Which of these systems of equations has infinitely many solutions? Explain your choice(s).
a. (1/2)x - 5y = 10
(-1/2)x + 5y = -10
b. 7x + 2y = -14
-7x + 2y = -14
c. x + 6y = -18
x - 6y = 18
d. (3/4)x - 9y = 12
(-3/4)x + 9y = 12

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

h(x) = (x+1)²

h(-2) = 1

h(-1) = 0

h(3) = 8

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

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Using the Pythagoras theorem, the value of y is [tex]6\sqrt{7}[/tex], and the value that goes in the green box is 6.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

Mark the intersections as A, B, C, and D.

It is given that BC=12 and CD=9.

The relationship between the height on the hypotenuse of a right triangle and the two line segments it generates on the hypotenuse is described by the right triangle altitude theorem, also known as the geometric mean theorem. It claims that the altitude is equal to the geometric mean of the two segments.

Apply the geometric mean theorem -

(AC)^2 = BC x CD

(AC)^2 = 12 x 9

(AC)^2 = 108

AC = [tex]\sqrt{108}[/tex]

AC = [tex]6\sqrt{3}[/tex]

Triangle ABC is a right-angled triangle, so apply Pythagoras theorem -

(AB)^2=(BC)^2+(AC)^2

(AB)^2=(12)^2+([tex]6\sqrt{3}[/tex])^2

(AB)^2=144+108

(AB)^2=252

AB=[tex]\sqrt{252}[/tex]

AB=[tex]6\sqrt{7}[/tex]

Therefore, the value of y is obtained as [tex]6\sqrt{7}[/tex].

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The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:

0.49x + 7.65 <= 10.00

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:

0.49x + 7.65 <= 10.00

This inequality can be read as "the cost of x number of stamps plus the cost of the package is less than or equal to Keshia's budget of $10.00."

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Yes, the expression; y = x³ is a function because it passes the vertical line test.

Function from a set x to a set y assigns to each element of x exactly one element of y. The set x is called the domain of the function and the set y is called the codomain of the function.

There are 4 types of functions:

On this note, the set containing all possible values of x is called the domain of the function and the set y is called the co-domain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.

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Answer:

Step-by-step explanation:

The expression you've provided is a combination of several fractions, but it's not clear how they are supposed to be combined. Without more information, it's impossible to know what the value of the expression is.

It would be helpful if you could provide more context or clarify how you want the fractions to be combined.

I can only tell you how the fraction works in mathematics and how you can evaluate the value of it if you have the complete information.

On solving the provided question, we can say that - the linear equation

y=mx+b = [tex]y=6.4(82)+1900= > y=524.8+1900= > y=2424.8[/tex]

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

y=mx+b

x=gallons of fuel

y=total weight of plane including fuel

m=slope=6.4

b=weight of plane, no fuel....a constant to be calc'd

[tex]y=mx+b\\2245.6=6.4(54)+b\\2245.6=345.6+b\\ b=1900\\ y=6.4x+1900\\ y=6.4x+1900\\ y=6.4(82)+1900\\ y=524.8+1900\\ y=2424.8[/tex]

82gallons fuel is 2424.80 lbs

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Answer: To calculate the sample mean of a distribution, you add up all the values and divide by the number of values in the sample. The sample mean is also known as the average.

The formula for the sample mean is:

X-bar = (X1 + X2 + ... + Xn) / n

To calculate the sample variance of a distribution, you first need to calculate the sample mean. Then, for each value, you subtract the sample mean and square the result. You add up all these squared differences, and divide the sum by the number of values in the sample.

The formula for the sample variance is:

s^2 = ( (X1 - X-bar)^2 + (X2 - X-bar)^2 + ... + (Xn - X-bar)^2 ) / (n - 1)

It would be helpful to have the sample data, however I cannot complete this task without it.

Please provide me with the data.

Step-by-step explanation:

By using the graph, a solution the given system of equations include the following:

x = 0, y = 3

x = 3, y = 6

In Mathematics, the graph of every quadratic functions (equations) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function (equation) would always form a parabolic curve.

In this scenario, we would use an online graphing calculator to plot the graph of the given system of equations and then determine the point of intersection.

y = x + 3

y = x² - 2x + 3

By critically observing the graph of the given system of equations, the solutions are as follows;

x = 0, y = 3.

x = 3, y = 6.

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Answer:

8RST. That is, N has thousands digit 8, hundreds digit R, tens digits S, and ones

(units) digit T, which means that N = 8000 + 100R + 10S + T. Suppose that the

following conditions are all true:

• The two-digit integer 8R is divisible by 3.

• The three-digit integer 8RS is divisible by 4.

The four-digit integer 8RST is divisible by 5.

