What is the common ratio in this recursive
definition?

The length of BC is 5

The length of AC is 10

From the given information, we are to calculate the length of the given parts of line AC

From the given information,

B is the midpoint of AC

Thus,

We can write that

AB + BC = AC

and

AB = BC

Also, from the given information,

AB = 5

Therefore,

BC = 5

From the equation,

AB + BC = AC

Substitute the values of AB and BC

5 + 5 = AC

10 = AC

AC = 10

Hence, BC = 5 and AC = 10

Learn more on Midpoint of a line: Calculating length of a line here: https://brainly.com/question/26034806

#SPJ1

Answer:

follow me if this helped

Step-by-step explanation:

A kite is a four-sided figure that has two acute angles and two obtuse angles. The angles are formed by the intersection of the diagonals, which are not parallel.

[asy]

size(5cm);

draw((0,0)--(1,1.5)--(3,1)--(2,-0.5)--cycle);

draw((1,1.5)--(2,-0.5));

label("$A$",(0,0),SW);

label("$B$",(1,1.5),NE);

label("$C$",(3,1),SE);

label("$D$",(2,-0.5),NW);

[/asy]

A bow tie shape is another four-sided figure that has two acute angles and two obtuse angles. The angles are formed by the intersection of the diagonals, which are not parallel.

[asy]

size(5cm);

draw((0,0)--(1,1.5)--(2,0)--(1,-1.5)--cycle);

draw((1,1.5)--(1,-1.5));

label("$A$",(0,0),SW);

label("$B$",(1,1.5),NE);

label("$C$",(2,0),SE);

label("$D$",(1,-1.5),NW);

[/asy]

The solution of the equation is x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex].

Now, According to the question:

What is Quadratic Equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

The given equation is :

40x² = 30

40x² - 30 =0

Common factor:

10(4x²- 3) = 0

Divide both sides by the same factor

10(4x²- 3) = 0

4x²- 3 = 0

Use the quadratic formula:

x = -b±[tex]\sqrt{b^2-4ac}[/tex]/ 2a

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula:

4x²- 3 = 0

a = 4

b = 0

c = -3

x =  -0±[tex]\sqrt{0^2-4(4)(-3)}[/tex]/ 2(4)

By simplify:

x = ±[tex]\frac{4\sqrt{3} }{8}[/tex]

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x = [tex]\frac{4\sqrt{3} }{8}[/tex]

x = -[tex]\frac{4\sqrt{3} }{8}[/tex]

Rearrange and isolate the variable to find each solution

x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex]

Hence, The solution of the equation is x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex].

Learn more about Quadratic Equation at:

https://brainly.com/question/30098550

#SPJ4

Answer:

[tex]\boxed{\bf u=7}[/tex]

Step-by-step explanation:

[tex]\sf 2u+2.17=16.17[/tex]

Subtract 2.17 from both sides:-

[tex]\sf u+2.17-2.17=16.17-2.17[/tex]

[tex]\sf 2u=14[/tex]

Divide both sides by 2:-

[tex]\sf \cfrac{2u}{2}=\cfrac{14}{2}[/tex]

[tex]\sf u=7[/tex]

Therefore, u = 7

______________________

Hope this helps!

Have a great day!

Answer: d-20

Step-by-step explanation:

if Mia has $20 less than Brandi, it means Brandi has d dollars, so we subtract Brandi 's money from $20.hope you understood.

A linear model can be represented by the equation y = mx + b, where y is the dependent variable (megawatt hours generated by hydropower), x is the independent variable (years since 2007), m is the slope of the line, and b is the y-intercept.

To find the slope (m) and y-intercept (b) for this problem, we can use the two points given: (2007, 248) and (2012, 277).

m = (277 - 248) / (2012 - 2007) = 29 / 5 = 5.8

b = 248 - (5.8)(2007) = 248 - 11456 = -11208

So the linear model representing the number of megawatt hours generated by hydropower as a function of the number of years since 2007 is:

y = 5.8x - 11208

where x is the number of years since 2007.

Answer:

Dilation of 3

Step-by-step explanation:

Note [tex]DE=2[/tex] and [tex]D'E'=6[/tex].

The scale factor is defined as the ratio of the length of the side of the image to the length of the corresponding side of the preimage.

So, the scale factor is [tex]\frac{6}{2}=3[/tex].

The dilation shown in the image is a dilation with a scale factor of 3

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (3x, 3y)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

Generally,  transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

Examining the figure, Using side DE as reference we can see that DE is 1 unit

After dilation side D' E' transformed to 3 units, showing an increment of 3.

The dilation is an enlargement and the scale factor is 3

Learn more about transformation here:

https://brainly.com/question/29601182

#SPJ1

The interquartile range (IQR) of this dataset is 8.25, it means that half of the observations fall between 53 and 61.25, while half of the observations fall outside of that range.

IQR stands for Interquartile Range, which is a measure of the variability of a dataset. It is defined as the difference between the third quartile (Q3) and the first quartile (Q1). To calculate the IQR, you first need to order the data set and find the median (middle value) of the dataset, and the Q1 and Q3.

Here is the dataset you provided, in order:

53 53 53 54 55 56 59 60 61 62 63 88

The median of the dataset is: (56+59)/2 = 57.5

Q1 is the median of the lower half of the dataset: (53+53+54)/3 = 53

Q3 is the median of the upper half of the dataset: (60+61+62+63)/4 = 61.25

Now you can calculate the IQR:

IQR = Q3 - Q1 = 61.25 - 53 = 8.25

So the interquartile range of this dataset is 8.25, it means that half of the observations fall between 53 and 61.25, while half of the observations fall outside of that range.

Read more about interquartile range here:

https://brainly.com/question/4102829

https://brainly.com/question/17083142

The correct question should be:

"Find the interquartile range (IQR) of the following dataset

53 53 53 54 55 56 59 60 61 62 63 88"

No, number 16 is not representing as a factor of 8. The given statement is false as it is a multiple of 8.

As given in the question,

Given number is equal to 8,

Given factor is equal to 16:

Factors are those numbers which divides the given numbers without leaving any remainder. It exactly divides the given original number.

Here given factor 16 does not divides the given number 8.

Instead 8 divides the the number 16.

here '8' is the factor of the number 16.

And 16 represents as a multiple of 8.

Therefore, the given statement is false and 16 is not considered as a factor of 8 instead it is a multiple of 8.

Learn more about factor here

brainly.com/question/29474540

#SPJ4

Answer:

I believe B, E, and F is the answer

So on solving the provided question we cans say that in the following linear equation values are y = -1, -3 , 3

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here ,

as we know that x = 0

so, y = 3x - 1 = -1

2y - 6x = 4 => y = 2

2y = -x + 6 = y = 3

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ1

The longest side in a right triangle is the hypotenuse, which is the side opposite the right angle.

In ∆ XYZ, if X is the right angle, then the hypotenuse would be the side connecting points Y and Z. This is because in a right triangle, the hypotenuse is always the side opposite the right angle and is also the longest side in the triangle. This can be proven using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Learn more about Hypotenuse here:

https://brainly.com/question/2217700

#SPJ4

Answer:

40

Step-by-step explanation:

total: 56+80+40+24 = 200

(80x100)/200

Answer:

What you first want to do is see what all of the numver of students add up to:

80 + 40 = 120

120 + 24 = 144

144 + 56 = 200

So there are a total of 200 votes. 40 of the 200 vote mystery, so you need to find how many times 40 will go into 200. To find this you can just divide.

200/40 = 5

5% prefer mystery books!

Step-by-step explanation:

Hope it helps! =D

I think I did the math wrong, but just by looking Im pretty sure its 5%

Answer:

168 deg

Step-by-step explanation:

Assuming the increase in temperature in constant during the 3 weeks, we do the following calculations-

8 deg * 7 = 56 deg / week (Since there are 7 days in a week)

56 * 3 = 168 deg in 3 weeks.

The constant of proportionality of the graph is 12.

Proportional relationships are relationships between two variables where their ratios are equivalent. In other words, a proportional relationship is one in which two quantities vary directly with each other.

Proportional relationship can be represented mathematically as follows:

y = kx

where

Therefore, let's use (3, 36) to find the constant of proportionality.

Hence,

y = kx

36 = 3k

divide both sides by 3

3k / 3 = 36 / 3

k = 12

Therefore, the constant of proportionality is 12.

learn more on proportional relationship here: https://brainly.com/question/28802461

#SPJ1

Sarah's error in the expression 3 so the correct answer is option D

Complete Question: Sarah used properties of operations to write the following three equivalent expressions to.

A. There are no errors. All of the expressions are equivalent.

B. Expression 1. Sarah can’t apply the Distributive Property if there are three addends.

C. Expression 2. Sarah can’t combine -4 and -6. She must combine -4 with 8.

D. Expression 3. Sarah applied the Distributive Property but incorrectly multiplied 1/2 (-6).

Expressions 1, and 2 are equivalent because they are using the distributive property to expand the term within the brackets before applying the 1/2 coefficient.

Expression 3 is not equivalent because it does not use the distributive property and does not have the same terms as the other expressions.

Sarah's error in expression 3 is that she did not use the distributive property and the terms inside the brackets are not the same as the other expressions, hence the results are different.

Therefore, Sarah's error in the expression 3 so the correct answer is option D

To learn more about Distributive Property,

Visit; brainly.com/question/5637942

#SPJ4

There are the Following three types of images they are written as follows:

1. Image of an element: If x is a member of X, then the image of x under, f, denoted, f(x), is the value of f when applied to x. f(x) is alternatively known as the output of f for argument x.

2. Image of a subset: Throughout, let: f: X→Y be a function. The image under f of a subset A of X is the set of all f(a) for a ∈ A.

It is denoted by f[A],} or by f(A) when there is no risk of confusion.

3. Image of a function: The image of a function is the image of its entire or full domain, also called as the range of the function. This last usage should be evaded because the word "range" is also commonly used to mean the codomain off.

To know more about Image:

https://brainly.com/question/1809747

#SPJ4

The endpoint of a titration can be found by various methods like visual indicators, conductometric titration, volumetric titration, etc.

The endpoint of a titration is the point at which the reaction between the acid and base is complete. In other words, it is the point at which the acid and base have been neutralized, and the solution reaches a neutral pH of 7.0. There are several ways to determine the endpoint of a titration, including:

To find the endpoint, it is important to use a suitable indicator that changes color in the range of pH close to the endpoint of the titration. It's also important to use a burette to measure the volume of the titrant added and use it to plot the titration curve.

Read more about Titration:

brainly.com/question/13307013

#SPJ4

The given statement as an expression is 6x + 15 = 6x - 41

From the question, we have the following parameters that can be used in our computation:

A mathematical statement

The mathematical statement is given as

6 times a number plus 15 is equal to 6 times a number minus 41

Represent the number with x

So, we have the following representation

6 times x plus 15 is equal to 6 times x minus 41

is equal to implies =

So, we have:

6 times x plus 15 = 6 times x minus 41

Plus implies +, minus implies - and times *

This gives

6x + 15 = 6x - 41

The question does not require that we solve the expression

So, we leave it at 6x + 15 = 6x - 41

Hence, the required expression is 6x + 15 = 6x - 41

Read more about expression at

brainly.com/question/15775046

#SPJ1

There are 21 yellow marbles anita receives

given that

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.

The term "percent" is derived from the Latin per centum, meaning "hundred" or "by the hundred". The sign for "percent" evolved by gradual contraction of the Italian term per cento, meaning "for a hundred". The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to two circles separated by a horizontal line, from which the modern "%" symbol is derived.

at the craft store , Anita bought a bag of yellow and green marble

The bag contained 70 marble,

30% percentage of them were yellow.

now, we need to find How many yellow marble did Anita receive

= 70 * 30%

= 70 * [tex]\frac{30}{100}[/tex]

= 7 *3

= 21

There are 21 yellow marbles anita receives

To learn more about percentage:

https://brainly.com/question/24159063

#SPJ4

Total water use in Spain = 810m^3 x 46.5 million = 37,425,000,000 m^3. it is important to be aware of the amount of water used in order to understand and mitigate any potential negative impacts.

1. Given that the per capita water use is 810m^3 and the population of Spain is 46.5 million.

2. Calculate the total water use by multiplying the per capita water use by the population of Spain.

3. Total water use in Spain

= 810m^3 x 46.5 million = 37,425,000,000 m^3

The total water use in Spain is calculated by multiplying the per capita water use (810m^3) by the population of Spain (46.5 million). This yields a total water use of 37,425,000,000 m^3. This number indicates the volume of water used in Spain annually by its citizens. Water use can have a variety of impacts on the environment, such as depletion of water resources, and it is important to be aware of the amount of water used in order to understand and mitigate any potential negative impacts.

Learn more about amount here

https://brainly.com/question/8082054

#SPJ4

Answer:

x<30

Step-by-step explanation:

3/6x-1/6x<10

1/3x<10

x<30

The principal of account A is $250.26

The principal of account B is $500

The account that would  earn you more interest in the first month is account B

Simple interest is the interest earned on an amount of money in a savings account.

Simple interest = principal x time x interest rate

Principal is the amount deposited

Principal = simple interest / ( time x interest rate)

Principal of account A = 4.88 / (6/12 x 0.039) = $250.26

Principal of account B = 24.75 / (27/12 xx 0.022) =$500

Interest earned in the first month:

Account A =  (1/12) x 250.26 x 0.039 = .81

Account B =  (1/12) x 500 x 0.022 =0.92

To learn more about simple interest, please check: https://brainly.com/question/27328409

#SPJI

Answer:175 are not suvs

Step-by-step explanation:

Answer: 175

Step-by-step explanation:

Answer: M= -3

Solve for m by simplifying both sides of the equation, then isolating the variable.

Answer: -c^12+9c^4

Step-by-step explanation:

Answer: 81 c^4 - c^12

Step-by-step explanation:

(9c^2+c^6)(9c^2-c^6)

Step-by-step explanation: (9c^2+c^6)(9c^2-c^6)

This is the difference of squares

(a+b) (a-b) = a^2 - b^2

(9c^2) ^2 - ( c^6)^2

81 c^4 - c^12

Answer:

35

Step-by-step explanation:

a=adult c=children

7a:4c

?a:20c

20 is 5 times more than 4 which I found by doing 20/4

So now we multiply 7 by 5 to get 35

35a:20c

There are 35 adults

Answer:

y = f(x) = a + bx

Step-by-step explanation:

Step-by-step explanation: A linear function is a function of the form f(x) = ax + b, where a and b are real numbers. Here, a represents the gradient of the line, and b represents the y-axis intercept (which is sometimes called the vertical intercept).