Find the solution(s) to (x + 2)^2 = 49. Check all that apply.

1) (m · n)(- 3) = 9

2) (m / n)(x) = x / x, for x ≠ 0

Herein we have two operations between two functions of the form n(x) = x: (i) Multiplication, (ii) Division. In the first part we find the case of a multplication between two functions:

(m · n) (x) = m(x) · n(x)            (1)

Then,

(m · n) (- 3) = m(- 3) · n(- 3) = (- 3) · (- 3) = (- 3)² = 9

The second part present a case of a division between two functions:

(m / n) (x) = m(x) / n(x)           (2)

Then,

(m / n) (x) = m(x) / n(x) = x / x, where x = 0 leads to an indetermination.

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Answer:

Step-by-step explanation:

At least two sides have the same length.

At least two angles have the same measure.

The base angles (angles opposite the equal sides) have the same measure.

The altitude (perpendicular segment from the base to the vertex) bisects the base and the corresponding base angle.

The median (segment connecting the vertex to the midpoint of the base) is also an altitude, angle bisector, and perpendicular bisector of the base.

Based on these characteristics, the properties that belong to all isosceles triangles are:

At least two sides have the same length.

At least two angles have the same measure.

The base angles have the same measure.

Therefore, the correct options are:

At least two sides have the same length.

At least two angles have the same measure.

The base angles have the same measure.

Answer:

-2

Step-by-step explanation:

bc math

Answer:

-2

Step-by-step explanation:

\(=\frac{-2}{3} \times\frac{3}{1}\)

\(=\frac{-2 \times3}{3\times1}\)

\(=\frac{-6}{3}\)

\(=\frac{-6 divided by 3}{3dividedby3}\) or = -6÷3/3÷3

\(=-2\)

They have to use 17.03 pounds of cashews and 17.03 pounds of nuts to make a 32 pounds mixture that sells for $5.75 per pounds

The cost of cashews per pounds = $7.20

The cost of nuts per pounds = $4.10

Consider the number of pounds of cashews as x and number of pounds of nuts as y

Total pounds of mixture = 32 pounds

The equation will be

x+y = 32

x = 32-y

Cost of the mixture for one pound = $5.75

Cost of the mixture for 32 pounds = 32×5.75

= $184

Then the equation will be

7.20x+4.10y = 184

Here we have to use the substitution method

Substitute the value of x in the equation

7.20(32-y)+4.10y = 184

230.4-7.20y+4.10y = 184

230.4-3.1y  = 184

-3.1y = 184-230.4

-3.1y = -46.4

y = 14.97 pounds

x+y = 32

x+14.97 = 32

x = 17.03 pounds

Hence, they have to use 17.03 pounds of cashews and 17.03 pounds of nuts to make a 32 pounds mixture that sells for $5.75 per pounds

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The only graph that represents a function is: Graph D

A function is defined as a relationship or expression that involves one or more variables. It typically has a set of input and outputs.  Each input has only one output. The function is the description of how the inputs relate to the output.

A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.

From the graphs, we can see that:

Graph A has 2 outputs at x = -2

Graph B has 2 outputs at x = 0

Graph C has two outputs at x = -1

Graph D has a unique output for every input and as such it is a function

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Answer:

y=5

Step-by-step explanation:

Plugging in the two points.

(2,5). y=mx+b or 5=0 × 2+b, or solving for b: b=5-(0)(2). b=5.

(0,5). y=mx+b or 5=0 × 0+b, or solving for b: b=5-(0)(0). b=5.

Hence, equals to y=5

Answer:

To calculate the selling price of each amplifier, we need to consider the cost, import duty, sales tax, and the desired profit margin.

Cost of each amplifier: sh. 3,750

Import duty of 125% on the cost:

Import duty = 125% of sh. 3,750

= 125/100 * sh. 3,750

= sh. (125/100 * 3,750)

= sh. 4,687.50

Cost of each amplifier including import duty:

Total cost = Cost + Import duty

= sh. 3,750 + sh. 4,687.50

= sh. 8,437.50

Sales tax of 20% on the total cost:

Sales tax = 20% of Total cost= 20/100 * sh. 8,437.50

= sh. (20/100 * 8,437.50)

= sh. 1,687.50

Total cost including sales tax:

Total cost = Total cost + Sales tax

= sh. 8,437.50 + sh. 1,687.50

= sh. 10,125

Desired profit margin of 10% on the total cost:

Profit = 10% of Total cost

= 10/100 * sh. 10,125

= sh. (10/100 * 10,125)

= sh. 1,012.50

Selling price of each amplifier:

Selling price = Total cost + Profit

= sh. 10,125 + sh. 1,012.50

= sh. 11,137.50

Answer:-6x^2+10x-5.

Step-by-step explanation: -6x^2-1−6x 2−1+x+9x+9                                                          -6x^2-1−6x 2−1+10x+9                                                                                                -6x^2-1-12−1+10x+9                                                                                                         -6x^2+10x-1-12-1+9                                                                                                                 6x^2+10x-5

The sum of the two expressions are -6x²+22x+9

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.

Given here the expressions here as -6x²+1+6x ×2-1, x+9x+9

The sum is -6x²+1+6x ×2-1 +x+9x+9=-6x²+22x+9

Hence, The sum of the two expressions are -6x²+22x+9

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Answer:

4^2

Step-by-step explanation:

Al cuadrado en ingles significa "to square", asi que basicamente significa multiplica el numbero por si mismo 2 veces (4 x 4 = 16)

Answer:

ehhh 0_0 ahhhhhhhhhhhhh

Step-by-step explanation:

Answer: We can start by using the concept of rates.

At 12:00 noon, oil is poured into the top of the tank at a rate of 2.1 gallons per minute and the valve at the bottom empties at a rate of 1.9 gallons per minute.

As the tank is empty at the beginning, the rate at which the oil is poured into the tank is equal to the rate at which the oil is leaving the tank.

2.1 gallons per minute - 1.9 gallons per minute = 0.2 gallons per minute

As the tank does not fill until 12:00 the next day, the difference between the rate of oil that enters the tank and the rate of oil that leaves the tank is equal to zero over the time frame.

0.2 gallons per minute * 1440 minutes = 288 gallons

So, the tank holds 288 gallons.

Step-by-step explanation:

Answer:

Step-by-step explanation:

208

Answer:

BOTH A and C

Step-by-step explanation:

The correct strategy to eliminate a variable in this system of equations is C: multiply the first equation by 5 and the second equation by 2, then add the equations.

An equation is a mathematical statement that expresses the equality between two or more expressions. It typically consists of two sides separated by an equal sign (=) or another symbol indicating equivalence. Each side of the equation can contain numbers, variables, operations, and functions, and the goal is to find the value(s) of the variable(s) that make the equation true.

To eliminate a variable, we need to manipulate the equations so that when we add them, one of the variables cancels out.

We can eliminate the variable "x" by using one of the following strategies:

A. Multiply the first equation by 2. Then add the equations.

This would result in the first equation becoming 10x + 6y = 8 and the second equation becoming -2x - 8y = 6. If we add these equations, the "x" term cancels out, but we are left with the equation 8x - 2y = 14, which still contains both variables.

B. Multiply the second equation by 5. Then add the equations.

This would result in the first equation becoming 5x + 3y = 4 and the second equation becoming -10x - 40y = 30. If we add these equations, the "x" term cancels out, but we are left with the equation -37y = 34, which only contains the variable "y". We cannot solve for both variables with this equation alone.

C. Multiply the first equation by 5 and the second equation by 2. Then add the equations.

This would result in the first equation becoming 25x + 15y = 20 and the second equation becoming -4x - 16y = 12. If we add these equations, the "y" term cancels out, and we are left with the equation 21x = 32. We can solve for "x" by dividing both sides by 21: x = 32/21.

D. Multiply the first equation by 2 and the second equation by 5. Then add the equations.

This would result in the first equation becoming 10x + 6y = 8 and the second equation becoming -10x - 40y = 30. If we add these equations, the "x" term cancels out, but we are left with the equation -34y = 38, which only contains the variable "y". We cannot solve for both variables with this equation alone.

Therefore, the correct strategy to eliminate a variable in this system of equations is C: multiply the first equation by 5 and the second equation by 2, then add the equations.

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Answer: 2 triangles to 5 circles or 2:5

In order to find the simplest ratio, we must find a number that both of our numbers can be divided by. Our starting ratio is 6:15. Both numbers can be divided by 3. So our equation will look like this

6/3 : 15/3

6 divided by 3 is 2 and 15 divided 3 is 5.

This means our new ratio is 2:5

2 and 5 can do not have a number that both can be divided by which means our simplest ratio is 2 triangles to 5 circles or 2:5

I hope this helped & Good Luck <3 !!!

Answer:

10

explanation:

60 divided by 6 equals 10, you could just use the division symbol, which is a slash, as we did above. The easiest way we found to answer the question "what 60 divided by 6 means", is to answer the question with a question: How many times does 6 go into 60?

Answer:

10

Step-by-step explanation:

Answer:

t=8

Step-by-step explanation:

t=8 is your answer

If you need solution do let me know in the comments

The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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Emily funded $6000 in stocks and $12,000 in bond funds. She also funded the remaining  $2,000 in her savings account.

Future value = $20,000

Simple interests rate = 1.5%

The return rate on bonds= 4.5%

The return rate on stocks = 6.2%

Total amount made on invests =  $942

Time period = 1 year

Let us assume that the amount of money Emily invested = x

Amount invested in stock = y

If the amount is twice = 2y

The interest earned = x * 0.015

Interest on bond = 2y * 0.045

Interest on stocks = y * 0.062

The equation will be:

(x * 0.015) + (2y * 0.045) + (y * 0.062) = 942

0.015x + 0.152y = 942  ------ Equation 1

Total future value is given as $20,000

x + 2y + y = 20000

x + 3y = 20000

x = 20000 - 3y

Substituting the x value in the first equation:

0.015(20000 - 3y) + 0.152y = 942

300 - 0.045y + 0.152y = 942

0.107y = 642

y = 6000

Therefore, we can conclude that Emily funded $6000 in stocks and $12,000 in bond funds.

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Answer:

4/7n+15

Step-by-step explanation:

Let the number be n

4/7 of a number means: 4/7 times a number (n). So 4/7n then, increase (add) that by 15

you'll get the equation 4/7n+15

According to the Pythagorean theorem, The Answer is Yes the third side is greater than 1 foot.

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

p=1 foot

b=1 foot

\(h^{2} = p ^{2} + b ^{2}\)

\(h=\sqrt {1^{2}+1^{2}}\\=\sqrt 2\\=1.41\\\)

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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On solving the provided question, we can say that Therefore, you would need multiply  approximately 27.84 pounds of food each day for your horse.

One of the four mathematical operations, along with arithmetic, subtraction, and division, is multiplication. Mathematically, adding subgroups of identical size repeatedly is referred to as multiplication. The multiplication formula is multiplicand multiplier yields product. To be more precise, multiplicand: Initial number (factor). Number two as a divider (factor). The outcome is known as the result after dividing the multiplicand as well as the multiplier. Adding numbers involves making several additions. as in 5 x 4 Equals 5 x 5 x 5 x 5 = 20. 5 times by 4 is what I did. This is why the process of multiplying is sometimes called "doubling."

First, we need to convert the weight of the horse from kilograms to pounds, so:

678 kg x 2.20462 lbs/kg = 1495.69 lbs

Next, we need to calculate how many Mcal the horse needs per day:

0.0333 Mcal/kg x 678 kg = 22.58 Mcal/day

Then, we can convert the Mcal to kcal:

22.58 Mcal/day x 1000 kcal/Mcal = 22,580 kcal/day

Finally, we can divide the total daily kcal needed by the kcal per pound of food to find the total pounds of food needed:

22,580 kcal/day ÷ 810 kcal/lb = 27.84 lbs/day

Therefore, you would need approximately 27.84 pounds of food each day for your horse.

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Answer:

Circle centered on origin,  (0, 0)

Radius = 7units

To find if the point lies on the circle , check if the distance from the center to the point is 7units.

\(distance = \sqrt{(x_{1} -x_{2})^{2} +(y_{1} -y_{2})^{2} } \\(x_{1} ,y_{1} ) =(0, 0)\\(x_{2}, y_{2}) = (-3, 2\sqrt{10} )\\\\distance = \sqrt{(0--3)^2+(0-2\sqrt{10})^2 } = \sqrt{9+40} = \sqrt{49} = 7units\)

Since the distance between the center and the point is 7units. the point lies on the circle.

Circle O is centered on the origin with a diameter of 14 units. Since the distance between the center and the point is 7units. So, the point lies in the circle.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

\(D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.\)

We have been given a Circle centered on the origin,  (0, 0)

Radius = 7units

In order to find if the point lies on the circle, check if the distance from the center to the point is 7units.

(x, y) = (0, 0)

(p, q) = (-3,2√10)

\(D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.\)

\(D = \sqrt{(0-(-3))^2 + (0-2\sqrt{10} )^2} \: \rm units.\\\\D = \sqrt{9+ 40} \\\\D = \sqrt{49} \\\\D = 7\)

Since the distance between the center and the point is 7units. So, the point lies on the circle.

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We may predict that, when rοunded tο the clοsest whοle number, 185 persοns οught tο be present at Sοcial Prοblems οn Sunday.

Detailed numbers the set οf integers that cοntains zerο and the natural numbers. nοt a decimal and fractiοn. Integer 0 thrοugh 2, 3, 4, 5, 6, 7, 8, 9, 10, and sο οn. a cοunting number, a negative number, οr zerο.

The library saw a sum οf 416 + 448 + 341 = 1205 visitοrs οn Saturday. By dividing the entire number οf visitοrs by the number οf visitοrs whο visited Sοcial Prοblems, and then multiplying the result by 100% tο represent the results as a percentage, we can determine what percentage οf these visitοrs visited Sοcial Issues:

Percentage οf visitοrs whο went tο Sοcial Issues = (448 ÷ 1205) x 100%

Percentage οf visitοrs whο went tο Sοcial Issues ≈ 37.18%

We may assume that a similar percentage οf Saturday's visitοrs will return οn Sunday in οrder tο estimate the number οf persοns whο can be expected tο attend Sοcial Prοblems οn that day. Tο determine hοw many peοple will visit Sοcial Prοblems οn Sunday, we can utilize the prοpοrtiοn mentiοned abοve:

Estimated number οf visitοrs tο Sοcial Issues οn Sunday = (37.18% οf 500 visitοrs)

Estimated number οf visitοrs tο Sοcial Issues οn Sunday ≈ 185

We may calculate that, if we rοund tο the next whοle number, 185 persοns shοuld be anticipated tο attend Sοcial Prοblems οn Sunday.

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Answer:

$17,404.5

Explanation:

To calculate the balance after t years, we can use the following equation:

Where P is the initial investment and r is the rate.

So, we can calculate the balance after 4 years, replacing t by 4, r by 3%, and P by $9000. Therefore the balance is:

Now, we can use this quantity to calculate the final value of the investment. So, replacing P by 10129.579, r by 7%, and t by 8 years, we get:

Therefore, the final value of the investment is $17,404.5

Answer:

3x - 2

Step-by-step explanation: