Using the area of triangles and rectangles, we know that the area of the shaded region is 255cm².
What is the formula for the area of a rectangle and triangle?Area of rectangle = length x widthArea of triangle = 1/2 x base x heightIn the given shaded region there is one rectangle and one triangle.
First, find the area of the shaded rectangle.
Here, length = 22 cm and width = 10 cm.So, Area of rectangle = length x width = 22 x 10Area of rectangle = 220 square cm.Now find the area of the shaded triangle.
Here, base = 10 cm and height = 7 cm.So, the Area of the triangle is:
Area = 1/2 × 10 × 7= 35cm²Therefore, the total area of the shaded region is:
Area of shaded region = Area of rectangle + Area of triangle= 220 + 35Area of shaded region = 255 square cm.Therefore, using the area of triangles and rectangles, we know that the area of the shaded region is 255cm².
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What are the steps needed to find x^3=64. I know the correct answer is 4, I just don't know the steps.
Step-by-step explanation:
x^3 =64
x^2+x=64( you can write x^3 like this .there is not problem with it )
x+x= root 64
2x= 8 ( 8×8=64)
x=8÷2
x = 4
Complete the table and graph the solutions of the equation y =-3x + 3. X -1 0 1 2 у co -7 -6 -5 -4 -3 -2 -1. 0 2 3
1) Since the equation is y= -3x+3, let's fill in that table by plugging into them the given values for x
x | y= -3x +3 | y
-1 | y=-3(-1)+3 | 6
0 | | 3
1 | | 0
2| | -3
2) Let's plot that equation for points (-1,6) (0,3), (1,0) and (2,-3)
1080 sec: 6 min: 1080 sec simplified
Answer: 18 mins
Step-by-step explanation
there is 3600 secs in an hour so do the same for this.
6 mins is 360 secs and times 360 by 3 is 1080 and then double it they figure out how many mins is 2160 im sorry if thats confusing.
Determine the approximate value of d.
4.29 cm
5.32 cm
6.24 cm
7.16 cm
Approximate value of d = 4.29 cm.
What is cosine rule?The Cosine Rule states in trigonometry that the square of the length of any side of a given triangle is equal to the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of angle contained between them. Cosine rule is also known as the law of cosines or the Cosine Formula.
In Δ ADR , AR = d, DR = 8 cm. AD = 5 cm. ∠D = 28°
By using cosine rule,
AR² = AD² + DR² - 2 AD ×DR CosD
AR² = 5² + 8² - 2×(5)×(8) × Cos 28°
AR² = 25 + 64 - 80 Cos 28°
AR² = 89 - 80 Cos 28°
AR² = 89 - 80 × (0.8829)
AR² = 89 - 70.6358
AR² = 18.3641
AR = 4.29 cm. = d
Thus, approximate value of d = 4.29 cm.
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what is the radius of the circle?
Answer:
The radius is from the middle to the edge, in this case it looks the radius is 4
Marilyn purchased 2,000 shares of stock for $25.43 per share. She sold them for $44.10 per share. Express her capitol gain to the nearest tenth of a percent.
Marilyn's capital gain is 73%.
How to find her capital gain?
Marilyn purchased 2,000 shares
$25.43 per share
She sold them for $44.10 per share
Solution:
Capital gain per share = 44.10 - 25.43 = $18.67
Capital gain for 2,000 shares = 2000*18.67
= $37,340
Her capital gain is $37,340.
The price of 2000 shares she bought initially = 2,000*25.43
= $50,860
Her capital gain in percentage = 37,340/50,860*100
= 73.41
That is,
73%
Her capital gain is 73%.
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Andrew writes the algebraic expression 2s+ 2.79 to represent the cost of his
lunch. He bought 2 sandwiches and a large drink. Identify any variables,
coefficients, and terms in the expression. Tell what each represents.
The sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant
What is Algebraic Expression?
An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. For instance, the algebraic formula 3x2 2xy + c
The cost of Andrew's lunch is written as the algebraic expression
2s + 2.79 as a given. He bought a huge drink and two sandwiches.
In the algebraic expression given;
2s + 2.79
Here, 2 stand in for the coefficients of s, which stands for the quantity of sandwiches he purchased.
The sandwich's price is represented by the variable s, which is a function of the coefficient.
And 2.97 represents both the cost of a big drink and a constant since no further letters have been added.
Hence, sandwich's price is represented by the variable s , 2 is the coefficient of s and 2.97 represents both the cost of a big drink and a constant
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-2.3x - 4.2x = -66.3
Solve the equation for x
Answer
x=10.
Step-by-step explanation:
-2.3x-4.2x=-66.3
-2.3+-4.2=-6.5x
-6.5x÷-6.5
-66.3÷-6.5
x=10.
The mass of the Rock of Gibraltar is 1.78-102 kilograms. The mass of the Antarctic iceberg is 4.55-103 kilograms. Approximately how many more kilograms is the mass of the Antarctic iceberg than the mass of
the Rock of Gibraltar? Show your work and write your answer in scientific notation (10 points)
4.372 × [tex]10^{13}[/tex] more kilograms the mass of the Antarctic iceberg than the mass of the Rock of Gibraltar.
Mass of the Antarctic iceberg = 4.55 × [tex]10^{13}[/tex]
Mass of the rock of Gibraltar = 1.78 × [tex]10^{12}[/tex]
Excessive mass of Antarctic Icebergs than the rock of Gibraltar,
4.55 × [tex]10^{13}[/tex] - 1.78 × [tex]10^{12}[/tex]
Subtract easily both should be in the same power of ten,
= 4.55 × [tex]10^{13}[/tex] - 1.78 × [tex]10^{12}[/tex]
= 43.72 × [tex]10^{12}[/tex]
= 4.372 × [tex]10^{13}[/tex]
Scientific notation is used to express quantities that are either too large or too little to be represented by decimals. Scientific format, standard index format, and standard format are other terms for the same thing.
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a triangle base is 6 inches long and it’s height is 5 inches. what the area of the triangle?
Answer:
Answer:The area of the triangle is 60 in.
explanation:
Because we have 6inches in the weigth and 5inches in the height .
A=1/2bhA=1/2x 5 x 6A=30A=1/2 ÷30A=60inin endurance horse racing, people over the age of 15 are called seniors and people 15 years or younger are called juniors. an endurance horse race consists of 30 seniors and 6 juniors. (give answer as a fraction or a decimal out to at least 4 places. if your answer is very small use scientific notation for example 3.3421e-6.)
a)P(all seniors) =(25C3)/(30C3) =0.5665
b)P(All Juniors)=(5C3)/(30C3) =0.0025
c)P(2 senior and 1 Junior) =(25C2)(5C1)/(30C3) =0.3695
d)P(1 senior and 2 Junior) =(25C1)(5C2)/(30C3) =0.0616
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For the bake sale, Lee baked 141 cookies. Esther baked 51 more cookies than Lee. How many cookies did Lee and Esther bake in all?
Answer: 333 Cookies
Step-by-step explanation:
Let E = Cookies by Esther
Let L = Cookies by Lee
The equation for amount of cookies: E+L
L=141
E=L+51
Substitute L
E=141+51=192
E+L=141+192=333
Answer:
[tex]10 \div x - 10 \div (x - 1) = 30[/tex]
2 $ 11 OA 1 2 3 4 5 -2 4 4 2 OB $ 4 5 2 1 C. 1 2 3 4 5 3 2 D.
C is the correct option
Here, we want to selct which of the plotted points in the graphs correctly represent the given points
The given points are (2,21/2) and (-1 1/2,-4)
As we can see on the graphs, there are four different marked points
We just need to select the graph that contains the points
What the point (2, 2 1/2) means is that we have point 2 on the x-axis and trace point 2 1/2 on the y-axis
This point is missing in the first two options
However, on the third option C, we can see this option
We can check if the second option is there too
(-1 1/2 , -4)
We have -1 1/2 on the x-axis and -4 on the y-axis
We can see this on the third option too
So option C is our correct answer
Graph the image of the figure using the transformation given.
A graph of the image of triangle V'W'X' after a rotation of 90° counterclockwise about the origin is: graph A.
What is a rotation?A rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
In Geometry, rotating a point 90° about the origin in a counterclockwise (anticlockwise) would produce a point that has the coordinates (-y, x).
Note: Each interval on this graph represents 1 unit.
By applying a rotation of 90° counterclockwise to triangle VWX, the coordinates of the vertices of the image triangle V'W'X' include the following:
(x, y) → (-y, x)
Point V = (-2, -4) → Point V' = (-(-4), -2) = (4, -2)
Point W = (-2, -2) → Point W' = (-(-2), -2) = (2, -2)
Point X = (-5, -4) → Point X' = (-(-4), -5) = (4, -5)
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Determine if √64 is rational or irrational and give a reason for your answer.
x-2=4(x+1) divided by 2
pls help
im grade 6
Math plsss help me ill give you 10 points
Answer:
7.25
Step-by-step explanation:
Barangay Maligaya is 28.5km
Since Ricardo traveled 12.75km by Jeep and 8.5km by tricycle and rest by hiking
Jeep = 12.75
Tricycle = 8.5
Hiking = 12.75 + 8.5
=21.25
Total= 28.5
=28.5 -21.25
= 7.25
The distance between Dallas and Austin on a map is about 9 centimeters. The map uses a scale in which 1 centimeter represents 20 miles. What is the actual distance between Dallas and Austin in miles
please help due in an hour and i cannot fail!!!
Answer:
180
Step-by-step explanation:
9x20
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
The values of x are x = 13 and x = 1 when we have [tex](x-7)^{2} = 36[/tex].
According to the question,
We have the following information:
[tex](x-7)^{2} = 36[/tex]
Now, we will solve the expression on the left hand side using an identity.
The identity that will be used here is [tex](a-b)^{2}= a^{2}+ b^{2} -2ab[/tex].
In this case, we have a = x and b = 7.
[tex]x^{2}+ 7^{2} -2x*7[/tex] = 36
[tex]x^{2} +49-14x = 36[/tex]
Moving 36 from the right hand side to the left hand side:
[tex]x^{2} +49-14x-36 = 0\\x^{2} -14x+13 = 0[/tex]
Now, to find the values of x, we will factorize this expression by splitting the middle term such that the sum of two terms is -14x and their multiplication is 13[tex]x^{2}[/tex].
The two terms will be -13x and -x.
[tex]x^{2} -13x-x+13 = 0\\[/tex]
Taking x common from the first two terms and -1 common from the last two terms:
x (x-13) -1(x-13) = 0
Taking (x-13) as common:
(x-13) (x-1) = 0
x-13 = 0 and x-1 = 0
x = 13 and x = 1
Hence, the values of x are 13 and 1.
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Use the graph to determine (a) open intervals on which the function is increasing, if any. (b) open intervals on which the function is decreasing, if any. (c) open intervals on which the function is constant, if any.
The behaviors of the function in the intervals is given as follows:
a) Increasing: (-∞, -4) and (-3, -2).
b) Decreasing: (-4, -3) and (-2, ∞).
c) Constant: No interval.
When a function is increasing, considering it's graph?Considering the graph of the function, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y increases.
Hence, in the context of this problem, considering the given graph the function is increasing on these following intervals:
(-∞, -4).(-3, -2).When a function is decreasing, considering it's graph?Considering the graph of the function, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.
Hence, in the context of this problem, considering the given graph the function is decreasing on these following intervals:
(-4,-3).(-2, ∞).When a function is constant?A function is constant when the graph is an horizontal line, that is, when changing the value of x causes no effect to the value of y, it remains constant.
Hence, there are no intervals in which the graph of the function is constant.
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Roy ate 2/3 of his personal pizza Roxy ate 3/5 of hers robbi ate 0.45 of hers and Russ ate 9/12 of his who ate the most of his or her pizza?
We will see that the largest number is 9/12, and Russ ate 9/12 of his pizza, so he is the one that ate most of his pizza.
Who ate the most of his/her pizza?Here we know that:
Roy ate 2/3 of his pizza.Roxy ate 3/5 of her pizza.Robby ate 0.45 of his pizza.Russ ate 9/12 of her pizza.So we just need to see which of the given numbers is the largest one.
We can rewrite the fractions as:
2/3 = 0.66
3/5 = 0.6
9/12 = 3/4 = 0.75
The largest number is 0.75, in this way we conclude that Russ is the one that ate more pizza.
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The average flight time for the pilots is found to be 8.12 hours. The
standard deviation reported by the FAA is 0.72 hours, and there
were 81 pilots in the sample. What is the t-statistic for this
hypothesis test? Report to two decimal points
(Flights generally limit pilots to 8 hours of flight time during a 24-hour period)
The test statistic for this hypothesis test is; t = 1.5
What is the Test Statistic?
The formula for test statistic is;
t = (x' - μ)/(σ/√n)
where;
x' is sample mean
μ is population mean
σ is standard deviation
n is sample size
We are given;
Sample mean; x' = 8.12 hours
Population mean; μ = 8 hours
Standard deviation; σ = 0.72 hours
sample size ; n = 81 pilots
Thus;
t = (8.12 - 8)/(0.72/√81)
t = 0.12/0.08
t = 1.5
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What is 80,023 written in scientific notation? A. 8.0023 x 10^3 B. 8.0023 x 10^4 C. 8.0023 x 10^5D. 8.0023 x 10^6
ANSWER
[tex]B\text{. 8.0023 }\cdot10^4[/tex]EXPLANATION
We want to write the number given in scientific notation. The number is 80,023
Putting a number in scientific notation involves writing that number as a product of a number between 1 and 10 and a power of 10.
We do this by moving the decimal point from behind the last digit of the number (3) to just after the first digit (8).
We move the decimal point 4 times to the left, that is why the power of 10 is +4.
So, we have that 80,023 becomes:
[tex]80,023\text{ = 8.0023 }\cdot10^4[/tex]
write a pair of fractions whose sum is 7/11and difference is 3/11
If;
[tex]\frac{x}{11}=a[/tex] and[tex]\frac{y}{11} =b[/tex]then these variables must meet the following conditions below;
[tex]a+b=\frac{7}{11}[/tex][tex]a-b=\frac{3}{11}[/tex]In rational expressions (fractional numbers), if the denominators are equal, arithmetic operations are performed with the numerators. Therefore;
[tex]x+y=7[/tex][tex]x-y=3[/tex]If we add both equations at the same time, we get the following result;
[tex]x+y+x-y=7+3[/tex][tex]2x=10[/tex][tex]x=5[/tex]Now that we have found the unknown x, we can find the unknown y.
[tex]x+y=7[/tex][tex]5+y=7[/tex][tex]y=2[/tex]Now let's write our fraction pairs.
[tex](\frac{5}{11},\frac{2}{11} )[/tex]Answer:
[tex]\frac{5}{11}[/tex] and [tex]\frac{2}{11}[/tex]
Step-by-step explanation:
let the 2 fractions be x and y , x > y , then
x + y = [tex]\frac{7}{11}[/tex] → (1)
x - y = [tex]\frac{3}{11}[/tex] → (2)
add the 2 equations term by term to eliminate y
2x + 0 = [tex]\frac{10}{11}[/tex]
2x = [tex]\frac{10}{11}[/tex] ( divide both sides by 2 )
x = [tex]\frac{5}{11}[/tex]
substitute x = [tex]\frac{5}{11}[/tex] into (1) and solve for y
[tex]\frac{5}{11}[/tex] + y = [tex]\frac{7}{11}[/tex] ( subtract [tex]\frac{5}{11}[/tex] from both sides )
y = [tex]\frac{2}{11}[/tex]
the pair of fractions are [tex]\frac{5}{11}[/tex] and [tex]\frac{2}{11}[/tex]
Another music store rents trombones for $30 per month plus a yearly fee of $48. Which deal is better? Should Maria change her rental plan? Part A: Maria needs a trombone for only 12 months. Renting the trombone costs $34 per month. She can buy the trombone for $495. Should she buy or rent the trombone? Explain. How much does she pay? dont have to answer part a but u can if u want i only put it there so u can see it all, thank you friend: )
Please, I need this ASAP! I'll give brainliest to a quick informative answer, thank you!!!
Step-by-step explanation:
Another music store rents trombones for $30 per month plus a yearly fee of $48. Which deal is better? Should Maria change her rental plan?
Part A: Maria needs a trombone for only 12 months. Renting the trombone costs $34 per month. She can buy the trombone for $495. Should she buy or rent the trombone? Explain.
Option 1, SHOP 1: [at $30 a month] When Maria rents for a year, or x = 12 months
This can be described by the equation:
30x + 48
where x = number of months rented
30(12) + 48
= $408
___________
Option 2, SHOP 2: [at $34 a month] When Maria rents for a year, or x = 12 months
This can be described by the equation:
34x + 48
where x = number of months rented
34(12) + 48
= $456
___________
Option 2, buy: for $495
ANALYSIS:
Because Maria only needs the instrument for a year (12 months), Maria would do best to rent her instrument from option 1, shop 1 (renting at $30 a month + $48 yearly fee). Purchasing the instrument is the most costly.
Should Maria need the instrument longer than a year, then the option preference would change.
Help pls thx
King David was born in 1015 BC and died in 970 BC. The Roman Emperor Augusta was born in 63 BC and died in 14 AD. Which of these two men lived longer?
PLEASE HELP ASAP!!!!!!!!!!!!!!!
The table describes the quadratic function h(x).
x h(x)
−3 −2
−2 −3
−1 −2
0 1
1 6
2 13
3 22
What is the equation of h(x) in vertex form?
h(x) = (x + 2)2 − 3
h(x) = (x + 1)2 − 2
h(x) = (x − 1)2 + 2
h(x) = (x − 2)2 + 3
The quadratic function of h (x) in vertex form will be;
⇒ h(x) = (x + 2)² − 3
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The values of x and h (x) for the quadratic function is given as;
x = -3, -2, -1, 0, 1, 2, 3,
h (x) = -2, -3, -2, 1, 6, 13, 22
Now,
Let the quadratic function is,
h (x) = ax² + bx + c
Substitute x = -3 and h (x) = -2 in above quadratic function we get;
h (x) = ax² + bx + c
- 2 = a × (-3)² + b × -3 + c
- 2 = 9a - 3b + c
And, Substitute x = -2 and h (x) = -3 in above quadratic function we get;
h (x) = ax² + bx + c
- 3 = a × (-2)² + b × -2 + c
- 3 = 4a - 2b + c
And, Substitute x = -1 and h (x) = -2 in above quadratic function we get;
h (x) = ax² + bx + c
- 2 = a × (-1)² + b × -1 + c
- 2 = a - b + c
After solving we get;
a = 1 , b = 4 and c = 1
Substitute all the values in above quadratic equation, we get;
h (x) = ax² + bx + c
h (x) = 1 × x² + 4x + 1
h (x) = x² + 4x + 1
h (x) = x² + 4x + 4 - 4 + 1
h (x) = (x + 2)² - 3
Thus, The quadratic function of h (x) in vertex form will be;
⇒ h(x) = (x + 2)² − 3
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grace and jack are playing a game with a gigantic bucket of markers. jack took a random sample of markers from the bucket and counted 121212 yellow markers, 373737 blue markers, and 111 red marker. use the observed frequencies to create a probability model for the color of the next randomly selected marker from the gigantic bucket of markers. input your answers as fractions or as decimals rounded to the nearest hundredth.
If grace and jack are playing a game with a gigantic bucket of markers. The probability are yellow 0.24, blue 0.74, red 0.02.
ProbabilityGiven data:
Yellow markers = 12
Blue markers =37
Red marker =1
Total number of markers = 12 + 37 + 1
Total number of markers = 50
Probability of an event occuring= Favorable number of outcomes / Total number of outcomes
Probability of getting an yellow marker = 12/50
Probability of getting an yellow marker = 0.24
Probability of getting an blue marker = 37/50
Probability of getting an blue marker = 0.74
Probability of getting an red marker = 1/50
Probability of getting an red marker = 0.02
Probability model
Type of maker Frequency Probability
Yellow 12 0.24
Blue 37 0.74
Red 1 0.02
Therefore the probability are 0.24, 0.74, 0.02.
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the cost per hour for fuel to run a train is v2 15 dollars, where v is the speed of the train in miles per hour. (note that the cost goes up as the square of the speed.) other costs, including labor, are $300 per hour. how fast should the train travel on a 300-mile trip to minimize the total cost for the trip?
The train should travel at a speed of 30√5 miles/hour on a 300-mile trip to minimize the total cost for the trip?
Given the cost per hour for fuel to run is v^2/15 dollars:
Labor cost=$300 per hour
Calculate the velocity to travel on a 300-miles trip:
Total time t=Distance/speed
=300/v
t=300/v
Total cost=(fixed cost*time)+(variable cost*time), where fixed cost is $300 per hour and variable cost is v^2/15 dollars , and time t=300/v
Total cost=(300*300/v)+((v^2/15)*(300/v))
=(90000/v)+(300v/15)
Now, to minimize the total cost on a 300-mile trip, we differentiate the total cost with respect to the velocity:
Let the d/dv of total cost be C(v):
C(v) =(-90000/v^2+300/15=0
(-90000/v^2+300/15)=0
90000/v^2=300/15
90000/v^2=20
v^2=90000/20
v^2=4500
v=√4500
v=30√5 miles/hour
Hence, the speed is 30√5 miles/hour
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Heston is thinking of a fraction equivalent to 6/7.
The numerator is greater than 20 and the denominator is less than 30.
What fraction is Heston thinking of?