Triangle ABC has the following angle measures:
m∠A = (x + 6)°, m∠B = (3x − 15)°, m∠C = (5x + 36)°
What is m∠C?
The measure of ∠C is 121 degrees.
Given that:-
There is a triangle ABC.
m∠A = (x + 6)°
m∠B = (3x - 15)°
m∠C = (5x + 36)°
We have to find the measure of ∠C.
We know that,
The sum of all the angles of a triangle is 180 degrees.
Hence, we can write,
m∠A + m∠B + m∠C = 180 degrees
(x + 6)° + (3x - 15)° + (5x + 36)° = 180 degrees
(x + 3x + 5x) + (6 - 15 + 36) = 180 degrees
9x + 27 = 180 degrees
9x = 180 - 27
9x = 153 degrees
x = 153/9 degrees
x = 17 degrees
Hence,
The measure of ∠C = 5x + 36 = 5*17 + 36 = 85 + 36 = 121 degrees.
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B. Write S if the expression is a sum of two cubes, D if a difference of two cubes, and N if neither.
1. 27x⁶ + y³=
2. 81 - b¹⁵=
3. 64x³ - 9z⁹=
4. 36m¹² - n⁶
5. 1 - d¹²=
6. 729 - y²⁹=
7. 343 - y⁶=
8. 4x³ + 8 =
9. 144 -125y² =
10. 64j⁶- k⁹=
Answers:
SNNNDNDNND==========================================================
Explanation:
Question 1
27x^6 = (3x^2)^3 which is one cube and y^3 is another cube
Therefore 27x^6+y^3 is a sum of two cubes.
It might help to think of it like A^3+B^3 where in this case A = 3x^2 and B = y.
----------------------------------------
Question 2
81 isn't a perfect cube since 81^(1/3) = 4.3267 approximately, which isn't a whole number. We need 81^(1/3) to be a whole number if we wanted 81 to be a perfect cube.
We don't even need to check b^15 since 81 being a non-perfect cube means the entire expression cannot be a sum of two cubes, nor a difference of cubes.
----------------------------------------
Question 3
64x^3 = (4x)^3 is a perfect cube
but 9z^9 is not a perfect cube
We can see this if we computed 9^(1/3) and the result is a non-whole number.
The answer here is the same as the previous question.
----------------------------------------
Question 4
36^(1/3) is not a whole number, so 36 isn't a perfect cube. By extension 36m^12 isn't a perfect cube either. The answer is the same as questions 2 and 3.
----------------------------------------
Question 5
1 is a perfect cube since 1 = 1^3
d^12 is a perfect cube because d^12 = (d^4)^3
Therefore, we have a difference of two cubes.
----------------------------------------
Question 6
729^(1/3) = 9 which rearranges to 9^3 = 729, showing 729 is a perfect cube.
However y^29 is not a perfect cube since the exponent 29 is not a multiple of 3.
The overall expression is "neither".
----------------------------------------
Question 7
343^(1/3) = 7 rearranges to 7^3 = 343, showing 343 is a perfect cube
y^6 is a perfect cube since (y^2)^3, i.e. the exponent 6 is a multiple of 3.
We have a difference of cubes.
----------------------------------------
Question 8
4 isn't a perfect cube since 4^(1/3) results in some decimal value that isn't a whole number. The entire expression is neither a sum nor difference of cubes.
----------------------------------------
Question 9
144^(1/3) isn't a whole number, so we get a similar result to problem 8.
----------------------------------------
Question 10
64j^6 = (4j^3)^3 is one cube
k^9 = (k^3)^3 is another cube
We have a difference of cubes
Write the equation for the vertical line and horizontal line that passes through each point. V(5, -2) AndT(10, -3)
Given
V(5, -2)
T(10, -3)
Procedure
For V:
The equation of the horizontal straight line corresponds to y = -2.
The equation of the vertical straight line corresponds to x = 5
For T:
The equation of the horizontal straight line corresponds to y = -3.
The equation of the vertical straight line corresponds to x = 10
Divide 7 and 2 over 3 ÷ negative 3 and 1 over 5.
negative 2 and 19 over 48
negative 24 and 8 over 15
negative 21 and 2 over 15
negative 3 and 19 over 93
Dividing 7 and 2 over 3 ÷ negative 3 and 1 over 5 will give a quotient of negative 2 and 19 over 48
How to determine the quotient of 7 and 2 over 3 ÷ negative 3 and 1 over 5information gotten from the question include
Divide 7 and 2 over 3 ÷ negative 3 and 1 over 5.
Division is a basic mathematical operator that performs the function of sharing
division of fraction is done as follows
7 and 2 over 3
= 7 2/3
= 23/3
negative 3 and 1 over 5.
= -3 1/5
= -16/5
= 23/3 ÷ -16/5
= 23/3 * -5/16
= -115/48
= -2 19/48
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I need help if you don't mind. I have to graph the linear equation using intercepts.
We want to find the places where the line
2x - 3y = 12
intercepts y-axis and x- axis
y- interceptWhen the line intercepts y axis, we know that x=0, we replace it in the equation so we can find y value:
2x - 3y = 12
↓
2 · 0 - 3y = 12
↓
0 - 3y = 12
-3y = 12
y = 12 / -3
y = -4
x - interceptIn the same way, we find the interception with x- axis when y = 0. We find the value of x replacing y by 0 in the equation:
2x - 3y = 12
↓
2x - 3 · 0 = 12
↓
2x - 0 = 12
2x=12
x = 12 / 2
x = 6
GraphWe locate both points: y = -4 and x = 6:
Finally, we join the points with a straight line
According to the rules of significant figures 7.898 + 5.23 = 13.13. This is because the least precise value in the problem is 5.23, which is precise only to the hundredths digit, so the answer must also be rounded to the nearest hundredths.True or False
The given expression is
[tex]7.898+5.23=13.13[/tex]It's important to know that the rules of significant figures state that the resulting number of a sum of decimal numbers may have no more significant numbers than the least number of significant figures.
In other words, the answers can't be more precise than the least precise number in the sum.
Therefore, the given statement is true.
The two angles pictured below are vertical angles.
Two lines intersect. The vertical angles measure eighty-four degrees and eight times x minus twelve.
What is the value of x?
The value of x in the vertical angles is 12.
What are vertically opposite angles?When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.
In other words, vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
Vertically opposite angles are congruent.
Therefore, the vertical angles measures 84 degrees and 8x - 12.
Let's find the value of x using the principle of vertically opposite angles.
Therefore,
84 = 8x - 12
add 12 to both sides of the equation
84 + 12 = 8x - 12 + 12
96 = 8x
divide both sides by 8
x = 96 / 8
x = 12
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what percentage grade should a road have if the angle of elevation of the road is 44 degrees? (the percentage grade is defined as the change in the altitude of the road over a 100100 -foot horizontal distance. for example a 5%5% grade means that the road rises 55 feet for every 100100 feet of horizontal distance.)
For a 44° elevation angle, the grade will be 96%.
Given that,
if the angle of elevation of the road is 44 degrees,
The difference in the road's altitude over a horizontal distance of 100 feet is what is referred to as the percentage grade. For instance, a road with a 5% slope will rise 5 feet for every horizontal 100-foot distance.)
A tangent ?
One of the six basic trigonometric functions is tangent, denoted as tan().
The ratio of the opposite side length to the adjacent side length is the definition of the tangent value of the one sharp angle,, in a right triangle.
[tex]tan \alpha = sin\alpha /cos \alpha[/tex]
The tangent of the angle is the ratio of rise to run.
tan(angle) = grade
tan(44°) ≈ 0.96 = 96%
Therefore, The grade will be 96% for an angle of elevation of 44°.
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please help with the question below (please add an explanation)
In order to get the volume of the irregular figure, let's cut it into two regular figures. See the cut below.
First, let's calculate the volume of the upper part.
The dimensions of the upper part are 7cm by 3 cm by 3 cm. Since the shape is a rectangular prism, let's multiply 7, 3, and 3.
[tex]V_{upper}=7cm\times3cm\times3cm=63cm^3[/tex]Hence, the volume of the upper figure is 63 cm³.
Let's now calculate the volume of the lower figure.
The dimensions of the lower figure are 5cm by 4 cm by 3 cm. Since this is a rectangular prism too, let's multiply the dimensions.
[tex]V_{lower}=5cm\times4cm\times3cm=60cm^3[/tex]The volume of the lower figure is 60 cm³.
Let's add the volume of the two figures to get the volume of the entire irregular figure.
[tex]V_{irregular}=V_{upper}+V_{lower}[/tex][tex]V_{irregular}=63cm^3+60cm^3=123cm^3[/tex]Therefore, the entire volume of the given irregular figure is 123 cm³.
Which one of these expressions doesn’t have a value less than 1 please help thank you if u do
The most appropriate choice for exponent will be given by-
Fourth option is correct
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2\times 2\times 2 \times 2[/tex], here, 2 is multiplied by itself 4 times.
If [tex]a^m = a\times a\times a \times.....\times a[/tex] (m times), a is the base and m is the index.
The laws of index are
[tex]a^m \times a^n = a^{m + n}\\\\\frac{a^m}{a^n} = a^{m-n}\\\\a^0 = 1\\\\(a^m)^n = a^{mn}\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\a^mb^m = (ab)^m[/tex]
Here,
For first option
[tex]\frac{4^{11}}{4^{14}}\\\frac{1}{4^{14 - 11}}\\\frac{1}{4^3}\\\frac{1}{64} < 1[/tex]
For second option
[tex](5^4)^2 \times 5^{-11}\\5^8 \times 5^{-11}\\5^{8-11}\\5^{-3}\\(\frac{1}{5})^3\\\frac{1}{125} < 1[/tex]
For the third option,
[tex](2^3)^{-2}\\2^{-6}\\(\frac{1}{2})^6\\\frac{1}{64} < 1[/tex]
For the fourth option
[tex]\frac{(3^5)^2}{3^4}[/tex]
[tex]\frac{3^{10}}{3^4}\\3^{10 - 4}\\3^6\\ 729 > 1[/tex]
Fourth option does not have an expression greater than 1
Fourth option is correct.
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3:5:7=....:30:...
help me keeds please
Answer:
3=6 5=10 7=14
Step-by-step explanation:
here's how to do it u wwould have to sum (+) up all the ratios then it would give u 15 after then u divide the sum by 15 hen u multiply by ratios .
Could someone please help me this is due at 3 pm and it's allready 2:43 and i only need these questions and i am done please help me. if you answer all you get 20 points! PLEASE HELP PLEASE HELP ANYONE PLEASE PLEASE
a) (2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex]) in standard form
The number in standard form is 345
explanation:
The given two multiplication of the numbers is :
(2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex])
First we multiply the non exponential terms as shown below
2.3 × 1.5 = 3.45
Now we multiply the exponential terms as shown below
[tex]$10^4[/tex] × [tex]$10^{-2}[/tex] = 100
Now multiplying the exponential and non exponential term we get the number in standard form as shown below
(2.3 × [tex]$10^4[/tex]) × (1.5 × [tex]$10^{-2}[/tex]) in standard form 345
(3.6 × [tex]10^-5[/tex])÷(1.8 × 10²) in standard form 0.0000002
(8 × 10^-3) × (2 × [tex]10^-4[/tex] in standard form 1.6 × [tex]10^-6[/tex]
(6 × 10²)/(3 × 10-5) in standard form 20,00,0000
5.1 × [tex]$10^-1[/tex] in ordinary number is 0.51
(1.7 × [tex]10^4[/tex]) × (8.5x ×[tex]0^-2[/tex]) in standard form 1.445 × 10³.
3.45 x 100 = 345
Therefore, the number in the standard form is 345
b) (3.6 × [tex]10^-5[/tex])÷(1.8 × 10²) in standard form
The number in standard form is 0.0000002
explanation:
By dividing 3.6 by 1.8 we get “2”, hence the above equation becomes,
(2 × [tex]10^-5[/tex]) /[tex]10^2[/tex]
We know that
[tex]\frac{x^{a} }{x^{b} } = x^{a-b}[/tex]
Therefore the above equation becomes,
2 × [tex]10^-7[/tex]
since the exponent of 10 is negative , therefore 7 zeros are written on the left hand side of the number = 0.0000002
Therefore, the number in the standard form is 0.0000002
c) (8 × [tex]10^-3[/tex]) × (2 × [tex]10^-4[/tex]) in standard form
The number in standard form is 1.6 × [tex]10^-6[/tex]
explanation:
Given the product of scientific notations:
(8 × [tex]10^-3[/tex]) × (2 × [tex]10^-4[/tex])
This can be expressed as:
(8 × 2) × ([tex]10^-3[/tex] × [tex]10^-4[/tex])
= 16 × [tex]10^-3[/tex]-4
= 16 × [tex]10^-7[/tex]
= 1.6 × [tex]10^1[/tex] × [tex]10^-7[/tex]
= 1.6 × [tex]10^-6[/tex]
Therefore, the number in the standard form is 1.6 × [tex]10^-6[/tex]
d) (6 × 10²)/(3 × 10-5) in standard form
The number in standard form is 20,00,0000
e) 5.1 × 10^-1 as an ordinary number
The ordinary number is 0.51
usual form of 5.1 × [tex]10^1[/tex] is
5.1 × 1/ [tex]10^1[/tex]
= 5.1/10
= 0.51
Therefore , ordinary number is 0.51
f) (1.7 × [tex]10^4[/tex]) × (8.5 × [tex]10^-2[/tex]) in standard form.
The number in standard form is 1.445 × 10³.
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Part A Write the multiplication expression shown by the model. Do not solve the problem. Part B
Explain the expression written in Part A. Include the final product and how it is shown with the model.
Part A: The multiplication expression is L×w
Part B: The expression is written as N= r+ g + w + b
The final product = 200 boxes
How to determine the expressionIt is crucial to note that the formula for determining the area of a rectangle is expressed as;
Area = lw
Given that;
l represents the length of the rectanglew represents the width of the rectangleThe area can be calculated by multiplying the length and the width and also by then adding the number of boxes.
We have the expression as;
10( 4 + 5 + 4 + 7)
Also,
L × w = r + g + w + b
Hence, we have that L×w is a multiplication expression.
Total number of boxes for the length = 20
Total number of boxes for the width = 10
Total area = L×w = 20×10=200
Number of available red boxes = 46Number of available green boxes = 46Number of available blue boxes = 46Number of available white boxes = 62We have;
N= r+ g + w + b
but r = g = b
Also,
L×B = 3r + w
Hence, a multiplication expression is an expression that has its variables or numbers being multiplied.
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Solve for y:
-3x+4y=28
Answer:
y = [tex]\frac{28+3x}{4}[/tex]
Step-by-step explanation:
- 3x + 4y = 28 ( add 3x to both sides )
4y = 28 + 3x ( isolate y by dividing both sides by 4 )
y = [tex]\frac{28+3x}{4}[/tex]
multiplicative inverse of 7^-2
Answer:
[tex] 7^2[/tex]
Step-by-step explanation:
multiplicative inverse of[tex] \:\:7^{-2} =7^2[/tex]Answer:
7²
Step-by-step explanation:
the product of a number and its multiplicative inverse is equal to 1 , that is
a ×[tex]\frac{1}{a}[/tex] = 1
given
[tex]7^{-2}[/tex] , then multiplicative inverse is [tex]\frac{1}{7^{-2} }[/tex] = 7² and
[tex]7^{-2}[/tex] × 7² = [tex]7^{0}[/tex] = 1
Let f(x) = -3x³ + 9x² - 5x + 15. Use the Factor Theorem to help answer the
following questions.
a) Is a
O Yes
O No
b) Is x + 1 a factor of f(x)?
O Yes
No
1 a factor of f(x)?
c) Is a 3 a factor of f(x)?
O Yes
O No
Answer:
See below. I added words tro the first question "Is a" so that I could answer it.
Step-by-step explanation:
f(x) = -3x³ + 9x² - 5x + 15
f(x) = -(x-3)(3x² + 5)
x((9-3x)x-5)+15
-3(x-1)[tex]x^{3}[/tex] + 4(x-1) + 16
=======
a) Is a [ghost happy]?
O Yes Yes, as long as it can haunt.
O No
b) Is x + 1 a factor of f(x)?
O Yes Yes
No
1 a factor of f(x)?
Always
c) Is a 3 a factor of f(x)?
O Yes
O No No, as far as I can see.
hellp please ?????????????
Answer:
see explanation
Step-by-step explanation:
since the dilatation is centred at the origin , then multiply each of the original coordinates by the scale factor of 2
Q (2, 2 ) → Q' (2(2), 2(2) ) → Q' (4, 4 )
P (0, 0 ) → P' (2(0), 2(0) ) → P' (0, 0 )
R (- 2, - 4 ) → R' (2(- 2), 2(- 4) ) → R' (- 4, - 8 )
S (4, - 2 ) → S' (2(4), 2(- 2) ) → S' (8, - 4 )
The sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet, write and solve a compound inequality to show the possible heights of the third tree.
The inequality to show the possible heights of the third tree is 8 ≤ x ≤ 18.
How to calculate the value?Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤
Let the height of the third tree be x.
By the given condition, this will be:
8 + 16 + x ≥ 32 and 8 + 16 + x ≤ 42
The first relation will give x ≥ 32 - 24 = x ≥ 8
The second relation will give:
8 + 16 + x ≤ 42
24 + x ≤ 42
x ≤ 42 - 24
x ≤ 18
The inequality is 8 ≤ x ≤ 18.
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If sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet. Then compound inequality is 8 ≤ x ≤ 18.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Let height of the third tree be x.
By the given condition
The sum of three palm tree heights range from 32 to 42 feet
8 + 16 + x ≥ 32 and 8 + 16 + x ≤ 42
Solve these inequalities
8 + 16 + x ≥ 32
24+x ≥ 32
x≥ 32-24
x≥ 8
and 8 + 16 + x ≤ 42
24+ x ≤ 42
x≤ 42-24
x ≤ 18
Hence the inequality is 8 ≤ x ≤ 18.
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A cereal bar contains 130 calories. The number c of
calories consumed is a function of the number b bars
eaten.
a. Does this situation represent a linear function?
Explain.
b. Find the domain of the function. Is the domain
discrete or continuous? Explain.
c. Graph the function using its domain.
The domain of the function will be; [0 ∞) and the domain is continuous.
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
The number c of calories consumed is a function of the number b bars
eaten is represented by the linear function b = 130c
The domain of the linear function would be [0 ∞).
A whole number or a decimal number may be c.
Any data which can be expressed as a decimal is continuous data.
Therefore, the domain of the function will be; [0 ∞) and the domain is continuous.
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A tent pole that is 9 feet tall is secured to the ground with a piece of rope that is 15 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.
Answer:
12 ft
Step-by-step explanation:
To find the base (b), you would first need to sketch a right triangle using the following:
a = 9
c = 15
Using the Pythagorean theorem [tex]a^{2} +b^{2} =c^{2}[/tex], you would change it to [tex]c^{2} -a^{2} =b^{2}[/tex] to fit the question. Next, you would plug in the numbers to the corresponding letter.
[tex]15^{2} -9^{2} =b^{2}[/tex]
[tex]225-81=144^{2}[/tex]
[tex]\sqrt{144} =b[/tex]
[tex]12=b[/tex]
The horizontal distance from the tent pole to the rope along the ground will be equal to 12 feet.
What is the Pythagoras' Theorem?According to the Pythagoras theorem, if a triangle has a straight angle (90 degrees), the hypotenuse's square is equal to the total of its other two sides' squares.
As per the given in the question,
Height of tent pole, p = 9 feet
Height of rope, h = 15 feet
Let the horizontal distance from pole to rope is b.
Use Pythagoras' theorem,
h² = p² + b²
15² = 9² + b²
b² = 225- 81
b = √144
b = 12 feet.
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if a child is 120cm tall, but they grow 4% bigger in a year, how tall will they be?
Answer
The height of the child in a year time = 124.8 cm
Explanation
The child is currently 120 cm tall.
The child grows 4% bigger in 1 year.
We now need to calculate how tall the child is in that 1 year.
New height for the child = (Current height) + (Increase in height)
Current height = 120 cm
Increase in height = 4% of 120 cm = 0.04 × 120 = 4.8 cm
New height for the child = (Current height) + (Increase in height)
= 120 + 4.8
= 124.8 cm
Hope this Helps!!!
a street light is at the top of a ft. tall pole. a man ft tall walks away from the pole with a speed of feet/sec along a straight path. how fast is the tip of his shadow moving when he is feet from the pole?
[tex]\frac{dx}{dy} = \frac{5}{3}. 4\frac{ft}{s} = \frac{20}{3}\frac{ft}{s}[/tex] is moving at the speed of the shadow
x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole. I assume the man and pole are standing straight up, which means the two cases are similar.
[tex]\frac{y-x}{y} = \frac{6}{15}[/tex]
15(y-x) = 6y
9y = 15x
[tex]\frac{5}{3}x\\[/tex] = y
differentiate both sides with respect to t or time.
[tex]\frac{dx}d{y} = \frac{5}{3}\frac{dx}{dt}[/tex]
you know [tex]\frac{dx}{dy} = 4\frac{ft}{s}[/tex] because the man is walking that speed away from the pole. you want to find [tex]\frac{dx}{dy}[/tex] , how fast the tip of the shadow is moving.
that means
[tex]\frac{dx}{dy} = \frac{5}{3}. 4\frac{ft}{s} = \frac{20}{3}\frac{ft}{s}[/tex]
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Two models are shown. Which expression does each model represent?
Move the correct answer to each box. Not all answers will be used.
Find the average rate of change of his annual salary between 2017 and 2020
We were told that the salary, t years after 2015 is given by the function,
S(t) = 3100t + 56000
When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2
We would substitute t = 2 into the function and find S(2)
Thus,
S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200
When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5
We would substitute t = 2 into the function and find S(2)
Thus,
S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500
Thus, we can say that
when
x1 = 2, y1 = 62200
when x2 = 5, y2 = 71500
Recall,
slope or average rate of change = (y2 - y1)/(x2 - x1)
average rate of change = (71500 - 62200)/(5 - 2) = 9300/3
average rate of change = 3100
The last option is correct
Think the length of a rectangle is 5 inches longer than its width if the perimeter of the rectangle is 42 inches find it’s area
The area of the rectangle is 104 inches²
Define Area of Rectangle
The area of a rectangle is the space occupied by the rectangle inside its perimeter.
Given that, the perimeter is 42 inches
we know, the formula of perimeter of rectangle = 2(L + W)
so, the first equation will be
2(L + W) = 42
or, 2L + 2W = 42 ----------eq(i)
Next, the length of a rectangle is 5 inches longer than its width, so
L = W + 5
or, L - 5 = W --------------eq(ii)
Now, the eq(i) is
2L + 2W = 42
Put W value from eq(ii),
2L + 2(L- 5) = 42
=> 2L + 2L - 10 = 42
=> 4L - 10 = 42
=> 4L = 52
=> L = 13
We got, L = 13 put this value in any of the equation
I'm putting the value in eq(ii) as it easy for to solve
=> 13 - 5 = W
=> W = 8
If you want to cross verify the values of L and W , then simply put the values in both the equation and LHS = RHS like that
2(13) + 2(8) = 42 (correct)
13 - 5 = 8 (correct)
Now, we got length and width so now just put the values of L and W in area of rectangle formula,
Area of rectangle = Length * width
= 13 * 8
Area of rectangle = 104 inches²
Hence, The area of the rectangle is 104 inches²
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An investor purchased 50 shares ofstock in a company for $40 pershare. One year later, the investorsold all the shares for $2,200. Whatis the investor's rate of return?A. 9.1%B. -9.1%C. -10.0%D. 10.0%
Investor purchased 50 shares of stock in a company for $40.
So, the total initial amount he invested is
[tex]50\cdot40=2000[/tex]Then the rate of return is:
[tex]\begin{gathered} \text{rate of return=}\frac{shares\text{ sold price-initial amount invested}}{\text{ initial amount invested}}\cdot100 \\ =\frac{2200-2000}{2000}\cdot100 \\ =\frac{200}{2000}\cdot100 \\ =10 \end{gathered}[/tex]So, the requied rate of return is 10.0%.
Kuta Software In Systems of Two Solve each system by graphing. 2) y=x+2 1) y=-3x +41 y= 3x - 2
ok
Equations : 4x + y = 2 x - y = 3
Equation 1 4x + y = 2 x - y = 3
x y x y
-2 10 -2 -5
-1 6 -1 -4
0 2 0 -3
1 -2 1 -2
2 -6 2 -1
The point where both lines cross is (1, -2) so it is the solution.
I need help please(˘・_・˘)
Answer:
with?
Step-by-step explanation:
Gary applied the distributive property using the greatest common factor to determine the expression that is equivalent to 66 + 36. His work is shown below.
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
66 + 36 = 3 (22 + 12)
What statement best describes Gary’s error?
Gary did not use correct factors for 66 in the equation.
Gary did not use correct factors for 36 in the equation.
Gary did not use two equivalent expressions in the equation.
Gary did not use the greatest common factor in the equation. pls hurry 10 mins left
A statement which best describes Gary’s error is that: Gary did not use correct factors for 66 in the equation.
What is the distribution property of multiplication?The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.
Mathematically, the distributive property of multiplication is given by this expression:
a(b + c) = ab + ac.
Also, the correct greatest common factor of 66 and 36 is given by:
Greatest common factor (GCF) = 6
By applying the distributive property of multiplication, we have:
66 + 36 = 6(11 + 6)
Read more on factor here; https://brainly.com/question/28216114
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what is the size of the angle between south and south east
The angle between north and south = 180°. The angle between East and South = 90°. The angle between South and West is 90° and between South and East is also 90°. So the sum of these two angles is equal to 180°. Since these two angles are adjacent to each other so they form a linear pair.