Which theorem shows that △ABC ≅ △DEF?There
are two triangles, triangle ABC and triangle DEF. Side AB is congruent
to side DE, side AC is congruent to side DF, side BC is congruent to
side EF.


A. The triangles are not congruent.

B. SAS Triangle Congruence Theorem

C. Isosceles Triangle Theorem

D. SSS Triangle Congruence Theorem

The total number of non-fictional biography books in the library will be equal to 1/5.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Let the total number of books is x.

3/5 of total books are non-fiction, then,

3/5 × x = 3/5x

1/3x of them are biographies.

Then, the number of non-fictional biographies are,

3/5 × 1/3

=1/5

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Answer:

100÷3 = 33.33, so 33.33 minutes

The required Inequality is $12x + $150 ≥ $380 where x is the minimum number of lawns Jacob will need to mow in order to buy the ticket. The solution of inequation is x ≥ 19.2 ~ 19.

An inequality is a mathematical expression in which both sides are not equal. Unlike equations, inequalities compare two values. Equal signs between are replaced by less than (or less than and equal), greater than (or greater than and equal ) sign.

When solving an inequality:

We have, total cost of electronic ticket i.e with all taxes = $380

Saved cost = $150

Cost of one mowing lawn = $12

let "x" be the number of lawns mowed by Jacob for earning the rest of money .

Total cost of x mowed lawns by Jacob।

= $12x .

Now, $12x + $150 ≥ $380 --(*)

This is the required Inequality and x is minimum number of lawns which Jacob have to mowed .

The solution of above Inequality,

Substracts 150 from both sides in (*)

12 x + 150 - 150 ≥ 380 - 150

=> 12x ≥ 230

dividing by positive 12 both sides we get,

=> x/12 ≥ 230/12

=> x ≥ 19.16

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Complete question:

Jacob is saving to buy an electronic ticket that costs $380 including tax and has saved $150. Jared plans to earn the rest of the money by mowing lawns and will charge $12 for each lawn he mows. Write an inequality to find x, the minimum number of lawns Jacob will need to mow in order to buy the ticket. Show how to solve the inequality and what is solution.

The division of the polynomial x^2 + 2*x - 6 by (x + 1), using the long division method of dividing polynomials is x + 1 - 7/(x + 1)

The long division method allows the division of large numbers (which is the dividend) into the number of groups of the divisor and a remainder which is a value less than the expressed value of the divisor.

The expression \_f_rac{x}{y} x^2 + 2*x - 6/x + 1 can be presented as follows;

The long division showing the steps can be obtained using code found online as follows;

[tex]\begin{array}{*1r {\arraycolsep}{\arraycolsep} *{11}l} & && x + 1 \\\cline{4-3}& &x+1& \longdiv {) x^2 +2\cdot x - 6& & & & & \\ & & & x^2 +x \\\cline{4-} && &\ \ \ x -6& \\ & & \ \ \ & \ \ \ x +1 \\\cline{4-} & & & \ \ \ \ \ \ \ -7 & \\ \cline{4-} \end{array}[/tex]

The remainder of the long division is -7, therefore, we get;

[tex]\dfrac{x^2+2\cdot x-6}{x + 1} = x + 1 - \dfrac{7}{x+1}[/tex]

The value of the expression, \_f_rac{x}{y} x^2 + 2*x - 6/x + 1 following the long division is; x + 1 - 7/(x + 1)

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Answer:

I don't know what is the answer

The total number of ways there are for eight blue-shirt and five red-shirt to stand in a line so that no two red-shirts stand next to each other is 609638400.

A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already ordered, or arranging its members into a sequence or linear order.

Given:

The eight blue-shirt and five red-shirt stands in a line,

Calculate the number of ways as shown below,

The total number of ways = Total no of permutations of blue ones × Total permutation of 9 positions, taken 5 at a time,

N = 8! × 9! / (9 - 5)!

N = 40320 × 362880 /24

N = 609638400

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To solve for x when y is given, we can use the given equation y=(1/4)x.By multiplying both sides of the equation by 4.x=28, we may find the value of x.

To solve for x when y is given, we can use the given equation y=(1/4)x. By multiplying both sides of the equation by 4.x=28, we may find the value of x. This gives us the equation 4y=x. Then, we can substitute the given value of y, 7, into the equation. This gives us 4(7)=x. Simplifying this equation gives us 28=x, which is the value of x when y is 7.

y=(1/4)x

4y=x

4(7)=x

28=x

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Answer:

Step-by-step explanation:

so we start with Sara's

-3x+14=18-5x

for properties of equality, we need to isolate the x variable

-3x=4-5x

2x=4

x=2

that is correct

now we go to Ethan's

2x=5-1/2x

2 1/2x=5

x=2

now we have confirmed that x is equal to 2

hope this helped

The integer for vector 1 {2,6,-7}, integer for vector 2 is 10,8,-14}, integer for vector 3 is {4,12,-14}, integer for vector 4 is {14,-2,-7} and integer for vector 5 is {22,0,-14}. (all these vectors are in span {V1 and V2})

List five vectors in Span {v_1, v_2}?

1) V1+v2={8,2,-7 }+{-6,4,0 }

={2,6,-7}

2) 2v1+v2={16,4,-14}+{-6,4,0}

={10,8,-14}

3)2v1+2v2={16,4,-14}+{-12,8,0}

={4,12,-14}

4)V1-v2={8,2,-7}-{-6,4,0}

={14,-2,-7}

5)2v1-v2={16,4,-14}-{-6,4,0}

={22,0,-14}

All of these vectors are contained within the span.

{v1,v2}={av1+bv2:ab∈r}

A matrix is a rectangular variety of ordered numbers (real or complex) or functions .Assume we want to express the following information about   Ram and his two friends Rohan and Yash's possession of pens and pencils:
Ram       has      20     pens       and       7       pencils,

Rohan    has      15     pens       and       5       pencils,

Yash       has      12     pens       and       3       pencils

Now, this could be arranged in tabular form as follows,
⎢20  7⎢
⎢15   5⎢                            
⎢12   3⎢        

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The critical points for the inequality (2x+5/x+2>_ x-1/x-2), are x = -2 and x = 2. Option A

Generally, To find the critical points for the inequality, you need to set the expression on the left side of the inequality equal to zero and solve for x. This will give you the values of x where the inequality changes direction.

In this case, the inequality is:

2x + 5/(x + 2) > 0

To find the critical points, you can set the expression on the left side equal to zero and solve for x:

0 = 2x + 5/(x + 2)

0 = 2x + 5 - 5/(x + 2)

0 = 2x - 5 + 5/(x + 2)

0 = 2x - 5 + 5(x + 2)/(x + 2)

0 = 2x - 5 + 5x + 10

0 = 7x - 15

x = -2, x = 2

Therefore, the critical points for the inequality are x = -2 and x = 2.

It is not correct to say that the critical points are x = -6 and x = 2, x = -4 and x = 2, or x = 2. These values do not correspond to any points where the inequality changes direction.

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Answer: B -6 and x=2

Step-by-step explanation: for edgen.

Answer:

0.44x + 0.85y <= 6

Step-by-step explanation:

We can write the total cost of the apples as 0.44x, and the total cost of the pears as 0.85y. Since the total cost cannot exceed $6, we can write the following inequality:

0.44x + 0.85y <= 6

This inequality represents the numbers of apples and pears you can buy at the market, given that you can spend at most $6.

Answer:

0.44x + 0.85y ≤ 6

Step-by-step explanation:

To represent the number of apples and pears you can buy, you can use the following inequality: 0.44x + 0.85y ≤ 6. This inequality states that the total cost of the apples and pears, which is 0.44x + 0.85y, must be less than or equal to $6. This means that you cannot spend more than $6 at the market, and the number of apples and pears you can buy is limited by this budget constraint.

