Which of the following systems of linear equations has an infinite number of solutions?

Answer:

B  [tex]x^4-x^3+x^2-x+1[/tex]

Step-by-step explanation:

Given,

Dividend = [tex](x^5+1)[/tex]

Divisor = [tex](x+1)[/tex]

Step 1: First The dividend is [tex](x^5+1)[/tex] and Divisor is [tex](x+1)[/tex] when divided first time the quotient will be [tex]x^4[/tex] and remainder will be [tex]-x^4+1[/tex]

Step: 2 Now the new dividend is [tex]-x^4+1[/tex] and Divisor is [tex](x+1)[/tex]  when divided the quotient will be [tex]x^4-x^3[/tex] and remainder will be [tex]x^3+1[/tex]

Step: 3 Now the new dividend is [tex]x^3+1[/tex] and Divisor is [tex](x+1)[/tex]  when divided the quotient will be [tex]x^4-x^3+x^2[/tex] and remainder will be [tex]-x^2+1[/tex]

Step: 4 Now the new dividend is [tex]-x^2+1[/tex] and Divisor is [tex](x+1)[/tex]  when divided the quotient will be [tex]x^4-x^3+x^2-x[/tex] and remainder will be [tex]x+1[/tex]

Step: 5 Now the new dividend is [tex]x+1[/tex] and Divisor is [tex](x+1)[/tex]  when divided the quotient will be [tex]x^4-x^3+x^2-x+1[/tex] and remainder will be 0.

Hence When the polynomial [tex](x^5+1)[/tex] is divided by  [tex](x+1)[/tex] the answer or quotient will be equal to  [tex]x^4-x^3+x^2-x+1[/tex] and remainder will be 0.

Answer:

None of these

Step-by-step explanation:

A perpendicular bisector is a segment which intersects a given segment at a 90° angle, and passes through the given segment's midpoint. Since point T divides segment SU into two parts with lengths 46 and 62 units, VT is not a perpendicular bisector.

A median of the triangle is a segment joining a vertex to the midpoint of the opposite side. Since point T divides segment SU into two parts with lengths 46 and 62 units, VT is not a median.

An altitude of the triangle is a segment passing through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). The diagram doesn't show the right angle at point T (VT is not perpendicular to SU), then VT is not an altitude.

Thus, option None of These is true.

Answer:

[tex]sin(\theta_1)=3\frac{\sqrt{21}}{17}[/tex]

Step-by-step explanation:

The complete question is

The angle θ1 is located in Quadrant 1, and cos (θ1)=10/17.

What is the value of sin(θ1)?

we know that

[tex]sin^2(\theta_1)+cos^2(\theta_1)=1[/tex] ---> trigonometric identity

we have

[tex]cos(\theta_1)=\frac{10}{17}[/tex]

The angle [tex]\theta_1[/tex] is located in Quadrant I, that means the sine of angle [tex]\theta_1[/tex] is positive

substitute the given value in the trigonometric identity

[tex]sin^2(\theta_1)+(\frac{10}{17})^2=1[/tex]

[tex]sin^2(\theta_1)+\frac{100}{289}=1[/tex]

[tex]sin^2(\theta_1)=1-\frac{100}{289}[/tex]

[tex]sin^2(\theta_1)=\frac{189}{289}[/tex]

take square root both sides

[tex]sin(\theta_1)=\pm\frac{\sqrt{189}}{17}[/tex]

Remember that the sine is positive (Quadrant I)

so

[tex]sin(\theta_1)=\frac{\sqrt{189}}{17}[/tex]

Simplify

[tex]sin(\theta_1)=3\frac{\sqrt{21}}{17}[/tex]

Answer:

equation: y = -2x + 7

Step-by-step explanation:

y = mx + b   M: slope     b: y intercept

m = -2

x = 3 and y = 1

b = y - mx = 1 - (- 2) x 3 = 7

equation: y = -2x + 7

check:     ( 3,1)     -2 x 3 + 7 = 1

Answer:

The equation of the required line is,

y = -2x + 7

Step-by-step explanation:

We know that equation of a line passing through the point (x₁, y₁) and having slope 'm' is given by

(y - y₁) = m(x - x₁)

Now, the required line passes through the point (3, 1) and has a slope of -2.

So, (x₁, y₁) = (3, 1) and m = -2

So, equation of the line passing through (3, 1) and having a slope of -2 is given by,

  y - 1 = -2(x - 3)

⇒y - 1 = -2x + 6

⇒y = -2x + 6 + 1

⇒y = -2x + 7

So, the required equation of line in point-slope form is,

y = -2x + 7

Answer:[tex]30 i -473 j -3 k[/tex]

Step-by-step explanation:

We are given two velocity vectors with its three components in unit notation:

Airplane's velocity:

[tex]\vec{p}=30i-492j+42k[/tex]

Crosswind velocity:

[tex]\vec{t}=0i+19j-45k[/tex]

Now, if we want to know the velocity of the airplane when it is affected by the wind, we have to add these two velocity vectors:

[tex]\vec{p} + \vec{t}=(30i-492j+42k) + (0i+19j-45k)[/tex]

Adding both vectors:

[tex]\vec{p} + \vec{t}=30i-473j-3k[/tex]

Answer:

D edge

Step-by-step explanation:

Question is Incomplete, Complete question is given below.

Prove that a triangle with the sides (a − 1) cm, 2√a cm and (a + 1) cm is a right angled triangle.

Answer:

∆ABC is right angled triangle with right angle at B.

Step-by-step explanation:

Given : Triangle having sides (a - 1) cm, 2√a and (a + 1) cm.  

We need to prove that triangle is the right angled triangle.

Let the triangle be denoted by Δ ABC with side as;

AB = (a - 1) cm

BC = (2√ a) cm

CA = (a + 1) cm  

Hence,

[tex]{AB}^2 = (a -1)^2[/tex] 

Now We know that

[tex](a- b)^2 = a^2+b^2 - 2ab[/tex]

So;

[tex]{AB}^2= a^2 + 1^2 -2\times a \times1[/tex]

[tex]{AB}^2 = a^2 + 1 -2a[/tex]

Now;

[tex]{BC}^2 = (2\sqrt{a})^2= 4a[/tex]

Also;

[tex]{CA}^2 = (a + 1)^2[/tex]

Now We know that

[tex](a+ b)^2 = a^2+b^2 + 2ab[/tex]

[tex]{CA}^2= a^2 + 1^2 +2\times a \times1[/tex]

[tex]{CA}^2 = a^2 + 1 +2a[/tex]

[tex]{CA}^2 = AB^2 + BC^2[/tex]

[By Pythagoras theorem]

[tex]a^2 + 1 +2a = a^2 + 1 - 2a + 4a\\\\a^2 + 1 +2a= a^2 + 1 +2a[/tex]

Hence, [tex]{CA}^2 = AB^2 + BC^2[/tex]

Now In right angled triangle the sum of square of two sides of triangle is equal to square of the third side.

This proves that ∆ABC is right angled triangle with right angle at B.

Answer:

x ÷ 15

Step-by-step explanation:

quotient is division

Answer:

4

Step-by-step explanation:

10 - 2 = 8

4 x 2 = 8

4 x 3 = 12

Final answer:

The answer explains how to find a number given that two-thirds of it increased by two equals ten, using clear step-by-step instructions.

Explanation:

The subject of the question is Mathematics.

The question states that two-thirds of a number increased by two is equal to ten. To solve this equation:

Let the number be represented by x.

Translate the given information into an equation: (2/3)x + 2 = 10.

Solve for x: (2/3)x = 8, x = 12. Therefore, the number is 12.

To find the missing number so that the equation has infinitely many solutions, subtract -2x from both sides to eliminate x and find that the missing number can be any real number.

To find the missing number so that the equation has infinitely many solutions, we need to look at the given equation: -2x - 10 = -2x + c. Since the variable x is present on both sides, we can subtract -2x from both sides to get rid of it. This leaves us with -10 = c. In order for this equation to have infinitely many solutions, the missing number c can be any real number.

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Answer:

It's C.

Step-by-step explanation:

x + y + x + y + 3(y + 5)

= x + y + x + y + 3y + 15

= 2x + 5y + 15.

Answer:

2x + y + 30

C.

Answer:

hi there!

the equation for this dot plot will be: y=15x

Step-by-step explanation:

if you look at the dots on the graph (2, 30) and (4,60) they both satisfy the equation

Answer:

The amount of electricity bill is $52.60.

Step-by-step explanation:

Given:

Victoria whit used 578 kwh of electricity.

The rate is 9.1 cents per kw-hr.

Now, to find the amount of her electric bill.

Electricity used = 578 kwh.

Rate of electricity = 9.1 cents per kw-hr.

So, to get the amount we multiply the electricity used by the rate of electricity:

[tex]Amount\ of\ electric\ bill=Electricity\ used\times rate\ of\ electricity[/tex]

[tex]Amount\ of\ electric\ bill=578\ kwh\times 9.1\ cents[/tex]

[tex]Amount\ of\ electric\ bill=5259.8\ cents.[/tex]

Thus, the amount of electricity bill = 5259.8 cents.

Now, converting the amount from cents to $ by dividing:

$1 = 100 cents.

So, 5259.8 cents ÷ 100 = $52.60 .

therefore, the amount of electricity bill is $52.60.

