The monthly payment will be $161.20.The total amount paid over the term of the loan is $38,688 and 58.2% is paid toward the principal while 41.8% is paid toward interest.
What is compound interest?Compound interest is applicable when there will be a change in principal amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount.
As per the given,
Principle amount P = $25,000
APR = 9% = 0.09
Time period T = 20 years
a) Monthly payment will be given as,
⇒ P(r/12)/(1 -(1 +r/12)^(-12t))
⇒ 22500·(0.06/12)/(1 -(1 +0.06/12)^(-12·20))
⇒ $161.20
b) After 20 years the amount as,
$161.20 x 240 = $38,688
c) (22500/38688)·100% = 58.2% is paid toward principal
The remaining amount, 41.8% is paid toward interest.
Hence "The monthly payment will be $161.20.The total amount paid over the term of the loan is $38,688 and 58.2% is paid toward the principal while 41.8% is paid toward interest".
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A regular hexagon has a perimeter of 120 m. Find its area. Express your answer in the simplest radical form.A) 1800√3m2B) 5 √3 m2C) 600 √3 m2D) 3600 √3 m2
The area of regular hexagon in simplest radical form is [tex]600\sqrt{3}[/tex] m².
There are many different types of hexagons. The most common type is a regular hexagon, which is a hexagon that has sides of equal length and angles of equal measure. The perimeter is the total length or distance around a two dimensional shape. In the figure below, the perimeter of each shape is the sum of the lengths of each side, shown in red. The perimeter of a circle or ellipse is called the circumference. For a polygon, the perimeter is the sum of its side lengths.
The given polygon is a regular hexagon with perimeter 120 m.
Thus, the length of each side,
s = 120/6 = 20 m.
The area, A, of a regular hexagon can be found given only its side length, s, with the formula:
[tex]A = \frac{3\sqrt{3} }{2} s^{2}[/tex]
Substitute s = 120 m in above formula:
[tex]A = \frac{3\sqrt{3} }{2} (20)^{2} \\A = \frac{3\sqrt{3} }{2}(400)\\A = 600 \sqrt{3}[/tex]
Thus, the area of regular hexagon in simplest radical form is [tex]600\sqrt{3}[/tex] m².
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Determine the domain of the rational function h (z) =
4/4z^2 +4
The domain of the given function is z<0 or z>0
What is a domain?The entire range of independent variable values is the domain of a function.
According to this definition, it means:
The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.
Keep these things in mind when locating the domain:
A fraction's denominator (bottom) cannot be 0.
In this section, the integer following a square root symbol must be positive.
Calculation:The domain of a function is a set of input of argument values for which the function is real or defined.
1) Finding the singularity point:
Taking the denominator 4×[tex]z^{2}[/tex] = 0 ⇒ z = 0
∴The following function will not be defined if z = 0
So the function domain is z>0 or z<0
The domain of the given function is z<0 or z>0
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Find the equation of a circle given by the points (-4,2),(-2,6) and (4,8)
Answer:
(x-3)²+(y-1)²=50
Step-by-step explanation:
we know,
general eqn of circle passing through a point is
r²=(x-h)²+(y-k)²------($)
then,at (-4,2) the eqn becomes
r²=(-4-h)²+(2-k)²----(1)
at (-2,6),
r²=(-2-h)²+(6-k)²-----(2)
at (4,8),
r²=(4-h)²+(8-k)²-------(3)
Now,
from (1) and(2),
(-4-h)²+(2-k)²=(-2-h)²+(6-k)²
or,16+8h+h²+4-4k+k²=4+4h+h²+36-12k+k²
or,h²-h²+8h-4h+k²-k²-4k+12k+16+4-4-36=0
or,4h+8k-20=0
or,4(h+2k)=20
or,h+2k=5------(4)
also,from (2) and (3),
(-2-h)²+(6-k)²=(4-h)²+(8-k)²
or,4+4h+h²+36-12k+k²=16-8h+h²+64-16k+k²
or,h²-h²+4h+8h+k²-k²-12k+16k+4+36-64-16=0
or,12h+4k-40=0
or,4(3h+k)=40
or,3h+k=10-------(5)
Now,multiplying eqn (5)by 2 then subtracting from (4),we get
h+2k=5
6h+2k=20
- - -
_________
-5h=-15
.:h=3
putting value of h in (4),we get
3+2k=5
or,2k=2
.:k=1
Now,putting value of k and h in eqn(1),
r²=(-7)²+(1)²
or,r²=49+1
.:r²=50
Now putting value of h,k and r² in eqn($),we get
(x-3)²+(y-1)²=50,which is required eqn of circle
Suppose the company desires to make a profit of shs. 195,000, what should be the output in units?
A) The break-even sales level in shillings XYZ Company needs to achieve is Shs.1,096,443.
B) The break-even sales level in units XYZ Company needs to achieve is 27,444 units to make a profit of Shs.195,000.
What is the break-even point?The break-even point is the sales level when total revenue equals total costs (fixed and variable).
At the break-even point, there is no profit or loss.
Selling price per unit = Shs.66
Variable production cost per unit = Shs.44
Variable selling cost per unit = Shs.4
Total variable cost per unit = Shs.48 (Shs.44 + Shs.4)'
Contribution margin per unit = Shs.18 (Shs.66 - Shs.48)
Contribution margin ratio = 27.27% (Shs.18/Shs.66 x 100)
Fixed production cost (total) = Shs.200,000
Fixed selling and administrative cost (total) Shs.99,000
Total fixed costs = Shs. 299,000 (Shs.200,000 + Shs.99,000)
Target profit = Shs.195,000
a) Break-even sales in shillings = Fixed costs/Contribution margin ratio
= Shs.1,096,443 (Shs.299,000/27.27%)
b) Break-even sales in units to achieve target profit = (Fixed costs + Target profit)/Contribution margin per unit
= (Shs.299,000 + Shs.195,000/Shs.18)
= Shs.494,000/Shs.18
= 27,444 units
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Question Completion:XYZ Company manufactures a product called "PERMA". Pertinent cost and revenue data relating to the manufacture of this product are given below:
Selling price per unit = Shs.66
Variable production cost per unit = Shs.44
Variable selling cost per unit = Shs.4
Fixed production cost (total) = Shs.200,000
Fixed selling and administrative cost (total) Shs.99,000
Required:
a) Calculate the break-even sales level in shillings;
b) Suppose the company desires to make a profit of shs.195,000, what should be the output in units?
Given: θ = 20° opposite = 45 Find: hypotenuse
The value of hypotenuse will be;
⇒ Hypotenuse = 132.35
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values are,
⇒ θ = 20° opposite = 45
Now,
Since, The values are,
⇒ θ = 20° opposite = 45
We know that;
⇒ sin θ = Opposite / Hypotenuse
⇒ sin 20° = 45 / Hypotenuse
⇒ Hypotenuse = 45 / sin 20°
⇒ Hypotenuse = 45 / 0.34
⇒ Hypotenuse = 132.35
Thus, The value of hypotenuse will be;
⇒ Hypotenuse = 132.35
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Which data set could be represented by the box plot shown below?
A horizontal boxplot is plotted along a horizontal axis marked from 20 to 36, in increments of 1. A left whisker extends from 24 to 27. The box extends from 27 to 33 and is divided into 2 parts by a vertical line segment at 31. The right whisker extends from 33 to 34. All values estimated.
Choose 1 answer:
(Choice A)
A
24, 25, 29, 30, 31, 31, 32, 34, 34
(Choice B)
B
24, 27, 29, 30, 30, 31, 32, 34, 34
(Choice C)
C
24, 25, 29, 31, 31, 31, 32, 34, 35
(Choice D)
D
24, 25, 29, 30, 30, 31, 34, 34, 34
Answer:
A
Step-by-step explanation:
A box plot shows the five-number summary of a set of data.
Five-number summary:
Minimum value = The value at the end of the left whisker.Lower quartile (Q₁) = The left side of the box.Median (Q₂) = The vertical line inside the box.Upper quartile (Q₃) = The right side of the boxMaximum = The value at the end of the right whisker.Therefore, from inspection of the given box plot:
Minimum value = 24Lower quartile (Q₁) = 27Median (Q₂) = 31Upper quartile (Q₃) = 33Maximum = 34The median of a set of data is the middle value when all data values are placed in order of size.
Therefore, the only answer option that has a maximum value of 34 and a median of 31 is answer option A.
as part of a science experiment, Carson designs and creates a cushioned egg carrier. he puts an egg inside it and then drops it from a window to see whether his design can safely cushion the egg and keep it from breaking. the egg's height in feet x seconds after being dropped is given by 27 - 16x^2. after how many seconds will the egg hit the ground?
Answer: To find out how many seconds it will take for the egg to hit the ground, we need to find the value of x when the height of the egg is 0 feet. We can do this by setting the height of the egg equal to 0 in the equation 27 - 16x^2 and solving for x.
The equation for the height of the egg in feet x seconds after being dropped is given as:
27 - 16x^2 = 0
Subtracting 27 from both sides of the equation gives us:
-16x^2 = -27
Dividing both sides of the equation by -16 gives us:
x^2 = 27/16
Taking the square root of both sides of the equation gives us:
x = sqrt(27/16)
Plugging this value into the equation for the height of the egg gives us:
27 - 16(sqrt(27/16))^2 = 0
Simplifying this equation gives us:
27 - 16(27/16) = 0
Which simplifies to:
27 - 27 = 0
This equation is true, so the value of x that we found is a solution to the equation. This means that the egg will hit the ground after sqrt(27/16) seconds.
I hope this helps! Let me know if you have any other questions.
How many four-digit odd numbers less than 5000 can be formed using the digits 2, 3, 4, 5, 6, and 9?
Answer: 6.
Step-by-step explanation: We can solve this problem by using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
In this case, n is the number of choices (the digits 2, 3, 4, 5, 6, and 9) and r is the number of items in each combination (4 digits).
Plugging in the values, we get:
C(6, 4) = 6! / (4! * 2!) = (6 * 5 * 4 * 3) / (4 * 3 * 2) = 30
Therefore, there are 30 four-digit odd numbers that can be formed using the digits 2, 3, 4, 5, 6, and 9. However, not all of these numbers will be less than 5000, so we need to further filter the list to only include those that meet this requirement.
The four-digit odd numbers that can be formed using these digits are:
2359, 2395, 2539, 2593, 2935, 2953, 3259, 3295, 3529, 3592,
3925, 3952, 5239, 5293, 5329, 5392, 5923, 5932, 9235, 9253,
9352, 9523, 9532
Out of these numbers, only 2359, 2539, 2935, 3925, 5239, and 9523 are less than 5000. Therefore, there are 6 four-digit odd numbers less than 5000 that can be formed using the digits 2, 3, 4, 5, 6, and 9.
Therefore, the final answer is 6.
Answer the questions about the following function.
f(x) = 3x²-x-2
(a) Is the point (2,8) on the graph of f?
(b) If x= -1, what is f(x)? What point is on the graph of f?
If f(x) = -2, what is x? What point(s) are on the graph of f?
(d) What is the domain of f?
(c)
(e) List the x-intercept(s), if any, of the graph of f.
(f) List the y-intercept, if there is one, of the graph of f.
Step-by-step explanation:
f(x)=3x²-x-2
a) (2,8)
f(2)=3(2²)-2-2
f(2)=3(4)-4
f(2)=12-4
f(2)=8
Hence, the point (2,8) is on the graph of f(x)
b) x=-1
f(-1)=3((-1)²)-(-1)-2
f(-1)=3(1)+1-2
f(-1)=3-1
f(-1)=2
c) x=-2
f(-2)=3((-2)²)-(-2)-2
f(-2)=3(4)+2-2
f(-2)=12+0
f(-2)=12
[tex]d)\ f(x)\in(-2\frac{1}{12} ,\infty)[/tex]
e) y=0
3x²-x-2=0
3x²-x-2=0
3x²-3x+2x-2=0
3x(x-1)+2(x-1)-0
(x-1)(3x+2)=0
x-1=0
x=1
3x+2=0
3x=-2
Divide both parts of the equation by 3:
x=-2/3
f) x=0
f(x)=3(0²)-0-2
f(x)=3(0)-2
f(x)=0-2
f(x)=-2
What is the equation of a line that is perpendicular to y=−3x+5 and goes through the point (−9, 5) ?
Answer:
hi
Step-by-step explanation:
help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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How many boards 6 5/6 in wide will cover a floor 205 in wide
By using fraction, it can be calculated that
30 boards are required to cover a floor of width 205 inches wide
What is fraction?
Suppose there is a collection and a part of collection has to be taken.
The part which is taken is called fraction. In other words part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
This is a word problem on fraction
Width of each board = [tex]6\frac{5}{6}[/tex] inches = [tex]\frac{41}{6}[/tex] inches
Total width of floor = 205 inches
Number of boards required = [tex]205 \div \frac{41}{6}[/tex] = [tex]205 \times \frac{6}{41}[/tex] = 30
30 boards are required
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5) if the 4 digit number 7,2d2 is divisible by 6, then what is the largest possible value of digit d?
Is 2 fourths greater than 2 thirds?
Answer:
NO
Step-by-step explanation:
Two fourths =
[tex] \frac{2}{4} = 0.5[/tex]
Two thirds =
[tex] \frac{2}{3} = 0.66667[/tex]
Therefore
0.66667 > 0.5
[tex] \frac{2}{3} > \frac{2}{4} [/tex]
or
0.5 < 0.66667
[tex] \frac{2}{4} < \frac{2}{3} [/tex]
i hope this helped
Answer: No, 2/4 is not greater than 2/3
Step-by-step explanation: To find an easy way to calculate their values we have 2 options. So, the 1st option is to turn them into a decimal. I already calculated their values which are:
2/4 = 0.5
2/3 = 0.667
Then, we compare the two decimal numbers to get the answer.
0.5 is not greater than 0.667.
The 2nd way is to find a common denominator, which would look like this:
2/4 = 6/12
2/3 = 8/12
8/12 is greater than 6/12, so that also proves that 2/4 is not greater than 2/3.
Given AC L BD, complete the flowchart proof below. Note that the last statement
and reason have both been filled in for you.
D
C
For each box, choose a statement format from the dropdown menu. You will then be able to change i
the letters to match the diagram for this problem.
In the triangle below, ΔABE≅ΔCBD. Reason (AAS)
How to show the postulates?We should know that the postulates talk about the proofs about the given diagram or flowchart
There is an attached diagram to support our answer
Below gives the correct explanations
S/n Statement Reason
1 <ABE≅<CDE Given in the diagram
2 <AEB≅CED The theory of vertical angles are equal 3 BE≅ED Also given in the diagram
4 ΔABE≅ΔCDE The rule of Angle, Side Angle proof
In conclusion the triangle below, ΔABE≅ΔCBD. Reason (AAS)
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Complete question:
Given AC 1 BD, complete the flowchart proof below. Note that the last statement and reason have both been filled in for you
What is the slope of the line that passes through the points (-6, 1) and
(-6, -4)? Write your answer in simplest form.
The slope of the line that passes through the points (-6,1) and (-6,-4) is Undefined.
The slope(m) of the line passing through two points is X1,Y1 and X2, Y2 is
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
we have (x1,y1) and (x2,y2) is (-6,1) and (-6,-4) respectively substitute the values in m=[tex]\frac{y2-y1}{x2-x1}[/tex],
we get m=[tex]\frac{-4-1}{-6-(-6)}[/tex] = -5/0 which is Undefined.
Whenever the slope of the line is undefined then the line must be vertical. Because the slope of the vertical line cannot be defined.
The slope of the line that passes through the points (-6,1) and (-6,-4) is Undefined.
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Ders: Attempt 1
Question 1 (3 points)
A tourist exchanged $1,000 US dollars for 910 British pounds. How many
pounds did she receive for each US dollar?
To solve set up a proportional equation and cross multiply.
She earned 0.91 pounds for every $1 US dollar when a visitor traded $1,000 US dollars for 910 British pounds.
What is proportion?A proportion is an equation that sets two ratios equal to each other. For example, if there is one guy and three girls, the ratio may be written as 1: 3. (for every one boy there are 3 girls) One-quarter are males and three-quarters are girls. 0.25 are males (by dividing 1 by 4). According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios or fractions are equivalent.
Here,
For 910 pounds, she spent $1000 US dollars.
For $1,
=910/1000 pound
=0.91 pounds
For each $1 US dollar, she received 0.91 pounds as tourist exchanged $1,000 US dollars for 910 British pounds.
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7/9 - 1/4 please please please please
Answer: 19/36
Step-by-step explanation:
First the LCM (Least Common Denominater) must be found, the LCM of 9 and 4 is 36
Since 9 x 4 is 36, the numerator and denominator of 7/9 will be multiplied by 4 making it 28/36
Since 4 x 9 equals 36, the numerator and denominator of 1/4 will be multiplied by 4 making it 9/36
Now that they have common denominators the numerators can be subtracted from each other as well as the denominators
28/36 - 9/36 = 19/36
19/36 cannot be simplified therefore 7/9 - 1/4 = 19/36
you deposit 8600 in an account that pays 1.32% annual interest. Find the balance after 4 years when the interest in compounded monthly
The balance in the account after 4 years as interest is compounded monthly is $9,066.02.
What is the balance after 4 years?The formula accrued amount in a compounded interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $8,600Compounded monthly n = 12Time t = 4 yearsInterest rate r = 1.32% = 1.32/100 = 0.0132Accrued amount A = ?Plug the given values into the above formula and solve for A.
A = P( 1 + r/n )^( n × t )
A = 8600( 1 + 0.0132/12 )^( 12 × 4 )
A = 8600( 1 + 0.0011 )^( 48 )
A = 8600( 1.0011 )^( 48 )
A = $9,066.02.
Therefore, the accrued amount after 4 years is $9,066.02.
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3. Given the function f(x) shown graphed below, what is its average rate of change from } x=1 to x=7 ?
(1) -1
(2) -4/3
(3) 8
(4) 3/5
4. A function h(x) has an average rate of change equal to 7 on the interval 5 ≤ x≤ 9. If h(5)=12, then which of the following must be the value of h(9) ?
3) The rate of change on the interval [1, 7] is -1, so the correct option is A.
4) By using the rate of change formula, we will see that h(9) = 40
How to find the average rate of change?We know that for a function f(x), the average rate of change on the interval [a, b] is:
r = ( f(b) - f(a))/(b - a)
Here the interval is [1, 7]
Using the graph we can see that:
f(1)= 6
f(7) = 0
Then the average rate of change is:
r = ( f(7) - f(1))/(7 - 1)
r = (0 - 6)/6 = -1
The correct option is A.
4) Which will be value of h(9)?
We know that the average rate of change of h(x) is 7 on the interval [5, 9]
Then we can write:
7 = ( h(9) - h(5))/(9 - 5)
We know that h(15) = 12, then we have the equation:
7 = (h(9) - 12)/4
Now we can solve that for h(9), we will get:
7 = (h(9) - 12)/4
7*4 = h(9) - 12
28 = h(9) - 12
28 + 12 = h(9)
40 = h(9)
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what is the simplified form of 89 ∛9
The expression given as 89 ∛9 cannot be further simplified
How to determine the simplified form of the expression?From the question, we have the following parameters that can be used in our computation:
89 ∛9
The above expression is a radical expression
And the radicand is ∛9
The radicand ∛9 implies that the cube root of 9
The cube root of 9 is a decimal number
So, it is better to leave the expression without changing its form
Hence. 89 ∛9 cannot be further simplified
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Please help I'm stuck
After solving the equation, the value of y obtained is equal to 10°.
What is an angle?An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol ∠.
Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.
As per the information obtained from the given figure,
Angle, C = 4y
Angle, E = 180 - 116 = 64 and,
Angle, D = 7y + 6
As we know, the sum of the angles of a triangle is 180°.
Then,
4y + 64 + 7y + 6 = 180
11y = 180 - 70
11y = 110
y = 110/11
y = 10°
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Write the systems of equations from the table below and find the solution?
The system of equations is y = 4x - 3 and y = -1/3x + 4 and the solution is (21/13, 45/13)
How to determine the system of equations?From the question, we have the table of values as the parameters that can be used in our computation:
From the table, we have
Table 1
(x, y) = (0, -3) and (4, 13)
A linear equation is represented as
y = mx + c
Where
Slope = m
c = y when x = 0
This means that
c = -3
So, we have
y = mx - 3
The point (4, 13) implies that
13 = m * 4 - 3
So, we have
4m = 16
m = 4
So, the equation is
y = 4x - 3
Table 2
(x, y) = (0, 4) and (4, 6)
A linear equation is represented as
y = mx + c
This means that
c = 4
So, we have
y = mx + 4
The point (4, 6) implies that
6 = m * 4 + 4
So, we have
4m = -2
m = -1/3
So, the equation is
y = -1/3x + 4
Substitute y = -1/3x + 4 in y = 4x - 3
-1/3x + 4 = 4x - 3
So, we have
-x + 12 = 12x - 9
Evaluate the like terms
13x = 21
Divide
x = 21/13
y = -1/3x + 4 implies that
y = -1/3 x 21/13 + 4
So, we have
y = -7/13 + 4
Evaluate
y = 45/13
So, the solution is (21/13, 45/13)
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suppose that functions p and q are defined as follows
p(x) = 2x
q(x) = x^2-2
find the following :
(q•p) (-3)=
(p•q) (-3)
You want to replace the tires on your car with tires that have a larger diameter. After you change the tires, for trips at the same speed and over the same distance, how will the angular velocity and number of revolutions change?
The change in the angular velocity and number of revolutions is given as,
when the angular velocity decreases the number of revolutions also decreases.
The rotation rate, which refers to how quickly an item rotates or circles in relation to another point, is measured vectorially by angular velocity.
Angular velocity can be defined as the speed at which an item rotates or revolves around an axis. The Greek letter omega stands for angular velocity. The SI unit of angular velocity is radians per second because it is measured in angle per unit time.
The only distinction between revolution and rotation is that the axis of rotation in a revolution is located outside the body. Both motions of an item or body in space are circular.
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A line has a slope of 1/4. The line passes through the
point (4, 6). The line also passes through the point (12, k). What is the value of k?
A. 8
B. 9
C. 14
D. 18
The value of k in which a line is has a slope 1/4 passing through the points (4,6) and (12,k) is 8.The option is A.8
Slope of straight line(m) which is passing through the point is y=mx+c, where m= slope of the line c is the intercept and x and y are distance from the respective x-axis and y-axis.
The line is passing through the 2 points say ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) then m=[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]we are having the points (4,6) and (12,k)( [tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex])and slope m=1/4.
Now substitute the values of( [tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) in m=[tex]\frac{x_{2}-x_{1} }{y_{2}-y_{1} }[/tex].
[tex]\frac{1}{4}[/tex]= [tex]\frac{k-6}{12-4}[/tex],
4(k-6)= 8
4k-24=8
4k=32
k=[tex]\frac{32}{4}[/tex]
k=8
The value of k in which a line is has a slope 1/4 passing through the points (4,6) and (12,k) is 8.The option is A.8
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Solve for x: log(x) - log(3) = 2 log(6)
Answer:
Below
Step-by-step explanation:
log x = 2 log 6 + log 3 using properties of logs, this becomes
log x = log 6^2 + log 3
= log (6^2 * 3 ) = log (108)
x = 108
5. Solve each equation using a function machine. The first one is started for you.
a. 3 x+4=25
c. 4 b-10=30
e. 5 n+2=37
g. 3 k+4=28
b. 3 x-4=11
d. 4 b+10=30
f. 2 w+10=2
h. 6 h-7=11
The solutions to the equations using function machine are x = 7, x = 5, b = 10, b = 5, n = 7, w = -4, k = 8 and h = 3
How to determine the solutions to the equations using function machineFrom the question, we have the following equations that can be used in our computation:
a. 3x+4=25 b. 3x-4=11c. 4b-10=30 d. 4b+10=30e. 5n+2=37 f. 2w+10=2g. 3k+4=28 h. 6h-7=11Using a function machine, we have:
Equation (a)
3x + 4=25
This becomes
x ⇒ [ ] ⇒ [ ] = [ ]
So, we have
x ⇒ [ 21 ] ⇒ [ +4 ] = [ 25 ]
This means that
x = 21/3
x = 7
Equation (b)
3x - 4 = 11
This becomes
x ⇒ [ ] ⇒ [ ] = [ ]
So, we have
x ⇒ [ 15 ] ⇒ [ -4 ] = [ 11 ]
This means that
x = 15/3
x = 5
Equation (c)
4b - 10 = 30
This becomes
b ⇒ [ ] ⇒ [ ] = [ ]
So, we have
b ⇒ [ 40 ] ⇒ [ -10 ] = [30]
This means that
b = 40/4
b = 10
Equation (d)
4b + 10 = 30
This becomes
b ⇒ [ ] ⇒ [ ] = [ ]
So, we have
b ⇒ [ 20 ] ⇒ [ +10 ] = [30]
This means that
b = 20/4
b = 5
Equation (e)
5n + 2 = 37
This becomes
n ⇒ [ ] ⇒ [ ] = [ ]
So, we have
n ⇒ [ 35 ] ⇒ [ +2 ] = [37]
This means that
n = 35/5
n = 7
Equation (f)
2w + 10 = 2
This becomes
w ⇒ [ ] ⇒ [ ] = [ ]
So, we have
w ⇒ [ -8 ] ⇒ [ +10 ] = [2]
This means that
w = -8/2
w = -4
Equation (g)
3k + 4 = 28
This becomes
k ⇒ [ ] ⇒ [ ] = [ ]
So, we have
k ⇒ [ 24 ] ⇒ [ +4 ] = [28]
This means that
k = 24/3
k = 8
Equation (h)
6h - 7 = 11
This becomes
h ⇒ [ ] ⇒ [ ] = [ ]
So, we have
h ⇒ [ 18 ] ⇒ [ -7 ] = [11]
This means that
h = 18/6
h = 3
Hence, the value of h is 3
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which is faster
A. 4 miles in 1/3 hour
B. 1.3 mile in 4hours
C. 1/2 mile in hours
The unit rate or the number of miles run in one hour is 12 miles thus, 4 miles in 1/3 hour will be the faster.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
4 miles in 1/3 hour ⇒ 4 x3/1 = 21 miles/hour
1.3 miles in 4 hours ⇒ 1.4/4 mile/hour
1/2 mile in hours ⇒ 0.5 miles/hour
Hence "The unit rate or the number of miles run in one hour is 12 miles thus, 4 miles in 1/3 hour will be the faster".
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Identify the quadratic function that is in standard form and has zeros -11 and 6. f(x) = x² + 5x + 66
f(x) = x² - 5x + 66
f(x)= x2 + 5x - 66
F(x)=x2-5x - 66
The standard quadratic equation is (c) y = x² + 5x - 66
How to determine the quadratic equation?From the question, we have the following parameters that can be used in our computation:
Zeros -11 and 6
This means that
x = -11 and x = 6
The quadratic equation can then be calculated as
y = (x - 6) * (x + 11)
Evaluate the products
y = x² - 6x + 11x - 66
Evaluae the like terms
y = x² + 5x - 66
Hence, the equation is y = x² + 5x - 66
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