Answers
Using Pythagoras Theorem, the lengths are 1)3√8 cm 2)2[tex]\sqrt{65}[/tex] cm 3) 8√2 cm and 4) 12 cm.
What is Pythagoras Theorem?Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.
1) Here the diagonal of the square is the hypotenuse.
Base length = 6 cm and Altitude length = 6 cm
(Diagonal length)² = 6² + 6²
= 72
Diagonal length = √72 = 3√8 cm
2) Longest side is the hypotenuse.
Length of longest side = [tex]\sqrt{14^2+8^2}[/tex] = [tex]\sqrt{260}[/tex] = 2[tex]\sqrt{65}[/tex] cm
3) When height divides the triangle into two, there are two right angled triangles.
Height is the altitude of the right angled triangle.
Hypotenuse is 12 cm and base is half of 8 cm.
Height² = 12² - 4²
Height² = 128
Height = [tex]\sqrt{128}[/tex] = 8√2 cm
4) Here, the base of the isosceles triangle is twice the base of the right triangle.
Base² = 10² - 8² = 36
Base of the right triangle = √36 = 6 cm
Base of the isosceles triangle = 2 × 6 = 12 cm
Hence using Pythagoras theorem, all the lengths are found.3
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Related Questions
My question is this, I don’t know what to do with this:
11. 0.45 × $6,800
Answers
Answer:
3060 US$
2,829.28 EU$ <—- I only added this because i live in EU.
Step-by-step explanation:
How do you translate a graph left and right?
Answers
To translate a graph left and right, you need to shift the graph horizontally. To shift the graph left, subtract the desired amount from the x-values and keep the y-values the same. To shift the graph right, add the desired amount to the x-values and keep the y-values the same.
To translate a graph left and right, you need to shift the graph horizontally. This means that the values on the x-axis will be changed while the values on the y-axis will remain the same. To shift the graph left, subtract the desired amount from the x-values and keep the y-values the same. This will move the graph to the left on the x-axis. To shift the graph right, add the desired amount to the x-values and keep the y-values the same. This will move the graph to the right on the x-axis. Both of these processes can be used to shift the graph to the desired position on the x-axis.
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75 POINTS!! Three questions in the attachments below, (please don't spam random stuff to claim points)!
Answers
1.AB || DC Given
m<BCD + m<BEF = 180 Given
2.<3 <1 Since AB and DC are parallel, corresponding angles are congruent
3.<4+<5 = 180 Substitution
4.<3 ≅<5 Angle Sum Property
5.<5 ≅<2 Since AB and DC are parallel, corresponding angles are congruent
6.<3≅ <2 Angle Sum Property
7. BC|| EF Transitive Property of Parallel Lines
What is corresponding angles?Corresponding angles are two angles that have the same position in relation to two other lines or planes. The two lines or planes are usually parallel. These angles are opposite each other and they share the same vertex. The angles are non-adjacent angles and they are usually congruent. Corresponding angles can be found in many everyday situations. For example, in architecture, corresponding angles are used to ensure that two walls that are parallel to each other have the same angles at the corners. This can be used to create interesting designs or to ensure the stability of a building. In mathematics, corresponding angles are used to prove that two lines are parallel. This is done by showing that the angles in the same position on either side of the two lines have equal measurements. This is known as the Alternate Interior Angles Theorem.Corresponding angles are also used in 3-D shapes. If a 3-D shape is cut into two pieces then the angles at the same position on either piece will be corresponding angles. This can be used to identify the shape of the original 3-D shape. Overall, corresponding angles are very useful in many different fields. They can be used to create interesting designs.To learn more about angles refer to:
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156.8 - 9.92 I don’t know how to solve it
Answers
Answer:
156.8 - 9.92 = 146.88
Step-by-step explanation:
If sin f° = eight ninths and the measure of segment YW is 24 units, what is the measure of segment YX?
21 units
24 units
27 units
30 units
Answers
Answer:
Step-by-1step explanation:
Val is going to plant b vegetable seeds in one garden and 4 b plus 8 vegetable seeds in another. How many seeds is Val going to plant?
Answers
The total number of seeds that Val is going to plant will be 5b + 8.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Val is going to plant b vegetable seeds in one garden and 4 b plus 8 vegetable seeds in another.
Then the total number of seeds that Val is going to plant will be calculated as,
⇒ b + 4b + 8
Simplify the expression, then we have
⇒ b + 4b + 8
⇒ 5b + 8
The total number of seeds that Val is going to plant will be 5b + 8.
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Marshall modeled the distance, y, that swimmers traveled during a race as a
function of time, x, that they swam. Which would best describe the domain of
this function?
Answers
The domain of the function modeling the distance swam by a swimmer as a function of time would be all positive real numbers greater than or equal to zero, representing the time spent swimming in the race.
This is because the time spent swimming in a race cannot be negative and must be greater than or equal to zero, which represents the start of the race. The domain of a function defines the set of all possible input values (in this case, time) for which the function produces a valid output (distance). In this case, the domain would be all positive real numbers greater than or equal to zero, since these are the only valid input values that can be used to calculate the distance swam by a swimmer during a race.
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On Monday, the theater club sells 30 tickets for the school play. On Tuesday, they sell 20 tickets. On those two days, they sell 25% of the total number of tickets. What is the total number of tickets?
Answers
The total number of tickets is 200 tickets.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given;
On Monday,
the theater club sells 30 tickets for the school play.
On Tuesday,
they sell 20 tickets.
On those two days,
they sell 30 + 20 tickets and that is 25% of total tickets.
So, total number of tickets,
here, 25% = 50
So, 25 x 4 = 100% = 50 x 4 = 200 tickets.
Therefore, 200 tickets are the total number of tickets.
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Rewrite [tex]\frac{\frac{x^{3}-xy^{2} }{y} }{\frac{y}{x}-1 }[/tex] as a single, simplified fraction. State any excluded values of the variables.
Answers
The simplified fraction is -x²(x + y)/y for the given expression.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
The fraction is given in the question, as follows;
{(x³ -xy²)/y}/{y/x - 1}
{x(x² -y²)/y}/{(y - x)/x}
{x(x - y)(x + y)/y}/{(y - x)/x}
Reciprocal the terms in the above fraction,
{x(x - y)(x + y)/y} × {x/(y - x)}
{x(x - y)(x + y)/y} × {-x/(x - y)}
Reduce the same term in the expression,
{x(x + y)/y} × {-x}
-x²(x + y)/y
This is the simplified fraction.
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The ratio of cats and dogs on Karen's farm is 4 to 5. If there are 424 cats. How many dogs are there?
A) Write a proportion that is defined by this situation.
B) Explain how the cross product is used to solve the problem
C) Answer the question.
(As you answer the following questions, write explanations for why your current answer is correct )
Answers
Answer: 530
Step-by-step explanation:
you need to put 4/5 then put 424/x then you multiply across and take 5x424 then devide your answer by 4 and get X=530
a local school newspaper's editor wants to survey students to determine the approval rating of the current student council president. how would the newspaper apply the cluster sampling method to find this information?
Answers
The newspaper staff surveys random students from every grade in the school.
Group sampling
In cluster sampling, a population is divided into clusters, which are smaller groups. They then choose a sample at random from these clusters. Often employed to investigate huge populations, particularly those that are extensively geographically distributed, cluster sampling is a probability sampling technique.
What kind of cluster sampling is that?
Single-stage cluster sampling illustration In order to give education, an NGO wishes to compile a sample of girls from five nearby communities. The NGO selects towns (clusters) at random to create a sample using single-stage sampling and then provides assistance to the girls who are denied schooling in those places.
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what is the inverses function of f(x)=4x-8
Answers
Answer:
f^-1(x) = (x+8)/4
Step-by-step explanation:
To find the inverse function,
FIRST, change f(x) to y.
f(x)=4x-8
y = 4x - 8
SECOND, switch the x and the y.
x = 4y - 8
NEXT, solve for y.
x = 4y - 8
add 8 to both sides.
x + 8 = 4y
divide both sides by 4.
(x+8)/4 = y
LAST, rewrite using f^-1(x) in place of y
f^-1(x) = (x+8)/4
If you have better functionality (than me typing on my phone) use a -1 exponent beside the f. Also, put the x+8 on top of the fraction with the 4 on the bottom of the fraction. Then you won't need the parenthesis around the x+8
Can someone help me understand this?
