Answers
Applying the definition of congruent triangles, the values of x and y are:
x = 11; y = 6
What are Congruent Triangles?If two triangles are congruent, all of it corresponding parts, which are angles and sides, will have equal measure.
Since triangles RWS and TUV are congruent triangles, therefore:
<R = <T
<W = <U
<S = <V
RW = TU
WS = UV
RS = TV
Thus, find the value of x:
90 + 8x - 27 + 29 = 180
92 + 8x = 180
8x = 180 - 92
8x = 88
Divide both sides by 8
8x/8 = 88/8
x = 11
Find the value of y:
RS = TV
Substitute
25 = 3y + 7
25 - 7 = 3y
18 = 3y
18/3 = y
y = 6
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Related Questions
What is the variable in this expression?
4b + 2b + 1⁄4
Answers
The variable in this expression 4b + 2b + 1⁄4 is b
How to determine the variable?From the question. we have the following expression
4b + 2b + 1⁄4
Take for instance, we have an expression
Ax
Where A is a number
It means that the expression x is a variable
This is so because the value of x can change
Similarly, the variable in 4b + 2b + 1⁄4 is b
This is so because the value of b can change
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How do you find the range on a graph?
Answers
The range of a graph can be found using the values depicted on the y-axis.
According to the question,
We have the following information:
We have a graph and we need to know how do we find the range of that graph.
We know that the domain of a graph is the collection or in other words set of input values depicted on x -axis and the range of a graph is the set of possible output values portrayed on y-axis of the graph.
In noting down the range of a graph, we first list down the down value and then the up value or in other words we move from down to up in order to find the range of a graph.
Hence, the range of a graph can be found using the values depicted on the y-axis.
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How do you find a polynomial?
Answers
Answer:
To find a polynomial, you must identify the terms, coefficients, and degrees. The degree of a polynomial is the highest exponent of the variable in the equation. The coefficients of a polynomial are the values that are multiplied by the variables. The terms of a polynomial are the pieces of the equation, including the coefficients and the variables. After identifying the terms, coefficients, and degree of the polynomial, you can write it in standard form.
Step-by-step explanation:
A certain forest covers an area of 2,000 square kilometers. Suppose that each year, this area decreases by 6%. What is the equation that best represents the area of the forest each year?
Hint: Use the formula y = P(1 + r)x.
y = 2,000(0.94)x
y = 2,000(1.06)x
y = 2,000(0.06)x
y = 2,000(1.94)x
Answers
The equation that best represents the area of the forest each year is A. y = 2,000(0.94)^x.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the certain forest covers an area of 2,000 square kilometers and each year, this area decreases by 6%.
The equation will be:
= 2000(1 - 6%)^x
= 2000(0.94)^x
In conclusion, the correct option is A.
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I need help bxbcbcbcbcbcbcbcbcbcb
Answers
The shape of Keisha's rectangular shaped planter would be the shape with the dimensions shown in the image below.
What is the Volume of a Rectangular Box?The volume of a rectangular box = length × width × height.
The shape of the planter is a rectangular box.
Given that the rectangular shaped planter would be filled first by 4 in. of rocks, it means the height of the rectangular shaped planter that the rock will occupy up to would be 4 in.
Find the volume the rock would fill:
Height = 4 in.Length = 10 inWidth = 10 in.Volume occupied by the rocks in the rectangular shaped planter = (10)(10)(4) = 400 in.²
If the soil to be filled must be exactly 800 in.², then the total volume of the shape of the rectangular planter that would be used would be: 400 + 800 = 1,200 in.².
From the options given, the last shape that has a height of 12 in., length of 10 in, and width of 10 in will have a volume = (12)(10)(10) = 1,200 in.².
Therefore, the last shape in the diagram below could be the shape of Keisha's rectangular shaped planter.
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A circular spinner has seven sections of equal size, each of which is colored either red or blue. Two colorings are considered the same if one can be rotated to yield the other. In how many ways can the spinner be colored?
