Brain Builders

Use the graph for Exercises 24 and 25.
24. Before leaving the grocery store, Kenny wrote the
y-coordinate first and the x-coordinate second when telling
his sister where to meet him. To his surprise, she was at
the right location. If his sister did not make an error, where
did the siblings meet? Explain how you know.

Using a straight line and either an open circle or a closed circle to indicate the end points, we can depict inequalities on a number line by displaying the range of integers.

By drawing a straight line and designating the end points with either an open circle or a closed circle, we can depict inequalities on a number line by illustrating the range of integers. An open circle indicates that it excludes the value. A closed circle indicates that it does contain the value.

Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.

With regard to the inequality expression

-3m + 5 > 14

5 from each side is subtracted.

-3m + 5 - 5 > 14 - 5

-3m > 9

Subtract -3 from both sides.

-3m/-3 < 9/-3

m < -3

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Answer:

1) 10/3

2) -1./3

3) -2/5

4) 1

5) undefined

6) 0

Step-by-step explanation:

Find two easy to read points. Go from one point to the other by going vertically first then horizontally. Moving up is positive and down is negative. Moving right is positive and left is negative.

slope = rise/run = (difference in y)/(difference in x)

1) slope = 10/3

2) slope = -1/3

3) slope = -2/5

4) slope = 1/1 = 1

5) slope = undefined (The slope of a vertical line is undefined.)

6) slope = 0 (The slope of a horizontal line is 0.)

Answer: The two numbers are $x = 5$ and $y = 7.5$.

Step-by-step explanation:

Let the two numbers be $x$ and $y$, where $x < y$. We can write the two given statements as the following two equations:

$$2y = 3x + 15$$

$$\frac{1}{5}x + \frac{1}{9}y = 10$$

We can solve this system of equations using elimination. Multiplying the first equation by 5 and the second equation by 9, we get

$$10y = 15x + 75$$

$$9x + y = 90$$

Subtracting these equations, we get

$$8y - 9x = 15$$

Multiplying this equation by 8, we get

$$64y - 72x = 120$$

Adding this equation to 5 times the first equation, we get

$$69y - 72x = 120 + 75$$

$$69y - 72x = 195$$

Dividing both sides by 3, we get

$$23y - 24x = 65$$

Subtracting this equation from 4 times the second equation, we get

$$96y - 36x = 360 - 260$$

$$96y - 36x = 100$$

Dividing both sides by 60, we get

$$\frac{16}{3}y - \frac{6}{5}x = \frac{5}{3}$$

Substituting the expression for $y$ from the first equation, we get

$$\frac{16}{3}(3x + 15) - \frac{6}{5}x = \frac{5}{3}$$

This simplifies to

$$\frac{16}{5}x + \frac{64}{5} = \frac{5}{3}$$

Solving for $x$, we find that $x = 5$. Substituting this value into the first equation, we find that $y = 15/2 = 7.5$. Therefore, the two numbers are $x = 5$ and $y = 7.5$.

The width of the two gardens will be equal to 5 feet.

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that a rectangular garden has a length twice as great as it’s width. a second rectangular garden has the same width as the first garden and a length that is 4 meters greater than the length of the first garden. the second garden has an area of 70 square meters.

For the first rectangle, the  dimensions will be,

L = 2w

For second rectangle width is same then the area is,

L x w = 70

( 2w +4 ) x w = 70

2w² + 4w - 70 = 0

w² + 2w -35 = 0

w² + 7w - 5w -35 = 0

w(w + 7 ) -5(w+7) = 0

w =-7 and  w = 5

Hence, the width is w = 5 ft.

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Therefore , the solution of the given problem of circle comes out to be Area = 154 meter square  or 49π meter square option 1 is correct.

A moving point on a plane is followed so that its distance from a specific point remains constant to produce the circular form known as a circle. The English term circle derives from the Greek word kirkos, which meaning hoop or ring. Area of circle= πr²

Here,

Given :

Diameter of circle : 14

Radius =14/2 =  7 meters

and

Using formula

Area= πr²

=> Area = π7²

=>Area = 22/7 * 7²

=> Area = 22*7

=> Area = 154 meter square or 49π meter square

Therefore , the solution of the given problem of circle comes out to be Area = 154 meter square  or 49π meter square option 1 is correct.

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Answer: A the first one 49π square meters

The two consecutive odd numbers such that the difference between their reciprocals is of 2/99 are given as follows:

9 and 11.

The two numbers are odd numbers and consecutive, hence they are symbolized as follows:

n and n + 2. (as n + 1 is even).

Their reciprocals are given as follows:

The difference of their reciprocals is obtained as follows:

1/n - 1/(n + 2) = 2/99.

The least common factor of n and n + 2 is of n x (n + 2), hence:

(n + 2 - n)/[n(n + 2)] = 2/99

2/[n(n + 2)] = 2/99.

As the numerators are equal, we take the denominators to solve for n as follows:

n(n + 2) = 99.

n² + 2n - 99 = 0.

(n - 9)(n + 11) = 0.

Applying the Factor Theorem, the solutions are given as follows:

We want the positive numbers, hence the numbers are:

n = 9 and n + 2 = 9 + 2 = 11.

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Answer:

S = pi^2 * (8^2 - 10^2)

= pi^2 * (-4)

= -12.57 pi^2

The value of S is approximately -12.57 * pi^2. To express this value to three significant figures, we would round it to -13 * pi^2, which is the same as -12.6 * pi^2. So the final answer is -12.6 * pi^2.

Answer:

B

Step-by-step explanation:

Center of the distributions -> mean/median (preferably mean)

The option with range is eliminated

Median might not be accurate as median is the center person, not the center result.

Based on the graphs, identify the graph with the intervals of greatest frequency.

For North Heights -> between 30 and 32 (right-skewed, some higher values)

For Southview -> between 28 and 30 (most concentrated there)

Hence, mean of Southview is lower than North Heights.

Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.

Expressions that equal one another are the building blocks of an equation. The equation 4x²+3x = 22. A equation is an equation that has at least two variables and depicts the relationship between them.

Here,

are the definitions of each equation:

1. x^2 + y^2 - 4x + 6y - 5 = 0

 The x2 and y2 terms share the same scaling factor, despite the fact that this equation contains a bunch of other garbage (which is 1). This ought to be screaming "circle" to you.

2. x^2 - 6y = 0

 The x term is squared, but the y term is not, which is an important distinction to make. A parabola is clearly indicated by this fact.

3. 4x^2 + 9y^2 = 1

This is the result of adding an x-squared and a y-squared phrase. That kind of sounds circular, but the results are scaled by those two coefficients. Additionally, they vary. So, a closed curve that resembles a circle but is slightly stretched out is what we're searching for. An ellipsis appears there.

4. 7x^2 - 9y^2 = 343

 A few squared terms for x and y are present here. However, we are removing rather than adding to them. This denotes a hyperbola.

Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.

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This is a simple cross multiplication problem! Any time you're given a ratio and then the actual quantity of something, you can use cross multiplication to figure out the quantity of the other thing!

We know that the ratio of toads to frogmen is 7 : 2. We also know there were 98 actual toads. Therefore we can set up our equations!

[tex]ratio_{toads}=ratio_{frogmen}\\actual_{toads}=actual_{frogmen}\\\\7=2\\98 = x\\\\7x=196\\x=28[/tex]

The first two equations above everything is how you would have everything set up! The second equations under them are the numbers plugged in, and the rest is just simplification.

So, your final answer should be 28 frogmen!

Answer: 5%

Step-by-step explanation:

Answer:

answer is 10

Step-by-step explanation:

The initial amount that was invested in the account was $49.

We know that we can be able to obtain the principal by the use of the formula for the simple interest and by that formula we would now have that;

I = PRT/100

I = interest

P = principal

R = rate

T = time

Then we are going to have that;

R = 2.7

P = ?

I = 6.62

T = 5

Then;

6.62 = P * 2.7 * 5/100

6.62 * 100 =  P * 2.7 * 5

P = 6.62 * 100/2.7 * 5

P = 662/13.5

P = 49

Thus we have but in at the beginning about $49

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Answer:

-1/3

Step-by-step explanation:

The cost to order 1, 000 pens and 2, 000 notebooks, by the Student Union, can  be found to be

The cost of ordering 1, 000 pens is shown to be 60 cents per pen so the total cost would be :

= Number of pens x Cost per pen

= 1, 000 x 60 cents

= $ 600

The cost of ordering 2, 000 notebooks is 76 cents per notebook which comes to a total of :

= 2, 000 x 76 cents

= $ 1, 520

The total cost of ordering the pens and notebooks is:
= 600 + 1, 520

= $ 2, 120

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Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex..

Trigonometry is a discipline of mathematics that examines relationships between triangles' degrees and sides. Trigonometry is used frequently in geometry because every straight-sided form may be broken down into a group of triangles. Trigonometry and other areas of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, have a staggering amount of interrelationships.

Here,

Angle of elevation to the balloon's peak: = 28°

When the balloon is erect, a right triangle is formed by the horizontal distance to the balloon, l, the height of the balloon, h, and the distance to the top of the balloon, d.

Aside from the hypotenuse

l = The leg next to the provided reference angle

,h = The leg perpendicular to the specified angle,

Trigonometric ratios give us;

Cosx is equal to the product of the hypotenuse and adjacent lengths.

where we obtain;

Cos x equals l/d

=>Cos 28 = 30 m /d

=> d = 30m/Cos 28 ≈ 33.977

Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex.

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The product of f(x) and g(x) is always a polynomial. By the definition of

polynomials the product of polynomials is always a polynomial because

the coefficient are real numbers and the exponents are whole

numbers. Real numbers and whole numbers are closed under addition

and subtraction.

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) with coefficients, that is either a constant or the indeterminates (also called variables or x's). The most common examples are the quadratic equation, cubic equation, and so on. The degree of a polynomial is the highest power of the indeterminate in the polynomial. For example, a polynomial with three indeterminates to the power of 2 is said to have a degree of 2.

Here f(x) and g(x) are two given polynomial,

let f(x) = x+1 ang g(x) = x-1

f(x).g(x) = (x+1)(x-1).

f(x).g(x) = x²-1.

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The system of equations will have no solutions if the two lines are parallel, then one example can be:

5x - 2y = 1

15x - 6y = 0

Here we have the following system of equations:

5x - 2y = 1

a*x - 6y = b

The system will have no solutions only if the two equations are parallel. You can see that the coefficient of y on the second equation is 3 times the coefficient on the first equation.

Then a should also be 3 times the coefficient of x on the first equation:

a = 3*5

a = 15

And b should be any number but 3 times the constant on the other equation:

b ≠ 3*1

So we can take b = 0, for example.

So the system with no solutions will be:

5x - 2y = 1

15x - 6y = 0

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Balance after 8 years is $2,306.86 at an interest rate of 15 % compounded yearly.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

given, Melissa opened a savings account and deposited $700.00 as principal. The account earns 15% interest

from the general formula of compound interest

A = [tex]P(1 + r/n)^{nt}[/tex]

where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.

Given, P = 700$

r = 15%

t = 8 years

A = 700(1 + 15/100)⁸

A = 2306.86$

Therefore, At a 15% annual compounded interest rate, the remaining balance after 8 years is $2,306.86.

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The truth value of "If 3 + 4 = 12, then 3 + 2 = 6", is true.

Truth value is defined as whether the given proposition is either true or false, not both.

Here the proposition is of the form if p, then q.

Here p is the statement 3 + 4 = 12 and q is the statement 3 + 2 = 6.

Here, both of the propositions are false.

The truth value of 'if p, then q' is false only when p is true and q is false. In all other cases the truth value is true.

Here, since both of the statements are false, the truth value is true.

Hence the truth value of the given proposition is true.

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Answer:

Step-by-step explanation:

sin40°=[tex]\frac{AC}{12}[/tex]
⇒AC=sin40°×12

⇒AC=7.713≈7.7
cos40°=[tex]\frac{AB}{12}[/tex]
⇒AB=cos40°×12

⇒AB=9.192≈9.2

as A=90°,B=40°

from A+B+C=180°

we can write C=180°-90°-40°

⇒C=50°

on solving the provided question we can say that - by unitary method we have 12 days.

What is unitary method ?

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

Sue ate one sweetie one day,

Sue ate 12 sweetie 12 day,

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The area of the square having the same length of the base of the triangle is 7245 square inches.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

From the given figure as the base of the triangle is an equal length of the side of a square we can obtain the area of the square by first applying Pythagoras on the right angle triangle having a height of 87 inches and a hypotenuse of 18 inches.

So,

Base = {√(87² - 18²)}.

Base = √(7245) inches.

Base = 85.11 inches.

Now, We also know that the area of a square is (side)².

Therefore it is (87.11)² which is the same as 7245 sq inches.

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The probability that they include at least five persons having blood of type O is given as follows:

0.1075 = 10.75%.

The number of donors needed so that the probability of including at least one student donor of type O shall be 0.9 or more is of 184 donors.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The values of the parameters for this problem are given as follows:

n = 200, p = 1/80 = 0.0125.

The probability of less than five is given as follows:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

Using a binomial distribution calculator, these probabilities are given as follows:

Hence the probability of less than five successes is given as follows:

P(X < 5) = 0.0808 + 0.2046 + 0.2576 + 0.2153 + 0.1342 = 0.8925.

Hence the probability of at least five is given as follows:

P(X >= 5) = 1 - P(X < 5) = 1 - 0.8925 = 0.1075.

The probability of at least one is given as follows:

P(X >= 1) = 1 - P(X = 0)

P(X >= 1) = 1 - (1 - 0.0125)^n.

This probability is of 0.9 when:

1 - (1 - 0.0125)^n = 0.9

(0.9875)^n = 0.1

log((0.9875)^n) = log(0.1)

nlog(0.9875) = log(0.1)

n = log(0.1)/log(0.9875)

n = 183.1.

Rounding up, at least 184 donors must be surveyed.

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The expression 10+(-8) is equivalent to 10 - 8.

Different branches of mathematics exist. The branch of knowledge that deals with numbers and operations is arithmetic. We learned how to add, subtract, multiply, and divide two or more numbers through arithmetic.

Shapes and how they are created with various tools, such as a compass, ruler, and pencil, are the focus of geometry. Another fascinating area of study is algebra, which helps us communicate the numerical and alphabetic aspects of daily life (variables).

Any mathematical statement made up of numbers, variables, and an operation between them is called an expression or an algebraic expression. As an illustration, the expression 4m + 5 consists of the terms 4m and 5, as well as the variable m, all of which are separated from one another by the arithmetic sign +.

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Full question

What expression is equivalent to 10-8?

Answer:

  (d)  (-1/4, 3/4)

Step-by-step explanation:

You want the solution to the graphed system of equations.

The solution is the point that satisfies both equations, the point where the lines intersect. That point is in the 2nd quadrant, where x-values are negative.

The only suitable answer choice is ...

  (x, y) = (-1/4, 3/4)

The expected values for each experiment are:

A) 3.4

B) 3.36

C) 3.33

If we have an experiment with the outcomes:

{x₁, x₂, ..., xₙ}

Each one with the correspondent probability:

{p₁, p₂, ..., pₙ}

Then the expected value of that experiment will be:

EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ

A) in this case we have 10 slips of paper, 8 of them with the number 3, and 2 of them with the number 5.

So the outcomes are:

{3, 5}

The probabilities are:

{8/10, 2/10}

Then the expected value is:

EV = 3*(8/10) + 5*(2/10) = 3.4

B) If we add another slip of paper with a number 3 on it, the new probabilities are:

{9/11, 2/11}

Then the new expected value is:

EV = 3*(9/11) + 5*(2/11) = 3.36

C) Finally, if we add 2 slips of paper with the number 3, now we will have a total of 12 slips of paper, then the new probabilities are:

{10/12, 2/12}

So the new expected value is:

EV = 3*(10/12) + 5*(2/12) = 3.33

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Answer: A. Quadrilateral

Step-by-step explanation:

The name for a polygon with 4 sides is a quadrilateral. Quadrilateral is a two-dimensional shape with four straight sides and four angles. The most common type of quadrilateral is the rectangle, which has four right angles. Other types of quadrilaterals include squares, parallelograms, trapezoids, and rhombuses.

Answer:

quadrilateral!!

Step-by-step explanation:

look at the beginning of the word, quad. Quad means 4 and is referring to a 4 sided figure.

If you list the number of tickets sold over time, the kind of sequence which you would see include the following: B. geometric.

In Mathematics, a geometric sequence can be defined as a series of real and natural numbers that are calculated by multiplying the next number by the same number (common or constant ratio) each time.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Assuming the variable x represents the number of ticket sold previously (initial year) and it sold 7 times as many tickets each year as it did the year before, a mathematical expression which models this situation is given by geometric sequence:

x, 7x, 49x, 343x, .....

Check:

7/1 = 49/7 = 343/49 = 7 (proof).

Therefore, this is a geometric sequence.

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Complete Question:

A growing amusement park is able to sell 7 times as many tickets each year as it did the year before. If you list the number of tickets sold over time, what kind of sequence will you see?​

arithmetic

geometric

both

neither