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Luda [366]
3 years ago
13

Which equation has a graph that is a parabola with a vertex at (5, 3)?

Mathematics
1 answer:
frozen [14]3 years ago
8 0

Answer: The equation that has a graph which is a parabola with a vertex at (5, 3) would be y = (x – 5)^2 + 3. The general form of a parabola which the vertex is not in the origin is expressed as y = a(x - h)^2 + k where (h,k) represents the vertex.

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The base of an isosceles triangle is one and a half times the length of the other two sides. A smaller triangle has a perimeter
stira [4]

Answer:

P = 1.5x.

Step-by-step explanation:

Let the length of each side of the first triangle be x, then

Perimeter of this triangle

= 2x + 1.5x

= 3.5x.

So perimeter of smaller triangle is:

P = 1/2 * 3.5x

P = 1,.5x.

5 0
3 years ago
16. Solve the linear equation.<br><br> 12x– 2 = 2x + 18
tino4ka555 [31]

Answer:

x=2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

6 0
2 years ago
Read 2 more answers
The ratio of boys to girls in a group is 5:3. If there are 18 more boys than girls, work out how
zmey [24]
<h3>Answer:  72 people total</h3>

45 boys, 27 girls

============================================================

Explanation:

g = number of girls

g+18 = number of boys, since there are 18 more boys than girls

For example, if g = 7, then g+18 = 7+18 = 25. In this example, we have 7 girls and 25 boys. The problem with this example is the ratio of boys to girls is 25:7 which is not equal to 5:3

We could use trial and error until we land on the solution, or we can use algebra as shown in the next section.

-------------------

The ratio of boys to girls is 5:3, meaning

(number of boys)/(number of girls) = 5/3

which turns into

(g+18)/g = 5/3

after we make the proper substitutions

Let's solve for g

(g+18)/g = 5/3

3(g+18) = 5g

3g+54 = 5g

54 = 5g-3g

54 = 2g

2g = 54

g = 54/2

g = 27

There are 27 girls.

This leads to,

g+18 = 27+18 = 45

So there are 45 boys

In total, we have 27+45 = 72 people

-----------------------------

Checking the answer:

The claim is that 45/27 is the same as 5/3

For now assume that claim is true. Set the fractions equal to each other and use cross multiplication like so

45/27 = 5/3

45*3 = 27*5

135 = 135

The third equation has the same thing on both sides, so it's a true equation. This must mean the first equation is true as well. Therefore, 45:27 and 5:3 are the same ratio and the answer is confirmed.

You could also use your calculator to note that

45/27 = 1.667

5/3 = 1.667

both decimal values are approximate.

8 0
3 years ago
You invest 1000 in an account at 2.5% per year simple interest how much will you have in the account at the beginning of the 4th
vodka [1.7K]
You will have gain $25 each year so after 4 years you will have $1100
7 0
3 years ago
Complete the sentences regarding demand. The demand for ________ goods increases with a decrease in income, whereas _________ ar
Dominik [7]

Answer:

Inferior, Public

Step-by-step explanation:

Complete the sentences regarding demand. The demand for inferior goods increases with a decrease in income, whereas public are goods that cannot be bought or sold.

8 0
3 years ago
Read 2 more answers
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