Answer:
Step-by-step explanation:
[tex]i^{20}+1=i^{2*10}+1\\\\(i^{2})^{10}+1=(-1)^{10}+1\\\\=1+1=2[/tex]
Which point is the y-intercept of the graph of 5x - 3y = 15 ?
(-5, 0)
(3, 0)
0, -5)
(0,3)
Answer:
c
Step-by-step explanation:
$5000 at 4% interest for 3 years?
Answer:
Simple Interest =$5600 (Principal and Interest)
Compound Interest = $5624.32 (Principal and Interest)
Step-by-step explanation:
Using Simple interest, use the formulae, Principal X Rate X Time
= 5000*4%*3
= $600 Interest
Principal plus Interest = $5600
Using compound Interest, use the formulae P(1+r)^n
P means Principal
R means rate
N means number of years
= 500(1+4%)^3
= $5624.32 (Principal with Interest)
Solve -3(2x-3)+10x=3q
Answer:
4x+9=3q
Step-by-step explanation:
-3(2x-3)+10x=3q
-6x+9+10x=3q
4x+9=3q
Answer:
q = 4/3x + 3
Step-by-step explanation:
-3(2x-3)+10x=3q
Multiply the -3 at the beginning by (2x - 3), the parenthesis
-6x + 9 + 10x = 3q
Now combine the like terms (add x's and variables separately)
(-6x + 10x) + 9 = 3q
4x + 9 = 3q
Divide both sides of the equation by 3
(4x + 9) ÷ 3 = q
4x/3 + 9/3 = q
Simplify
q = 4/3x + 3
Hope this helps :)
Write a function rule for the area of a rectangle whose length is 7 ft more than its width. What is the area of the rectangle when it’s width is 8ft?
Answer:
[tex]A = w^2 + 7w[/tex] is the rule for the area of a rectangle.
A = 120 sq ft, when it’s width is 8 ft.
Step-by-step explanation:
Here, let us assume the width of the rectangle = w
So, the length here = Width + 7 ft = (w + 7) ft
Now, AREA of a RECTANGLE = Length x Width
Substituting here the values of length and width, we get:
A = (w) x (w + 7) [tex]= w^2 + 7 w[/tex]
[tex]\implies A = w^2 + 7w[/tex]
The above function is the rule for the area of a rectangle.
Given: w = 8 ft
To find the area: put w = 8 in [tex]A = w^2 + 7w[/tex]
We get: A = 8² + 7(8)
= 64 + 56 = 120
or, A = 120 sq ft.
Hence, area = 120 sq ft, when it’s width is 8 ft.
the coordinatinates of the centroid of a triangle with the given vertices 3,3 5,-1 -2,1
Answer:
Therefore, the coordinates of the centroid of a triangle is
[tex]G(x,y)=(2,1)[/tex]
Step-by-step explanation:
Given:
Let,
point A( x₁ , y₁) ≡ ( 3, 3)
point B( x₂ , y₂) ≡ (5 , -1)
point C( x₃ , y₃) ≡ (-2 , 1)
To Find:
Centroid, G (x,y) = ? (say)
Solution:
Centroid:
Centroid is a point where all the three medians of the triangle intersect.
It is denoted as G and the coordinates are give by
[tex]G(x,y)=(\dfrac{x_{1}+x_{2}+x_{3}}{3},\dfrac{y_{1}+y_{2}+y_{3}}{3})[/tex]
Substituting the values we get
[tex]G(x,y)=(\dfrac{3+5+-2}{3},\dfrac{3+-1+1}{3})[/tex]
[tex]G(x,y)=(\dfrac{6}{3},\dfrac{3}{3})=(2,1)[/tex]
Therefore, the coordinates of the centroid of a triangle is
[tex]G(x,y)=(2,1)[/tex]
evaluate x+6 when x=7
Answer:
13
Step-by-step explanation:
x + 6 = ?
[Replace x with 7]
7 + 6 = 13
Find the cosine of ∠U. A) 15 17 B) 17 15 C) 8 15 D) 8 17
The calculated cosine of the angle U is 8/17
How to determine the cosine of the angle U
From the question, we have the following parameters that can be used in our computation:
The triangle
By definition:
The cosine of the angle is calculated using
cos(U) = VW/UW
Where
VW = 8 and UW = 17
Substitute the known values into the equation
cos(U) = 8/17
Hence, the cosine of the angle U is 8/17
A swimming pool has an average depth of 1.6 m. It is 50 m long and 30 m wide. What is the volume?
Answer:
2400m³
Step-by-step explanation:
50 * 30 * 1.6 =
1500 * 1.6 = 2400m³
PLEASE HELP MEHHH
Which of the following represents a function?
Answer: The top one
Step-by-step explanation:
Because there can only be one input for one output. (X’s can’t repeat)
2 3/4 convert this number into an Improper fraction
Answer:
11/4
Step-by-step explanation:
The number 57 is more than the number of situps Lyle can do. Which of the following inequalities represents the number of situps Lyle can do?
A.
x = 57
B.
x > 57
C.
x = 49
D.
x < 57
Final answer:
The correct inequality to represent the number of situps Lyle can do, if 57 is more than he can do, is D. x < 57, indicating that Lyle can do fewer than 57 situps.
Explanation:
The inequality that represents the number of situps Lyle can do, given that the number 57 is more than the number of situps Lyle can do, is x < 57. This is because if 57 is more than what Lyle can do, then Lyle can do any number of situps that is less than 57.
To represent this relationship mathematically, we use the inequality sign '<'. Thus, the correct option from the provided choices is D. x < 57. This means Lyle can do 56, 55, 54, etc., situps, but not 57 or any number greater than 57.
Evaluate a Composit
Given f(x) = x - 7 and g(x) = x2
Find g(4)).
G(f(4)) =
g(x) = x²
g(4) = 4² = 16
g(f(4)) = (f(4))² = (4-7)² = (-3)² = 9
Dominic collected data on the favorite sports of the
grades. The table shows the relative frequencies of rows for the data collected:
Favorite Sport
Swimming Running Volleyb
Grade 8 0.24 0.17
Grade 9 0.18
Column totals 0.42
ON
Based on the data, which statement is most
O in Grade 8, 14 students liked swimmin
O In Grade 8, 17% of students liked running
O in Grade 9, 31% of students liked volleyball
O in Grade 9, 22 students liked volleyball
Answer:
In Grade 8, 17% of students liked running
Step-by-step explanation:
Although this table is incomplete, there are still enough information to answer.
First, we need to be aware that the data here is written in decimal numbers, which is another way to write percentages.
In other words, 100% equals to 1, which is to say that if we multiply decimal number with 100 we'll get the percentage:
0.39 = 39%
0.04 = 4%
Another important thing to establish is that the value of decimal number DOES NOT mean the number of people, it only suggests the ratio:
0.26 does not mean 26 people etc.
Knowing this, from this incomplete table, we see that 0.17 students from grade 8 liked running. And now we know that 0.17 equals to 17%, which makes B the correct answer.
Answer:
B. In Grade 8, 17% of students liked running
Step-by-step explanation:
The track team needs new uniforms. The students plan to sell plush toy hawks (the school mascot) for $5 each. The students find three companies on line that sell stuffed mascots. Company A sells 18 hawks for $49.14. Company B sells 12 hawks for $33.12. Company C charges $40.65 for 15 hawks. Which company has the Best Buy?
After calculating the cost per hawk for each company, Company C offers the best buy at $2.71 per hawk.
The goal is to find out which company offers the best buy for the plush toy hawks. To do so, we'll calculate the cost per hawk from each company and compare them.
Company A: 18 hawks for $49.14 so $49.14 ÷ 18 = $2.73 per hawkCompany B: 12 hawks for $33.12 so $33.12 ÷ 12 = $2.76 per hawkCompany C: 15 hawks for $40.65 so $40.65 ÷ 15 = $2.71 per hawkCompany C offers the lowest cost per hawk at $2.71, thus they have the best buy.
What is the answer? 56b×77b÷11
Answer:
392b²
Step-by-step explanation:
56b×77b÷11
56b×7b
392b²
Lesson 8-5
Using the Distributive Property
b (b + 12) = 0
The value of b is -12
Solution:
The given equation, b (b + 12) = 0
On distributing the b inside the parentheses we get,
[tex]\Rightarrow\bold{ b\times b+b\times12=0}[/tex]
[tex]\bold{\Rightarrow b^{2}+12b=0}[/tex]
[tex]\bold{\Rightarrow b^{2}=-12b}[/tex]
[tex]\bold{\Rightarrow 1=\frac{-12b}{b^2}}[/tex]
[tex]\bold{\Rightarrow 1=\frac{-12}{b}}[/tex]
[tex]\bold{\Rightarrow b=-12}[/tex]
Steps to use distributive property to solve an equation:
Multiply the term outside of the parentheses by each term in the parentheses.Distribute a negative number together with its negative sign.Combine like termsSolve the equation.For fractions:
Identify any fractional coefficients or constants.Find the lowest common multiple (LCM) for all denominators.Multiply all terms of the equation by the LCM.Combine like terms and solve the equation.-3(x+5) = -9
Please answer asap
Steps to solve:
-3(x + 5) = -9
~Distributive Property
-3x - 15 = -9
~Add 15 to both sides
-3x - 15 + 15 = -9 + 15
~Simplify
-3x = 6
~Divide -3 to both sides
-3x/-3 = 6/-3
~Simplify
x = -2
Best of Luck!
Answer:
x= -2
Step-by-step explanation:
First, distribute the 3 into the parenthesis.
(-3)x+ (-3)5= -9
Then, multiply.
-3x-15= -9 *The negative makes it into becoming subtraction.
Now, add 15 to both sides since that's the opposite of subtraction.
-3x-15= -9
+15 +15
Then, divide by 3 to both sides to isolate the variable.
-3x= 6
-3 -3
x= -2
27/9+8ggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg
Answer:
3+8g
Step-by-step explanation:
27/9+8g=3+8g
Find the inverse of f(x)=5x+11
Answer:
f^-1 (x)=1/5x-11/5
Step-by-step explanation:
y=5x+11
x=5y+11
5y=x-11
y=1/5x-11/5
The width of a rectangle is 4 1/6 feet, and its area is 35 square feet. What is the perimeter of this rectangle?
The perimeter of rectangle is 25.13 feet
Solution:
Given that,
width of a rectangle = [tex]4\frac{1}{6} \text{ feet }[/tex]
Convert the mixed fraction to improper fraction
[tex]\rightarrow 4\frac{1}{6} = \frac{6 \times 4 + 1}{6} = \frac{25}{6}[/tex]
Therefore,
[tex]\text{width of rectangle } = \frac{25}{6} \text{ feet }[/tex]
Area of rectangle = 35 feet
The area of rectangle is given by formula:
[tex]area = length \times width[/tex]
Substituting the given values, we get
[tex]35 = length \times \frac{25}{6}\\\\length = 35 \times \frac{6}{25} = \frac{42}{5}[/tex]
Thus we get,
[tex]\text{length of rectangle } = \frac{42}{5} \text{ feet }[/tex]
The perimeter of rectangle is given as:
perimeter = 2(length + width)
[tex]perimeter = 2(\frac{42}{5} + \frac{25}{6})\\\\perimeter =2(8.4+4.167)\\\\perimeter = 2(12.567)\\\\perimeter = 25.13[/tex]
Thus perimeter of rectangle is 25.13 feet
13. Charles runs at a rate of 12 kilometers per hour.
What is Charles' speed in meters per minute?
A. 12 meters per minute
B. 20 meters per minute
C. 120 meters per minute
D. 200 meters per minute
Answer:
B.
Step-by-step explanation:
1000 meters in a kilometer and 60 minutes in a hour. 1000/60= 16.6666
(rounds to 20)
Final answer:
Charles' running speed of 12 kilometers per hour is equivalent to 200 meters per minute when converted, which corresponds to option D.
