Answer:
27/8
Step-by-step explanation:
First, note that 3 3/8 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:
3 = whole number
3 = numerator
8 = denominator
To convert mixed number 3 3/8 to improper fraction, you follow these steps:
1. Multiply the whole number by the denominator
3 × 8 = 24
2. Add the product from Step 1 to the numerator
24 + 3 = 27
3. Write answer from Step 2 over the denominator
27/8
The mixed number 3 3/8 converted to improper fraction is therefore :
27/8
Any help pls. Question is : Find the equation of line B, which is perpendicular toy-2x=-8(x-8)and passes through the point (6,-6). Find the midpoint of the line segment AB in the following figure
Answer:
Perpendicular line ⇒ 2x + 9y + 42 = 0
midpoint: (-1,1)
Step-by-step explanation:
Let's find the coordinates of midpoint of AB
Here, from figure, A = (-3,-2), B = (1,4)
So midpoint:
[tex]P = (\frac{-3+1}{2},\frac{-2+4}{2})[/tex]
∴ P = (-1, 1)
Now, given straight line is x - 2y = -8(x-8)
⇒x - 2y = -8x+64
⇒9x - 2y - 64 = 0
Perpendicular line to 9x - 2y - 64 = 0 is 2x + 9y + k = 0
Perpendicular line passes though (6,-6)
Putting the values, we get
2(6) + 9(-6) + k = 0
⇒12 - 54 + k = 0
⇒k = 42
∴ Perpendicular line ⇒ 2x + 9y + 42 = 0
An acute angle, θ, is in a right triangle such that sin of theta is equal to 3 over 8 period What is the value of cot θ?
An acute angle, θ, is in a right triangle such that sin of theta is equal to 3 over 8 period The value of cot θ is (√55)/3.
What is the value of cot θ?To determine the value of cot(θ), Since is an angle in a right triangle and sin() = 3/8, we obtain:
cot(θ) = (√55)/3
In light of the fact that is an acute angle in a right triangle, we may calculate:
sin(θ) = 3/8
Keep in mind:
Hypotenuse = ((opposite cathetus)2 + (adjacent cathetus)2), where sin() = (opposite cathetus)/(hypotenuse)
Next, we have:
contrary cathetus = 3
Using the formula hypotenuse = 8 = (3 + neighboring cathetus)2,
In order to solve this for the nearby cathetus, we obtain:
(82 - 32) = 55 adjacent cathetus
And we are aware of:
(Cot) = (nearby cathetus) (opposite cathetus)
Next, we have:
cot(θ) = (√55)/3
The value of cot θ is (√55)/3.
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Which of the binomials below is a factor of this trinomial? x^2 + x - 30
The binomials which correctly represent the factors of the given trinomial; x² + x - 30 as required in the task content are; ( x - 5 ) and ( x + 6 ).
Which binomials correctly represents the factors of the given trinomial?As evident in the task content; the given trinomial whose binomial factors are to be determined is; x² + x - 30.
By factorisation; the given trinomial expression can be written as;
x² + 6x - 5x - 30
x ( x + 6 ) -5 ( x + 6 )
( x - 5 ) ( x + 6 )
On this note, the required binomials which are factors of the given trinomial expression are; ( x - 5 ) and ( x + 6 ).
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If you’re currently making $10.50 per hour and you’re offered a new job that pays $11.75 per hour, what will be your percent of increase in pay?
Answer: To find the percent increase in pay, you can use the following formula:
percent increase = ((new pay - old pay)/old pay) * 100
Plugging in the values given in the question, you get:
percent increase = ((11.75 - 10.50)/10.50) * 100
= (1.25/10.50) * 100
= 0.119047619 * 100
= 11.9047619%
Therefore, the percent increase in pay is approximately 11.9%.
Step-by-step explanation:
Cassie rolls a fair number cube with 6 faces labeled 1 through 6. She rolls the number cube 300 times. Which results are
probable to happen according to theoretical probability? Select TWO answers.
On solving the question, we can say that - the probability of given will be P(a/c) = 3/6 = 1/2
What is probability?A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.
here,
the probability that event the dice will roll is 6
and chances of geting even numbers are = 3
so P(a/c) = 3/6 = 1/2
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(c) Ben changes £800 to Euros before he goes on holiday.
