If ƒ(x) = x − 4 and g(x) = 3x + 5, find (ƒ + g)(x).

Answer:

1) Yes

2) No, this polynomial has complex roots

3) No, this polynomial has irrational roots

Step-by-step explanation:

a. Rational roots theorem provide a complete list of all roots of

f (x) = 4x² - 25

b. Rational roots theorem does not provide a complete list of all roots of

g (x) = 4x² + 25

c. Rational roots theorem does not provide a complete list of all roots of

h (x) = 3x² - 25

What is Function?

A relation between a set of inputs having one output each is called a function.

Functions are given as;

f (x) = 4x² - 25

g (x) = 4x² + 25

h (x) = 3x² - 25

Now,

a. f (x) = 4x² - 25

To find the roots we can set up 0,

f (x) = 4x² - 25 = 0

4x² - 25 = 0

4x² = 25

Divide by 4,

x² = 25/4

Take square root both side,

x = √25/4

x = ±5/2

Thus, The function has rational roots.

So, Rational roots theorem provide a complete list of all roots.

b) g (x) = 4x² + 25

To find the roots we can set up 0,

4x² + 25 = 0

4x² = - 25

Divide by 4,

x² = - 25/4

Taking square root,

x = √-25/4

x = ±5i/2

Thus, The function has complex roots.

So, Rational roots theorem does not provide a complete list of all roots.

c) h (x) = 3x² - 25

To find the roots we can set up 0,

3x² - 25 = 0

3x² = 25

Divide by 3,

x² = 25/3

x² = 8.333

Take square root both sides,

x = √8.333

x = ±2.89

Thus, The function has irrational roots.

So, Rational roots theorem does not provide a complete list of all roots.

Therefore,

a. Rational roots theorem provide a complete list of all roots of

f (x) = 4x² - 25

b. Rational roots theorem does not provide a complete list of all roots of

g (x) = 4x² + 25

c. Rational roots theorem does not provide a complete list of all roots of

h (x) = 3x² - 25

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Answer:

3.5 foot

Step-by-step explanation:

To find the distance from the wall, you will need to use cosine:

cos 60 = x / 7

x = 3.5 foot

Answer:

a .30 degrees

plz mark as brainliest

Answer:

6

Step-by-step explanation:

Answer:

$5.67, or $6 rounded to the nearest dollar.

Step-by-step explanation:

To determine the amount that both Ian and Addison will have in their respective accounts after 13 years, knowing that they both invested $ 100 in accounts with daily compound interest, but Ian did it in one with an interest of 9.25% while Addison did it in one with a interest of 9.375%, the following calculations must be made:

Ian = 100 x (1 + 0.00925 / 365) ^ 13x365

Ian = 332.79

Addison = 100 x (1 + 0.009375 / 365) ^ 13x365

Addison = 338.46

338.46 - 332.79 = 5.67

Therefore, Addison will have $ 5.67 more than Ian after the investment term.

Answer:

11) 4/11

12) -0.2

Step-by-step explanation:

Answer:

1.17 x 10^2

Step-by-step explanation:

Im pretty sure its right

Given:

[tex]\Delta ABC\sim \Delta D E F[/tex]

[tex]AB=18,BC=21,AC=24,EF=7[/tex]

To find:

The scale factor of [tex]\Delta ABC[/tex] to [tex]\Delta D EF[/tex].

Solution:

We have,

[tex]\Delta ABC\sim \Delta D EF[/tex]

So, side BC is the corresponding side of EF.

Now, scale factor of [tex]\Delta ABC[/tex] to [tex]\Delta D EF[/tex] is

[tex]\text{Scale factor}=\dfrac{\text{ Side of }\Delta D EF}{\text{Corresponding side of }\Delta ABC}[/tex]

[tex]\text{Scale factor}=\dfrac{EF}{BC}[/tex]

[tex]\text{Scale factor}=\dfrac{7}{21}[/tex]

[tex]\text{Scale factor}=\dfrac{1}{3}[/tex]

Therefore, the scale factor of [tex]\Delta ABC[/tex] to [tex]\Delta D EF[/tex] is [tex]\dfrac{1}{3}[/tex].  

Answer:

15.4

Step-by-step explanation:

cos A = b^2 + c^2 - a^2 / 2bc

cos X = 98^2 + 95^2 - 26^2 / 2(98) (95)

cos X  = 17953 / 18620

cos X = 0.964

X = cos^-1 (0.964) = 15.38 = 15.4

Answer:

(2k+1)(k+3)

Step-by-step explanation:

14k²+49k+21

simplify by dividing the whole equation by 7

2k²+7k+3

factorise

(2k+1)(k+3)

Answer:

10

Step-by-step explanation:

Answer:

Stefan originally paid $120 for the bicycle and helmet.

He made $72 by selling them to Jin.

Step-by-step explanation:

Given that:

Selling price of bicycle = $176

Selling price of helmet = $16

Total price = 176+16 = $192

This is 160% of what Stefan paid originally.

Let,

x be the original amount paid by Stefan.

160% of x = 192

[tex]\frac{160}{100}x=192\\1.6x=192[/tex]

Dividing both sides by 1.6

[tex]\frac{1.6x}{1.6}=\frac{192}{1.6}\\x=120[/tex]

Original amount paid by Stefan = $120

Profit = 192 - 120 = $72

Hence

Stefan originally paid $120 for the bicycle and helmet.

He made $72 by selling them to Jin.

Answer:

Books Galore has the lowest unit price

Step-by-step explanation:

if you divide main streets books, 10 ÷ $5.20 = $1.92

Books galore : 6 ÷ $3.60 = $ 1.66

Answer:

c

Step-by-step explanation:

I I don't even know why it seems I just chose that because

The distance between (4, 3) and (9, 15) on the coordinate plane is 13 units.

The distance between two points is defined as the length of the line segment between two places representing their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.

The formula of distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁)².

We have to determine the distance between (4, 3) and (9, 15) on the coordinate plane.

As per the question, the required distance would be as:

distance = √ (9 – 4)² + (15 – 3)²

distance = √ (5)² + (12)²

distance = √ (25 + 144)

distance = √ 169

distance = 13 units

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Answer:

The answer is [tex]y = - \frac{1}{4} x + \frac{9}{4} [/tex]

Step-by-step explanation:

❃Incase you forgot what the slope-intercept formula is ☟

[tex]y = mx + b[/tex]

❃Incase you also forgot, what the slope formula is ☟

[tex]m =  \frac{y_2 - y_1}{x_2 - x_1} [/tex]

☆ First: We are going to be solving for the slope.

[tex]m =  \frac{2- 3}{1 - ( - 3)} = \frac{ - 1}{4} = - \frac{1}{4} [/tex]

☆Second: We are going to find the y-intercept.

[tex]y = mx + b \\ 3 = - \frac{1}{4} ( - 3) + b \\ 3 = \frac{3}{4} + b \\ \frac{ - \frac{3}{4} = - \frac{3}{4} \: \: \: \: \: \: \: \: \: \: \: }{ \frac{ 9}{4} = b \: \: \: \: \: \: \: \: } [/tex]

☆Third: Plug in.

[tex]y = - \frac{1}{4} x + \frac{9}{4} [/tex]

Answer:

Step-by-step explanation:

I'm sorry forgot how to exactly solve it

Answer:

The rate of change in the value of the watch is modeled by 0.93.

The rate of change represents a decrease in value.  

The rate represents a 7% change per year.

Step-by-step explanation:

The rate of change in the value of the watch is modeled by 0.93.

The rate of change represents a decrease in value.  

The rate represents a 7% change per year.

The following information should be considered:

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Answer:193/500

Step-by-step explanation:

Answer:

Shirt: $7.5

Sweater: $17.5

Step-by-step explanation:

25/2=12.5

Shirt is 5 less than Sweater

12.5-5=7.5

Add 5 to sweater cost

12.5+5=17.5

Shirt=7.5 Sweater=17.5

17.5+7.5=25

Answer:

DAMMMMM U KNOW ME TOO WELLL

Step-by-step explanation:

Answer:

the anime is fire force

Step-by-step explanation:

In Year 198 of the Solar Era in Tokyo, Special Fire Force's are fighting against a phenomenon called Spontaneous Human Combustion where humans beings are turned into living infernos called “Infernals.” While the Infernals are First Generation cases of spontaneous human combustion

Answer:

3/4

Step-by-step explanation:

divide each by 2

28/2 = 14

12/2 = 6

14/2 = 7

6/2 = 3

therefore 3/7

Answer:

The answer to the question provided is 0.432.

Answer:

(2,4)

Step-by-step explanation:

Answer:

3/12= 4/16

1/4= 2/8

1/2= 3/6

2/5= 4/10

there are other possible answers but these are just ones i know

Answer:

It takes ( hours for 6 people to lay floors

Step-by-step explanation:

2=5 divide it and for one person it would take 1 1/2 so then times 1 1/2 by 6.

Answer:

c

Step-by-step explanation: