Two similar figures have sides in the ratio of 2:3. If a side of the smaller triangle has a length of 7, what is the length of
the corresponding side of the other triangle?
014
021
02
0 10/

The area of the parallelogram ABCD with the vertices is 40 square units

The vertices are given as

(2, 3), B (7, 3), C (8, -5), and D (3, -5)

From the graph, we have the following dimensions

Base = 5 units i.e. distance AB

Height = 8 units i.e. the distance between the parallel sides

The area of the parallelogram is then calculated as

Area = Base * Height

So, we have

Area = 5 * 8

Evaluate

Area = 40

Hence, the area of the parallelogram ABCD with the vertices is 40 square units

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Numbers in the first 20 rows of pascal's triangle are 210

Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra.

We have been given that:

Numbers of rows = 20

Pascal's triangle formula

1 + 2 + 3 + ….+ 19 + 20  = n (n + 1) / 2  

n=20

 (20)×(21)/ 2  = 210

Pascal's triangle patterns is its symmetry. Observe that in any row, if we read the consecutive numbers from the left, we will obtain the same as if we read them from the right.

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Answer:

y = [tex]\frac{1}{4}[/tex] x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + y = 7 ( subtract 4x from both sides )

y = - 4x + 7 ← in slope- intercept form

with slope m = - 4

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex] , then

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute )- 4, 5 ) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

y = [tex]\frac{1}{4}[/tex] x + 6 ← equation of perpendicular line

The length and width of rectangle is 160 feet and 100 feet.

The perimeter of the rectangle is calculated by the formula -

Perimeter = 2 × (length + width)

As per the given information, length = (60 + width)

Keep the values in formula to find the breadth of rectangle.

520 = 2 × (60 + width + width)

520 = 2 × (60 + 2 × width)

(60 + 2 × width) = [tex]\frac{520}{2}[/tex]

(60 + 2 × width) = 260

2 × width = 260 - 60

2 × width = 200

Width = [tex]\frac{200}{2}[/tex]

Width = 100 feet

Keep the value in formula to find the length of perimeter

520 =  2 × (length + width)

Length + 100 = [tex]\frac{520}{2}[/tex]

Length = 260 - 100

Length =  160 feet

Hence, the length and width of rectangle is 160 feet and 100 feet.

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Answer:-41/4 try that

Answer: (2, -3)

Step-by-step explanation:

To get these points, you just need to multiply the coordinates by 1/4, or divide by 4

The largest integer whose square has exactly digits when written in base is 28 in base 9 .

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z .

Largest base 9 three digit number = 888  

And it can be represented as 728 in base 10, largest square is 26^2       26 that is 28 in base 9.

Therefore the largest integer whose square has exactly digits when written in base is 28 in base 9 .

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20867

The total cost for going to the concert = $90.

The loss of value or benefit that'd result from engaging in a particular activity option in comparison to engaging in such an alternative activity which offers a higher come back on value or benefit is referred to as opportunity cost. The value of the best alternative picked during the decision-making process is provided.

We can select the best option out of all the options available with the aid of the idea of opportunity cost. It helps us use all of our resources as skillfully and productively as possible in order to maximize our financial gains.

For her part-time job, Karen receives a $10 hourly wage. The cost of the concert ticket after the discount is $50, so she decided to go.

It will cost money to take four hours off work. $10 x 4

                                                                           =$40

Opportunity costs of going to the concert = $50 + $40

                                                                      = $90

It is evident that the opportunity cost will be $90.

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I understand that the question you are looking for is:

Karen earn $10 per hour. she wants to go to a concert on Saturday and the price of the ticket is $75, but her friend sold her a ticket for $50. if Karen had to take 4 hours off of work to attend the concert ,What was her opportunity cost of attending the concert?

a.$40

b.$50

c.$75

d.$90

A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).

A relation in mathematics that compares two numbers or even other mathematical expressions in an unequal way is known as an inequality. When comparing two numbers on a number line, it is most frequently used to compare their sizes.

5 sin(x) > 5 cos(x)

To removing constant we divide both the side by 5:

5sin(x) > 5 cos(x)

sin(x) >  cos(x)

sin x > cos x;

sin x = cos x; tan x = 1; x = π/4 or x = 5π/4

sin x > cos x for x ∈ (π/4, 5π/4)

A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).