The digits of N are not necessarily all different.

The number of possible values for the integer N is

(A) 8

(B) 16

(C) 12

(D) 10

87

(E) 14

Since 8R is divisible by 3, R must be a multiple of 3. The possible values for R are 3, 6, and 9.

Since 8RS is divisible by 4, S must be a multiple of 2. The possible values for S are 0, 2, 4, 6, and 8.

Since 8RST is divisible by 5, T must be 0 or 5.

The possible values for N are therefore:

8000 + 300 + 00 + 0 = 8300

8000 + 600 + 00 + 0 = 8600

8000 + 900 + 00 + 0 = 8900

8000 + 300 + 20 + 0 = 8320

8000 + 600 + 20 + 0 = 8620

8000 + 900 + 20 + 0 = 8920

8000 + 300 + 40 + 0 = 8340

8000 + 600 + 40 + 0 = 8640

8000 + 900 + 40 + 0 = 8940

8000 + 300 + 60 + 0 = 8360

8000 + 600 + 60 + 0 = 8660

8000 + 900 + 60 + 0 = 8960

8000 + 300 + 80 + 0 = 8380

8000 + 600 + 80 + 0 = 8680

8000 + 900 + 80 + 0 = 8980

8000 + 300 + 00 + 5 = 8305

8000 + 600 + 00 + 5 = 8605

8000 + 900 + 00 + 5 = 8905

8000 + 300 + 20 + 5 = 8325

8000 + 600 + 20 + 5 = 8625

8000 + 900 + 20 + 5 = 8925

8000 + 300 + 40 + 5 = 8345

8000 + 600 + 40 + 5 = 8645

8000 + 900 + 40 + 5 = 8945

8000 + 300 + 60 + 5 = 8365

8000 + 600 + 60 + 5 = 8665

8000 + 900 + 60 + 5 = 8965

8000 + 300 + 80 + 5 = 8385

8000 + 600 + 80 + 5 = 8685

8000 + 900 + 80 + 5 = 8985

There are a total of 30 possible values for N. The answer is therefore (E) 14.

Step-by-step explanation:

The total amount of interest you will have to pay is $21,849.92. As a result, choice A is accurate.

Compound monthly is the term used to describe a loan's interest rate, which is added to the principle each month and charged in installments. For instance, a $1,000 loan with a 12% annual interest rate compounded monthly would become $1,010 after the first month if the interest rate was 1%.

Monthly compounding is calculated by multiplying the principal amount by one plus the interest rate by the number of periods, raised to the power of the number of periods. This quantity is subtracted from the principal amount to determine the interest amount.

Thus;

[tex]Interest = 44,500(1 + 0.1311/100)^{6.5} \\= $21,849.92[/tex]

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Answer:

The researcher compiled a data set consisting of variables such as age, income, and marital status for a sample of 100 retired men

Step-by-step explanation:

A discrete variable is a type of variable that can only take on specific, distinct values that can be counted. Examples of discrete variables include the number of countries visited, shoe size, and number of pets living in a household.

On the other hand, a continuous variable is a type of variable that can take on any value within a certain range through measurement. Examples of continuous variables include pounds of chocolate consumed in the past and height in inches.

a) The fraction of chocolate distributed is given as follows: 4/3.

b) The fraction of chocolates left with Paul is given as follows: 8/3.

The fractions are obtained applying the proportions used in the context of this problem.

He distributes 1/3 of each bar to 4 children, hence the total number of bars distributed is given as follows:

4 x 1/3 = 4/3.

(multiplication of fractions, multiply the numerators and the denominators, keeping the quotient).

The total number of bars that Paul had initially is given as follows:

4 bars.

Then the fraction of chocolate remaining with Paul is given by the subtraction of the total amount of bars by the amount given to the children, as follows:

4 - 4/3 = 12/3 - 4/3 = 8/3 bars.

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The money invested in a  account with 3% interest is $3000 and the money invested in a  account with 6% interest is $6000.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, Susan invested a total of $9000 in two account.

One account pays 3% interest and the other account pays 6% interest.

Let the money invested in a  account with 3% interest be x.

Then, the money invested in a  account with 6% interest be 9000-x.

The total return from both accounts was $450.

Here, (x×3×1)/100 + ((9000-x)×6×1)/100 =450

3x+54000-6x=45000

54000-3x=45000

3x=9000

x=$3000

So, 9000-x=$6000

Therefore, the money invested in a  account with 3% interest is $3000 and the money invested in a  account with 6% interest is $6000.

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Answer: She can multiply the numerator and the denominator by the same number. For example, 30/100 × 2/2

So what you're doing multiplying the numerator & the denominator each by 2. 30 ×2 = 60 and 100 x 2 = 200, ending up with 60/200.

when reduced it would simplify back to 30/100.

You can do the same for each similar. Problem asking for an equivalent. Just multiply both the numerator and denominatorby the same number.

Step-by-step explanation:

In this question, we're looking for the number Malcom used to scale the two numbers. We can see there's a pattern, 9 is 1/6 of 54 and 40 is 1/6 of 240!

(54 divided by 9 is 6 and 240 divided by 40 is 6!)

therefore, the scale factor must be 6

Therefore , the solution of this is  the required system of equation is,

y=-x+6 and y=x+10.

A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.

Here,

(0,6) and the blue line pass through them (-2,8). You may figure out the equation for the blue line as,

=> y-6/x-0 =  8-6 /-2-0

=>y-6/x = 2/-2

=> y-6=-1(x)

y=-x+6

(-2, 8) and the red line pass through them (-3,7). The red line's equation can be calculated as,

y-8/x- (-2) = 8-7 /-2-(-3)

y-8 /x+2 = 1

y-8=x+2

y = x + 10

Thus, the required system of equations is,

y=-x+6 and y=x+10.

Therefore , the solution of this is  the required system of equations is,

y=-x+6 and y=x+10.

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Answer:

wouldn't it be 1/25 black??

Answer:

x = 45

Step-by-step explanation:

2x + 6 and 96 are vertically opposite angles and are congruent , then equation is

2x + 6 = 96 ( subtract 6 from both sides )

2x = 90 ( divide both sides by 2 )

x = 45

now, we're assuming this is some rectangular area, and thus is simply the product of both quantities, let's change all mixed fractions to improper fractions firstly.

[tex]\stackrel{mixed}{12\frac{1}{2}}\implies \cfrac{12\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{25}{2}} ~\hfill \stackrel{mixed}{11\frac{3}{4}} \implies \cfrac{11\cdot 4+3}{4} \implies \stackrel{improper}{\cfrac{47}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{25}{2}\cdot \cfrac{47}{4}\implies \cfrac{1175}{8}\implies 146\frac{7}{8}~ft^2[/tex]

Answer:

= 18√2

decimal =25.45584412

Answer: 0.155

Step-by-step explanation:

To find the probability of a certain event occurring in a Poisson distribution, we can use the formula:

P(k) = (μ^k * e^(-μ)) / k!

Where:

Plugging in the given values, we get:

P(5) = (9^5 * e^(-9)) / 5! = 126,441 * 0.000123 = 0.1550

So the probability of the event occurring 5 times is approximately 15.5%.

On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x).

[tex]lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5[/tex]

from the graphs n f (x) and g( x) are 1 and 5 .

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Answer:

Step-by-step explanation:

y= 265

The rate of change of the equation is 25.

The rate at which one quantity changes in relation to another quantity is known as the rate of change function. Simply put, the rate of change is calculated by dividing the amount of change in one item by the corresponding amount of change in another.

Given that the linear equation is y = 25x + 115. The rate of change of the equation is represented by the slope or gradient of the equation of the line.

Here in the equation y = 25x + 115 the rate of change is 25. Which is equivalent to the slope of the line.

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Answer:

D+Q = 31

10D + 25Q = 595

10D + 10Q = 310

subtract to get

15Q = 285 Q = 285/15 = 19 quarters D = 31-19 = 12 dimes

Answer:

-sqrt(2)/2 , the last option of your document.

Step-by-step explanation:

sin(7pi/4) = -sin(7pi/4 - pi)

                = -sin(7pi/4 - 4pi/4)

                 = - sin(3pi/4)

sin(3pi/4) is a special angle , which is sqrt(2)/2

Hence, sin(7pi/4) = -sin(3pi/4)

                             = -sqrt(2)/2

Answer:

-sqrt(2)/2

Step-by-step explanation:

did the test

Answer:

D

Step-by-step explanation:

first simplify everything

2/9v + 1/3v - 5/9

A and B is wrong because it is - 5/9 not + 5/9

C is wrong because it is -1/3v not 1/3, it is supposed to be - 5/9

You can solve this problem without much solving

hope this helps :)

Answer:

Step-by-step explanation:

Which problem situation matches the

equation $95.25 = 15p?

So We Can Just Cross B Cause $6.35 Wasnt Even In The equation

Lets look at A.

So Im pretty sure its A, But Lets look at the rest.

.

D Wouldnt Work Cause It Says The Spend $95.25 EACH

C dont work so its A.

The answer is: 55 crayons.

Explanation: He has 6 boxes with 8 crayons in each. 6 times 8 = 48. Plus the seven left from the other box = 48+7= 55 crayons.!!