The measure of angles are 22.5 degree and 67.5 degree
Solution:
Given that, measures of two complementary angles are in ratio 1 : 3
one angle : another angle = 1 : 3
Let the first complementary angle 1x
Let the another complementary angle be 3x
If the angles are complementary, then their sum is 90 degrees
Therefore,
1x + 3x = 90
4x = 90
x = 22.5
Then, first angle = 1x = 1(22.5) = 22.5
Another angle = 3x = 3(22.5) = 67.5
Thus the measure of angles are 22.5 degree and 67.5 degree
What 3 consecutive integers equal 84
First represent your 3 consecutive integers as follows.
X ⇒ first integer
X + 1 ⇒ second integer
X + 2 ⇒ third integer
Since their sum is 84, our equation reads x + (x + 1) + (x + 2) = 84.
Simplifying on the left side we get 3x + 3 = 84.
Now subtract 3 from both sides to get 3x = 81.
Dividing both sides by 3, we find that x = 27.
Finally, make sure you list all your answers.
If x is 27 then x + 1 is 28 and x + 2 is 29.
Answer:
27 + 28 + 29 = 84
Step-by-step explanation:
Let the three consecutive integers be x +1, x+2 and x+3
Thus,
[tex](x + 1) + (x + 2) + (x + 3) = 84[/tex]
Remove the brackets
[tex]x + 1 + x + 2 + x + 3 = 84[/tex]
Group the like terms
[tex]x + x + x + 1 + 2 + 3 = 84[/tex]
[tex]3x + 6 = 84[/tex]
To make 3x subject of formula, subtract 6 from both sides of the equation thus,
[tex]3x + 6 - 6 = 84 - 6[/tex]
[tex]3x = 78[/tex]
Divide through by 3
[tex] \frac{3x}{3} = \frac{78}{3} [/tex]
[tex]x = 26[/tex]
Since x = 26
[tex]x + 1 = 26 + 1 = 27[/tex]
[tex]x + 2 = 26 + 2 = 28[/tex]
[tex]x + 3 = 26 + 3 = 29[/tex]
Therefore, the three consecutive integers are 27, 28 and 29
Check
[tex]27 + 28 + 29 = 84[/tex]
What is the value of the y-coordinate of the solution to the system of equations x-2y=1 x+4y=7
Answer:
A system of equations is shown below: x + y = 3 2x − y = 6 The x-coordinate of the solution to this system of equations is _____. I'm thinking it could be X=3
Step-by-step explanation:
The value of the y-coordinate of the solution to the system of equations is; y = 1.
According to the question;
We are required to find the y-coordinate of the solution to the system of equations.The equations given are;
x-2y=1 x+4y=7By solving the pair of equations simultaneously; we have;
-6y = -6y = 1Read more;
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What is a dependent variable in algebra
Answer:
A dependent variable is when it's variable depends on independent variable
If y varíes directly as x, and y es 48 when x is 6? Which expression can be used to find the value of y when x is 2? Pleaseeee!!
Answer:
Therefore the expression for y when x is 2 is
[tex]y=\dfrac{48}{6}\times 2[/tex]
Step-by-step explanation:
Given:
y varies directly as x, and y is 48 when x is 6
Means Direct Variation.
Therefore,
[tex]y=kx[/tex]
Where,
k = Constant of Proportionality
To Find:
y when x = 2
Solution:
First step we need to Find Constant of Proportionality
So put y = 48 and x = 6
Substituting the values we get
[tex]48=k\times 6\\\\k=\dfrac{48}{6}[/tex]
Now When x = 2 and [tex]k=\dfrac{48}{6}[/tex] y will be
[tex]y=\dfrac{48}{6}\times 2[/tex]
Therefore the expression for y when x is 2 is
[tex]y=\dfrac{48}{6}\times 2[/tex]
Will mark brainliest and 12 points
RSM QUESTION NEED HELP!!!!!! A biker traveling at his usual speed can go from his house to work in 4 hours. When the weather is bad, he travels 6 miles per hour slower, and it takes him half an hour more. How far is his work from his house?
=======================================
Work Shown:
d = distance from work to his house
x = speed when weather is good
y = speed when weather is bad
y = x-6 since he travels 6 mph slower
------------------------
On a good weather day, he travels for 4 hours and goes at x mph
distance = rate*time
d = r*t
d = x*4
d = 4x
----------------------
On a bad weather day, he travels 4.5 hours (half hour more than 4 hrs) and goes at y = x-6 mph
d = r*t
d = y*4.5
d = 4.5y
d = 4.5(x-6) .... replace y with x-6
d = 4.5x-27 .... distribute
----------------------
The values of d for both equations are the same, as the biker is traveling the same distance. So we can equate the two right hand sides (RHS) and solve for x.
4.5x-27 = 4x
4.5x-4x = 27
0.5x = 27
x = 27/0.5
x = 54
The biker's speed on a good weather day is 54 mph.
A bad weather day's speed would be y = x-6 = 54 - 6 = 48 mph.
----------------------
Now compute the value of d
d = 4x
d = 4*54
d = 216
The biker travels 216 miles on a good weather day
or,
d = 4.5*y
d = 4.5*48
d = 216
the biker travels that same distance on a bad weather day.
A store has a display case with cherry, peach,
and grape fruit chews. There are 160 fruit chews
in the display case. Given that 25% of the fruit
chews are cherry and 40% are peach, how many
grape fruit chews are in the display case?
Answer:
56 grape
Step-by-step explanation:
160 fruit chews
25% are cherry, 40% are peach.....25 + 40 = 65%....so 65% of the fruit chews are NOT grape....meaning (100 - 65) = 35 % ARE grape.
so 35% of all the fruit chews are grape
35% of 160 = 0.35 * 160 = 56 are grape <===
The number of grape fruit chews in the display are 56.
To find the number of grape fruit chews in the display case:
Calculate the percentage of cherry and peach fruit chews: 25% cherry + 40% peach = 65% cherry and peach combined.
Subtract the combined percentage from 100% to find the percentage of grape fruit chews: 100% - 65% = 35% grape.
Calculate the number of grape fruit chews by finding 35% of 160 (total fruit chews): 35% of 160 = 0.35 x 160 = 56 grape fruit chews.
Which is least to greatest 1/4,6/7 or 3/5
ANSWER :
In order from least to greatest, it is 1/4, 3/5, 6/7
Step-by-step explanation:
If you make them all decimals, 1/4 is .25, 6/7 is around .8, and 3/5 is .6. In order form least to greatest, that is .25, .6, .8. That would mean in fraction form it is 1/4, 3/5, 6/7.
Which box will require less material? A 10x10x3 inches or 8x3x11 inches
Answer:
the 8×3×11 one
Step-by-step explanation:
we need to find the surface area of each.
[tex]2(lw + hl + hw)[/tex]
for the 10×10×3=
2(10×3+10×10+10×3)
2(30+100+60)
2(190)
380
for the 8×3×11
2(8×3+11×8+11×3)
2(24+88+33)
2(145)
290
aanswer now! pls oh pls
Answer: 25
Step-by-step explanation:
If two shapes are similar , then the ratio of their sides are also similar.
From the shapes given:
[tex]\frac{x}{50}[/tex] = [tex]\frac{20}{40}[/tex]
[tex]\frac{x}{50}[/tex] = [tex]\frac{1}{2}[/tex]
2x = 50
x = 25
Isabella has a bag containing 14 nickels and quarters. The total value of these coins is 2.50$
Answer:
If it contains 14 nickels and 14 quarters then it would actually be $4.20 in total.
Step-by-step explanation:
250 people went to couples only party at 9pm. 70 people left at 11pm.vhow many couples remain at the party? ar
Answer:
The answer is that 90 couples remain at the party after 11 pm
Step-by-step explanation:
Number of people who went to the couples only party at 9 pm = 250
Number of people who left the party at 11 pm = 70
How many couples remained at the party?
People that remained at the party = 250 - 70 = 180
Couples that remained at the party = 180/2 = 90
The answer is that 90 couples remained at the party after 11 pm
Is y=4x-5 proportional or non proportional
Answer:
therefore the given equation is linear but it is not proportional.
Step-by-step explanation:
i) Is y = 4x - 5 proportional or non- proportional.
ii) therefore we can see that the equation is the same as the equation for a line, therefore the given equation is linear but it is not proportional.
For the set D = (4,6,8,10), determine n(D)
n(D) = 4
Step-by-step explanation:
Given Data:
Set D = {4, 6, 8, 10}
The number of elements in a set is called the cardinal elements (or) cardinality of the sets. This is denoted by n(A).
Here it is denoted by n(D).
The number of elements in the set D is 4.
The cardinality of the set is 4.
Hence, n(D) = 4.
For the given set D; the number of elements in the set D as denoted by n(D) is; 4.
Elements of a set.According to the question;
We are required to determine n(D)The number of elements in a set is given by the notation n(D).
On this note, the set given in this question;
D = (4,6,8,10) has 4 elements.Ultimately, n(D) = 4 elements.
Read more on number of elements in a set;
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What is the slope-intercept form of the equation y- 7 = 3(x-11)?
O
A. y=-3x - 40
O
B. y = 3x - 26
O
C. y=-3x - 36
O
D. y = 3x - 40
Answer: B. y = 3x - 26
Step-by-step explanation:
The equation of line in slope - intercept form is given as :
y = mx + c , where m is the slope and c is the y - intercept.
To write the given equation in this form , all we need do is to make y the subject of the formula.
y - 7 = 3 ( x - 11 )
y - 7 = 3x - 33
add 7 to both sides
y = 3x - 33 + 7
y = 3x -26
Julie and her brother go to Atlanta to ride the SkyView Ferris wheel. It measures 200 feet in diameter.
A)I want to know the distance around the Ferris Wheel. Would I use Circumference or Area?
B)What is the formula needed to solve this problem?Look in your notes!
C)What is the distance traveled in one rotation? Explain how you used the formula to solve the problem.
Answer:
Part A) Circumference
Part B) C=π D
Part C) The distance traveled in one rotation is 628.32 feet
Step-by-step explanation:
Part A) we know that
The distance around the circle is equal to the circumference.
The Ferris Wheel have a circular shape
so
To find out the distance around the Ferris Wheel you should use the circumference
Part B) What is the formula needed to solve this problem?
we know that
The circumference is equal to multiply the number π by the diameter of the circle
so
C=π D
Part C) What is the distance traveled in one rotation?
we know that
One rotation subtends a central angle of 360 degrees
The distance traveled in one rotation is the same that the circumference of the Ferris wheel
we have
[tex]D=200\ ft[/tex] ----> diameter of the Ferris wheel
substitute in the formula of circumference
[tex]C=\pi (200)\\C=200\pi\ ft[/tex]
assume
[tex]\pi=3.1416\\C=200(3.1416)=628.32\ ft[/tex]
therefore
The distance traveled in one rotation is 628.32 feet
PLEASE HELP!
A charter is to a city government as a ___ is to a state government.
A) law
B) bill
C) executive order
D) state constitution
A charter is to a city government as a state constitution is to a state government.
Answer: Option D
Explanation:
Apart from the national level constitution, in the United States of America, every state has its own constitution. They are more detailed when compared to the national constitution as they tend to have more words or content when compared to the national level constitution.
The shortest one belongs to Vermont and the longest one belongs to Alabama. These constitutions tell how the government of each state must function and carry out its day to day activities.
A bag contains 10 marbles: 2 are green, 2 are red, and 6 are blue. Deshaun chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that the first marble is green and the second is red?
Answer:
Step-by-step explanation:
Total marble = 10
No. Blue = 6
No. Red = 2
No. Green = 2
Prob(1st Green) = 2/10 = 1/5
Now there are 9 marble left because it is not replaced back
Prob(2nd Red) = 2/9
Prob(1st green and 2nd red)
=1/5×2/9 = 2/45
9(x + y) = 9x + 9y what algebraic property is that
Answer:
its a desperctive property
Step-by-step explanation:
A suit with an original price of $300 was marked down 30%. You have a coupon good for an additional 20% off. What is the suits final cost?
The suit's final cost after a 30% markdown and an additional 20% off coupon is $168.
Explanation:To find the suit's final cost, we first calculate the price after the 30% markdown. Subtracting 30% of $300 gives us: $300 - ($300 x 0.30) = $210. Next, we apply the additional 20% off coupon. Subtracting 20% of $210 gives us: $210 - ($210 x 0.20) = $168. Therefore, the suit's final cost is $168.
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Find the exact length of the third side.
Answer:
√41 or 6.40
Step-by-step explanation:
Pythagorean theorem:
a² + b² = c²
The third side is considered the hypotenuse (c²).
a² and b² will be represented by the legs.
a² = 4²
b² = 5²
c² = c²
4² + 5² = c²
16 + 25 = c²
31 = c²
√41 = c
[tex]\displaystyle\bf\\\textbf{A third side is hypotenuse.}\\\\The~length~of~the~hypotenuse=\sqrt{cat1^2+cat2^2}~~~(T.Pithagoras)\\\\The~length~of~the~hypotenuse=\sqrt{4^2+5^2}=\sqrt{16+25}=\boxed{\bf\sqrt{41}}[/tex]
Find the LCM of the pair of numbers. 6 and 9 The LCM is .
Answer:
So the LCM of 6 and 9 is 18.
Step-by-step explanation:
List the factors of both numbers.
6: 6, 12, 18, 24, 30, 36,
9: 9, 18, 27, 36
The LCM of 6 and 9 is found by prime factorizing each number and taking the highest power of each prime that appears, resulting in an LCM of 18.
To find the LCM (Least Common Multiple) of the pair of numbers 6 and 9, we first need to prime factorize each number. The number 6 can be prime factorized as 2 times 3, and 9 can be prime factorized as 3 times 3 or 3². In order to find the LCM, we take the highest power of each prime number that occurs in the factorization of both numbers. So, we take 2 from the factorization of 6 (since it's the highest power of 2) and 3² from the factorization of 9 (since it's the highest power of 3), and multiply them together to get the LCM.
The LCM of 6 and 9 is 2 times 3² = 2 times 9 = 18.
Thus, the Least Common Multiple of 6 and 9 is 18.
please hurry, i don’t need an explanation
Sasha has 20 starbursts in a bag, 8 are yellow, 6 are pink, 4 are red, and
2 are orange. Sasha will randomly select two starbursts from the bag
with no replacement. What is the probability that she will select
yellow starburst and then a red starburst? (give your answer as a
fraction in a reduced form)
Answer:
D
Step-by-step explanation:
Answer: Helping a fellow teen in need. I got you. lol. It's most likely A. Good luck miss Isabella
Step-by-step explanation:
In the triangle ABC, angle A = 30° and angle B = 60°. The perimeter of the triangle is 5(3 + 13). Find the area of
the triangle. Give your answer in exact
form.
Answer:
Perimeter of triangle ABC = 5(3+13) = 5 x 16 = 80
Angle A = 30°, Angle B = 60°
Therefore Angle C = 90°
Pythagorean triplet = 40/3, 96/3, 104/3
Area of triangle ABC = 1/2 x b x h
= 1/2 x 40/3 x 96/3
= 1920/9
= 213.3 cm^2
Hope this helps!
The area of the triangle is found by recognizing that it is a special 30-60-90 triangle with sides in the ratio of 1: √3 : 2. The area, using these ratios and the given perimeter, is calculated as 25√3 square units.
Explanation:This problem pertains to the area of a triangle. Because we know the two acute angles of triangle ABC, it is a 30-60-90 triangle. This is a special type of right triangle where the sides are in a particular ratio. In a 30-60-90 triangle, the sides across from the 30°, 60° and 90° angles are in the ratio of 1: √3 : 2.
Given that the perimeter is 5(3 + √13), we can set up the ratio for the sides as x, x√3, and 2x. Adding these together equals the perimeter: x + x√3 + 2x = 5(3 + √13). Solving this equation, we find x = 5.
The area of a triangle is calculated using the formula 1/2*base*height. Using the sides of the triangle, 5, 5√3, and 10, we will use the side across from the 90° angle (10) as the base and the side across from the 60° angle (5√3) as the height, giving us a triangle area of 1/2 * 10 * 5√3 = 25√3 square units.
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Which of the relations given by the following sets of ordered pairs is a function?
A. {(5,4),(4,3),(3,2),(4,5),(2,1)}
B. {(6,1),(-3,1),(3,5),(2,4),(-1,2)}
C. {(1,2),(-4,8),(-3,5),(1,-2),(7,12)}
D. {(5,4),(5,6),(5,8),(5,10),(5,12)}
Answer:
B
Step-by-step explanation:
You can solve this by using the vertical line test. When you do the vertical line test, the vertical line should only pass through one point on the function. That means that there can to be only one value of x for every y. Set B is the only set where the x value doesn't repeat.
In the provided sets of ordered pairs, B and D are considered functions. A function is a relation where each input corresponds to exactly one output, and in sets B and D, this requirement is met.
Explanation:
In mathematics, a relation is considered a function if and only if every input (also called the domain or the x-coordinate) corresponds to exactly one output (also called the range or the y-coordinate). In the language of ordered pairs, an ordered pair presents itself as (x, y). If x repeats with a different y in the set, then the relation is not a function.
So let's examine the sets of ordered pairs given:
A. {(5,4),(4,3),(3,2),(4,5),(2,1)} : The input 4 has two outputs (3 and 5); thus it's not a function.B. {(6,1),(-3,1),(3,5),(2,4),(-1,2)}:: Each input has only one output; thus it's a function.C. {(1,2),(-4,8),(-3,5),(1,-2),(7,12)} : The input 1 has two outputs (2 and -2); thus it's not a function.D. {(5,4),(5,6),(5,8),(5,10),(5,12)} : Although it might seem wrong as the input 5 repeats, the rule 'every input corresponds to exactly one output' isn't violated. Here, the function is just a vertical line (not a function in traditional sense), which doesn't contradict the definition of function.Therefore, the set of ordered pairs which are functions are B and D.
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what is the percent rate of growth? y=300(1+0.5)^x
___%
Answer:
y = abx. Where a ≠ 0, the base b ≠ 1 and x is any real number ... When given a percentage explanation:
PLEASE HELP
f(x) = x^2 -2x + 3 g(x) = x^3 - x^2 + 4x find f(x) + g(x)
Answer:
A
Step-by-step explanation:
f(x) + g(x)
= x² - 2x + 3 + x³ - x² + 4x ← collect like terms
= x³ + 2x + 3 → A
Find an equation of the line through the points (-7,-8) and (-5,-3)
Answer:
[tex]y = \frac{5}{2} + \frac{19}{2}[/tex]
Step-by-step explanation:
From the question;
We are given, two points; (-7,-8) and (-5,-3)We are required to determine the equation of a line that passes through points (-7,-8) and (-5,-3).
Note that we can get the equation of a line when;
We are given two points where the line is passing through We are given the slope of the line and one point where the line is passing throughTherefore, since we are given two points where the line is passing through we can get the equation;
First, we determine the slope of the line;
slope = change in y ÷ change in x
That is;
[tex]slope=\frac{(-3--8)}{(-5--7)}[/tex]
[tex]=\frac{5}{2}[/tex]
Second, we take another point (x,y) and one of the points, in this case, we take (-5,-3).
Therefore;
[tex]\frac{y+3}{x+5}=\frac{5}{2}[/tex]
[tex]2(y+3)=5(x+5)\\2y + 6 = 5x +25\\2y= 5x + 19\\y = \frac{5}{2} + \frac{19}{2}[/tex]
Therefore, the equation of the line is [tex]y = \frac{5}{2} + \frac{19}{2}[/tex]
2 Points
Which of the following is most likely the next step in the series?
A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues, what will be the population of moose after 12 years? Show all your work! Round your answer to the nearest whole number. (5 points)
The table referred to in the question is:
years=x population =y
0 40
1 62
2 96
3 149
4 231
Answer:
7,692 mooseExplanation:
To discover the pattern followed by the data in the table, since it is indicated that the moose population is growing exponentially, you can find the multiplicative rate by dividing any two consecutive terms:
rate = 62/40 ≈ 96/62 ≈ 149/96 ≈ 231/149 ≈ 1.55
Thus, using the first ordered pair of the sequence, (0,40), you get the equation that models the exponential growing:
[tex]p(x)=A_0(1.55)^{x}\\ \\ 40=A_0(1.55)^0\\ \\ 40=A_0\times 1\\ \\ A_0=40\\ \\ p(x)=40(1.55)^x[/tex]
Then, to find the population of moose after 12 years, you substitute x = 12:
[tex]p(12)=40(1.55)^{12}=7,692[/tex]