Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form. perpendicular to 5y = x − 4 and passes through the point (−2, 1)

The value of a is 16 and b is 18 by similarity of triangles.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same form but may not be the exact same size.

Two triangles are said to be similar if their corresponding angles are equal. Equiangular triangles are what they are called. Two equiangular triangles were the subject of a significant finding made by the well-known Greek mathematician Thales. He applied the Basic Proportionality Theorem, sometimes known as the Thales Theorem, as a conclusion.

In triangle OXY and ONM

[tex]\frac{4}{16} = \frac{6}{6 + b}[/tex]

⇒ 24 + 4b = 96

⇒ 4b = 72

⇒ b = 18

again ,

[tex]\frac{4}{16} = \frac{4}{a}[/tex]

⇒ a = 16

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Answer:

There were 3 children in the room

Step-by-step explanation:

Let x be the number of children in the room

Since each child has 10 fingers including their thumbs, total number of fingers =10x

Each child has 2 ears so total number of ears = 2x

Since they had 24 more fingers than ears we get the equation:
10x - 2x = 24

8x = 24

x = 24/8 = 3

Scientific notation 295000 is 295×10³ and standard notation of  7.3×10⁻⁴ is 0.00073 and From least to greatest is 1, 3/2, π/2, √3, 9 and E is the best estimate of √3

A number system is defined as a system of writing to express numbers.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

295000 is 295×10³

Now let us write 7.3×10⁻⁴ is standard notation

7.3/10000=0.00073

We have to arrange from least to greatest

1, 9, 3/2, √3, π/2

1, 9, 1.5, 1.732, 1.57

From least to greatest is 1, 3/2, π/2, √3, 9

E is the best estimate of √3

Hence, scientific notation 295000 is 295×10³ and standard notation of  7.3×10⁻⁴ is 0.00073 and From least to greatest is 1, 3/2, π/2, √3, 9

E is the best estimate of √3

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Answer: he use 4 pepperoni more than sausage every times he put 10 meat on the pizza

Step-by-step explanation: both are on 10 so you don't need to change it so 7-3=4 and it's on ten which mean that every times he put 3 sausage, he have to put 7 pepperoni

Answer:

2.92 it is so easy. Just you have to subtract them

Answer:2.92 pounds

Step-by-step explanation:

Eli needs to buy at least 24 sets of knives, as each set contains 10 knives and the restaurant needs 546 knives in total. This can be determined by solving the inequality 10x ≥ 234, where x is the number of sets of knives.

1. 312 + 10x ≥ 546

2. 10x ≥ 234

3. x ≥ 23.4

4. Therefore, Eli needs to purchase at least 24 sets of knives for the restaurant to have enough knives.

Eli needs to order new supplies for the restaurant where he works, and he needs to order at least 546 knives. There are currently 312 knives, so he needs to order more. If each set of knives contains 10 knives, then he needs to determine how many sets of knives he needs to order in order to have enough knives. To do this, we need to set up and solve an inequality. The inequality we need to solve is 10x ≥ 234, where x is the number of sets of knives. This can be solved by dividing both sides by 10, which gives us x ≥ 23.4. This means that Eli needs to purchase at least 24 sets of knives for the restaurant to have enough knives.

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The fraction of red apples in the bag is 3/ (4+x).

Let there be "x" number of green apples and "y" number of red apples in the bag.

According to the given information,

3/4 * x = y

Therefore, y = 3/4 * x

Since the fraction of red apples is y/ (x+y)

Therefore, fraction of red apples = 3/4 * x / (x+3/4 * x)

Simplifying,

Fraction of red apples = 3/ (4+x)

Therefore, the fraction of red apples in the bag is 3/ (4+x).

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Answer: b+164

Step-by-step explanation:

Answer: B + 164 = T

Step-by-step explanation:

T = TOTAL

B = LAST WEEK

Answer:

[tex]a=15, b=0[/tex]

Step-by-step explanation:

The numbers are [tex]5w-1, 5w, 5w+1[/tex].

So. the sum is [tex]5w-1+5w+5w+1=15w \implies a=15, b=0[/tex].

At the end of 1.51 seconds, the velocity is 6.9 m/s, and at the end of 2.86 seconds, it is 24.64 m/s.

The dislocation that an article of particle experiences with regard to the time is expressed vectorially as velocity. The meter per moment (m/s) is the accepted unit of velocity profiles (also known as speed).

A. F = ma, where F is force, m is mass and a is acceleration.

a = 2.65/0.58

Performing division

a = 4.57 m/s²

With respect to final and starting velocities, acceleration, and time, the formula is v = u + at.

v = 4.57×1.51

The act of multiplying

v = 6.9 m/s.

B). New acceleration = 3.60/0.58

The act of multiplying

New acceleration = 6.2 m/s²

v = u + at

v = 6.9 + 6.2×2.86

Performing multiplication

v = 6.9 + 17.75

Performing addition

v = 24.64 m/s.

At two different locations, the velocities are 6.9 m/s or 24.64 m/s.

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The simple interest rate that you are charged, based on the loan amount and the period of the loan, is 3. 5 %

Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.

Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

To find the simple interest rate, find the simple interest charged per year to be:

= 175 / 2

= $ 87. 50

Then , the simple interest rate would be:

= Simple interest per year / Loan amount

= 87. 50 / 2, 500

= 3. 5 %

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As per given digits of integers, the largest number of possible integers are 84.

Here we have given that the number is a multiple of 5 and the units digit must be 0 or 5.

Then let us consider that if 5 is the units digit then the thousands digit can be 1,2,3, or 4 so here we have 4 options.

Then let us consider that the hundreds digit also has 4 options because it can have 0.

Then the tens digit has 3 options which is written as,

=> 4*4*3 = 48

Similarly, let us consider that if 0 is the units digit, then 5 is the largest digit, there must be a 5 in the integer.

Here we have also note that if the 5 is the hundreds digit, then there are 12 ways.

And here there are 3 places the 5 could be so it can be written as

=> 12*3=36.

Therefore, the total possible numbers are written as

=> 48+36=84 Integers

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The measure of the largest angle of the quadrilateral is 88 degrees.

The sum of the angles of a quadrilateral is 360 Degrees. This is derived from the property named Angle Sum property of quadrilateral. We can use this fact to set up an equation using the given information:

x + (5x + 15) + (3x - 25) + (4x - 20) = 360

Simplifying this equation:

13x = 350

x = 27^

Now we can substitute this value of x back into the equation for any of the four angles to find the largest angle:

4x - 20 = 4(27) - 20 = 108 - 20 = 88

Therefore, the measure of the largest angle of the quadrilateral is 88 degrees.

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Answer:

scalene

Step-by-step explanation:

It is a scalene triangle, meaning all sides are different lengths.  It is NOT a right triangle because the 6 cm side is "too short" to be a hypotenuse.  

Simplification of the exponential expressions using laws of exponents gives;

A) 1

B)  ¹/₂

C) 2

D) 2

Some of the laws of exponents states that;

1) When we multiply like bases, we must keep the base the same and add the exponents.

2) When we raise a base with a power to another power, we must keep the base the same and multiply the exponents.

3) When dividing like bases, we must keep the base the same and subtract the denominator exponent from the numerator exponent.

A) [(2 * 3⁻²)³(5 * 3²)²]/(3⁻²)(5 * 2)²

Applying laws of exponents, we have;

[(2² * 3⁻²*³)(5² * 3²*²)]/(3⁻²)(5² * 2²)

= 2² and 5² will cancel out to give;

3⁻⁶ * 3⁴ * 3²

= 3⁻⁶ * 3⁴⁺²

= 3⁻⁶ * 3⁶

= 3⁰ = 1

B) (3³) (4⁰)²(3 * 2)⁻³ (2²)

This can be broken down into;

3³ * 1 * 3⁻³ * 2⁻³ * 2²

= 2⁻¹ = ¹/₂

C) (3⁷ * 4⁷)(2 * 5)⁻³(5²)]/(12⁷ * 5⁻¹ * 2⁻⁴)

= (3⁷ * 4⁷)(2⁻³ * 5⁻¹)/((3⁷ * 4⁷ * 5⁻¹ * 2⁻⁴)

3⁷ * 4⁷ * 5⁻¹ will cancel out to get;

2⁻³/2⁻⁴ = 2

D) ((2 * 3⁻¹) * 2⁰)/(2 * 3⁻¹)

(2 * 3⁻¹) will cancel out to get;

2⁰ = 1

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3/7 of the posters are hanged in the hallway.

A fraction represents a part of a whole.

Given that Dave spreads out a roll of paper and cuts it into 7 equal-sized posters.

He decorates the posters and takes them to school.

Dave hangs 4 posters on the side of the gym

4/7 of the posters are on the  side of the gym.

The remaining posters are in the hallway.

1-4/7

LCM is 7

7-4/7

3/7

Hence, 3/7 of the posters are hanged in the hallway.

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The earned commission would be $437.50.

What is a commission?

A commission is a payment made to an employee, typically in sales or finance, for services rendered in the form of a percentage of the revenue generated by the employee's efforts. It is a way for companies to incentivize employees to sell more products or services, as the employee's income is directly tied to the success of their sales efforts.

The salesperson earns $437.50 on commission. This can be calculated by multiplying $1,750.00 by 25% (0.25).

$1,750.00 * 0.25 = $437.50

Hence, the earned commission would be $437.50.

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50 different greek armies, the upper class and the lower class soldiers battalions can be sent.

The Greek army can form different battalions by choosing 4 upper class soldiers and 8 lower class soldiers from a total of 5 upper class soldiers and 10 lower class soldiers. This problem can be solved using a combination formula known as a binomial coefficient.

The number of different battalions that can be sent is:

(5 choose 4) * (10 choose 8) = 5*10 = 50

Different battalions can be formed by choosing 4 upper class soldiers and 8 lower class soldiers from a total of 5 upper class soldiers and 10 lower class soldiers. Therefore, 50 different battalions can be sent.

So, 50 different battalions can be sent.

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Answer:

Step-by-step explanation:

You need to give more information. There is nothing you can tell from the information you gave. Nothing is fixed.

The number of non-similar 1000-pointed stars is

[tex]$\frac{1000-600-2}{2}= \boxed{199}.$[/tex]

If we join the adjacent vertices of the regular [tex]$n$[/tex]-star, we get a regular [tex]$n$[/tex][tex]-gon[/tex]. We number the vertices of this [tex]$n$[/tex][tex]-gon[/tex] in a counter clockwise direction: [tex]$0, 1, 2, 3, \ldots, n-1.$[/tex]

A regular [tex]$n$[/tex]-star will be formed if we choose a vertex number m where [tex]$0 \le m \le n-1$[/tex], and then form the line segments by joining the following pairs of vertex numbers:[tex]$(0 \mod{n}, m \mod{n}),$ $(m \mod{n}, 2m \mod{n}),$ $(2m \mod{n}, 3m \mod{n}),$ $\dots,$ $((n-2)m \mod{n}, (n-1)m \mod{n}),$ $((n-1)m \mod{n}, 0 \mod{n}).$[/tex]

If [tex]$\gcd(m,n) > 1$[/tex], then the star degenerates into a regular [tex]$\frac{n}{\gcd(m,n)}$-gon[/tex] or a (2-vertex) line segment if [tex]$\frac{n}{\gcd(m,n)}= 2$[/tex]. Therefore, we need to find all $m$ such that [tex]$\gcd(m,n) = 1$.[/tex]

Note that [tex]$n = 1000 = 2^{3}5^{3}.$[/tex]

[tex]Let $S = \{1,2,3,\ldots, 1000\}$, and $A_{i}= \{i \in S \mid i\, \textrm{ divides }\,1000\}$. The number of $m$'s that are not relatively prime to $1000$ is: $\mid A_{2}\cup A_{5}\mid = \mid A_{2}\mid+\mid A_{5}\mid-\mid A_{2}\cap A_{5}\mid$ $= \left\lfloor \frac{1000}{2}\right\rfloor+\left\lfloor \frac{1000}{5}\right\rfloor-\left\lfloor \frac{1000}{2 \cdot 5}\right\rfloor$ $= 500+200-100 = 600.$[/tex]

[tex]Vertex numbers $1$ and $n-1=999$ must be excluded as values for $m$ since otherwise a regular n-gon, instead of an n-star, is formed.[/tex]

The cases of a 1st line segment of (0, m) and (0, n-m) give the same star. Therefore we should halve the count to get non-similar stars.

Therefore, the number of non-similar 1000-pointed stars is

[tex]$\frac{1000-600-2}{2}= \boxed{199}.$[/tex]

[tex]Note that in general, the number of $n$-pointed stars is given by $\frac{\phi(n)}{2} - 1$ (dividing by $2$ to remove the reflectional symmetry, subtracting $1$ to get rid of the $1$-step case), where $\phi(n)$ is the Euler's totient function.[/tex] [tex]It is well-known that $\phi(n) = n\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right)\cdots \left(1-\frac{1}{p_n}\right)$, where $p_1,\,p_2,\ldots,\,p_n$ are the distinct prime factors of $n$.[/tex] [tex]Thus $\phi(1000) = 1000\left(1 - \frac 12\right)\left(1 - \frac 15\right) = 400$, and the answer is $\frac{400}{2} - 1 = 199$.[/tex]

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1) The function f(x) is defined as follows: B. F(x) = -(x + 2)²(x - 2).

2) The standard definition of function f(x) is given as follows: A. F(x) = ax³ + bx² + cx + d.

4. The solution to the system of equations is approximated by the following option:

A. (-3.43, 6.30).

The function for item 1 is defined considering it's roots, as follows:

Hence the function is defined as follows:

F(x) = a(x + 2)²(x - 2).

The y-intercept is positive, meaning that:

-8a > 0.

Thus the leading coefficient a is negative, and the correct option is given by option B.

The cube function, with all positive coefficients, is given by option A in item 2.

The graphic solution of a system of equations is given by the point of intersection of all the equations that compose the system.

The equations that compose the system in this problem are given as follows:

For this problem, the systems are composed by a third degree function v(x) and a linear function b(x), hence we graph them and obtain the point of intersection.

From the graph given by the image presented at the end of the answer, the coordinates of the point of intersection are presented as follows:

(-3.432, 6.296).

This means that, using rounding, the correct option is given by option A for the solution of the system of equations.

Item 1 asks to define the graphed function, while item 2 asks for the standard cube function.

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We can use a proportion to determine how many flyers Sam needs to deliver to earn $45. A proportion is an equation that states that two ratios are equal. In this case, we can use the ratio of the number of flyers delivered to the amount of money earned.

What in mathematics is a linear equation?

According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Let x be the number of flyers Sam needs to deliver to earn $45. The proportion can be written as:

x/45 = 10/1

We can solve for x by multiplying both sides of the proportion by 45:

x = (10/1)*45 = 450

So, Sam needs to deliver 450 flyers to earn $45.

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The probability of having a 2 on first roll, 3 on second roll and 4 on third roll is 1 / 216

A fair dice is a dice that is equally likely to land on any of its faces, meaning that each face has the same probability of facing up after a roll. The probability of getting a specific face on a fair dice is represented by the number of ways that face can appear divided by the total number of possible outcomes.

For a standard six-sided fair dice, the total number of possible outcomes is 6, since there are six faces on the dice. The probability of getting a specific face (for example, the number 4) is 1/6, because there is only one way to get that number out of the six possible outcomes.

The probability of landing 2 on first roll, 3 on second roll and 4 on third roll is given as;

P = (1/6 * 1/6 * 1/6)

P = 1 / 216

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Answer:

3x^2−2

Step-by-step explanation:

Given f(x)=3x−5 and g(x)=x^2+1

∴f(g(x))=f(x^2+1)

=3(x^2+1)−5

=3x^2−2

The equation to find the amount the rental car company will charge for any number of days is y = 75+20(n-3).

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

Given that,

The charge per day for a 3-day rental = 75/3 = 25

The additional charge for an extra 4 days is (155-75)= 80 which is $20 per day.  

The charge for a period of n days (n>3) is then 75+20(n-3).

Thus, The equation to find the amount the rental car company will charge for any number of days is y = 75+20(n-3).

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Substitute 2x+3y=6 into the first equation:

4x^2+4y^2=(2x+3y)^2

4x^2+4y^2=4x^2+12xy+9y^2

0=12xy+5y^2

Divide both sides by 5:

0=2.4xy+y^2

Subtract 2.4xy from both sides:

-2.4xy=y^2

Take the square root of both sides:

y=±√-2.4xy

Substitute y=±√-2.4xy into the equation 2x+3y=6:

2x+3(±√-2.4xy)=6

2x±3√-2.4xy=6

Add 2x to both sides:

4x±3√-2.4xy=6+2x

Subtract 4x from both sides:

±3√-2.4xy=6-4x

Divide both sides by 3:

±√-2.4xy=2-4/3x

Square both sides:

-2.4xy=(2-4/3x)^2

-2.4xy=4-16/3x+8/9x^2

8/9x^2-16/3x+4+2.4xy=0

Use the quadratic equation to solve for x:

x= (16 ± √(256+192y^2))/18

Substitute this back into the equation 2x+3y=6 to solve for y:

2(16 ± √(256+192y^2))/18 + 3y = 6

3y = 6 - 32 ± √(256+192y^2))/9

3y = -26 ± √(256+192y^2))/9

y = (-26 ± √(256+192y^2))/27

Therefore, the solution is:

x = (16 ± √(256+192y^2))/18

y = (-26 ± √(256+192y^2))/27

Answer: 21 boxes are needed

Step-by-step explanation:

Total area:  length  =  1.5 + 6.25 + 1.5  =  9.25     height  =  1.5 + 6.25  =  7.75

Total Area  =  9.25 x 7.75  =  71.6875

Area of the patio  =  6.25 x 6.25  =  39.0625

Area of the extension  =  Total Area - Area of the patio  =  71.6875 - 39.0625  =  32.625

Area covered by one box of tiles:  25 x 0.25 x 0.25  =  1.5625

Number of boxes needed:  32.625 / 1.5625  =  20.88  =  21 boxes

I hope this helps even though you already figured it out!

Step-by-step explanation:

Let x be the number of bricks Ram laid.

Shyam laid x/2 bricks.

Therefore, x + x/2 + 250 = x(3/2) + 250 = x(3/2) = 300

x = (2*300)/3 = 200

Ram laid 200 bricks.

Shyam laid 200/2 = 100 bricks.

Answer:A system of linear equations has no solution when the graphs are parallel. Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

Step-by-step explanation:

The probability of flipping four coins is 0.0625

Total coins = 4

The study of chances, which are determined by the ratio of favourable occurrences to probable cases, is known as probability.

When flipping a coin, there are two possible outcomes (heads or tails), hence the likelihood of flipping a head-up coin is equal to the likelihood of flipping a tail-up coin.

Thus, the probability is = 1/2

Calculating the probability of getting all heads or all tails when flipping 4 coins -

= 1/2 x 1/2 x 1/2 x 1/2

= 1/16

In decimal form, this will be 0.0625

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