These triangles are congruent by the triangle congruence postulate ___

Answer:

78 13/24

Step-by-step explanation:

3 5/8=29/8

21 2/3=65/3

29/8×65/3=1885/24=78 13/24

So, your answer is 78 13/24

Hey there!

3 5/8 * 21 2/3

= 3 * 8 + 5 / 8 * 21 * 3 + 2 / 3

= 24 + 5 / 8 * 63 + 2 / 3

= 29 / 8 * 65 / 2

= 29 * 65 / 8 * 2

= 1,885 / 16

= 78 13/24

Therefore, your answer should be:

78 13/24

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer: 4 10/11

Step-by-step explanation:

Well, doing 4021836 - 1987269 on paper, you would get the answer of 2034567

solu. 2034272

Alternate form. 2.034272*10^2

The total surface area of the box is 138in².

What is surface area of cuboid?

Formula for calculating the surface area of the box S = 2(LW+LH+WH) where

L is the length of the box

W is the width of the box

H is the height of the box

If the box is square based with dimension 4 * 4in, then L = W = 4in. substituting this values given into the formula we will have;

S = 2(4(4)+4H + 4H)

S = 2(16+8H)

S = 32+16H

Hence, The function that represents the surface area of this box as a

function of its height is S = 32+16H where H is the height of the box

Given H = 6.5in, to evaluate the function, we will substitute h = 6.5in into the modeled equation;

S = 32+16H

S = 32+16(6.5)

S = 32+106

S = 138in²

Hence the total surface area of the box is 138in².

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Answer:

Solutions below

Step-by-step explanation:

This question requires the concept of substitution and order of operations (Bracket > Multiplication / Division > Addition / Subtraction).

Given x = - 2, y = - 3 and z = 4,

a) 2 x + 3 y = 2 (- 2) + 3 (- 3) = - 4 + (- 9) = - 4 - 9

= - 13

b) 2(y - z) = 2 (- 3 - 4) = 2 (- 7) = - 14

c)

[tex] \frac{6x}{2y} \\ = \frac{6( - 2)}{2( - 3)} \\ = \frac{ - 12}{ - 6} \\ = 2[/tex]

The given arithmetic series can be expressed in summation notation as [tex]\sum\limits^8_{n=1} {(2n+5)}[/tex] or in simplified notation [tex]40+2 \sum\limits^8_{n=1} {n}[/tex]

The summation notation is used to express long summation in one expression.

The given arithmetic series is:

       7+9+11+ . . . . . . +21

Find the explicit formula for the nth term in the given series.

Recall:

a(n) = a(1) + (n-1) . d

where:

a(1) = the first term

d = common difference = a(2) - a(1) = a(n) - a(n-1)

From the series, we get:

a(1) = 7

d = 9 - 7 = 2

Hence,

a(n) =  a(1) + (n-1) . d

a(n) = 7 + (n-1) . 2

a(n) = 2n + 5

Find number of terms in the given series.

From the given series, we know that the last term is 21.

Let the last term be a(n), then,

a(n) = 2n + 5

21 = 2n + 5

2n = 16

n = 8

Write the summation notation with lower limit n = 1 and upper limit n = 8.

[tex]\sum\limits^8_{n=1} {a(n)}= \sum\limits^8_{n=1} {(2n+5)}[/tex]

If necessary, simplify the summation.

[tex]\sum\limits^8_{n=1} {(2n+5)}= \sum\limits^8_{n=1} {2n}+ \sum\limits^8_{n=1} {5}[/tex]

[tex]= \sum\limits^8_{n=1} {2n}+ 8\times5[/tex]

[tex]=40+2 \sum\limits^8_{n=1} {n}[/tex]

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According to the given statement;

The probability of student Who scored less than 350 is 0.0643.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. The concept of probability was developed to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.