Answers
When the values of x and y are replaced into a linear inequality in two variables, such as Ax + By > C, the solution is an ordered pair (x, y) .
what is linear inequalities ?In mathematics, an inequality is a connection between two expressions or values that is not equal. As a result, inequality results from imbalance. In mathematics, an inequality establishes a connection between two non-equal numbers. Egality is different from inequality. Use the not equal sign, which is most frequently used, when two values are not equal (). Values of any size can be contrasted using various inequalities. By changing the two sides until only the variables are left, many straightforward inequalities can be resolved. But a lot of factors support inequality: On either side, negative values are split or added.
given
Rule 1: An inequality sign remains unaltered when the same amount is added to or subtracted from both sides.
Rule 2: The inequality sign remains constant when both sides are multiplied or divided by a positive number.
When the values of x and y are replaced into a linear inequality in two variables, such as Ax + By > C, the solution is an ordered pair (x, y) .
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How do you graph a linear equation 3x 2y 6?
Answers
We can draw the graph a linear equation 3x + 2y = 6 by isolating y then putting the different value of x to find the value of y.
We have to explain, how we graph a linear equation 3x + 2y = 6.
The given linear equation is 3x + 2y = 6.
To graph the linear equation, we have to first isolate the y.
Subtract 3x on both side, we get
2y = 6 - 3x
Divide by 2 on both side, we get
y = [tex]\frac{6 - 3x}{2}[/tex]
Now we finding the value of y in the different value of value of x
x 0 2
y 3 0
Now we draw that points.
The graph of the given linear equation is given below:
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The complete question is:
How do you graph a linear equation 3x + 2y = 6?
2. Manasi wants to plant flowers in her square field of side 10m.. If Lekha also wants to plant flowers in her rectangular field of length 8m and the same perimeter as that of the square field, whose field will be able to sow more seeds?
please tell the answer
Answers
The number of seeds that can be sown in a given area depends on the size and spacing of the seeds.
What is the area of the square?
A square is a 2D figure in which all the sides are of equal measure. Since all the sides are equal, the area would be length times width, which is equal to side × side. Hence, the area of a square is a side square.
It is not possible to determine which field will be able to sow more seeds without additional information.
The square field has an area of 100 square meters,
while the rectangular field has an area of 40 square meters, but the perimeter of the rectangular field is not given and it is not possible to calculate it.
Hence, The number of seeds that can be sown in a given area depends on the size and spacing of the seeds, as well as the type of soil and other environmental factors.
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if f(x) = x + 3/x
Find f¹(x).
Answers
The value of f¹(x) is 1-3/x^2 when the given function is f(x) = x+3/x .
What is Differentiation ?Differentiation is the process of calculus that finds the rate of change or slope of a function at a particular point. This is represented by the symbols 'd/dx' or '∂/∂x'. where x is a variable. The result of differentiation is called the derivative of the function. There are several techniques for finding the derivative of a function. B. Use power, product, and quotient rules. Differential processes are also useful in solving various problems in physics and engineering, such as: B. Find the maximum or minimum value of a function to understand its behavior around a certain point.
Given function,
f(x) = x+3/x
Differentiating on both sides , so we get
on LHS = f¹(x)
and on RHS = 1+d(3/x) / dx
Hence,
f¹(x) = 1+d(3/x) / dx
d(x)/dx = 1
d(1/x) = - 1/ x^2
so we get,
f¹(x) = 1-3/x^2
Hence, The value of f¹(x) is 1-3/x^2 when the given function is f(x) = x+3/x
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A laptop computer was purchased for $1050. Each year since, the resale value has decreased by 29%.
Lett be the number of years since the purchase. Let y be the resale value of the laptop computer, in dollars.
Write an exponential function showing the relationship between y and t.
Answers
An exponential function is a function of the form y = ab^x, where a and b are constants, and x is the input variable.
In this case, the input variable is t, the number of years since the purchase, and the output variable is y, the resale value of the laptop computer.
We are given that the resale value decreases by 29% each year, so we can express the decrease as a decimal by dividing 29 by 100: 29/100 = 0.29
The relationship between y and t can be written as:
y = 1050(1 - 0.29)^t
In this function, 1050 is the initial value, 1-0.29 is the decreasing factor, and t is the number of years since the purchase. This function shows the relationship between y and t, that is the resale value of the laptop computer in relation to the number of years since the purchase.
The diameter of a circle is 14 meters. What is the circle's circumference?
Use 3.14 for л.
d=14 m
meters
Answers
Answer: 43.96 [tex]m^{2}[/tex]
Step-by-step explanation:
Diameter = 14m
Circumference = D * pi = 14 * 3.14 = 43.96
Answer:
Step-by-step explanation:
To find the circumference of a circle, the formula is 2πr or πd.
So you have 14π or 43.96 meters
Answer:43.96 meters
Use the Law of detachment to draw a conclusion
1. If a figures 's a rectangle, then it has four right angles.
Figure PQRS is a rectangle.
2. If a quadrilateral is a trapezoid, then it has exactly one pair of parallel sides.
Quadrilateral ABCD is a trapezoid.
3. If a convex polygon is a pentagon, then the sum of the measures of its interior angles is 540°. Figure ABCDE is a pentagon.
4. If an angle is acute, then its measure is greater than 0° but less than 90°.
5. If two angles are congruent, then their measures are equal.
Answers
PQRS has four right angles, ABCDE is a pentagon and ABC measure greater than 0 but less than 900.
What is quadrilateral?
Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.
If a figure is a rectangle, then it has four right angles. Figure PQRS is a rectangle.
• Figure PQRS has four right angles.
If a convex polygon is a pentagon, then the sum of the measures of its interior angles is 540°.
• Figure ABCDE is a pentagon.
If an angle is acute, then its measure is greater than 0 but less than 90. ABC is an acute angle.
• ABC measure greater than 0 but less than 900
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What is the base in 7?
Answers
The simplest scenario is that the number fits in one bit, hence it must be less than two. If so, the output is the number itself, whether it be 0 or 1.
We employ the digits 0 through 6 in the base system of 7, however 7 won't be present. We use 10 to write 7 in base system 7. A number in base 7 can only be expressed using the numbers 0 through 6. 1 x + 3 x 7 + 5 = 75 in base 10 corresponds to the number 135 in base 7.
Let's now translate 384605 into Base 7. Divide 384605 by 7 to get the answer:
384605 ÷ 7 = 54943 + R(4)
Next, split the 54943-quotient by the following:
384605 ÷ 7 = 54943 + R(4)
54943 ÷ 7 = 7849 + R(0)
Repeat these steps with 7849 until the quotient equals 0:
384605 ÷ 7 = 54943 + R(4)
54943 ÷ 7 = 7849 + R(0)
7849 ÷ 7 = 1121 + R(2)
1121 ÷ 7 = 160 + R(1)
160 ÷ 7 = 22 + R(6)
22 ÷ 7 = 3 + R(1)
3 ÷ 7 = 0 + R(3)
The Base 7 numbers will make up the remainders. Use the remainders' digits in the order of bottom to top. Therefore,
384605 = [tex]3161204_7[/tex]
A number with the digits 0, 1, 2, 3, 4, 5, and 6 is known as a base 7 number. If the given integer has a subscript of 7, it has been written in Base 7. Heptimal system is another name for the base-7 system.
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3. Trapezoid A'B'C'D was created by dilating trapezoid ABCD using D as the center of dilation.
a. What was the scale factor of the dilation?
b. Based on the scale factor, how many copies of ABCD, including the
original, should fit inside A'B'C'D'?
c. How can you see your answer to these questions in the diagram?
Answers
a. The scale factor is solved to get 3
b. There 9 copies of the of the original shape in the scaled image
c. the top has 2 and a remaining part shaded and labelled O which is joined to the part labelled P at the base to form 3
The middle has 3 while the last has 3 and the part labelled P
3 + 3 + 2 + 1 = 9
How to calculate the scale factorScale factors are used to increase or decrease image. The situation of increment is usually called magnifying.
For the given graph the values with prime is assumed to be the the image while the the values without prime represent the original shape.
Taking a point of reference say CB and C'B'.
CB = 2
C'B' = 6
solving for the factor, assuming the factor is k
2k = 6
k = 6/2 = 3
b. The area of the original shape is solved using the formula for area of trapezoid
= 0.5 (sum of parallel lines) * height
= 0.5 * (2 + 4) * 2
= 6 square units
area of the image
= 0.5 * (6 + 12) * 6
= 54 square units
the number of the original shape in the scaled copy
= area of the image / area of the original shape
= 54 / 6
= 9
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Which ordered pair is a solution to the linear inequality y ⩾ 2x–4?a.(1,2)
b.(1, 1)
c.(2,-3)
d.(2,4)
Answers
The linear inequality y⩾2x–4 can be expressed in the standard form of an inequality as y-2x⩾–4.
This means that the y-value must be greater than or equal to the result of the calculation 2x–4. To solve this inequality, we can substitute an x-value and calculate the corresponding y-value. For example, if we choose an x-value of 1, then we can calculate the y-value as y = 2x–4 = 2(1)–4 = –2. Therefore, the ordered pair (1,2) is a solution to the linear inequality, as the y-value (2) is greater than or equal to the result of the calculation 2x–4 (–2). The ordered pair (1,1) is not a solution to the linear inequality, as the y-value (1) is less than the result of the calculation 2x–4 (–2). The ordered pair (2,–3) is not a solution to the linear inequality, as the y-value (–3) is less than the result of the calculation 2x–4 (–4). The ordered pair (2,4) is a solution, as the y-value (4) is greater than or equal to the result of the calculation 2x–4 (–4).
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i suck at this please help
Answers
Answer: 1904 for the first question
Step-by-step explanation: I am not completely sure so might want to look into it some more.
which equation models this situation
Answers
m = 2.58 b is a linear function that models the scenario as stated.
What is Linear function?A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.
Given, At the bakery, loaves cost $2.58 each. The total money spent at the bakery (m) is equal to the product of 2.58 and the number of loaves of bread that were bought (b).
Linear Function for the given condition
(Since all money is spent on the loaves)
m = 2.58 b
Therefore, a Linear function that models the given situation is m = 2.58 b.
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How do you know if a graph is inverse or direct?
Answers
In a direct relationship, Y increases when X increases. On a graph, a direct relationship always has a positive slope. Inverse relationship: An inverse relationship means that the variables change in opposite directions: one increases while the other decreases, and vice versa.
Now, According to the question:
Let's know:
Direct relationship:
A direct relationship means that both variables increase together or both decrease together.
In a direct relationship, Y increases when X increases.
On a graph, a direct relationship always has a positive slope.
Inverse relationship:
An inverse relationship means that the variables change in opposite directions: one increases while the other decreases, and vice versa.
In an inverse relationship, Y decreases when X increases.
On a graph, an inverse relationship always has a negative slope.
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What is the value of 18 exponet of 3?
54
21
5,832
324
Answers
Answer: 5832
Step-by-step explanation:
18^3 = 324 * 18 = 5832
Answer:
5,832
Step-by-step explanation:
18^3 = (18)(18)(18) = 5,832
How do you solve a system of equations with two variables by substitution?
Answers
To see the steps of Solutions Using Substitution with Two Variables.
Now, According to the question:
An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
Linear Equations: Solutions Using Substitution with Two Variables
To solve systems using substitution, follow this procedure:
Select one equation and solve it for one of its variables.In the other equation, substitute for the variable just solved.Solve the new equation.Substitute the value found into any equation involving both variables and solve for the other variable.Check the solution in both original equations.Learn more about Linear Equation at:
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What is the degree of the polynomial 2x² 5x³ 7x 8?
Answers
Answer:he degree of the polynomial 3x 8 + 4x 3 + 9x + 1 is 8. We know that the polynomial can be classified into polynomial with one variable and polynomial with multiple variables
Step-by-step explanation:
how to simplify and what the answer is
Answers
Answer: 27x to the power of 6, y to the power of 12
Step-by-step explanation:
Look at picture because the actual explanation is way too long.
the sum of he digits of a certain two digit number is 7 reversingits digits increase the number by nine
Answers
The first digit is 3 and the second 4 so the original number is 34
What is an order of an equation?
The highest-order derivative that a differential equation has is used to define the equation's order. The highest-order derivative of a differential equation is defined as its degree, which is expressed as a power.
Here, We
Let the first digit be a
Let the second digit be b
a + b = 7....(1)
The first order value:
a is a counting in tens. So actual value is 10(a)
b is counting in units. So actual value is 1(b)
10a + b...(2)
The second order value:
b is a counting in tens. So the actual value is 10(b)
a is counting in units. So actual value is 1(a)
10b + a....(3)
Now, we subtract equation(3) from (2) and we get
= (10b + a) -(10a + b) = 9
= 9b - 9a = 9
= b - a = 1...(4)
From equation(1)
a = 7 - b
Now, we put the value of a in equation(4) and we get
= b - (7-b) = 1
= b - 7 + b = 1
= 2b = 8
b = 4
Now, substitute the value of b in equation (1) and we get
a = 3
Hence, The first digit is 3 and the second 4 so the original number is 34
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