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I understand that the question you are looking for is:

Find all values of x in the interval [0, 2] that satisfy the inequality. (Enter your answer using interval notation.) 5 sin(x) > 5 cos(x)

Answer:      10/3

Step-by-step explanation:

multiply the denominator, "3", by the mixed number "3", then add the numerator "1". So 3*3+1=10/3 (the denominator stays the same)

Answer: [tex]\frac{10}3}[/tex]

Answer:

156, because the mean is 13, and the mean in equal to all of the numbers added up and divided by how many numbers there are.

Answer:

1. 104F

2. 95F

Step-by-step explanation:

Formula for Celsius to Fahrenheit is

[tex](C*1.8) + 32 = F[/tex]

Question one:

40 times 1.8 = 72

72+32 = 104 Fahrenheit

Question two:

35 times 1.8 = 63

63+32 = 95 Fahrenheit

Final answer obtained is 2/3

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. For instance, the geometric progression 2, 6, 18, 54, etc. has a common ratio of 3. Similar to that, the geometric series 10, 5, 2.5, 1.25,... has a common ratio of 1/2.

Powers [tex]r^{k}[/tex] of a given non-zero number r, like [tex]2^{k}[/tex] and [tex]3^{k}[/tex], are examples of a geometric sequence. A geometric sequence's basic structure is

[tex]ar,ar^{2},ar^{3}.ar^{4},-----[/tex]

where a is not equal to 0 is a scale factor that is equal to the initial value of the series and r is not equal to 0 is the common ratio.

A series is a sum, whereas a progression is a sequence. This is the difference between the two.

∑[tex]_{i=0}^{n}[/tex] [tex]ar^{i}=\frac{a(1+r^{n+1})}{1-r}[/tex]

We see that n= 99, r= -1/2, a=1

∑[tex]_{i=0}^{99}[/tex] [tex](\frac{-1}{2}) i=[/tex] [tex]\frac{1-(\frac{-1}{2})^{99+1} }{1-\frac{1}{2} }=\frac{1-(\frac{-1}{2})^{100} }{1+\frac{1}{2} }=\frac{1-\frac{1}{2}^{100} }{\frac{3}{2} }[/tex]

[tex]=\frac{\frac{2^{100}}{2^{100}} -\frac{1}{2^{100}} }{\frac{3}{2} } =\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]

[tex]\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]

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Blue whale is 15 times longer than otter.

To find how many times the blue whale is  longer than the otter, we will perform division. We will divide the length of blue whale by length of otter, which we will give us the desired result.

Now, performing calculation as per the above statements -

Number of times longer length = [tex]\frac{3*10^{4} }{2*10^{3} }[/tex]

Performing division of numbers. Also, as we know, on division the exponents are subtracted. Hence, subtracting the exponents to get the desired result.

Number of times longer length = 1.5*[tex]10^{4-3}[/tex]

The result will be -

Number of times longer length = 1.5*10

Performing multiplication -

Number of times longer length = 15

Hence, we get that blue whale is 15 times longer than otter.

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Answer:

B

it is the right equation

Step-by-step explanation:

In the equation y = mx + b for a straight line, the number m is called the slope of the line. In the equation y = mx + b for a straight line, the. number b is called the y-intercept of the line.

Answer: 1.42 x 10^1

Step-by-step explanation:

Answer: 1.42x10

Step-by-step explanation:

Answer:

Hello,

Step-by-step explanation:

1. We must decompose the conic into 2 lines.

[tex]f(x,y)=x^2-5xy+y^2+5x-2y+1=0\\\\We\ are\ going\ to\ find\ the\ center\\\\\left\{\begin{array}{ccc}\dfrac{ \partial{f} }{\partial{x} }&=&12x-5y+5=0\\\\\dfrac{ \partial{f} }{\partial{y} }&=&-5x+2y-2=0\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}x=0\\y=1\\\end {array} \right.\\\\We\ must\ find\ an\ other\ point\ of\ f(x,y).\\\\if\ y=0\ then\ x=\dfrac{-1}{2} \ or\ x=\dfrac{-1}{3}[/tex]

The 2 lines are: 2x-y+1=0 and 3x-y+1=0

Paralleles are y=2x and y=3x

Perpendiculars are x+2y=0 and x+3x=0

Answer:

(a) 75 minutes

(b) 50 minutes

The solution to the system of equation is (-1, -6)

Given the system of equations

2x - 3y = 16

5x - 3y = 13

Subtract to have:

2x-5x = 16 - 13

-3x = 3

x = -3/3

x = -1

Substitute x = -1 into 1 to have:

2(-1) - 3y = 16

-2 - 3y = 16

-3y = 16 + 2

-3y = 18

y = -6

Hence the solution to the system of equation is (-1, -6)

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Answer:

1.5797 x 10^-4

Step-by-step explanation:

Step-by-step explanation:

could it be that the equation is rather

-5 = (-8 + v)/3

?

that is a huge difference ...

to solve such an equation we keep transforming it (every change we make we have to do on both sides of the equation to keep the equality), until we have only the variable on one side, and everything else (which is then the solution) on the other side.

1st step : we get rid of the "/3" by multiplying both sides by 3.

that gives us

-5×3 = ((-8 + v)/3)×3 via the multiplication property.

2nd step : we simplify

-15 = -8 + v

3rd step : we get rid of the -8 on the side of the variable by adding 8 to both sides.

that gives us

-15 + 8 = -8 + 8 + v via the addition property.

4th step : we combine like terms (or simplify, if we can use it a second time) :

-7 = 0 + v

-7 = v

that's it.

El grafico de la ecuación lineal se puede ver en la imagen al final.

En este caso queremos graficar la ecuación lineal:

5y - 15 = -4x

Para ello debemos encontrar dos puntos en la linea, y para hacer eso podemos evaluar en dos valores de x.

Sí x = 0 obtenemos:

5y - 15 = -4*0

5y = 15

y = 15/5 = 3

Sí x= 5 obtenemos:

5y - 15 = -4*5

5y = -20 + 15

5y = -5

y = -5/-5 = -1

Entonces solo tenemos los dos puntos (0, 3) y (5, 1), ahora debemos graficar estos en un eje de coordenadas y trazar una linea que pase por ambos, como en el ejemplo de abajo.

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Yes,  the moving boxes will fit in this volume.

The current volume of box :

Volume = height * width * depth

Volume = 12 * 9 * 2

Volume = 216 in³

New dimension :

Height and volume are the same

Width = 9 - 1 = 8

Depth = x

Volume = height * width * depth

216 = 12 * 8 * x

216 = 96x

x = 216 / 96

x = 2.25 inch

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.

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Answer:

The first rectangle is 3x² - 6x + 13 more square feet then the second rectangle

Step-by-step explanation:

A rule for subtracting polynomials

Steps

At the end of the expression is (7x²- 4x + 12) + -4x² - 2x + 1

At this point you combine like terms like you do with adding polynomials so ( 7x² + (-4x²) is 3x², (-4x) + (-2x) is (-6x), and 12 + 1 is 13) so the final answer would be 3x²-6x+13

The amount of silver that  should be added is 48% . A jeweler is said to have 5 rings that weigh 12 g apiece and are composed of an alloy of 20% silver and 80% gold.

What are linear equations?

An equation between two variables that, when plotted on a graph, produces a straight line.

The material will weigh 12 × 5 = 60 grams after melting all 5 rings.

The alloy's 20% silver and 80% gold content have been disclosed to us. Let's further say that the melted material receives an additional x grams of silver, resulting in a composition of 64% gold and 36% silver.

Thus, we can construct the following equation:

Amount of gold before = Amount of gold after mixing

So the equation we get

80% of 60 grams =64% of (X + 60) gram

0.80 × 60 = 0.64 (x + 60)

48 = 0.64x + 38.4

0.64x = 9.6

x = 9.6/0.64

x = 15

So

Amount of silver that needed to be added

= 0.64(15 + 60)

= 0.64(75)

= 48%

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The measure of angle 2 and angle3 are 133 ad 47 degrees respectively

From the given diagram, the measure of angle 1 and 2 are congruent. (vertical angles)

Given he following parameters

m<1 = 133 degrees

Since m<1 = m<2, hence m<2 = 133 degrees

Also;

m<2 + m<3 = 180

133 + m<3 = 180

m<3 = 180 - 133

m<3 = 47 degrees

Hence the measure of angle 2 and angle3 are 133 ad 47 degrees respectively

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The graph of function f(x) = [tex]2^{x}[/tex] + 3 will be increases without bound As x increases without bound and As x decreases without bound, f(x) approaches the line y = 3 therefore option (C) and (D) will be correct.

A graph is a diametrical representation of any function between the dependent and independent variables.

The graph is easy to understand behavior of the graph.

Given the function,

f(x) = [tex]2^{x}[/tex] + 3

At x = 0 → f(0) = 2⁰ + 3 = 3

This is an exponential function as shown below which will be increasing as x increase while it will gain the value y = 3 as x decrease.

Hence "The graph of function f(x) = [tex]2^{x}[/tex] + 3 will be increases without bound As x increases without bound and As x decreases without bound, f(x) approaches the line y = 3".

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