promotion rates favoring males.
C. Evidence suggests a large difference in promotion rates favoring males.
D. No way to tell.
Answers
Answer:
1. B. False
2. B. Evidence suggests a small difference in promotion rates favoring males.
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis.
What should be added to p to get p+q?
Answers
Answer:
Step-by-step explanation:
The correct answer is q
Because we have been given the equation p + q already so if we observe the equation carefully we see that if we add the variable q to the variable p we get the answer p + q
Find the length of GV¯¯¯¯¯¯¯¯ A. 43.92 B. 33.1 C. 41.45 D. 68.87
Answers
Answer:
The answer is option AStep-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find GV
To find GV we use cosine
cos∅ = adjacent / hypotenuse
From the question
GV is the adjacent
GC is the hypotenuse
So we have
[tex] \cos(37) = \frac{GV}{GC} [/tex]GC = 55°
GV[tex] \cos(37) = \frac{GV}{55} [/tex]GV = 55 cos 37
GV = 43.92495
We have the final answer as
GV = 43.92Hope this helps you
Question 1: A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse?
A)Right
B)Obtuse
C)Can't be determined
D) Acute
Question 2: A 15-foot statue casts a 20-foot shadow. How tall is a person who casts a 4-foot-long shadow?
A)0.33 feet
B)3.75 feet
C)3 feet
D)5 feet
Question 3: A triangle has sides with lengths 17, 12, and 9. Is the triangle right, acute, or obtuse?
A)Acute
B)Right
C)Can't be determined
D)Obtuse
Question 4: Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?
A)21.34 ft.
B)21.93 ft.
C)27.73 ft.
D)19.21 ft.
Answers
Answer:
Question 1 = D) Acute
Question 2 = C)3 feet
Question 3 = D) Obtuse
Question 4 = C)27.73 ft.
Step-by-step explanation:
Question 1: A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse?
In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem
Where:
If a² + b² = c² = Right angle triangle
If a² +b² > c² = Acute triangle.
If a² +b² < c² = Obtuse triangle.
It is important to note that the length ‘‘c′′ is always the longest.
Therefore, for the above question, we have lengths
5 = a, 6 = b and c = 7
a² + b² = c²
5² + 6² = 7²
25 + 36 = 49
61 = 49
61 ≠ 49, Hence 61 > 49
Therefore, this is an Acute Triangle
Question 2: A 15-foot statue casts a 20-foot shadow. How tall is a person who casts a 4-foot-long shadow?
This is question that deals with proportion.
The formula to solve for this:
Height of the statue/ Length of the shadow of the person = Height of the person/ Length of the shadow of the person
Height of the statue = 15 feet
Length of the shadow of the person = 20 feet
Height of the person = unknown
Length of the shadow of the person = 4
15/ 20 = Height of the person/4
Cross Multiply
15 × 4 = 20 × Height of the person
Height of the person = 15 × 4/20
= 60/20
Height of the person = 3 feet
Therefore, the person is 3 feet tall.
Question 3: A triangle has sides with lengths 17, 12, and 9. Is the triangle right, acute, or obtuse?
In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem
Where:
If a² + b² = c² = Right angle triangle
If a² +b² > c² = Acute triangle.
If a² +b² < c² = Obtuse triangle.
It is important to note that the length ‘‘c′′ is always the longest.
Therefore, for the above question, we have lengths 17, 12, 9
9 = a, 12 = b and c = 17
a² + b² = c²
9² + 12² = 17²
81 + 144 = 289
225 = 289
225 ≠ 289
225 < 289
Hence, This is an Obtuse Triangle.
Question 4: Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?
To calculate how far apart the two friends are we use the formula
Distance = √ ( Length² + Breadth²)
We are given dimensions: 12ft by 25ft
Length = 12ft
Breadth = 25ft
Distance = √(12ft)² + (25ft)²
Distance = √144ft²+ 625ft²
Distance = √769ft²
Distance = 27.730849248ft
Approximately ≈27.73ft
Therefore, the friends are 27.73ft apart.
What is the value of x in the geometric sequence x,3,−1/3
Answers
Answer:
x=27
Step-by-step explanation:
the answer is proved in the diagram above
The value of x is 27
What is Geometric progression?A geometric progression is a special type of progression where the successive terms bear a constant ratio known as a common ratio. It is also known as GP. The GP is generally represented in form a, ar, ar2.... where a is the first term and r is the common ratio of the progression. The common ratio can have both negative as well as positive values. To find the terms of a geometric series, we only need the first term and the constant ratio.
The geometric progression is of two types. They are
finite geometric progression andinfinite geometric progression.Given:
x,3,−1/3
First term, a
second term
ar= 3
a= 3/r
third term
ar² = -1/3
a= -1/3r²
So,
3/r= - 1/3r²
9r= 1
r= 1/9
So,
ar= 3
a= 27.
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Find an equation for the surface consisting of all points P in the three-dimensional space such that the distance from P to the point (0, 1, 0) is equal to the distance from P to the plane y
Answers
Answer:
x^2 +4y +z = 1
Step-by-step explanation:
Surface consisting of all points P to point (0,1,0) been equal to the plane y =1
given point, p (x,y,z ) the distance from P to the plane (y)
| y -1 |
attached is the remaining part of the solution
100 pointer and will mark brainliest thank you. Hi! I ask that you provide a digital scatter plot image of this graph and predict the line of best fit and make sure to sketch it on the graph aswell. Thank you. Arm Span (inches) Height (inches) 58 60 49 47 51 55 19 25 37 39 44 45 47 49 36 35 41 40 46 50 58 61 And then provide the answers to these questions about the scatter plot which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way. Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined. What does the slope of the line represent within the context of your graph? What does the y-intercept represent Test the residuals of two other points to determine how well the line of best fit models the data. Use the line of best fit to help you to describe the data correlation. Using the line of best fit that you found, approximate how tall is a person whose arm span is 66 inches According to your line of best fit, what is the arm span of a 74-inch-tall person
Answers
I used arm span as the x-axis and height as the y-axis; arm span is the independent variable because height is typically dependent on arm span. Although the opposite could be argued for.
The equation of the line of best fit is y= 12+(7/9)x. To get the slope I used the points (37,39) and (19,25). The slope is therefore 14/18=7/9. The slope represents that height increases by 7/9 inches when arm span increases by 1 inch. The y-intercept 12 represents roughly the height when arm size is very small. I tested the residuals of the points (47,49) and (58,61). The respective predictions are 48.556 and 57.111. The respective residuals are then (49-48.556)=0.444 and (61-57.111)=3.889. It seems that the line models the data well until the x values get larger, where the performance decreases. The line of best fit with its positive slope indicates that there is a positive correlation with arm span and height.
Using the model, a person with arm span 66 inches has a height of 12+(7/9)*66= 63.333 inches. A person with 74 inches height has an estimated arm span of 62*9/7= 79.714 inches.
The equation of best fitted line is given as follows
[tex]\rm y = 0.955x+ 3.787 \\with \; R^2 = 0.951[/tex]
The y intercept 3.787 represents the height of that is independent of Arm span.
The height of the person whose arm span is 66 inches is 66.817 inch.
The arm span of a person whose height is 74 inches is 73.52 inch
According to the given data the arm span and heights are given in inches
Using Microsoft excel we can draw the scatter plot of both the variables such that arm span is on X axis and Height is on Y axis
The image for the excel work done showing calculations and scatter plot is attached.
Now we can fit the linear tread line and to find out the equation of fitted line just tick on the " show equation" line option of trend line fitting
The equation of best fitted line is given as follows
[tex]\rm y = 0.955x+ 3.787 .....(1) \\with \; R^2 = 0.951[/tex]
Slope of line of best fit = 0.955
So we can conclude that height (Y) is related to Arm span according to equation (1)
Equation (1) shows the equation of line of best fit for the given data
The y intercept 3.787 represents the height of that is independent of Arm span.
So the height of the person whose arm span is 66 inches is given following
[tex]\rm y = 0.955 \times 66+ 3.787 \\y = 66.817 \; inch[/tex]
Similarly the arm span of a person whose height is 74 inches
[tex]\rm 74 = 0.955x +3.787 \\x = 73.52 \; inches[/tex]
For more information please refer to the link given below
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What is the sum of the interior angles of a regular polygon with 5 sides?
A. 1260
B. 180
C. 360
D. 540
Answers
Answer:
540 is the ans
Step-by-step explanation:
this is the correct answer
180
Step-by-step explanation:
the measure of interior angles of polygon =180×(n-2)
and is in group 38 Rock she can put them into groups of 10 rocks or as single rocks what are the different ways Ann can group the rocks?
and is grouping 38 rocks she can put them into groups of 10 rocks or has single rocks what are the different ways and can group The Rocks
Answers
Answer:
She can put the rocks into groups of 19.
That would give her 2 groups.
Step-by-step explanation:
How many vehicles have been driven less than 200 thousand kilometers?
Answers
The number of vehicles that drove less than 200, 000 km is 12 vehicles
How to find the vehicle that drove less than 200 thousand km?The bar char represents the distance in thousand of km vehicles drove.
3 vehicle drove for 50 thousand kilometres.
4 vehicle drove for 100 thousand kilometres.
5 vehicle drove for 150 thousand kilometres.
Therefore, the total vehicle that drove for less than 200 thousand kilometres is as follows:
total vehicle that drove for less than 200, thousand km = 3 + 4 + 5 = 12 vehicles
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Answer:
2
Step-by-step explanation:
write the first 10 multiples of 2 and 3 and find LCM.
Answers
Answer:
multiples of 2 2,4,6,8,10,12,14,16,18,20
multiples of 3 3,6,9,12,15,,18,21,24,27,30
Step-by-step explanation:
Lcm is 6
Select the table representing a linear function. (Graph them if necessary.)
O A. x 0
7
2 3
y 1 2 56
B. х 0
7
3
2
0
y -2 -1
-1
O c. xo
1
N
3
y 10 12 14 16
-OD. x 0 1 2 3
y 5 3 1 2
Answers
Answer:
Option C
Step-by-step explanation:
the linear equation y = 2x+10 matches with option c
PLEASE HELP!!
Solve for y
a) 8
b) 12
c) 3V7
d) 4V7
Answers
Answer:
C. [tex] y = 3\sqrt{7} [/tex]
Step-by-step explanation:
Based on the right triangle altitude theorem, the altitude, y, in the diagram above, equals the geometric mean of 9 and 7.
This implies => [tex] y = \sqrt{9*7} [/tex]
Thus, solve for y.
[tex] y = \sqrt{9} * \sqrt{7} [/tex]
[tex] y = 3\sqrt{7} [/tex]
The answer is C. [tex] y = 3\sqrt{7} [/tex]
Apply the square root principle to solve (x-5)^2-40=0
Answers
Answer: {5 ± 2√10, 5 - 2√10}
Step-by-step explanation: First isolate the binomial squared by adding 40 to both sides to get (x - 5)² = 40.
Next, square root both sides to get x - 5 = ± √40.
Notice that root of 40 can be broken down to 2√10.
So we have x - 5 = ± 2√10.
To get x by itself, add 5 to both sides to get x = 5 ± 2√10.
So our answer is just {5 ± 2√10, 5 - 2√10}.
As a matter of form, the number will always come before the
radical term in your answer to these types of problems.
In other words, we use 5 ± 2√10 instead of ± 2√10 + 5.
Use the graph showing Debra's account balance to answer the question that follows. ^
About how long will it take for Debra's account balance to equal $60?
A - 6 months
B - 6 years
C - 3 months
D - 3 years
Answers
Answer: 2 years
Step-by-step explanation:
In the given graph, we have
Account Balance ($) on y-axis
Time (years) on x-axis.
To know the time taken to get a balance of $60 , we check the point corresponding to 60 at y-axis and then join it to the line of the function and stop.
Then from there we drop a line to x-axis.
We get x=2.
That is it will take 2 years to get $60 balance in Debra's account.
So the correct answer is 2 years.
A fifth grade teacher calculates that 27% of her students are late for class. If the teacher is right, what is the probability that the proportion of late students in a sample of 724 students would differ from the population proportion by less than 4%? Round your answer to four decimal places.
Answers
Answer:
answer: 0.9479
hope I helped
y x1 x2
10 1 16
11 5 11
15 5 14
15 9 11
20 7 1
23 11 8
27 16 7
32 21 3
a. Using technology, construct a multiple regression model with the given data.
b. Interpret the meaning of the values for b1 and b2.
Answers
Answer:
ŷ = 0.964X1 - 0.336X2 + 13.066
b1 = 0.964 which is the unit change in the value of y when x1 changes.
b2 = - 0.336 which is the unit change in the value of y when x2 changes
Step-by-step explanation:
Y
10
11
15
15
20
23
27
32
X1
1
5
5
9
7
11
16
21
X2
16
11
14
11
1
8
7
3
The general form of a multiple regression equation is in form:
ŷ = b1x1 + b2x2 + c
Where,
ŷ = predicted or dependent variable
b1 and b2 = slope or gradient Coefficient for the independent or predictor variables x1 and X2 respectively.
c = intercept (constant)
Using the online multiple regression calculator, the model obtained by Inputting the values is written below:
ŷ = 0.964X1 - 0.336X2 + 13.066
Value of b1 = 0.964 which is the unit change in the value of y when x1 changes.
Value b2 = - 0.336 which is the unit change in the value of y when x2 changes
What is the opposite of the opposite of negative 52?
Answers
Answer:
-52
Step-by-step explanation:
Think of it this way. Opposite means to take the negation. So we are taking the negation of the negation of negative 52. This means mathematically:
- ( - ( -52 ) ) == -52
Cheers.
Which geometric sequence has a first term equal to 55 and a common ratio of -5? {-55, 11, -2.2, 0.44, …} {55; 275; 1,375; 6,875; …} {55, 11, 2.2, 0.44, …} {55; -275; 1,375; -6,875; …}
Answers
Answer:
The answer is 55, -275, 1375, -6875......
Step-by-step explanation:
I need help on this question :(
Answers
Explanation:
FT bisect angle EFD dividing it into 2 equal angles (EFT and DFT)
And EFD = 80
We get :
EFT = 80/2
EFT = 40
And EFT + DFT = EFD = 80 degree
Therefore EFT = 40 degrees
What's 955 ÷ 35 ?
[tex]955 \div 35[/tex]
Answers
Answer:
Hello
Step-by-step explanation:
955÷35
27.2857142857
Or
35/955
35)955(27
-945
________
10
I hope this works♥️
The weight of an object on moon is 1/6 of its weight on Earth. If an object weighs 1535 kg on Earth. How much would it weigh on the moon?
Answers
Answer:
255.8
Step-by-step explanation:
first
1/6*1535
=255.8
The number under the radical sign or square root sign is called the
Answers
Answer:
Radicand
Step-by-step explanation:
The term (or number) whose square root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in this case 9.
Fourteen boys and 21 girls will be equally divided into groups. Find the greatest number of groups that can be created if no one is left out.
Answers
Answer:
7 groups can be made each with five people :)
Solve this and I’ll give u 5 stars and brainleist
Answers
Answer:
notice: temperature rises quickly at sunrise, and drops before sunsetwonder: whether this location is shaded by mountains later in the dayStep-by-step explanation:
notice
The temperature starts off below zero in the early morning and stays cold until the sun comes up. Then it warms rapidly to an above zero temperature that peaks in early afternoon. Once the sun gets lower, the temperature starts cooling off again. (The daily temperature range of 25-27 degrees is pretty typical for partly-cloudy sky conditions and stable weather.)
wonder
We wonder if this isn't a location that is on the east- or north-side of a mountain, or in a mountain valley, where the sun hits it early and is shaded later in the day. (The topo map attached seems to show it is in such a location.)