Question 2: Write each of the following in index form
(a) √√
(b) √y
(c) √
Va
(d) √ (e) x (1) c

Answer: TRUE

Step-by-step explanation:

i got it right.

If the expression is log₇49 x y z, then the expansion of the expression is 2+log x/ log 7+log y/log 7 +log z/ log 7.

Given that  expression is log₇49 x y z.

We are required to find the expanded value of the expression.

The change of base formula is basically used to re-write a logarithm operation as a fraction of logarithms with a new base.

The expression is log₇49 x y z.

log₇49xyz= (log 49+log x+log y+log z)/log 7

We know that log mn=log m+ log n.

=log [tex]7^{2}[/tex]/ log 7+log x/log 7+log y/ log 7+ log z/log 7

=2 log 7/log 7+log x/log 7+log y/ log 7+ log z/log 7

=2+log x/log 7+log y/ log 7+ log z/log 7

Hence if the expression is log₇49xyz, then the expanded form is

2+log x/log 7+log y/ log 7+ log z/log 7.

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32. [tex]256^{\frac{1}{2} }[/tex] can be simplified into 512.

Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.

Prime factorization of 32 = 2 x 2 x 2 x 2 x 2 = [tex]2^{5}[/tex]

Prime factorization of 256= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = [tex]2^{8}[/tex]

According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.

i.e., [tex](x^{m})^{n} = x^{mn}[/tex]

Another law of indices says that if two terms having same base are multiplied together, then their indices are added.

i.e., [tex]a^{m} . a^{n } =a^{m+n}[/tex]

According to the given condition,

∴[tex]32 = 2^{5}[/tex]

[tex]256^{\frac{1}{2}} = (2^{8})^{\frac{1}{2} }[/tex]

∴ 32. [tex]256^{\frac{1}{2} }[/tex]  = [tex]2^{5}[/tex] × [tex](2^{8})^{\frac{1}{2} }[/tex]

Applying the laws of indices mentioned above,

32. [tex]256^{\frac{1}{2} }[/tex]  = [tex]2^{5}[/tex] × [tex](2^{8 X }^{\frac{1}{2} })[/tex]

= [tex]2^{5}[/tex] × [tex]2^{4}[/tex]

= [tex]2^{5 + 4}[/tex] = [tex]2^{9}[/tex]

= 512.

Thus, 32. [tex]256^{\frac{1}{2} }[/tex] can be simplified into 512.

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Julia = 10 miles in 30 minutes

Jasmine = 3 miles in 12 minutes

Julia= 10/30 *2 = 20/60. Julia drove 20 mph

Jasmine= 3/12*5= 15/60. Jasmine drove 15mph

Julia drive faster.

Answer:

724,862.58

Step-by-step explanation:

7 (hundred thousands)

2 (ten thousands)

4 (one thousands)

,

0 (hundreds)

6 (tens)

2 (ones)

.

5 (tenths)

8 (hundreths)

Answer:

I think that your answer would be 724,862.58

Step-by-step explanation:

The solutions of the expressions are as below:

13. (a, b) are points located on the first quadrant that is a is positive x axis and b is positive y axis

(-a, b) are points located on the second quadrant that is: a is negative x axis and positive y axis

(a, -b) are points located on the fourth quadrant that is: a is positive x axis and negative y axis

(-a, -b) are points located on the third quadrant that is: a is negative x axis and negative y axis

10. -9x - 2; x = -4

-9x - 2 for x = -4

= -9 * -4 - 2

= 36 - 2

= 34

11. 24 - 8x; x = -2.25

= 24 - 8 * - 2.25

= 24 + 18

= 42

12. 15x + 9; x = -1/10

= 15 * -1/10 + 9

= -1.5 + 9

= 7.5

13.

a are points in the x axis and b are points in the y axis

(a, b) are points located on the first quadrant that is a is positive x axis and b is positive y axis

(-a, b) are points located on the second quadrant that is: a is negative x axis and positive y axis