Answer:

$358.4

Step-by-step explanation:

To calculate the salesperson's commission, you can multiply the total sales by the commission rate. In this case, the commission is $3600 * 0.099 = $<<3600*0.099=358.4>>358.4. So the salesperson's commission would be $358.4.

The number of transgendered people would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis is 19.00

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is H0.

To determine if a theory regarding markets, investing methods, or economies is correct or wrong, quantitative analysts employ the null hypothesis, often known as the conjecture.

The number of transgendered people would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis is 19.00

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The assumption of normality is important for valid results. If the residuals do not follow a normal distribution, then confidence intervals may not be accurate and should not be trusted.

The assumption of normality is a key element of statistical analysis. It suggests that a dataset follows a normal bell-shaped curve, which is important for reliable results. If the residuals of a dataset do not follow a normal distribution, then the assumptions of statistical techniques such as confidence intervals, least-squares formulas, and sample randomness, may be unreliable. This means that the results of any statistical analysis will be affected and not be as accurate as they could be. In this case, confidence intervals may be particularly unreliable since they rely on the assumption that the data is normally distributed. Therefore, if the residuals do not follow a normal distribution, it is important to investigate further to ensure the accuracy of the results.

example;

The mean of the data is 8.3 and the standard deviation is 4.2.

We can calculate the z-score for any given value by subtracting the mean from the value and then dividing by the standard deviation.

if the value is 16, then the z-score would be:

z = (16 - 8.3) / 4.2 = 2.33.

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The largest number of stones that could be in the box in the wagon will be 30.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

His wagon can carry 1.2 kg without falling apart.

And, The stones are in a wooden box that weighs 150 grams, and each stone weighs 35 grams.

Now,

Let the number of stones = x

So, We can formulate;

⇒ 150 + 35x = 1200

Solve for x as;

⇒ 35x = 1200 - 150

⇒ 35x = 1050

⇒ x = 1050/ 35

⇒ x = 30

Thus, There are 30 largest number of stones that could be in the box in the wagon.

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The angles ∠ 5 and ∠ 7  are supplementary angles.

Supplementary angles are those angles that sum up to 180 degrees.

Given is a figure, with two parallel lines and a transversal

In the options,

(∠ 5 and ∠ 8) (∠ 2 and ∠ 3) are vertically opposite angles.

∠ 1 and ∠ 5 are corresponding angles

But ∠ 5 and ∠ 7 are forming linear pair, and we know that, two angles forming linear pairs are supplementary angles,

Hence, The angles ∠ 5 and ∠ 7  are supplementary angles.

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Answer:

d. y = (x - 1)(x-3)²(x + 2)²

Step-by-step explanation:

When there is a local max or local min on the x-intercept, then the function on the x-intercept is raised to an even power.

At x=3 and x=-2, the function goes up then down, or down then up.

If the function goes through an x-intercept when there is no local max or local min on the x-intercept, then the function on the x-intercept is raised to an odd power.

At x=1, the function goes through the x-intercept.

Hence, d is the answer.

Answer:

A

Step-by-step explanation:

Sequence A works.

With sequence B, the triangles will be next to each other.

Answer: A

Mr. Green mowed more of the lawn. 2/5 of the lawn still needs to be mowed, according to the concept of proportion or ratio.

To get this answer, we can first set up a proportion or ratio to compare how much of the lawn each person mowed. Mr. Green mowed 2/5 of his lawn and his son mowed 1/3 of it.  

2/5 = x/1, We can then cross multiply to solve for x.

2x = 5/3 x = 5/6  Since 5/6 is greater than 1/3, this means that Mr. Green mowed more of the lawn than his son. This means that 2/5 of the lawn still needs to be mowed.

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Answer:

[tex]\sin(\theta ) = \dfrac{\textrm{opposite}}{\textrm{hypotenuse}}[/tex]

Hence,

[tex]\sin(A) =\dfrac{20}{29}[/tex]

Answer:

Step-by-step explanation:

they are telling you the standard deviation ,  it's 500

then they ask, what's 3 times that.   It's kinda obvious,  when I put it in words like that so i'll let you do that math.  17,000 + (3*500) = ?

b)

17000 - (2*500) = ?

c)

This is the bell curve numbers of 1 deviation,    it's 68%, if you don't recall

d)

it will be  1/2 of the 2nd deviation, or  95% * 0.5  = 47.5%

e)

this is the tiny amount outside of the main part of the 2 deviation on the bell curve.

5% is outside of the 2nd deviation.   so it's half of that or  2.5%

Understand?????

:/

The chemical formula for ammonium carbonate is (NH₄)₂CO₃. Therefore, option (C) is correct.

When heated, ammonium carbonate, also known as ()2, rapidly breaks down into ammonia and carbon dioxide. It functions as a smelling salt and a leavening agent. Ammonium carbonate, often known as baker's ammonia, was used before baking soda and baking powder as leaveners.

Sal volatile contains ammonium carbonate, and salt of hartshorn when baked emits a strong odour. At standard pressure and temperature, two processes lead to the gradual breakdown of ammonium carbonate. The pure ammonium carbonate sample will combine with different byproducts.

Upon spontaneous dissociation, ammonium carbonate can separate into ammonium bicarbonate and ammonia. which results in the addition of more ammonia, carbon dioxide, and water.

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Answer:

The formula for the ammonium ion: NH4+

The formula for the nitrate ion: NO3–  

A chromate ion consists of four oxygen atoms bonded to a chromium atom. It has two extra electrons. The formula of this ion: CrO42–

Heres all three. Hope i helped

By setting up the equation and solving we get the total amount of money was 1800.

A ratio is a way of comparing two or more quantities. It is expressed as a fraction or a decimal, and it represents the relative sizes of the quantities being compared.

An equation is a mathematical statement that shows the equality of two expressions. An equation typically consists of two expressions separated by an equals sign (=), and it states that the expressions are equal in value.

we can set up the following equation:

(2700 / X) = (3 / 4)

We can solve this equation for X by multiplying both sides by X:

2700 = (3 / 4) * X

2700 = (3 / 4) * X

5400 = 3X

X = 5400 / 3

X = 1800

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By RHS congruence criterion, since it is given that EB=BD, AE=CB, ∠A=∠C=90°

RHS Congruence Property:

Two right triangles are congruent if the hypotenuse and one side of the first triangle are respectively equal to the hypotenuse and one side of the second.

If the length of the hypotenuse and one side of one triangle is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent.

ΔABE ≅ ΔACD

The hypotenuse and one side of a right-angled triangle are respectively equal to the hypotenuse and one side of another right-angled triangle.

Therefore,

ΔABE≅ΔCDB.

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Answer:

Unit price 12.16 for 4.07 pounds is $2.99 per pound

Unit price 14.99 for 5.11 pounds is $2.93 per pound

The best deal is the 14.99 per 4.11 pounds

Step-by-step explanation:

Unit price 12.16/4.07 = 2.99 rounded to the nearest cent

Unit price 14.99/5.11 = 2.93 rounded to the nearest cent.

Answer:

1) $2.99

2)$2.93

The better buy is the 4.07 pound bag

Step-by-step explanation:

To find the unit price you find the cost per pound

$12.16 : 4.07

? : 1

4.07x = 12.16

x = 2.98771499

$2.99

$14.99 : 5.11

? : 1

5.11x = 14.99

x= 2.9334638

One solution for the equation [tex]\frac{1}{2} (6x - 2) = 2[/tex] is x = 1

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

According to the given information

The equation given to us is

[tex]\frac{1}{2} (6x - 2) = 2[/tex]

Solving the above equation

We get

3x - 1 = 2

3x = 2 + 1

3x = 3

x = 1

We have only

One solution for the equation [tex]\frac{1}{2} (6x - 2) = 2[/tex] is x = 1

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When metal is composed of copper and zinc in a 3:2 by volume ratio, the mass of metal in a 100cm cube is 1600g.

A percentage is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province. The population percentage is marked by the letter p, whereas the sample proportion is denoted by the letter p. Thus, p=0.43 if 43% of individuals visiting a business make a purchase before leaving. If 78 customers out of 200 enter the store and make a purchase, p=78200=0.39.

Here,

1/8.9=100/x

x=890g

1/7.1=100/x

x=710g

Total mass of metal=890+710

=1600g

The mass of metal in 100cm cube is 1600g when metal is made up of copper and zinc in the ratio 3:2 by volume.

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Answer: n > 3

Step-by-step explanation:

A circle above 3 going right

The value of [tex]r^{\prime}(t)[/tex] is [tex]\left\langle 3,4 t, 12 t^2\right\rangle[/tex].

The value of unit tangent vector T(1) is [tex]\left\langle\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right\rangle \quad[/tex]

The value of r''(t) is [tex]\langle 0,4,24 t\rangle[/tex]

The value of r'(t) × r ''(t) is [tex]\left(48 t^2\right) \vec{i}-(68 t)\vec{j}+(12)\vec{k}[/tex]

As per the data given in the question r(t) = 3t, [tex]2t^{2}[/tex], [tex]4t^{3}[/tex]

From r(t) we can find the value of [tex]r^{\prime}(t)[/tex].

For that we have to differentiate each term of r(t).

[tex]r^{\prime}(t)=\left\langle 3,4 t, 12 t^2\right\rangle[/tex]

Tangent and Normal Vectors:

The tangent and unit normal vectors are calculated from the derivatives of the parameter settings of the curve.

In particular, to determine the unit tangent vector, we have:

[tex]& \vec{T}(t)=\frac{\partial^{\prime}(t)}{\left|r^{\prime}(t)\right|} \\[/tex]

Therefore [tex]\vec{T}(1)=\frac{\partial^{\prime}(1)}{\left|\partial^{\prime}(1)\right|}[/tex]

[tex]\partial^{\prime}(1)=\langle 3,4,12\rangle \\& \therefore\left|r^{\prime}(1)\right|=\sqrt{9+16+144}\\=\sqrt{169}\\=13[/tex]

[tex]\vec{T}(1)=\frac{\langle 3,4,12\rangle}{13}[/tex]

[tex]& =\left\langle\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right\rangle[/tex]

[tex]\vec{T}(1)=\left\langle\frac{3}{13},\frac{4}{13}, \frac{12}{13}\right\rangle[/tex]

[tex]\vec{T}(1)=\left\langle\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right\rangle \quad[/tex]

Now [tex]r^{\prime}(t)=\left\langle 3,4 t, 12 t^2\right\rangle \\[/tex]

From r'(t) we can find the value of r''(t).

For that we have to differentiate each term of r'(t)

[tex]r^{\prime \prime}(t)=\langle 0,4,24 t\rangle[/tex]

Now we have to find the value of r'(t) × r ''(t).

[tex]\partial^{\prime}(t) \times \partial^{\prime \prime}(t)=\left|\begin{array}{ccc}i & j & k \\3 & 4 t & 12 t^2 \\0 & 4 & 24 t\end{array}\right|[/tex]

[tex]&=i\left(96 t^2-48 t^2\right)-j(68 t)+k(12) \\&=\left(48 t^2\right) \vec{i}-\vec{j}(68 t)+\vec{k}(12) \\[/tex]

[tex]r^{\prime}(t) \times r^{\prime \prime}(t)=\left(48 t^2\right) \vec{i}-\vec{j}(68 t)+\vec{k}(12)[/tex]

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