Explanation:
Charles runs at a rate of 12 kilometers per hour, and the question asks us to convert this speed to meters per minute. First, we need to convert kilometers to meters. One kilometer is equivalent to 1,000 meters.
So, Charles' speed in meters per hour is:
12 km/hr × 1,000 m/km = 12,000 m/hr
To convert this speed from meters per hour to meters per minute, we divide by 60 minutes, since there are 60 minutes in one hour:
12,000 m/hr ÷ 60 min/hr = 200 m/min
Therefore, Charles' speed is 200 meters per minute, which corresponds to option D.
Angela puts $520 in an account that earns 6% per year. What interest will she get at the end of 1 year?
Answer:
$31.20
Step-by-step explanation:
Angela will get an amount of $31.2 as the interest at the end of 1 year.
What is Simple Interest?Simple interest is defined as the interest obtained over the principal amount on a certain rate.
Given that Angela puts $520 in an account that earns 6% per year.
Principal or initial amount = $520
Rate of interest = 6% = 6 / 100 = 0.06
We have to calculate the amount of interest.
Interest amount = $520 × 0.06
= $31.2
Hence the amount of interest that Angela get at the end of the year is $31.2.
To learn more about Simple Interest, click on the link given below :
https://brainly.com/question/22621039
#SPJ3
(I will give brainliest, a thanks, 30 points, and 5 stars if you can answer these 2 questions)
1.C=6π yd, find area, answer in terms of π
2. C=22π in^2, find area, answer in terms of π
Answer:
1. 9 pi, 2. 121 pi
Step-by-step explanation:
The formula for circumference is pi d. So for the first question the radius would be three. The you do pi r ^2 for area so 3 times pi squared. Which is 9 pi. For the second you will do the same thing you will do 22 pi divided by 2 which is 11 pi then you will square 11pi and get 121 pi
A 41-foot ladder is placed against a vertical wall of an apartment building. The base of the ladder is 9 feet from the base of the apartment building
The ladder reaches 40 feet up the wall.
41 squared (1681) minus 9 squared (81) is 1600. 40 is the square root of 1600.
The required distance between the top of the ladder and the ground is 40 feet.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
We can use the Pythagorean theorem to solve this problem. Let's call the distance from the base of the ladder to the wall "x", and let's call the length of the ladder "y".
According to the problem statement, we know that the ladder is 41 feet long and that the base of the ladder is 9 feet from the base of the apartment building.
y = 41 feet
x = 9 feet
We can use the Pythagorean theorem to solve for the distance between the top of the ladder and the ground. The Pythagorean theorem tells us that:
y² = x² + z²
where "z" is the distance between the top of the ladder and the ground. Plugging in the values we know,
(41 feet)² = (9 feet)² + z²
1681 = 81 + z²
1600 = z²
z = 40 feet
Therefore, the distance between the top of the ladder and the ground is 40 feet.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
#SPJ5
I need help please and thank you
Answer:
75
Step-by-step explanation:
6 and 4 are alternate interior angles meaning they have the same value
equation in slope intercept form for a line that passes through (1,5) and (1,1)
Answer:
x = 1
Step-by-step explanation:
If you graph this, you will see that you will get a line that is straight up and down (or perpendicular to the x axis). No matter what y is, x will always be 1.
what are the domain and range and asympote of h(x)=6^x -4?
Answer:
Domain: (-oo, oo)
Range: (-4,oo)
Horizontal asymptote: y=-4
Answer:
The domain is all Real numbers.
The range is all real values > -4.
Step-by-step explanation:
The asymptote is y = -4.
How do you workout 28 divided by 812
Answer:
29
Step-by-step explanation:
Look at image
6 times a number plus 21 is greater than 6
A. 6 x plus 21 greater than 6
B. 6 x plus 21 less than or equals 6
C. 6 x plus 21 greater than or equals 6
D. 6 x plus 21 less than 6
Brainliest if you are right
Answer:
e
Step-by-step explanation:
because the lines are less scattered and they all are going straight up. they are also higher then all of the other ones.