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Varvara68 [4.7K]
3 years ago
15

What is an equation of the line with slope 3 that goes through point (-1/2,5/2)?

Mathematics
1 answer:
svetoff [14.1K]3 years ago
3 0
Y= 3x+4 an equation of the lien with slope 3 that goes through point of (-1/2, 5/2)
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7.60. When Paul crossed the finish line of a 60-meter race, he was ahead of Robert by 10 meters and ahead of Sam by 20 meters. S
Lelechka [254]

Answer:

The number of meters Robert will beat Sam is 12 meters.

Step-by-step explanation:

Given:

When Paul crossed the finish line of a 60-meter race, he was ahead of Robert by 10 meters and ahead of Sam by 20 meters. Suppose Robert and Sam continue to race to the finish line without changing their rates of speed.

Find:

the number of meters by which Robert will beat Sam

Step 1 of 1

When Paul finishes, Robert has run 60-10=50 meters and Sam has run 60-20=40 meters.

Therefore, when Robert and Sam run for the same amount of time, Sam covers $\frac{40}{50}=\frac{4}{5}$ of the distance that Robert covers. So, while Robert runs the final 10 meters of the race, Sam runs $\frac{4}{5} \cdot 10=8$ meters.

This means Robert's lead over Sam increases by 2 more meters, and he beats Sam by 10+2=12 meters.

5 0
2 years ago
If 30.s g of milk contains 18 C, how many
liubo4ka [24]

Answer:

the answer would be (244/30.5) x 18, so the answer should be 144!

Step-by-step explanation:

Put me the brainest. thanks

8 0
3 years ago
Read 2 more answers
two opposite angles are congruent, necessary or not, and sufficient or not for a quadrilateral to be a parallelogram
hjlf

Answer: Ok here we go

Step-by-step explanation: Consecutive Angles

[insert drawing of irregular quadrilateral BEAR]

If you were to go around this shape in a clockwise direction starting at ∠B, you would next get to ∠E. Those two angles are consecutive. So are all these pairs:

∠E and ∠A

∠A and ∠R

∠R and ∠B

Consecutive angles have endpoints of the same side of the polygon.

Supplementary Angles

Supplementary angles are two angles adding to 180°. In a parallelogram, any two consecutive angles are supplementary, no matter which pair you pick.

Parallelograms

Parallelograms are special types of quadrilaterals with opposite sides parallel. Parallelograms have these identifying properties:

Congruent opposite sides

Congruent opposite angles

Supplementary consecutive angles

If the quadrilateral has one right angle, then it has four right angles

Bisecting diagonals

Each diagonal separates the parallelogram into two congruent triangles

Parallelograms get their names from having two pairs of parallel opposite sides.

Another interesting, and useful, feature of parallelograms tells us that any angle of the parallelogram is supplementary to the consecutive angles on either side of it.

We can use these features and properties to establish six ways of proving a quadrilateral is a parallelogram.

Proving A Quadrilateral is a Parallelogram

Can you be certain? Only by mathematically proving that the shape has the identifying properties of a parallelogram can you be sure. You can prove this with either a two-column proof or a paragraph proof.

Six Ways

Here are the six ways to prove a quadrilateral is a parallelogram:

Prove that opposite sides are congruent

Prove that opposite angles are congruent

Prove that opposite sides are parallel

Prove that consecutive angles are supplementary (adding to 180°)

Prove that an angle is supplementary to both its consecutive angles

Prove that the quadrilateral's diagonals bisect each other

Two-Column Proof

We can use one of these ways in a two-column proof. Bear in mind that, to challenge you, most problems involving parallelograms and proofs will not give you all the information about the presented shape. Here, for example, you are given a quadrilateral and told that its opposite sides are congruent.

Statement Reason:

GO ≅ TA and TG ≅ OA (Given)

Construct segment TO Construct a diagonal

TO ≅ TO Reflexive Property

△GOT ≅ △ TOA Side-Side-Side Postulate: If three sides of one △

are congruent to three sides of another △, then the two △ are congruent

∠GTO ≅ ∠ TOA CPCTC: Corresponding parts of congruent △ are

∠GOT ≅ ∠ OTA congruent

GO ∥ TA and TG ∥ OA Converse of the Alternate Interior Angles

Theorem: If a transversal cuts across two lines and the alternate interior angles are congruent, then the lines are parallel

▱ GOAT Definition of a parallelogram: A quadrilateral

with two pairs of opposite sides parallel

The two-column proof proved the quadrilateral is a parallelogram by proving opposite sides were parallel.

Paragraph Proof

You can also use the paragraph proof form for any of the six ways. Paragraph proofs are harder to write because you may skip a step or leave out an explanation for one of your statements. You may wish to work very slowly to avoid problems.

Always start by making a drawing so you know exactly what you are saying about the quadrilateral as you prove it is a parallelogram.

Here is a proof still using opposite sides parallel, but with a different set of given facts. You are given a quadrilateral with diagonals that are identified as bisecting each other.

[insert drawing of quadrilateral FISH with diagonals HI and FS, but make quadrilateral clearly NOT a parallelogram; show congruency marks on the two diagonals showing they are bisected]

Given a quadrilateral FISH with bisecting diagonals FS and HI, we can also say that the angles created by the intersecting diagonals are congruent. They are congruent because they are vertical angles (opposite angles sharing a vertex point).

Notice that we have two sides and an angle of both triangles inside the quadrilateral. So, we can use the Side-Angle-Side Congruence Theorem to declare the two triangles congruent.

Corresponding parts of congruent triangles are congruent (CPCTC), so ∠IFS and ∠ HSF are congruent. Those two angles are alternate interior angles, and if they are congruent, then sides FI and SH are parallel.

You can repeat the steps to prove FH and IS parallel, which means two pairs of opposite sides are parallel. Thus, you have a parallelogram.

In both proofs, you may say that you already were given a fact that is one of the properties of parallelograms. That is true with both proofs, but in neither case was the given information mathematically proven. You began with the given and worked through the problem, but if your proof "fell apart," then the given may have been wrong.

Since neither our two-column proof or paragraph proof "fell apart," we know the givens were true, and we know the quadrilaterals are parallelograms.

5 0
3 years ago
Toya is using a cake recipe that calls for two cups of sugar and 3 cups of flour. she wants to make a larger amount of cake batt
posledela

Answer:

4 cups of sugar

Step-by-step explanation:

2 x 2 = 4

Toya will use 4 cups of sugar.

5 0
2 years ago
11/20 as a simplified fraction
strojnjashka [21]
11/20 is already reduced you cannot simplify this fraction
3 0
3 years ago
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