£1 = 1.25 Euro
He spends 895 Euros.
He changes the Euros that he has left to Pounds (£).
The exchange rate is now £1 = 1.40 Euro
How many Pounds does he get back?
Amount of pounds that Ben get back is £75.
What is Exchange Rate?Exchange rate is defined as the value of a currency with respect to another currency in order to convert the currency.
Ben changes £800 to Euros before he goes on holiday.
Before holiday, exchange rate is, £1 = 1.25 Euro
£800 = 800 × 1.25 Euros = 1000 Euros
He spends 895 Euros.
Euros left = 1000 - 895 = 105 Euros
Now, the exchange rate is £1 = 1.40 Euro.
or 1.40 Euro = £1
⇒ 1 Euro = £ 1/1.40
⇒ 105 Euros = £ (1/1.40) × 105 = £75
Hence Ben got £75 of pounds back.
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2x^5 + 4y^12/12x^2 = ?
Solve in simplest form
Answer:
2x^5+y^12*x^2/3
Step-by-step explanation:
Find the midpoint and distance between (-3,10) and (15,-2)
The midpoint and distance between (-3,10) and (15,-2) are ( 6,4 ) and 6√13 respectively.
What is the midpoint and distance between the given coordinates?The midpoint formula is expressed as;
[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]
The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Given the data in the question;
Point 1(-3,10)
x₁ = -3y₁ = 10Point 2( 15,-2 )
x₂ = 15y₂ = -2Plug the given values into the midpoint formula and simplify.
[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]
[ ( -3 + 15)/2, ( 10 + (-2) )/2 ]
[ ( 12)/2, ( 10 - 2 )/2 ]
[ ( 12)/2, ( 8 )/2 ]
( 12/2, 8/2 )
( 6,4 )
Therefore, the midpoint is (6,4).
Plug the given values into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
D = √( ( 15 - (-3) )² + ( -2 - 10 )² )
D = √( ( 15 + 3 )² + ( -2 - 10 )² )
D = √( ( 18 )² + ( -12 )² )
D = √( 324 + 144 )
D = √( 468 )
D = 6√13
Therefore, the distance between the points is 6√13.
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Directions: Solve the following problem in a way that makes sens
PROBLEM-SOLVING:
1. Students at Grossmont College are planting a community garden.
One-fifth of the garden will be planted with roses. Three students ar
equally sharing the planting of the rose section. How much of the
whole garden will each of the 3 students plant?
Therefore , the solution of the given problem of algebra comes out to be
60 garden beds in the students plans.
Algebra: What Is It?Algebra, a subfield of mathematics, is concerned with symbols and the mathematical operations carried out on them. Because these symbols don't have predetermined values, they are referred to as variables. These symbols are additionally put through a variety of addition, subtraction, multiplication, and division arithmetic operations in order to obtain the values.
Here,
Given: actual flower bed: 18
This represents 30% of all garden beds.
Assume that x is the size of the entire flowerbed.
So, 30% of x= 18
30/100 x = 18
x= 1800/ 30
x= 60
60 garden beds are therefore planned by the students.
Therefore , the solution of the given problem of algebra comes out to be
60 garden beds in the students plans.
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Divide. Round to the nearest tenth.
3.5/2.29
Answer:
The answer will be 1.53 after dividing and rounding to the nearest tenth 3.5 divided by 2.29.
help me with this question please
Answer:
[tex] \sf \: a) \: 1[/tex]
Step-by-step explanation:
Given values of variables,
→ e = 3.2
→ d = 10
→ u = 7
The problem needed to solve is,
[tex] \sf \rightarrow \: \frac{ue}{eu} [/tex]
Let's solve the problem,
[tex] \sf \rightarrow \: \frac{ue}{eu} [/tex]
[tex] \sf \rightarrow \: \frac{(7 \times 3.2)}{(3.2 \times 7)} [/tex]
[tex] \sf \rightarrow \: \frac{22.4}{22.4} [/tex]
[tex] \sf \rightarrow \: \frac{1}{1} = 1[/tex]
Hence, option (a) is correct.
