The 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions
What are linear equations?
Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
6x - 5y = -8
6x - 5y = -8
Subtract the equation 6x - 5y = -8 from the equation 6x - 5y = -8
6x - 5y = -8
- 6x - 5y = -8
----------------------
0 = 0
This in other words means that the difference between both equations is 0
When the solution to a system of equation is 0 = 0, it means that the system of equations have infinitely many solutions
Hence, the 0 = 0 in the solution to the system implies that the system of equations involving the equations 6x - 5y = -8 and 6x - 5y = -8 have infinitely many solutions
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Answer: The answer is D for those who don't like to read extra long expert answers (no offense to experts, just shorten answers to the direct answer pls)
Step-by-step explanation: Edge 2022
Find the shaded area. Round to the nearest 10th, if necessary.
Answers:
16 cm²
24 cm²
40 cm²
Step-by-step explanation:
The area of a rectangle can be found with A = L * W where A is the area, L is the length, and W is the width.
[1] First shaded area
A = L * W
A = (4 cm) * (12 cm - 5 cm - 3 cm)
A = (4 cm) * (4 cm)
A = 16 cm²
[2] Second shaded area
A = L * W
A = (2 cm) * (12 cm)
A = 24 cm²
Lastly, we add them together.
16 cm² + 24 cm² = 40 cm²
Charlie is watching hot air balloons. balloon a has risen at a 50° angle. balloon b has risen at a 78° angle. if the distance from balloon a to the ground is 1,000 feet, how far is balloon b from balloon a? round your answer to the nearest whole number.
The distance from Balloon A to Balloon B, d ≈ 1,052 feet
What is distance ?
Distance is defined to be the magnitude or size of displacement between two positions. Note that the distance between two positions is not the same as the distance traveled between them. Distance traveled is the total length of the path traveled between two positions. Distance traveled is not a vector.The given parameters are;
The angle at which Balloon A rises, x° = 50° above horizontal
The angle at which Balloon B rises, y° = 78° above horizontal
The (vertical) distance of Balloon A to the ground, h = 1,000 ft.
The required parameter;
The distance from Balloon A to Balloon B, d
We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule
Let,
The height of the balloon strings are equal
The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.
The distance of the Balloon A from Charlie, l₁, is given as follows;
l₁ × sin(x°) = h₁
∴ l₁ = h₁/(sin(x°))
Which gives;
l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.
l₁ ≈ 1,305.41 ft.
For Balloon B, we get;
h₁ = h₂ = 1,000 ft.
∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.
l₂ ≈ 1,022.34 ft
The angle between the balloon strings, θ = 180° - (x° + y°)
∴ θ = 180° - (50° + 78°) = 52°
The angle between the balloon strings, θ = 52°
By cosine rule, we have;
d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))
∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet
Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet
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sketch graphs of the following on the same plane using different colours y=2x-3;y=-3;x=-3;2x+3y-6=0
The graph of the four linear equations is the one we can see below, such that:
Blue line is y = -3Green line is x = -3Orange line is y = 2x - 3Purple line is 2x + 3y - 6 = 0.How to graph the linear equations?
Here we have the set of linear equations:
y = 2x - 3y = -3x = -32x + 2y - 6 = 0We want to graph these 4 lines on the same coordinate axis.
The line:
y = -3
Is an horizontal line at y = -3
The line:
x = -3
Is a vertical line at x = -3.
And the other two are common linear equations that are graphed in the usual way, then the graph of all the linear equations is the one you can see below.
Where:
Blue line is y = -3Green line is x = -3Orange line is y = 2x - 3Purple line is 2x + 3y - 6 = 0.If you want to learn more about linear equations:
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Enduro solved -4x > 120 by adding 4 to each side of the inequality. What mistake did he make?
The mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides
What are inequalities?Inequalities are expressions that have unequal values, when compared
How to determine Enduro's mistake?The inequality is given as
-4x > 120
When 4 is added to both sides, the inequality becomes
4 - 4x > 120 + 4
The above is not the solution to the inequality.
The solution is as follows:
We have:
-4x > 120
Divide both sides inequality by -4
x < -30
Hence, the mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides
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find the average rate of change of the function in the interval 6,13
Using it's concept, the average rate of change of the function on the interval [6,13] is given by:
[tex]r = \frac{f(13) - f(6)}{7}[/tex]
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In this problem, we want to find the rate in the interval [6, 13], which is given as follows:
[tex]r = \frac{f(13) - f(6)}{13 - 6} = \frac{f(13) - f(6)}{7}[/tex]
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A regular hexagon has an apothem of 14.7 inches and a perimeter of 101.8 inches. what is the area of the hexagon? square inches
Answer:
748.23 in^2.
Step-by-step explanation:
Area = 1/2 * apothem * perimeter
= 1/2 * 14.7 * 101.8
= 748.23 in^2.
Answer:
748.23
Step-by-step explanation:
Which rule describes the composition of transformations that maps ΔJKL to ΔJ"K"L"?
90 degree rotation about point 0 composition translation of 0 units x, negative 2 units y
Translation of 0 units x, negative 2 units y composition 90 degree rotation about point 0
90 degree rotation about point 0 composition translation of negative 2 units x, 0 units y
Translation of negative 2 units x, 0 units y composition 90 degree rotation about point 0
A rule which describes the transformations that maps ΔJKL to ΔJ"K"L" is: D. translation of -2 units x, 0 units y composition 90 degree rotation about point 0.
What is a transformation?A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
In Geometry, there are different types of transformation and these include the following:
DilationReflectionRotationTranslationBased on the diagram (see attachment), we can infer and logically deduce that a rule which describes the transformations that maps triangle JKL to triangle J"K"L" is a rotation of 90 degrees about the origin and then translated 2 units left.
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In a local shop some items are being sold at a third off. They now cost the following amounts. What was the original full price? 40 POINTS AND BRAINLIEST
1.£6.46
2.£58.24
3.£114.28
4.£12.50
5.£10.86
Answer:
1) 9.69
2) 87.36
3) 171.42
4) 18.75
5) 16.29
Step-by-step explanation:
Treat each value's full price as x. then, all of the values are (2/3)x. To get (2/3)x back to x, we must multiply (2/3)x*(3/2)=x. Multiply each of the questions given by 3/2 or 1.5
what is - 4x +7 > x -13
Answer:
[tex]\huge\boxed{\sf x < 4}[/tex]
Step-by-step explanation:
Given inequality:-4x + 7 > x - 13
Subtract x to both sides
-4x - x + 7 > -13
-5x + 7 > -13
Subtract 7 to both sides
-5x > -13 - 7
-5x > -20
Divide -5 to both sides
x < -20/-5
x < 4[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex]x < \bf 4[/tex]
Step-by-step explanation:
[tex]-4x + 7 > x -13[/tex]
We have to make [tex]x[/tex] the subject of the equation:
• Subtract [tex]x[/tex] from both sides:
[tex]-4x - x + 7 > -13[/tex]
⇒ [tex]-5x + 7 > -13[/tex]
• Now subtract 7 from both sides:
[tex]-5x > -13 - 7[/tex]
⇒ [tex]-5x > -20[/tex]
• Next divide both sides by -5, and remember that dividing an inequality by a negative number reverses the inequality symbol:
[tex]x < \frac{-20}{-5}[/tex]
⇒ [tex]x < \frac{20}{5}[/tex]
⇒ [tex]x < \bf 4[/tex]
#6 pls quick answer!!!
Answer:
ANSWER: mix 120 ml of 35% acid solution with 60 ml of 65% acid solution to obtain 180 ml 0f 45% acid solution
Step-by-step explanation:
If x = number of ml of 35% acid solution and 60 = number of ml of 65% acid solution, then x + 60 = number of ml of the mixture.
Acid content of first ingredient + acid content of second ingredient = acid content of the mixture
So, 0.35x + 0.65(60) = 0.45(x + 60)
0.35x + 39 = 0.45x + 27
12 = 0.10x
120 = x
If (fg)(x) = h(x) such that h of x is equal to the square root of the quantity 8 times x plus 6 end quantity which of the following could accurately represent f and g?
The value of the functions f(x) and g(x) will be √(4x + 3) and √2. Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
If (f g)(x) = h(x) such that h(x) = √(8x + 6). Then we have
(f g)(x) = h(x)
f(x) · g(x) = h(x)
Then put the value of h(x), then we have
f(x) · g(x) = √(8x + 6)
f(x) · g(x) = √2(4x + 3)
f(x) · g(x) = √(4x + 3) × √2
Thus, the value of the functions f(x) and g(x) will be √(4x + 3) and √2.
Then the correct option is B.
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Jack wants to plant a border of flowers in the shape of an arc along the edge of a circular walkway. if the circle has a radius of 5 yards and the angle subtended by the arc measures 1.5 radians, what is the length of the curved border?
[tex]5(1.5)=\boxed{7.5 \text{ yd}}[/tex]
The length of the curved border or arc is 7.5 yards.
the length of the arc = [tex]\theta \times r[/tex]
given that [tex]\theta[/tex] = 1.5 radian
radius = 5 yards
then the length of arc from the above formula
[tex]l = \theta \times r\\l = 1.5 \times 5 = 7.5[/tex] yards
What is arc?A circle's arc is referred to as a portion or section of its circumference.A chord of a circle is a straight line that might be created by joining the arc's two ends.A semicircular arc is one whose length is exactly half that of a circle.To know more about arc with the given
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Can you please answer this question
Answer:
look above
Step-by-step explanation:
hope it helps
The water usage at a car wash is modeled by the equation w(x) = 4x3 6x2 − 11x 7, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day. c(x) = 4x3 4x2 − 11x 8 c(x) = 3x3 4x2 − 11x − 8 c(x) = 3x3 4x2 − 11x 8 c(x) = 4x3 4x2 − 11x − 8
A function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.
What is an equation?A relationship between two variables is defined as an equation; if we plot the graph of the linear equation, we will get a straight line.To find a function, C(x), to model the water used by the car wash on a shorter day:
Given information -
The water usage at a car wash is modeled by the equation W(x) = 4x³ + 6x² − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open.The amount of decrease in water used is modeled by D(x) = x³+ 2x² + 15, where D is the amount of water in cubic feet and x is time in hours.Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.
We are trying to find:
C(x) = W(x) - D(x)C(x) = (4x³ + 6x²− 11x + 7) - (x³ + 2x² + 15)C(x) = 4x³ - x² + 6x² - 2x³ - 11x + 7 - 15C(x) = 3x³ + 4x² - 11x - 8Therefore, a function, C(x), to model the water used by the car wash on a shorter day will be (B) 3x³ + 4x² - 11x - 8.
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The correct question is given below:
The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day
Use the standard deviation to identify any outliers in the given data set.
{35, 31, 29, 34, 6, 31, 32, 30}
Considering the standard deviation, the data-set has no outliers.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.For the given data-set, the mean is:
(35+31+29+34+6+31+32+30)/8 = 28.5.
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(35-28.5)^2+(31-28.5)^2+(29-28.5)^2+(34-28.5)^2+(6-28.5)^2+(31-28.5)^2+(32-28.5)^2+(30-28.5)^2}{8}} = 8.7[/tex]
A measure is said to be an outlier if it is more than 3 standard deviations for the mean. Hence the thresholds are:
Less than 28.5 - 3 x 8.7 = 2.4.More than 28.5 + 3 x 8.7 = 54.6.Since all values are between 2.4 and 54.6, the data-set has no outliers.
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Half of the children in a library group like pets, one fourth don't like pets and seven children do not have any
preference. How many students in the library group like pets?
Answer:
14 children
Step-by-step explanation:
Half the children like pets and a quarter of the children do not, so another quarter does not have preference. Let x = total number of children, and we would have this equation.
0.25x = 7
x = 28
Since we are asked to give the number of children who like pets, 28/2 = 14 is the answer.
If a = 1,b=2 and c=-3 find
a^b-c b^c-a c^a-b
Answer:
The value of
[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b \: [/tex]
is
[tex] \frac { 19}{8} [/tex]
Step-by-step explanation:
Greetings ![tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b[/tex]
where,
a=1b=2c=-3Thus, substitute these values to the given equation to find the values.
[tex]a {}^{b} - c \: b {}^{c} - a \: c {}^{a} - b ... \: substitute \: \\ given \: values \\ (1) {}^{2} - ( - 3)(2) {}^{ - 3} - 1( - 3) {}^{1} - 2 \\ 1 + 3 \: ( \frac{1}{8} ) - 1( - 3) - 2 \\ 1 + \frac{3}{8} + 3 - 2 \\ \frac{11}{8} + 3 - 2 \\ \frac{35}{8} - 2 \\ \frac{19}{8} = 2 \frac{3}{8} [/tex]
Hope it helps
Mrs. wright made 92 cups of fruit punch for a party. how many gallons of punch did she make?
Answer:
5.75 - 5 3/4
Step-by-step explanation:
1 Cup = 0.0625 gallons
92 cups = 5.75 gallons
A teacher prepares a test. She gives 5 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices.
The total number of ways in which 4 questions can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336
How to find probability combinations?We are given;
Total number of objective questions = 5 questions
Number of choices of first 2 questions = 3 choices
Number of choices of last 3 questions = 4 choices
Number of ways of answering the first 2 questions = 3 * 3 = 9 ways
Number of ways of answering the last 3 questions = 4 * 4 * 4 = 64 ways
Total number of ways of answering the five questions = 9 * 64 = 576 ways
Now, she has to answer only 4 which means it can be either 2 of the first and 2 of the last of 1 of the first and 3 of the last.
Thus, total number of ways of answering 4 questions if it is fist 2 and last 2 = 9 * 16 = 144
Total number of ways of answering 4 questions if 1 of the first and 3 of the last = 3 * 64 = 192
The total number of ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336
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808, 408, 208,108, 68 find out wrong number.
68 is the wrong number in the sequence 808, 408, 208,108, 68
What is Number system?A number system is defined as a system of writing to express numbers.
Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The given sequence is 808, 408, 208,108, 68
Eight hundred eight, Four hundred and eight, two hundred and eight, one hundred eight and sixty eight.
808, 408, 208,108, 68
Let us find the difference between the consecutive numbers
400, 200, 100, 40
As we observe the first three terms having the common ratio where as 40 and 100 has different ratio.
Hence, 68 is the wrong number in the sequence 808, 408, 208,108, 68
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Gwen and $660 per week and has 18% of this amount withheld for taxes Social Security and Medicare find amount withheld
What is the period of y=−5 cos( 8 π x)+3? Give an exact value. units PLEASE MAKE IT QUICK
Answer:
Maximum/Minimum Value: (0,−2) is a local minima (1/8,8) is a local maxima
Explanation: Use the derivative to find the maximum and minimum
Answer:
Period = ¹/₄
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function:
f(x) = A cos(B(x + C)) + D
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftGiven function:
[tex]y=-5 \cos (8 \pi x)+3[/tex]
Comparing the given function with the standard form:
A = 5B = 8πC = 0D = 3[tex]\implies \sf Period=\dfrac{2 \pi}{B}=\dfrac{2 \pi}{8 \pi}=\dfrac{1}{4}[/tex]
Therefore, the period of the given function is ¹/₄.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]3x + y = - 4 \\ 3x + 0 = - 4 \\ 3x = - 4 \\ x = \frac{ - 4}{3} = - 1.333[/tex]
It has to be the last line in the second picture since it intersects the x axis at approximately x=-1.333[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex] \bm{Last \: option \: (D.)}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Write the equation in slope-intercept form. Then solve y.
▪ [tex]\small\longrightarrow \sf{3x-3x + y = −3x -4}[/tex]
▪ [tex]\small\longrightarrow \sf{y= -3x-4}[/tex]
Identify the x-intercept,
[tex]\small \sf \longrightarrow{3x + 0 = - 4}[/tex]
[tex]\small\longrightarrow \sf{3x=-4}[/tex]
[tex]\small\longrightarrow \sf{x = - \dfrac{4}{3} }[/tex]
[tex]\small\longrightarrow \sf{x = -1.33}[/tex]
The graph has the next properties:
[tex]\small\longrightarrow \sf{Slope: \: 3}[/tex]
[tex]\small\longrightarrow \sf{x-intercept: \: (-1.33,0)}[/tex]
[tex]\small\longrightarrow \sf{y-intercept: \: (0,4) }[/tex]
What equation represents a line that passes through points (-1,2) and (3,1)
4x - y = -6
X + 4y = 7
X - 4y = -9
4x + y = 2
Answer:
B.) x + 4y = 7
Step-by-step explanation:
(Step 1) ----------------------------------------------------------------------------------------------
To find the equation, we first need to find the slope using the point-slope form:
y₁ - y₂ = m(x₁ - x₂)
In this form, "m" represents the slope, "x₁" and "y₁" represent the values from the first point, and "x₂" and "y₂" represent the values from the second point.
Point 1: (-1, 2) Point 2: (3, 1)
x₁ = -1 x₂ = 3
y₁ = 2 y₂ = 1
y₁ - y₂ = m(x₁ - x₂) <----- Point-slope form
2 - 1 = m(-1 - 3) <----- Insert values
1 = m(-4) <----- Subtract
-1/4 = m <----- Divide both sides by -4
(Step 2) ---------------------------------------------------------------------------------------------
The given equations are in the slope-intercept form. The general structure looks like this:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. To find the y-intercept, you can plug the newfound slope and values from one point into the equation.
x = -1
y = 2
m = -1/4
y = mx + b <----- Slope-intercept form
2 = (-1/4)(-1) + b <----- Insert values
2 = 1/4 + b <----- Multiply -1/4 and -1
8/4 = 1/4 + b <----- Make common denominators
7/4 = b <----- Subtract both sides by 1/4
(Step 3) ---------------------------------------------------------------------------------------------
The equation in slope-intercept form is thus: y = -1/4x + 7/4.
While this equation is accurate, it seems that it must be slightly manipulated. Therefore, we need to alter this equation to look like one of the answer choices. For instance, we can multiply the entire equation by 4 to remove the denominator.
y = -1/4x + 7/4 <----- Equation
4y = -x + 7 <----- Multiply all terms by 4
x + 4y = 7 <----- Add "x" to both sides
20 points !!!
help me please !!
Minimum: 59
Lower Quartile: 67
Median: 76
Upper Quartile: 86
Maximum: 92
Interquartile Range: 19
Find a power series representation for the function. (center your power series representation at x = 0. ) f(x) = 1 9 x f(x) = [infinity] n = 0
The power series representation for the function, so the interval of convergence is (-9,9).
The definition of convergence refers to 2 or more matters coming together, joining collectively, or evolving into one. An example of convergence is when a crowd of people all move collectively into a unified organization.
Convergence is when two or extra matters come collectively to shape a brand new whole, like the convergence of plum and apricot genes within the plucot. Convergence comes from the prefix con-, meaning collectively, and the verb verge, because of this to show closer to.
The simple concept of convergence permits multiple responsibilities to be accomplished on a single device, which efficiently conserves space and power. for example, as opposed to wearing separate devices – like a cell cellphone, digital camera, and virtual organizer – each era converges on a single tool or telephone.
We have given f(x)=1/(9+x)
f(x)=(1/9)*(1/(1-(-x/9))
f(x)=summation of (n=0 to infinity) [1/9*(-x/9)n]
=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]
f(x)=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]
Let an=(-1)n*(xn/9n+1)
using the Ratio Test
L=lim n-->infinity|an+1/anL=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]/[(-1)n*(xn/9n+1)]|
=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]*[9n+1/(-1)n*(xn)]|
=lim n-->infinity|(-1)*(x)/9)|
=|-x/9|<1
x/9<1 and x>9>-1
x<9 and x>-9
x is -9<x<9
for x=9 the series ,summation of (n=0 to infinity) [(-1)n*(9n/9n+1)] =summation of (n=0 to infinity) [(-1)n*(/9)]
=1/9*summation of (n=0 to infinity) [(-1)n]
By the geometric series this summation of (n=0 to infinity) [(-1)n] diverges
=1/9*diverges
the series diverges for x=9
for x=-9 the series ,summation of (n=0 to infinity) [(-1)n*(-9)n/9n+1)] =summation of (n=0 to infinity) [(-1)2n*(/9)]
=1/9*summation of (n=0 to infinity) [(-1)2n]
which is diverges
so the interval of convergence is (-9,9)
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how do you find the length of a rectangle if the diagonal is 10 inches long and the width is 8 inches
Answer:
Step-by-step explanation:
Use pythagorean theorem (a^2+b^2=c^2). The diagonal represents c and the width represents b or a. 8^2+b^2=10^2->64+b^2=100->b^2=36->b=6. So your height would be 6.
How old is David
please help me
Answer: 25 ?
Step-by-step explanation:
Magda utilizó una cuadrícula de 1 cm de lado para dibujar la figura sombreada, usando triángulos
rectángulos.
The area of the figure Magda shaded with side lengths of 1 and √2 centimeter is equal to 1.21 cm².
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this formula:
Area = 1/2 × b × h
Where:
b represents the base area.h represents the height.In order to calculate the area of the figure Magda shaded with side lengths of 1 and √2 centimeter, we would determine the area of each triangle as follows:
For triangle 1, we have:
Area = 1/2 × b × h
Area = 1/2 × 1 × 1
Area = 0.5 cm².
For triangle 2, we have:
Area = 1/2 × b × h
Area = 1/2 × √2 × 1
Area = 0.71 cm².
Total area = Area of triangle 1 + Area of triangle 2
Total area = 0.5 + 0.7
Total area = 1.21 cm².
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Complete Question:
Magda used a 1 cm square grid to draw the shaded figure, using right triangles. 1 cm 3 cm √2 cm 1 cm 1 cm what is the area of the figure Magda shaded?
What is the radius of the sector of the circle below, if the area is 30.39 m^2 and the central angle < AOB measures 43 °. (round answer to the nearest whole meter)
Answer:
a. 9m
Step-by-step explanation:
Pi = 3.14 = 22/7
formula :
Area of a Sector of a Circle = (central angle)/360 * πr² =
(central angle)/360 * πr² = Area of a Sector of a Circle
43/360 * Pi * r^2 = 30.39
r^2 = (30.39 * 360) / (Pi * 43)
r^2 = (30.39 * 360) / (22/7 * 43)
r = √ (30.39 * 360 * 7) / (22 * 43)
r = √76582.8/946
r = √80.9543340381
8.99746264444 which is roughly
9
The radius of the sector will be 9m. The correct option is A.
What is the arc length of the circle?The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc segment by simulating it as a network of connected line segments.
The radius will be calculated as below:-
Area of a Sector of a Circle = (central angle)/360 * πr² =
(Ф)/360 * πr² = Area of a Sector of a Circle
43/360 * Pi * r²= 30.39
r² = (30.39 * 360) / (Pi x 43)
r²= (30.39 x 360) / (22/7 x 43)
r = √ (30.39 x 360 x 7) / (22 x 43)
r = √76582.8/946
r = √80.9543340381
r = 9
Therefore, the radius of the sector will be 9m. The correct option is A.
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