Each diagram shows △ABC and △DEF on the coordinate plane, with ∠A ≅ ∠E,
and ∠C ≅ ∠F. Identify whether the two triangles are congruent. If they are not
congruent, explain how you know. If they are congruent, find the length of each
side of each triangle.

Please help a brother out, I need this for a test.

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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[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:

$12/$28

Step-by-step explanation:

Let x and y represent the two amounts of money adding up to $40.

Assume that x is the smaller amount.  Then:

 x        3

----- = -----    Remembering that x + y = $40, we get x = $40 - y

 y        7

amd sp we have

 $40 - y          3

-------------- = ------   which, after cross-multiplication, is $280 - $7y = 3y

       y             7

Simplifying this, we get $280 = 10 y, so that y must be $28.  If y = $28, x must be $40 - $28, or $12.

                                                                             $12

Then $40, split in the ratio 3/7, is the ratio ----------------

                                                                            $28

Check:  Note that $12 + $28 = $40, as required, and that $12/$28 = 3/7.

Answer:

(2.5, 4)

Step-by-step explanation:

(4, 7) (1, 1)

midpoint formula is ( (x1 + x2) / 2  , (y1 + y2) / 2 )

=>( (4 + 1)/2 , (7 + 1)/2 )

=> (5/2, 4)

=> (2.5, 4)

Answer:

25%

Step-by-step explanation:

15 times 6 is 90

90 is 25 % of 360

Answer: y=-1/4x+4

Step-by-step explanation:

slope goes down 1, and right 4 so it's -1/4. Y-intercept is positive 4 so it will be +4

Answer:

66.8421% decrease

Step-by-step explanation:

Answer:

Its 65

1ft=304.8mm

Answer:

2 students study neither french or Spanish

Answer:

Y^2/a = x

Step-by-step explanation:

Y = a sqr X

Square both sides

Y^2 = a * x

Divide a

Y^2/a = x

Answer:

[tex] x = \dfrac{y^2}{a^2} [/tex]

Step-by-step explanation:

[tex] y = a\sqrt{x} [/tex]

Square both sides.

[tex] (y)^2 = (a\sqrt{x})^2 [/tex]

[tex] y^2 = a^2(\sqrt{x})^2 [/tex]

[tex] y^2 = a^2x [/tex]

Divide both sides by a².

[tex] \dfrac{y^2}{a^2} = x [/tex]

Switch sides.

[tex] x = \dfrac{y^2}{a^2} [/tex]

Answer:

Answer:Back 2

Step-by-step explanation:Blue + Red=-2

Step-by-step explanation:

Answer:

x ≤ -14

Step-by-step explanation:

Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially over time.

Given monthly income of Ron is $3,142.23

Ron is 25 years old and is retiring at the age of 65. so he has 40 years to contribute.

Total amount he contribute in 40 years paying 5.5% compounded monthly is given by

interest rate(r) = 0.055/12

time period = 40 years = 480 months

Principal amount = $314.223

Future value = [tex]P(\frac{(1+r)^{n}-1 }{r} )[/tex]

Substitute, we get,

= 3142.23 [tex].10(\frac{(1+\frac{0.055)^{12.40}-1) }{12} }{\frac{0.055}{12} }[/tex]

Thus, future value is $547074.681009.

After retirement his monthly income when he has $547074.681009 amount.

P = (A.i/2)/(1-(1+i/12)⁻ⁿ)

Putting values, we get,

P = (547074.68×0.55/12)/1-(1+0.055/12)⁻²⁴⁰

P = $3763.25

He will receive a monthly income of $3763.25.

But  given he will need a monthly income of $4,123 for 20 years, which is not met by Ron.

So, the amount he needs to supplement his monthly income when he retires by (4123-3763.25)= $359.74

Hence, Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

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Answer:

I think letter B

Step-by-step explanation:

Yyyyyyyygggggggggggggggg

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 :)

Answer:

-9?????????????????????????

Step-by-step explanation:

Answer: − 34359738368

Answer:

15°

brainlest

Step-by-step explanation:

Since P is on the median of ΔABC, it is equidistant from points B and C as well as from C and Q. Thus, points B, C, and Q all lie on a circle centered at P. (See the attached diagram.)

The base angles (B and C) of triangle ABC are (180° -30°)/2 = 75°. This means arc QC of the circle centered at P has measure 150°. The diameter of circle P that includes point Q is defined to intersect circle P at R.

Central angle RPC is the difference between arcs QR and QC, so is 180° -150° = 30°. Inscribed angle RQC has half that measure, so is 15°.  Angle PQC has the same measure as angle RQC, so is 15°.

Angle PQC is 15°.

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.

Please mark Brainliest. It would mean a lot to me.

~An emotional teen who helps others with joy

Good luck.

Answer:

  a) b^3

  b) x^3

Step-by-step explanation:

It can be helpful to think of the exponent as specifying the number of times the base is a factor in the product. Of course, common factors in the numerator and denominator cancel.

  [tex]\dfrac{b^7}{b^4}=\dfrac{b\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b}{b\cdot b\cdot b\cdot b}=b\cdot b\cdot b=b^{7-4}=\boxed{b^3}[/tex]

__

  [tex]\dfrac{x\cdot x^5}{x^2\cdot x}=\dfrac{x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x\cdot x}=x\cdot x\cdot x=x^{6-3}=\boxed{x^3}[/tex]

Answer:

0 us the answer for this question

Answer:

Step-by-step explanation:

Verify if the ratio of corresponding sides is same:

Since the ratios are same the triangles are similar

Answer:

Where's the question?

Step-by-step explanation:

Answer:

600,000 cm²

Step-by-step explanation:

We know the conversion from meters to centimeters to be

1 m = 100 cm.

We need the conversion factor from square meters to square centimeters.

Start with

1 m = 100 cm

Square both sides.

(1 m)² = (100 cm)²

1 m² = 10,000 cm²

Now that we have the correct conversion factor from m² to cm², we can do the conversion of 60 m² into cm².

60 m² × (10,000 cm²)/(1 m²) = 600,000 cm²

Answer:

luna

Step-by-step explanation:

compare the y values when x=0. looking at the table, gracey was 1 lb at week 0, and looking at the graph, Luna was 2 lbs at week 0 (y-intercept) so luna was heavier at birth

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.