Answer:

5/12x

Step-by-step explanation:

Answer:

y = 5/12x - 2

Step-by-step explanation:

5x - 12y = 24

We get -12y = -5x + 24

Divide all of the equation by -12

You get y = 5/12x -2

Option A is correct, A shows a mapping diagram which represents a function from x → y

A relation is a function if it has only One y-value for each x-value.

A mapping diagram that represents a function from x to y is a diagram that shows a set of ordered pairs (x, y), such that each x-value has exactly one corresponding y-value

For option A, the ordered pairs are (4, 5)(5,5),(6,1),(8,2).

For each value of x there is only one value of y or else the values of x are not repeated so the diagram represents a function.

In other option the x has 2 values of y.

Hence, option A is correct, A shows a mapping diagram which represents a function from x → y

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A mapping diagram that represents a function from x → y include the following: A. mapping diagram A.

In Mathematics, a function is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (Set A) to an output variable (Set B).

Based on the mapping diagram shown above, we can reasonably infer and logically deduce that the inputs (4, 5), (5, 5), (6, 1), and (8, 2) are ordered pairs that represents a function because they indicate unique mappings of each input value to an output value.

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Answer:

[tex]r=0.05[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

A is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=3\ years\\ P=\$3,000\\I=\$450\\r=?[/tex]

substitute in the formula above

[tex]450=3,000(3r)[/tex]

solve for r

[tex]450=9,000(r)[/tex]

[tex]r=450/9,000[/tex]

[tex]r=0.05[/tex]

Answer:

719

Step-by-step explanation:

ones place is 8 and we add 1 if the right hand number is 5 or greater than 5.

Answer:

The answer is 719

Step-by-step explanation:718.521 when rounded up to the nearest one be comes 719 because .5 is converted to 9. Thanks

Answer:

1\times 28=28\\2\times 14=28\\4\times 7=28

Step-by-step explanation: To obtain number 28, we will find the factors of this number.

Factors of this number are: 1, 2, 4, 7, 14, 28

From the given factors, we can find the combinations which will givs us the product as 28

We are asked to find the multiplication ( times) of two number that will yield a number 28. So, the combinations will be

1\times 28=28\\2\times 14=28\\4\times 7=28

Step-by-step explanation:

Final answer:

To find numbers that multiply to 3.75, we can identify factor pairs like 1.5 and 2.5, or 1 and 3.75. Multiplying these pairs will result in 3.75.

Explanation:

To find which numbers multiplied together equal 3.75, we can look for factor pairs of the number 3.75. A factor pair is a set of two numbers that, when multiplied together, result in the given number. Since 3.75 can also be expressed as the fraction ⅓75/100 (or 15/4 in simplest form), we can find factor pairs by considering both whole numbers and decimals that multiply to give us the fraction equivalent.

For example, one obvious pair is 1.5 and 2.5. If we multiply 1.5 by 2.5, we get 3.75:

1.5 × 2.5 = 3.75

Another pair could be 1 and 3.75 as any number multiplied by 1 equals the number itself.

1 × 3.75 = 3.75

These are just two examples of factor pairs for 3.75, but there can be other combinations as well, particularly if we consider fractions or more decimal places.

Answers:

a) [tex]t=\sqrt{\frac{d}{4.9}}[/tex]

b) 0.299 s

Step-by-step explanation:

a) We are given the following equation:

[tex]t=\sqrt{\frac{2d}{9.8}}[/tex]

If we divide by 2 both the numerator and the denominator, we will have:

[tex]t=\sqrt{\frac{2d/2}{(9.8)/2}}[/tex]

[tex]t=\sqrt{\frac{d}{4.9}}[/tex]

b) From this equation:

[tex]t=\sqrt{\frac{2d}{9.8}}[/tex]

[tex]t[/tex] is the reaction time in seconds

[tex]d=44 cm \frac{1 m}{100 cm}=0.44 m[/tex] is the distance

[tex]9.8 m/s^{2}[/tex] is the acceleration due gravity

Solving:

[tex]t=\sqrt{\frac{2(0.44 m)}{9.8 m/s^{2}}}[/tex]

[tex]t=0.299 s[/tex] This is the reaction time

Answer:13/24

Step-by-step explanation:

Answer:

13/24

Step-by-step explanation:

3/8+1/6=9/24+4/24=13/24

Answer:

216

Step-by-step explanation:

Multiply 80x270, which gives you 21,600, then move the decimal at the end of the number two times to the left and you'll get 216

Answer:

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  

 0.580   0.805   1.160   1.085   1.345   1.470

The figure attached represent the boxplot obtained.

Step-by-step explanation:

We can use the following excel code:

data<-c(1.16, 0.72, 1.01, 1.36, 1.28, 1.47, 1.33, 0.68, 1.45, 0.58, 0.89)

> summary(data)

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max.  

 0.580   0.805   1.160   1.085   1.345   1.470

We can order the data on increasing way:

> sort(data)

[1] 0.58 0.68 0.72 0.89 1.01 1.16 1.28 1.33 1.36  1.45 1.47

And for this case we got this:

The minimum on this case is: [tex]Minimum =0.58[/tex]

The maximum would be: [tex]Maximum = 1.47[/tex]

In order to find the median we need to find the value on the 6 position from the data ordered, and we got:

[tex]Median = 1.16[/tex]

And in order to obtain the boxplot we can use R to grapth the boxplot"

> boxplot(data,main="Boxplot")

And the result is on the figurea attached.

The five-number summary of the given data set is 0.58, 0.72, 1.16, 1.36, 1.47, representing the minimum, first quartile, median, third quartile, and maximum values of the data. These can be used to create a box plot to visualize the data.

The five-number summary of a data set includes the minimum, first quartile, median, third quartile, and maximum values of the data set. Here's how we can find those for the given radiation absorption rates:

So, the five-number summary is: 0.58, 0.72, 1.16, 1.36, 1.47.

To make a box plot, draw a number line from the minimum to the maximum and draw a box from the first quartile to the third quartile. Draw a line (the 'median line') inside the box at the median. Finally, draw 'whiskers' from the box to the minimum and maximum.

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Answer:

f(3)=3/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

The GCF is the common "thing" in each one of the terms in our polynomial.  Since 3 doesn't divide evenly out of 10, 3 is not a GCF.  But b-squared is common in both.  So for part A. the GCF is b-squared.

part B.  Factor out the GCF:

[tex]b^2(3b+10)=0[/tex]

For part C. What are the solutions?  The solutions are found in the Zero Product Property which states that if the factors of a polynomial, when multiplied together, equal 0, then either one of the factors or both of the factors have to equal 0 because 0 times anything equals 0.  That means that

[tex]b^2=0[/tex] and/or 3b + 10 = 0

Solving the first equation:

[tex]b^2=0[/tex] and b = 0.

Solving the second equation:

3b + 10 = 0 and

3b = -10 so

[tex]b=-\frac{10}{3}[/tex]

Answer:

it is 4,000

Step-by-step explanation:

since you are rounding it to the nearest thousand, you loo at the 4, and the 2, the 2 is blow five, so it doesn't change the thousands place, but everything else becomes a 0

Answer: 4,000

Explanation: To round 4,279 to the nearest thousand, we first locate the digit in the rounding place which in this case is the 4 in the thousands place.

Next, we look at the digit to the right of the 4 which is 2. The rules of rounding tell us that if the digit to the right of the rounding place is less than 5, we round down and if the digit to the right of the rounding place is greater than or equal to 5, we round up.

In this problem, the digit to the right of the rounding place is less than 5 so we round down. This means that the 4 in the rounding place stays the same and all digits to the right of the 4 become zero.

Therefore, 4,279 rounded to the nearest thousand is 4,000.

Answer:

C. x – 7

E. x + 2

Step-by-step explanation:

Answer:

C. and E. on edge

Step-by-step explanation:

Answer:

38 [tex]ft^{2}[/tex]

Step-by-step explanation:

We can see this figure as

WHOLE RECTANGLE - PORTION OF RECTANGLE CUT OUT

We know area of a rectangle is length * width

If this was the WHOLE RECTANGLE, the area would have been:

5 * 10 = 50 sq. ft.

The portion cut out is also a rectangle with dimensions:

Length = 6

Width = 5 - 3 = 2

Thus,

Area = 6 * 2 = 12 sq. ft.

So, the area of the figure is 50 - 12 = 38 sq. ft.

Answer:

14x+28, where x = cost of each souvenir

Step-by-step explanation:

Given that  Rose visited 14 cities on her vacation. She bought 8 souvenirs in each city to send to her friends. Rose paid $2 in postage for each souvenir she sent. 1.

Here the cost of each souvenir is not given.

Let this cost be x

Then we get

Total cost = [tex]14x+2(14) = 14x+28[/tex]

2) Strategy used it total cost = cost of souvenir +cost of postage.

3) Rose spent 14x+28

Answer:

A)

Step-by-step explanation:

300 students attend Washington middle school.

Step-by-step explanation:

Given,

Percentage of students who play sport = 64%

Number of students who play sport = 192

Let,

x represent the total number of students at Washington middle school.

64% of x = 192

[tex]\frac{64}{100}x=192\\0.64x=192[/tex]

Dividing both sides by 0.64

[tex]\frac{0.64x}{0.64}=\frac{192}{0.64}\\x=300[/tex]

300 students attend Washington middle school.

Keywords: percentage, division

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