Denominator has been factorized on the right.
Now we need to write this fraction as a sum of two fraction.
[tex]\frac{3x-5}{(x+4)(x-8)}=\frac{A}{(x+4)}+\frac{B}{(x-8)}=\frac{A(x+4)+B(x-8)}{(x+4)(x-8)}[/tex][tex]A(x+4)+B(x-8)=3x-5\text{ at this stage we will find A B constants}[/tex]when x = 8 we have following
[tex]A(8+4)+B(8-8)=3\cdot8-5\rightarrow12A+0=19\rightarrow A=\frac{19}{12}\approx1.58[/tex]Similarly when x =-4 A = 17/12 these are the constants
Questions 12-15. Data from Ivy Tech’s advising center shows that their wait times follow a normal distribution. Use theEmpirical Rule to answer the following questions. 5 10 15 20 25 30 3512. What percent of students will wait between 15 and 25 minutes? (round to the nearest whole number)13. What percent of students will wait less than 20 minutes? (round to the nearest whole number)14. What percent of students will wait more than 35 minutes? (round to the hundredths place)15. If 5,300 students come to the advising center, how many students would wait more than 35 minutes? (round to thenearest student)
Answer:
12. 68%
13. 50%
14. 0.15%
15. 8 students
Step-by-step explanation:
Given a normal distribution with mean 20 and standard deviation 5, you want several probabilities based on the empirical rule.
Empirical ruleThe empirical rule tells you the percentages of a normal distribution that are within 1, 2, or 3 standard deviations of the mean. They are ...
within 1: 68%within 2: 95%within 3: 99.7%12. Between 15 and 25Wait times between 15 and 25 are within 20±5, so within 1 standard deviation of the mean. The percentage of students waiting 15–25 minutes is 68%.
13. Less than 20The mean of the distribution is 20, which is its line of symmetry.
50% of students will wait less than 20 minutes.
14. More than 3535 is 3 standard deviations above the mean, so the fraction in this group is half of the difference between 1 and 99.7%.
0.15% of students will wait more than 35 minutes.
15. How many?Of 5300, the number waiting more than 35 minutes is ...
0.15% × 5300 = 7.95 ≈ 8
About 8 students will wait more than 35 minutes.
__
Additional comment
These values are based on the empirical rule, as required by the problem statement. The actual number for P(Z>3) is about 0.0013499 (0.13%), and the number of students is about 7.15 ≈ 7. That is, the result using the empirical rule is slightly different than what you get using a calculator, spreadsheet, or table.
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QuestionIn ABC, C = 64°, c = 32, and b = 33. What are the two possible values for angle B to the nearest tenth of a degree?Select both correct answers.
Two possible diagrams of the triangle are shown below
To find angle B in each triangle, we would apply the law of sines which is expressed as
a/SinA = b/SinB = c/SinC
For either of the triangles, by applying the sine law, we have
33/Sin B = 32/Sin 64
By crossmultiplying, we have
32 SinB = 33 Sin 64
Sin B = (33 Sin 64)/32 = 0.9269
We would find angle B by finding the inverse of sine 0.9269
Thus,
B = Sin^-1(0.9269) = 68
This is an acute angle. B can also be an obtuse angle. Greater than 90 but less than 180 degrees). Thus, another value for B is
Given that bisects use the diagram above to complete the following statement.m∠AOB= m∠…
A line is said to bisect an angle if it divides it in two equal parts.
Since the segment OB bisects the angle AOC, then the angles AOB and BOC have the same measure.
Therefore, the complete statement is:
[tex]m\angle AOB=m\angle BOC[/tex]Teri ran 8 kilometers. One mile is approximately equal to 1.6 kilometers. Which measurement is closest to the number of miles Teri ran?
The closest distance or the number of miles Teri ran is equal to 5 miles.
What is the unitary method ?
The unitary method is a method in which you find the value of one unit and then the value of required no. of units.
It is given that Teri ran 8 kilometers.
It is also given that , 1 mile is approximately equal to 1.6 kilometers.
This is a question of unitary method. We know that value of one unit is given as 1 mile is equal to 1.6 kilometers approximately. We know have to calculate the no. of miles Teri ran , by converting 8 kilometers to miles.
So ,
1 miles = 1.6 kilometers
This implies :
8 kilometers = 8 / 1.6 miles
or
8 kilometers = 5 miles
or
8 kilometers is approximately equal to 5 miles.
Therefore , the closest distance or the number of miles Teri ran is equal to 5 miles.
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What is the effect on the graph of f(x)=x^2 when it is transformed to h(x)=2x^2 + 15
Answer and Explanation:
If f(x) = x^2 is transformed to h(x)=2x^2 + 15, the below will be the effect on the its graph;
* The graph will be shifted up 15 units
*The graph will be vertically stretched since the value o
Solve by factoring: f(x) = 2x² + 7x+6
Write the final answers in the two blanks. Do NOT write x =, just the number. If there is a fraction in your answer, write as #/#.
The factoring of the expression 2x² + 7x + 6 is (2x + 3)(x + 2).
How to illustrate the information?It should be noted that a factor of a number is a number that can be multiplied with another number to get the original number.
In this case, 2x² + 7x - 6 will be factored thus:
= 2x² + 7x + 6
= 2x² + 4x + 3x + 6
= 2x(x + 2) + 3(x + 2)
= (2x + 3)(x + 2)
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uncle grandpa once said, “400 reduced by twice my age is 262.” what is his age? Show work
Answer:
69
Step-by-step explanation:
400-262=138
138÷2=69
is B the right answer? If not, which one is?
Given the rational function;
[tex]f(x)=\frac{3x+4}{x(x-2)}[/tex]To determine the constraint for this function, we shall set the denominator equal to zero;
[tex]\begin{gathered} x(x-2)=0 \\ \text{Hence;} \\ x=0 \\ x-2=0 \\ x=2 \end{gathered}[/tex]This means the equation does not exist when x = 0, and when x = 2.
ANSWER:
The correct answer is option C.
Transit Technologies plans to produce 2-way radios that will sell for $59 per radio. They estimate fixed costs
in manufacturing the radios to be $41,500. The variable costs of producing each radio will be $14. How many
radios must the company sell to break even?
The company should must sell 923 radios to break even.
Fixed cost refer to those costs which do not vary directly with the level of output. For example salary given to staff.
Variable cost that cost which vary directly with the level of output..
The selling price of radio is $59.
Total radios sell are of value $41500. This is the fixed cost.
Let us say that they sell x number of radios,
As we know,
For break even point,
Total revenue = Total cost
Cost of one radio x number of radio = fixed cost plus variable cost of all radios
54x = 41500 + 14x
40x = 41500
x = 922.22~923
So, they should sell 923 radio to break even.
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6. Solve for x. **THINK! a) what type of angles do you have? b) what is theirrelationship (add up to 90, add up to 180, or congruent)? c) set up an equationand solve *
a) The types of angles present are:
- 1 right angle
- 1 angles of 50 degrees and 1 angle of 4x degrees
b) their relationship is add up to 90°
c) 50° + 4*x° = 90°
4*x° = 90 - 450
x° = 40/4 = 10
x = 10°
Triangles DEF and HJK are similar. DEF has side lengths DE=4, EF=6, FD=8. Which of the following could be the side lengths of HJK?• 2, 6, 7• 2, 5, 7• 8, 12, 16• 5, 7, 9
Answer:
(c) 8, 12, 16
Step-by-step explanation:
You want to identify the side lengths that are proportional to lengths 4, 6, and 8.
RatiosReducing the ratios to lowest terms, we can compare them:
desired ratio: 4 : 6 : 8 = 2 : 3 : 42 : 6 : 7 — reduced, not equivalent2 : 5 : 7 — reduced, not equivalent8 : 12 : 16 = 2 : 3 : 4 . . . . . same as the desired ratios5 : 7 : 9 — reduced, not equivalentSide lengths 8, 12, 16 will form a triangle similar to ∆DEF.
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if A(-3,4) is on BC and divides it in the ratio of BA:AC = 1:2 find C if B is (-9,8)
The coordinate of the point C on the line segment is (9, -4)
How to determine the coordinates of the endpoint C?On the segment, we have the following endpoints
A = (-3, 4)
B = (-9, 8)
The ratio of point A on the line is given as
Ratio, B : C = 1 : 2
Rewrite as
m : n = 1 : 2
The coordinate of point A is calculated using
A = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)
Where x and y are the coordinates defined above
So, we have
(-3, 4) = 1/(1+2) * (1 * x + 2 * -9, 1 * y + 2 * 8)
Evaluate
(-3, 4) = 1/3 * (x - 18, y + 16)
So, we have
(x - 18, y + 16) = (-9, 12)
This means that
x - 18 = -9
y + 16 = 12
Solve
x = 9
y = -4
Hence, the location of the point C is (9, -4)
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What term must go in the space to complete the statement?
The term that should go in the space to complete the statement is 5.
The complete statement is 5c + 15 = 5(c + 3).
What exactly does it mean to simplify an expression?Simplifying an expression is the same as solving a math problem. When you simplify an expression, you are attempting to write it in the simplest feasible manner.Combining similar terms is a frequent strategy for reducing algebraic expressions. Like Terms have identical variable components (same variable(s) and same exponent(s)).The given statement is 5c + 15 = __(c + 3).
Now, we will combine the like term from the left side of the expression which is 5, and place it on the right side space to make the expression equivalent.
Hence, the complete statement is 5c + 15 = 5(c + 3).
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The quadratic function -2x ^ 2 + 4x + 6 is shown below. What are the solutions of this function? *
The solution for this function will be x = -1 and x = 3
Describe the quadratic function.Quadratic polynomials are those with at least one variable and a variable with a maximum exponent of two. Since the second-degree term is the highest degree term in a quadratic function, it is sometimes referred to as the polynomial of degree 2. In a quadratic function, at least one term must be of the second degree. It has qualities in algebra.
The given function is -2x² + 4x + 6
So, we'll employ the middle term splitting strategy.
-2x² + 4x + 6 = 0
- 2x² + 6x - 2x + 6 = 0
-2x ( x-3) -2 (x-3) = 0
(-2x-2) (x-3) = 0
So, the solution will be
-2x - 2 = 0
-2x = 2
x = 2/-2
x = -1
And, x-3 =0
x = 3
So, the solution of the quadratic function will be
x =-1 and x = 3
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PartA)What are the transformations are needed in in order to obtain the graph of G(x) from the graph of f(x) Select all that applyPartB) Graph g(x)
Part A)
Recall that:
1) The function represented by the graph of the function f(x) translated vertically n units up and horizontally m units left is:
[tex]f(x+m)+n\text{.}[/tex]2) The function represented by the graph of the function f(x) reflected over the x-axis is:
[tex]-f(x)\text{.}[/tex]Now, notice that g(x) is the function f(x) reflected over the x-axis and then translated vertically 6 units up and horizontally 4 units left.
Answer Part A:
Options B, C, and D.
Part B) To graph g(x) we will reflect the graph of f(x) over the x-axis and then we will translate it vertically 6 units up and horizontally 4 units left.
We know that the graph of f(x)=|x| is:
The above graph reflected over the x-axis is:
Finally, the above graph translated vertically 6 units up and horizontally 4 units left is:
Answer part B:
There are multiple choices. but they didn’t fit in the picture
Explanation
In the question,
The number of tomatoes is described as x
The number of lettuce is described as y
As per the question, the number of vegetables Aneil can plant in the garden is modelled by:
[tex]2x+3y=60[/tex]The graph of the above model can be seen above.
From the graph, we have the y-intercept to be 20 and the x-intercept to be 30.
Answer:
Y-intercept = 20 ---- This is the number of lettuce plants Aneil can plant if he plants zero tomatoes
X- intercept =30 ---- This is the number of tomatoes plants Aneil can plant if he plants zero lettuce
Evaluate r(x) = 3x - 10 when x= -4. r(-4)=_
Answer:
The answer is: r is equal to -22.
Hola!, me ayudan porfa!!
En la cerrada economía Chalupa, el consumo familiar triplica el de las unidades productivas y este supera en $2,500 al del gobierno, que tiene un equilibrio presupuestario y sus ingresos fueron $6,700. Si el consumo de capital fijo es 25% del PNB pm y el monto de impuestos netos de subsidios $1750 encuentre el ingreso nacional.
Answer:
hola comasa due when 123 dfosb971 24
a. pi/3 b. pi/2c. 2pi/3d. 3pi/2 These are 4 options but there can be more than 2 or 3 correct answers.Find the solution of each equation the interval
so the answer is pi/2, 3pi/2, and pi/3
Which is true?A. 2680 > 2806B. 2860 > 2806C. 2680 < 2086D. 2806 < 2680
from the options;
The correct is B
because 2860 is greater than 2806
Other options are false
Use the Law of Sines to find the indicated side x."(Assume c = 23.2. Round your answer to one decimal place.)
ANSWER
x = 21.6
EXPLANATION
We have that:
c = 23.2
To be able to solve this, we must first find angle
The sum of angles in a triangle is 180 degrees.
This means that:
=> 52 + 70 + 122+ =>
Sine Law says that the ratio of angle and side opposite the angle for any triangle equal.
This means that:
[tex]\frac{\sin A}{a}\text{ = }\frac{\sin B}{b}=\text{ }\frac{\sin C}{c}[/tex]So, we can say that:
[tex]\begin{gathered} \frac{\sin52}{x}=\text{ }\frac{\sin58}{23.2} \\ \text{Cross}-\text{multiply:} \\ 23.2\cdot\text{ sin52 = x }\cdot\text{sin58} \\ \Rightarrow\text{ x = }\frac{23.2\cdot\text{ sin52}}{\sin58} \\ x\text{ = }21.6 \end{gathered}[/tex]That is the value of x.
Find the value of x. The diagram is not to scale. Lines fand g are parallel. f g
5x
9x+26
A. 10
B. 11
C. 12
D. -11
X has a value of 11
What is an angle?
The vertex of an angle is the common point of contact where two straight lines or rays come together to produce an angle.
As far as we are aware, this question is answered utilizing a quadrilateral's unique property that the sum of its adjacent angles is 180 degrees.
By quadrilateral, what do you mean?
A closed polygon with four sides, four vertices, and four angles is known as a quadrilateral.
thus, A.T.Q:-
We possess 5x+9x+26=180
14x +26=180
14x=154
x = 11 degrees
Consequently, x = 11 degrees.
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the last six days of August 2011 all time records for high temperatures in Austin Texas which of the following values that identifies the mean absolute deviation for these temperatures F. 4G. 107H. 103J. 3.3
We have to calculate the mean absolute deviation (MAD) for these temperatures.
We can express the MAD as:
[tex]\text{MAD}=\frac{1}{n}\sum ^n_{i=1}|x_i-\bar{x|}[/tex]So first we have to calculate the mean of the sample. We can do this as:
[tex]\bar{x}=\frac{1}{n}\sum ^n_{i=1}x_i=\frac{1}{6}(103+110+112+109+105+103)=\frac{1}{6}\cdot642=107[/tex]Now we can calculate the MAD as:
[tex]\begin{gathered} \text{MAD}=\frac{1}{6}(|103-107|+|110-107|+|112-107|+|109-107|+|105-107|+|103-107|) \\ MAD=\frac{1}{6}(4+3+5+2+2+4) \\ \text{MAD}=\frac{1}{6}(20) \\ \text{MAD}\approx3.3 \end{gathered}[/tex]Answer: The MAD is approximately 3.3.
A mixture of 20 pounds of candy sells for $1.15. The mixture consists of chocolates worth $1.45 a pound and chocolatesworth $0.90 a pound. If x represents the pounds of $0.90 chocolates used, then which of the following represents thepounds of $1.45 chocolates used?20 - x20 xOX-20
Answer
The 1.45 dollar chocolates will weigh (20 - x) pounds.
Explanation
We are told that the mixture weighed 20 pounds and one of the chocolates in the mixture weighed x pounds.
We are then to cslculate the weight of the other type of chocolate in the mixture.
Total mixture = 20 pounds
0.90 dollar chocolate weighed x pounds
The 1.45 dollar chocolates will weigh (20 - x) pounds.
Hope this Helps!!!
what is 3 1/2 x 4 1/2 x 5 ft * 5 1/6 x 5 1/4 x 3 1/3 x 4 1/2 in 5 ft x 5 1/3 * 2/3
ANSWER
[tex]V=72\operatorname{cm}[/tex]EXPLANATION
h. We want to find the volume of the rectangular prism given.
The volume of a rectangular prism is given as:
[tex]V=l\cdot w\cdot h[/tex]where L = length
w = width
h = height
Therefore, we have that the volume of the prism is:
[tex]\begin{gathered} V=12\cdot2\cdot3 \\ V=72\operatorname{cm}^3 \end{gathered}[/tex]Find the equation of the line with slope −3/5 and y-intercept (0,−3).
The equation of the line will be [tex]y = -\frac{3}{5}x -3[/tex]
In the question given, It is stated that the slope of the line is m = -3/5, and the y-intercept of the line is (0, -3). We have to find out the slope-intercept form of the line. To find out the equation of line first the standard equation for slope intercept form is y = mx + b, where m is the slope, and b is the y-intercept.
Now, we have slope m = -3/5 and y-intercept is -3. Putting these values in the slope intercept form we get:
=> y = mx + b
=> [tex]y = -\frac{3}{5}x -3[/tex]
Hence, we get equation of line [tex]y = -\frac{3}{5}x -3[/tex]
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A map is drawn using the scale 2cm: 100miles. On the map, Town B, is 3.5 cm from Town A and Town C is 2 cm past Town B. How many miles apart are Town A and Town C
SOLUTION
From the question, town B is 3.5cm from town A and town C is 2cm from town B. Therefore C is 5.5 cm from town A.
The scale is 2cm for every 100miles. This means 1cm for every 50 miles.
You get this by dividing 100 by 2.
Now 5.5 cm becomes 5.5 x 50 miles = 275miles.
So town A and town C are 275 miles apart
To indirectly measure the distance across a lake, Ethan makes use of a couple
landmarks at points B and C. He measures AE, EC, and DE as marked. Find the
distance across the lake (BC), rounding your answer to the nearest hundredth of a
meter.
To the nearest tenth, the distance across the lake is DE = 207.68 m.
The corresponding side lengths of two triangles that are similar are always proportional to each other.
ΔCDE and ΔCFG are similar to each other
FG = 142.1 m
FC = 130 m
DF = 60 m
DC = 130 + 60 = 190 m
Therefore,
DE/FG = DC/FC
Substitute
DE/142.1 = 190/130
Cross multiply nearest hundredth
Therefore, applying the similarity theorem, the distance across the lake to the nearest hundredth is DE = 207.68 m
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which graph represents the equation x - 4y = -16
the given equation is
x - 4y = -16
put x = 0
0 - 4y = -16
y = 4
so at x = 0 ,, y is 4
put x = 4
4 - 4y = -16
-4y = -16- 4
y = 20/4
y = 5
so, at x = 4 the value of y is 5
thus, the correct graph is option B
Answer this please I really need you to do this
Answer:
x ≥ 2
Step-by-step explanation:
Given inequality:
[tex]-\dfrac{4(x+3)}{5} \leq 4x-12[/tex]
Values of x less than 2
Substitute two values where x < 2 into the inequality:
[tex]\begin{aligned}x=1 \implies -\dfrac{4(1+3)}{5} & \leq 4(1)-12\\\\ -\dfrac{4(4)}{5} & \leq 4-12\\\\ -\dfrac{16}{5} & \leq -8 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies -\dfrac{4(0+3)}{5} & \leq 4(0)-12\\\\ -\dfrac{4(3)}{5} & \leq 0-12\\\\ -\dfrac{12}{5} & \leq -12 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]
The values of x < 2 are not solutions to the inequality.
--------------------------------------------------------------------------------
Substitute the value of x = 2 into the inequality:
[tex]\begin{aligned}x=0 \implies -\dfrac{4(2+3)}{5} & \leq 4(2)-12\\\\ -\dfrac{4(5)}{5} & \leq 8-12\\\\ -\dfrac{20}{5} & \leq -4\\\\ -4 & \leq -4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]
The value of x = 2 is a solution to the inequality.
--------------------------------------------------------------------------------
Values of x more than 2
Substitute two values where x > 2 into the inequality:
[tex]\begin{aligned}x=3 \implies -\dfrac{4(3+3)}{5} & \leq 4(3)-12\\\\ -\dfrac{4(6)}{5} & \leq 12-12\\\\ -\dfrac{24}{5} & \leq 0 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]
[tex]\begin{aligned}x=4 \implies -\dfrac{4(4+3)}{5} & \leq 4(4)-12\\\\ -\dfrac{4(7)}{5} & \leq 16-12\\\\ -\dfrac{28}{5} & \leq 4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]
The values of x > 2 are solutions to the inequality.
--------------------------------------------------------------------------------
Therefore, the solution to the inequality appears to be x ≥ 2.
To check, solve the inequality:
[tex]\begin{aligned} \implies -\dfrac{4(x+3)}{5} &\leq 4x-12\\-4(x+3) &\leq 5(4x-12)\\-4x-12 &\leq 20x-60\\ -24x & \leq-48\\x & \geq 2\end{aligned}[/tex]
When graphing inequalities on a number line:
< or > : open circle.≤ or ≥ : closed circle.< or ≤ : shade to the left of the circle.> or ≥ : shade to the right of the circle.To graph the solution to the inequality on number line, place a closed circle at x = 2 and shade to the right. (See attachment).