Given the table below for selected values of f(x), use 6 left rectangles to estimate the value of

.
x
1
3
4
6
7
9
10
f(x)
4
8
6
10
10
12
16

Numerical Answers Expected!
Answer for Blank 1:

Answer:

x = log base 4 of 2

Step-by-step explanation:

I'm assuming this is truly an exponential function as you state and not a mistype.

6^x = 2

Take the log of each side:

x · log(6) = log(2)

Divide each side by log(6):

x = log(2) / log(6)

x = 0.30103 / 0.77815

x = 0.3869... (rounded)

Answer:

the answer is D. 3^7√3

Step-by-step explanation:

For this case we have to define properties of powers and roots:

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

We also have to:

[tex]3 ^ {15} = 3 ^ {14} * 3[/tex]

So:

[tex]\sqrt {3 ^ {15}} = \sqrt {3 ^ {14} * 3} = 3 ^ {\frac {14} {2}} * \sqrt {3} = 3 ^ 7 * \sqrt {3}[/tex]

Answer:

[tex]3 ^ 7 * \sqrt {3}[/tex]

Option D

a) Yes, s is a subspace of v because the three conditions for a subspace are satisfied. b) Yes, s is a subspace of v because the three conditions for a subspace are satisfied. c) Yes, s is a subspace of v because the three conditions for a subspace are satisfied.

a. v=mn(r) is the vector space of all m x n matrices with entries in the real numbers. In this case, s is a subspace of v if it satisfies the three conditions: (1) the zero vector is in s, (2) s is closed under vector addition, and (3) s is closed under scalar multiplication. Since the zero matrix is an upper triangular matrix, it satisfies the first condition. If two upper triangular matrices are added, the result will also be an upper triangular matrix, satisfying the second condition. And if an upper triangular matrix is multiplied by a scalar, the result is still an upper triangular matrix, satisfying the third condition. Therefore, s is a subspace of v.

b. In this case, v is the vector space of all real-valued functions defined on the interval (-∞, ∞). The subset s consists of functions satisfying f(0) = 0. Similar to part a, we need to check if s satisfies the three conditions to be considered a subspace. The zero function satisfies f(0) = 0, so it satisfies the first condition. If two functions in s are added, the sum will also have f(0) = 0, satisfying the second condition. And if a function in s is multiplied by a scalar, the result will still have f(0) = 0, satisfying the third condition. Therefore, s is a subspace of v.

c. In this case, v is the vector space of all second-order linear homogeneous differential equations. The subset s consists of functions satisfying y'' - 4y' + 3y = 0. To be considered a subspace, s would need to satisfy the three conditions: (1) the zero element is in s, (2) s is closed under addition, and (3) s is closed under scalar multiplication. The zero function satisfies the differential equation, so it satisfies the first condition. If two functions in s are added, the sum will also satisfy the differential equation, satisfying the second condition. And if a function in s is multiplied by a scalar, the result will still satisfy the differential equation, satisfying the third condition. Therefore, s is a subspace of v.

Answer:

your answer is x=16/11

explanation:

solve for x by simplifying both sides of the equation then isolation the variable.

exact form: 16/11

decimal form: 1.45

mixed number form: 1  5/11

hope this helps

~~bangtanboys7

Answer: [tex]x=\frac{16}{11}[/tex]

Step-by-step explanation:

To solve the equation shown in the problem you must:

- Add the like terms, as following:

[tex]\frac{3}{4}x+2x=\frac{5}{3}+\frac{7}{3}\\ \frac{11}{4}x=4[/tex]

- Multiply both sides by 4.

- Divide both sides of the equation by 11.

Therefore, the result is:

 [tex](4)\frac{11}{4}x=4(4)\\11x=16\\x=\frac{16}{11}[/tex]

Answer:

Original price of the dress was $97.88

Step-by-step explanation:

40/100=39.15/d

0.4d=39.15

0.4d=39.15

d=39.15/0.4

d=97.88

The original price of the dress is $97.875.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Danielle paid $39.15.

But Danielle paid after 40% off.

So, the price before discount

40% of x = 39.15

x= 3915/40

x= $97.875

Hence, the original price is $97.875.

Learn more about Algebra here:

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ANSWER

[tex] \angle \: KGI =50 \degree[/tex]

[tex]\angle \: KJI = 130 \degree[/tex]

EXPLANATION

Angles in the same segment are equal.

This implies that;

[tex] \angle \: KGI = \angle \:H[/tex]

Hence,

[tex] \angle \: KGI =50 \degree[/tex]

Also GJKI is a cyclic quadrilateral.

The opposite angles of a cyclic quadrilateral sums up to 180°.

This means that,

[tex] \angle \: KJI + \angle \: KGI = 180 \degree[/tex]

[tex] \angle \: KJI +50 \degree = 180 \degree[/tex]

[tex]\angle \: KJI = 180 \degree - 50 \degree[/tex]

[tex]\angle \: KJI = 130 \degree[/tex]

Answer:

5 books must be read in 1 month for the total charges from each club to be equal.

Step-by-step explanation:

Monthly Charges of ABC club = 40$

Per book read charges of ABC club = 2$

amount of book read = x

Total charges of ABC club = 40 + 2x

Monthly Charges of Easy book club = 40$

Per book read charges of Easy Book club = 3$

Total charges of Easy book club = 35 + 3x

To calculate how many books must be read in 1 month for the total charges from each club to be equal,

Total charges of ABC club =  Total charges of Easy book club

40 + 2x = 35 + 3x

40 - 35 = 3x -2x

5 = x

x = 5

Therefore, 5 books must be read in 1 month for the total charges from each club to be equal.

Answer:

see explanation

Step-by-step explanation:

(1)

given

4x² = 81 ( divide both sides by 4 )

x² = [tex]\frac{81}{4}[/tex] ( take the square root of both sides )

x = ± [tex]\sqrt{\frac{81}{4} }[/tex] = ± [tex]\frac{9}{2}[/tex]

---------------------------------------------------------------------

(2)

subtract 7 from both sides

(4x - 3)² = 32 ( take the square root of both sides )

4x - 3 = ± [tex]\sqrt{32}[/tex] = ± 4[tex]\sqrt{2}[/tex]

Add 3 to both sides

4x = 3 ± 4[tex]\sqrt{2}[/tex] ( divide both sides by 4 )

x = [tex]\frac{3}{4}[/tex] ± [tex]\sqrt{2}[/tex]

Answer:

17.85 months

Step-by-step explanation:

original number of rabbits=50

% increase per month=12%

number of months=x

form equation for 1000 rabbits

(112/100) ×50× x = 1000

56x=1000

x=1000/56

x=17.857 months

Answer:

  your choices are correct

Step-by-step explanation:

sin(x +π/2) is a translation of the sine function to the left by π/2 units, which makes it look exactly like the cosine function that you want.

cos(-x) is the same as cos(x), since the cosine function is an even function.

___

sin(x -π/2) will look like -cos(x), not what you want.

The third choice is a reflection across the x-axis of the function you started with. It is not equivalent.

Answer:

Final answer is [tex]x=\frac{\pi}{3}[/tex] and [tex]x=\frac{5\pi}{3}[/tex].

Step-by-step explanation:

Given equation is [tex]1-\cos\left(\theta\right)=\frac{1}{2}[/tex]

Now we need to find the solution of  [tex]1-\cos\left(\theta\right)=\frac{1}{2}[/tex] in given interval [tex][0, 2\pi ][/tex].

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

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

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

[tex]\cos\left(\theta\right)=\frac{1}{2}[/tex]

which gives [tex]x=\frac{\pi}{3}[/tex] and [tex]x=\frac{5\pi}{3}[/tex] in the given interval.

Hence final answer is [tex]x=\frac{\pi}{3}[/tex] and [tex]x=\frac{5\pi}{3}[/tex].

In the interval [0, 2π], the cosine function takes on the value 1/2 at two specific angles: π/3 and 5π/3.

To solve the equation 1 - cos(theta) = 1/2 on the interval [0, 2π], this is done by:

Subtract 1/2 from both sides of the equation to isolate the cosine term:

1 - cos(theta) - 1/2 = 0

-cos(theta) + 1/2 = 0

So multiply both sides by -1 to get rid of the negative sign: cos(theta) - 1/2 = 0

1/2 can be written as 2/4: cos(theta) - 2/4 = 0

So look for common denominator for the fraction on the left side, and is 4:

(4*cos(theta) - 2)/4 = 0

Then Multiply both sides by 4 to remove the fraction: 4*cos(theta) - 2 = 0

So, add 2 to both sides: 4*cos(theta) = 2

Lastly divide both sides by 4: cos(theta) = 1/2

Therefore, the solutions to the equation are: theta = π/3 and theta = 5π/3.

Read more about  interval  here:

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The correct equation to find out how much was spent on the clothes is 50 - c = 16. Solving this, we find that c, the cost of the clothes, is $34.

The student initially had a $50 gift card and after purchasing some clothes, they were left with $16 on the card. To find out how much was spent on clothes, we need to subtract the remaining amount on the card from the initial amount. The correct equation to represent this situation is:

B. 50 - c = 16

We can then solve for c, which represents the cost of the clothes:

50 - 16 = c
34 = c

So, the amount spent on clothes is $34.

Answer:

The answer is 9.6

hope this helps!

Answer:

[tex]3,358\ people[/tex]  

Step-by-step explanation:

The formula to calculate the exponential growth function is equal to

[tex]f(x)=P(e)^{rx}[/tex]  

where  

f(x) is the population  

P is the population in the year 2000  

r is the rate in decimal  

x is number of years since 2000  

e is the mathematical constant number

we have  

[tex]x=2020-2000=20\ years\\ P=2,400\\ r=0.0168[/tex]  

substitute in the formula above  

[tex]f(x)=2,400(e)^{0.0168*20}[/tex]  

[tex]f(x)=3,358\ people[/tex]  

BCA is 90 degrees, because a tangent line is perpendicular to the raduis line BC.

Final answer:

The measure of angle M is 90 degrees.

Explanation:

The measure of angle M is 90 degrees. To understand why, we can use the fact that a line tangent to a circle is perpendicular to the radius drawn to the point of tangency. In this case, line AD is tangent to circle B at point C, so we can draw line AC, which is the radius of the circle, and find the measure of angle M by finding the complement of the angle formed by lines AD and AC. Since the complement of a 90-degree angle is 90 degrees, the measure of angle M is 90 degrees.

Answer:

i think its B on edge

Final answer:

The division algorithm for polynomials establishes that a polynomial p(x) can be divided by a non-zero polynomial d(x) (with degree less or equal to p(x)), to yield unique quotient q(x) and remainder r(x), with r(x) having a lower degree than d(x).

Explanation:

The division algorithm in the context of polynomials is a fundamental concept in algebra that stipulates for any two polynomials p(x) and d(x), with d(x) ≠ 0 and the degree of d(x) less than or equal to the degree of p(x), there exist unique polynomials q(x) and r(x) such that p(x) = d(x) × q(x) + r(x).

In this scenario, q(x) is referred to as the quotient and r(x) is the remainder. The degree of the remainder r(x) will always be less than the degree of d(x), following the division algorithm.

When applying this algorithm to special sets of polynomials like Legendre polynomials, additional properties can be observed, such as the roots of the polynomials or specific transformations like the Poisson bracket that could arise in mathematical physics. Moreover, the concept extends to rational functions, which are the quotients of polynomials.

Answer:

5x = 14

Step-by-step explanation:

If 5 yards of fabric is $14 you need an equation that would solve how much 1 yard of fabric costs. You can say 5x = 14 or x = 2.8 which means that one yard of fabric (1x or just x) is $2.80.

Answer: [tex]y==\frac{14}{5}x[/tex]

Step-by-step explanation:

By definition, we know that Direct proportion equation has the following form:

[tex]y=kx[/tex]

Where k is the constant of proportionality.

Then, If 5 yards of fabric cost $14, you can calculate k as following:

[tex]14=k(5)\\k=\frac{14}{5}[/tex]

Therefore substituting the value of k into the first equation, you obtain the following equation:

[tex]y==\frac{14}{5}x[/tex]

Answer:

S3 = 39

Step-by-step explanation:

* an = 3(3)^(n-1) is a geometric sequence

* The general rule of the geometric sequence is:

 an = a(r)^(n-1)

Where:

a is the first term

r is the common difference between each consecutive terms

n is the position of the term in the sequence

The rules means:

- a1 = a , a2 = ar , a3 = ar² , a4 = ar³ , ........................

∵ an = 3(3)^(n-1)

∴ a = 3 and r = 3

∴ a1 = 3

∴ a2 = 3(3) = 9

∴ a3 = 3(3)² = 27

* S3 = a1 + a2 + a3

∴ S3 = 3 + 9 + 27 = 39

Note:

We can use the rule of the sum:

Sn = a(1 - r^n)/(1 - r)

S3 = 3(1 - 3³)/1 - 3 = 3(1 - 27)/-2 = 3(-26)/-2 =3(13) = 39

Answer:

The correct answer is S₃  = 39

Step-by-step explanation:

It is given that,

aₙ = 3(3)ⁿ⁻¹

To find a₁

a₁ = 3(3)¹⁻¹ = 3(3)°

= 3 * 1 = 3

To find a₂

a₂ = 3(3)²⁻¹ = 3(3)¹

= 3 * 3 = 9

To find a₃

a₃ = 3(3)³⁻¹ = 3(3)²

= 3 * 9 = 27

To find the value of S₃

S₃ = a₁ + a₂ + a₃

 = 3 + 9 + 27 = 39

Therefore the correct answer is S₃  = 39

Answer:

B - closing costs are increased

Step-by-step explanation:

All of the other options are advantages to purchasing points. You want lower monthly payments (a), a tax break (c), and lower interest rate (d)

Answer:                

The correct answer is option B.closing costs are increased.

Step-by-step explanation:                        

Mortgage points or discount points refers to the fees paid directly to the lender during closing in exchange for a reduced interest rate.

In this way the buyer buys down the rate, that helps in reducing his monthly mortgage payments.

So, option A, C and D are the advantages of purchasing discount points.

Answer:

Step-by-step explanation:

Look at the picture.

A₁ = 2 · 2 = 4

A₂ = 2 · 3 = 6

The area of a rhombus:

A = A₁ + A₂ ⇒ A = 4 + 6 = 10

You can use the formula of an area of a rhombus:

[tex]A=\dfrac{d_1d_2}{2}[/tex]

d₁ = 4, d₂ = 5

Substitute:

[tex]A=\dfrac{(4)(5)}{2}=(2)(5)=10[/tex]

Answer:

10 ft²

Step-by-step explanation:

A = 1/2 (d1) (d2)

A = 1/2 (4) (5)

1/2 x 20

=10 ft²

[tex]\\Rewrite \ in \ form.\\\\(7x)^2 - (6y)^2\\\\\\\\Use \ difference \ of \ squares \  rule.\\\\(7x  + 6y) (7x - 6y)\\\\\\Therefore, \ you \ get \fbox{(7x+6y)&(7x-6y)}.[/tex]

Answer:

The answer is 1/2 which i think that's what you meant from C.

Step-by-step explanation:

A standard deck of cards has 52 cards. 13 of these cards are spades and 13 are diamonds.

the answer to your question is c :]

Answer:

log9(11x)

Step-by-step explanation:

log9(11) + log9(x)

We know that loga(b) + loga(c) = loga(b*c)

log9(11*x)

log9(11x)

Final answer:

To rewrite a sum of two logarithms as a single logarithm, combine them using the property that the log of a product equals the sum of the logs. For example, log a + log b becomes log (ab).

Explanation:

To rewrite the sum of two logarithms as a single logarithm, we use the relevant log properties. One of the most important properties of exponents is that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers, which is log xy = log x + log y. Conversely, the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers. So, if you have two logarithms of the same base you're adding, like log a + log b, you can combine them into a single log by multiplying the two arguments to get log (a*b).

An example using numbers could look like this:

log₂(3) + log₂(5) = log₂(3*5) = log₂(15)

Therefore, the sum of two logarithms, log a + log b, can be rewritten as log (ab), which expresses the multiplication of a and b within a single logarithm.

Answer:

0.0085 centimeters.

Step-by-step explanation:

85/10000 is equal to 0.0085 centimeters, which is absurdly thin for anything, really.

Answer:

The distance from the balloon to the soccer fields = 3.6 miles ⇒ answer (b)

Step-by-step explanation:

* Let the hot air balloon  at point A , the soccer fields

  at point B and the football field at point C

∵ The measure of the angle of depression to the

   soccer fields is 20° 15'

∴ The measure of angle B = 20° 15'

∵ The measure of the angle of depression to the

   football field is 62° 30'

∴ The measure of angle C = 62° 30'

∵ The sum of measures of the interior angles of any triangle = 180°

∴ The measure of angle A = 180 - (20° 15' + 62° 30') = 97° 15'

* The distance between the balloon and the soccer field

  is represented by the side AB of triangle ABC

- Use the sin Rule to find the length of side AB

∵ a/sin(A) = b/sin(B) = c/sin(C)

- a is the side opposite to angle A, b is the side opposite

 to angle B and c is the side opposite to angle C

∵ AB = c ⇒ opposite to angle C

∵ The distance between the two fields = 4 miles

∴ BC = 4 miles

∵ BC = a ⇒ opposite to angle A

∴ 4/sin(97° 15') = c/sin(62° 30')

∴ c = (4 × sin(62° 30')) ÷ sin(97° 15')

∴ c = 3.6 miles

∴ The distance from the balloon to the soccer fields = 3.6 miles

   answer (b)

$240

800x.06= 48

48x5=240

➷ The formula for a right triangle is:

(b x h) / 2

We know this:

(12 x n) / 2 = 30

Multiply both sides by 2:

12 x n = 60

Divide both sides by 12:

n = 5

Now we know the height is 5

We can now use Pythagoras' theorem to calculate the hypotenuse:

c^2 = 5^2 + 12^2

c^2 = 169

Square root it:

c = 13

The hypotenuse is 13 ft

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

The formula for working out the area of a triangle:

(b x h) / 2

[tex](12*h)/2=30\\(*2)\\12*h=60h\\h=5[/tex]

Pythagoras' theorem to calculate the hypotenuse:

c² = 5² + 12²

c² = 169

c = 13

The hypotenuse is 13 ft

Step-by-step explanation:

Answer:

1 mile a minute.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The ratios of corresponding linear dimensions are identical:

  5/2 = 15/6 = 2.5

so we can conclude the figures are similar. The scale factor is the ratio of corresponding dimensions:

  first : second = 5 : 2 . . . or . . . 2.5 : 1

Answer:

Yes.

Scale factor = 2.5.

Step-by-step explanation:

They are similar because corresponding dimensions are in the same ratio:

2/5 = 6/15.

The scale factor = 5/2 = 2.5.