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2 years ago

Which of the following is the graph of f(x) = x2 + 3x − 4?

Mathematics

1 answer:

chubhunter [2.5K]2 years ago

8 0

The graph of the function for values of x ranging from -6 to +6 is shown below.

<h3>Graphing a Quadratic function</h3>

From the question, we are to graph the given quadratic function

The given quadratic function is

f(x) = x² + 3x − 4

The graph of the function for values of x ranging from -6 to +6 is shown below.

The table of values are

x f(x)

-6 14

-5 16

-4 0

-3 -4

-2 -6

-1 -6

0 -4

1 0

2 6

3 14

4 24

5 36

6 50

Learn more on Graphing a quadratic function here: brainly.com/question/9028052

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Least Common Factor of 9 42 57

AlexFokin [52]

Should be 3

hope this helps

7 0

3 years ago

Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

4 0

3 years ago

Solve the following simultaneous linear equations.<br>2x + y = 5<br>4x – 3y = -10

Jet001 [13]

Answer:

(1/2,4)

Step-by-step explanation:

First, determine y in first equation: 2x+y=5 or y=5-2x

replace value of y determined in first equation (5-2x) into 2nd equation

4x-3(5-2x)=-10

4x-15+6x=10

10x=5

x=1/2

put value of x into either equation to solve for y so

2(1/2)+y=5

1+y=5

y=4

answer: x=1/2, y=4

check answer by substituting x and y into either equation:

4x-3y=-10

4(1/2)-3(4)=-10

2-12=-10

-10=-10

2x+y=5

2(1/2)+4=5

1+4=5

5=5

7 0

3 years ago

Write an equation for each line.

Tems11 [23]

Answer:

Step-by-step explanation:

Equation of blue line:

blue line is parallel to y-axis

⇒ x = 5

Equation of green line:

Green line is parallel to x-axis.

y = 2

Equation of red line:

At y-intercept x = 0. Point on red line is (0,5)

So, y-intercept = 5

y = mx + b Here, m is slope any b is y-intercept.

y = mx + 5

Now, choose any other point in red line. ((1,7)

Substitute this value in the above equation and we can find m

7 = m*1 + 5

7 - 5 = m

m = 2

y = 2x + 5

Equation of black line:

Black line and red line are parallel and so, they have same slope.

y = 2x + b

y-intercept (0,-6) ; b = -6

y = 2x - 6

5 0

1 year ago

Find 55% of 164 I don't get it I need help can someone help me like right now please

IgorC [24]

$55\%\ of\ 164\ is...\\\\ \frac{55}{100} \times \frac{164}{1} =\\\\55*164=9020\\100*1=100\\\\ \frac{9020}{100}\approx90\\\\20\ is\ left\ over.\\\\90.20\\\\\\55\%\ of\ 164\ is\ 90.2$

7 0

3 years ago