The function is equal to zero when x = -3 or +4
What are the zeros of a function?We know that a function is a mathematical rule. It is an instruction to perform an operation on a given set of values. In this case, we have the function given as; f(x)= x^2-x-12/x^2+x-12. Recall that the function is equal to zero when the numerator is equal to zero.
Now we have to solve the quadratic equation;
x^2-x-12 =0
x^2 - 4x + 3x - 12 = 0
x(x - 4) + 3(x - 4) = 0
(x - 3) (x - 4) =0
x = -3 or +4
We can now see that the function is equal to zero when x = -3 or +4
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I need help please……
Answer:
Its 3D 6U
or -2/-2
Step-by-step explanation:
a. Solve 3-√(x-3)=x algebraically.
After solving the expression 3-√(x-3)=x algebraically, we get the result as 3.
Isolate the square root from the left hand side √x-3 = 3-x
Eliminate the radical on the left hand side by squaring on both sides-
Both sides must be raised to the second power.
(√x-3)² = (3-x)²
After squaring we get
x-3 = x²-6x+9
Solving the quadratic equation-
We get rearranged equation as -
x² - 7x + 12 = 0
(x-4)(x-3)=0
x=4,3
Check if the first solution is correct by putting it in original equation-
putting x=3 in 3-√(x-3)=x we get 3-0=3
Hence 3 is correct.
Check if the second solution is correct by putting it in original equation-
putting x=4 in 3-√(x-3)=x we get 3-1=4 which is not true
hence 4 is rejected.
Therefore, after solving the expression 3-√(x-3)=x algebraically, we get the result as 3.
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+ Over the first 20 games of the season, the distribution of a basketball team's scores is bell shaped with a mean of 94 points per game and a high of 109. Over the next 10 games, the team scored 94, 110, 102, 93, 98, 99, 121, 96, 94, and 108 points. Which statement best describes the change in the team's average number of points per game? X The new mean is greater than the previous mean. The new mean is less than the previous mean. The new median is the same as the previous median. The new median is less than the previous median.
The new mean 101.5 is greater than the previous mean 94.
By adding up all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined. The median is the middle when a data set is sorted from least to greatest.
The distribution of a basketball team's score with a mean of 94 points per game and a high of 109 for the first 20 games.
Mean = 94,
Points per game = 94, 110, 102, 93, 98, 99, 121, 96, 94, and 108 points.
Therefore,
The new mean = ( sum of observations) / Number of observations
New mean = ( 94 + 110 + 102 + 93 + 98 + 99 + 121 + 96 + 94 + 108) / 10
New mean = 1015 / 10
New mean = 101.5
101.5 > 94
Now, the new mean is greater than the previous mean.
Hence, the correct option is (A).
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Life expectancy for all the different countries in the world ranges from a low of only 52.2 years (in sierra leone) to a high of 84.7 years (in hong kong). life expectancies are clustered at the high end, with about half of all the countries having a life expectancy between about 74 and the maximum of 84.7. a few countries, such as sierra leone, have a very low life expectancy.
a. what is the shape of the distribution of life expectancies for all countries?
a) symmetric.b) skewed to the right.c) skewed to the left.d) none of these.b. from the information given, estimate the median of the life expectancies.c. will the mean be larger or smaller than the median?
From the given distribution, we have that:
a) The distribution is skewed to the left.
b) The median is of 74.
c) The mean will be smaller than the median.
Figuring the skewness with the mean and the median:Mean greater than median: Positively(right) skewedMean less than the median: Negatively(left) skewedSince life expectancies are clustered at the high end, the outliers are small life expectancies, meaning that the mean will be smaller than the median and the distribution is skewed to the left.
The median of a data-set is the 50th percentile, the value that separates the bottom 50% of the data-set from the upper 50%.
In this problem, we have that about half of all the countries having a life expectancy between about 74 and the maximum of 84.7, meaning that 74 is the median.
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For two events X and Y, P(X) = , P(Y) = , and P(X|Y) = . Find the probabilities. 1. P(Y · X) = 2. P(Y/X) =
1. The probability given as P(Y∩X) is; 2/25
2. The probability given as P(Y) * P(X) is; 4/15
What is the probability?
We are given the following probabilities;
P(X) = 2/3 , P(Y) = 2/5 , and P(X|Y) = 1/5
1. We want to find P(Y ∩ X).
This means probability of the set intersection of Y and X
Since P(X) = 2/3 , P(Y) =2/5 , and P(X|Y) =1/5, it means that we have a conditional probability.
Thus; P(Y∩X) = P(Y) * P(X|Y)
P(Y∩X) = 2/5 × 1/5
P(Y∩X) = 2/25
2. We want to find P(Y) * P(X)
Plugging in the relevant values gives;
P(Y) * P(X) = 2/3 × 2/5
P(Y) * P(X) = 4/15
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Complete question is;
For two events X and Y, P(X) =2/3 , P(Y) =2/5 , and P(X|Y) =1/5 . Find the probabilities.
1. P(Y∩X) = ____
2. P(Y)· P(X) =____
I'm thinking of a number and if I subtract 8 and
multiply by -3, I get 21, what is my number?
Answer:
15
Step-by-step explanation:
Answer:
The number is 1
Step-by-step explanation:
Let the number be x
Subtract 8 from x ==> x - 8
Multiply by -3 ==> -3(x - 8) = -3(x) -3(-8) = -3x - 24
This equals 21
So
-3x + 24 = 21
Subtract 24 from both sides:
-3x + 24 - 24 = 21 - 24
==> -3x + 0 = - 3
-3x = -3
Divide by -3
==> -3x/-3 = -3/-3
x = 1
Check
1 - 8 = -7
-3(1-8) = -3 x -7 = 21
an electrical appliance will not work unless component qk does. component qk's reliability is 0.95. every other part of the appliance is 100% reliable. assume that we add a second back up for qk with reliability of 0.80 (this back up is the same as component qk but purchased from another manufacturer, so the reliability is different but it is also cheaper). what is the probability that the appliance does not work? (in this case, you have qk with reliability 0.95, qk first back up with reliability 0.95 and a second backup with reliability 0.80)
Answer:
0.99 or 99%
Step-by-step explanation:
This is actually much more simple than it sounds
Take 95% and add 80% of 5 because 5% of the time the QK piece will not work. 80% of 5 is 4. 95+4=99
Someone please help me! Ik its Sunday but i got sick so i couldnt do it over the weekend
Step-by-step explanation:
6 = 5/2x + k
6 = ( 5/2 . 2/1) + k
6 = 10/2 +k
6-5 = k
k = 1
For each pair of functions, find f(g(x)) and g(f(x)) .
f(x)=-x-7, g(x)=4 x
A composite function exists as a function that depends on another function. The values for f(g(x)) = 4x-7 and g(f(x)) = 4x -28
What is meant by composition function?In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.
Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.
Let the two functions be f(x) = -x-7 and g(x) = 4 x
f(g(x)) = f(4x)
f(4x) = 4x-7
g(f(x)) = g(x-7)
simplifying the above equation, we get
g(x-7) = 4 (x - 7) = 4x -28
g(x-7) = 4x - 28
Therefore, the value of f(g(x)) = 4x-7 and g(f(x)) = 4x -28
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What is this " the temperature is 1f at dusk. it is 8 degrees colder at dawn what is the temperature at dawn?'
The temperature at dawn is -7 F.
What is the temperature at dawn?If it is 8 degrees colder at dawn than it is at dawn, it means that the temperature is lower in the dawn than it is in the dusk. Thus, to determine the temperature at dawn, subtract 8 from the temperature at dusk.
Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign used to represent subtraction is -.
Temperature at dawn = termpature at dusk - difference in termpature
1 - 8 = -7
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Multiply and simplify. 3∛2x² . 7 ∛32x⁴
On multiplying and then simplifying 3∛2x² . 7 ∛32x⁴, we get, 84x⁶
How can square roots be multiplied?1. Split the radicands in half. A number known as a radicand appears underneath the radical symbol.
2. To multiple radicands, multiply the integers as if they were whole numbers. Always keep the item beneath a single radical sign.
3. Use factoring to exclude any perfect squares from the radicand. To achieve this, check whether any perfect squares have the radicand as a factor.
4. Position the square root of the ideal square before the radical sign. Don't change the second component of the radical symbol.
5. Square the square's root. Sometimes it is necessary to multiply a square root by itself.
Given,
3∛2x² . 7 ∛32x⁴
⇒ [tex]21 (2^{1/3} ) x^{2+4} . 32^{1/3}[/tex]
⇒ [tex]21 (2^{1/3} ) x^{6} . 2^{5/3}[/tex]
⇒ [tex]21 (2^{1/3 + 5/3} ) x^{6}[/tex]
⇒ [tex]21 (2^{2} ) x^{6}\\84x^{6}[/tex]
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What is the value of the expression below when y=5?
3y^2 +7y+2
Answer:
112
Step-by-step explanation:
3y^2 + 7y + 2
if y = 5, then 3(5^2) + 7(5) + 2
= 3(25) + 35 + 2
= 75 + 37
= 112
Find the values of x and y in parallelogram PQRS. PTy, TRx1, QTy, TSx = 7x+ 11
The values of x and y of the parallelogram PQRS are x = 2 and y = 11
What is the side length of the parallelogram?We're given the dimensions of parallelogram PQRS as;
PT = y
TR = 5x + 1
QT = 2y
TS = 6x + 10
T is the intersection of the two diagonals PR and QS and so the diagonals bisect each other.
The diagonal PR is cut into PT and TR, both of which are congruent or equal. Thus, PT = TR.
Similarly, the other diagonal QS is split in half as well. The two equal pieces are QT and TS. So QT = TS.
PT = TR
y = 5x + 1
and
QT = TS
2y = 6x + 10
Plugging the values gives;
2y = 6x + 10
2(y) = 6x + 10
2(5x + 1) = 6x + 10
2*5x + 2*1 = 6x + 10
10x + 2 = 6x + 10
10x + 2 - 6x = 6x + 10 - 6x
4x + 2 = 10
4x + 2 - 2 = 10 - 2
4x = 8
4x/4 = 8/4
x = 2
If x = 2, then y is...
y = 5x+1
y = 5*x+1
y = 5*2+1
y = 10+1
y = 11
Thus, the values of x and y of the parallelogram PQRS are x = 2 and y = 11
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Amy bought 8 packs of cherry fruilt snacks. Each pack has 7 fruilt snacks Mary bought tropical fruit snacks. Each tropical fruit snack packs has 9 trult
snacks
Amy bought 11 more fruit snacks than Mary. How many packs of tropical fruit snacks pid Mary buy?
A 12
B 5
C 8
D 10
Answer:
B - 5
Step-by-step explanation:
Amy = 8 packs × 7 snacks
Amy = 56 snacks altogether
Mary = Amy - 11
Mary = 56 - 11
Mary = 45 snacks altogether
Mary = 45 snacks / 9 tropical fruit snacks
Mary = 5 packs of tropical fruit snacks
Hope this Helps! :)
- Riona
Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total $1215 x $445
was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor was needed to complete the job?
Joy was charged the labor of 11 hours .
Joy was charged a total of $1215 from the landscaper for listed parts and labor.
He was charged $445 for listed parts
He was charged the rest for labor
The hourly rate for labor is $ 70
Let the number of hours worked by labor be x
so, we can form a linear equation here as 445 + 70x = 1215
Now we have to solve this linear equation
445 + 70x = 1215
70x= 1215 - 445
70x = 770
x = 770/ 70
x = 11
Therefore, 11 hours of labor were needed to complete the job.
The correct question is Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total $1215. $445 was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor were needed to complete the job?
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|5x|=3
this is absolute value of five x equals three
The value of the modulus function |5x| = 3 is x = 3/5 or x = -3/5.
What is a modulus function ?In mathematics modulus function is the absolute or numerical value of the function irrespective of the sign.It represents magnitude.We modulus functions when we want length, mass and for other variables when we want to represent their weight.
According to the given question |5x| = 3.
We know |x| = a implies x = a or x = -a.
∴ |5x| = 3 is
5x = 3
x = 3/5
Or
5x = -3.
x = -3/5.
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The cities M, N, and O, in respective order, lie approximately in a straight line. The distance from city M to city N is 45 miles. The distance from city M to city O is 50 miles. Find the distance from city N to city O.
Step-by-step explanation:
so, MN + NO = MO
MO = 50 miles
MN = 45 miles
therefore,
45 + NO = 50
NO = 50 - 45 = 5 miles
Sasha is aware that in the past few months her hips have become wider and her breasts have started to increase in size. these changes are due to?
Answer:
Probably puberty
Given f(x) = x² + 5x +6 and g(x) = x +2, find (g ◦ f)(x)
Answer:
x² + 5x + 8
Step-by-step explanation:
This issue is about "function composition",
(g ° f) means
g(f(x)) = g(x² + 5x +6)
= x² + 5x +6 + 2
= x² + 5x +8
The measure of ∠BQS is 78°. What is m∠NQS? *picture of the question is at the bottom*
Step-by-step explanation:
BQS=78
BQN=48
BQS+BQN=78+48=126
180-126=54°
NQS=54°
comfirm=BQN+BQS+NQS=180
48+78+54=180
Answer:
30°
Step-by-step explanation:
∠NQS + ∠BQN = ∠BQS
Knowing this information, we use the known measures to find ∠NQS
∠NQS + 48° = 78°
∠NQS = 78° - 48°
∠NQS = 30°
Thus, angle NQS is 30 degrees.
Hope this helps!
What can be concluded from the graph shown here?
Correct answer is D. Nothing can be determined from the given graph.
What may a graph be used to analyze?A graph is a type of graphic used to display data and show relationships. Graph analysis is helpful for identifying the overall trend, connecting experiment findings to the hypothesis, and creating hypotheses for next studies.
You may compare various figures, comprehend how various components affect the overall, or examine patterns using a chart or graph. Charts and graphs can also be helpful for seeing data that deviates from what you're used to or for assisting in the understanding of group relationships.
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Last year at a certain high school, there were 150 boys on the honor roll and 84 girls
on the honor roll. This year, the number of boys on the honor roll decreased by 12%
and the number of girls on the honor roll decreased by 25%. By what percentage did
the total number of students on the honor roll decrease? Round your answer to the
nearest tenth (if necessary).
The total percentage decrease in the number of students on the honor roll is 16.67%.
What is the percentage decrease?
Percentage is a measure of frequency that is used to express a number as a fraction of an amount out of 100. The sign used to denote percentage is %. In order to convert a number to percentage, multiply the number by 100.
The first step is to determine the number of boys on the honor roll this year.
Number of boys on the honor roll this year : (1 - percentage decrease) x number of boys last year
(1 - 0.12) x 150
0.88 x 150 = 132
The second step is to determine the number of girls on the honor roll this year.
Number of girls on the honor roll this year : (1 - percentage decrease) x number of girls last year
(1 -0.25) x 84
0.75 x 84 = 63
Total number of students on the honor roll last year = 150 + 84 = 234
Total number of students on the honor roll this year = 63 + 132 = 195
Percentage decrease :[ (195 /234) - 1] x 100 = 16.67%
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12z=108 what’s the value of z
Answer:
z = 9Step-by-step explanation:
12z=108 what’s the value of z
12z = 108
z = 108 : 12
z = 9
check
12 * 9 = 108
108 = 108
the answer is good
Find the acceleration of a car that takes 4 seconds to stop at a red light from a velocity of 80 km/h
Given the initial speed and time elapsed by the car, the negative acceleration that brings the car to a stop at the red light is -5.56m/s².
What is the acceleration of the car?
Newton's first equation of motions states that;
v = u + at
Where v is final velocity, u is initial velocity, a is acceleration and t is time.
Given the data in the question;
Since the car is stopping, final velocity v = 0Initial velocity u = 80 km/hTime elapsed t = 4sAcceleration = ?First, convert the unit of the initial velocity from kilometer per hour to meter per seconds
Initial velocity = 80 km/h = ( 80 × 5/18 )m/s = 2.2222 m/s
Now, plug these values into the equation above and solve for a.
v = u + at
0 = 22.2222m/s + ( a × 4s )
a × 4s = -22.2222m/s
a = 22.2222m/s ÷ 4
a = -5.56m/s²
Negative sign shows that the car is slowing down.
Given the initial speed and time elapsed by the car, the negative acceleration that brings the car to a stop at the red light is -5.56m/s².
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Write the given rate as a fraction in simplest form 452 calories un 8 servings
The calorie serving in simplest form is 56.5
The rate in mentioned question will be number of calories present per serving.
So writing the given information in the form of rate -
Rate of calorie per serving = 452/8
Now, to convert the rate of calories in simplest form, we will perform division of both numerator and denominator of fraction by a common number. We can directly divide the numerator and denominator of fraction with 8. Else, we can perform division by simpler numbers too.
Indirect method -
Lets begin the division by 4
Rate of calorie per serving = 113/2
Further dividing by 2
Rate of calorie per serving = 56.5
Direct method will also give the same result, which is rate of calorie per serving = 56.5.
Hence, in simplest form (decimal) the rate of calorie per serving is 56.5.
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What is the relationship between 23 and 26?
Answer:
23 and 26? which numbers would you like to know?
Step-by-step explanation:
Solve. Check for extraneous solutions. √2 x+6 - √x-1 =2
x = 5 is not an extraneous solution of the equation.
✓(2x + 6) - ✓(x - 1) = 2
✓(2x + 6) = 2 + ✓(x - 1)
Squaring both the sides of equation, we get
(✓(2x + 6))² = (2 + ✓(x - 1))²
2x + 6 = (2)² + (✓(x - 1))² + 2(2)(✓(x - 1))
2x + 6 = 4 + x - 1 + 4(✓(x - 1))
x + 3 = 4✓(x - 1)
Squaring again on both the side of the equation, we get
(x + 3)² = (4✓(x - 1))²
x² + 3² + 2×3×x = 16(x - 1)
x² + 9 + 6x = 16x - 16
x² - 10x + 25 = 0
By applying middle term splitting on equation (1), we get
x² - 5x - 5x + 25 = 0
x(x - 5) -5(x - 5) = 0
(x - 5) (x - 5) = 0
x = 5 and 5.
Check for extraneous solutions by putting value of x in original equation -
✓(2×5 + 6) - ✓(5 - 1) = 2
✓16 - ✓4 = 2
4 - 2 = 2
2 = 2
LHS = RHS
x = 5 is not an extraneous solution of the equation.
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Example 2:
If f(x) = 2x+5, find each value. Show all work.
a) f(-2)
b) f(1)+5
c) f(x+3)
Answer: a. 1
b. 12
c. 2x+11
Step-by-step explanation:
f(x) = 2x+5
a. f(-2)=
2(-2)+5=
-4+5=1
b. f(1)+5=
2(1)+5+5=
2+5+5=12
c. f(x+3)=
2(x+3)+5=
2x+6+5=2x+11
26.
A gallon of milk costs $2.30 per gallon.
What is the cost per cup of milk?
What is the cost per fluid ounce of milk?
What is the cost per quart of milk?
The cost per cup of milk as required in the task content is; $0.14375.
The cost per fluid ounce of milk as required in the task content is; $0.018.
The cost per quart of milk as required in the task content is; $0.575.
What is the cost per unit measure of milk as given in each case scenario in the task content?It follows from the task content that the cost of each unit measure of milk is to be determined. Therefore, since the cost per gallon of milk is; $2.30.
1). Since there are 16 cups of milk per gallon, it follows that the cost per cup of milk is; 2.30/16 = $0.14375
2). Also, Since there are 128 fluid ounces of milk per gallon, it follows that the cost per fluid ounce of milk is; 2.30/128 = $0.018
3). Also, Since there are 4 quarts of milk per gallon, it follows that the cost per quart of milk is; 2.30/4 = $0.575
Ultimately, the cost per unit measure of milk in each case scenario has been determined and is as represented above.
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Look at this graph.
y
x
-100
-80
-60
-40
-20
20
40
60
80
100
-100
-80
-60
-40
-20
20
40
60
80
100
0
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
The equation of the line in the graph in slope-intercept form is: y = -5x - 30.
How to Write an Equation of a Line in Slope-intercept Form?To be able to write the equation of a line in slope-intercept form, y = mx + b, find the value of the slope (m) = rise/run, and the value of the y-intercept (b), which is the value of y where the line intercepts the y-axis.
From the given graph, we have:
Slope (m) = rise/run = -50/10
Slope (m) = rise/run = -5
The y-intercept (b) = -30
Substitute m = -5 and b = -30 into y = mx + b:
y = -5x + (-30)
y = -5x - 30
Thus, the equation of the line in the graph in slope-intercept form is: y = -5x - 30.
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