According to the given value;

Population Mean,μ = 528

Population Standard Deviation,σ = 117

X follows normal distribution

I.e X ~ N ( μ = 528 ,σ = 117 )

formula for z score is

Z =

0

Subtract the mean and then divide by the standard deviation to turn x into a standard Normal z

X ≤ 350

(x-528)/117 ≤ (350-528)/117

z ≤ -1.52

Now, by using standard normal distribution table

area left of -1.52

= 0.0643

Hence,The required probability is 0.0643.

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8.06 is  the distance between the two points  .

What is distance in math?

distance d = [tex]\sqrt{( 5 + 3)^{2} + ( -2 + 1)^{2} }[/tex]

              d = [tex]\sqrt{8^{2} + (-1)^{2} }[/tex]

                d = [tex]\sqrt{64 + 1}[/tex]

                d = √ 65

                d = 8.06225  ≈ 8.06

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b*7<= -24

<= iz a less than or equal symbol

IfIf you swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder is: 0.54 seconds.

First step is to calculate the different in speed between first and fourth length

Using this formula

Speed =-First length time in seconds +(- Fourth length time in seconds)

Let plug in the formula

Speed=-0.23+(-0.42)

Speed=-0.65

Second step is to calculate the third length

Speed=-0.65+0.11

Speed=-0.54 seconds

Therefore If you swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder is: 0.54 seconds.

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Answer:

well done ......hope it's helpful

Answer:

(y+4)²

Step-by-step explanation:

[tex](a+b)^2=a^2 + 2ab+b^2[/tex]

Here, a=y and b=4.

Answer: 4.95

Step-by-step explanation:

54.25÷6.2−3.8=

54.25/6.2−3.8=

8.75-3.8=

8.75-3.80=

8-3+0.75-0.80=

5-0.05=4.95

Answer:

A. -17/5

Step-by-step explanation:

h= -17/5

Hope this helps! :)

The value of x so that the equation based on a and b has a solution is x = -4/3

 An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

   Equations can be graphed, just like a function.

     As we can see, we have the following equation:

a + 8 = -4(xb)

  and we have the values of the coefficients a and b, and these are:

   We substitute these values in the equation:

(8) + 8 = -4 [x(3)] We solve the equation

16 = -4(3x)

16 = -12x

x = 16-/12

x = 8/-6

x = 4/-3

x = -4/3

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The triangle of ABC is a right-angle triangle is true.

In Triangle of ABC

⇒(AC)^2=(BC)^2+(AB)^2 ----equation (1)

given by

Pythagoras theorem,

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

The hypotenuse is the longest side in this situation because it makes an angle of 90°

⇒(hypotenuse)^2=(one side)^2+(other side)^2 ---equation (2)

comparing one (1) and (2)

we get, AC is a hypotenuse of a triangle.

⇒ hypotenuse is the longest side of a right-angled, opposite the right angle.

⇒ opposite angle of AC is ⇒∠ B.

Hence, ∠ B is a right angle of triangle ABC. so, the triangle of ABC is a right angle triangle is true.

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Answer:

256

Step-by-step explanation:

20-8=12

12+4=16

16x16=256

Answer:

256

Step-by-step explanation:

Answer:

radius: 3.66 Diameter: 7.32

Step-by-step explanation:

Radius =  C/2π  3.6605636911136

Diameter = C/2π7.3211273822272

After determining whether y is a function of x we have come to conclusion that y is not a function of x.

x² = 3y + y

x² = 4y

y = x²/ 4

Here x has two values of -x and x as -x² = x². Therefore, y is not a function of x.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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In topology, the Pointcare conjecture is the one that states a 3-dimensional mainfold is the same as the 3-dimensional sphere.

Topology is a branch derived from geometry, this branch focuses on studying and analyzing geometrical properties and spatial relationships. One of the focuses of this area is the equivalences of some shapes or spaces.

This conjecture created by Pointcare in the 19th century proposes a three dimensional mainfold is the same or it is equivalent to a three dimensional sphere.

This conjecture was first proven as valid by Pointcare and other mathematicians/experts in the topic. However, some years later the same Pointcare and other experts showes this conjuction is not always true and therefore it is not valid.

Despide this, to this day this conjecture remains very popular and people around the world are still trying to prove it or dispprove it.

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The best method to solve a problem is Brainstorming.

According to the statement

We have to find that the which method is the best for solving the problem.

So, For this purpose, we know that the

A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem.

From the given information:

There are different methods to solving this problem.

Then

we know that the to solve a problem there are lot of the method, but the some method are the best to solve the problem.

The method is called a brainstorming session.

It is the Brainstorming is a problem-solving activity where students build on or develop higher order thinking skills. Encourages creative thought. Brainstorming encourages students to think creatively.

And due to their special capability it is the best method.

So, The best method to solve a problem is Brainstorming.

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Using proportions, it is found that she would save $900 in a year.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

She spends $150 a month on clothing and accessories, hence, if she saves half of that, the amount saved in a month is:

0.5 x 150 = $75.

In a year, this amount will add up to:

75 x 12 = $900.

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Answer:

1.381796

2.87258

3.69047

4.774225

Step-by-step explanation:

Align the numbers as an ordinary subtraction problem. Write the larger number above the smaller number. If the smaller number has fewer digits, line them up on the right, as you would in a decimal (base ten) subtraction problem.

Answer:

682,548 - 300,752 = 381,796

92,730 - 5,472 = 87,258

47,569 + 21,478 = 69,047

741,658 + 32,567 = 774,225

Step-by-step explanation:

the required area of shaded part is 549.3807mm^2

Four quarter circles are cut out from a 16 cm square

that is we have given that square has each side 16 cm

we know that

area of square = (side) ^2

                      = 16*16 cm^2

                       = 256 cm^2

four quarter circles are cut out from a 16 cm square

we know that

area of sector = N/360 ( pi *r^2)

                       = 90/360( pi* 8^2)   it makes angle 90 degree and r=8cm

                       = 1/4( pi* 64)

therefore area of four quarter circles is given by

=4*(1/4)*(64*pi)

=64pi

now the required area of the shaded part is equal to

=area of square - area of four quarter circles

=       256 -  64pi

= 256 - 201.06193

= 54.93807 cm^2

we know that 1cm is equal to 10mm

54.93807*10 =549.3807mm^2

Hence the required area of shaded part is 549.3807mm^2

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If JM ≅KM then M is the midpoint of ΔJKL then LM is the median of

JM  ≅ KM.

A perpendicular bisector is a 90° angle line that intersects and passes through the midpoint of a given segment.

The median of a triangle is a line segment that connects a vertex to the midpoint of the opposing side. Each triangle has three medians, one from each vertex, which all intersect at the triangle's centroid.

The altitude of a triangle is a line segment that runs through a vertex and is perpendicular to the baseline.

We know that JM ≅ KM then M is the midpoint of ΔJKL. Therefore, LM is the median of JM ≅ KM.

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4.313

Step-by-step explanation:

The length of BC is B. 2.20 cm

As per the known fact, the linear angle is 180°. As per this writing the equation -

∠ BC + 168 = 180

∠ BC = 180 - 168

∠ BC = 12°

Now, using formula  for calculation of length of arc -

Length = angle/360×2πr, where r refers to radius

Calculating radius as -

Radius = diameter ÷ 2

Radius = 21 ÷ 2

Radius = 10.5 centimeters

Now keep the values in formula to find the length of arc, which is the value of BC

Length = 12/360×2×3.14×10.5

Length = 252×3.14/360

Length = 2.2 centimeters

Hence, the length of BC is B 2.20cm.

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The complete question is attached in image.

Answer:

the answer is 12.

Step-by-step explanation:

to find the answer divide 60 by 5 and you'll get the answer (aka 12)

Answer:

12

Step-by-step explanation:

5h=60

h= 60÷5

=12

ans: h=12

Answer:

Step-by-step explanation:

Okay

x+2y=7

x+2y-2y=7-2y

x=7-2y

4x+2y=10

4x+2y-2y=10-2y

4x=10-2y

divide both sides by 4

4x/4=(10/4)-(2y/4)

x=(5-y)/2

Hope this helps! ^^