Answer:
c. no solution
Step-by-step explanation:
6d + 3f = 12
2d = 8 - f
Multiply the second equation by 3
3*2d = 3(8-f)
6d = 24-3f
Substitute into the first equation for 6d
(24-3f) +3f = 12
Combine like terms
24 =12
This is never true, so there are no solutions
Answer:
c. No Solution.
Step-by-step explanation:
6d + 3f = 12
2d = 8 - f
Rearranging the second equation:
2d + f = 8 Multiply this equation by 3:
6d + 3f = 24
Note that the left side of this equation = the left side of the first equation but the right sides are different. So this system does not make sense and there are No Solutions.
Draw a diagram for this statement.
one sixth of the 48 vegetable plants were tomato plants.
use your diagram to determine how many of the vegetable plants were tomato plants
Answer:
8
Step-by-step explanation:
one sixth of 48 is 8 therefore you have eight tomato plants
A bag contains 12 red marbles, 5 yellow marbles, and 15 green marbles. How many additional red marbles must be added to the 32 marbles already in the bag so that the probability of randomly drawing a red marble is ?
Answer:
18 red marbles.
Step-by-step explanation:
The complete question asks the probability of randomly drawing a red marble is 3/5?
Let x be the number of red marbles that must be added.
To find x we will do the following:
[tex]\frac{x+12}{x+32} =\frac{3}{5}[/tex]
=>[tex]5(x+12)=3(x+32)[/tex]
=> [tex]5x+60=3x+96[/tex]
=> [tex]2x=36[/tex]
This gives x = 18
Hence, 18 red marbles will be added to the bag.
I need help on understanding this one! Thank you!
Answer:
(6^⅕) (cos(-24°) + i sin(-24°))
Step-by-step explanation:
First, we convert from Cartesian to polar:
r = √((-3)² + (-3√3)²)
r = √(9 + 27)
r = 6
θ = atan( (-3√3) / (-3) ), θ in the third quadrant
θ = atan(√3)
θ = 240° + 360° k
Notice that θ can be 240°, 600°, 960°, etc.
Therefore:
-3 − 3√3 i = 6 (cos(240° + 360° k) + i sin(240° + 360° k))
Now we take the fifth root:
[ 6 (cos(240° + 360° k) + i sin(240° + 360° k)) ]^⅕
(6^⅕) [ (cos(240° + 360° k) + i sin(240° + 360° k)) ]^⅕
Applying de Moivre's Theorem:
(6^⅕) (cos(⅕ × 240° + ⅕ × 360° k) + i sin(⅕ × 240° + ⅕ × 360° k))
(6^⅕) (cos(48° + 72° k) + i sin(48° + 72° k))
If we choose k = -1:
(6^⅕) (cos(-24°) + i sin(-24°))
Elijah drove 45 miles to his job in an hour and ten minutes in the morning. On the way home: however, traffic was much heavier and the same trip took an hour and half. What was his average speed in miles per hour for the round trip?
Answer:
33.75
Step-by-step explanation:
You first need to determine the total distance of the round trip. This is twice the 45 mile trip in the morning, which is 90 miles. In order to determine the total amount of time spent on the round trip, convert the time travel to minutes.
1 hr + 10 mins = 70 mins
1hr + 30 = 90 mins
So his total travel time would equal to 90+70=160 minutes
his average speed is:
90mi/160min * 60min/1hr = 90*60/160
= 33.75
Elijah's average speed for the round trip is approximately 31.76 miles per hour.
To calculate the average speed for the round trip, we need to determine the total distance traveled and the total time taken.
In the morning, Elijah drove 45 miles in 1 hour and 10 minutes. To convert the minutes to hours, we divide 10 minutes by 60, which gives us 10/60 = 1/6 hours. Therefore, his morning travel time is 1 hour + 1/6 hour = 7/6 hours.
On the way home, the same trip took him 1 hour and 30 minutes. Converting the minutes to hours, we divide 30 minutes by 60, which gives us 30/60 = 1/2 hours. Therefore, his return travel time is 1 hour + 1/2 hour = 3/2 hours.
To calculate the total distance traveled, we sum the distance from the morning trip and the return trip: 45 miles + 45 miles = 90 miles.
The total time taken for the round trip is the sum of the morning travel time and the return travel time: 7/6 hours + 3/2 hours = 17/6 hours.
To calculate the average speed, we divide the total distance by the total time: 90 miles / (17/6 hours).
Dividing 90 miles by 17/6 hours is the same as multiplying 90 miles by 6/17, which gives us (90 * 6) / 17 = 540/17.
Therefore, Elijah's average speed for the round trip is approximately 31.76 miles per hour.
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Three fourths of a gasoline storage tank is emptied by filling each of five trucks with the same amount of fuel what part of the total capacity of the storage tank did each vehicle receive
Answer:
Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank
Step-by-step explanation:
we know that
To find out what part of the total capacity of the storage tank that each vehicle received, divide three fourths by five
so
[tex]\frac{(3/4)}{5}=\frac{3}{20}[/tex]
therefore
Each vehicle received [tex]\frac{3}{20}[/tex] of the total capacity of the storage tank
The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table below to help answer the question.
16%
32%
34%
84%
Answer:
The answer is 16%
Step-by-step explanation:
Given a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes
so a time less than or equal to 3 hours and 20 minutes is a time 1 standard deviation OUTSIDE from the mean
Use the probability table:
The probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes
= Probability of z being outside 1 SD from mean
= 1 - Probability of z within 1 SD from mean
= 1 - 0.84
= 0.16 or 16%....
Question about Radicals.
Answer:
Conjugate
Step-by-step explanation:
Those are conjugates. In factoring polynomials, if you have one with a + sign separating the a and the square root of b, you will ALWAYS have one with a - sign. They will always come in pairs. Same with imaginary numbers.
Please help *image attached*
Answer:x=25
Step-by-step explanation:
One line is 180 , AB equals 180 ,angle AD is 110,180-110=70
So corner O on line DC is 70 and angle CE is 60. 60+70=130
180-130=50, 2x=50,50/2=25
The variable z is inversely proportional to x. When x is 16, z has the value 0.5625. What is the value of z when x= 25?
Answer:
0.36
Step-by-step explanation:
z is inversely proportional to x:
z = k / x
When x is 16, z has the value 0.5625.
0.5625 = k / 16
k = 9
What is the value of z when x= 25?
z = 9 / 25
z = 0.36
Answer:
The answer is 9/25 or .36 if you prefer it in decimal form.
Step-by-step explanation:
inversely proportional means there is a constant that we are going to divide by.
So z is inversely proportional to x means z=k/x where k is a constant.
We are given when x=16, z=0.5625. This information will be used to find our constant value k.
0.5625=k/16
Multiply both sides by 16:
16(0.5625)=k
Simplify:
9=k.
This means no matter what (x,z) pair we have the constant k in z=k/x will always be 9.
The equation we have is z=9/x.
Now we want to find z when x=25.
z=9/25
z=.36
You bought a guitar 6 years ago for $400. If its value decreases by
about 13% per year, how much is your guitar worth now?
$351.23
$226.55
$322
$173.45
Answer:
$173.45
Step-by-step explanation:
the beginning value is $400. if it loses 13%, that means it keeps 87% of its value. so you multiply by 0.87 6 times for each year
URGENT PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
The image is (0 , -6)
Step-by-step explanation:
* Lets explain some important facts
- When a point reflected across a line the perpendicular
distance from the point to the line equal the perpendicular
distance from its image to the same line
- If the line of the reflection is horizontal then the perpendicular
distance between the point and the line is y - y1 , and the
perpendicular distance between the image and the line is y2 - y
- If point (x , y) reflected across the x- axis, then its image is (x , -y)
* Lets solve the problem
∵ Point (0 , 0) reflected across the line y = 3
∴ y = 3 and y1 = 0
∴ The distance between the point and the line is 3 - 0 = 3
∴ The distance between the image and the line also = 3
∴ y2 - 3 = 3 ⇒ add 3 to both sides
∴ y2 = 6
∴ The y-coordinate of the image is 6
∴ The image of point (0 , 0) after reflection across the line y = 3 is (0 , 6)
- The image of the point reflected across the x-axis, then change the
sign of the y-coordinate
∴ The final image of point (0 , 0) is (0 , -6)
* The image is (0 , -6)
Suppose that the length of a certain rectangle is four centimeters more than three times its width. If the area of the rectangle is 95 square centimeters, find its length and width.
Answer: The length and width of the rectangle are 19 cm and 5 cm respectively.
Step-by-step explanation: Given hat the length of a rectangle is four centimeters more than three times its width and the area of the rectangle is 95 square centimeters.
We are to find the length and width of the rectangle.
Let W and L denote the width and the length respectively of the given rectangle.
Then, according to the given information, we have
[tex]L=3W+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Since the area of a rectangle is the product of its length and width, so we must have
[tex]A=L\times W\\\\\Rightarrow 95=(3W+4)W\\\\\Rightarrow 3W^2+4W-95=0\\\\\Rightarrow 3W^2+19W-15W-95=0\\\\\Rightarrow W(3W+19)-5(3W+19)=0\\\\\Rightarrow (W-5)(3W+19)=0\\\\\Rightarrow W-5=0,~~~~~3W+19=0\\\\\Rightarrow W=5,~-\dfrac{19}{3}.[/tex]
Since the width of the rectangle cannot be negative, so we get
[tex]W=5~\textup{cm}.[/tex]
From equation (i), we get
[tex]L=3\times5+4=15+4=19~\textup{cm}.[/tex]
Thus, the length and width of the rectangle are 19 cm and 5 cm respectively.
The length of the rectangle is 19 and the width is 5 and it can be determined by using the formula of area of the rectangle.
Given that,The length of a certain rectangle is four centimeters more than three times its width.
If the area of the rectangle is 95 square centimeters,
We have to determine,The length and width of the rectangle.
According to the question,Let the length of the rectangle be L,
And the width of the rectangle is W.
The length of a certain rectangle is four centimeters more than three times its width.
The perimeter of a square is the sum of the length of all its four sides.The perimeter formulas of different two-dimensional shapes:
Then,
[tex]\rm L = 3W+4[/tex]
And If the area of the rectangle is 95 square centimeters,
The area of any polygon is the amount of space it occupies or encloses.It is the number of square units inside the polygon.
The area is a two-dimensional property, which means it contains both length and width
[tex]\rm Area \ of \ the \ rectangle = length \times width\\\\L\times W = 95[/tex]
Substitute the value of L from equation 1,
[tex]\rm L\times W = 95\\\\(3W+4) \times W = 95\\\\3W^2+4W=95\\\\3W^2+4W-95=0\\\\3W^2+19W-15W-95=0\\\\W(3W+19) -5(3W+19) =0\\\\(3W+19) (W-5) =0\\\\W-5=0, \ W=5\\\\3W+19=0, \ W = \dfrac{-19}{3}[/tex]
The width of the rectangle can not be negative than W = 5.
Therefore,
The length of the rectangle is,
[tex]\rm L = 3W+4\\\\L = 3(5)+4\\\\L=15+4\\\\L=19[/tex]
Hence, The length of the rectangle is 19 and the width is 5.
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Which of the following statements is(are) NOT applicable to typologies? a. They are typically nominal composite measures. b. They involve a set of categories or types. c. They may be used effectively as independent or dependent variables. d. They are often used when researchers wish to summarize the intersection of two or more variables.e. All of these choices apply to typologies.
Answer: The following statements is not applicable to typologies, "They may be used effectively as independent or dependent variables."
Typology is a complex measurement that affect the categorization of observations in terms of their property on multiple variables.They are typically nominal composite measures.They involve a set of categories or types. They are often used when researchers wish to summarize the intersection of two or more variables.
Stone Pine Corporation, a calendar year taxpayer, has ending inventory of $150,000 on December 31, 20X2. During the year 20X2, the corporation purchased additional inventory of $375,000. If cost of goods sold for 20X2 is $470,000, what was the beginning inventory at January 1, 20X2?
Answer:
beginning inventory is $245000
Step-by-step explanation:
Given data
ending inventory = $150,000
purchased additional inventory = $375,000
goods sold = $470,000
to find out
beginning inventory
solution
according to question beginning inventory is calculated by this formula i.e.
beginning inventory = ( cost of goods sold + ending inventory ) - amount of inventory purchase .....................1
now put all value cost of goods sold, ending inventory and amount of inventory purchase in equation 1 and we get beginning inventory
beginning inventory = ( cost of goods sold + ending inventory ) - amount of inventory purchase
beginning inventory = ( 470000 + 150000 ) - 375000
beginning inventory = 245000
so beginning inventory is $245000
Please help! Brainliest if correct!
Answer:
x:(x +15)
Step-by-step explanation:
The corresponding sides that are in proportion are apparently ...
PS:PQ = PT:PR
PT = x
PR = x+15
so the proportion of interest is ...
28:40 = x:(x+15)
The variable z is directly proportional to x, and inversely proportional to y. When x is 4 and y is 10, z has the value 0.8. What is the value of z when x= 13, and y= 18
Answer:
13/9
Step-by-step explanation:
Directly proportional means it will be multiply to our constant k.
Inversely proportional means it will divide our k.
So we are given z is directly proportional to x and inversely proportional to y.
This means:
[tex]z=k \cdot \frac{x}{y}[/tex].
We are given (x=4,y=10,z=0.8). We can use this to find k. The k we will find using the point will work for any point (x,y,z) since k is a constant. A constant means it is to remain the same no matter what.
[tex]0.8=k \cdot \frac{4}{10}[/tex]
[tex]0.8=k(.4)[/tex]
Divide both sides by .4:
[tex]\frac{0.8}{0.4}=k[/tex]
[tex]k=2[/tex]
The equation for any point (x,y,z) is therefore:
[tex]z=2 \cdot \frac{x}{y}[/tex].
We want to find z given x=13 and y=18.
[tex]z=2 \cdot \frac{13}{18}[/tex]
[tex]z=\frac{2 \cdot 13}{18}[/tex]
[tex]z=\frac{13}{9}[/tex]
The problem is in the pictures, please show step by step how to do it. Thanks! :)
Answer:
-4,-5/2
Step-by-step explanation:
2x^2+3x-20 =0
2x^2+8x-5x-20 =0
2x(x+4)-5(x+4) =0
(x+4)(2x-5) =0
Either,
x+4=0
x=-4
Or,
2x-5=0
2x=5
x=5/2
[tex]2x^2+3x-20=0\\2x^2+8x-5x-20=0\\2x(x+4)-5(x+4)=0\\(2x-5)(x+4)=0\\x=\dfrac{5}{2} \vee x=-4[/tex]
What is the magnitude of the position vector whose terminal point is (-2, 4)?
Answer:
2√5
Step-by-step explanation:
The Pythagorean theorem tells you how to find the distance from the origin.
d = √((-2)² +4²) = √20 = 2√5
The vector's magnitude is 2√5 ≈ 4.47214.
Answer:
The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]
Step-by-step explanation:
Given : Vector whose terminal point is (-2, 4).
To find : What is the magnitude of the position vector?
Solution :
We have given, terminal point (-2,4)
The magnitude of the point x(a,b) is given by,
[tex]|x|=\sqrt{a^2+b^2}[/tex]
Let point x=(-2,4)
[tex]|x|=\sqrt{(-2)^2+(4)^2}[/tex]
[tex]|x|=\sqrt{4+16}[/tex]
[tex]|x|=\sqrt{20}[/tex]
Therefore, The magnitude of the position is [tex]|x|=\sqrt{20}[/tex]
To find the standard equation for a circle centered at the origin, we use the distance formula, since the radius measures? A. The distance from any point in the circle to the origin.B. The circumference c. The distance from any point inside the circle to the origin.D. The distance from the x-coordinate to the origin.
Answer:
A. The distance from any point in the circle to the origin
Step-by-step explanation:
The distance formula tells you that the distance (d) is related to the coordinates of two points (x1, y1) and (x2, y2) by ...
d² = (x2 -x1)² +(y2 -y1)²
For points (x, y) on the circle and (0, 0) at the origin, this becomes ...
d² = (x -0)² +(y -0)²
If we want the distance to the point (x, y) to be equal to the radius of the circle, this becomes ...
x² +y² = r² . . . . . . the standard equation of a circle centered at the origin
Answer: The distance from any point in the circle to the origin
Step-by-step explanation:
answer key
Please help with #12
Answer:
a. 1 1/8 b. 8/9
Step-by-step explanation:
You can set this up as a proportion to solve. For part a. we know that 2/3 of the road is 3/4 mile long. 2/3 + 1/3 = the whole road, so we need how many miles of the road is 1/3 its length. Set up the proportion like this:
[tex]\frac{\frac{2}{3} }{\frac{3}{4} } =\frac{\frac{1}{3} }{x}[/tex]
Cross multiplying gives you:
[tex]\frac{2}{3}x=\frac{1}{3}*\frac{3}{4}[/tex]
The 3's on the right cancel out nicely, leaving you with
[tex]\frac{2}{3}x=\frac{1}{4}[/tex]
To solve for x, multiply both sides by 3/2:
[tex]\frac{3}{2}*\frac{2}{3}x=\frac{1}{4}*\frac{3}{2}[/tex] gives you
[tex]x=\frac{3}{8}[/tex]
That means that the road is still missing 3/8 of a mile til it's finished. The length of the road is found by adding the 3/4 to the 3/8:
[tex]\frac{3}{4}+\frac{3}{8}=\frac{6}{8}+\frac{3}{8}=\frac{9}{8}[/tex]
So the road is a total of 1 1/8 miles long.
For b. we need to find out how much of 1 1/8 is 1 mile:
1 mile = x * 9/8 and
x = 8/9. When 1 mile of the road is completed, that is 8/9 of the total length of the road completed.
Use division of numbers in scientific notation to answer the question.
(8.64 × 104)
(2.4 × 102)
What is the quotient in scientific notation?
3.6 × 102
6.24 × 102
1.104 × 107
2.0736 × 109
Answer:
[tex]3.6*10^{2}[/tex]
Step-by-step explanation:
we have
[tex]\frac{8.64*10^{4}}{2.4*10^{2}}=\frac{8.64}{2.4}*10^{4-2}\\ \\=3.6*10^{2}[/tex]
Answer:
A) 3.6 × 10^2
Step-by-step explanation:
Got it right in the instruction on Edge 2021 ;D
A nontoxic furniture polish can be made by combining vinegar and olive oil. The amount of oil should be three times the amount of vinegar. How much of each ingredient is needed in order to make 18 oz of furniture polish?
To make 18 oz of furniture polish, ___ oz of vinegar and
_______ oz of olive oil are needed.
Answer:
To make 18 oz of furniture polish, 4.5 oz of vinegar and 13.5 oz of olive oil are needed.
Step-by-step explanation:
The ratio of ingredients is ...
oil : vinegar = 3 : 1
So vinegar is 1 of the 3+1 = 4 parts of the polish mix. The amount of vinegar required for 18 oz of polish is ...
(1/4)×(18 oz) = 4.5 oz
The remaining quantity is olive oil:
18 oz - 4.5 oz = 13.5 oz
To make 18oz of furniture polish, 4.5 oz of vinegar and 13.5 oz of olive oil are needed. These quantities are found by setting up an equation based on the problem's conditions and solving for x.
Explanation:To begin solving the problem we need to understand that both the vinegar and the olive oil are together making up the 18oz of furniture polish. Since the amount of olive oil is three times the amount of vinegar, we can denote the quantity of vinegar as 'x'. Thus, the quantity of olive oil will be '3x'.
Adding these together gives us the total ounces, thus, we have our equation: x + 3x = 18. Solving this, we get 4x = 18. Dividing by 4 gives us x = 18/4 = 4.5.
Therefore, to make 18oz of furniture polish, you will need 4.5 oz of vinegar and 13.5 oz (3 times 4.5) of olive oil.
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In the spinner below the large wedges are twice the size of the smaller ones. What is true about the probablilty of landing on 6 and the probability of landing on 5
Answer:
we need an image of the spinner to answer the question. are we supposed to just know what it looks like?
Step-by-step explanation:
flvs she cheating
Find the GCF of the following numbers:
n and (n-1), where n is a natural number, greater than 1.
13 POINTS! NEED ANSWER QUICK! THANKS!!
Answer:
1
Step-by-step explanation:
The numbers are mutually prime, so the GCF is 1.
Answer:
1
Step-by-step explanation:
n-1 and n are consecutive integers.
Examples of consecutive pairs:
(7,8)
(10,11)
(100,101)
and so on...
The remainder will always be 1 when doing n divided by n-1.
n=(n-1)(1)+1.
All this is here to try to convince you that n and n-1 will only have common factor of 1.
State the domain and range of the function f(x) =2[[x]]
A. reals Even integers.
B. reals odd integers.
C. reals all integers.
D. reals positive integers.
Just to let you guys know, people thought the answer was C, but the correct answer was A. i don't know why it is A, please explain:(
Answer:
A real Even integers
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
It's all down the the double parentheses. They mean 'round down to the nearest integer'. Also because of the 2 the integer will be even.
There are 24,000 square miles of forest in a western state. Forest fires decrease this area by 9.2% each year. The state needs to have more than 15,000 square miles of forest to keep their funding from a nonprofit wildlife organization.
Which inequality represents this situation, and if the fires continue to decrease the area of the forests at the same rate, will the state be able to keep their funding from the nonprofit wildlife organization in 5 years?
24,000(1.092)t > 15,000; no
24,000(0.092)t > 15,000; yes
24,000(0.908)t > 15,000; no
24,000(1.098)t > 15,000; yes
Answer:
24,000(0.908)^t > 15,000; no
Step-by-step explanation:
The multiplier each year is 100% - 9.2% = 90.8% = 0.908. There is only one answer choice with this as the yearly multiplier.
_____
In order to answer the yes/no question, we chose to rewrite the inequality as ...
24000·0.908^t -15000 > 0
The graph shows that is true for t < 4.87. In 5 years, the forest area will be below the minimum.
A widget company produces 25 widgets a day,5 of which are defective.Find the probability of selecting 5 widgets from the 25 produced where none are defective
Answer:
1/5
Step-by-step explanation:
The probability of selecting 5 widgets from the 25 produced where none are defective is 0.2914.
To calculate the probability of selecting 5 non-defective widgets from the 25 produced.
The number of ways to choose 5 non-defective widgets:
[tex]\[ \binom{20}{5} = \frac{20!}{5!(20-5)!} \][/tex]
[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{1860480}{120} \][/tex]
= 15504
The total number of ways to choose 5 widgets from the 25 produced:
[tex]\[ \binom{25}{5} = \frac{25!}{5!(25-5)!} \][/tex]
[tex]\[ = \frac{25 \times 24 \times 23 \times 22 \times 21}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{7893600}{120} \][/tex]
= 53130
The probability:
Probability = (Number of ways to choose 5 non-defective widgets)/(Total number of ways to choose 5 widgets)
[tex]\[ = \frac{15504}{53130} \][/tex]
[tex]\[ = 0.2914 \][/tex]
Complete question:
A widget company produces 25 widgets a day, 5 of which are defective. Find the probability of selecting 5 widgets from the 25 produced where none are defective.
Need help big time...please explain how you got the answer.
Answer:
Step-by-step explanation:
This is a right triangle with the 90 degree angle identified at D and the 60 degree angle identified at B. Because of the triangle angle sum theorem, the angles of a triangle all add up to equal 180 degrees, so angle C has to be a 30 degree angle.
There is a Pythagorean triple that goes along with a 30-60-90 triangle:
( x , x√3 , 2x )
where each value there is the side length across from the
30 , 60 , 90 degree angles.
We have the side across from the 90 degree angle, namely the hypotenuse. The value for the hypotenuse according to the Pythagorean triple is 2x. Therefore,
2x = 2√13
and we need to solve for x. Divide both sides by 2 to get that
x = √13
Now we can solve the triangle.
The side across from the 30 degree angle is x, so since we solved for x already, we know that side DB measures √13.
The side across from the 60 degree angle is x√3, so that is (√13)(√3) which is √39.
And we're done!
In a right triangle, the measure of one of the acute angles is 60 degrees more than the measure of the smallest angle. Find the measures of all three angles.
Answer:
90°, 75°, and 15°
Step-by-step explanation:
In a right triangle, one of the angles is 90°.
Let x = the smallest angle
Then 60 + x = the third angle
The sum of the three angles is 180°.
90 + 60 + x + x = 180
150 + 2x = 180
2x = 30
x = 15
Measure of right angle = 90°
Measure of smallest angle = x = 15°
Measure of third angle = 60 + x = 75°
The measures of the angles are 90°, 75°, and 15°.
Mustafa, Heloise, and Gia have written more than a combined total of 222222 articles for the school newspaper. Heloise has written \dfrac{1}{4}
4
1
start fraction, 1, divided by, 4, end fraction as many articles as Mustafa has. Gia has written \dfrac{3}{2}
2
3
start fraction, 3, divided by, 2, end fraction as many articles as Mustafa has.
Write an inequality to determine the number of articles, mmm, Mustafa could have written for the school newspaper.
What is the solution set of the inequality?
Answer:
m + m/4 + 3m/2 > 22m > 8 . . . . m restricted to multiples of 4, perhapsStep-by-step explanation:
Let m represent the number of articles Mustafa has written. Then the total number of articles written must satisfy the inequality ...
m +m/4 +3m/2 > 22
This has solution ...
(11/4)m > 22
m > (4/11)22
m > 8 . . . . . . . . the solution to the inequality
If all the numbers are integers, and the ratios are exact, then we must have m be a multiple of 4 (that is, 4 times the number of articles Heloise wrote).
The solution set will be ...
m ∈ {12, 16, 20, 24, ...} (multiples of 4 greater than 8)
Answer:
inequality - m+ 1/4m + 3/2m > 22
solution set - m>8
Step-by-step explanation:
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