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Answer: The solution to the system of equations is (1/3,-4/3).

Step-by-step explanation: Yes

Answer:

Step-by-step explanation:

To prove that a quadrilateral ABCD is a trapezium when the diagonals intersect at a point O such that AO/BO=CO/DO, we can use the fact that opposite sides of a trapezium are parallel.

First, let's draw a diagram to represent the given information:

[asy]

pair A, B, C, D, O;

A = (0,0);

B = (2,0);

C = (3,2);

D = (1,2);

O = intersection point(A-C, B--D);

draw(A--B--C--D--cycle);

draw(A-C);

draw(B--D);

label("A", A, W);

label("B", B, E);

label("C", C, E);

label("D", D, W);

label("O", O, N);

label("$\theta_1$", (B+O)/2, NE);

label("$\theta_2$", (O+D)/2, NE);

label("$\theta_3$", (O+C)/2, NW);

label("$\theta_4$", (A+O)/2, NW);

[/asy]

Since the diagonals intersect at point O, the angles formed by the diagonals at O are supplementary (that is, they add up to 180 degrees). In other words, we have:

θ1 + θ2 = 180 degrees

θ3 + θ4 = 180 degrees

Since AO/BO=CO/DO, the triangles AOB and COD are similar. This means that the ratios of their sides are equal. We can write this as:

AO/BO = CO/DO

We can also write this as:

AO/DO = CO/BO

Then, since the angles formed by the diagonals at O are supplementary, we have:

θ1 + θ2 = 180 degrees

θ1 + θ4 = 180 degrees

Subtracting these two equations gives us:

θ2 - θ4 = 0

Since the angles are equal, they are also opposite angles of the quadrilateral ABCD. Therefore, the opposite sides of AB and CD are parallel, which means that ABCD is a trapezium.

Answer:

2(x-3)

Step-by-step explanation: 2 is being multiplied by the difference (subtraction) of x-3.

1). The relation given; { (−1, 8), (0, 15), (1, –4), (2, 0) } as given is a function.

2). The relation given; { (-5, 2), (5, 2), (0, -3), (3,-8) } as given is a function.

3). The relation given; { (-2, 7), (6, 2), (−2, −3), (0, 9) } as given is not a function.

4). The relation given; { (7,2), (4,-6), (2,-2). (4,-9) } as given is not a function.

5). The relation given; { (2, 3), (2, 4), (2, 5), (2,6) } as given is not a function.

6). The relation given; { (1,4), (2, 4), (3, 4), (4, -4) } as given is a function.

It is important to know that a function is a special kind of relation in which case no one input value, x is assigned more than one output value.

On this note, when a relation is such that one of its input values is assigned two or more output values; such relation is not a function.

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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

The values of a , b and c from the equation is ( 3 , 0 , -1 )

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

( 6 × 10ᵃ ) + ( 6 × 10ᵇ ) + ( 6 × 10^c ) = 6006.6   be equation (1)

Now , the number 6006.6 is written as

6000 + 6 + 0.6 = 6006.6

On simplifying the equation , we get

( 6 × 10ᵃ ) = 6000

Divide by 6 on both sides of the equation , we get

10ᵃ = 1000

So , 10ᵃ = 10³

Therefore , the value of a = 3

Now , ( 6 × 10ᵇ ) = 6

Divide by 6 on both sides of the equation , we get

10ᵇ = 1

when b = 0

10⁰ = 1

Therefore , the value of b = 0

Now , ( 6 × 10^c ) = 0.6

Divide by 6 on both sides of the equation , we get

10^c = 0.1

when c = -1

10⁻¹ = 0.1

Therefore , the value of c = -1

Hence , the value of a , b and c is 3 , 0 and -1 respectively

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Answer: A linear model is a type of mathematical equation that describes the relationship between two variables, such as median income and the number of bachelor's degrees per 1000 people. In order to estimate the number of bachelor's degrees per 1000 people for Mississippi based on the median income, you would need a linear equation that describes that relationship.

Without that equation, it's not possible to estimate the number of bachelor's degrees per 1000 people for Mississippi based on the median income.

Additionally, without more information about the data that the model was trained on, the correlation between median income and the number of bachelor's degrees per 1000 people and how accurate and reliable the model is, it's difficult to determine the goodness of this estimate. However, in general, a linear model may provide only a rough estimate, especially if the relationship between the variables is complex or non-linear.

Step-by-step explanation:

The solution is Option A. , Option C.

The equations which are also proportional is y = 3x and x = 2y

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the values of x = { 0 , 3 , 6 }

Let the values of y = { 3 , 6 , 9 }

Now , the proportional equation is y = 3x

So , the proportionality constant is k = 3

b)

Let the values of x = { 0 , 6 , 12 }

Let the values of y = { 0 , 3 , 6 }

Now , the proportional equation is x = 2y

So , the proportionality constant is k = 2

Hence , the equations are y = 3x and x = 2y

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Answer: The solution is Option A. , Option C.

Step-by-step explanation:

The equations which are also proportional is y = 3x and x = 2y

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the values of x = { 0 , 3 , 6 }

Let the values of y = { 3 , 6 , 9 }

Now , the proportional equation is y = 3x

So , the proportionality constant is k = 3

b)

Let the values of x = { 0 , 6 , 12 }

Let the values of y = { 0 , 3 , 6 }

Now , the proportional equation is x = 2y

So , the proportionality constant is k = 2

Hence , the equations are y = 3x and x = 2y

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The answer is: 55 crayons.

Explanation: He has 6 boxes with 8 crayons in each. 6 times 8 = 48. Plus the seven left from the other box = 48+7= 55 crayons.!!

Answer:

0.22

Step-by-step explanation:

Since 5 rounds up, it would be 0.22

Answer:

0.22 Is the answer.

I wish you luck on your assignments.

Answer:

To solve this problem, we can set up the following equation:

Huilan's age + Thomas's age = 79

Let H be Huilan's age and T be Thomas's age. We can then rewrite the equation as:

H + T = 79

We are told that Huilan is 7 years older than Thomas, so we can write the following equation:

H = T + 7

Substituting the second equation into the first equation, we get:

(T + 7) + T = 79

Combining like terms, we get:

2T + 7 = 79

Subtracting 7 from both sides, we get:

2T = 72

Dividing both sides by 2, we get:

T = 36

Therefore, Thomas's age is 36 years.

Step-by-step explanation:

Answer:

let Thomas age be a

there fore, hullans age is a+7

(a+7)+a=79

2a=79-7

2a=72

a=36

Eric picks 17/40 baskets of strawberries more than Kiki.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

Eric picks 5/8 basket of strawberries.

And, Kiki picks 1/5 basket of strawberries.

Hence, After subtraction we get;

Number of baskets of strawberries more than Kiki = 5/8 - 1/5

                                                                              = (25 - 8) / 40

                                                                              = 17/40

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The term below that refers to events that all have the same probability of occurring is; (2) equal probability events

By definition, we can say that the probability of occurrence of an event is defined as the number of trials in which a particular event happened divided by the total number of trials.

Probability = number of trials in which event happened/total number of trials.

Now, when we say that all items have the same probability of occurring, what we simply mean is they all have equal chance of occurrence or they all have equal outcomes. For example when we flip a coin, we have equal chance of getting a head or tail.

Thus, the term that best defines the above would be Option 2.

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On solving the provided question we can say that - the increased value in fraction will be [tex]3\frac{1}{4}[/tex]

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

we have,

initial =  [tex]4\frac{5}{6}[/tex]

increased by =  [tex]4\frac{1}{4}[/tex]

son difference is = [tex]3\frac{1}{4}[/tex]

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so, we can say that therefore, the sample of 20 cheerleaders used for the study provides the solution to the issue.

A sample is a controlled, abridged version of a bigger group. It is a demographic subset containing characteristics from a larger population. Samples are used in statistical testing when population sizes are too large to accommodate all prospective participants or observers in the experiment.

The 20 cheerleaders that are used as a sample for this study are.

Explanation: Because only 20 cheerleaders were chosen from high schools in California for the research of the banana influence on speed and endurance, the sample available was limited to those 20 cheerleaders. As a result, the sample's results were based on those 20 cheerleaders.

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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

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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The ratio of number of burgers without onions to the number of burgers with onions is 4:1.

The ratio of numbers implies the relationship between the numbers when expressed in its simplest fraction. The relationship can be written in form of a/ b or a:b.

Given in the question that Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. Then the ratio required can be expressed as;

ratio of number of burgers without onions to burgers with onions = (number of burgers without onions)/ (number of burgers with onions)

                = 12/ 3

                = 4/ 1

The ratio of number of burgers without onions to burgers with onions = 4:1

Therefore, the ratio of the number of burgers without onions to the number of burgers with onions is 4:1.

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Answer:

x = 12

Step-by-step explanation:

i. 29 = 2x + 5 [The length of two tangents to a circle at the point of contact from the same external point are equal]

ii. 29 - 5 = 2x

iii. 24 = 2x

iv. x = 24/2

v. x = 12

The total amount that Latoya ended up paying for the machinery, was $ 13, 080 .96

The amount of interest that Latoya paid was $ 980.96

The total amount paid by Latoya for the machinery can be found as :

= Down payment of the machinery + ( Monthly payments x Number of months per year x Number of years )

= 1, 800 + ( 313. 36 x 12 x 3 )

= $ 13, 080 .96

The total interest paid on the loan was :

= ( Monthly payments x Number of months per year x Number of years ) - Worth of the machine - down payment

= ( 313. 36 x 12 x 3 ) - 12, 100 - 1, 800

= $ 980.96

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The number of students at the open house is B. 468.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

We know if a and b are two quantities in a total quantity (ax + bx) the amount of a single quantity can be obtained by [a/(a+b)]× (ax + bx).

Given, The ratio of students to adults at the open house is 9 : 7 and the total number of students and adults at that place is 832.

Therefore,

The number of students is,

= (9/9+7)×832.

= (9/16)×832.

= 9×52.

= 468.

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Answer:

A.

domestic: 316 / 96 / 412

international: 76 / 51 / 127

total: 392 / 147 / 539

B. 51 its the smallest number

C. I don't know what association means but 76.2% of domestic flights land on time and 63% of international flights land on time so id say its positive

Answer: what

Step-by-step explanation:

I'm assuming x and y intercepts which would be (2.5,0) and (0,10)

Summary of slope of parallel lines:

Parallel lines have equal slopes. The parallel lines are equally inclined with regard to the positive x-axis, and this is taken into account when calculating a line's slope.

If one line has a slope of m1, another line has a slope of m2, and both lines are parallel, then we get m1 = m2.

The coefficients for "x" and "y" in the equations that depict parallel lines are identical.

Ax + by + c2 = 0 is the line that is parallel to ax + by + c1 = 0. Observation reveals that the x and y coefficients in both equations are equivalent.

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The number remaining in the village is 30.

We have to note that the case in which the population of the community is being reduced because of the fact that the community is being ravaged by disease is a case of a decrease in the population and is a problem of exponential decrease.

Then we would have that;

N =Noe^-rt

N = Number at time t

No = Initial number

r = spread rate

t = time taken

Then;

N = 200e^-0.95 * 2

N = 30

Thus, they would have only 30 people left.

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The representation of the set builder notations are:

From the question, we have the following parameters that can be used in our computation:

The set builder notations

Solving: set builder notation 1

This is given as

{y | 22.3 < y ≤ 77.5}

The less than (<) operator means that the smallest value of y is greater than 22.3 and the operator ≤ means that the highest is 77.5

Solving: set builder notation 2

This is given as

{w | w ∈ Z}

The notation Z means integers

This means that the set w is the set of all integers

Solving: set builder notation 3

This is given as

{x | x > -1}

The greater than (>) operator means that the smallest value of y is greater than -1

Solving: set builder notation 4

This is given as

{t | t ∈ Q}

The notation Q means rational numbers

This means that the set t is the set of all rational numbers

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The closest to the number of yards of ribbon Mario had altogether will be 11 yards

A fraction is a part of the whole number, and a way to split up a number into equal parts. Or, A number that is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

Given that;

Mario had 8 1/5 yards of ribbon for a project.

And, Sue gave him 2 3/4 more yards of ribbon.

Since Mario had 8 1/5 yards of ribbon for a project. And, Sue gave him 2 3/4 more yards of ribbon.

Hence, Total ribbon for the project Mario have = 8 1/5 yards + 2 3/4 yards

= 41/5 + 11/4

= (164 + 55) / 20

= 219 / 20 yards

= 10.95 yards

≈ 11 yards

Thus, the total ribbon for the project Mario has = 11 yards

The complete question is given below;-

Mario had 8 1/5 yards of ribbon for a project. Sue gave him 2 3/4 more yards of ribbon. Which is closest to the number of yards of ribbon Mario had altogether?

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Answer:  To calculate the area of each part of the circle, we need to first find the total area of the circle and then divide it by the number of parts.

The formula for the area of a circle is A = πr², where A is the area, r is the radius, and π is approximately equal to 3.14.

In this case, the radius of the circle is 8 cm, so the area of the circle is A = π * 8² = 3.14 * 64 = 200.96 cm².

Since the circle is divided into 6 parts of equal size, the area of each part is equal to the total area of the circle divided by the number of parts. Therefore, the area of each part is 200.96 cm² / 6 = 33.49 cm².

Rounded to 2 decimal places, the area of each part is 33.49 cm² ≈ 33.50 cm².

Step-by-step explanation: