Find The Missing Number
1. 1:2=4N
2: 3:8=N:16
3.15:20=30:N
4.N:25=2:5
5.10:N=40:80

The  age of the older brother is 21 years

Two or more expressions with an Equal sign is called as Equation.

Six years ago, the sum of the ages of two brothers was 22

x+y=22

The product of their ages is 21

xy=21

y=21/x

x+21/x=22

x²+21=22x

x²-22x+21=0

Factorize the equation

x²-21x-x+21=0

x(x-21)-(x-21)=0

(x-1)(x-21)=0

x=1 and x=21

21+y=22

y=1

Hence, the  age of the older brother is 21 years

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Answer:

Step-by-step explanation:

the solution of number line is all the options are correct.

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

Here,

Kendra and Jamal are standing in line. The number line shows their positions in meters with positive numbers representing positions to the right.

The position of Kendra is -6 and Jamal is 0.

Kendra is 6 meters left of Jamal.

Kendra and Jamal are 1-6 meters apart.

Jamal is 6 meters right of Kendra.

Hence, all the options are correct.

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Answer:

(9b-4c)(9b+4c)

Step-by-step explanation:

81b^2-16c^2

Using the the difference of square formula: a^2-b^2=(a-b)(a+b)

(9b-4c)(9b+4c)

Toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, There are  6ways it can be selected

Generally, There are 3! = 6 ways for the toddler triplets to choose their coats, but since the question asks for exactly one of them to end up with their coat, we need to consider the 3 cases where exactly one of them chooses their coat.

In the case where Red chooses their own coat, there are 2! = 2 ways for Green and Blue to choose their coats. In the case where Green chooses their own coat, there are 2! = 2 ways for Red and Blue to choose their coats. In the case where Blue chooses their own coat, there are 2! = 2 ways for Red and Green to choose their coats.

So in total, there are 2 + 2 + 2 = 6 ways for exactly one of the toddler triplets to end up with their coat.

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Answer:

--------------------------------

Consecutive exterior angles are supplementary.

It proves a and b are parallel.

Corresponding angles are congruent.

It proves a and b are parallel.

Given two vertical angles showing the relation between one line and the transversal and not a reason to state the lines are parallel.

Given two angles of same value. Since they are alternate interior angles, it proves the lines a and b are parallel.

Given two angles with the sum of 180. They are same side interior angles. It proves the lines a and b are parallel.

Given two angles of same value. They are alternate exterior angles but in relation to one of the lines and it proves the two transversals are parallel but not the lines a and b.

Answer:

1.80642 rounded to the nearest thousandth is 1.806.

Step-by-step explanation:

The guy above me is correct

Answer:

To the nearest dollar, Savannah would have $8,007 more in her account than Lincoln.

Step-by-step explanation:

To find out how much more money Savannah would have in her account than Lincoln after 20 years, we need to calculate the future value of both investments using the appropriate interest rate and compounding period.

For Lincoln's investment:

Future value = $6,500 * (1 + (3^3/4/100) / 4)^(4*20) = $6,500 * (1 + 0.046875)^80 = $6,500 * 2.611 = $16,917.50

For Savannah's investment:

Future value = $6,500 * e^(0.041875*20) = $6,500 * 3.843 = $24,924.50

To find the difference between the two investments, we can subtract Lincoln's future value from Savannah's:

$24,924.50 - $16,917.50 = $8,007

To the nearest dollar, Savannah would have $8,007 more in her account than Lincoln.

[tex]\cfrac{1}{4}x+1=32\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{1}{4}x+1 \right)=4(32)}\implies x+4=128\implies x=124[/tex]

Answer:

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Everytime x increases by 3 units, y increases by 1 unit.

Hence, when Δx=3, Δy=1  (Δx = change in x)

m=Δx/Δy

m=1/3

Using the above equation 1/i is equal to 2/(9-5j^2+3k)

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given; 2i+5j^2-3k=9

2i+5j^2-3k=9

2i=9-5j^2+3k

i=(9-5j^2+3k)/2

1/i=2/(9-5j^2+3k)

Therefore, the value of 1/i according to the given equation will be

2/(9-5j^2+3k)

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The area of the triangle KLM is found using Heron's formula as:

A = 60 in².

     S = (a+b+c)/2

     where a, b, and c are the triangle's three sides.

The sides of the triangle KLM are:

Then,

Semi perimeter s = a + b + c / 2

s = (13 + 13 + 10)/ 2

s = 18 in

Thus,

s - a : 18 - 13 = 5

s -b : 18 - 13 = 5

s - c : 18 - 10 = 8

By Heron's formula;

area of triangle KLM = √(s - a)(s -b)(s - c)

A = √18*5*5*8

A = 60

Thus, the area of triangle KLM is found using Heron's formula as:

A = 60 in².

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Number of pounds of banana sold is, 14

And, Number of pounds of grapes sold is, 36

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Each pound of banana sell for $2.

And, Each pound of grapes sell for $1.

Now, Let number of pounds of sell banana = x

And, Number of pounds of sell grapes = y

Since, There are 50 pounds of fruits are sell.

So, We can formulate;

⇒ x + y = 50   .. (i)

And, Each pound of banana sell for $2.

And, Each pound of grapes sell for $1.

Hence, We get;

⇒ $2x + $1y = $64

⇒ 2x + y = 64  .. (ii)

Substitute value of y from (i) in (ii), we get;

⇒ 2x + y = 64

⇒ 2x + (50 - x) = 64

⇒ 2x + 50 - x = 64

⇒ x = 64 - 50

⇒ x = 14

And, From (i);

⇒ x + y = 50

⇒ 14 + y = 50

⇒ y = 50 - 14

⇒ y = 36

So, Number of pounds of sell banana = 14 pounds

And, Number of pounds of sell grapes = 36 pounds

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Answer:

1,000 was the interest charge which leaves you with 24000 as the regular vaule

Step-by-step explanation:

Answer:

y=1/6x+2 is the slope formula.

The equation of a line passing through the point (0,2) and having slope 1/6 is: x-6y+12=0

Step-by-step explanation:

Equation of a line passing through a point (x1,y1) and having slope m is: [tex]y-y_{1} =m(x-x_{1} )[/tex]

where m= slope of the line

Given point (x1 , y1)= (0 , 2)

So, the Equation of a line: [tex]=y-y_{1} =m(x-x_{1} )[/tex]

[tex]y-2 =(\frac{1}{6} )(x-0 )[/tex]

[tex]y-2 =(\frac{1}{6} )(x)[/tex]

[tex]6*(y-2) =(x)[/tex]

[tex]6y-12=x[/tex]

[tex]6y-12-x=0[/tex]

[tex]-x+6y-12=0[/tex]  OR [tex]x-6y+12=0[/tex]

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The solution for the absolute value equation is:

|7 - 11| = 4

Here we want to solve an absolute value equation:

|7 - 11| = ?

First, remember how the absolute value works, it is:

|x| = x  if x  ≥ 0

|x| = -x  if x < 0.

Now let's return to our equation:

|7 - 11|

If we simplify the left side, we will get:

|-4|

Notice that it is a negative number, so we just need to change the sign:

|-4| = 4

Then the equation is:

|7 - 11| = 4

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Answer:

[tex] \sf \: ∣7-11∣ = 4[/tex]

Step-by-step explanation:

Given problem,

→ ∣7 - 11∣

Let's solve the problem,

→ ∣7 - 11∣

→ ∣-4∣ = 4

=> Absolute value

=> It is always positive

Hence, the answer is 4.

Answer: x is 17

Step-by-step explanation:

Distribute the -5: -5x + 50 = -35

Subtract 50 from both sides: -5x = -85

Divide both sides by -5: x = 17

Answer: x is representing here.

Step-by-step explanation: as the equation is -5(x-10) = -35

(-) sign in both sides will cancel out each other so the equation will become 5(x-10)= 35

now we will solve the equation

5x-50 = 35

5x = 35+50

5x = 85

x=85/5 = x =

The difference between the functions G(x) and h(x) is 4 units.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The functions are given in the question, as follows:

G(x)=-f(x)+10 and h(x)=-f(x-4)+10

Since the functions, g and h differ

This can be seen by subtracting G(x) from h(x):

h(x) - G(x) = (-f(x-4) + 10) - (-f(x) + 10)

h(x) - G(x) = 4.

This means that for any value of x, the output of h(x) will be 4 units greater than the output of G(x).

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Answer:

1.  Hypothesis: "All 120° angles"

    Conclusion: "are obtuse angles"

    If-then statement: If an angle measures 120°, then it is an obtuse angle.

2.  It is not raining.

Step-by-step explanation:

Conditional statement

"If this happens, then that will happen."

For the statement "All 120° angles are obtuse angles":

Therefore, the statement written in the if-then form is:

Given statement:

The definition of a negation of a statement is the opposite of the given statement.  For example, the negation of statement "p" is "not p."

Therefore, the negation of the given statement is:

Answer: To determine this percentage, we would need to know the current market share for Category A and the desired market share goal of 50%. With this information, we could calculate the difference between the current market share and the desired market share and express that difference as a percentage of the current market share. Without this information, I am unable to provide an exact percentage.

Step-by-step explanation:

Answer:

(-7,3)

Step-by-step explanation:

Therefore , the solution of purchased so that the consumer has an equal amount of each LCM if hot dogs are packaged with 10 dogs per pack .

"Sandwich rolls or hot dog buns are typically sold in packs of eight because the buns are baked in clusters of four in pans designed to hold eight rolls." Because hot dogs are sold by the pound and store-bought standard-sized hot dogs weigh 1.6 ounces,

Here,

purchased so that the consumer has an equal amount of

each if hot dogs are packaged with 10 dogs per pack and hot dog buns are packaged with 8 buns per pack  LCM is 40.

hot dog buns are packaged with 8 buns per pack  LCM is 40. 4 packages of hot dogs and 5 packages of buns are required.

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The solution to the given complex number expression is; 0 + [1/(-2√6))]i

We are given the expression as;

(√-4)/[(√-8)√-12)]

Now, when it comes to complex numbers, we know that the square root of a negative number for example √-25 would result in 5i.

Similarly, i² = -1

Thus, our expression is now;

2i/(2i√2 * 2i√3)

= 2i/(-4√6)

= i/(-2√6))

= 0 + [1/(-2√6))]i

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Answer:

$5.91

Step-by-step explanation:

The amount of simple interest gained from a sum of money can be represented as:

[tex]\textrm{Interest} = P\cdot r\cdot t[/tex]

where [tex]P[/tex] is the principal amount (original sum of money), [tex]r[/tex] is the rate of simple interest per time period, and [tex]t[/tex] is the period of time in relation to a year.

To solve this problem, we simply have to plug the given values into the above formula and round the result to the hundredths place (cents).

[tex]P = \$525[/tex],  [tex]r = \dfrac{4.5\%}{\textrm{month}}[/tex],  [tex]t = 3 \textrm{ months} = \dfrac{1}{4} \text{ year}[/tex]

[tex]\textrm{Interest} = \$525 \cdot 4.5\% \cdot \dfrac{1}{4}[/tex]

[tex]\boxed{\textrm{Interest} \approx \$5.91}[/tex]

Answer:

$5.91 (nearest cent)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I=Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

As the value of t has been given in months, we need to convert it to years before inputting it into the formula.

[tex]\sf \implies 3\; months=\dfrac{3}{12}\;year=\dfrac{1}{4}\; year[/tex]

Therefore, the values to input into the formula are:

Substitute the values into the formula and solve for I:

[tex]\implies I=525 \cdot 0.045 \cdot \dfrac{1}{4}[/tex]

[tex]\implies I=23.625 \cdot \dfrac{1}{4}[/tex]

[tex]\implies I=5.90625[/tex]

Therefore, the amount of interest you would receive on a deposit of $525 for three months at a rate of 4.5% is $5.91 (nearest cent).

The constant of proportionality will be $0.79

It is defined as the rate or the ratio of two proportional values which are known to be at the same value.

The two variable values are said to have a proportional association if or when either of their ratio or their product are known to bring about a constant.

Hence, the proportionality constant's value is known by the proportion between the two said quantities.

Jason bought 4 pounds of bananas for $3.16.

k = $3.16/4

k = $0.79

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Answer:

41, 49

Step-by-step explanation

It goes up in 8 if you work out 25-17 or 33-25.

33+8=41, 41+8=49

Answer:

Step-by-step explanation:

Let's start by labeling the sides of the triangle ABC:

A = 12

B = x

C = 10

Using the Law of Cosines, we can write the following equation:

C² = A² + B² - 2ABcos(C)

Substituting the values we have, we get:

10² = 12² + x² - 2(12)(x)cos(10)

Simplifying, we get:

100 = 144 + x² - 24xcos(10)

Rearranging, we get:

x² - 24xcos(10) + 44 = 0

Solving for x, we get:

x = [24cos(10) ± √(576cos²(10) - 176)]/2

Calculating the values, we get:

x = [24cos(10) + √(5232)]/2 ≈ 18.3

x = [24cos(10) - √(5232)]/2 ≈ 7.7

Therefore, BC = 18.3 or BC = 7.7

The mean is of 0.15. The standard deviation is of 0.0326.0.1774 of incoming kindergarteners are nearsighted.

The central limit theorem and the normal distribution are used to determine that:

a) A 0.15 is the mean.

b) A standard deviation of 0.0326 is present.

c) There is a 0.063 = 6.3% chance that fewer than 10% of the kindergarten applicants have nearsightedness.

d) 0.1774 percent of kindergarten students have nearsightedness.

The mean is of 0.15.

Item b:

s = p (1-p)/n = 0.15(0.85)/120

=  0.0326.

The standard deviation is of 0.0326.

Item c:

The probability is the p-value of Z when X = 0.1.

By the Central Limit Theorem

Z=  0.1 -0.15/ 0.0326.

=  -1.53

Z = -1.53 has a p-value of 0.063.

There is a 0.063 = 6.3% probability that less than 10% of the incoming kindergarteners are nearsighted.

Item d:

X = 0. 1774

The proportion is X when Z has a p-value of 0.8, so X when Z = 0.84.

0.1774 of incoming kindergarteners are nearsighted.

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Answer:

Step-by-step explanation:

The area of the rectangle is 48 square feet.

Write an equation you can use to find the value of x.

48 : 4 = x

12 = x

48=4x is the equation which can be used to find the value of x.

Given that area of the rectangle is 48 square feet.

We have to find the value of x.

We know that area of rectangle is length times width.

Area = length × width

Length =x ft

Width = 4 ft

Area = 48 square feet.

Plug in the values of length, width and area in above formula.

48=4x

Divide both sides by 4:

x=12

Hence, 48=4x is the equation which can be used to find the value of x.

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