write the equations in logarithmic form 7^3=343​

When Joshua Is 6 he reads 6 books, when he is 7 he reads 12 books, when he turns 8, he reads 24 books, when he turns 9 he reads 48 books, when Joshua turns 10 he reads 96 books

6+12+24+48+96=186

The answer is C

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Answer:

Joshua read 186 books form 6 to 10 years of age.

Step-by-step explanation:

Joshua reads 6 books at the age of 6.

He doubled the number of books he read the previous years.

Now the sequence will be a geometric sequence as

6, 12, 24, ......

We have to calculate the number of books he read from 6 years to 10 years of his age.

Since sum of n terms of a geometric sequence is given by

[tex]S_{n}=\frac{a(r^{n}-1 )}{r-1}[/tex]

where a = first term

r = common ratio

n = number of terms

[tex]S_{5}=\frac{6(2^{5}-1 )}{2-1}[/tex]

   = [tex]\frac{6(32-1)}{1}[/tex]

   = 6×31

   = 186 books

Therefore Joshua read 186 books form 6 to 10 years of age.

Answer:

C. >

Step-by-step explanation:

The answer is C. because 65 is greater than 56!

The average speed is the ratio of the total distance traveled to the time taken

The correct option for the interval with the greatest average speed is option  (1) the first hour to the second hour

The procedure by which the above option was arrived at is as follows:

The given table of values for the graph is presented as follows;

[tex]\begin{array}{|c|cc|} \mathbf{Time}&&\mathbf{Distance}\\1&&40\\2&&110\\4&&180\\6&&230\\8&&350\\10&&390\end{array}\right][/tex]

[tex]Average \ speed = \dfrac{Distance}{Time}[/tex]

The average speed of each interval in distance per hour are given as follows;

[tex]First \ and \ second \ hour, \ average \ speed = \dfrac{110 - 40}{2 - 1} = 70[/tex]

[tex]Second \ and \ fourth \ hour, \ average \ speed = \dfrac{180 - 110}{4 - 2} = 35[/tex]

[tex]Sixth \ and \ eight \ hour, \ average \ speed = \dfrac{350 - 230}{8 - 6} = 60[/tex]

[tex]Eight \ and \ tenth \ hour, \ average \ speed = \dfrac{390 - 350}{10 - 8} = 20[/tex]

Therefore the interval in which their average speed was the greatest is the first hour to the second hour

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Answer:

Answer 64*sqrt(2)

Step-by-step explanation:

Givens

c = 128 cm

a = b = ??

formula

a^2 + b^2 = c^2                            combine the two equal legs.

2a^2 = c^2                                    Substitute 128 for c

2a^2 = 128^2                                Square

2a^2 = 16384                               Divide by 2

a^2 = 16384/2                  

a^2 = 8192                                   Factor (8192)

8192 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2    count the 2s

8192 = 2^13                                 Break 13 into 2 equal values with 1 left over

sqrt(8192) = sqrt(2^6   *   2^6    *    2^1)

sqrt(8192) = 2^6 * sqrt(2)

The length of one leg is 64*sqrt(2)

Answer:

Length of one leg of the given triangle will be 64√2 cm.

Step-by-step explanation:

Length of the hypotenuse of a 45°- 45°- 90° triangle has been given as 128 cm.

Since two angles other than 90° are of same measure so other two sides of the triangle will be same in measure.

Therefore, by Pythagoras theorem,

Hypotenuse² = Leg(1)² + Leg(2)²

Let the measure of both the legs is x cm

(128)² = 2x²

16384 = 2x²

x² = [tex]\frac{16384}{2}[/tex]

x² = 8192

x = √8192

  = 64√2 cm

Therefore, length of one leg of the given triangle will be 64√2 cm.

Answer:

the second one

Answer:

Smallest angle = 23

Middle angle = 23 + 44 = 67

Right angle = 90

Step-by-step explanation:

Givens

Let the smallest angle = x

Let the middle angle = x + 44

Let the right angle = 90   which it always does.

All triangles = 180 degrees.

Equation

x + x + 44 + 90 = 180

Solution

2x + 44 + 90 = 180                       Combine the left

2x + 134 = 180                               Subtract 134 from both sides

2x +134-134 = 180 - 134                Combine

2x = 46                                          Divide by 2

2x/2 = 46/2                                   Do the division

x = 23

Answer:

2+3

Step-by-step explanation:

Answer:

A: Scalene - None of the sides are congruent or have the same measurements.

E: Acute - None of the triangle's angles are 90° or greater.

~

Answer:

Initial speed:

Step-by-step explanation:

Both equations are concerned about the time differences between A and B. To avoid unknowns in the denominators,

First equation:

"A takes 3 hours more than B to walk 30 km."

[tex]x = y + 3[/tex].

[tex]x - y = 3[/tex].

When A doubles his pace, he takes only 1/2 the initial time to cover the same distance. In other words, now it takes only [tex]x/2[/tex] hours for A to walk 30 km.

Second equation:

"[A] is ahead of B by 3/2 hours [on their 30-km walk.]"

[tex]\displaystyle \frac{x}{2} + \frac{3}{2} = y[/tex].

[tex]\displaystyle \frac{1}{2}x - y = -\frac{3}{2}[/tex].

Hence the two-by-two linear system:

[tex]\left\{\begin{aligned}&x - y = 3\\&\frac{1}{2}x - y = -\frac{3}{2}\end{aligned}\right.[/tex].

Solve this system for [tex]x[/tex] and [tex]y[/tex]:

Subtract the second equation from the first:

[tex]\displaystyle \frac{1}{2}x = \frac{9}{2}[/tex].

[tex]x = 9[/tex].

[tex]y = 6[/tex].

It initially takes 9 hours for A to walk 30 kilometers. The initial speed of A will thus be:

[tex]\displaystyle v = \frac{s}{t} = \rm \frac{30\; km}{9\; h} = \frac{10}{3}\; km/h[/tex].

It takes 6 hours for B to walk 30 kilometers. The speed of B will thus be:

[tex]\displaystyle v = \frac{s}{t} = \rm \frac{30\; km}{6\; h} = 5\; km/h[/tex].

Answer:

Pick an answer from below.

Step-by-step explanation:

Rounded to which place?

2/7 = 0.285714285714...

Nearest tenth: 0.3

Nearest hundredth: 0.29

Nearest thousandth: 0.286

Nearest ten-thousandth: 0.2857

etc.

Answer:

0.29

Step-by-step explanation:

To convert fractions to decimals, divide the numerator by the denominator.

2/7= 0.285

Round 0.285 to 0.29

Answer:

Option B. [tex]tan(2\theta)= -\frac{336}{527}[/tex]

Step-by-step explanation:

we know that

[tex]tan(2\theta)= \frac{sin(2\theta)}{cos(2\theta)}[/tex]

[tex]sin(2\theta)=2(sin(\theta))(cos(\theta))[/tex]

[tex]cos(2\theta)=cos^{2}(\theta)-sin^{2}(\theta)[/tex]

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

we have

[tex]sin(\theta)=\frac{24}{25}[/tex]

step 1

Find the value of cosine of angle theta

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

[tex]cos^{2}(\theta)+(\frac{24}{25})^=1[/tex]

[tex]cos^{2}(\theta)=1-\frac{576}{625}[/tex]

[tex]cos^{2}(\theta)=\frac{49}{625}[/tex]

[tex]cos(\theta)=\frac{7}{25}[/tex]

The value of cosine of angle theta is positive, because angle theta lie on the I Quadrant

step 2

Find [tex]sin(2\theta)[/tex]

[tex]sin(2\theta)=2(sin(\theta))(cos(\theta))[/tex]

we have

[tex]sin(\theta)=\frac{24}{25}[/tex]

[tex]cos(\theta)=\frac{7}{25}[/tex]

substitute

[tex]sin(2\theta)=2(\frac{24}{25})(\frac{7}{25})[/tex]

[tex]sin(2\theta)=\frac{336}{625}[/tex]

step 3

Find [tex]cos(2\theta)[/tex]

[tex]cos(2\theta)=cos^{2}(\theta)-sin^{2}(\theta)[/tex]

we have

[tex]sin(\theta)=\frac{24}{25}[/tex]

[tex]cos(\theta)=\frac{7}{25}[/tex]

substitute

[tex]cos(2\theta)=(\frac{7}{25})^{2}-(\frac{24}{25})^{2}[/tex]

[tex]cos(2\theta)=(\frac{49}{625})-(\frac{576}{625})[/tex]

[tex]cos(2\theta)=-\frac{527}{625}[/tex]

step 4

Find the value of [tex]tan(2\theta)[/tex]

[tex]tan(2\theta)= \frac{sin(2\theta)}{cos(2\theta)}[/tex]

we have

[tex]sin(2\theta)=\frac{336}{625}[/tex]

[tex]cos(2\theta)=-\frac{527}{625}[/tex]

substitute

[tex]tan(2\theta)= -\frac{336}{527}[/tex]

By using the Pythagorean identity and the double angle identity for tangent, it is found that the value of tan 2θ when sin θ =24/25 and 0 ≤ θ ≤ π/2 is -527/336.

In the field of Mathematics, particularly in trigonometric equations, the problem given is asking for the value of tan 2θ, given that sin θ=24/25 and 0 ≤ θ ≤ π/2.

Firstly, we can find cos θ by using the Pythagorean identity sin²θ + cos²θ = 1. This gives us cos θ = sqrt (1 - sin²θ) = sqrt (1 - (24/25)²) = 7/25.

Then, knowing that tan θ = sin θ/cos θ, we can plug in these values to get tan θ = (24/25) / (7/25) = 24/7. Finally, using the double angle identity for tan (tan 2θ = 2 tan θ / (1 - tan²θ)), we can find that tan 2θ = 2(24/7) / (1 - (24/7)²) = -527/336.

So, the exact value of tan 2θ when sin θ =24/25 and 0 ≤ θ ≤ π/2 is -527/336, which is answer option A.

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With 5 pounds of lasagna, where each serving is 1 pound, the lunch lady can make 5 servings of lasagna.

The subject of this question is simple division in Mathematics. The problem states that the lunch lady has 5 pounds of lasagna left over and each serving is 1 pound. So, to find out how many servings of lasagna can be made, we divide the total amount of lasagna (5 pounds) by the size of each serving (1 pound).

5 pounds / 1 pound per serving = 5 servings

Therefore, the lunch lady can serve 5 servings of lasagna with the amount left over.

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Answer: Last option.

Step-by-step explanation:

You can observe in the table provided that the values of "x" represent the time in minutes and the values of "y" represent the distance in meters.

Then, in order to find the ratio of the change in y-values to the change in x-values, you can divide any value of "y" (distance) by its corresponding value of "x" (time).

So, this is:

[tex]\frac{2,400}{2}=\frac{1,200}{1}[/tex]

Since the ratio can also be written in the form [tex]a:b[/tex], you get:

[tex]1,200:1[/tex]

Answer:

D) 1,200 meters per minute

Step-by-step explanation:

Answer: 8 remainder 2

Step-by-step explanation:

3 • 8 = 24

26 - 24 = 2

Your answer is 8 with a remainder of 2

Answer:

8 r2

Step-by-step explanation:

Answer:

[tex]x^2-10x+2[/tex]

Step-by-step explanation:

Multiply out the two monomials first because of PEMDAS.

[tex](-x + 2) * (2x + 3)=-2x^2+x+6[/tex]

Now add them together.

[tex]3x^2-11x-4-2x^2+x+6=x^2-10x+2[/tex]

To find the area you multiply the length by the width.

W = the width, and you are told the length is 5 meters longer, so the length would be (W +5)

Now multiply those together to equal 20,000 square meters:

w(w+5) = 20,000

Step-by-step explanation:

Answer:

Octagon

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides, so

180° (n - 2) = 1080° ( divide both sides by 180° )

n - 2 = 6 ( add 2 to both sides )

n = 8 ← octagon

Answer:

A, D

Step-by-step explanation:

for this table:

x    0  5 10 15 20 25 30 35 40

f(x) 5  6  7  8  9    10   11  12  13

A, assuming it's supposed to say f(5)=6, is true since 5 in x corresponds to 6 in f(x)

B is false, since the domain would be the set of all numbers in x, since domain corresponds to input (x) and range corresponds to output (f(x))

C is false, the range is not all real numbers since it is a defined set of numbers

D is true, since 15 in x corresponds to 8 in f(x)

Therefore, A and D are true

ANSWER

{[tex]x | x \in \: R[/tex]}

EXPLANATION

From the graph, the given quadratic inequality is

[tex] {(x + 3)}^{2} \geqslant 0[/tex]

We can see that the corresponding quadratic function is a perfect square.

Since the graph opens upwards and it is always above the x-axis, any real number you plug into the inequality, the result is greater than or equal to zero.

Hence the solution set is

{[tex]x | x \in \: R[/tex]}

The correct answer is A

Answer:

-44

Step-by-step explanation:

We have the expression

[tex]-2|6x - y|[/tex]

We need to find the value of the expression when x = -3 and y = 4

Then we must replace the variable with the number -3 and the variable y with the number 4

This is:

[tex]-2|6(-3) - (4)|[/tex]

[tex]-2|-18 - 4|[/tex]

[tex]-2|-22|[/tex]

Remember that the absolute value always results in a positive number.

So

[tex]-2|-22| = -2(22)=-44[/tex]

the answer is -44

Answer:

The correct answer is -44

Step-by-step explanation:

Points to remember

|x| = x

|-x| = x

To find the value of  –2|6x – y|

We have  –2|6x – y|  When x = -3 and y = 4

Substitute the value of x and y

–2|6x – y| =  –2|(6 * -3)  – 4|

 = -2|-18 - 4|

 = -2|-22|

 = -2 * 22

 = -44

Therefore the value of –2|6x – y|  when x = -3 and y = 4

–2|6x – y|

ANSWER: -252

HOW TO GET IT:

Simply follow PEMDAS. Solve each exponent first, then do the rest.

Answer:

144

Step-by-step explanation:

5-7 = 2 2^2 + 6 = 10 - 7 = 3^2 = 9 + 10 = 19 - 7 = 12^2 = 144

I hope this helps even if I am too late! :)

Answer:

= 2a³b - 2ab² + a²b - b³

Step-by-step explanation:

We multiply the each term in the first polynomial by each in the other as follows.

2ab(a² - b²) + b(a² - b²)

We then open the brackets and get the following.

2a³b - 2ab² + a²b - b³

We can not simplify the product further than this since it has no like terms.  

Answer:

First is C

Second is 2

Step-by-step explanation:EDGE 2021

Answer:

y = -4x² + 4x -3

Step-by-step explanation:

The standard form of quadratic equation is:

y = ax² + bx + c

We need to use the points given to find the value of a, b and c

We are given point (-1,-11) where x =-1 and y=-11 putting values in the above equation

y = ax² + bx + c

-11 = a(-1)² + b(-1) +c

-11 = a -b+c      eq(1)

Now putting the point(0, -3) where x =0 and y =-3

y = ax² + bx + c

-3 = a(0)² + b(0) + c

-3 = 0 + 0 + c

=> c = -3

Now Putting the point (3, -27) where x =3 and y = -27

y = ax² + bx + c

-27 = a(3)² +b(3) + c

-27 = 9a + 3b + c  eq(2)

Putting value of c= -3 in eq(2)

-27 = 9a + 3b -3  

-27 +3 = 9a +3b

-24 = 9a + 3b

=> 3(3a+b) = -24

3a + b = -24/3

3a + b = -8     eq(3)

Putting value of c= -3 in eq(1)

