Answers
12. The area of the shaded portion is the sum of the areas of a trapezoid and a parallelogram.
What is a trapezoid?An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.
A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
The altitude is the measurement of the angle perpendicular to the parallel sides.
The area of a trapezoid is (1/2)×(sum of the two parallel sides)×height.
9. The area of the shaded region is the area of the smaller trapezoid subtracted from the area of the larger trapezoid which is,
= [{(1/2)×(10 + 6)×8} - {(1/2)×(5 + 3)×4}].
= [8×8 - 4×4] cm².
= 64 - 16 cm².
= 48 cm².
10. Similarly the figure in (10) is twice the area of the two trapezoids.
11. We have subtract the sum of the areas of the trapezoid and the triangle from the larger rectangle.
12. The total area is the sum of the areas of the trapezoid and the parallelogram.
13. The larger figure is a rectangle with a right-angle triangle on top.
We have to subtract two rectangles from this to obtain the area of the shaded region.
14. To obtain the area of the shaded region we have to subtract the area of the trapezoid from the larger triangle with a height of 10cm.
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Related Questions
The temperature during the night was -4. In the morning the temperature increased by 3. What is the temperature in the morning
Answers
Answer:
-1
Step-by-step explanation:
Night: -4
Morning: -4 + 3 = -1
[tex]if \: x = 1 - \sin( \alpha ) \: and \: y = 1 + \cos( \alpha ) \\ [/tex]
Express y in terms of x and alpha only
Answers
Answer:
A sample of helium was compressed at 35 °C from a volume of 0.5 L
to 0.25 L where the pressure is 500 mmHg. What was the original pressure?
Step-by-step explanation:
The Singh family ordered a large pizza with a diameter of 16 inches for dinner. If one of the members of the family ate one eighth of the pizza, how many square inches of pizza are remaining? Use 3.14 for π.
200.96 square inches
175.84 square inches
100.48 square inches
25.12 square inches
Answers
Answer: D
Step-by-step explanation: 25.12
Answer: The actual answer is (175.84 square inches)
Step-by-step explanation:
First, find the area of the pizza.
You need to use the formula for area of a circle: A = πr^2
or in words, the area of a circle is equal to pi times radius to the second power.
So find the radius which is half the diameter.
The diameter is 16 inches, so the radius is 8 inches.
Now raise 8 to the second power, meaning that you need to times 8 by 8
(8 * 8 = 64) Now you times 64 by pi or 3.14. (64 * 3.14 = 200.96)
That is the area of the entire pizza.
But you still need to find how many square inches are left after 1/8 is eaten.
If 1/8 is eaten, then that means the pizza is divided into eighths.
Take 200.96 and divided that by 8 to find how much the individual pieces are.
200.96/8 = 25.12
But you need to find what is left is the pizza, so times 25.12 by 7 because that is how many pieces are left. 25.12 * 7 = 175.84
Sorry for the long explanation, but here is proof that the answer is correct. I took the same test and got the answer right
Here is a photo from my test:
Have a good day
BRAINLIEST FOR ANSWER UNDER 10 MINUTES The table shown represents a linear relationship.
x 0 1
3
4
y-8-6-20
Based on the table, what is the equation of the linear relationship in slope-intercept form?
Oy=2x-8
Oy = 2x+8
Oy = -2x + 4
Oy=-2x - 4
Answers
Answer: y = 2x-8
Step-by-step explanation:
Let's try to determine by substitution method. Starting from the first equation:
y = 2x-8
2·0-8 = -8
2·1-8 = -6
2·3-8 = -2
2·4-8 = 0
The first equation satisfies the conditions of the table.
24.
-2
2
NO
2
y-int=
slope =
equation:
y
2
X
Answers
Answer:
y-int = 0
slope = -1
equation: y = -x
Step-by-step explanation:
The line crosses the y-axis at y = 0, so the y-intercept is 0.
Go from (0, 0) to (-1, 1).
slope = m = rise/run = 1/(-1) = -1
y = mx + b
y = -x
y-int = 0
slope = -1
equation: y = -x
Which of the following functions describes the graph of g(x)? (5 points)
Rational function with one piece decreasing from the left asymptotic to the line y equals 2 and going through a hole at the point negative 2 comma eight-fifths and going down through the point 2 comma 0 asymptotic to the line x equals 3 and another piece decreasing from the left asymptotic to the line x equals 3 and going through the point 5 comma 3 going up to the right asymptotic to the line y equals 2
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared minus x minus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared plus x minus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared plus 5 x plus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared minus 5 x plus 6 end quantity
Answers
The equation of rational function is (c) g(x) = (2x + 4)/(x + 1).
What is a function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that,
The function g(x).
The graph of a function never touches the x = 1 line
At x = -1 there will be a vertical asymptote.
At x = -2 there will be a horizontal asymptote.
The equation of the function g(x) will be:
g(x) = (2x + 4)/(x + 1)
The equation of rational function is g(x) = (2x + 4)/(x + 1)
Therefore, g(x) = (2x + 4)/(x + 1) is correct.
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Rahquez and Francesca both leave the coffee shop at the same time, but in opposite directions. If
Francesca travels 5 mph faster than Rahquez and after 3 hours they are 105 miles apart, how fast is each
traveling?
Answers
So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph in opposite direction.
Define acceleration.Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time. If an object is speeding up, it is said to have a positive acceleration, while if it is slowing down, it has a negative acceleration.
What is velocity?Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time. The direction of velocity is the direction of the motion of an object. The standard unit of velocity is meters per second (m/s) or miles per hour (mph).
Let's call Rahquez's speed "R" and Francesca's speed "F". We know from the problem that:
F = R + 5 (Francesca is traveling 5 mph faster than Rahquez)
We also know that after 3 hours they are 105 miles apart, so we can set up an equation using distance = speed x time:
105 = (R + F) * 3
Now we can substitute the first equation into the second equation:
105 = (R + (R + 5)) * 3
Simplifying and solving for R, we get:
R = 20 mph
So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph (since F = R + 5).
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A builder buys a 21.5 acres of land to develop a new community of homes and parks.The builder plans to use 0.75 of the land for a park.How many acres will he use for the park?
Answers
He will use 9.375 acres of the land for the park
How to determine how many acres he will use for the park?A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.
Since the land is 21.5 acres and 0.75 of the land was used for a park. we can write:
acres used for the park = 0.75 × 12.5 = 9.375 acres
Thus, he will use 9.375 acres for the park
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A person is standing 18 feet from the base of a tree and there's a bird's nest in the tree 10 feet above the ground. what is the angle of elevation from the person to the birds nest? round to the nearest tenth of a degree?
Answers
The angle of elevation from the person to the birds nest is 29^o.
What is angle of elevation?When an object is observed at an angle above the horizontal plane, the angle formed with the horizontal plane with the line of observation is called an angled of elevation. It is measured in degree by a clinometer.
From a sketch of the narration in the given question, we apply the appropriate trigonometric function since the triangle is a right angled triangle.
So, to determine the measure of the required angle of elevation of the bird's nest, we have;
Tan θ = opposite/ adjacent
Tan θ = 10/18
= 0.5556
θ = Tan^-1 0.5556
= 29.05
θ = 29^o
Thus, the angle of elevation from the person to the bird's nest is 29^o.
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Which is a rational function?
A. Y= 2/x
B. Y=x^2 - x + 4
C. Y= x-3^x/x^2
D. Y= x-5/2
Answers
A rational function is the algebraic expression y = 2 / x. (Correct choice: A)
What function is a rational function?
Rational functions are algebraic expressions, whose form is described below:
R(x) = P(x) / Q(x)
Where:
P(x) - Numerator polynomic function.Q(x) - Denominator polynomic function.Please notice that Q(x) must be a polynomial whose grade is greater than zero.
Polynomials are algebraic expressions of the form:
P(x) = ∑ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., n, ..., m}, where m is the grade of the polynomial.
Therefore, by direct inspection, we conclude that algebraic expression y = 2 / x is a rational expression.
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Help me
Like just draw on it
Answers
Answer:
Step-by-step explanation:
which is the highest 4,16,77 and lowest
Answers
Answer:
highest 77 and lowest is 4
The function f(x)= -3x^3 + x^2 +2x rises as x grows very small.
A. True
B. False
Answers
When x is very small (close to 0), the term -3x^3 is much smaller in magnitude than the term x^2. Therefore, the overall value of the function will be dominated by the x^2 term, which is positive. This means that the function will decrease as x becomes very small.
False, the function f(x)=[tex]-3x^3 + x^2 +2x[/tex] does not rises as x grows very small.
How to determine the statementFirst, we need to know that functions are described as laws, expressions or rules that are used to show the relationship between two variables in an equation.
These variables are known as;
The independent variableThe dependent variableThe function f(x) =[tex]-3x^3 + x^2 + 2x[/tex] does not rise as x grows very small. When x approaches negative infinity, the dominant term is [tex]-3x^3[/tex], which becomes increasingly negative.
Therefore, the function decreases as x grows very small in the negative direction.
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Solve each equation for both variables help please 15 points
Answers
Answer:
I hope this helps. Do let me know if you have any doubts and wish me luck I have my maths exams tomorrow!
Given f(x)+3f(-x) = 2x+6, find f(x)
Answers
The function f(x) = -x-3.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given function:
f(x)+3f(-x) = 2x+6.
Let the function is an even function.
So, f(-x) = f(x)
To solve for f(x):
Substituting the property of an even function,
f(x) - 3f(x) = 2x + 6
-2f(x) = 2x + 6
f(x) = -x-3
Therefore, f(x) = -x-3 is the function.
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Latisha plans to purchase her school pictures. The prints cost $108 plus any add-ons she wants to purchase. If she saves $18 per week, which solution represents how many weeks, w, it will take Latisha before she can purchase her school pictures?
Answers
The number of weeks w is given by the equation w = 6 weeks
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number of weeks be represented as w
The prints cost $108 plus any add-ons she wants to purchase
The amount saved by Latisha per week = $ 18
So , the total amount saved by Latisha for w weeks = 18w
Now , the equation will be
18w = 108 be equation (1)
On simplifying the equation , we get
Divide both sides of the equation by 18 , we get
w = 108 / 18
w = 6 weeks
Therefore , the value of w is 6
Hence , the number of weeks is 6 weeks
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There are a total of 32 books and calculators on a table. The ratio of the number of books to the
number of calculators is 5: 3. How many calculators are on the table?
A. 3
B. 12
C. 20
D. 24
Answers
Answer:
B. 12
Step-by-step explanation:
Your ratio of 5:3 means that the ratio includes 8 objects (5+3). If you multiply the whole ratio by 4, then you have 32 objects on your table. Multiplying your ratio by 4 gives you 5*4 : 3*4 which is 20:12. and since 20 is your amount of books and 12 is your amount of calculators, you have 12 calculators on your table.
Solve the inequality:
4-3x<16
Answers
Answer:
x > -4
Step-by-step explanation:
This is solved just like as if it was an equation. Its a two-step equation (inequality) The only thing that's different is with an inequality, it is imperative that you flip the inequality symbol if you multiply or divide by a negative number.
Here, we'll subtract 4 from both sides. Then divide by -3 on both sides. Flip! the < to a >.
see image.
x > -4.
Step-by-step explanation:1. Write the expression.[tex]4-3x < 16[/tex]
2. Subtract "4" from both sides of the equation.[tex]4-3x-4 < 16-4\\ \\-3x < 12[/tex]
3. Divide both sides by "-3" and switch the inequality symbol.[tex]\frac{-3x}{-3} < \frac{12}{-3} \\ \\x > -4[/tex]
Important. See that we switched the inequality symbol from "<" to ">", and this is because the symbol of the coefficient of variable "x" changed from negative to positive when it was divided by "-3". This rule will always be true, any time the symbol of the variable changed, the inequality symbol changes.
4. Verify.If x >-4 is the correct answer, then substituting x by "-4" in the inequation should make the inequation return the same value on both sides of the inequality symbol (>).
[tex]4-3(-4) > 16\\ \\4-(-12) > 16\\ \\4+12 > 16\\ \\16 > 16[/tex]
That's correct! x > -4 is the correct answer.
Find the coordinates of the circumcenter of the triangle with the given vertices.
L(3,−6), M(5,−3), N(8,−6)
Answers
P(1.6,-2.9) are the coordinates of circumcentre of the triangle
How to find the coordinates of the circumcenter of a triangle?The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect.
Let L(3,−6), M(5,−3), N(8,−6) be the vertices of the given △LMN.
Let P(x,y) be the circumcentre of △LMN. Then,
PL = PM = PN
Also, PL² = PM² = PN²
PL² = PM²
(x-3)² + (y-(-6))² = (x-5)² + (y-(-3))²
(x-3)² + (y+6)² = (x-5)² + (y+3)²
x²-6x+9 + y²+12y+36 = x²-10x+25 + y²+6y+9
4x + 6y = -11 ---- (1)
Also, PM² = PN²
(x-5)² + (y-(-3))² = (x-8)² + (y-(-6))²
(x-5)² + (y+3)² = (x-8)² + (y+6)²
x²-10x+25 + y²+6y+9 = x²-16x+64 + y²+12y+36
6x - 6y = 27 ---- (2)
Solve (1) and (2) simultaneously by elimination:
6 × (4x + 6x = -11)
4 × (6x - 6y = 27)
24x + 36y = -66
24x - 24y = 108
subtract:
60y = -174
y = -174/60
y = -2.9
Put y = -2.9 into (1):
4x + 6x = -11
4x + 6(-2.9) = -11
4x - 17.4 = -11
4x = 6.4
x = 1.6
Thus, the coordinates of the circumcentre of △LMN are P(1.6, -2.9)
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4 3/5+ 2 2/3= l need someone to help me out
Answers
if (x+A)^2 -3 = x^2 + 4x + B. Find the value of A and B
Answers
The values of A and B are 2 and 4 respectively.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the equation as -
(x + A)² - 3 = x² + 4x + B
We can write the given equation as -
(x + A)² - 3 = x² + 4x + B
x² + A² + 2Ax = x² + 4x + B
A² + 2Ax = 4x + B
A² + 2Ax = B + 4x
Equating both sides, we get -
A² = B
and
2A = 4
A = 2
Then B will be equivalent to 4.
B = 4
Therefore, the values of A and B are 2 and 4 respectively.
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(7/8 x 14) / (3/8 x 6) + 2 1/5
Answers
Answer:
7/8 x 14= 12.25 or 49/4 or 12 1/4
(3/8 x 6) + 2 1/5= 4.45
(hope this helps I probably wasn't fully understanding)
please help fast for my math project and its due today !!!!!!! fasttttb pleaseeee
Answers
1) Note that in the problem above, the complete table is given as:
Team Number: 1 2 3 4 5
Best Jump (ft) 20.6 21.5 20.9 19.4 20.2
2) If Best Jump is denoted as y and Team number as x then, Best Jump is the Range while Team Number is the Domain.
3) For each element of the domain, there is a corresponding element of the range. So this relation is a function.
Why are the Domain and Range Important?Domain and range are crucial characteristics that aid in the definition of a relationship. The domain is a collection of input values.
The independent variable represents these values, which are graphed on the axis of a coordinate graph. A function's range is its collection of output values.
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A system of linear equations with an infinite number of solutions is a(n) __________ system.
Answers
A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
When a system of linear equations consists of an infinite number of solutions then this equation should be dependent and consistent as well, and this system is said to be a system of equivalent equations.
Thus, A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.
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What is 507 less than 607
Answers
Why is the discriminant a useful tool to use when solving quadratic equations?
Answers
If d>0, the the quadratic has 2 real solutions
If d=0, the quadratic has one (repeated) solution
If d<0, the quadratic has no real roots.
You must plug d in for these inequalities to determine which one is true, and that will tell you how many solutions a quadratic contains.
What is a b c d and e?
Answers
Answer:
Step-by-step explanation:
Solve for -10 - 9/2 x <80
Answers
Answer:
X > -20
Step-by-step explanation:
-10 - 9/2 x < 80
Move 10 to the other side
- 9/2 x < 80 + 10
Simplify
-9/2 x < 90
-9 x < 180
x > -20
(We switch the inequality sign if we are dividing with negatives)
Six families went to the food festival. Each family has 2 adults and 4 children. The entry fee for each child ticket costs $4, and an adult ticket costs $8. What would be the total cost of the festival tickets?
Answers
By solving an expression we will see that the total cost for the tickets is $192.
What would be the total cost of the festival tickets?We know that six families went to the food festival, each family has 2 adults and 4 children, then there are:
6*2 = 12 adults in total.
6*4 = 24 children in total.
We know that each child ticket costs $4, and an adult ticket costs $8, then the total cost of all the tickets is what we get when we solve the expression below:
12*$8 + 24*$4
That is, the number of adults times the cost of an adult ticket plus the number of children times the cost of a children ticket.
The total cost is then:
12*$8 + 24*$4 = $192
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A triangle has dimensions 9ft by 12ft if you wanted to increase the size of the triangle by a scale factor of 10/3 what would the area of the new triangle be?
Answers
Answer:
The area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2
Step-by-step explanation:
To increase the size of a triangle by a scale factor of 10/3, you can multiply each side length of the triangle by 10/3.
The new dimensions of the triangle would be (10/3) * 9ft = 30ft and (10/3) * 12ft = 40ft.
The area of a triangle is given by the formula A = (1/2) * b * h, where b is the length of the base and h is the height of the triangle.
Using the new dimensions of the triangle, the area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2.