What is the gcf of 45 and 9?​

log₁₆64 is3/2

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a fixed number, base b, must be raised in order to create a specific number x, is represented by the logarithm of that number.

Given

log₁₆(64) = x

16ˣ=64

(2⁴)ˣ=2⁶

2⁴ˣ=2⁶

4x=6

x=3/2

To know more about logarithm refer to :

https://brainly.com/question/27407133

#SPJ2

The log₁₆64 exists 3/2. Therefore, the correct answer is option c.3/2.

The logarithm exists as exponentiation's opposite function in mathematics. This signifies that the exponent to which a fixed number, base b, must be presented to make a specific number x, exists characterized by the logarithm of that number.

Given:

log₁₆(64) = x

16ˣ = 64

Simplifying the above equation, we get

(2⁴)ˣ = 2⁶

2⁴ˣ = 2⁶

4x = 6

x = 3/2

log₁₆(64) = 3/2.

Therefore, the correct answer is option c.3/2.

To learn more about logarithm

https://brainly.com/question/9046022

#SPJ2

Answer:

[tex]y = \frac{1}{2}x+10[/tex]

Step-by-step explanation:

The given path is:

y = -2x+5

Comparing with the standard form of equation:

y = mx+b

So,

m = -2

We know that product of slopes of two perpendicular lines is -1

Let m1 be the slope of the perpendicular line

m*m1=-1

-2*m1 = -1

m1 = -1/-2

m1 = 1/2

So the slope of perpendicular path is 1/2.

Since the new path passes through (-2,9)

[tex]9 = \frac{1}{2}(-2) +b\\9 = -1 +b\\b = 10[/tex]

Putting the values of m and b in standard form

[tex]y = \frac{1}{2}x+10[/tex]

Hence the equation of new path is:

[tex]y = \frac{1}{2}x+10[/tex] ..

x-8= 15

x-8+8=15+8

x= 23

Check answer by using substitution method

x-8= 15

23-8= 15

15= 15

Answer is X= 23 (D.)

[tex](100\%-15\%-25\%)\cdot240=60\%\cdot240=144[/tex]

Answer:

C) 144

Step-by-step explanation:

Somewhat Dissatisfied is 15%, and Completely Dissatisfied is 25%. The two dissatisfied parts add to 40%.

That means the two satisfied parts add to 60%.

60% were either Somewhat Satisfied or Completely Satisfied.

240 customers responded to the survey.

60% of 240 = 0.6 * 240 = 144

Answer: C) 144

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=9\\ \theta =6 \end{cases}\implies s=\cfrac{\pi (6)(9)}{180}\implies s=\cfrac{3\pi }{10}\implies s\approx 0.94[/tex]

The arc length s cut off by a central angle of 6 degrees

[tex]$s=\frac{3 \pi}{10} f t$[/tex].

Let 's' define the arc length, '[tex]$\theta$[/tex]' define the central angle in radians and 'r' be the radius of the circle. Then a central angle of '[tex]$\theta$[/tex]' radians in a circle of radius r subtends an arc of length.

We must define [tex]$6^{\circ}$[/tex] in radians

[tex]$s=r \theta$[/tex]

[tex]$180^{\circ}-\pi \mathrm{rad}$[/tex]

[tex]$6^{\circ}-\theta \mathrm{rad}$[/tex]

Then

[tex]$\theta=\frac{6}{180} \cdot \pi=\frac{\pi}{30}$$[/tex]

The arc length s cut off by a central angle of 6 degrees

[tex]$s=9 f t\left(\frac{\pi}{30}\right)=\frac{3 \pi}{10} \mathrm{ft}$$[/tex]

[tex]$s=\frac{3 \pi}{10} f t$[/tex].

Therefore, the arc length s cut off by a central angle of 6 degrees is

[tex]$s=\frac{3 \pi}{10} f t$[/tex].

To learn more about arc length

https://brainly.com/question/1597355

#SPJ2

Angle a is opposite to angle b because they're vertical angles.

It should be noted that vertical angles mean the angle that are opposite each other.

In this case, angle a is opposite to angle b because they're vertical angles. This means they are congruent. In the image of the intersecting roads, angles 'a' and 'b' are opposite, and angles 'c' and 'd' are opposite. Another name for opposite angles is vertical angles because the two angles share the same vertex or corner.

Learn more about angles on:

https://brainly.com/question/14362353

#SPJ2

Answer:

x = 4 ± 3[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given

4(x - 4)² - 180 = 0 ( add 180 to both sides )

4(x - 4)² = 180 ( divide both sides by 4 )

(x - 4)² = 45 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{45}[/tex] = ± 3[tex]\sqrt{5}[/tex]

Add 4 to both sides

x = 4 ± 3[tex]\sqrt{5}[/tex]

The value of x is equal to [tex]4 +3\sqrt{5}[/tex] and [tex]4 -3\sqrt{5}[/tex] by solving the quadratic equation that is taking the square root of both sides and also by using the concept of transposition.

Given the quadratic equation [tex]4(x-4)^2-180=0[/tex] by taking the square root of both sides

To solve a quadratic equation [tex]4(x-4)^2-180=0[/tex] by taking the square root of both sides, follow steps:

Step 1: Consider the given quadratic equation:

[tex]4(x-4)^2-180=0[/tex]

Add by  18  on both sides, gives;

[tex]4(x-4)^2-180+180=0+180[/tex]

On operating algebra sum results:

[tex]4(x-4)^2=180[/tex]

Step 2: Isolate the LHS [tex]4(x-4)^2[/tex]  from number 4 by dividing both sides by 4 yields:

[tex]\frac{4(x-4)^2}{4} =\frac{180}{4}[/tex]

On cancelation of 4 on LHS and divide 180 by 4 on RHS results in :

[tex](x-4)^2=45[/tex]

Factorize RHS with a perfect square 9 :

[tex](x-4)^2=9\times5[/tex]

Step 3: Taking the square root of both sides results :

[tex]\sqrt{(x-4)^2} = \sqrt{9\times5}[/tex]

On taking square roots results:

[tex](x-4) = \pm3\sqrt{5}[/tex]

Add by 4 on both sides, gives:

[tex]x=4 \pm3\sqrt{5}[/tex]

Therefore, the value of x is equal to [tex]4 +3\sqrt{5}[/tex] and [tex]4 -3\sqrt{5}[/tex] by solving the quadratic equation that is taking the square root of both sides and also by using the concept of transposition.

Learn more about quadratic equation here:

https://brainly.com/question/30098550

#SPJ4

Option: B is the correct answer.

         B)    [tex]\dfrac{24}{25}[/tex]

We know that the cosine trignometric ratio corresponding to a angle theta(θ) is defined as the ratio of the adjacent side to the angle theta to the hypotenuse of the triangle containing θ as one of the angle.

By looking at the figure we observe that the triangle is a right angled triangle and the length of the side adjacent to angle 16° is: 24 and the hypotenuse of the triangle is: 25.

Hence, we get:

[tex]\cos 16=\dfrac{24}{25}[/tex]

According to the given figure, the value of Cos 16° = 24/25.

Hence the correct option is B.

Given that a right triangle with hypotenuse 25, base 24 and the perpendicular is 7 units.

We need to find the value of Cos16°.

To find the value of cos(16°) in the given right triangle, we can use the trigonometric ratio for cosine:

cos(θ) = adjacent side / hypotenuse

In this case, θ = 16°, and we know the adjacent side is the base of the right triangle, which is 24 units, and the hypotenuse is 25 units.

Now, plug the values into the formula:

cos(16°) = 24 / 25

Hence the value of Cos(16°) = 24 / 25

Hence the correct option is B.

Learn more about Cosine Function click;

https://brainly.com/question/3876065

#SPJ6

Answer:

A-4+3=3+4

Step-by-step explanation:

The commutative property of addition, also known as the order property of addition, means that a given group of numbers can be added in any order and their sum will always be the same.

Answer:

A

Step-by-step explanation:

commutative is where one equals out to another and then when using addition you have to use the plus sign

D{-3,2,7} is the domain of the set {(-3,5),(2,0),(7,-5)}

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

To know more about domain refer to :

https://brainly.com/question/11787743

#SPJ2

Answer:

The equivalent trigonometric ratio in Quadrant I is [tex]-\cos (\frac{3\pi}{8})[/tex]

Step-by-step explanation:

The terminal side of [tex]\frac{27\pi}{8}[/tex] is in the 3rd quadrant.

The principal angle is [tex]\frac{3\pi}{8}[/tex]

In other words, the terminal side of [tex]\frac{27\pi}{8}[/tex]  makes an acute angle of [tex]\frac{3\pi}{8}[/tex] radian with the positive x-axis. Acute angles are in the first quadrant.

Since the cosine ratio is negative in the 3rd quadrant,

[tex]\cos (\frac{27\pi}{8})=-\cos (\frac{3\pi}{8})[/tex]

Answer:

c on edgen

Step-by-step explanation:

Answer:

1. F(x) = 5/4 x - 1

2. F(x) = 3x - 9

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

(1)

let (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (4, 4), then

m = [tex]\frac{4+1}{4-0}[/tex] = [tex]\frac{5}{4}[/tex]

Note the line crosses the y- axis at (0, - 1) ⇒ c = - 1

y = [tex]\frac{5}{4}[/tex] x - 1 ← in slope- intercept form

(2)

let (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (1, - 6), then

m = [tex]\frac{-6-3}{1-4}[/tex] = [tex]\frac{-9}{-3}[/tex] = 3, hence

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 3), then

3 = 12 + c ⇒ c = 3 - 12 = - 9

y = 3x - 9 ← in slope- intercept form

Answer:

h(1) = 1.81 and h(2) = 21.44

Step-by-step explanation:

* Lets read the problem and solve it

- Evaluate means find the value, so evaluate h(x) means find the value

 of it at the given values of x

∵ h(x) = 2.8x³ + 0.01x² - 1

∵ x = 1 and x = 2

- Then find h(1) by substitute x by 1 and find h(2) by substitute x by 2

# At x = 1

∴ h(1) = 2.8(1)³ + 0.01(1)² - 1

∴ h(1) = 2.8(1) + 0.01(1) - 1

∴ h(1) = 2.8 + 0.01 - 1

∴ h(1) = 1.81

# At x = 2

∴ h(2) = 2.8(2)³ + 0.01(2)² - 1

∴ h(2) = 2.8(8) + 0.01(4) - 1

∴ h(2) = 22.4 + 0.04 - 1 ⇒ simplify

∴ h(2) = 21.44

* h(1) = 1.81 and h(2) = 21.44

Answer:

Part 1) Option a. [tex]240\ dices[/tex]

Part 2) Option c. [tex]9.156.24\ pounds[/tex]

Step-by-step explanation:

Part 1)

step 1

Find the volume of one dice

The volume is equal to

[tex]V=b^{3}[/tex]

we have

[tex]b=2\ cm[/tex]

substitute

[tex]V=2^{3}=8\ cm^{3}[/tex]

step 2

Find the volume of the box

The volume is equal to

[tex]V=LWH[/tex]

we have

[tex]L=20\ cm[/tex]

[tex]W=12\ cm[/tex]

[tex]H=8\ cm[/tex]

substitute

[tex]V=20*12*8=1,920\ cm^{3}[/tex]

step 3

Find the number of dices

Divide the volume of the box by the volume of one dice

[tex]1,920/8=240\ dices[/tex]

Part 2)

step 1

Find the volume of the cylinder

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=9\ ft[/tex]

[tex]h=12\ ft[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]V=(3.14)(9)^{2}(12)[/tex]

[tex]V=3,052.08\ ft^{3}[/tex]

step 2

Find how many pounds of sand will fit into the cylinder

using proportion

[tex]\frac{3}{1}\frac{pounds}{ft^{3}}=\frac{x}{3,052.08}\frac{pounds}{ft^{3}}\\ \\x=3,052.08*3\\ \\x=9.156.24\ pounds[/tex]

Answer:

B. Your didn't move but you went up to the C marking.

The  coordinates for point A of the square without using any new variables will be (O, d), i.e. option A.

Square is a 2D shape, having all sides equal and interior angles at 90 degrees.

We have,

A square on a graph with vertex at O, A, B, (c, d).

Now,

Side OB and A(c, d) are on x-axis,

While side OA and A(c, d) are on y-axis.

So,

We have to find the coordinates of A ,

So,

We know that sides of a squares are equal,

So,

OA = B(c, d)

So,

The coordinates of A will be (0, d).

Hence, we can say that the  coordinates for point A of the square without using any new variables will be (O, d), i.e. option A.

To know more about square click here

https://brainly.com/question/12875060

#SPJ2

a = interest rate of first CD

b = interest rate of second CD

and again, let's say the principal invested in each is $X.

[tex]\bf a-b=3\qquad \implies \qquad \boxed{b}=3+a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=240\\\\ \left( \frac{b}{100} \right)X=360 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=240\implies X=\cfrac{240}{~~\frac{a}{100}~~}\implies X=\cfrac{24000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{b}{100}~~}\implies X=\cfrac{36000}{b} \\\\[-0.35em] ~\dotfill\\\\[/tex]

[tex]\bf X=X\qquad thus\qquad \implies \cfrac{24000}{a}=\cfrac{36000}{b}\implies \cfrac{24000}{a}=\cfrac{36000}{\boxed{3+a}} \\\\\\ (3+a)24000=36000a\implies \cfrac{3+a}{a}=\cfrac{36000}{24000}\implies \cfrac{3-a}{a}=\cfrac{3}{2} \\\\\\ 6-2a=3a\implies 6=5a\implies \cfrac{6}{5}=a\implies 1\frac{1}{5}=a\implies \blacktriangleright 1.2 = x\blacktriangleleft[/tex]

[tex]\bf \stackrel{\textit{since we know that}}{b=3+a}\implies b=3+\cfrac{6}{5}\implies b=\cfrac{21}{5}\implies b=4\frac{1}{5}\implies \blacktriangleright b=4.2 \blacktriangleleft[/tex]

Answer: 300 feet

Step-by-step explanation:

Note that:

[tex]120-90 = 30[/tex]

[tex]150-120 = 30[/tex].

Then the balloon rises at a constant rate of 30 meters per minute.

We can represent this situation through an arithmetic sequence as shown below

[tex]a_n =a_1 + d(n-1)[/tex]

Where [tex]a_1=90[/tex] is the first term of the sequence and [tex]a_n[/tex] is the n-th term of the sequence and [tex]d=30[/tex] is the common difference between two consecutive terms.

In this case we look for the height of the balloon after 8 minutes.

Then we look for [tex]a_8[/tex]

[tex]a_8 = 90 + 30(8-1)[/tex]

[tex]a_8 = 90 + 30(7)[/tex]

[tex]a_8 = 300[/tex]

Answer:

[tex]\boxed{\text{300 ft}}[/tex]

Step-by-step explanation:

You have an arithmetic sequence in which

a₁ =  90

a₂ = 120

a₃ = 150

1. Calculate the explicit formula

This is an arithmetic sequence, because there is a constant difference of 30 between consecutive terms.

The explicit formula for the nth term of an arithmetic sequence is

aₙ = a₁ + d(n - 1 )

a₁ is the first term, and d is the difference in value between consecutive terms. Thus,  

aₙ = 90 + 30(n - 1) = 90 + 30n - 30

aₙ = 30n + 60

2. Calculate the eighth term

a₈ = 30 × 8 + 60 = 240 + 60 = 300

[tex]\text{In 8 min, the balloon rises }\boxed{\textbf{300 ft}}[/tex]

Answer:

(3,2)

Step-by-step explanation:

y=4x-10 y=2

2=4x-10

12=4x

3=x , so that's (3, _)

y=2 is given, so (3,2)

Answer:

a

Step-by-step explanation:

ANSWER

[tex]{(x + 1)}^{2} =12(y - 2)[/tex]

EXPLANATION

The original parabola has equation

[tex] {x}^{2} = 12y[/tex]

This parabola has its vertex at the origin:

If the parabola is shifted one unit left and two units up, then its new vertex is at (-1,2).

The equation of the new parabola is now of the form:

[tex] {(x - h)}^{2} =1 2(y - k)[/tex]

where (h,k) is the vertex.

Substitute the vertex to get:

[tex] {(x - - 1)}^{2} =12(y - 2)[/tex]

[tex]{(x + 1)}^{2} =12(y - 2)[/tex]

Answer:

1st box ⇒ perpendicular

2nd box ⇒ B and E

3rd box ⇒ congruent

Step-by-step explanation:

* Lets revise the case SAS of similarity

- SAS similarity : In two triangles, if two sets of corresponding sides  

   are proportional and the included angles are equal then the two  

   triangles are similar.

- Example : In triangle ABC and DEF, if m∠A = m∠D and  

  AB/DE = AC/DF then the two triangles are similar by SAS

* Lets solve the problem

- In Δ ABC and Δ DEF

∵ AB/DE = BC/EF = 1/2

- That means two sets of corresponding sides are proportion

∵ AB is a vertical side and BC is a horizontal side

∵ DE is a vertical side and EF is a horizontal side

∵ Horizontal and vertical lines are perpendicular

∴ AB ⊥ BC and DE ⊥ EF

- So angles B and E are right angles by definition of perpendicular

   lines

∵ All right angles are congruent

∴ m∠B = m∠D

∵ The two triangles have two sets of corresponding sides are

  proportion and the included angles are equal then the two

  triangles are similar

∴ △ABC ~ △DEF by the SAS similarity theorem

Answer:

1. Perpendicular

2. B and E

3. Congruent

Step-by-step explanation:

Horizontal and vertical lines are always perpendicular. So, the answer for the first gap is PERPENDICULAR.

Line BC is horizontal line, line AB is vertical line, so lines BC and AB are perpendicular and, therefore, angle B is right angle. Line EF is horizontal line, line ED is vertical line, so lines EF and ED are perpendicular and, therefore, angle E is right angle. So, answer for the second option is angles B and E.

Every two right angles are congruent.

Having two pairs of proportional sides and a pair of congruent adjacent angles, you can apply SAS similarity Postulate.

Answer

700 is 87.5% of 800

Step-by-step explanation:

Answer:

Option B is correct.

Step-by-step explanation:

[tex]\sqrt[5]{32x^5y^10z^15}[/tex]

We need to solve the above expression.

32 = 2x2x2x2x2 = 2^5

and we know 5√ = 1/5

solving

[tex]=\sqrt[5]{2^5x^5y^{10}z^{15}}\\=(2^5)^{1/5}(5x^5)^{1/5}(y^{10})^{1/5}(z^{15})^{1/5}\\=2xy^2z^3[/tex]

So, simplified form is 2xy^2z^3

So, Option B is correct.

Answer:

Step-by-step explanation:

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

We have the equation of the line in the point-slope form:

[tex]y-4=\dfrac{3}{4}(x+8)[/tex]

Convert it to the standard form:

[tex]y-4=\dfrac{3}{4}(x+8)[/tex]        multiply both sides by 4

[tex]4y-16=3(x+8)[/tex]          use the distributive property

[tex]4y-16=3x+24[/tex]           add 16 to both sides

[tex]4y=3x+40[/tex]         subtract 3x from both sides

[tex]-3x+4y=40[/tex]        change the signs

[tex]3x-4y=-40[/tex]

Answer:

19 red beads

Step-by-step explanation:

We first need to find a common denominator of 4/9, 1/5 and 1/4.

The common denominator is 180. Like in an expression, what we do to one side we have to do to the other.

Silver - 180/9 = 20 ; 20*4 = 80 so there are roughly 80 sliver beads.

Gold - 180/5 = 36 ; 36*1 = 36 so there are roughly 36 gold beads.

Blue - 180/4 = 45 ; 45*1 = 45 so there are roughly 56 blue beads.

180 - (silver+gold+blue) = red beads

180-161 = 19 red beads b/c ----->

80+36+45+19 = 180

To find the estimate of beads that are red, you add the fractions of silver, gold, and blue beads first and subtract that from the total. In this case, it is estimated that the red beads are 19/180 of Julia's total collection.

To find the fraction of the red beads that Julia collects for her craft projects, we first need to sum up the fractions of the silver, gold, and blue beads as these are given fractions.

By addition, we have 4/9 (silver beads) + 1/5 (gold beads) + 1/4 (blue beads). Add these fractions together to get the total fraction of non-red beads. Now, to get the fractions into a form that's easier to add, find the least common denominator (LCD).

The LCD of 9, 5, and 4 is 180. Then, convert each fraction to have this denominator: 80/180 (silver) + 36/180 (gold) + 45/180 (blue). Now you can add these fractions directly to get 161/180.

Since the total should be 1 (or 180/180 to keep the denominator constant), to find the fraction of the red beads, subtract the sum of the other beads from 1. Thus, 1 - 161/180 = 19/180. Therefore, Julia’s collection consists of approximately 19/180 red beads.

https://brainly.com/question/33261284

#SPJ2

Answer:

  The polynomial is prime.

Step-by-step explanation:

There are no factors of -6 that add to give +8. The polynomial cannot be factored using integers. It is prime.

Answer:The polynomial is prime.

Step-by-step explanation:

[tex]\bf \underset{\stackrel{\textit{declining}}{\textit{so it's negative}}}{\stackrel{\textit{grade of 8\%}}{-\cfrac{8}{100}}}\implies \stackrel{\textit{slope}}{-\cfrac{\stackrel{rise}{8}}{\stackrel{run}{100}}}\implies -\cfrac{2}{25}[/tex]

Answer:

p v q = x < -3 or x > 3

Step-by-step explanation:

We are given

p: x < -3

q: x > 3

and we need to find p v q

v symbols represents disjunction and in simple terms it is called "or"

So, p v q represents either p holds or q holds

So, p v q = x < -3 or x > 3

[tex]x<-3 \vee x>3[/tex]

Answer:

2.6  cm

Step-by-step explanation:

7 - 4.4 = 2.6 cm

-

The difference between 7 cm and 4.4 cm is 2.6 cm. But since we need to round to the place value of the less precise measurement (7 cm), our final answer is 3 cm.

To find the difference between 7 cm and 4.4 cm, we simply subtract the smaller number from the larger one. So, we have 7 cm - 4.4 cm which equals 2.6 cm. However, we need to round to the place value of the less precise measurement. The least precise measurement here is 7 cm (as it's rounded to the nearest whole number), so we round our answer to the nearest whole number as well, which gives us 3 cm.

https://brainly.com/question/16029533

#SPJ3

Answer:

x^1/12

Step-by-step explanation:

Hope this helped!

Answer:

How many characteristics are used to describe living things?

Step-by-step explanation:

Answer: 84

Step-by-step explanation:

Subtract the total (180 degrees) from the known angle (96 degrees).

180-96=84