Please! Determine which system below will produce infinitely many solutions.
A. 2x + 5y = 24
2x + 5y = 42
B. 3x - 2y = 15
6x + 5y = 11
C. 4x - 3y = 9
-8x + 6y = -18
D. 5x - 3y = 16
-2x + 3y = -7

Answer: 175

Step-by-step explanation:

Most table tops are square, rectangular, or circular.

The ΔXYZ is an Right Angled triangle.

Pythagoras Theorem states that the sum square of two sides of triangle is equal to the  square of longest side.

Distance Formula is used to calculate distance between two points A(a,b) and B(c,d)

denoted by [tex]d=\sqrt{(c-a)^{2} +(d-b)^{2} }[/tex]

In the given question , first calculate the length of each side of the triangle.

given X(3,1),Y(3,7),Z(11,1)

using distance formula

XY=[tex]\sqrt{(3-3)^{2} +(7-1)^{2} } =\sqrt{36} =6[/tex]

YZ=[tex]\sqrt{(11-3)^{2} +(1-7)^{2} } =\sqrt{8^{2}+(-6)^{2} } =\sqrt{64+36}= \sqrt{100} =10[/tex]

XZ=[tex]\sqrt{(11-3)^{2}+(1-1)^{2} } =\sqrt{8^{2} } =\sqrt{64} =8[/tex]

The longest side is 10 and other two sides are 8,6.

by using Pythagoras Theorem

[tex]hypotnuse^{2} =base^{2} +perpendicular^{2}[/tex]

[tex]YZ^{2} =XY^{2} +XZ^{2} \\ \\ 10^{2} =8^{2} +6^{2} \\ \\ 100=64+36\\ \\ 100=100[/tex]

Since Pythagoras Theorem is satisfied It is a right  angled triangle.

Therefore ,  The ΔXYZ is an Right Angled triangle.

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Answer: 16:35 16 bannas to 35 apples

Step-by-step explanation:

PLs mark brainlist

Using integer addition, the total profit from the Spanish Club's bake sale is $270.

Integer refers to whole numbers(non-fractional numbers) that can either be positive or negative, and zero.

Adding positive integers will result to a positive integer while adding negative integers will result to a negative integer. But, adding a negative integer to a positive integer is the same as subtracting its positive.

If the income from the Spanish Club's bake sale was $300 and the expenses for the sale is $30, the total profit will be:

income = +$300

expenses = -$30

Using integer addition,

profit = income + expenses

profit = +$300 + (-$30)

profit = $300 - $30

profit = $270

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Answer:

a ) mean = 1.8

b ) new mean = 11.8

c ) new mean = 23.6

hope this helps

The length of BD is 4.29

BF is the radius of circle and CE is the chord. BF perpendicularly bisects the chord into two equal halves. Thus, we can say that -

CD = 1/2CE

Keep the values in equation to find the value of CD

CD = 1/2×13.5

CD = 6.75

Now, taking BCD as right angled triangle, we can say -

BC is hypotenuse, CD is base and BD is perpendicular. Using Pythagoras theorem to find the length of BD.

BC² = CD² + BD²

8² = 6.75²  + BD²

BD² = 64 - 45.5625

BD² = 18.4375

BD = √ 18.4375

BD = 4.29

Hence, the length of BD is 4.29

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The complete question is attached in the image below.

Answer:

8

Step-by-step explanation:

maths go brrrrrrrrrrr

The coordinates of one point in the solution set are (2, 0)

The system of inequality is given as

-7x + 3y < 3

5x + 7y ≥ -7

The graph that completes the question is added as an attachment

From the question, we also have the graph that represents the inequalities in the above system of inequality

As a general rule, the shaded region in a system of inequality represents the solution set

From the attached graph, the point (2, 0) is in the shaded region

Hence, the coordinates of one point in the solution set are (2, 0)

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In Δ SZU, UJ = 9, VI = 3 , and ZT = 18 then the value of SV = 9.

The triangle's centroid is the point where the three medians intersect. According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.

The centroid has the unique property that the distance from a vertex to the centroid is twice that of the distance from the centroid to the midpoint of the side opposite that vertex for each median. In addition, the three medians of a triangle divide the triangle into six equal-area regions.

Given: In Δ SZU, UJ = 9, VI = 3 , and ZT = 18 .

Since ZV ≅ VU, Y is the midpoint of UZ and SV is a median of Δ ZSU. Similarly, points Y and T are also midpoints of SZ and SU, respectively, so YU and ZT are also medians. Therefore, point J is the centroid of

Δ ZSU and, according to the Centroid Theorem, SJ is 2/3 of SV.

SJ = 2/3 (SV)

= 2/3 (SJ + VJ)

simplifying the above equation, we get

(3SJ/2) - SJ = VJ

SJ/2 = 3

SJ = 4.5

Therefore, to find SV, we can now add SJ and VJ

SV = SJ + VJ

= 6 + 3

= 9

Therefore, the value of SV = 9.

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answer:

7

explanation:

7+14=21

21/3=7

Answer:

Step-by-step explanation:

3x = 7 + 14

3x = 21 (7 + 14 = 21)

x = 7 (divide 3 from both sides) (3x / 3 = x and 21 / 3 = 7)

By using logarithim quotient rule the given lograthimic expression log₅ x - 1/5 log₅ y can be written as log₅ (x/y^(1/5)).

According to the given question.

We have lograthimic expression.

log₅ x - 1/5 log₅ y

As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.

Also according to the logratimic quotient rule we know that

[tex]log_{b} (\frac{m}{n} ) = logm - logn[/tex]

Thereofore,by using logarithim quotient rule the given lograthimic expression log₅ x - 1/5 log₅ y can be written as

log₅ x - 1/5 log₅ y

= log₅ x - log₅ (y^(1/5))

= log₅ (x/y^(1/5))

Hence, by using logarithim quotient rule the given lograthimic expression log₅ x - 1/5 log₅ y can be written as log₅ (x/y^(1/5)).

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Answer:

Step-by-step explanation:

has 25 sections of seating

Answer: 48x⁸y⁶

Step-by-step explanation:

[tex]6x^2y^3(2x^2y)^3=\\6x^2y^32^3(x^2)&^3y^3=\\(6)(8)(x^2)(x^{(2)(3)}})(y^{3+3})=\\48(x^2)(x^6)y^6=\\48x^{2+6}y^6=\\48x^8y^6[/tex]

Answer:

[tex]48 {x}^{8} y^{6} [/tex]

Step-by-step explanation:

[tex]1. \: 6 {x}^{2} y {}^{3} \times 2 {}^{3}( {x}^{2}) {}^{3} y {}^{3} \\ 2. \: 6x {}^{2} y {}^{3} \times 8( {x}^{2} ) {}^{3} y {}^{3} \\ 3. \: 6x {}^{2} y {}^{3} \times 8x {}^{6} y {}^{3} \\ 4. \: (6 \times 8)x {}^{2}x {}^{6} y {}^{3} y {}^{3} \\ 5. \: 48 {x}^{2} x {}^{6} y {}^{3} y {}^{3} \\ 6. \: 48x {}^{2 + 6} y {}^{3 + 3} \\ 7. \: 48x {}^{8} y {}^{3 + 3} \\ 8. \: 48x {}^{8} y {}^{6} [/tex]

Using Pythagorean theorem, the student walked 53.58 meters more compared to the total displacement from the starting point.

If a student walks 100 meters north, then 100 meters west, then the path he travels resembles the sides of a right triangle (see attached photo).

Using Pythagorean theorem, we can solve for the total displacement from the starting point to the end point.

c^2 = a^2 + b^2

where c is the total displacement from the starting point to the end point

a is the distance he walks up north

b is the distance he walks to the west

c^2 = 100^2 + 100^2

c^2 = 10,000 + 10,000

c^2 = 20,000

c = 141.42 meters

Comparing the total distance the student walked and the total displacement from the starting point to the end point by subtraction.

100 meters + 100 meters - 141.42 meters = 53.58 meters

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Probability that Julio will see the ad again during his favorite 30-minute sitcom the next day as ad replays at a random time in each 3 hours interval is 1/6.

As given,

Ad replays at a random time in each 3- hour interval

Julio will watch again during his favorite 30 minutes sitcom

Six times 30 minutes is equals to  3 hours

Ad can appear in any of the six slots of 30 minutes

Probability of watching ad again during his favorite 30 minutes sitcom

=1/6

Therefore, probability of watching ad again during his favorite 30 minutes sitcom is 1/6.

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Answer:

5x - 6y + 126 = 0

Step-by-step explanation:

y-y1=m(x-x1)

y - 6 = 5/6 (x - (-18))

6y - 36 = 5x + 90

5x - 6y + 126 = 0

Answer:

Inverse Property of Addition

Step-by-step explanation:

The solution to the system of equations is (2.5, -2)

The system of equations is given as:

2x + y = 3

2x - 5y = 15

Subtract the equations to eliminate the variable x

This is represented as

2x - 2x + y - -5y = 3 - 15

Evaluate the like terms in the above equation

So, we have

y + 5y = 3 - 15

Evaluate the like terms in the above equation

So, we have

6y = -12

Divide both sides of the above equation by 6

So, we have

y = -2

Substitute y = -2 in 2x + y = 3

2x - 2 = 3

This gives

2x = 5

Divide by 2

x = 2.5

Hence, the solution to the system of equations is (2.5, -2)

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Answer:

2.5, -2

Step-by-step explanation:

Mr. Shaw can use 70 shelves with 2 books each.

or

Mr. Shaw can use 35 shelves with 4 books each.

or

Mr. Shaw can use 28 shelves with 5 books each.

or

Mr. Shaw can use 20 shelves with 7 books each.

or

Mr. Shaw can use 14 shelves with 10 books each.

Mr. Shaw has 140 books in his library.

