A student says that the function f(x)=3x^4+5x^2+1 is an even function.

Is the student's statement true or not true, and why?

The student's claim is true, because for any input of x, f(x)=−f(x).

The student's claim is true, because for any input of x, f(x)=f(−x).

The student's claim is not true, because for any input of x, f(x)=f(−x).

The student's claim is not true, because for any input of x, f(x)=−f(x).

Answer: I think it’s t II k

Step-by-step explanation:

If m is parallel to k and m is also parallel to ℓ, then by the transitive property of parallel lines, k must be parallel to ℓ.

If m ∥ k and m ∥ ℓ, then k is parallel to ℓ. In terms of geometry, when a line m is parallel to lines k and ℓ, and all the lines are coplanar, then lines k and ℓ must be parallel to each other as well. This is due to the transitive property of parallel lines which states that if two lines are parallel to the same line, they are parallel to each other. An example of this could be railway tracks: if the sleepers (the wooden blocks) are considered to be line m, which is parallel to both rails (k and ℓ), the rails (k and ℓ) have to be parallel to each other in order for the train to travel smoothly.

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Answer:

$14.40 for 24 markers

Step-by-step explanation:

Lets find the price per marker

$8.04 /12 = .67

$5.60/8 =.70

$14.40 /24 =.60

$10.40/16 =.65

The lowest amount is .60, which is the best deal

$14.40 for 24 markers

Answer:

15

Step-by-step explanation:

37.5÷2.5 goes in 15 times

Answer:

37.5 ÷ 2.5 = 15

Answer:

x = 5

Step-by-step explanation:

3x + 1 = 16

Subtracting 1 on both sides of the equation,

3x + 1 – 1 = 16 – 1

Summing algebraically (in this case subtracting by having different signs) on both sides,

3x = 15

Isolating x by dividing both sides by 3

3x / 3 = 15 / 3

Dividing,

x = 5

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

We have the following expression:

[tex]3x+1=16[/tex]

and we need to solve for [tex]x[/tex], so the first thing we have to do (in order to leave the x alone on one side of the equation) is move the +1 to the left sife with the opposite sign (-1):

[tex]3x=16-1\\3x=15[/tex]

now we divide each side by 3, and we get:

[tex]\frac{3x}{3}=\frac{15}{3} \\x=5[/tex]

the answer is [tex]x=5[/tex]

Answer:

$26

Step-by-step explanation:

Start with $56.

Add $265, obtaining a + balance of $321.

Let x represent the unit price of the backpacks.  Then:

$321 - 3x = $243.

Combining like terms:

3x = $78

Then x, the price of the individual backpack, was $78/3, or $26.

Answer:

A

Step-by-step explanation:

Sn=a(n-1) d

this formula for Calculating arithmetic sequence

Answer:  D. [tex]a_n=6+(n-1)(-3)[/tex]

Step-by-step explanation:

Given : An arithmetic sequence has this recursive formula:

[tex]a_1=6 \ \ \; \ a_n=a_{n-1}-3[/tex]

Using the given information, Second term of arithmetic sequence will be :-

[tex]a_2=a_{1}-3=6-3=3[/tex]

That means common difference = [tex]a_2-a_1=3-6=-3[/tex]

The explicit formula for arithmetic sequence is given by :-

[tex]a_n=a+(n-1)d[/tex], where a is the first term and d is the common difference.

Put a= 6 and d= -3, we get

The explicit formula for this sequence :-

[tex]a_n=6+(n-1)(-3)[/tex]

Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2}{3}[/tex] × [tex]\frac{3}{5}[/tex]

Cancel the 3 on the numerator/denominator of the fractions leaving

[tex]\frac{2}{1}[/tex] × [tex]\frac{1}{5}[/tex] = [tex]\frac{2}{5}[/tex]

Answer:

2 over 5

Step-by-step explanation:

Answer:

The solution of given equation is x = ±√2

Step-by-step explanation:

It is given that an equation

6x² + 1 = 13

To find the solution of given equation

6x² + 1 = 13 can be written as,

⇒ 6x²  = 13 - 1

6x² = 12

x² = 12/6 = 2

x = ±√2

Therefore the solution of given equation is x = ±√2

Answer:

The net of a rectangular pyramid is consisting of a rectangle, for the base, and there are 4 more triangles that make up the lateral faces, and the triangles make the pyramid.

Answer:

C. X= -1.25

Step-by-step explanation:

x + 5 = -3^x + 4

We change x for  -1.25

-1.25 + 5 = -3^(-1.25) + 4

3.75=-0.25+4

3.75=3.75

Same number on both sides, therefore is correct!

I hope you find this information useful and interesting! Good luck!

Answer:

[tex]\frac{g(7)-g(4)}{7-4}=\frac{5}{6}[/tex]

So it looks like C.

Step-by-step explanation:

Average rate of a function g(x) on the interval from x=a to x=b is given by the formula:

[tex]\frac{g(b)-g(a)}{b-a}[/tex].

You can even say:

[tex]\frac{g(a)-g(b)}{a-b}[/tex].

So we have from x=4 to x=7, so the formula becomes:

[tex]\frac{g(7)-g(4)}{7-4}[/tex]

We are given this is equal to 5/6.

Answer:

Its C

Step-by-step explanation:

For this case we must find an expression equivalent to:

[tex]\sqrt [4] {f}[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So, rewriting the given expression we have:

[tex]f ^ {\frac {1} {4}}[/tex]

Answer:

Option 1

Answer:

f^(1/4)

Step-by-step explanation:

The fourth power of f, expressed with a rational exponent, is f^(1/4).

please insert the entire of the question

Answer:

1, 4, 5

Step-by-step explanation:

Answer:

The amount of flour added to each box was 0.64 kg

Step-by-step explanation:

Let

x ----> the amount of flour added to each box in kg

Remember that

1 kg=1,000 g

8,600 g=8,600/1,000=8.6 kg

we know that

The linear equation that represent this situation is

(8.6+x)=4(1.67+x)

Solve for x

8.6+x=6.68+4x

4x-x=8.6-6.68

3x=1.92

x=0.64 kg

To solve this problem, we'll use algebra. Let's denote the initial amount of flour in Box A as A and in Box B as B. Also, let the amount of flour added to each box be x (in kilograms).
Given:
A = 1.67 kg
B = 8600 g, which we need to convert to kilograms. Since 1 kilogram is 1000 grams, we get:
B = 8600 / 1000 kg
B = 8.6 kg
After adding x kg of flour to each box, Box B contains 4 times as much flour as Box A. Therefore, we can set up the following equation:
B + x = 4(A + x)
Now, we plug in the values for A and B:
8.6 + x = 4(1.67 + x)
Distribute the 4 on the right side of the equation:
8.6 + x = 6.68 + 4x
Now we'll consolidate like terms:
8.6 - 6.68 = 4x - x
1.92 = 3x
To solve for x, we divide both sides by 3:
x = 1.92 / 3
x = 0.64 kg
So 0.64 kg of flour was added to each box.

[tex]X\cup Y=\{0,10,100,1000\}[/tex]

Answer:

I think (c) 120 is right answer.

Answer:

C. 120°

Step-by-step explanation:

Since this is an isosceles triangle [two congruent sides], m<B is also 30°. Now, we have to the m<A by using the Interior Angles Theorem [m<1 + m<2 + m<3 = 180°]. So we do this:

60 + m<A = 180; 120 = m<A

I am joyous to assist you anytime.

Answer:

Summation notation is:

[tex]\sum_{n=1}^{16}[5(x-1)-9][/tex]

If you prefer it a little more simplified:

[tex]\sum_{n=1}^{16}(5x-14)[/tex]

Step-by-step explanation:

First my favorite part, finding a pattern between the consecutive terms.

This is an arithmetic series because the terms are going up by 5 each time.

So arithmetic sequence, think linear equations:

x     |      y

1            -9

2           -4

3             1

4             6

..................

n             66

We are going to have to find that n but will will eventually...

The equation for a line in point slope form is [tex]y-y_1=m(x_x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and m is the slope.

We are already have the slope is 5 (the slope is the common difference in arithmetic sequence).

I'm going to use the first point (1,-9).

So the equation in point slope form is [tex]y-(-9)=5(x-1)[/tex]

Subtract 9 on both sides:

[tex]y=5(x-1)-9[/tex]

Now we need to know how many terms we are adding so what is x if y=66.

[tex]66=5(x-1)-9[/tex]

Add 9 on both sides:

[tex]75=5(x-1)[/tex]

Divide both sides by 5:

[tex]15=x-1[/tex]

Add 1 on both sides:

[tex]16=x[/tex]

We have 16 terms in this sequence where the 16th term is 66.

Summation notation is:

[tex]\sum_{n=1}^{16}[5(x-1)-9][/tex]

You could simplify the 5(x-1)-9.

Distribute:  5x-5-9

Add like terms:  5x-14

Answer:

Step-by-step explanation:

Answer:

All real numbers

Step-by-step explanation:

The given equation is:

[tex]f(x) = 2 {x}^{2} - 4x - 9[/tex]

where x is Ana's speed.

This is a quadratic function.

A quadratic function is a polynomial function.

All polynomial functions are are continuous and defined for all real values of x.

Therefore the domain of

[tex]f(x) = 2 {x}^{2} - 4x - 9[/tex]

is all real numbers.

Answer:

All real numbers

Step-by-step explanation:

The domain of a continuous parabola is always all real numbers or −∞ ≤ x ≤ ∞ because the ends of the parabola continue forever and when you graph this equation, you see that the ends of the parabola never stops, it continues on and on and on.

Answer: [tex]36.1\ units^2[/tex]

Step-by-step explanation:

You need to use the SAS area formula. This is:

[tex]A=\frac{a*b*sin(\alpha)}{2}[/tex]

Given the triangle ABC, you know that:

[tex]a=AC=10\ units\\b=BC=17\ units\\\alpha=\angle ABC=25.1\°[/tex]

 Therefore, substituting these values into the formula, you get that the area of the triangle ABC is:

[tex]A=\frac{(10\ units)(17\ units)*sin(25.1\°)}{2}\\\\A=36.1\ units^2[/tex]

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x^{-2}y^{-4}x^3)^{-2}\implies (x^{-2}x^3y^{-4})^{-2}\implies (x^{-2+3}y^{-4})^{-2}\implies (x^{1}y^{-4})^{-2} \\\\\\ \stackrel{\textit{distributing the exponent}~\hfill }{(x^{-2\cdot 1}y^{-2\cdot -4})\implies x^{-2}y^8}\implies \cfrac{1}{x^2}\cdot y^8\implies \cfrac{y^8}{x^2}[/tex]

The correct recursive function is: [tex]\[ f(n) = f(n-1) \times (1 - 0.30) + 25 \][/tex]

Let's break down the problem:

At the start, there are 100 t-shirts in the store (f(0) = 100).

Each month, 30% of the current stock is sold, and 25 new t-shirts arrive.

So, if we denote the number of t-shirts in the store at the beginning of the nth month as f(n), we can represent the recursive relationship as follows:

f(n) = f(n-1) * (1 - 0.30) + 25

This equation means that the number of t-shirts in the store at the beginning of the nth month is equal to 70% of the number of t-shirts at the beginning of the previous month (because 30% were sold), plus 25 (because 25 new t-shirts arrive).

In this function:

- [tex]\( f(n) \)[/tex] represents the number of t-shirts in the store at the beginning of the nth month.

- [tex]\( f(n-1) \)[/tex] represents the number of t-shirts in the store at the beginning of the (n-1)th month.

- [tex]\( (1 - 0.30) \)[/tex] represents 70% of the t-shirts from the previous month remaining after 30% are sold.

- [tex]\( + 25 \)[/tex] represents the 25 new t-shirts that arrive each month.

Complete question: A store had 100 t-shirts. Each month, 30% of the t-shirts were sold and 25 new t-shirts arrived in shipments. Which recursive function best represents the number of t- shirts in the store, given that f(0)=100?

a-f(n)=f(n-1) 0.3+25,n>0

b-f(n)=100-f(n-1) = ( 3.3+25 n>0

c-f(n)=f(n-1) -( 0.7+25 n>0

d-f(n)=100-f(n-1) - C 7+25 n>0

Answer:

a. Arithmetic

b. [tex]a_{n} = a_{n-1} + 15[/tex]

c. [tex]a_{n} = 15n + 125[/tex]

Step-by-step explanation:

A sequence is arithmetic when the difference between one term and the next is a constant. On the other hand, a sequence is geometric when the next term is found by multiplying the previous by a constant.

In this case, the next term of the sequence can be found by adding $15. Therefore, the sequence is ARITHMETIC ✔️

The recursive formula will be the following: [tex]a_{n} = a_{n-1} + 15[/tex]

The explicit formula is the following: [tex]a_{n} = 15n + 125[/tex]

Answer:

(1,9)

Step-by-step explanation:

For this case we must locate the point M in the coordinate system, once we visualize it we count the number of grid that are between the axis "x" and the point M, we have that there are 9 grids, then the coordinate "y" from the point M is 9. Now we count the number of grids between the "y" axis and the point M, we see that there is a grid, so the coordinate "x" of the point M is 1.

Point M: (1,9)

Answer:

Option C

Answer:

First: 15

Second: 21

Third: 45

Step-by-step explanation:

In order to create the equation we need to represent the evenings with an alebraic term, in thsi case we are going to represent the second evening with an X

Second evening:x

The first night she got 6 fewer calls than the second: Second-6=x-6

The third night she received 3 times the first: 3(first night)=3(x-6)

The equation is First Night plus second night plus third night equals 81.

[tex]First+second+third=81\\x+(x-7)+3(x-6)=81\\x+x-7+3x-18=81\\5x=81+21+6\\5x=105\\x=\frac{105}{5} \\x=21[/tex]

So the first evening he received 15 calls, the second he received 21 and the third one he received 45.

Answer:

144 people

Step-by-step explanation:

1 gallon  = 4 quarts

6 gallons = 6*4 quarts

6 gallons = 24 quarts

1 quarts= 2 pts

24 quarts = 2*24 = 48 pts

1 pts = 2 cups

48 pts = 48 * 2 cups = 96 cups

We know 6 gallons = 96 cups

96 cups ÷ 2/3 cups per person =

Copy dot flip

96 * 3/2 = 144 people

Answer:

Step-by-step explanation:

The graph of the new function would be the graph of the old one, translated 14 units to the left.

Answer:

C. After gaining independence, territory in both former colonies was divided due to religious conflicts

Step-by-step explanation:

The British had India as their colony, and Palestine as their mandate. Once the World War II ended though, the British saw that they are not in a financial position to be able to keep their colonies and mandates, so they decided to grant them independence. The independence didn't went as desired by the locals though, as both India and Palestine got partitioned because of religious reasons. India was partitioned into Hindu and Muslim part, while Palestine and Muslim and Jewish part. The situation in the Indian subcontinent quickly escalated, as well as in Palestine where the Arabs saw the formation of Israel as stealing of their land.

Answer:  C. After gaining independence, territory in both former colonies was  divided due to religious conflicts.

Answer:

cosine theta equals plus or minus two times square root of two over three, tangent theta equals plus or minus square root of two over four

Step-by-step explanation:

Given:

sinθ=1/3

θ=19.47 degrees

then

cosθ= cos(19.47)=0.942 = 2(√2/3)

tanθ=tan(19.47)=0.35= √2/4

Hence option two is correct:cosine theta equals plus or minus two times square root of two over three, tangent theta equals plus or minus square root of two over four!

Answer:

So second choice.

[tex]\cos(\theta)=\pm \frac{2\sqrt{2}}{3}[/tex]

[tex]\tan(\theta)=\pm \frac{\sqrt{2}}{4}[/tex]

Step-by-step explanation:

I'm going to use a Pythagorean Identity, name the one that says:

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex].

We are given: [tex]\sin(\theta)=\frac{1}{3}[/tex].

Inserting this into our identity above gives us:

[tex](\frac{1}{3})^2+\cos^2(\theta)=1[/tex]

Time to solve this for the cosine value:

[tex]\frac{1}{9}+\cos^2(\theta)=1[/tex]

Subtract 1/9 on both sides:

[tex]\cos^2(\theta)=1-\frac{1}{9}[/tex]

[tex]\cos^2(\theta)=\frac{8}{9}[/tex]

Square root both sides:

[tex]\cos(\theta)=\pm \sqrt{\frac{8}{9}}[/tex]

9 is a perfect square but 8 is not.

8 does contain a factor that is a perfect square which is 4.

So time for a rewrite:

[tex]\cos(\theta)=\pm \frac{\sqrt{4}\sqrt{2}}{3}[/tex]

[tex]\cos(\theta)=\pm \frac{2\sqrt{2}}{3}[/tex]

So without any other give information we can't know if cosine is positive or negative.

Now time for the tangent value.

You can find tangent value by using a quotient identity:

[tex]\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}[/tex]

[tex]\tan(\theta)= \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}[/tex]

Multiply top and bottom by 3 get's rid of the 3's on the bottom of each mini-fraction:

[tex]\tan(\theta)=\pm \frac{1}{2 \sqrt{2}}[/tex]

Multiply top and bottom by sqrt(2) to get rid of the square root on bottom:

[tex]\tan(\theta)=\pm \frac{1(\sqrt{2})}{2\sqrt{2}(\sqrt{2})}[/tex]

Simplifying:

[tex]\tan(\theta)=\pm \frac{\sqrt{2}}{2(2)}[/tex]

[tex]\tan(\theta)=\pm \frac{\sqrt{2}}{4}[/tex]

Answer:

Y=3

Step-by-step explanation:

Sin30=y/6

y=6sin30

Y=3