-11 = a -b+c

-11 = a -b -3

-11 + 3 = a - b

-8 = a - b    

=> a - b = -8   eq(4)

Now adding eq(3) and eq(4)

3a + b = -8  

a - b = -8

__________

4a = -16

a = -16/4

a = -4

Putting value of a in equation 4

a - b = -8

-4 -b = -8

-b = -8+4

-b = -4

=> b = 4

The values of a , b and c are a= -4, b =4 and c= -3

Putting these values in standard quadratic equation

y = ax² + bx + c

y = -4x² + 4x -3

Answer:

All seed plants share two characteristics. They have vascular tissue and use seeds to reproduce. In addition, they all have body plans that include leaves, stems, and roots. Most seed plants live on land.

Step-by-step explanation:

All seed plants have the ability to produce seeds. Seeds contain an embryo and stored food and can withstand harsher conditions, staying dormant until conditions for growth are ideal. This trait is seen across all seed plants, which includes both gymnosperms and angiosperms.

All seed plants, also known as spermatophytes, share a key characteristic that they have the ability to produce seeds. This is a common trait and allows seed plants to reproduce. Seeds contain an embryo and stored food wrapped in a protective coat. They can withstand harsher conditions and can stay dormant until the conditions for growth are favorable. Seed plants include gymnosperms, such as conifers, and angiosperms, which are flowering plants.

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Answer:

your answer is C.$5.55

Step-by-step explanation:

NOW TAKE THE TOTAL OF BOTH,THEN WE GET

NOW DO THE DIVIDE OF 333 BY 60, THEN WE GET

Answer:

Applying the trigonometric functions, 8/b=Tan40

b=8/Tan40

Answer:

C) 9.53 cm

Step-by-step explanation:

We know this is a right triangle, so we can use trig relations

tan A = opposite side/ adjacent side

tan 40 = 8/b

Multiply each side by b

b tan 40 = 8

Divide each side by tan 40

b tan 40 / tan 40 = 8 / tan 40

b = 8/ tan 40

b = 9.534028741

we know the center of the circle, and we also know a point on the circle, well, the distance from the center to a point is just the radius.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[4-(-6)]^2+[-2-7]^2}\implies r=\sqrt{(4+6)^2+(-2-7)^2} \\\\\\ r=\sqrt{10^2+(-9)^2}\implies r=\sqrt{100+81}\implies r=\sqrt{181} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{7}{ k})\qquad \qquad radius=\stackrel{\sqrt{181}}{ r}\\[2em] [x-(-6)]^2+[y-7]^2=(\sqrt{181})^2\implies (x+6)^2+(y-7)^2=181[/tex]

Answer:

A

Step-by-step explanation:

Linear functions go into a straight line in order

Y in set b goes from 2 to 1250 so it is traveling much faster than set A

Answer:

     g(-1) = 5 - 4 = 1

Step-by-step explanation:

Please use " ^ " to denote exponentiation:  g(x) = x^3 + 6x^2 + 12x + 8.

Substitute -1 for x in this equation:                 g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8

Then:                                                            g(-1) = -1 + 6 - 12 + 8, or

                                                                     g(-1) = 5 - 4 = 1

Answer:

The answer is C

Step-by-step explanation:  

I just took the test and got it right.

Hopefully this helps you :)

pls mark brainlest ;)

Answer:

4x+6

Step-by-step explanation:

f(x)=8x-3

g(x)=4x-9

f(x)-g(x) = 8x-3-(4x-9)=8x-3-4x+9=4x+6

The value of f(x) - g(x) is 4x+6 and The domain is all real value of x.

A function can be defined as a mathematical expression which establishes relation between a dependent variable and an independent variable.

It always comes with a defined range and domain.

It is given in the question

functions f and g

f(x) = 8x - 3; g(x) = 4x - 9

f- g = ?

The value of f(x) - g(x) = 8x -3 - (4x -9)

f(x) - g(x) = 8x -3 - 4x +9

f(x) - g(x) = 4x +6

h(x) = 4x+6

The domain is all real value of x.

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