Answer:
Option A ) 1
Step-by-step explanation:
[tex]\frac{ue}{eu} = \frac{3.2X7}{7X3.2} = \frac{22.4}{22.4} = 1[/tex]
Hence , Option A ) is the answer
Help
Complete the puzzle so that each row, column, and diagonal adds up to the same total.
Complete the puzzles with values -4, 0, -3 and 2
How to complete the puzzle?Since each row, column, and diagonal adds up to the same total.
For the 1st row, the total is:
3 + (-2) + (-1) = 0
That means each row, column, and diagonal will always adds up to 0.
3 + w + 1 = 0
w = -3-1
w = -4
w + y + 4 = 0
-4 + y + 4 = 0
y = 0
-1 + 4 + t = 0
3 + t = 0
t = -3
1 + h + t = 0
1 + h + (-3) = 0
h -2 = 0
h = 2
(Check the attached image for labeling)
Thus, complete the puzzle with the values accordingly
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given f''(x)=4x-2 and f'(-1)=0 and f(-1)=4
find f'(x)=
find f(4)=
Whose inverses are also functions
Functions whose inverses are also functions.
What is inverse function?Inverse function is represented by [tex]f^{-1}[/tex] with regards to the original function and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.
If a horizontal line intersects the original function in a single region, the function is a one-to-one function and inverse is also a function.
Every function has an inverse, but not every inverse will be a function. The inverse may fail the vertical line test. If the original function is a one-to-one function, then its inverse will be a function. A one-to-one function not only passes the vertical line test, it also passes a horizontal line test.
Therefore, functions whose inverses are also functions.
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Select all the correct answers. A farmer wants to build two fenced-off sections within his field, one in the shape of a rectangle and the other in the shape of a square. The side of the square must be equal to the width of the rectangle, x feet. The length of the rectangle must be 50 feet longer than its width. The field the farmer wants to build the two fenced sections in has an area of y square feet. The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet. In addition, the sum of the fenced areas must be less than the area of the field. This is the system of inequalities that represents this situation. Which points represent viable solutions?
(20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that the side of the square must be equal to the width of the rectangle, x feet.
The length of the rectangle must be 50 feet longer than its width
The field the farmer wants to build the two fenced sections in has an area of y square feet.
The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet
the sum of the fenced areas must be less than the area of the field.
y≥x²+1000
y>2x²+50x
(20, 2,200) and (5, 3,000) are the viable solutions
Hence, (20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.
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For the function f(x) shown below, find the definite integral ∫₀⁶ f?(x)dx
========================================================
Explanation:
The left-most rectangle spans from x = 0 to x = 2. It has base 2 and height 2, which means it has an area of 2*2 = 4 square units. Let A = 4 since we'll use it later.
The middle rectangle goes from x = 2 to x = 4. It has base 2 and height 3 (because it goes from y = 0 to y = -3). The area is B = 2*3 = 6
Draw a vertical line through 6 on the x axis. This forms the final rectangle we need. It has base 2 (because it goes from x = 4 to x = 6) and height 5. The area is C = 2*5 = 10.
The small sliver to the right of x = 6 is ignored completely.
--------------------
Summary so far:
A = 4B = 6C = 10Those represent the areas of the rectangles from left to right. We ignore the portion to the right of x = 6.
Since rectangle B is below the x axis, we treat this as a negative area, or we subtract off this area. The positive areas of rectangles A and C are added.
So,
A-B+C = 4-6+10 = 8 is the final answer
We can write [tex]\displaystyle \int_{0}^{6}f(\text{x})d\text{x} = \boldsymbol{8}[/tex]
Kendra and Dalisay practice archery. Kendra hits the target 3 times every 5 misses. Dalisay hits the target 5 times every 7 misses. Who hits the target more?
Dalisay hits the target more.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Kendra hits the target 3 times every 5 misses.
And, Dalisay hits the target 5 times every 7 misses.
Since, Kendra hits the target 3 times every 5 misses.
Hence, In 1 misses Kendra hits the target = 3/5 times
= 0.6 times
And, Dalisay hits the target 5 times every 7 misses.
Hence, In 1 misses Dalisay hits the target = 5/7 times
= 0.74 times
Thus, Dalisay hits the target more.
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An art museum opens at 9 am and closed at 5 pm the function V gives the number of visitors in a museum h hours after it opens explain what this statement tells us about the situation: V(5)=36
Answer:
Five hours after the museum opens, there are 36 visitors.
Step-by-step explanation:
V(5)=36 means that when h is 5, V is 36. Assuming this is a function from what information this gives.
to solve 2/5 x = 14, you multiply both sides of the equation by 5/2. your friend divides both sides of the equation by 2/5. who is right? explain.
Both of you are correct because using either way can solve the equation for the value of x.
How to solve for x ?In the case of solving for x in 2/5 x = 14, the goal is to get rid of the fraction that is multiplying x on the left side. This can be done by either multiplying both sides of the equation by the inverse of 2 / 5 ( which is 5 / 2 ) or by dividing both sides by 2 / 5.
Doing either of these things would get rid of the 2 / 5 and give an answer to x as shown below :
Multiplying :
2/5 x = 14
5 / 2 x 2 / 5 x = 14 x 5 / 2
x = 35
Dividing :
2/5 x = 14
2 / 5 x / 2 / 5 = 14 / 2 / 5
x = 35
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i’m not sure if the first one right but i need help
The formula is written as (3x+9)(x+9) of + 36x + 81 = 0. A second-degree polynomial equation can be used to define quadratics.
A quadratic equation is defined.Multiplying a variable by itself is the mathematical operation known as "squaring," which is frequently used to refer to a quadratic issue. This vocabulary is based on the notion that a square's area is equal to the sum of its side lengths. The word "quadratic" derives from the Latin quadratum, which meaning square.
here ,
[tex]= + 36x + 81 = 0\\= 3x^2 + 27x + 9x + 81\\= 3x(x+9) + 9(x+9)\\= (3x+9)(x+9)\\= 3(x+3)(x+9)[/tex]
factorized form is [tex](3x+9)(x+9) of + 36x + 81 = 0 .[/tex]
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Sketch the Asymptotes and graph the function.
the quadratic equation have been solved and the required graph is attached below.
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The equation:
[tex]\frac{x^{2}-7x+12 }{x^{2} -1}[/tex]
Its a quadratic equation in both numerator and denominator, by dividing the x² will be get a graph as given in the attached file.
Hence, the quadratic equation will be solved and the required graph is attached below.
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Length of insect is 23mm and length of drawing is 85mm. So what is Magnification
Answer:
The magnification is the ratio of the size of the image to the size of the object. In this case, the length of the insect is the size of the object, and the length of the drawing is the size of the image.
To find the magnification, we can divide the size of the image by the size of the object:
Magnification = size of image / size of object
Plugging in the values, we have:
Magnification = 85mm / 23mm
Calculating, we find that the magnification is approximately 3.7. This means that the length of the drawing is 3.7 times the length of the insect.
Step-by-step explanation:
Aregular decagon has a radius of 8 cm. What is the approximate area of the decagon?
Using a calculator we can approximate this to be A ≈ 568.89 cm^2.
What is regular decagon?A regular decagon is a two-dimensional geometric shape with ten sides of equal length and ten interior angles of equal measure. It is a polygon, which is a two-dimensional shape made up of line segments (straight sides).
The approximate area of a regular decagon can be calculated using the formula A = (5/2) * a^2 * tan(π/5), where a is the length of each side. Since the radius of the decagon is 8 cm, the length of each side can be calculated using the formula a = 2r * sin(π/10) where r is the radius.
Plugging these values into the formula we get A = (5/2) * (2 * 8 * sin(π/10))^2 * tan(π/5) which simplifies to A = 320 * sin^2(π/10) * tan(π/5).
Using a calculator we can approximate this to be A ≈ 568.89 cm^2.
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For FFA, Mr. Sink bought 7 calves for $3,500. He later bought another calf for $600. What is the mean cost for all of the calves?
Answer: Mr. Sink bought 7 calves for a total of $3,500, and he later bought another calf for $600, for a total of $4,100.
In total, Mr. Sink bought 7 + 1 = 8 calves.
The mean cost for all of the calves is equal to the total cost of all of the calves divided by the number of calves.
Therefore, the mean cost for all of the calves is 4,100 / 8 = $512.50.
Step-by-step explanation:
Evaluate each expression for x = 3 & y = 4
4. x² + 2(x+y)
5. (xy)^3
4х² - 3ху
4x -
Using the values for x and y and substituting these values in the expression of equations provided, The answer is 23 and 1728.
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.
What do you mean by substitution?When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated.
x=3 and y=4
[tex]x^2 + 2(x+y)\\=3^2 + 2* (3+4)\\=9+2*7\\=9+14\\=23[/tex]
[tex](xy)^3\\=(3*4)^3\\=12^3\\=1728[/tex]
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You have a pipe where the last 9/16 of an inch is threaded. Due to error, you need to trim of 4/32" off the threaded part. How long will the threaded section be? A. 17/32, Bl 7/8, C. 7/16 D. 15/32
The length of 9/16 of an inch threaded section of the pipe indicates that the new length of the threaded section after 4/32 of an inch is trimmed off obtained by the difference between the fractions is; C. 7/16 of an inch
What is a fraction?A fraction is the representation of only a part of a whole of an item in the form of a quotient, consisting of a numerator, being divided by a denominator.
The length of the threaded section of the pipe = 9/16 of an inch
The length of the threaded part trimmed off due to an error = 4/32 of an inch
The new length of the threaded section following the trimming off of 4/32 is therefore;
New length of the threaded section = 9/16 - 4/32
The value of the difference between the fractions is found as follows;
[tex]\dfrac{9}{16} -\dfrac{4}{32} =\dfrac{2 \times 9 - 4}{32} = \dfrac{14}{32}[/tex]
[tex]\dfrac{14}{32}=\dfrac{7}{16}[/tex]
Therefore;
[tex]\dfrac{9}{16} -\dfrac{4}{32} =\dfrac{7}{16}[/tex]
The new length of the threaded section will be 9/16 - 4/32 = 7/16
The correct option that indicates the new length of the threaded section is C. 7/16
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Graph the parabola.
y=x²+2x+2
(Will mark brainliest)
Answer:
Step-by-step explanation:
The solution set of the equation x² + 5x = 0 is:
A. {0}
B. {5}
C. {-5}
D. {0, -5}
Answer:
D
Step-by-step explanation:
x²+5x=0
by factorizing;
x(x+5)=0
x=0 or x+5=0
Therefore, x= 0 or x=-5 ---> {0, -5}
Helen draws a random circle, she then measures the circumference and diameter.
She gets a circumference C of 405mm correct to 2 significant figures
She gets a diameter D of 130mm correct to 2 significant figures
Helen wants to find the value of [tex]\pi[/tex] using the formula [tex]\pi[/tex] = C÷D
Calculate the lower and upper bound for Helens value of [tex]\pi[/tex]
Give your answer correct to 3 decimal places
The value of π can be written with upper and lower limits as -
3.12 ± 0.062.
What are significant figures?Significant figures of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something.
Given is that Helen draws a random circle, she then measures the circumference and diameter. She gets a circumference {C} of 405mm correct to 2 significant figures She gets a diameter {D} of 130mm correct to 2 significant figures.
We can write -
Circumference {C} = (405 ± 2) mm
Diameter {D} = (130 ± 2) mm
The value of π can be calculated as -
π = {C}/{D}
π = (405 ± 2)/(130 ± 2)
Now, divide the numbers without errors first -
405/130
3.12
Now, we will calculate the relative errors in each number -
2/405 = 0.004
2/130 = 0.016
Adding the relative errors -
0.004 + 0.016
0.02
Absolute error = 0.02 x 3.12 = 0.062
The value of π can be written with upper and lower limits as -
3.12 ± 0.062
Therefore, the value of π can be written with upper and lower limits as -
3.12 ± 0.062.
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What are the dimensions of this shape in terms of the dimensions of the circle?
The diameter or radius of the circle is the dimension of a circle.
What is a circle?The circular line is drawn equidistant from the center point of a circle, which is a two-dimensional geometry object on a plane.
A geometrical rule states that the dimension of an object with n dimensions is n+1. For instance, a square is made up of line segments that are 1d and a cube is built up of squares that are 2d. The circle is therefore 2d or two-dimensional space since it is made up of 1d diameters.
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Answer:
The length of the parallelogram is half of the circumference of the circle, and its height is equal to the radius of the circle.
Step-by-step explanation: