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3 years ago

Which triangles in the diagram are congruent?

Mathematics

2 answers:

Leona [35]3 years ago

8 0

Answer is C.) triangle 1 and triangle 3

triangle 1 and triangle 3 are congruent by SAS

Igoryamba3 years ago

3 0

i guess its triangle 1 and triangle 3

the first 2 sides are equal and angle 70° is equal

so through SAS congruence we can prove it....

i jhope im right ....

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PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

sineoko [7]

When you plot the offered points on the graph, you find only one of them falls inside the shaded region:

... D. 43 pepperoni slices and 25 cheese slices

6 0

3 years ago

HELP I will give brainlist

prohojiy [21]

Answer:

1. 2+2 = 4

2. 2x +2 = y

3. Terms - 16ab, 5c, 8, 2l, 2w, h, w, l

Coefficients - 16, 5, 8, 2, 2

Constants - 8, h, w, l

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3 years ago

Cynthia had a credit card with a 17% APR and a $3,265 balance. She had budgeted to have the credit card paid off in 24 months. B

monitta

Answer:

Cynthia will have to pay $152.16 extra in finance charges.

Step-by-step explanation:

Cynthia had a credit card with a 17% APR and a $3,265 balance.

Cynthia’s credit card company has increased her interest rate to 21%.

Here we have two scenarios, 1st when p = 3265 r = 17% and n = 24

Second when p = p = 3265 r = 21% and n = 24

Scenario 1:

$r =17/12/100=0.014166$

EMI formula is :

$\frac{p\times r\times(1+r)^{n}}{(1+r)^{n}-1}$

Putting the values in formula we get;

$\frac{3265\times0.014166\times(1+0.014166)^{24}}{(1+0.014166)^{24}-1}$

= $\frac{3265\times0.014166\times(1.014166)^{24}}{(1.014166)^{24}-1}$

EMI = $161.43

Scenario 2:

r = $21/12/100=0.0175$

Putting the values in formula we get;

$\frac{3265\times0.0175\times(1+0.0175)^{24}}{(1+0.0175)^{24}-1}$

= $\frac{3265\times0.0175\times(1.0175)^{24}}{(1.0175)^{24}-1}$

EMI = $167.77

Now, difference in EMI's = $167.77-161.43=6.34$ dollars

And for 24 months this amount becomes = $24\times6.34=152.16$ dollars

Therefore, Cynthia will have to pay $152.16 extra in finance charges.

6 0

3 years ago

A service station will be built in the highway, and a road will connect it with cray. How long will the new road be?

abruzzese [7]

Answer: 24 mi

Step-by-step explanation:

Let the points A, B, C and S represent Alba, Blare, Cray and Service station respectively,

Then According to the question,

We have to find out the line segment CS = x = ?

Now, In the triangles ACB and CSB,

$\angle ACB\cong \angle CSB$ ( Right angles )

$\angle ABC\cong \angle CBS$ ( Reflexive angles )

Thus, by AA similarity postulate,

$\triangle ACB\sim\triangle CSB$

By the property of similar triangles,

$\frac{AB}{CB}=\frac{AC}{CS}$

$\implies \frac{50}{30}=\frac{40}{x}$

$\implies 50x=30\times 40$

$\implies 50x = 1200$

$\implies x =24$

Thus, the length of the new road = 24 miles

7 0

3 years ago

All 3 questions 3 pictures for find the missing angles, please with reasoning why? 100 points

Katyanochek1 [597]

Answer:

Problem 1)

$m\angle DEG = 38^\circ$

Problem 2)

$m\angle x =140^\circ \text{ and } m\angle y = 49^\circ$

Problem 3)

$m\angle EDG = 65^\circ$

Step-by-step explanation:

Problem 1: ∠DEG

From the diagram, we know that ∠DFG intercepts Arc DG.

Inscribed angles have half the measure of its intercepted arc. Therefore:

$\displaystyle \frac{1}{2}m\stackrel{\frown}{DG}=m\angle DFG$

We know that m∠DFG = 38°. So:

$\displaystyle \frac{1}{2}m\stackrel{\frown}{DG}=38\Rightarrow m\stackrel{\frown}{DG}=76^\circ$

∠DEG also intercepts Arc DG. Hence:

$\displaystyle m\angle DEG=\frac{1}{2}m\stackrel{\frown}{DG}$

We know that Arc DG measures 76°. Hence:

$\displaystyle m\angle DEG =\frac{1}{2}\left(76\right)=38^\circ$

Alternate Explanation:

Since ∠DEG and ∠DFG intercept the same arc, ∠DEG ≅ DFG. So, m∠DEG = m∠DFG = 38°.

Problem 2: Circle with Centre O

(Let the bottom left corner be A, upper be B, and right be C.)

∠ACB intercepts Arc AC.

Inscribed angles have half the measure of its intercepted arc. Therefore:

$\displaystyle \frac{1}{2}m\stackrel{\frown}{AC}=m \angle ACB$

Since m∠ACB = 70°:

$\displaystyle \frac{1}{2}m\stackrel{\frown}{AC}=70\Rightarrow m\stackrel{\frown}{AC}=140^\circ$

∠x is a central angle and also intercepts Arc AC.

The measure of a central angle is equal to its intercepted arc. Thus:

$\displaystyle m\angle x =m\stackrel{\frown}{AC}=140^\circ$

The sum of the interior angles of a polygon is given by the formula:

$(n-2)\cdot 180^\circ$

Where n is the number of sides.

Since the inscribed figure is a four-sided polygon, its interior angles must total:

$(4-2)\cdot 180^\circ =360^\circ$

Therefore:

$21+70+y+(360-x)=360$

Substitute and solve for y:

$91+y+(360-140)=360\Rightarrow y +311=360\Rightarrow m\angle y = 49^\circ$

Problem 3: ∠EDG

∠EFG intercepts Arc EDG.

Inscribed angles have half the measure of its intercepted arc. Therefore:

$\displaystyle \frac{1}{2}m\stackrel{\frown}{EDG}=m\angle EFG$

Since m∠EFG = 115°:

$\displaystyle \frac{1}{2}m\stackrel{\frown}{EDG} = 115\Rightarrow m\stackrel{\frown}{EDG} = 230^\circ$

A full circle measures 360°. Hence:

$m\stackrel{\frown}{EDG}+m\stackrel{\frown}{EFG}=360^\circ$

Since we know that Arc EDG measures 230°:

$230^\circ + m\stackrel{\frown}{EFG}=360$

Solve for Arc EFG:

$m\stackrel{\frown}{EFG}=130^\circ$

∠EDG intercepts Arc EFG.

Inscribed angles have half the measure of its intercepted arc. Therefore:

$\displaystyle m\angle EDG = \frac{1}{2}m\stackrel{\frown}{EFG}$

Since we know that Arc EFG measures 130°:

$\displaystyle m\angle EDG = \frac{1}{2}(130)=65^\circ$

7 0

3 years ago

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