(a, -b) are points located on the fourth quadrant that is: a is positive x axis and negative y axis

(-a, -b) are points located on the third quadrant that is: a is negative x axis and negative y axis

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Answer:

This is for #12

-2 > x

set notation: {x│x < -2}

interval notation: x∈(-∞, -2)  

Step-by-step explanation:

-3(x+2) > 10+5x

-3x-6 > 10+5x

+3x           +3x

-6 > 10+8x

-10   -10

-16 > 8x

÷8    ÷8

-2 > x

set notation: {x│x < -2}

interval notation: x∈(-∞, -2)

The length of the longest altitude of the triangle is 24 √5 cm.

The sides of the triangle that are given are:

35 cm, 54 cm and 61 cm

We need to find the longest altitude of the triangle.

We know that:

s = ( a + b + c ) / 2

s = ( 35 + 54 + 61 ) / 2

s = 150 / 2

s = 75

s - a = 75 - 35

s - a = 40

s - b = 75 - 54

s - b = 21

s - c = 75 - 61

s - c = 14

Area, A = √ s (s − a)(s − b)(s − c)

A = √ 75 (40) (21) (14)

A = 420 √ 5 cm²

Now, area is also equal to:

Area = 1 / 2 × b × h

420 √5 = 1 / 2 × 35 × h

h = 420 √ 5 × 2 ÷ 35

h = 24 √5 cm

Therefore, the length of the longest altitude of the triangle is 24 √5 cm.

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The function is exponential growth function and the y- intercept is (0,$2000).

Given that the we put $ 2000 into a college savings account for four years and the account pays 6% interest annually.

Exponential growth or decay describes the process of reducing or growing an amount by a consistent percentage rate over a period of time and it is represented by the function y=a(1-b)ˣ where, y is the final amount, a is the original amount and b is the growth or decay factor and x is the amount of time passed.

If a is positive and b is greater than 1 then it is exponential growth.

If a is positive and b is less than 1 but greater than 0 then it exponential decay.

When we put $2000 in our college savings account  and we receive  6% annual interest then this situation can be modeled by using equation f(x)=a(1+r)ˣ in which we put a=$2000, r=6%, x=4

Thus we will receive the amount after 4 years:

f(4)=2000(1+(6/100))⁴

Since equation is an exponential growth function so it is also an exponential growth function.

Now, to find the y-intercept we will put x=0.

So, y-intercept is (0,$2000).

Hence, By putting $2000 into a college savings account for four years and the account pays 6% interest annually the function is exponential growth function and the y-intercept is (0,2000).

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The value of h is 3

The line that includes the point (h, 3) and (9, -3) has a slope of -1.

Using the slope intercept equation,

y = mx + b

where

Therefore,

y = mx + b

y = -x + b

using (9, - 3)

-3 = - 9 + b

b = -3 + 9

b = 6

Therefore, the equation is as follows:

y = -x + 6

using (h, 3)

y = -(h) + 6

3 = -h + 6

-h = 3 - 6

-h = -3

h = 3

Therefore, the value of h is 3.

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Answer:

Step-by-step explanation:

I think it´s the polygamous

Answer:

320

Step-by-step explanation:

Use PEMDAS - order of operations

5(2)^2 + 3(10)^2

5 x 4 + 3 x 100

20 + 300

320

The probability that at least one of the top three cards is a jack, queen, or king is 0.289%.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

A deck has a total of 52 cards.

A deck of cards has four jacks.

A deck of cards has four queens.

A deck of cards has four kings.

The total number of jacks, queens, and kings is 4 + 4 + 4 = 12.

Then the probability that at least one of the top three cards is a jack, queen, or king will be:

P = ( 12 / 52 ) × ( 8 / 51 ) × ( 4 / 50 )

P = ( 6 / 26 ) × ( 8 / 51 ) × ( 2 / 25)

P = 96 / 33150

P = 0.289%

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Answer:

124°

Step-by-step explanation:

MLI=56°

JIG=180°-56°

=124°

Answer:

5miles : 1hour

Step-by-step explanation:

source: trust me

no really dont

Using the law of sines, the length of side x, to 1 decimal place, is: 10.8 cm.

The law of sines states that:

Sin A/a = sin B/b = sin C/c.

Let:

Measure of angle A = 81°

a = x = ?

Measure of angle B = 40°

b = 7 cm

Plug in the values into Sin A/a = sin B/b to find the value of x

Sin 81/x = sin 40/7

Cross multiply

(x)(sin 40) = (sin 81)(7)

Divide both sides by sin 40

(x)(sin 40)/sin 40 = (sin 81 × 7)/sin 40

x = (sin 81 × 7)/sin 40

x = 10.8 cm (to 1 decimal place)

Therefore, using the law of sines, the length of side x, to 1 decimal place, is: 10.8 cm.

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Answer:

Find K between M(1, -3) and N(4, 6) such that the

ratio of MK to KN is 1:2.

Step-by-step explanation:

Find K between M(1, -3) and N(4, 6) such that the

ratio of MK to KN is 1:2.

The coordinates of point K are (2, 0).

Given that there are three points M, K and N, such that M = (1, -3) and N = (4, 6) and the ratio of MK to KN is 1:2.

We need to find the coordinates of point K.

To find point K between M(1, -3) and N(4, 6) such that the ratio of MK to KN is 1:2, we can use the concept of section formula.

Let's assume the coordinates of point K are (x, y).

The section formula states that if a point K divides a line segment MN in the ratio m:n, then the coordinates of K are given by:

x = (n·x₁ + m·x₂) / (m + n)

y = (n·y₁ + m·y₂) / (m + n)

where (x₁, y₁) are the coordinates of point M and (x₂, y₂) are the coordinates of point N.

In this case, the ratio of MK to KN is 1:2, so m = 1 and n = 2.

Substituting the coordinates of M(1, -3) and N(4, 6) into the formula:

x = (2·1 + 1·4) / (1 + 2)

= (2 + 4) / 3

= 6 / 3 = 2

y = (2·(-3) + 1·6) / (1 + 2)

= (-6 + 6) / 3

= 0 / 3

= 0

So, the coordinates of point K are (2, 0).

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When choosing a loan, the best scenario is lower APR, shorter loan, and extra principal payments.

A loan is a type of debt that a person or other entity incurs. The lender advances the borrower a certain amount of money, typically on behalf of a business, financial institution, or government. The borrower accepts a specific set of terms in return, which may include any financial costs, interest, a repayment schedule, and other requirements.

APR represents the total yearly cost of a loan to the borrower, including all fees. The APR is stated as a percentage, just like an interest rate. It does, however, contain other costs or fees such as mortgage insurance, the majority of closing costs, discount points, and loan origination fees, unlike an interest rate. It should be noted that the APR simply means the annual percentage rate which is the interest that's generated on the amount borrowed.

Therefore, it should be noted that when choosing a loan, the best scenario is a lower APR, shorter loan, and extra principal payments

This is important in order to reduce the value that the person will pay and make it easier to return the loan.

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The equation which illustrates and meets the conditions given is 1.25 × 0.2

First number = 1.25

First number = 1.25Second number = 0.2.

Product = 0.25

First number, x = 1.25

First number, x = 1.25 Second number, y = 0.2

= first Number × second number

= 1.25 × 0.2

= 0.25

Evaluating the result : 0.25

Number of digits = 3

Non - zero digits = 2

There are several values of x and y that will satisfy the 3 conditions given.

Therefore, the product of the values 1.25 and 0.2 gives the required output

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Answer:

hola

Si por qué le tenías que restar ala fracción equivalente

Answer: The square root of -50 is undefined

Step-by-step explanation: I put it in a calculator It said undefined

Answer: (262 - 70) ÷ 24

Step-by-step explanation:

the three equivalent ratios to the ratio 1 : 3 will be 2 : 6 , 3 : 9 and 4 : 12.

We are given a fraction 1 / 3

This can also be written as a ratio as 1 : 3

Now, the equivalent ratios to it will be:

First one:

1 × 2 : 3 × 3

= 2 : 6

Second one:

1 × 3 : 3 × 3

= 3 : 9

Third one:

1 × 4 : 3 × 4

= 4 : 12

Therefore, the three equivalent ratios to the ratio 1 : 3 will be 2 : 6 , 3 : 9 and 4 : 12.

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Answer: inverse of 2,48 there is none and the inverse of 56,2130 there is none

Step-by-step explanation: hope this helps

Answer:

[tex]z=\frac{s}{h-4c^4}[/tex]

Step-by-step explanation:

Switch the subject

[tex]s=zh-4zc^4\\zh-4zc^4=s[/tex]

Factor

[tex]zh-4zc^4\\=z\left(h-4c^4\right)\\z\left(h-4c^4\right)=s[/tex]

Divide: remember that h - 4c^4 is not equal to zero

[tex]\frac{z\left(h-4c^4\right)}{h-4c^4}=\frac{s}{h-4c^4}[/tex]

Simplify your solution where z is the redefined subject

[tex]z=\frac{s}{h-4c^4}[/tex]

Step-by-step explanation:

s=zh-4zc^4

we will factorise

s=z(h-4c^4)

we will divide both sides by (h-4c^4)

s/(h-4c^4)=z

z=s/(h-4c^4)

pls rate as brainliest

Answer:

x = 12

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{XY}{RS}[/tex] = [tex]\frac{XZ}{RT}[/tex] ( substitute values )

[tex]\frac{5x-3}{3x+2}[/tex] = [tex]\frac{60}{40}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

2(5x - 3) = 3(3x + 2) ← distribute parenthesis on both sides )

10x - 6 = 9x + 6 ( subtract 9x from both sides )

x - 6 = 6 ( add 6 to both sides )

x = 12

The correct option B: (-9/4 × 3/2)×(6/3 × 5/7) = -9/7×(3/2×6/3)×5/7 is the associative property of multiplication.

The formula for associative property of multiplication is-

a×(b×c) = (a×b)×c

For four digits;

(a×b)×(c×d) = a×(b×c)×d

Thus, from the given option the condition for associative law is only satisfied in option B.

(-9/4 × 3/2)×(6/3 × 5/7) = -9/7×(3/2×6/3)×5/7

Thus, the correct option for the associative property of multiplication s chosen.

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The logarithmic form of 8 = (1/2)⁻³ is given by log₍₁/₂₎(8) = -3.

The logarithm is exponentiation's opposite function in mathematics. This means that the logarithm of a fixed number, base b, represents the exponent to which that fixed number must be raised in order to create a particular number x.. The logarithm counts the number of times the same factor appears during repeated multiplication in the simplest scenario.

The given exponential form of the equation is 8 = (1/2)⁻³

To transform this exponential form into logarithmic form, we are requested.

Consider the given exponential form: 8 = (1/2)⁻³

Taking logarithm on both sides with the base as (1/2), we get,⇒ log₍₁/₂₎(8) = log₍₁/₂₎(1/2)⁻³

Now using the logarithmic rule logₐ(aⁿ) = n × logₐ(a) in the RHS of the above equation, we get

⇒ log₍₁/₂₎(8) = (-3) × log₍₁/₂₎(1/2)

⇒ log₍₁/₂₎(8) = (-3) × 1                  

(Since logₐ(a) = 1, for a &gt; 0)

⇒ log₍₁/₂₎(8) = -3

Therefore, the logarithmic form of 8 = (1/2)⁻³ is given by log₍₁/₂₎(8) = -3.

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The value of  ln x-ln 3=4 is 163.7

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

given, our equation is -

ln x-ln 3=4

It can be expressed in the form of

⇒ loge (x/3) = 4

⇒ e⁴ = x/3

⇒ x = 3e⁴

⇒ 163.7

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