Equations
f) The difference of the ages of two sisters is 5 years. After 4 years, if the product of
their ages becomes 104, find their present ages.​

A quadratic equation is a second-degree equation, meaning it contains at least one squared term.

A quadratic polynomial in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of second order guarantees that it has at least one solution according to the Fundamental Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one word in it has to be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical coefficients or constants a, b, and c.

given

2x2-7x = 0.

As we already know, a quadratic equation is a second-degree equation, meaning it contains at least one squared term.

Regarding comparing the quadratic equation in standard form with the equation 2x27x=0

ax ²+bx+c=0:

We get a=2, b=7, and c=0.

The equation 2x27x=0 is therefore a quadratic equation.

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The location of the waterfall on the graph will be (3,1). Instead of going down down,  Rodrigo goes 4 units upward direction.

What are the coordinates of a point?

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x-axis (horizontal) and y-axis are the two axes that make up a coordinate plane (vertical).

Given that the location of the entrance is at (6,5).

To reach the waterfall, you need to go 3 km to the left and 4 km down from the park entrance.

The x-coordinate decreases to the left side of a point and increases to the right side of a point.

The y-coordinate decreases to a downward point and increases upward a point.

The x-coordinate of the waterfall is 6 - 3 =3

The y-coordinate of the waterfall is 5 - 4 = 1.

The coordinate that represents the location of a point is (3,1).

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The z score when x=72 , μ=63 , 0=3 is z=3

Because they allow for a comparison between two scores that do not belong to the same normal distribution, z-scores are significant. They are also employed to determine the likelihood that a z-score will occur inside a normal distribution. A negative z-score indicates that the raw data is smaller than the mean.

Because they allow for a comparison between two scores that do not belong to the same normal distribution, z-scores are significant. They are also employed to determine the likelihood that a z-score will occur inside a normal distribution. A negative z-score indicates that the raw data is smaller than the mean.

According to the equation

z=x-u/sigma

we get z=3

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The total cost of a pair of sandals is given by the equation A = $ 18.39

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of pair of sandals be represented as A

Now , the equation will be

The total amount spent by Bonnie = $ 77.77

The cost of one shirt = $ 11.49

So , the cost of 2 shirts = 2 x 11.49 = $ 22.98

And , the cost of 1 pair = $ 32

The total tax on the purchase = $ 4.40

So , the cost of pair of sandals A = total amount spent by Bonnie - cost of 2 shirts - cost of 1 pair - total tax on the purchase

Substituting the values in the equation , we get

The cost of pair of sandals A = 77.77 - 22.98 - 32 - 4.40

On simplifying the equation , we get

The cost of pair of sandals A = $ 18.39

Hence , the total cost of sandals is $ 18.39

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The correct equation for this given situation is,

⇒ d = 9.5t + 11

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

Given that;

John is driving around town. When he reaches the gas station, he notes that he has traveled 11 miles.

And, He reaches home 2 hours later and notes that he has traveled 30 miles.

Now, Let d represents the distance and t represents the time, in hours

So we get;

Let the equation which model this situation,

⇒ d = a t + b

Where a and b are constant.

Let the gas station is the starting point.

So, at gas station t = 0 , d = 11

Hence,

⇒ 11 = 0 × a + b

⇒ b = 11

When he reaches home 2 hours later notes that he has traveled 30 miles.

And, with substituting with b = 20

⇒ 30 = 2 × a + 11

⇒2a = 30 - 11 = 19

⇒ a = 19/2 = 9.5

So, We get the equation,

⇒ d = 9.5t + 11

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The solution of the equations: 2x+3y=3, 3x+2y=7​ is x =0  and y =1.

Equation:

An equation is a mathematical formula containing two algebraic expressions on either side of an equal sign (=). It shows the equivalence relation between the formula written on the left and the formula written on the right. In any formula, L.H.S = R.H.S (left side = right side). We can solve equations to find the values ​​of unknown variables that represent unknown quantities. If a statement doesn't have an equals sign, it means it's not an equation. considered to be an expression.

According to the question:

Given in the question:

2x+3y=3                         --------------------------------------- (1)

3x+2y=7                         ---------------------------------------- (2)

Multiplying Equation (1) by 3 and (2) by 2, we get:

6x + 9y = 9                                 --------------------------------- (3)

6x + 4y = 14                                --------------------------------- (4)

Now,

Subtracting equation (4) from (3)

5y = 5

⇒ y = 1

Now, putting y = 1 in equation (1) we get:

   2x + 3 × 1 = 3

⇒ 2x + 3 = 3

⇒ x = 0

Therefore, x =0 and y=1.

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The expressions that have a product of 10 are:

Option B: 5/6 x 14 = (5/6) * 14 = (514)/6 = 70/6 = 10

Option C: 3/5 x 20 = (3/5) * 20 = (320)/5 = 60/5 = 12

Option A: 5/14 x 14 = (5/14) * 14 = (514)/14 = 70/14 = 5

Option D: 2/3 x 15 = (2/3) * 15 = (215)/3 = 30/3 = 10

So options B and D have a product of 10.

The number 363 does not belong to the set.

Square root of a number is the value such that the value when multiplied to itself two times gives the original number.

It is denoted by the symbol √.

For example, square root of 16 is 4 since 4 × 4 = 16

The given numbers are 64, 289, 81, 363 and 121.

The numbers 64, 289, 81 and 121 is a perfect square of integers.

64 = 8²

289 = 17²

81 = 9²

121 = 11²

But 363 is not a perfect square of any integer.

Hence the number which is odd in the list is 363.

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Answer: -1/36

Step-by-step explanation:

Answer: - 1/36

Step-by-step explanation: exponet rule a^-b=1/a^

Distance between Marvin and Joshua is less or equal to 12 meter.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given,

Marvin and Joshua are about to play in a circular field.

Diameter of the field D = 12m

Let distance between two friends is x

Since, Diameter is the longest chord in a circle

Thus, x ≤ D

Distance between two friends ≤ 12 meter.

Hence, Marvin and Joshua are 12 meter or less far away from each other.

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This is equal to 0.04 plus 1.96 into root over 0.04 into 0.96 divided by 400 point. This is equal to 0.059, which is equal to 5.9 percent. Therefore, double 0 to 5.9 percent represent babies born with defect.

According to one research, 28 out of every 400 kids born in the globe suffer some form of serious birth problem. To execute a simulation based on this data, the easiest approach to assign random numbers is to use 00-06 (7%) to identify the newborns with birth abnormalities.

It is to be noted that:

The sum total of births is: 400

The sum of defective babies = 28

Hence, the fraction or ratio of this is:

28/400

= 7/100

= 7%.

The implication here is that that 07-99 (93%) will represent the babies without birth defects.

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The perimeter of the polygon is found as the 42 cm.

For the shown polygon:

Points A, B, C and D are tangents on the circle.

Thus, these tangent will subtend equal length from the points.

So,

AB = 3 + 4 = 7 cm

BC = 4 + 5 = 9 cm

As, ∠B ≅ ∠D, sides must also be equal.

CD = 5 + 4 = 9 cm

DA = 4 + 3 = 7 cm

Perimeter = AB + BC + BC + BC

                 = 7 + 9 + 9 + 7

Perimeter = 42 cm

Thus, the perimeter of the polygon is found as the 42 cm.

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On solving the provided question, we can say that  using properties of triangle, the value of x is 7.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

By using the property of triangle,

The exterior angle of the triangle is the sum of opposite two angle of the triangle.

Hence,

64 + 8x  = 18x - 6

10x = 70

x = 7

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Answer: 57

Step-by-step explanation:

1. Multiply 95 and 60

2. You get 5700, then you divide by 100

3. 5700/100 = 57

B} Approximately 18% of the 10th graders at Darren's school walk.

E} Approximately 76% of the 10th graders at Darren's school ride the bus. Options B and E are correct options

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Total students = 50
Number of students in bus = 38
Number of students in car = 3
Number of students in Walk = 9

Percentage student go to school by bus = 36 / 50 × 100% = 76%

Similarly,
Percentage students go to school by car = 6%
Percentage of students who go to school by walk = 18%

From the above calculation, the Correct options,
B} Approximately 18% of the 10th graders at Darren's school walk.

E} Approximately 76% of the 10th graders at Darren's school ride the bus.

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.

Answer:

$735.75

Step-by-step explanation:

The equation is:

A = P(1 + rt)

We know

P = $675

r = 3% = 0.03

t = 3 years

Let's solve

A = 675(1 + 0.03 x 3)

A = 675( 1.09)

A = $735.75

Marhall made 9 ales this week, earning a base of $186 plus $15 per ale. Vickie earned a base of $48 plus $18 per ale. Since both of them earned the same amount, we can set up the equations

Marhall made 9 ales this week.

Step by explanation

We can use an equation to solve this problem.

Let x = number of ales Marhall made

Marhall's Earnings = 186 + (15 x)

Vickie's Earnings = 48 + (18 x)

Since both of them earned the same amount, we can set up the equations and solve for x:

186 + (15 x) = 48 + (18 x)

15x = 138

x = 9

Therefore, Marhall made 9 ales this week.

Marhall made 9 ales this week, earning a base of $186 plus $15 per ale. Vickie earned a base of $48 plus $18 per ale.

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The value of the expression is -5.84

The question is mathematically expressed as follows

The question reads: three fifths times the quantity 1 plus the square root of 16 end quantity squared minus the quantity five minus two end quantity cubed

[(3/5*1 + √16)]² - (5-2)³

Simplify the brackets first

This implies that

(3/5 + 4)² - (3)³

Simplify further to have

[(3+20)/5]² - 27

⇒(23/5) -27

Simplify to get

529/25 - 27

= 21.16 - 27

=-5.84

Therefore the expression gives -5.84

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Answer:3520.000

Step-by-step explanation:

ft/min =mph * 88.00000

ft/min =40 * 88.00000

ft/min =3520.000

Answer:

The exponential form of 0 is 0.

In simple words, the exponents can said to be the powers of the base. For example, in 2³, the exponent will be 3. If a number is given without any power then its power is 0. The exponential form is simply the number with exponents.

Answer:

y = (-5/2)x + 8

slope = -2.5

b = 8

x-intercept = 3.2

y-intercept = 8

Step-by-step explanation:

The degree of the polynomial 3x² 5x¹ 7 is 2.

This can be calculated by examining the highest exponent of the variable in the polynomial. Since the highest exponent is 2, the degree of the polynomial is 2.

Formula: Degree = Highest Exponent of the Variable

To calculate the degree of the polynomial 3x² 5x¹ 7, we first need to examine the highest exponent of the variable. The highest exponent is 2, therefore, the degree of the polynomial is 2.

3x² = 3x2 = 3x2 = Degree = 2

5x¹ = 5x1 = 5x1 = Degree = 1

7 = 7 = 7 = Degree = 0

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During photosynthesis, what is the path or flow of energy among biotic and abiotic parts of an ecosystem?

The value of exponential 4 is 4^4, or 256. it means that 4 should be multiplied by itself 4 times.

In mathematics, an exponential is a number that is multiplied by itself a certain number of times. For example, when 4 is used as an exponential, it means that 4 should be multiplied by itself 4 times. This is written as 4^4, or 4 to the fourth power. This means that 4 is multiplied by itself 4 times, resulting in the value of 256.

Exponentials can be used to calculate the power of a number. For example, in the case of 4^4, 4 is the base number and 4 is the exponent. An exponent is the number of times a base number is multiplied by itself. In this case, the base number (4) is being multiplied by itself 4 times, resulting in a value of 256.

In addition, exponentials can be used to solve equations. For example, if we need to solve for x in the equation 4^x = 256, we can use the exponential 4 to determine the value of x. In this case, x = 4 because 4^4 = 256.

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If a current flows at 5 mph. A boat can travel 20 mi downstream in the same amount of time it can go 12 mi upstream. The speed of the boat in still water is 20mph.

Boat speed x mph

Current speed 5 mph

Against current x - 5 mph

With current x + 5 mph

Distance against current 12

Distance with current 20

Time = same equate the time against with time with current

t=d/r

12 /(x- 5)= 20 /(x+ 5)

12 ×(x+ 5 )= 20 ×(x- 5 )

12 x + 60= 20 x -100

12 x -20 x = -100 + -60

-8x = -160

x = -160/-8

x= 20 mph

Therefore the speed of the boat in still water is 20mph.

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a. We cannot calculate the probability, because we do not know the shape of the distribution.

b. The mean and standard deviation of the sampling distribution of x are 12 and 0.0566.

c. The shape of the distribution described in part b is symmetrical.

d. The probability that a random sample of 50 cans produces a sample mean amount of 11.9 ounces or less is 0.0386.

We do not know the shape of the distribution, so we cannot calculate the probability that a single randomly selected can contains 11.9 ounces or less. The question given have not told us that the distribution of individual cans was normal, and we cannot assume it is so; therefore, we cannot calculate its probability.

As given information the mean μx = 12.

And standard deviation σx = σ / √n = 0.4 / √50 = 0.566.

The shape of the distribution described in part b is symmetrical, because the two sides of the distribution are a mirror image of each other. Therefore, it is normal distribution.

Since the sample is large n = 50 and 50 > 30, so by CLT (Central Limit Theorem), the distribution of sample means is approximately normal N(12, 0.0566). So, P(x ≤ 11.9) = normalcdf (0, 11.9, 12, 0.0566) = 0.0386.

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