Last week, 188 students went to a museum. All 4 buses were full and 8 students had to ride in cars. How many students rode on each bus?

A = 1, y = -2/3, The value of a for which the system of equations has a unique solution is a = -3.

1. Set the first equation equal to 0:

2x + ay = 2

2. Subtract 2x from both sides of the equation to get:

ay = -2

3. Divide both sides of the equation by a to get:

y = -2/a

4. Substitute this value of y into the second equation to get:

6x + 3(-2/a) = 3

5. Multiply both sides of the equation by a and simplify to get:

6ax - 6 = 3a

6. Add 6 to both sides of the equation to get:

6ax = 3a + 6

7. Divide both sides of the equation by 6 to get:

x = (3a + 6)/6

8. The value of a for which the system of equations has a unique solution is a = -3.

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Answer:

1/2 foot

Step-by-step explanation:

1 x 1 = 1

1/2 = 1/2

Stefan spend price $110 and made price $60 by selling bicycle and helmet to Jin.

A percentage is a number or ratio that can be expressed as a fraction of 100.

Here, given that,

Selling price of bicycle = $146

Selling price of helmet = $19

Total = 146+19= $165

Let,

x represents the original cost Stefan to buy the bike and helmet.

150% of x = $165

1.5x=$165

Dividing both sides by 1.5

we get ,

x=$110

Stefan bought bicycle and helmet for $110.

Profit made by Stefan = Selling price - buying price

Profit made by Stefan = 165-110= 55

Hence, Stefan spend price $110 and,  made $55 by selling bicycle and helmet to Jin.

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Therefore , the solution of standard deviation is  because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.

Standard deviation, often known as variance in a set of data, is a statistical measure of variation. A low standard deviation indicates that the values are more likely to be near the mean of the collection, whereas a high standard deviation indicates that the values are widely distributed. How far the data depart from the mean is expressed by the standard deviation, abbreviated as.

Here,

Considering the details here,

The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.

The much lower results are u-2 = 11169.8-2(126.2) => 917.4.

Reason: According to the range rule of thumb, the required incredibly low values are 91.7 cm3 or less.

Hint: Use the algorithm to identify values that are at least considerably high.

Step: 2

Considering the data supplied,

The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.

Significantly higher values include,

u-2α = 11169.8+ 2(126.2)

=> 1422.2

Justification: According to the range rule of thumb, the necessary significantly high values must be 1422.2 cm3 or higher.

Hint: To determine whether the value 1452.2 cm3 is very high, use the findings of steps (1) and (2).

Step: 3

Using step 1 and step (4),

917.4 is among the significantly low numbers or less.

The significantly high values are 1422.2 or higher.

Yes, 1452.2 cm3 is a noticeably high value.

The apt response is choice (B).

Reason: The value is much higher than expected based on the range rule of thumb because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.

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Answer:

$3,600

Step-by-step explanation:

what you do is multiple 600 and 6 together and you'll get 3,600

Answer:

He will have saved $3600.

Step-by-step explanation:

$600 x 6=$3600

Answer:

5%

Step-by-step explanation:

2,125 interest/5 years=425 interest/year

425/8500=.05 or 5%

Answer:

the real answer is 4.25

Step-by-step explanation:

hope this helps

by the way to calculate the interest you have to divide the total interest by how many days or years then put in percent form example 2.125 divided by 5 wich equals 4.25

Answer:

113.04 cm.

Step-by-step explanation:

Step 1: Formula/explain

To find the area of a circle, multiply the radius by itself twice, then multiply the product pi.

[tex]a=\pi r^2(3.14*radius*radius)[/tex]

Step 2: Solve

According to the word problem, the circle has a diameter of 12. This means it has a radius of 6.

Now, we plug the numbers into formula.

[tex]\pi 6^2 (3.14*6*6)=113.04[/tex]

Step 3: Conclude

Therefore, the area of this circle is 113.04 cm.

B. Belly button

Step-by-step explanation:

It can't be knees or ankles because they are too far down, and shoulders are at head level

The schedule of her course in 120 ways.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression. Operations include addition, subtraction, multiplication, and division.

A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.

The three different types of algebraic expressions are monomial, binomial, and polynomial.

According to the question there are five spaces for different subjects which are arranged in different order so the number of ways are

2(5,4)

= 5 * 4 * 3 *  2

=120 ways

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The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the G.C.F. defines the greatest factor present between any given pair of two or more numbers.

LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).

The highest common factor (HCF) between two or more numbers is two or more. The LCM, on the other hand, is the lowest common multiple that exactly divides these two figures. The greatest common factor between any two numbers is also known as HCF. Between two or more numbers, LCM is also known as Least Common Divisor.

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The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.

What is iteration ?

iteration can be defined as the repeating itself to perform a particular task.

Given

X2 is when n=1

X2 = X1+1 = X1 ^ 3 - 5/10

because X1 = -1

so X2  = -1-5/10 = -6/10 = -0.6

X3 is when n=2

X3 = X2+1

= X2 ^ 3 -5/10

because X2 = -3/5

so X3 could be

X3 = (-0.6*-0.6*-0.6) - 5 / 10

X3 = -0.041600

Hence, The values of X1, X2 , X3 could be -1 , -0.6 , -0.041600 using the iterative process.

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The explicit formula for the sequence will be an = 10 + 5n. The correct option is C.

The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression.

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.

Given series is 15,20,25,30,...,

The common difference is d = 20 - 15 = 5

First term is, 15

The formula can be written as,

an = a₁ + d(n-1)

an = 15 + 5 ( n - 1 )

an = 15 + 5n - 5

an = 10 + 5n

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The degree of the given polynomial is 4.

A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.

The given polynomial is y=3x²-7x⁴+5-9x.

a) The polynomial in standard form is -7x⁴+3x²-9x+5.

b) The degree of the polynomial is 4.

c) The number of terms in the polynomial are 4.

d) Use the degree and the leading coefficient to determine the behavior.

Falls to the left and falls to the right

e) Use the derivative to find the maximum and minimum.

(−0.78859507, 11.25584002) is a local maxima

f) Here the y-intercept is (0, 5)

g) The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x. x≈−1.33755842,0.5797309.

h) Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,∞),{x|x∈R}

i) Range: (−∞,11.25584002],{y|y≤11.25584002}

Therefore, the degree of the given polynomial is 4.

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Answer:

measure of CBD is 125 degrees

Step-by-step explanation:

ABC + CBD is equal to 180 degrees

8x - 41 + 9x + 17 = 180

combine like terms

17x - 24 = 180

add 24 to both sides

17x = 204

divide both sides by 17

x = 12

then plug in to find CBD

9 (12) + 17

108 + 17 = 125 degrees

Answer:

angle CBD = 125°

Step-by-step explanation:

Because ABD is a straight angle we know it is equal to 180°

because we have this information we can create the equation

(8x-41) + (9x+17) = 180

17x - 24 = 180

(here you would add 24 to both sides)

17x = 204

(divide both sides by 17)

x = 12

Then you would plug in 12 for x in the equation for CBD which will then get you 125°

Slope = (-2 - 4)/(14 - (-1)) = -6/15

Answer:

x = 90

Step-by-step explanation:

If x = 3 and y = 4 then when y = 120 just find out what times 4 = 120

which is 30.

so just multiply 30 for x = 3, then the answer will be 90

x = 90

Answer:

x=90

Step-by-step explanation:

x is directly proportional to y

Therefore, if the initial y value was 4 and the final y value is 120. This means that y initial had been multiplied 120/4 times, which is 30.

Same goes for x. If x initial is 3, then the final x value would be x/3=30. This means that x=3×30, which is equal to 90.

Answer:

3. vertical line

4. A

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

2x + 3x + 40 =180

5x= 180 - 140

5x=140

x= 28

Answer:

Step-by-step explanation:

We know that the sum of interior angles of a triangle is 180° so we can say:

40 + 2x + 3x = 180°

40 + 5x = 180°

5x = 140°

x = 28°

Now substitute in 28 for the value of x in Angle A:

=> 2x would become 2(28)

=> 56° = ∠A

Hope this helps!

In one of the equations, separate one of the two variables. In the other equation, replace the expression with the value of the isolated variable from Step 1. Consequently, a linear equation with just one variable ought to emerge.

The one y-value in the substitution method is replaced with the other. We'll give an example to illustrate this. Since y = y, we can replace y in the second equation with y from the first equation. The linear system's solution is (1, 6).

Numerous solutions, no solutions, and a singular solution.

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The complate table is,

Statement                                                 Reasons

1) K is the midpoint of segments                      Given

  RM and JL.

2) RJ ≅ ML                                                  SSS Congruence Postulate

3) RK ≅ MK ,  JK ≅ LK                                 Definition of Midpoint

4) RK = MK , JK = KL                                    Definition of Congruence

                                                                   Segments

5) Δ EGF ≅ Δ EGH                                      CPCTC

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

K is the midpoint of segments RM and JL.

Now,

Since, K is the midpoint of segments RM and JL.

Hence, We get;

   Statement                                                 Reasons

1) K is the midpoint of segments                      Given

  RM and JL.

2) RJ ≅ ML                                                  SSS Congruence Postulate

3) RK ≅ MK ,  JK ≅ LK                                 Definition of Midpoint

4) RK = MK , JK = KL                                    Definition of Congruence

                                                                   Segments

5) Δ EGF ≅ Δ EGH                                       CPCTC

Thus, The complete table is shown above.

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x = 5

AB = 6

BC = 13

A line can be defined as a straight set of points that extend in opposite directions, It has no ends in both directions(infinite). It has no thickness. It is one-dimensional.

Given,

AB = 2x - 4

BC = 3x - 2

AC = 19

By the figure

AB + BC = AC

2x - 4 + 3x - 2 = 19

5x - 6 = 19

5x = 25

x = 5

AB = 2 × 5 - 4 = 10 - 4 = 6

BC = 3 × 5 - 2 = 15 - 2 = 13

Hence the value of x, AB and BC is 5, 6, 13 respectively.

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Equation that will determine the amount of last year’s budget

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

Given that a school plans to spend twice the amount it did last year on its winter dance , less the cost of the disco ball which was $150 since they have it from last year

A total of $1,500 is being spent this year.

We need to find the equation which determine the amount of last year’s budget

2a-150=1500

When a is the amount of last year’s budget

Hence, 2a-150=1500 is the equation that will determine the amount of last year’s budget

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Let's say we have an expression P^A then the negation of  P^A  will be not(  P^A  ). This is an example of negation.

As the name suggests negation means the negative of a term or expression and it comes under the branch of mathematical logical reasoning.

When not word is added in front of an expression it becomes the opposite , this is how we negate something. A statement is only admissible if it is always true or always false.

It is sometimes required in mathematics to find the inverse of a particular mathematical statement, this is when negation is used. Negation thus, refers to the process of determining the inverse of a given assertion.

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Answer:

330

Step-by-step explanation:

The prism is a triangular prism

9 * (12 + 5 + 13) + (2 * 30)= 330

30 being the base area

Answer:

330

Step-by-step explanation:

We can break each surface area into it pieces.

For the squares:

9x13=117

9x5=45

9x12=108

For the triangles:

12x5÷2=30

12x5÷2=30

Add all of those together to get the total square area, which is

330

Answer:

Radius= 8.86 m

Step-by-step explanation:

Pie x r^2 x 0.7= 172.48

Pie x r^2= 246.4

r^2= 78.43

R= square root of 78.43

Radius= 8.86m

Answer:

a

Step-by-step explanation:

Divide distance by time for speed per hour, that is

speed = 540 ÷ 4.5 = 120 mph

Then distance travelled in 11 hours

= 11 × 120 = 1320 miles → a

3u^2-84 = 0 then u=5.29 is the nearest hundredth

The union of both rational and irrational numbers is known as a real number. They are represented by the letter "R" and can be either positive or negative.

This category includes all natural integers, decimals, and fractions.

In the number system, real numbers are only the fusion of rational and irrational numbers.

These numbers can generally be used for all arithmetic operations and can also be expressed on a number line.

Imaginary numbers, which are often known as unreal numbers since they cannot be stated on a number line, are frequently used to symbolize complex numbers. Examples of actual numbers include 23, -12, 6.99, 5/2, and so forth.

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Answer:

It would be y = 2x+4

Step-by-step explanation:

This is because Isabella has started with 4 baked pies and is gaining additional pies with in amounts of 2 pies.

With this, 4 would be by itself and 2 would be attached to the variable x for the unknown amount of additional pies.

Lastly, you would have this all equaling y, as y is the total amount of pies.

To evaluate (3 x 8 x 5)⁷, you need to first multiply 3, 8, and 5 together to get the base, then raise that result to the seventh power.

What does a math exponent mean?

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 23) signifies 2 x 2 x 2 = 8. 23 and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.

So,

(3 x 8 x 5)⁷ = (120)⁷ = 120 x 120 x 120 x 120 x 120 x 120 x 120

= (1.2 x 10^2)^7 = 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2 x 1.2 x 10^2

=1.2^7 x 10^14 = 1.2^7 x 10^14

=4096 x 10^14

=4.096 x 10^17

Therefore (3 x 8 x 5)⁷ = 4.096 x 10^17

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