Answers
The number of ways that the spinner can be colored is 21 ways.
How to calculate the number of ways?Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Based on the information given, the number of ways will be to select 2 out of 7. This will be:
= 7! / (7 - 2)!2!
= 7! /5!2!
= (7 × 6) / 2
= 42/2
= 21
There'll be 21 ways.
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What would the answer be? I tried 4 and -4 and a lot more.
Answers
Answer:
-2
Step-by-step explanation:
a is -3
d is -1
you subtract the two
-3 - (-1)
when you have two negatives they cancel each other out and become positive
-3 + 1
-3 + 1 = -2
that is your answer
The perimeter of a rectangle is 204 centimeters. Find the length and width if the length is an even integer and the width is 3 times the next consecutive even integer.
Answers
Step-by-step explanation:
2×length + 2×width = 204 cm
length = x
width = 3×(x + 2)
as consecutive even integers are always spaced out by 2 (2, 4, 6, ...).
we are using these 2 equations in the first main equation :
2×x + 2×3×(x + 2) = 204
2x + 6x + 12 = 204
8x + 12 = 204
8x = 192
x = 192/8 = 24
length = x = 24 cm
width = 3(x + 2) = 3×26 = 78 cm
What is a prime multiple?
Answers
The multiples of a number are numbers found by multiplying the original number by any whole number. Prime multiples are number which multiply each other and form a prime
What are Prime Numbers ?
A prime number is a number that is only divisible by 1 and itself. So, prime numbers have only two factors, 1 and the number itself.
This means these numbers cannot be divided by any number other than 1 and the number itself without leaving a remainder.
Numbers that have more than 2 factors are known as composite numbers.
For example :
The factors of 3 are 1 and 3.
Therefore, the prime multiples of 3 are 1 and 3.
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In the right △ABC with m∠C90°, m∠A75°, and AB = 12 cm. Find the area of △ABC. pls help immedietyly right now experts ik ur watching i didnt put alot of point but pls
Answers
The area of triangle ABC is 18cm².
What is a triangle?A triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.
This property is called angle sum property of a triangle. A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.
= 72*sin(75)*cos(75)
= 36*(2sin(75)cos(75))
= 36*sin(150)
= 18
In conclusion, the area of the triangle is 18cm².
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In Exercises 13-16, find the area of the polygon with the given vertices. (See Example 3.)
13. E(3,1), F(3,-2), G(-2,-2)
14. J(-3,4), K(4,4), L(3,-3)
Answers
The area of the polygon EFG with given vertices is, 7.5 units.
What is area of triangle?
The area of a triangle is the area that it completely encloses in a two-dimensional plane. A triangle is a closed shape that, as we all know, has three sides and three vertices. As a result, the total area occupied by a triangle's three sides is known as its area. The general formula for calculating a triangle's area is the product of the triangle's base and height divided by half.
Let the given vertices are,
E(3, 1), F(3, -2), G(-2, -2)
There are three vertices, so the polygon is a triangles.
Since,
Area of triangle = 1/2 x base x height.
If we draw the given vertices on the coordinate plane then the base is FG and the height of the triangle is EF.
Now to find the lengths of side FG and EF.
By using the distance formula,
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\EF =\sqrt{(3-3)^2+(-2-1)^2} = \sqrt{9} = 3\\ FG = \sqrt{(-2-3)^2 + (-2-(-2))^2} = \sqrt{25+0} = 5[/tex]
⇒ Area = 1/2 x 5 x 3
= 1/2 x 15
Area = 7.5
Hence, the area of the polygon EFG is 7.5 units.
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There are 28 students in the classroom. Each student needs 2 pencils for the exam. How many pencils in all are needed for the exam?
Answers
Total 56 pencils are needed for the exam.
What is Multiplication?Multiplication is one of the arithmetic operation used to find total numbers of items or things.
Given,
Total students in the classroom = 28
Total number of pencils needed by each student for the exam=2 pencils
Total number of pencils needed for the exam are,
= Total student × Number of pencils needed by each student
= 28 × 2
= 56 pencils
Hence , The total number of pencils needed by the students for the exam would be 56 .
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The table shows that the total cost of a ride-sharing trip, y, is a function of the distance traveled, a.
What is the rate of change and what does it mean?
2; the ride costs $2 per mile.
43; the ride costs $3 per mile.
2; it costs $2 as soon as you start the ride.
4) 3; it costs $3 as soon as you start the ride.
Distance (mi), Total Cost ($). y
2
5
8
11
14
0
1
2
3
4
Answers
Answer:3; the ride costs $3 per mile
Step-by-step explanation:
Rate of Change of the function is 3. then the ride costs $3 per mile.
What is the average rate of change?The average Rate of Change of the function f(x) can be calculated as;
[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]
We are given the total cost of a ride-sharing trip, y, is a function of the distance traveled,
Distance (mi), Total Cost ($). y
2 0
5 1
8 2
11 3
14 4
Therefore,
Rate of Change of the function
(5 - 2) / (1- 0)
= 3 / 1
Hence, we can conclude that the ride costs $3 per mile.
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Is it true that 5 2/3 - 3 3/4 = 1+ 2/3 + 3/4?
Answers
The fraction 5 2/3 - 3 3/4 is not equal to 1+ 2/3 + 3/4.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, 5 2/3 - 3 3/4 will be:
= 5 2/3 - 3 3/4
= 5 8/12 - 3 9/12
= 1 11/12
Therefore 1 + 2/3 + 3/4
= 1 + 2/3 + 3/4
= 1 + 8/12 + 9/12
= 2 5/12
They are not the same.
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how many sides does a regular polygon have
Answers
Answer: a polygon is a shape with at least three straight sides and angles, and typically five or more
Step-by-step explanation:
(1 point)
Solve this inequality, and write your answer in interval notation.
|x|>-5
Please type:
- int for oo,
- no solution if there are no real solutions
- U for the union symbol U
You have attempted this problem 8 times.
Your overall recorded score is 0%
You have unlimited attempts remaining.
Answers
Answer: [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
Absolute value is always non-negative.
When a transversal cuts parallel lines, how can one angle measurement be used to determine all of the other measurements?
Answers
Answer: If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Step-by-step explanation:
Question 3 of 10
If r^n = a, then which of the following are true statements?
Check all that apply.
A. Va=r
B. a¹/n=r
C. n¹/r= a
D. a = n
Answers
Answer:
Option B is the correct option
Step-by-step explanation:
What is an example of a domain on a graph?
Answers
The function f(x) is represented by the graph attached below. The domain of the graph is given by [-5,5] or {x | -5 ≤ x ≤ 5 ,x ∈ R} .
A function's domain in mathematics is the set of potential inputs that it can take. It can also be written as b, where f is the function.
Formally speaking, X is the domain of f given a function. It is important to note that, in terms of contemporary mathematics, a function's domain is a part of its definition rather than a property.
The function f can be graphed in the Cartesian coordinate system in the uncommon case where X and Y are both subsets of. In this instance, the function's graph, which is projected onto the graph's x-axis, serves as a representation of the domain.
A real function, f, may not be defined for all possible values of the variable if it is specified in a formula. The natural domain, also known as the domain de definition of f, is the set of real numbers to which the formula in this case can be evaluated to either a real number. It is common to refer to a partial function as just a function and its natural domain as just a domain.
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"Even in winter, the roadsides were places of beauty, where countless birds came to feedon the
berries and on the seed heads of the dried weeds rising above the snow. The countryside was, in
fact, famous for the abundance and variety of its bird life, and when the flood of migrants was
pouring through in spring and fall, people came from great distances to observe them"
(paragraph 5).
Why most likely does the author give a detailed description of a healthy ecology (the
study of organisms and how they interact to the environment around them) as noted in
paragraph 5?
A. To promote birdwatching to people visiting the town
B. To give the natural history of a specific region
C. To describe different tourist activities of people pouring through the town
D. To contrast how the town changed once the ecology was compromised with the use of
harmful pesticides
Answers
The author gives a detailed description of a healthy ecology D. To contrast how the town changed once the ecology was compromised with the use of harmful pesticides.
What is the ecology about?
Ecology also teaches us about the benefits of ecosystems and how to use the Earth's resources in a way that protects the environment for future generations. We can learn more about our surroundings thanks to the various fields of ecology, which include statistical ecology, marine ecology, and vegetation ecology.
With the help of this information, we can manage our natural resources, protect human health, and improve the environment. In this case, the author give a detailed description of a healthy ecology.
The correct option is D.
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Find the length of the hypotenuse, side c, of a right triangle with legs of length a = 6 and b = 12. Use a calculator to estimate
the square root to one decimal place.
6
12
The length of the hypotenuse, c, is approximately
The solution is
Answers
Answer:
c=13.4
Step-by-step explanation:
Slopes of Parallel/Perpendicular Lines (5x - 4y = -24) Show steps please
Answers
The slope of the perpendicular line to the equation 5x - 4y = -24, is: 4/5.
How to Find the Slope of Perpendicular Lines?The slope values of two lines which lie perpendicular to each other on a coordinate plane are always negative reciprocals to each other.
Rewrite the equation, 5x - 4y = -24 in slope-intercept form:
5x - 4y = -24
-4y = 5x - 24
Divide both sides by -4
-4y/-4 = 5x/-4 - 24/-4
y = -5/4x + 6
The slope of y = -5/4x + 6 is -5/4. The negative reciprocal of -5/4 is 4/5. Thus, the slope of the line that is perpendicular to the equation of the given line is: 4/5.
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When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle it means that we are going to use what postulate?
Answers
The used postulate is explained below.
What is congruent triangles?
Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.
When angles and facet blanketed in among those angles of 1 triangle are identical as any other one, each those triangle are Congruent.
This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.
Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.
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What information is needed to show that △ ABC ≅ △ DEF by SAS congruence?
Answers
In order to show that △ ABC ≅ △ DEF by SAS congruence, we need the sides of triangles ABC and DEF with the angle between the respective sides.
What do we understand by congruency of a triangle?Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "" is the congruence symbol. When two figures are comparable to one another in terms of their size and shape, this is what mathematicians mean by congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables.
Congruency Requirements:
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle-Side)
RHS (Right angle-Hypotenuse-Side)
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1. The unit price of an item is how much it costs for one item. It's useful to know the unit price when buying in bulk. If we're buying 100 items, then you'll save quite a bit of money if you buy the unit priced item that costs $10 per item compared to the unit price of $12 per item!
You can calculate a unit price by dividing the total amount of money you spent for items by the number of items you purchased. For instance: $7.99 per oz of goldfish is $ 7.99 / 30= 0.26$ per ounce.
Which purchase has the lower unit price - $\$ 200$ for 15 flower arrangements, or $70 for 5 flower arrangements?
Answers
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a problem sum of division
Cost of 15 flowers = $200
Cost of 1 flower = $200 [tex]\div[/tex] 15 = $13.33
Cost of 5 flowers = $70
Cost of 1 flower = $70 [tex]\div[/tex] 5 = $14
So unit price of 15 flower arrangement of $200 is lower than unit price of 5 flower arrangement of $70
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What are the 5 ways triangles are congruent?
Answers
The correct answer is the 5 ways to find if two triangles are congruent are SSS, SAS, ASA, AAS and HL.
Two triangles are congruent if and only if they have the same three sides and angles.
SSS (side, side, side): SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.
SAS (side, angle, side): "Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal. The triangles are congruent if two sides and the included angle of one triangle equals the corresponding sides and angle of another triangle.
ASA (angle, side, angle): ASA, which stands for "angle, side, angle," denotes the existence of two triangles whose included side and two known angles are equal. The triangles are congruent if two angles and the included side of one triangle match the corresponding angles and side of another triangle.
AAS (angle, angle, side): AAS, which stands for "angle, angle, side," denotes the equality of the non-included side and two angles in two triangles. The triangles are congruent if two of one triangle's angles and its excluded side are equal to the corresponding angles and sides of another triangle.
HL (hypotenuse, leg): The two triangles are congruent if one right-angled triangle's hypotenuse and one of its legs are equal to its corresponding hypotenuse and leg in another right-angled triangle.
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write an equation to find the number of chickens on juniors farm based on the number of months junior has been farming
Answers
Answer:
c = 5m + 30
Step-by-step explanation:
It is given that:
c = total amount of chickens.
m = total amount of months.
x = amount of chickens per month.
30 is the base amount that Junior will have no matter how much months have passed.
Plug in 4 for m (months), and 50 for c (total amount of chicken) in the given equation:
c = xm + 30
50 = x(4) + 30
50 = 4x + 30
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponent (& root)
Multiplication
Division
Addition
Subtraction
~
First, subtract 30 from both sides of the equation:
50 = 4x + 30
50 (-30) = 4x + 30 (-30)
50 - 30 = 4x
20 = 4x
Next, divide 4 from both sides of the equation:
(20)/4 = (4x)/4
x = 20/4
x = 5
The amount of chicken per month is 5.
Set the equation. Plug in 5 for x in the given equation:
c = xm + 30
c = 5m + 30
c = 5m + 30 is your answer.
Check. Plug in time per month and find the number of chickens:
Time in months = 0 ; Number of Chickens = 30
(30) = 5(0) + 30
30 = 0 + 30
30 = 30
Time in months = 4 ; Number of chickens = 50
(50) = 5(4) + 30
50 = 20 + 30
50 = 50
Time in months = 720 ; Number of chickens 3630
(3630) = 5(720) + 30
3630 = 3600 + 30
3630 = 3630
~
Eight workers are hired to harvest strawberries from a field. Each is given a plot with an area of 72 ft² What is the total area
strawberry field?
Answers
Answer:
576 ft squared
Step-by-step explanation:
8 x 72 ft= 576 total area
Hope this helps!
A rectangular piece of paper with length 25 cm and width 12 cm has two semicircles cut out of it, as shown below.
Find the area of the paper that remains. Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
The area of the rectangular paper left after two semi circles are cut out of it is 186.96 cm².
What is a rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel.
To caluculate the area of the paper that remains, we use the formula below.
Formula:
Ar = lb-π(b/2)²............ Equation 1Where:
Ar = Area of the paper that remainl = Length of the rectangular paperb = width of the rectangular paperr = Radius of the semi circleFrom the question,
Given:
l = 25 cmb = 12 cmr = 12/2 = 6 cmπ = 3.14Substitute these values into equation 1
Ar = (25×12)-(3.14×6²)Ar = 300-113.04Ar = 186.96 cm²Hence, the area of the paper left is 186.96 cm².
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Directions: Find the value of each variable.
11) x=?
y=?
12) x=?
y=?
13) x=?
y=?
14) x=?
y=?
15) x=?
y=?
z=?
Answers
The value of the variables x and y are,
11) x = 13, y = 18.4
12) x = 6.9, y = 8.
What is right angle triangle?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
11)Let the given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(45) = \frac{x}{13} \\x = 13(tan(45))\\x = 13[/tex]
Using this to find the value of y.
[tex]sin(45) = \frac{x}{y} \\sin(45) = \frac{13}{y} \\y = \frac{13}{sin(45)} \\y = 18.4[/tex]
So, the values of x and y are x = 13 and y = 18.4.
12) The given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(30) = \frac{4}{y}\\ y = \frac{4}{tan(30)} \\y = 6.9[/tex]
Now to find the value of x.
[tex]sin(30) = \frac{4}{x} \\x = \frac{4}{sin(30)} \\x = 8[/tex]
Hence, the values of x and y are, x = 6.9 and y = 8.
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