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3 years ago

Solve the system of linear equations by elimination −2x+3y=7 and 5x+8y=−2

1 answer:

4 0

You would need to make them eliminate so I would multiply the entire first one by 2.5 to make the X's cancel out. So you would end up with -5X+7.5Y=17.5. The X's would cancel and you would be left with 15.5Y=15.5. So Y=1. Then replace Y into one of the equations. I'm going to use the top again. -2X+3(1)=7. Subtract 3 from both sides to get -2x=4. Divide both sides by negative 2 to get X=-2. So the solution would be (-2,1)

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Consider the function f(x) = ex and the function g(x), which is shown below. How will the graph of g(x) differ from the graph of

SIZIF [17.4K]

Answer: Option C

Step-by-step explanation:

If the graph of the function $g(x)=f(x) +b$ represents the transformations made to the graph of $y= f(x)$ then, by definition:

If $b> 0$ the graph moves vertically upwards.

If $b$ the graph moves vertically down

In this problem we have the function $g(x)=e^x+5$ and our parent function is $f(x) = e^x$

therefore it is true that $b =5 > 0$

Therefore the graph of $f(x)=e^x$ is moves vertically upwards by a factor of 5 units.

The answer is the Option C: "The graph of g(x) is the graph of f(x) shifted up 5 units"

6 0

3 years ago

Solve x + 3y = 9<br> 3x – 3y = -13 (1 point)

Mariana [72]

Answer:

The values of x and y to the given equations are x=-1 and $y=\frac{10}{3}$

The solution is (-1, $\frac{10}{3}$ )

Step-by-step explanation:

Given equations are $x+3y=9\hfill (1)$

and $3x-3y=-13\hfill (2)$

to solve the given equations by elimination method :

Adding the given two equations (1) and (2) we get

$x+3y=9$

$3x-3y=-13$

_______________

4x=-4

$x=-\frac{4}{4}$

Therefore x=-1

Now substitute the value x=-1 in equation(1) we get

(-1)+3y=9

3y=9+1

$y=\frac{10}{3}$

Therefore the values of x and y to the given equations are x=-1 and $y=\frac{10}{3}$

The solution is (-1, $\frac{10}{3}$ )

8 0

4 years ago

A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t2 + 704t

Sever21 [200]

At least 20 charactersssssssssssss

7 0

4 years ago

if a pair of standard dice are rolled what is the probability that one die shows a six but not both of them. reduced fraction an

Novay_Z [31]

Answer:

$P=\frac{5}{18}$

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.

The size of the sample space is the total number of possible outcomes

The event space is the number of outcomes in the event you are interested in.

Let

x------> size of the event space

y-----> size of the sample space

if a die is rolled the sample space is

$\{1,2,3,4,5,6\}$

if two dice rolled the sample space is

$\{1,2,3,4,5,6\}*\{1,2,3,4,5,6\}$

The possible pairs are

$y=6*6=36$

The size of the event space x is

$\{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}$

$x=10$

$P=\frac{x}{y}$

substitute

$P=\frac{10}{36}$

Simplify

$P=\frac{5}{18}$

6 0

3 years ago

How do I solve this ?

timofeeve [1]

Answer:

$\large\boxed{\{4,\ 7,\ 10\}}$

Step-by-step explanation:

$X\ \cup\ Y\\\text{The union of a collection of sets is the set of all elements in the collection.}\\\\X\ \cap\ Y\\\text{The intersection}\ X\cap Y\ \text{of two sets X and Y is the set that contains}\\\text{all elements of X that also belong to Y, but no other elements.}\\\\A'\\\text{When A is a subset of a given set U, the absolute complement A}\\\text{is the set of elements in U, but not in A.}$

$U=\{3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10\}\\A=\{4,\ 6,\ 8\}\\B=\{3,\ 4,\ 7,\ 10\}\\C=\{3,\ 5,\ 9\}\\\\A\ \cup\ B=\{4,\ 6,\ 8\}\ \cup\ \{3,\ 4,\ 7,\ 10\}=\{3,\ 4,\ 6,\ 7,\ 8,\ 10\}\\C'=\{3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10\}-\{3,\ 5,\ 9\}=\{4,\ 6,\ 7,\ 8,\ 10\}\\B\ \cap\ C'=\{3,\ \b4,\ \b7,\ \b1\b0\}\ \cap\ \{\b4,\ 6,\ \b7,\ 8,\ \b1\b0\}=\{\b4,\ \b7,\ \b1\b0\}\\\\(A\ \cup\ B)\ \cap\ (B\ \cap\ C')=\{3,\ \b4,\ 6,\ \b7,\ 8,\ \b1\b0\}\ \cap\ \{\b4,\ \b7,\ \b1\b0\}=\{\b4,\ \b7,\ \b1\b0\}$

6 0

4 years ago