Divisibility rule of 2:

A number is always entirely divisible by 2 if it is even or has an even last digits, such as 2,4,6,8, or 0.

The last digit of 140 is 0 which is an even number. So, 140 is divisible by 2.

Therefore,

Number of shelves = 140/2 = 70

Divisibility rule of 4:

An integer is divisible by 4 if its last two digits are also divisible by 4. A number is divisible by 4 if its last two digits are zeros since 4 divides 100.

The last two digits of 140 are 4 and 0.

Now, 40/ 2 = 20. Hence, 140 is divisible by 4.

Therefore,

Number of shelves = 140/4 = 35

Divisibility rule of 5:

If the last digit of a given integer is either 5 or 0, then the number is divisible by 5 according to the divisibility rule of five.

Since the last digit of the number 140 is 0. Hence 140 is divisible by 5.

Therefore,

Shelves = 140 / 5 = 28

Now,

Divisibility rule of 7:

According to the divisibility rule of 7, if a number is divisible by seven, then "the difference between twice the unit digit of the provided number and the remaining part of the given number should be a multiple of seven or it should be equal to zero."

140 = 14 - 2 × 0 = 14

Since 14 is divisible by 7. Hence 140 is divisible by 7.

Therefore,

Number of shelves = 140 / 7 = 20

Similarly,

Divisibility rule of 10:

The divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.

As the last digit of 140 is 0, hence 140 is divisible by 10.

Therefore,

Number of shelves = 140/10 = 14

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Using it's concept, the domain of function m is given as follows:

-∞ < x < ∞.

The domain of a function is the set that contains all the values of the input. In a graph, it is the set that contains all values of x of function.

In this problem, the function is defined for all real values of x, as it keeps increasing to left and right, hence the domain of function m is given as follows:

-∞ < x < ∞.

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The 46th term of a Arithmetic Progression (AP) is (a₄₆ = 95.)

The difference between the two numerical orders is a constant value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.

We'd end up coming across a few key words in AP, which were denoted as:

The AP can also be defined in terms of common differences, as shown below.

Now, in the question, the given sequence is;  3,5,7, ...........

Assume the first term is'a₁' = 3

Assume 'a₂' = 5 is the second term.

Assume the third term is 'a₃' = 7

Find the common difference;

d = a₂ - a₁  

Substitute the values in the above equation;

d = 5 - 3 = 2

Now, to calculate the value of the 46th term use the formula of nth term.

an = a + (n − 1) × d , n = total number of terms = 46.

Substitute all the values;

a₄₆ = 5 + (46 - 1) × 2

a₄₆ = 5 + 45 × 2

a₄₆ = 5 + 90

a₄₆ = 95

Therefore, the value of the 46th term is estimated as 95.

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Will they have enough money for their trip?Yes.They will have $1407.35

If not, how much more do they need?

Given:

a1 = $125

r = 1.25

n = 6(march-august)

[tex]S_n=\frac{a(1-r^{n})}{1-r} \\\\S_6=\frac{125(1-(1.25)^{6})}{1-1.25}\\\\S_6=1407.35[/tex]

The family will have $1407.35 after making the final deposit in August.

So, they will have enough money for their trip.

They have an additional amount of $32.35 ($1407.35-$ 1375)

What is a geometric sequence?

The complete question is:

In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $ 1375 . They start with $125 . Each month they plan to deposit 25% more than the previous month. Will they have enough money for their trip? If not, how much more do they need?

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Answer:

-4.7

Step-by-step explanation:

25.85÷ -5.5

by changing the fraction to a decimal, just do regular long division

Answer:

[tex]p= \dfrac{1}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]p^3=\dfrac{1}{8}[/tex]

Cube root both sides:

[tex]\implies \sqrt[3]{p^3}= \sqrt[3]{\dfrac{1}{8}}[/tex]

[tex]\implies p= \sqrt[3]{\dfrac{1}{8}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies p= \left(\dfrac{1}{8}\right)^{\frac{1}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]

[tex]\implies p= \dfrac{1^{\frac{1}{3}}}{8^{\frac{1}{3}}}[/tex]

[tex]\textsf{Apply exponent rule} \quad 1^a=1:[/tex]

[tex]\implies p= \dfrac{1}{8^{\frac{1}{3}}}[/tex]

Rewrite 8 as 2³:

[tex]\implies p= \dfrac{1}{(2^3)^{\frac{1}{3}}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies p= \dfrac{1}{2^{(3 \cdot \frac{1}{3})}}[/tex]

Simplify:

[tex]\implies p= \dfrac{1}{2^{\frac{3}{3}}}[/tex]

[tex]\implies p= \dfrac{1}{2^{1}}[/tex]

[tex]\implies p= \dfrac{1}{2}[/tex]

Answer:

P(17.4 < X < 22.6) = P((X-20)/2.6 < (22.6-20)/2.6) = P(Z < 1.38)

From a standard normal table, we find that P(Z < 1.38) = 0.9128

Step-by-step explanation:

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