Solve the inequality. 2(b

!!!!!PLEASE HELP!!!!! *30 POINTS PLEASE*

Lelechka [254]

Answer:

Part 1)

Part a) Yes, triangle ABC is congruent with triangle DEC by SAS

Part b) No, triangle ABC is not congruent with triangle DCE

Part 2) No, is not enough information

Part 3) Yes, triangle RST is congruent with triangle VUT by ASA

Part 4) Yes, triangle DEF is congruent with triangle DHG by SAS

Step-by-step explanation:

Part 1) we have two cases

Part a) Is triangle ABC and DEC congruent?

Yes, triangle ABC is congruent with triangle DEC by SAS

we know that

The Side Angle Side postulate ( SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent

In this problem

AC≅DE

BC≅EC

and

∠ACB≅∠DCE ---> by vertical angles

Part b) Is triangle ABC and DCE congruent?

we know that

If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent

In this problem

the corresponding sides are not congruent

because

AB is not congruent with DC

Part 2) we have that

No, is not enough information

If AC≅XZ then the triangles ABC and XYZ will be congruent by SSS

or

If ∠ABC≅∠XYZ then the triangles ABC and XYZ will be congruent by SAS

Part 3) we have that

Yes, triangle RST is congruent with triangle VUT by ASA

we know that

If any two angles and the included side are the same in both triangles, then the triangles are congruent by Angle -Side-Angle (ASA) postulate

In this problem

ST≅UT

∠RST≅∠VUT ----> is a right angle

∠RTS≅∠VTU ---->by vertical angles

so

Two angles and the included side are the same in both triangles

therefore

triangles RST and VUT are congruent by ASA

Part 4) we have that

Yes, triangle DEF is congruent with triangle DHG by SAS

we know that

The Side Angle Side postulate ( SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent

In this problem

DE≅DH

DF≅DG

and

∠EDF≅∠HDG ---> by vertical angles

7 0

3 years ago

Solve the problem-282-(1,017)=

Anuta_ua [19.1K]

-282-(1,017)
-282 + (-1017)

Keep the sign (since they both share the same sign), and add them.

282 + 1017 = 1299

Answer: -1299

5 0

3 years ago

Read 2 more answers

How do you turn 68 out of 80 in a fraction percent decimal?

serg [7]

$As \ a \ fraction: \frac{17}{20}
 \\ As \ a \ percent:0.85
 \\ As \ a \ decimal:0.0085
 \\$

8 0

4 years ago

Someone pls help, its on trig ratios.

Mars2501 [29]

Answer:

$BC=12.8,\\AC=15.1$

Step-by-step explanation:

In right triangles only, the tangent of an angle is equal to its opposite side divided by its adjacent side.

Therefore, we have the following equation:

$\tan 58^{\circ}=\frac{BC}{8}$

Solving, we get:

$BC=8\tan 58^{\circ}\approx \boxed{12.8}$

Also in right triangles only, the cosine of an angle is equal to its adjacent side divided by the hypotenuse of the triangle.

$\cos 58^{\circ}=\frac{8}{AC},\\AC=\frac{8}{\cos 58^{\circ}},\\AC\approx \boxed{15.1}$

We can also use the Pythagorean theorem now that we've found BC. However, if you choose to do so, make sure you don't use a rounded value for BC, as that could cause a notable deviation in your final answer.

Using the Pythagorean theorem to verify our answers:

$8^2+(8\tan 58^{\circ})^2=\left(\frac{8}{\cos 58^{\circ}}\right)^2\:\checkmark$

6 0

3 years ago

Suppose the vertex of a parabola is in the first quadrant and the parabola opens upwards. What can be determined about the value

schepotkina [342]

A parabola is the graph of a quadratic function,

that is the graph of $f(x)=a x^{2} +bx+c$ , where a is not 0.

from a, b and c we can derive the following informations about the shape of a parabola:

if a>0, the parabola opens upwards.
if a<0, the parabola opens downwards.

Consider the discriminant $D= b^{2} -4ac$

If D>0, the parabola intersects the x-axis at 2 points.
If D=0, the parabola intersects the x-axis at 1 point.
If D<0, the parabola does not intersect the x axis.

"the vertex of a parabola is in the first quadrant and the parabola opens upwards."

the vertex is in the first quadrant means that the vertex is above the x-axis, and it opens upwards, so the parabola does not intersect the x-axis.

This means that:

Answer: a>0, the discriminant D<0

4 0

3 years ago

Solve the inequality. 2(b – 8) > 12