Write the equation of a parabola, in standard form, that goes through these points: (0, 3) (1, 4) (-1, -6)

Answers

Answer 1

Answer: Hello,

P:y=ax²+bx+c is the equation.

(0,3)∈P==>3=a*0+b*0+c==>c=3
(1,4)∈P==>4=a+b+3==>a+b=1 (1)
(-1,-6)∈P==>-6=a-b+3==>a-b=-3 (2)

(1)+(2)==>2a=-2==>a=-1
(1)==>b=1-(-1)==>b=2

y=x²+2x+3
y=(x+1)²+2
Vertex is (-1,2)

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F(x) = 4x^2 - 3x + 2kx + 1 What's the value of k for which the function has two zeros??
Can someone show me step by step?

Answers

$f(x)=4x^2-3x+2kx+1=4x^2+(2k-3)x+1\n\na=4;\ b=2k-3;\ c=1\n\nfunction\ has\ two\ zeros\ when\ \Delta=b^2-4ac > 0\n\n\Delta=(2k-3)^2-4\cdot4\cdot1=4k^2-12k+9-16=4k^2-12k-7 > 0\n\na_k=4;\ b_k=-12;\ c_k=-7\n\n\Delta_k=(-12)^2-4\cdot4\cdot(-7)=144+112=256\n\nk_1=(-b_k-√(\Delta_k))/(2a_k);\ k_2=(-b_k+√(\Delta_k))/(2a_k)$

$√(\Delta_k)=√(256)=16\n\nk_1=(12-16)/(2\cdot4)=(-4)/(8)=-(1)/(2);\ k_2=(12+16)/(2\cdot4)=(28)/(8)=(7)/(2)\n\na_k=4 > 0\ (up\ parabola\ arms-see\ the\ picture)\n\nAnswer:k\in(-\infty;-(1)/(2))\ \cup\ ((7)/(2);\ \infty)$

Which of the following best describes a consumer? someone who studies economics
a person who buys goods and services
a business owner who sells clothes
a farmer who sells his crops

Answers

Answer: Second option is correct.

Step-by-step explanation:

Since we have ask that

Consumer refers to those person who used to consume things like purchase goods and services for personal use.

Someone who studies economics are known as economists they are not consumers, they are known for their study of economics.

A business owner who sells clothes can be known as traders or merchants or business man but they do not consider as consumers as they don't buy goods and services but they provide all of these.

A farmer who sells his crops are known as producers instead of consumers.

So, Second option is correct.

A person who buys good and services is known as consumer.

a person who buys goods and services. Think of it this way: To consume means to eat or use something. A consumer is someone who buys things to eat or use.

Mr. Johnson has $15,000 to invest. Part of it is put in the bank at 4 percent, and part he puts in a savings and loan at 7 percent. If his yearly (simple) is $951, how much did he invest at each rate?

Answers

Answer:

$3300 at 4%

$11700 at 7%

Step-by-step explanation:

Total investment = $15000

Total simple interest on investment = $951

Investment A:

Rate = 4% =0.04

Investment B:

Rate = 7% =0.07

Simple interest (S. I) = principal * rate * time

(S. I on investment A + S. I on investment B)

Let principal amount in investment A = A

principal amount in investment B = B

(A * 0.04 * 1) + (B * 0.07 * 1) = $951

0.04A + 0.07B = $951 - - - - (1)

A + B = $15000 - - - - (2)

from (2)

A = 15000 - B

Substitute A = 15000 - B into (1)

0.04(15000 - B) + 0.07B = 951

600 - 0.04B + 0.07B = 951

600 + 0.03B = 951

0.03B = 951 - 600

0.03B = 351

B = 351 / 0.03

B = $11700

From (2)

A + B = $15000

A + $11700 = $15000

A = $(15000 - 11700)

A = $3300

What is 75%,1/6,3/8,and 0.625 from least to greatest

Answers

Convert each term in decimal form. This is avoid confusion and for uniformity and ease in comparing the value of each term.

75%   is   0.750
1/6   is   0.167
3/8   is   0.375
0.625 is   0.625

From least to greatest, the order is:

0.167 , 0.375 , 0.625 , 0.750

a six-foot-tall tent standing next to a cardboard box cast a nine foot Shadow if the cardboard box cast a shadow that is 6 foot long and how tall is it

Answers

I think it's 3 foot long but I'm not sure...

Answer: 9ft

Step-by-step explanation:

9 x 6 = 54 ÷ 6 = 9

He price of a computer component at the QRCC bookstore is decreasing at a rate of 2.25% per year. Decide whether this decrease is linear or exponential.

Answers

Answer:

The decrease is exponential.

Step-by-step explanation:

An exponential decrease is something like:

f(x) = A*(r)^x with 0 < r < 1

A linear decrease is something like:

g(x) = -a*x + b with a > 0

First ai general formula.

If you have a quantity Q, decreased by an X%, the new quantity will be:

New Quantity = Q - Q*(X%/100%)

Now let's look at the question:

Suppose that the original price of the computer component is K

And the price as a function of the year is P(y)

Then we know that, in the year zero, the price is K.

P(0) = K

One year after, the price decreases by 2.25%

Then:

P(1) = K - K*(2.25%/100%) = K*(1 - 0.0225)

After another year, we will have another decrease of 2.25%

Then:

P(2) = K*(1 - 0.0225) - K*(1 - 0.0225)*(2.25%/100%)

P(2) = K*(1 - 0.0225)*(1 - 0.0225) = K*(1 - 0.0225)^2

We already can see the pattern, we can expect that in the year y, the price of the component will be:

P(y) = K*(1 - 0.0225)^y

This clearly is an exponential decrease.

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