Theorem 8.9 : The line segment joining the mid-points of two sides of a triangle is parallel to the third side.
prove this theorem
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Answer:

1. 3 yards= 9 feet

2. 78 cups=5 gallons

3. 72 inches = 2 yards

4. 80 ounces = 5 pounds

5. 84 inches = 7 feet

6. 24 feet = 8 yards

7. 40 pints = 5 gallons

8. 16 cups = 5 quarts

9. 144 inches = 4 yard

10. 48 ounces = 3 pounds

Answer:

The properties of right angle triangle are as follows

Answer:

see details below

Step-by-step explanation:

a) week 1 :  #10" / (#10"+#12") = 509 / 736 =  69% (to nearest percent)

b) week 2 :  #10" / (#10"+#12") = 766 / 1076 = 383/538 = 71% (to nearest percent)

A).69% for week 1

B)71% for week 2

Answer:

Step-by-step explanation:

This a right triangle so we will use the Pythagorian theorem. x is the hypotenus.

■■■■■ Pythagorian theorem ■■■■■

● x^2 = √10^2 + √10^2

● x^2 = 10 + 10

● x^2 = 20

● x = √20 yd

Answer:

9.8 units

Explanation:

According to Pythagoras theorem, the square of length of the hypotenuse is equal to the sum of squares of lengths of other two sides.

Let the third side be x units.

Then,

x² + 10² = 14²

=> x² + 100 = 196

=> x² = 196 - 100

=> x² = 96

=> x = √96

=> x = 4√6

=> x = 9.79....

=> x = 9.8 (Rounding to the nearest tenths)

So, the length of the third side is 9.8 units.

Answer:

The answer is below

Step-by-step explanation:

Let lines be drawn from D to F (line DF) and from F to G (line FG) as shown in the diagram attached.

∠FDE = ∠FGE (angles in the same segment).

Also, ∠EFD = ∠EGD (angles in the same segment)

∠FDE + ∠EFD = ∠FGE + ∠EGD = ∠FGD

Adding ∠FED on both sides gives:

∠FDE + ∠EFD + ∠FED = ∠FGD + ∠FED

But ∠FDE + ∠EFD + ∠FED = 180° (sum of angles in a triangle)

Therefore ∠FGD + ∠FED = 180°

m∠G + m∠E = 180° (sum of opposite angles in a cyclic quadrilateral is 180°)

Answer:

144°

Step-by-step explanation:

Complement angles add up to 180°

Therefore.....

x=4(180-x)

x=720-4x

5x=720

x=144°

When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other. The measure of the given angle is 40.

When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.

for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.

Let the given angle be represented by x.

Now, the complement of this angle will be,

Complement angle = (90 - x)

Further, it is given that 4 times the complement of this angle is equal to 200°. Therefore, we can write,

4(90 - x) = 200

360 - 4x = 200

-4x = -360 + 200

-4x = -160

x = -160 / -4

x = 40

Hence, the measure of the given angle is 40.

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The answer is Like terms.

Answer:

-14

Step-by-step explanation:

5-y=19

collect all the like terms on one side

-y=19-5

when 5 moves over the the other side of the equation it becomes a negative

-y=14

divide both sides by a negative sign

y=-14

Answer:

C

Step-by-step explanation:

Okay, here we have a reduction in the number of students by 20% from 2010 to 2011.

In 2011, we had k students, so we want to calculate the number of students we had in 2010.

Let the number of students present in 2010 be x

So mathematically;

x - 20% of x = k

x - 0.2(x) = k

0.8x = k

x = k/0.8

x = k * 1/0.8

x = k * 1.25

x = 1.25k

Answer:

373.66 cm².

Step-by-step explanation:

The following data were obtained from the question:

Pi (π) = 3.14

Radius (r) = 7 cm

Slant height (l) = 10 cm

Surface Area (SA) =?

The surface area of the cone can be obtained by using the following formula:

SA = πr² + πrl

SA = (3.14 × 7²) + (3.14 × 7 × 10)

SA = (3.14 × 49) + 219.8

SA = 153.86 + 219.8

SA = 373.66 cm²

Therefore, the surface area of the cone is 373.66 cm².

Answer:

x=17

Step-by-step explanation:

I hope you understood well !

Answer:

x = 17

Step-by-step explanation:

3x + 16 +45 + 68 = 180

             3x + 129 = 180

Subtract 129 form both sides

          3x + 129 -129 = 180 - 129

                           3x = 51

Divide both sides by 3

                         3x/3 = 51/3

                              x = 17

Answer:

$635

Step-by-step explanation:

$5x7 birdhouses=$35want

So, $35+$600=$635 total!

I hope this helps you!

Multiplication is the process of multiplying. The cost of building 7 birdhouses will be $635.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The cost of the birdhouse is the sum of the fixed cost, which is the setup cost of the business of $600, and the variable cost is the cost that is needed to make a single house, therefore, $5.

Now, the total cost of making n number of houses will be,

Cost of making n house = Fixed cost + variable cost

                                        = $600 + $5(n)

Further, the table can be filled using the above formula by substituting the value of n for the number of houses. Therefore,

Number of bird houses     Total cost to build

       1                                     $600+$5(1) = $605

       2                                    $600+$5(2) = $610

       3                                    $600+$5(3) = $615

       4                                    $600+$5(4) = $620

       5                                    $600+$5(5) = $625

       6                                    $600+$5(6) = $630

       7                                    $600+$5(7) = $635

Hence, the cost of building 7 birdhouses will be $635.

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Answer:

1209

Step-by-step explanation:

| - 403 | × | - 3 |

= | 403 | × | 3 |

= 403 × 3

= 1209

Answer:

[tex]\frac{64}{27}[/tex] cm³

Step-by-step explanation:

The volume (V) of the prism is calculated as

V = lbh ( l is length, b is breadth and h is height ), thus

V = [tex]\frac{4}{3}[/tex] × [tex]\frac{4}{3}[/tex] × [tex]\frac{4}{3}[/tex] = [tex]\frac{4^3}{3^3}[/tex] = [tex]\frac{64}{27}[/tex] cm³

Answer:

Step-by-step explanation:

I am more than happy to answer anymore questions. If needed an explanation I can put one in the comments.

the expression is "2 + 8." To find the quotient of 12 and 6, divide 12 by 6. The result is 2.

Step 1: Add 8 to the quotient.

Now, add 8 to the quotient found. The expression is "quotient + 8."

Step 2: Write the final expression.

The final expression that represents "8 more than quotient of 12 and 6" is "quotient + 8."

So, the expression is "2 + 8."

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Answer:

90 degrees

Step-by-step explanation:

Add them together. 58+32=90

90 degrees

add them togather

Answer:

3.25

Step-by-step explanation:

μX = 2(0.3) + 3(0.2) + 4(0.4) + 5(0.1) = 3.3

The mean of the distribution represented by the histogram is 3.25

The mean is the product of the value of X and its corresponding probability (P(x)).

The mean can be expressed thus :

From the histogram :

Mean = (1 × 0.05) + (2 × 0.2) + (3 × 0.35) + (4 × 0.25) + (5 × 0.15)

Mean = 0.05 + 0.40 + 1.05 + 1.00 + 0.75 = 3.25

Therefore, the mean value of the distribution depicted by the histogram ls 3.25

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Answer:

9/8 or 1.125

Step-by-step explanation:

We want to find the area of a rectangular postage stamp

The area of a rectangle can be found by multiplying the length by the width

Given length: 3/2

Given width: 3/4

Area = 3/2 * 3/4 = 9/8 or 1.125

The area of a 2D form is the amount of space within its perimeter. The area of the stamp in square inches is 1 1/8 inches².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given that a rectangular postage stamp has a length of 3/2 inches and a width of 3/4 inch. Therefore, the area of the stamp in square inches is,

Area of the stamp = Length × Width

                              = 3/2 inches × 3/4 inches

                              = 9/8 inches²

                              = 1 1/8 inches²

Hence, the area of the stamp in square inches is 1 1/8 inches².

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Answer:

Approximately 13.4 units.

Step-by-step explanation:

To find the distance between two points, use the distance formula. The distance formula is:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

x₁ and y₁ is one coordinate while x₂ and y₂ is the other.

Let (-3,10) be x₁ and y₁ and let (3,-2) be x₂ and y₂. Plug in the numbers and simplify:

[tex]d=\sqrt{(3-(-3))^2+(-2-10)^2}\\ d=\sqrt{6^2+(-12)^2} \\d=\sqrt{36+144} \\d=\sqrt{180}\\ d=\sqrt{36\cdot5}=6\sqrt{5}\approx13.4164[/tex]

Edit: Typo

Answer:

100

Step-by-step explanation:

Answer:

11 terms.

Step-by-step explanation:

We are given the arithmetic sequence:

17, 13, 9, ...

And we want to find the number of terms required such that the sum is -33.

Recall that the sum of an arithmetic series is given by:

[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]

Where k is the number of terms, a is the first term, and x_k is the last term.

The desired sum is -33. The first term is 17 as well. Thus:

[tex]\displaystyle (-33) = \frac{k}{2} \left( (17) +x_k\right)[/tex]

Simplify:

[tex]-66 = k(17 + x_k)[/tex]

We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:

[tex]x_ n = a + d(n-1)[/tex]

Where a is the initial term and d is the common difference.

The initial term is 17 and the common difference is -4. Hence:

[tex]\displaystyle x_n = 17 - 4(n-1)[/tex]

Then the last term is given by:

[tex]x_k = 17 - 4(k-1)[/tex]

Substitute:

[tex]\displaystyle -66 = k\left( 17 + \left( 17 - 4(k-1)\right)\right)[/tex]

Solve for k:

[tex]\displaystyle \begin{aligned} -66 &= k(17 + (17 - 4k + 4)) \\ -66 &= k(38 -4k) \\ -66 &= -4k^2 + 38k \\ 4k^2 -38k -66 &= 0 \\ 2k^2 - 19k -33 &= 0 \\ (k-11)(2k+3) &= 0 \\ k-11&= 0 \text{ or } 2k+3 = 0 \\ \\ k &= 11 \text{ or } k = -\frac{3}{2}\end{aligned}[/tex]

Since we cannot have a negative amount of terms, we can ignore the second solution.

Therefore, the given sequence must have 11 terms such that it sums to -33.

Answer:

Here is 2 methods

Step-by-step explanation:

1) we use excel to find n=11 for lasy students

2) mathematical method

[tex]u_1=17\\u_2=13=17+(2-1)*(-4)\\u_3=9=17+(3-1)*(-4)\\\\\\\boxed{u_n=17+(n-1)*(-4)}\\\\\\\displaystyle s_n=\sum_{i=1}^nu_i\\=\sum_{i=1}^n(17+(i-1)*(-4))\\\\\\=(\sum_{i=1}^n 17) + (-4)*\sum_{i=1}^n (i) +4*\sum_{i=1}^n (1)\\\\\\=17*n+4*n-4*\frac{n*(n+1)}{2} \\\\\\=21n-2n^2-2n\\\\\\=-2n^2+19n\\\\=-33\\\\\\\Longrightarrow\ 2n^2-19n-33=0[/tex]

[tex]\Delta=19^2+4*2*33=625=25^2\\\\n=\dfrac{19-25}{4} =-1.5\ (excluded)\ or\ n=\dfrac{19+25}{4}=11\\\\[/tex]

Answer:

The third table is the correct answer

Step-by-step explanation:

Here in this question, we are concerned with determine which of the tables correctly represents what an exponential function is.

An exponential function is a function of the form;

y = x^n

where the independent variable x in this case is raised to a certain exponent so as to give the results on the dependent variable axis (y-axis)

In the table, we can see that we have 2 segments, one that contains digits 1,2 and so on while the other contains purely the powers of 10.

Now, let’s set up an exponential outlook;

y = 10^x

So we have;

1 = 10^0

10 = 10^1

1/10 = 10^-1

1000 = 10^3

1/100 = 10^-2

We can clearly see here that we have an increase in the value of y, depending on the value of the exponent.

However it is only this table that responds to this successive correctness as the other tables in the answer do have a point where they fail.

For example;

10^-2 is not 10 which makes the fourth table wrong

10^4 is not 100 which makes the first table wrong

we have same error on second table too

Answer:

(4,2) is the answer on AP EX

The coordinate of the image of point A is (-4,-2)

Transformation is the process of changing the graph to a new graph by Rotation, Reflection, Translation, and Dilation.

The coordinate of A is (4,-2)

When it is reflected across y axis, the coordinate (x,y) changes to ----> (-x,y)

So, the coordinates of A (4,-2) changes to (-4,-2)

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probability = favourable outcomes/total outcomes

you need 1 banana, out of 4 and there are total of 6 items so probability will be 4/6

when you take out 1 banana, there are 3 banana left and total of 5 items

so probability of this action will be 3/5

now, next action is taking out another banana.

this is NOT an independent event.

so by we will multiply the probabilities of these events according to rule of products.

so the answer is [tex] \frac{4\cdot3}{6\cdot5}=\frac25[/tex]

or 2×100/5=40%

Answer:

A is the answer

Step-by-step explanation:

Answer:

the answer is A.

Step-by-step explanation:

Answer:(x,z)=(5,-3)

Step-by-step explanation:

Given

We move  5 units in x-axis

3 units in downward along z-axis

Suppose a z-axis is vertical and x -axis is horizontal as shown in fig.

So, coordinates after movement is given by the movement along x-axis and z-axis.

So, final coordinates is (5,-3) in x-z Plane .

As there is no movement in z-axis , so Y-coordinate will remain zero.

Answer:

MN = 3

Step-by-step explanation:

The following are congruent to each other as each pair are tangents of a circle drawn from the same external point:

PQ = QJ = 1

JK = KL = 4 - 1 = 3

MN = ML

Thus, ML = KM - KL

ML = 6 - 3 = 3

Therefore, MN = ML = 3 (both are tangents drawn from the same external point, M.

Answer:

the answer is 3

Step-by-step explanation: