Collect like terms: a) a³, a², 2ab, 2a², a, -a²​

If the expression is log₄5 x,then the expansion of this will look like

(log 5+ log x)/log 4.

Given that the expression is log₄5 x.

We are required to find the expansion of the expression.

Base change theorem says that [tex]log_{a}b[/tex]=[tex]log_{x}b/log_{x}a[/tex]. We use the change of base formula to re-write a logarithm operation as a fraction of logarithms with a new base.

The expression is log₄5 x.

log₄5 x=(log 5+log x)/log 4

(We know that [tex]log_{a}b[/tex]= log b/ log a and log mn =log m +log n)

Hence if the expression is log₄5 x then the expansion of this will look like (log 5+ log x)/log 4.

Learn more about base change theorem at https://brainly.com/question/14998693

#SPJ4

The original price based on the gift card of $15 and discount of 30% is $55.50

What deductions are taken from the original price?

In order to arrive at the total cost before taxes, the gift card of $15 was first of all deducted from the original price before grossing up to 100% since the total cost before taxes represents 70% after the gift card has been deducted

original price(total cost before taxes+gift card)/(1-discount rate)

total cost before taxes=$23.85

gift card=$15

discount rate=30%

original price=($23.85+$15)/(1-30%)

original price=$55.50

Find out more about original price on:https://brainly.com/question/22359582

#SPJ1

A triangle is congruent, and Range of values for x is 5 < x < 29

According to the figure, if L(AB) is less than L(AD), the ∠ACB must be less than the ∠ACD. Take note of how these angles are opposite to the sides stated.

∴ ∠ACB < ∠ACD

⇒2x-10 < 48

At the same time, 2x-10 > 0.

∴ 0< 2x-10 < 48

0+10 < 2x < 48+10 , add 10 to both sides

10 < 2x < 58

10/2 < x < 58/2 , divide 2  by both the side

∴ 5 < x < 29

Range of values for x is 5 < x < 29

Complete question is

Enter the range of values for x:

AB =15, ∠BCA =( 2X-10)°, and AD=18 have angle ∠DCA= 48°

To know more about Congruent triangles, use the following link.

https://brainly.com/question/22062407

#SPJ9

Answer: $33

Step-by-step explanation: I've done it before Have a nice day <3

Two cities have the same longitude .The latitude of the city a is 6 degree north and the latitude of city b is 30 degree north. Then the distance between two cities is 1658.844 miles

Two cities have the same longitude. the latitude of the city a is 6 degree north

and the latitude of city b is 30 degree north.

assume the radius of earth is 3960 miles.

find the distance between two cities.

City A = 6°   = 6°× π/180 =  0.1047 rad

City B = 30° = 30° × π /180= 0.5236 rad

multiply by π/180 to convert the degree to radian

radius of Earth = 3960 miles

to find out

distance between City A and City B

solution

we first get here central angle between A and B city is

central angle between A and B city = 0.5236rad - 0.1047 rad

and

now by arc length so  we get distance

distance = 3960 miles × (0.5236 rad - 0.1047rad )   as radius given 3960

distance = 1658.844 miles

learn more about of distance here

https://brainly.com/question/14436976

#SPJ4

Step-by-step explanation:

I can't draw here, but I can tell and explain to you what happens to the points (incl. N).

remember the slope of lines, and what happens when we have to create a perpendicular slope (90°) ?

x and y in the slope ratio y/x go upside down and the sign flips (that means it flips for one of them).

a rotation by 90° follows the same principles.

x and y trade places, and for one of them the sign flips.

the only "difficult" trick is to determine, if the sign of x or of y flips.

let's look at N first.

N = (-5, -4)

the rotation counterclockwise takes it over into the 4th (bottom right) quadrant, where x values are positive.

aha, so the sign of x flips after x and y trade places, and we get

N' = (4, -5)

now for the other points

X = (-3, -2)

the same principle as for N

X' = (2, -3)

B = (-4, 1)

this is now moving from the 2nd (where y values are positive) to the 3rd quadrant (where x and y are negative).

so, again the sign of x flips after x and y trade places

B' = (-1, -4)

with the new coordinates of the points you can now easily draw the new triangle'.

Answer:

y = x − 6

Step-by-step explanation:

Find slope: (y2-y1)/(x2-x1)

(6-3)/(1-0) = 3/1 = 3

Y = 3x + b, plug in point

3 = 3(0) + b, b = 3

Equation: y = 3x + 3

The slope intercept form of the equation of a line is:

y

=

m

x

+

b

where m is the slope and b is the value of y when x is 0.

We are given that the slope is 1 and the given point shows us that y is -6 when x is 0. Therefore, the equation of the line is:

y = x - 6

Answer: Sam has 7 quarters and 2 dimes

Step-by-step explanation: If you have 7 quarters you would have $1.75 and with the 2 dimes which make 20 cents more give you $1.95 in total! and every quarter is worth 25 cents multiplied by 7 gave me 175 but in decimal form would 1.75

Hope this helps! :D

Answer:

GD.

Step-by-step explanation:

Answer:

[tex]x^2-8x+12[/tex]

Step-by-step explanation:

Knowing both intercepts we can write the equation in factored form:

[tex](x-2)(x-6)[/tex]

Now use distributive property to find the equation in standard form:

[tex](x-2)(x-6)\\x^2-6x-2x+12\\x^2-8x+12[/tex]

Answer:

  2√2 -√6

Step-by-step explanation:

You want to know the surd representation of the irrational number that rounds to 0.378937382.

The plural "surds" suggests this is the difference of two irrational roots. Looking at √(n+1) -√n, we find that √3 -√2 is the nearest, but does not match.

Looking at √(n+2) -√n, we find that √8 -√6 matches all 9 digits when rounded to the 9th decimal place. 20 digits of that value are ...

  0.37893738196301199941

The given number approximately matches the irrational value ...

  2√2 -√6

__

Additional comment

We programmed a calculator to find the values of √(n+2) -√n for n = 1..10. The result is attached. The 6th value matches, and corresponds to n=6.

In general, finding a surd representation of an arbitrary value seems to be a matter of trial and error. Perhaps your curriculum materials offer an algorithm.

Kyra wants the total length of the tree to the nearest inch it will be 193.68 inches.

The measurement couldn't have been added earlier because they're in different units

Kyra measures 4 feet. This in centimeters will be:

= 4 × 30.48 = 121.92 cm

Tai measures 3.5 yards. This in centimeters will be:

= 91.44 × 3.5

= 320.04 cm

Rodney measures 50 centimeters.

Therefore, the addition will be:

= 121.92 cm + 320.04 cm + 50cm

= 491.96 cm

The total length in inches will be:

1 inch = 24 cm

= 491.96 / 2.54

= 193.68 inches.

Learn more about measurement on:

brainly.com/question/27233632

#SPJ1

The value of x based on the equation illustrated as BM=x+7,DM=2x+3 is 10.

It should be noted that an equation is used to show the relationship that exists between rte variables.

The expression given are

BM=x+7

DM=2x+3

Equate both equations

x + 7 = 2x - 3

Collect like terms

2x - x = 7 + 3

x = 10

Therefore, the value of x is 10.

Learn more about equations on:

brainly.com/question/13763238

#SPJ1

The area of a rectangular patio with the dimensions of 18-3/4 feet and 12 feet will be determined by using the formula for the area of rectangle.

Area of rectangle is calculated by multiplying the length of the rectangle to the width of the rectangle. i.e.,

Area of rectangle= Length*Width

In the given situation,

Length= 18-3/4feet

Width=12 feet.

1. Convert the value of length to improper fraction:

18-3/4=75/4

2. Multiply the length and width to find the area:

Area=(75/4)x12

Solving the expression:

3. Area=75x3=225 sq. feet

The area of a 18-3/4 feet and 12 feet rectangular patio is 225 sq. feet.

Learn more about Area of rectangle:

https://brainly.com/question/25292087

#SPJ4

Answer:

The answer is 7

Step-by-step explanation:

The formula is y=mx+b so m=10 and b=7

Answer:

Hope this helps :)

The y-intercept is 7.

Step-by-step explanation:

This is because the in the slope-intercept form, y = mx + b, so the b in this case is 7.

The following system of equations is solved to find how many minutes of each exercise type she should do now:

In which a is the amount of calories lost per minute running, and b is the amount of calories lost per minute jogging.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

She still wants to exercise for 40 min every other day, hence:

x + y = 40.

She wants to burn 460 calories during each session, hence:

ax + by = 460.

In which a is the amount of calories lost per minute running, and b is the amount of calories lost per minute jogging. (the problem is incomplete and I couldn't find it anywhere, hence I am speaking into general terms).

Then the following system of equations is solved to find how many minutes of each exercise type she should do now:

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

Two identical figures with all sides of equal length = Both are square

Solution :

The perimeter of a square is defined as the total length that its boundary covers. The perimeter of any closed geometrical shape is calculated by finding the distance around that shape. For a square, the perimeter can be calculated by finding the sum of all the sides. Since all four sides are equal, it is four times the length of each side of a square. Let us learn about perimeter of square in detail in this article.

Derivation of Perimeter of Square Formula

The perimeter of the square is defined as the total length of the boundary of a square. In order to calculate the perimeter of the square, we will find the sum of all of its sides. Since all sides of a square are equal for a square, with each side measuring "s" units, perimeter will thus be given as,

Perimeter of square = s + s + s + s

⇒ Perimeter of square = 4s, where "s" is the side length of the square.

Squares :

A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one). A square has four axes of symmetry, and its two finite diagonals (as with any rectangle) are equal. Bisection of a square by diagonal results in two right triangles.

The formula for the perimeter of a square is,

P = Side + Side + Side + Side. Or,

P = 4 × Side.

two identical figures with all sides of equal length the combined perimeter of the figure is 80centimeters

2(4*side ) = 80

8*side = 80

side = 10

length of one side =10

#SPJ2

More details : brainly.com/question/2189895

Based on the given equation which has been solved in the table (see attachment), we know that: D. the subtraction property of equality was not applied to solve this equation.

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

The subtraction property of equality states that the two (2) sides of an equation would still remain equal even when the same number has been subtracted from both sides of an equality.

Based on the given equation which has been solved in the table (see attachment), we can reasonably and logically deduce that the subtraction property of equality wasn't applied to solve this equation.

Read more on subtraction property of equality here: https://brainly.com/question/1601404

#SPJ1

The given function y=4(0.2) ^x+1 is a exponential function because value of x could be any number. Whenever we have a degree of x in terms of y then it is a part of exponential function.

In the biological sciences, exponential functions are frequently used to simulate the evolution of a particular quantity over time, such as population size. Experimental data graphs are typically created with the quantity on the y-axis and the time on the x-axis.

Exponential functions play a key role in economic analysis of growth and decay. Examples include investment values that rise by a fixed percentage each period, business sales that rise by a fixed percentage each period, models of economic expansion, or models simulating the spread of an epidemic.

Learn more about Exponential functions here

https://brainly.com/question/2456547

#SPJ4

=========================================================

Explanation:

We'll use Heron's Formula.

When given the three sides a,b,c, the area of the triangle is

[tex]A = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s = (a+b+c)/2 is the semi-perimeter, aka half the perimeter.

Let's compute the value of s first

s = (a+b+c)/2 = (8+9+3)/2 = 20/2 = 10

Then we can say,

[tex]A = \sqrt{s(s-a)(s-b)(s-c)}\\\\A = \sqrt{10(10-8)(10-9)(10-3)}\\\\A = \sqrt{140}\\\\A \approx 11.8321595661992\\\\A \approx 11.83\\\\[/tex]

The triangle has area of roughly 11.83 square meters.

Statements 2, 4 and 5 are true.

Let us check each statement one by one-

1. The square root of a positive number cannot be negative-

This statement is false. Let us take an example. If we take a number, say 4, 4 has 2 square roots- 2 and -2. This is because 2 × 2 = -2 × -2 = 4. Thus, the square root of a positive number can be negative.

2. All positive numbers have two square roots.

This statement is true. It follows from the example in 1 that any positive number has 2 square roots- one negative and one positive.

3. √18 = 9 because 9(2) = 18

The given statement is false. √18 ≠ 9. If √18 was equal to 9, then 9 × 9 must be 18. But 9 × 9 is 81. Hence, false.

4. √49 = 7 because 7(7) = 49

The given statement is true. √49 = 7 as 7 × 7 = 49

5. √25 = 5 because 5²= 25

The given statement is true. √25 = 5 as 5 × 5 = 25

Learn more about square roots here-

https://brainly.com/question/3120622

#SPJ9

The x-intercept will be 5 , y-intercept will be 4 and the coordinate will be (x , y) = (5 , 4).

What is an intercept ?

An intercept is a location on the y-axis where the line's slope passes. It is the y-coordinate of the location where a line or curve crosses the y-axis.

It is given that we have to find out the x and y intercepts from the given graph.

We know that , a function's x-intercept is the value of x at the point where the graph crosses the horizontal axis, or when y = 0. As a result, while examining the function's graph, we find out that the x-intercept is equal to 5.

Similarly , The value of y when the graph crosses the vertical axis, or the value of y when x = 0, is the y-intercept of a function. As a result, while examining the function's graph, we find out that the y-intercept is equal to 4.

So , the coordinate will be (x , y) = (5 , 4).

Therefore , the x-intercept will be 5 , y-intercept will be 4 and the coordinate will be (x , y) = (5 , 4).

Learn more about x and y intercepts here :

https://brainly.com/question/28248581

#SPJ1

Answer: The dimensions are 8 and 28

Answer:

J.o.i.n p.l.z pqp-yuth-ygd

The required statement is proved.

Given y = ax² ₊ bx ₊ c, which is the general formula of quadratic form)

vertex = (-b/2a , 4ac ₋ b²/4a) which is the quadratic vertex formula

according to y = ax² ₋ 2px ₊ ap² ₊ q

therefore, a = a

b = ₋2xp

c = ap²₊q

⇒ (₋(₋2p/2a , 4a× (ap² ₊ q)₋ (2ap)²/4a)

⇒ (p , 4a²p² ₊ 4aq ₋ 4a²p²/4a)

⇒ (p , 4aq/4a)

⇒ (p,q)

hence we proved the quadratic equation .

Learn more about Quadratic equation here:

brainly.com/question/776122

#SPJ9

The coordinates of A are (3, 5).

According to the section formula-

If a point (x , y) divides a line in the ratio of m : n, where the two endpoints of the line are (x1, y1) and (x2, y2), then-

x = (nx1 + mx2)/ (m + n)

and y = (ny1 + my2)/ (m + n)

Here, M (4,6) is the midpoint of AB and B is (5,7)

Let the coordinates of A be (x2, y2)

Therefore,

x1 = 5, y1 = 7

x = 4, y = 6

Since, midpoint divides a line segment into two equal halves, m : n = 1 : 1

Now, substituting the values in the section formula we get-

4 = (5 + x2)/2

4 × 2 = 5 + x2

8 = 5 + x2

5 + x2 = 8

x2 = 8 - 5

x2 = 3

and 6 = (7 + y2)/2

6 × 2 = 7 + y2

12 = 7 + y2

7 + y2 = 12

y2 = 12 - 7

y2 = 5

Thus, the coordinates of A are (3, 5).

Learn more about the section formula here-

https://brainly.com/question/11888968

#SPJ9

The inverse function of f(x) is; f-¹(x) = x³ + 5

To find the inverse of the function;

We should represent f(x) as y.

Now we have;

By taking the cube of both sides;

y³ = x - 5

By solving for x;

x = y³ + 5

By swapping x and y; we have;

y = x³ + 5

f-¹(x) = x³ + 5.

The inverse function of f(x) is; f-¹(x) = x³ + 5.

To learn more about visit https://brainly.com/question/19755382

#SPJ9