What is the slope of this line?
A - 1/5
B 5
C -5
D 1/5

The given information on the diagram of the projector and the image can

be used to prove the congruency of the triangles.

∠ABD, ∠BDA, and side [tex]\overline {AD}[/tex] on ΔABD are congruent to ∠CBD, ∠BDC, and

segment [tex]\overline {CD}[/tex] on ΔCBD, therefore, ΔABD ≅ ΔCBD, by AAS Theorem

Reasons:

The figure of the projector that casts an image on the screen is attached.

The bisector of the line [tex]\overline {AC}[/tex] = [tex]\overline {BD}[/tex]

From the drawing, we have;

∠ABD ≅ ∠CBD by equal number arc mark.

The two column proof is therefore, presented as follows;

Statement [tex]{}[/tex]                                            Reason

[tex]\overline {BD}[/tex] is perpendicular bisector of   [tex]{}[/tex][tex]\overline {AC}[/tex]   Given

[tex]\overline {AD}[/tex] = [tex]\overline {CD}[/tex]   [tex]{}[/tex]                                             Definition of bisected line [tex]\overline {AC}[/tex]  

∠BDC = 90°       [tex]{}[/tex]                                      [tex]\overline {BD}[/tex] is perpendicular [tex]\overline {AC}[/tex]  

∠BDA = 90°                         [tex]{}[/tex]                    [tex]\overline {BD}[/tex] is perpendicular [tex]\overline {AC}[/tex]  

∠ABD ≅ ∠CBD [tex]{}[/tex]                                       Given on the diagram

ΔABD ≅ ΔCBD  [tex]{}[/tex]                          by Angle-Angle-Side AAS Congruency rule

The Angle-Angle-Side, AAS, Congruency postulate states that two

triangles are congruent where two adjacent angles and a non included side

on one triangle are congruent to the corresponding two adjacent angles

and a non included side on the other triangle.

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O centroid

Step-by-step explanation:

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

Answer:

[tex]\frac{6}{5}[/tex]

Step-by-step explanation:

The similarity ratio is the ratio of corresponding sides, image to original

ratio = [tex]\frac{LK}{FG}[/tex] = [tex]\frac{24}{20}[/tex] = [tex]\frac{6}{5}[/tex] ( = 1.2 )

Answer:

Surface of[tex]35,875.86 cm^2[/tex]

Voliume of [tex]234,671.58 cm^3[/tex]

Long and painful calculations

Ok, this is going to take some time. The volume is the sum of all the solids, minus the half cylinder that makes the "tunnel" beneath it. That said, we can split the item into 3 main shapes, and the cylinder: The pyramid in the top left, the square based prism below the pyramid, and the trapezoid prism to the right. I edited a bit the image with paint to add measurements. It's paint so quality is what it is and deal with comic sans as a font.

Let's find the total surface first. We have the surface of the four faces of the pyramid, which are triangles of base 54 and height (red line)[tex]\sqrt{36^2+(\frac{54}2)^2} =\sqrt{2025}=45cm[/tex], givins us a total area of [tex]4\times \frac{bh}2 = 2\times 45\times 54 = 4860 cm^2[/tex]

We add the two lateral faces of the left prism: they are two rectangles of side length 70 and 54, for a total area of [tex]2(70)(54) = 7580 cm^2[/tex]

Take the rectangle to the side of the prism, of sides 54 and 70-34 = 36, giving an area of [tex]54\times 36 = 1944 cm^2[/tex]

Pick the inclined "roof" of the right prism, again a rectangles, sides 54 and 61: surface is [tex]3294 cm^2[/tex]

Two side faces of the right building: first pick the height (magenta line), with pythagorean theorem again, equal to [tex]\sqrt{ 61^2-11^2} = \sqrt{3600} = 60 cm[/tex]. The surface becomes [tex]2 \frac{(B+b)h}2 = (34+45)(60)= 4740 cm^2[/tex]

Missing the short sides and the half cylinder making the gallery. The sides - if you imagine un-hinging one and attaching to the bottom of the other - will make a rectangle of sides (45+70) cm and 54 cm with a circular hole in the middle. surface is [tex](45+70)\times54 - \pi(54/2)^2 =[/tex][tex]3920.94 cm^2[/tex].

Finally, the half cylinder. It's a "rectangle) tall (60+54) cm - the length of the whole contraption, and long half the circle, or [tex]27\pi[/tex]. It's surface is  [tex](60+54)\times\27\pi = 9664.92 cm^2[/tex]

Done with surfaces. At this point we just add everything together. Grab a calculator and start adding up, if I didn't miss anything the total surface will be [tex]35875.86 cm^2[/tex]

Volumes now. You wished this was over? I totally did.

Bulk of the calculations are done luckly. It's just to cut and paste here and there.

Pyramid first. We know the side length, we know the height, volume is the usual formula

[tex]\frac 13l^2h = \frac 13 54^2\times 36= 33,048 cm^3[/tex]

Cube beneath. This one is also easy Sides are 54cm, 54cm and 70cm, volume is their product:

[tex]54*54*70= 204,120 cm^3[/tex]

Side prism now: again base surface times height, let's use the trapezoid as a base since we already have the area from above:

[tex]A_th = 2370\times54 = 127,980 cm^3[/tex]

From this we take half a cylinder of radius 27 tall as the whole structure is long. [tex]\frac12 \pi r^2h = \frac12 \pi (27)^2(60+54) = 130,476.42 cm^3[/tex]

We're done. Let's add the volume of the first 3 solids and subtract the last one - hope you have your calculator handy, to get in total a volume of [tex]234,671.58 cm^3[/tex]

Double and triple check numbers, even if I rand them with excel.

[tex]4 \leq \dfrac{r}{18} +10\\\\\\\implies 4-10 \leq \dfrac{r}{18}\\\\\\\implies -6 \leq \dfrac r{18}\\\\\\\implies -6(18) \leq r\\\\\\\implies -108 \leq r\\\\\\\implies r \geq -108\\\\\\\text{Interval,}~ [-108 , \infty)[/tex]

Answer:

You need to select ALL of the fractions listed that are GREATER than 1/2.

One of those is 3/4.

Step-by-step explanation:

Make all of the fractions equal to 1/2, and then compare to what they really are. For example, taking 3/4 and making it equal to 1/2, which would be 2/4. Since it is 3/4 though, we know that it is GREATER than 1/2.

Answer:

the Answer is:

△DEF is congruent to △D′E′F′ because the rules represent a translation followed by a reflection, which is a sequence of rigid motions.

Step-by-step explanation:

I got 100% on the quiz

The two triangles ΔPQR and ΔP'Q'R' are congruent.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

The statement that correctly describes the relationship between △PQR and △P′Q′R′ is:

2. △PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the y-axis, which is a rigid motion.

From the attached graph we can observe that the given Triangle PQR is reflected across the y-axis.

In this case, a translation, a reflection across the x-axis, but a reflection across the y-axis can map △PQR onto △P′Q′R′. Therefore, the two triangles are congruent.

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Answer:

1 : 2

Step-by-step explanation:

this is a 30-60-90 triangle which is a special right triangle. the ratio of the sides is x: x*sqrt(3): 2x, in the order short leg: long leg: hypotenuse. so the ratio of the short leg to the hypotenuse is x:2x or 1:2

Answer:

f(x) = (1/2)x

Step-by-step explanation:

f(x) = mx + b

m is the slope

b is the y-intercept

m = rise/run

for every run of 2 in x

f(x) rises 1

m = 1/2

The y-intercept occurs when x = 0

from the table f(0) = 0

b = 0

Therefor

f(x) = (1/2)x + 0

f(x) = (1/2)x

Answer:

[tex]f(x) = 1/2*x[/tex]

Step-by-step explanation:

Linear functions are functions of the form "f(x) = a * x + b" where 'a' and 'b' are constants (numbers) and x is the input.

In this problem, you are given the inputs and outputs of the function. Since you know it is linear, you begin thinking about what number you can multiply on the left to get the value on the right.

-4 / 2 = -2

-2 / 2 = -1

0 / 2 = 0

We find that dividing x by 2 gives the correct output. Dividing by 2 is the same as multiplying by 1/2. Therefore, we have found the answer!

f(x) = 1/2 * x

Answer:

-1/28

Step-by-step explanation:

You need to convert 2/7  and 1/4 into the same denominator. The GCD is 28. 2/7=8/28 and 1/4=7/28. 7/28-8/28=-1/28

Answer:

-1/28

Step-by-step explanation:

You have to find the least common multiple for 7 and 4, the denominators, to add the fractions. The LCM of 7 and 4 would be 28. You would have to multiply 7 by 4 and 4 by 7, meaning you have to multiply the numerators by the same number. 1x7/4x7-2x4/7x4= -1/28.

Hello there, hope you are having a nice day.

This is the rule for rounding:

    - Example: 3.4 =>3

     - Example: 6.7 =>7

Using this rule, we can round 3.5:

3.5 =>4

Hope it helps. Ask me if you have any queries.

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~An emotional teen who helps others with joy

Good luck.

Answer:

I think letter B

Step-by-step explanation:

Yyyyyyyygggggggggggggggg

Answer:

2 11/12

Step-by-step explanation:

This is what I got for the answer in the test.

The value of m in the given equation would be; m = 2.91

An equation is an expression that shows the relationship between two or more numbers and variables.

We need to find the value of m.

This equation could also be given by;

−2.4(m−5/6)=−5

Distribute the negative;

−2.4(m−5/6)=−5

- 2.4m + 2.4 x 5/6 = -5

Now we get;

- 2.4m = -5 - 2

- 2.4m = -7

m = 2.91

Hence, the value of m in the given equation would be; m = 2.91

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Answer:

.770

Step-by-step explanation:

Answer: 28,000,000

Step-by-step explanation:

This is a long one.

Start with (1) 2.66 times 10 to the 13th = 26,600,000,000,000 {2.66E13}

(2) 9.5 times 10 to the 5th = 950,000

(3)  2.66E13 divided by 950,000 = 28,000,000

If this dosnt make any sense dont hesitate to say so.

Answer:

120 / (x+y) = 8

Step-by-step explanation:

120 / (x+y)

= 120 / (3+12)

= 120/15

= 8

Answer:

125 is answer .........:)

Answer:

x ≤ -14

Step-by-step explanation:

Answer:

Its 65

1ft=304.8mm

Answer:

-20

Step-by-step explanation:

-14 x 2 = -28

-28 + 8 = -20

There you go :D

Answer:

-10

Step-by-step explanation:

first Solve for the fraction

-8/2= -4

x-4= -14

next add the negative 4 to 14

x=-10

and there's you're answer!

Answer:

2 students study neither french or Spanish

Answer:

133°

Step-by-step explanation:

The angle X is the same as the given.

[tex]\mathbb{ANSWER:}[/tex]

⇒ The two parallel lines are cut by a transversal so the interior angles on the same side of a transversal are congruent. This means that the measurement of the second angle is also 133 degrees.

Hence, the measurement of the angle is also 133 degrees.

Step-by-step explanation:

x - 1 + 5x = 23

6x - 1 = 23

6x = 23 + 1 = 24

6x = 24

x = 24/6

x = 4 ans.

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE.

Answer: the answer is line 2

Step-by-step explanation:

Answer:

D. 5/4

Step-by-step explanation:

Reciprocal is flipping that number around

Answer:

2.42

Step-by-step explanation:

I AM VERY SORRY IF ITS WRONG

Answer:

x=9

Step-by-step explanation:

23=7/9(6x-36)+9

Distribute 7/9.

23=14/3x-28+9

Add.

23=14/3x-19

Add 19 to both sides of the equation.

42=14/3x

Divide 14/3 from both sides of the equation.

X=9

Hope this helps :)

The domain and range of the function is domain: {x | x is a real number}; range: {y | y > 2}

Given the exponential function expressed as;

[tex]f(x)=(\frac{1}{6})^x + 2[/tex]

The domain of the function will be the input value "x" for which it exists. For the function given, it exists for any value of "x".

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Answer:

The answer is C on edge

Step-by-step explanation: