Answer: (1)
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals. So, since the slope of the given line is 2/3, the slope of the line we want to find is -3/2.
Rearranging equations 1 and 2 into slope intercept form,
[tex]3x+2y=12 \implies 2y=-3x+12 \implies y=-\frac{3}{2}x+6\\\\3x-2y=12 \implies 2y-3x=-12 \implies 2y=3x-12 \implies y=\frac{3}{2}x-6[/tex]
From this, we see that equation 1 is the answer.
A wealthy businessman invests $10,000 and expects a 6.75% rate of return annually. How many years will it take the investment to reach $15,000 in value?Round your answer to the nearest number of years.
Answer
7 years
Explanation
Given:
Principal, P = $10,000
Rate, R = 6.75%
Amount, A = $15,000
What to find:
The years will it take the investment to reach $15,000 in value.
Step-by-step solution:
You need to first calculate the total interest on the investment using;
Interest, I = Amount, A - Principal, P
Interest, I = $15,000 - $10,000
Interest, I = $5,000
The final step is to find the years it takes the investment to reach $15,000 in value using simple interest formula.
[tex]\begin{gathered} S.I=\frac{T\times P\times R}{100} \\ \\ \Rightarrow T=\frac{S.I\times100}{P\times R} \end{gathered}[/tex]Putting the values of the parameters into the formula, we have;
[tex]\begin{gathered} T=\frac{5000\times100}{10000\times6.75}=\frac{500,000}{67,500}=7.407\text{ }years \\ \\ To\text{ }the\text{ }nearest\text{ }number\text{ }of\text{ }years, \\ \\ T=7\text{ }years \end{gathered}[/tex]Therefore, it will take 7 years for the investment to reach $15,000 in value.
Evaluate without a calculator.[tex] log_{4}(16) + log_{3}(27) [/tex]please show your work..!
Answer:
The value of the given expression is;
[tex]5[/tex]Explanation:
Given the logarithmic expression;
[tex]\log _416+\log _327[/tex]To solve, Recall the rules of logarithm;
[tex]\begin{gathered} \log _ax^y=y\times\log _ax\text{ ------1} \\ \log _aa=1\text{ -------2} \end{gathered}[/tex]Apply the above rules;
[tex]\begin{gathered} \log _416+\log _327 \\ \log _44^2+\log _33^3 \\ \text{Applying rule 1;} \\ 2\log _44+3\log _33 \end{gathered}[/tex]Aplplying rule 2;
[tex]\begin{gathered} 2\log _44+3\log _33 \\ =2(1)+3(1) \\ =2+3 \\ =5 \\ \log _416+\log _327=5 \end{gathered}[/tex][tex]\begin{gathered} \text{Note that from the rule 2;} \\ \log _aa=1 \\ so\text{ when a logarithm has the same number as the base it will equal to 1;} \\ \text{for example;} \\ \log _44=1 \\ \log _33=1 \\ \log _55=1 \end{gathered}[/tex]Therefore, the value of the given expression is;
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Question
On Friday, there were 6 snowboarders for every 2 skiers at a local ski resort. Or
Saturday, the ratio of the number of snowboarders to the number of skiers
was 5:3. There were 144 snowboarders at the ski resort on Friday. There were
same number of people at the ski resort on Saturday as there were on Friday
How many more skiers were there than snowboarders at the ski resort on
Saturday?
As calculated by the given ratios, 36 more skiers were there than snowboarders at the local resort on Saturday.
What is ratio?
A ratio illustrates how two or more values differ in terms of size.
Ratios can be displayed in a variety of ways, including as decimals (after dividing one value by the whole), percentages (after dividing one value by the entire), and using the ":" or "/" to separate values.
As given in the question,
Ratio of Snowboarders to Skiers
On Friday: ratio is 6:2
On Saturday: 5:3
Population = 144
Now, lets calculate the number of snowboarders and skiers at Saturday:
Given ratio: 5:3
total = 5+3
total = 8
No. of skiers is:
= (3/8)(144)
= 54
No. of snowboarders is:
= (5/8)(144)
= 90
Now lets calculate the difference between no. of snowboarders and skiers:
= 90-54
= 36
Hence, there are 36 more snowboarders than skiers.
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tod has 20 books he donated 2/5 how many books did he donate?
Given:
Total number of books is, N = 20.
Number of books donated is, d = 2/5 of books.
The objective is to find the number of books donated.
Consider the number of books donated as x.
[tex]\begin{gathered} x=\frac{2}{5}\cdot20 \\ x=8 \end{gathered}[/tex]Hence, the number of books donated is 8.
I need help with please!!!
Maria is to weld a support for a 23-m conveyor so that it will operate at a 20 degree angle. What is the length of the support?
The length of the support when Maria is to weld a support for a 23-m conveyor is 7.87 m.
How to illustrate the information?From the information, Maria is to weld a support for a 23-m conveyor so that it will operate at a 20 degree angle.
Let AB = 23m
Let x = 20°
We can then use the sine rule to find the length. This will be illustrated thus:
Sin x = AC / AB
Sin 20° = AC / 23
AC = 23 × sin 20°
AC = 7.87
The length is 7.87m
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15. Which of the following is true about the relationship in the table shown? Х 7 11 20 25 100 8.4 13.2 24 30 120 A. The table is non-proportional because it does not include the point (0,0). B. The table is non-proportional because the x-values do not increase at a constant interval. C. The table is proportional because all of the x and y-values are positive and increasing, D. The table is proportional because the ratio between y and x is constant.
Explanation:
To determine if the table is proportional or not, we need to find the ratio between x and y for each of the data. if it is constant, then it is proportional
Proportional relationship:
y = kx
k = constant of proportionality
k = y/x
for the x = 7, y = 8.4
k = 8.4/7 = 1.2
for x = 11, y = 13.2
k = 13.2/11 = 1.2
for x = 20, y = 24
k = 24/20 = 1.2
for x = 25, y = 30
k = 30/25
k = 1.2
when x = 100, y = 120
k = 120/100
k = 1.2
Since the ratio between y and x is the same for all, the table is proportional
The correct option:
The
If 2x+y=4 and 2x-y=8, then what does 3x-y equal?
THE TRICK IS TO FIND THE VALUE OF X AND Y FIRST.
I WILL USE SUBSTITUTION TO SOLVE THIS SYSTEM OF EQUATIONS.
[tex]y = 4 - 2x......(3)equation[/tex]
[tex]2x - (4 - 2x) = 8 \\ 2x - 4 + 2x = 8 \\ 2x + 2x = 8 + 4 \\ 4x = 12 \\ \frac{4x}{4} = \frac{12}{4} \\ x = 3[/tex]
[tex]y = 4 - 2(3) \\ y = 4 - 6 \\ y = - 2[/tex]
THEN FOR 3X-Y PLUG IN THE VALUES YOU FOUND FOR X AND Y
[tex] = 3(3) - ( - 2) \\ = 9 + 2 \\ = 11 \\ 3x - y = 11[/tex]
ATTACHED IS THE SOLUTION
There are 36 students in s2a some of them usually bring their own lunch and the other buy lunch.if 1/5 of the students who usually bring their own lunch buy their lunch today , the ratio of the number of students bringing their own lunch to number of students buying lunch becomes 1:2. how many students are there who usually bring thier own lunch ?
The no. of students who usually bring their own lunch is 15.
What is the ratio?The ratio is a comparison between two or more quantities in simplest form.
Given there are 36 students in an s2a class some of them bring their own lunch and the others buy their lunch.
Assuming x students bring their own lunch hence (36 - x) students buy their lunch.
(1/5)th of the student who brings their own lunch is (1/5)×x = (x/5).
∴ x - (x/5) : (36 - x) + (x/5) = 1 : 2. (The reduced students are added to the
other category).
4x/5 : 36 - 4x/5 = 1 : 2.
4x/5 : (180 - 4x)/5 = 1 : 2.
(4x/5)÷(180 - 4x)/5 = 1/2.
(4x/5)×5/(180 - 4x) = 1/2.
4x/(180 - 4x) = 1/2.
4x = (180 - 4x)/2.
8x = 180 - 4x.
12x = 180.
x = 15.
∴ 15 students usually bring their own lunch.
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what function is represented in the table ?- y = 3 (4x )- y = 2 ( .25x )- y = 4 ( .25 ) x - y = 4 ( 3x )
1) To determine which is the function from the table we need to attentively look for a constant factor in the y-column.
2) As we can see from this table, the factor we can tell that goes from 64 to 16 and then 4 is 1/4. Or in decimal form 0.25. So, we can tell the factor "b" is going to be 1/4 considering this model:
[tex]\begin{gathered} y=a(b)^x \\ y=a(0.25)^x \end{gathered}[/tex]3) Let's pick one point (0,4) and plug it to find the other elements:
[tex]\begin{gathered} y=a(\frac{1}{4})^x,(0,4) \\ 4=a(\frac{1}{4})^0 \\ a=4 \end{gathered}[/tex]And finally, we can tell the function is:
[tex]undefined[/tex]Question 94 ptsONLY write your answer as a number. You do not needto write the unit measurement.Round you answer to the nearest tenth.15. A fireman leaned a 42-foot ladder against a building. If he placed the ladder 8.5 feetfrom the base of the building, what angle is formed between the ladder and the ground
The length of ladder is L = 42 foot.
The distance between base of building and ladder is b = 8.5.
Determine the measure of angle by using the trigonometry.
[tex]\begin{gathered} \cos \theta=\frac{8.5}{42} \\ \theta=\cos ^{-1}(0.20238) \\ =78.323 \\ \approx78.3 \end{gathered}[/tex]So measure of angle is 78.3 degree.
Karl earned $188 last month doing chores after school. If 68% of the money he earned was from doing yard work, about how much did Karl earn doing yard work?
URGENT HELP PLEASE SOLVE QUESTIONS FIVE AND SIX USING THE INSTRUCTIONS IN THE PIC VERY URGENT PLEASE HELP ME!!!!!!
Answer:
4.number 1
5.number 2
Step-by-step explanation:
4.Because the the expression tan can be written as sin divided by cos it will be beneficial to write the square of cos as cos multiplied by cos so that after canceling out we are left with cos multiplied by sin of the left hand side.
5.because transforming cos squared to 1-sin squared will allow us to to have a fraction where both the numerator and denominator are the same which equals one.
Four friends use a spinner to decide the luckiest person. Who is more likely to be the luckiest person?
The luckiest person is Clinton because it is more likely.
Answer: Clinton
The weight M of an object on the moon varies directly as its weight E on earth. A person who weighs 162.71lb on earth weighs 27.66lb on the moon. How much would a 220lb person weigh on the moon?
A 220lb person on earth would weigh 23.81lb on moon
Given
Weight of an object on moon varies same as that on the planet earth
This means the weights are directly proportional
Weight of person on earth = 162.7lb
Weight of person on moon = 27.66lb
Also,
Weight of person on earth = 220lb
We need to find weight of this person on moon.
Let weight of person on moon be x
According to the data equation can be formed as
27.66 x 220 = 162.71x
3885.2 = 162.71x
x= 23.81
Hence the weight of the person on moon is 23.lb
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Use the slope formula to find the slope of the line through the points (−8,−6) and (0,−7).
Answer:
Slope formula is given as (y2-y1) ÷ (x2-x1) or (y1-y2) ÷ (x1-x2), where x and y are the coordinates of the points.
Slope = (-7-(-6)) ÷ (0-(-8))
= (-7+6) ÷ (0+8)
= -1/8
Consider the function whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree. Is this a one-to-one function? Explain why or why not.
No, a function whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree is not a one-to-one function.
What is a one-to-one function?A one-to-one function is also referred to as an injective function and it can be defined as special type of function in which every element of the range is mapped to exactly a single element of its domain. This ultimately implies that, the output values (y-values) of a one-to-one function never repeat themselves.
Additionally, a one-to-one function maps distinct elements of its domain (y-values) to distinct elements of the range (x-values) and as such, it connotes the mapping of two (2) sets.
In this context, we can reasonably and logically deduce that this function is not a one-to-one function because it fails the horizontal line test as there could be the same temperature at different times of the day.
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The hypotenuse of a right triangle is four times the length of one of the legs. The length of the other leg is sqrt(240) feet. Find the lengths of the leg and hypotenuse
ANSWER
Hypotenuse: 16 ft
Leg: 4 ft
EXPLANATION
Given:
A right angle triangle with only one leg = sqrt(240) feet
Desired Outcomes:
Lengths of the leg and hypotenuse
Declaration of variables
Let x represent the length of leg
Hypotenuse = 4 times the length of leg = 4x
Apply Pythagorean theorem
[tex]\begin{gathered} Hyp^2=Opp^2+Adj^2 \\ (4x)^2=x^2+(\sqrt{240})^2 \\ 16x^2\text{ = }x^2\text{ + 240} \\ 16x^2-x^2\text{ = 240} \\ 15x^2\text{ = 240} \\ x^2\text{ = }\frac{240}{15} \\ x\text{ =}\sqrt{16} \\ x\text{ = 4 ft} \end{gathered}[/tex]Hypotenuse = 4x = 4 (4) = 16 ft
Hence, the Lengths of the leg and hypotenuse are 4 ft and 16 ft respectively.
PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
1) [tex]VX=ZX, \angle XVY=\angle XZW[/tex] (given)
2) [tex]\angle X=\angle X[/tex] (reflexive property)
3) [tex]\triangle VXY \equiv \triangle ZXW[/tex] (ASA)
A 20-foot ladder is leaning against the side of a house so that the bottom of the ladder is 12 feet from the base of the house. Will the ladder reach a window that is 14.5 feet above the ground?
Yes, because the ladder will reach 32 feet high
Yes, because the ladder will reach 16 feet high
No, because the ladder will only reach 16 feet high
No, because the ladder will only reach 12 feet high
Yes, because the ladder will reach 16 feet high
what is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem.
According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
Given:
Hypotenuse= 20 feet
base= 12 feet
Using Pythagoras theorem
H²= P² + B²
20² =12² +P²
P²= 400-144
P²= 256
P= 16 FEET.
Hence, Yes, because the ladder will reach 16 feet high
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Thomas invested $1498 at
6% Sumple interest per annum.
Calculate.
1) The interest, in dollars,
earned after six months
well, keeping in mind that a year has 12 months, that means 6 months is 6/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1498\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases} \\\\\\ I = (1498)(0.06)(\frac{1}{2}) \implies I = 44.94[/tex]
The measure of the angle 6 = _____
helllpppppppppppppp.
Answer:
See below
Step-by-step explanation:
can someone please help me with this angle puzzle?!
Answer:
See below
Step-by-step explanation:
If I did the math numbers correctly : ( a = 51° too)
A box of chocolates contains five milk chocolates and five dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. What is the probability that both pieces are milk chocolate?
SOLUTION
This is a probability question that has to do with the "without replacement" scenario, because every chocolate eaten leaves the box and never returns
The probability that both pieces are milk chocolate is calculated thus:
[tex]\frac{Number\text{ of milk chocoltes}}{Total\text{ number of chocoltes in the box}}\times\frac{Number\text{ of milk chocolates-1}}{Total\text{ number of chocoltes -1}}[/tex]Number of milk chocolates = 5
NUmber of dark chocolates = 5
Total number of chocolates in the box = 5+5 =10
The probability that both pieces are milk chocolate is:
[tex]\begin{gathered} \frac{5}{10}\times\frac{5-1}{10-1}(since\text{ it is without replacement of chocolates)} \\ \frac{5}{10}\times\frac{4}{9} \\ \frac{20}{90} \\ =\frac{2}{9} \end{gathered}[/tex]The probability that both pieces are milk chocolate is:
[tex]\frac{2}{9}[/tex]
⦁ A room 12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square. Answer the following questions. Assume there is no waste in materials, and round off your answer to the next largest unit. Show both exact and rounded figures in the blanks provided.
The amount of wall surface in square feet is there to paint is: 364 square ft. While the floor area is 169.58sq ft. See the calculations below:
What is Square Feet?The square foot is an imperial measure of area and a customary unit of area in most countries. It is defined as the area of a square with one-foot sides.
The calculation for the above solution is given as:
Step I - Recall the Given Stats:
Dimensions of the room are:
12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square.
Let Lenght (l) = 13'9" = 13(9/12) ft = 13(3/4) = 55/4 ft.
Let Width(w) = 12'4" = 12(4/12) ft = 12(1/3)ft = 37/3 ft
Let Height h = 8'0" = 8ft.
Recall that we have a door with dimensions 3' x 7' and two windows 4'x4'
Step II - A) Surface area of the wall to be painted is:
Area of 4 walls less (area of door plus area of window)
Surface Area = 2LH + 2WH - ((3 x7) + 2(4x4))
= 2(l +w)h - (21 + 32)
= 2 ((55/4) + (37/3))8 -53
= 220 + 592/3 - 53
= 167 + 592
= (501+ 592)/3
= 1093/3
Hence,
The Surface Area to be painted is = 364.33 Sq ft.
Step III - B) The Area of the Floor = Lx W
= (55/4) x (37/3)
= 2035/12
= 169.583333333
Hence,
Area of the Floor is approximately = 169.58
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Full Question:
A room 12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square.
Answer the following questions. Assume there is no waste in materials, and round off your answer to the next largest unit. Show both exact and rounded figures in the blanks provided.
A. How much wall surface in square feet is there to paint?
B. What is the floor area?
The table below shows the number of house calls three different plumbers made on three different days.
Number of House Calls
Plumber A
Plumber B
Plumber C
Monday
2
8
8
Tuesday
4
7
10
Wednesday
3
9
9
The total amount of money earned by all three plumbers on Monday was $1,400. On Tuesday they earned a total of $1,660, and on Wednesday, they earned a total of $1,650. On Thursday, Plumber A made four house calls, Plumber B made six house calls, and Plumber C made three house calls. How much total money is earned on Thursday?
$250
$1,060
$1,090
$1,130
The total money that is earned on Thursday is $1090
How to determine the total money that is earned on Thursday?From the question, we have the following table of values
Monday Tuesday Wednesday
Plumber A 2 8 8
Plumber B 4 7 10
Plumber C 3 9 9
Using the given parameters in the question, we have the following system of equations
2a + 8b + 8c = 1400 --- (1)
4a + 7b + 10c = 1660--- (2)
3a + 9b + 9c = 1650 --- (3)
Subtract equation (2) from twice equation (1)
So, we have
(4a + 16b + 16c = 2,800) - (4a + 7b + 10c = 1,660)
This gives
9b + 6c = 1140 --- (4)
Subtract four times equation (3) from three times equation (2)
So, we have
12a+ 21b +30c = 4,980 -(12a + 36B + 36c = 6,600)
This gives
-15b - 6c = -1,620 --- (5)
Add equations (4) and (5)
(9b + 6c = 1140) + (-15b - 6c = -1620)
So, we have
-6B = -480
Divide by -6
b = 80
Substitute b = 80 in -15b - 6c = -1,620
-15 x 80 - 6c = -1,620
Evaluate
-1200 - 6c = -1,620
So, we have
-6c = -420
Divide
c = 70
In (2), we have
4a + 7b + 10c = 1660
This gives
4a + 7 * 80 + 10 * 70 = 1660
Evaluate
4a = 400
Divide
a = 100
On Thursday, we have
a = 4, b = 6 and c = 3
So, we have
Total = 4 * 100 + 6*80 + 3*70
Evaluate
Total = 1090
Hence, the total earnings is 1090
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Write an equation of function g(x) and describe the effects on the graph of the parent function f(x)=x^2. g(x)=f(x)+d where d=2
Given:
a.) f(x) = x²
b.) g(x) = f(x) + d
c.) d = 2
To be able to complete the equation of function g(x), let's substitute the function of f(x) and d.
We get,
g(x) = f(x) + d
g(x) = x² + 2
Therefore, g(x) = x² + 2.
Enter the ratio as a fraction in lowest terms6 ft to 78 in.
To answer this question, we need to remember that a ratio is a comparison of two or more units. We can also need to have into account that these units must be in the same units.
We have one of the quantities is 6ft, the other is equal to 78 inches. We can convert 6ft to its equivalent in inches, or 78 inches into its equivalent in feet. Then, we have:
[tex]6ft\cdot\frac{12in}{1ft}=72in[/tex]Then, we can conclude that the ratio of 6feet (72 inches) to 78 inches is equivalent to:
[tex]\text{Ratio}=\frac{72in}{78in}=\frac{12}{13}\Rightarrow Ratio=\frac{12}{13}[/tex]An anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. The results were as follows: 855 drankalcohol regularly, 657 smoked cigarettes, 192 used illegal drugs, 418 drank alcohol regularly and smoked cigarettes, 109 drank alcohol regularly and used illegal drugs,116 smoked cigarettes and used illegal drugs, 88 engaged in all three behaviors, and 251 engaged in none of these behaviors.Answer parts a, b, c, d, e, f, g for this question.
To solve the question, we will be using a Venn Diagram. Let's list down what's given first:
855 drank alcohol
657 smoked cigarettes
192 used illegal drugs
418 both drank alcohol and smoked cigarettes
109 drank alcohol and used illegal drugs
116 smoked cigarettes and used illegal drugs
88 engaged in all three
and 251 engaged in none of these
We will draw a Venn Diagram with 3 circles, one for each vice. Then we will start with the intersection of all three and the area outside of the circles (for those who do not engage in vices).
Because we know how many engaged in all 3 vices, we can deduct that number from those who belong to the intersection of 2 vices since they have already been counted in that too.
418 - 88 = 330 drank and smoked, but not used drugs
109 - 88 = 21 drank and used drugs, but not smoked
116 - 88 = 28 smoked and used drugs but not drank
Then, we subtract the numbers in each circle from the total for each vice.
855 - (330 + 88 + 21) = 416 drank only
657 - (330 + 88 + 28) = 211 smoked only
192 - (88 + 21 + 28) = 55 used drugs only
To find the total number of surveyed students, we just need to add all the numbers in the Venn Diagram.
416 + 330 + 88 + 21 + 211 + 28 + 55 + 251 = 1,400
Therefore, there were 1,400 students who were surveyed.