If a system of equations has one solution, what does the graph look like?

F(x)= x^2 -16x+63 find the x-intercepts of this function

Ahat [919]

Answer:

The x-intercepts will be, x= 7 or x =9

Step-by-step explanation:

f(x)= x^2 -16x+63

At the x-intercept, f(x) is zero.

Therefore;

x² - 16x + 63 = 0

solving it quadratically;

product = 63

Sum = -16

x² - 9x - 7x + 63 = 0

x(x-9) - 7( x-9) = 0

(x-7) (x-9) = 0

x = 7 or x = 9

Therefore;

The x-intercepts will be, x= 7 or x =9

8 0

3 years ago

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The rate at which a professional tennis player used carbohydrates during a strenuous workout was found to be 1.7 grams per minut

Alex787 [66]

Answer:

m=1.7

C=68 gr

Step-by-step explanation:

Function Modeling

We are given a relationship between the carbohydrates used by a professional tennis player during a strenuous workout and the time in minutes as 1.7 grams per minute. Being C the carbohydrates in grams and t the time in minutes, the model is

$C=1.7t$

The slope m of the line is the coefficient of the independent variable, thus m=1.7

The graph of C vs t is shown in the image below.

To find how many carbohydrates the athlete would use in t=40 min, we plug in the value into the equation

$C=1.7\cdot 40=68\ gr$

8 0

3 years ago

Determine if this relationship forms a direct variation. Verify your answer.

leva [86]

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or y=kx

so

we have

a) for x=1 y=0.50--------> y/x=0.50/1------> 0.50

b) for x=2 y=1--------> y/x=1/2-------> 0.50

c) for x=3 y=1.50--------> y/x=1.50/3-----> 0.50

d) for x=5 y=2.50--------> y/x=2.50/5----> 0.50

the value of k is equal to 0.50

so

the relationship forms a direct variation.

the equation is

y=0.50*x

Verify

for x=1

y=0.50*(1)------> y=0.50-----> is correct

for x=2

y=0.50*(2)------> y=1.00-----> is correct

for x=3

y=0.50*(3)------> y=1.50-----> is correct

for x=5

y=0.50*(5)------> y=2.50-----> is correct

4 0

3 years ago

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you correctly answered 2/3 of the questions on your history exam there were 75 questions on the exam how many questions did you

GaryK [48]

2/3 of 75 is 2/3 times 75, which is 50. Hope this helps. :D

8 0

3 years ago

I need help with #4 a-d

lesya [120]

a repeating decimal is placed over 9's instead of 0's. for example: 0.23 = $\frac{23}{100}$ , but 0.232323... = $\frac{23}{99}$

a) x = 0.121212

b) 100(x) = 100(0.121212)

100x = 12.1212

c) 100x = 12.1212

- x = 0.1212

99x = 12

x = $\frac{12}{99}$

d) -2 $\frac{12}{99}$ = -2 $\frac{4}{33}$ when simplified

The number is rational becase it has a repeating decimal

6 0

3 years ago