Consider the original triangle and the scale drawing enlargement.

A triangle with a side measurement of 2 centimeters. 2 triangles have corresponding side lengths of 2 centimeters and 8 centimeters.
Figures not drawn to scale.

What is the scale factor?

Answer:

3n-10

Step-by-step explanation:

Goes up by three and the first number of this sequence is 10 below 3.

Answer:

(-3±√61)÷2

Step-by-step explanation:

First we expand the brackets to give us :

x²+5x-14 = -1 +2x

Now we make this into the quadratic format (x²+ax+b=0) by subtract -1 and 2x from both sides :

x²+3x-13 = 0

This quadratic cannot be factorized so we must use the quadratic formula :

x = [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex]   or   x = [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]

a = 1 , b = 3 , c = -13

Now we simplify as much as possible by first substituting values known :

x = [tex]\frac{-3+\sqrt{3^{2} -4(1)(-13)} }{2(1)}[/tex]    or   x = [tex]\frac{-3-\sqrt{3^{2} -4(1)(-13)} }{2(1)}[/tex]

Now we evaluate the exponent :

x = [tex]\frac{-3+\sqrt{9 -4(1)(-13)} }{2(1)}[/tex]   or     x = [tex]\frac{-3-\sqrt{9 -4(1)(-13)} }{2(1)}[/tex]

Now we multiply the numbers :

x = [tex]\frac{-3+\sqrt{9 +52 } }{2(1)}[/tex]    or   x = [tex]\frac{-3-\sqrt{9 +52 } }{2(1)}[/tex]

Now we add the numbers :

x = [tex]\frac{-3+\sqrt{61} }{2(1)}[/tex]   or   x = [tex]\frac{-3-\sqrt{61} }{2(1)}[/tex]

Now we multiply the denominator:

x = [tex]\frac{-3+\sqrt{61} }{2}[/tex]   or   x = [tex]\frac{-3-\sqrt{61} }{2}[/tex]

So our final answer is (-3±√61)÷2

Hope this helped and 5 stars, a heart and brainliest please

Answer:

Step-by-step explanation:

Multiplicative inverse of 26/5 is 5/26

(4/13 + 5/26)

13/26 ᴏʀ 1/2

For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The value of e and f is -34 and 2 respectively.

What is a system of equations?

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

For the given system of equations, the value of e will be -34, while the value of f will be 2.

Hence, the value of e and f is -34 and 2 respectively.

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Answer:

he value of e and f is -34 and 2

The cost of the family rug with dimensions 10-ft-by-11-ft given a proportional relationship is $159.50

Cost = $348.00

Area of rug = length × width

= 15 ft × 16 ft

= 240 square feet

Cost of a new rug = x

Area = length × width

= 10 ft × 11 ft

= 110 square feet

348 : 240 = x : 110

348/240 = x/110

cross product

348 × 110 = 240 × x

38,280 = 240x

x = 38,280 / 240

x = $159.50

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Explanation:

Add up the four numbers given: 4+8+4+10 = 26 items total

Kick out the 4 black shirts since they are neither blue, nor are they pants.

So we have 26-4 = 22 items that are blue or a pair of pants (or both).

Divide that over the total (26) to get the probability we're after:

22/26 = (11*2)/(13*2) = 11/13

Side note: 11/13 = 0.8462 = 84.62% approximately

if i was i your class or in bigger class i will help you

Answer:

[tex]x = -\dfrac{48}5[/tex]

Step by step explanation:

[tex]~~~~~~~\dfrac{x^2+12x+36}{2x^2}-\dfrac{x^2 +7x +12}{2x^2}= \dfrac 5{4x}\\\\\\\implies \dfrac{x^2 +12x +36 -x^2 -7x -12}{2x^2 } = \dfrac 5{4x}\\\\\\\implies \dfrac{5x+24}{2x^2} = \dfrac 5{4x}\\\\\\\implies 4x(5x+24) = 5(2x^2)\\\\\\\implies 20x^2+96x= 10x^2\\\\\\\implies 20x^2 -10x^2 +96x=0\\\\\\\implies 10x^2 +96x= 0\\\\\\\implies 5x^2 +48x = 0\\\\\\\implies x(5x+48)=0\\\\\\\implies x = -\dfrac{48}5~~~~~;[x\neq 0][/tex]

Answer:

-1

Step-by-step explanation:

ecuacion de la pendiente está dada por:

Y-yo=m(X-xo)

donde m es la pendiente

del problema :

y-6 = - (x - 3

m=-1

In this case, we must use our trigonometric equations to help us solve this problem:

    ⇒ look at the diagram attached

Let's examine what the problem wants:

Let's examine what the problem gives us:

Let's solve:

  [tex]tan(41)=\frac{12}{x} \\12=x*tan(41)\\x=\frac{12}{tan(41)} \\x=13.80[/tex]

Answer: 13.8 (rounded to nearest tenth)

Hope that helps!

The conditions for which it is possible to construct a triangle include:

This is defined as a three-sided polygon which has three edges and three vertices and a total internal angles of 180 degrees.

The triangle with side lengths 4 cm, 5 cm, and 15 cm can't be constructed due to the length of sides not being equal according to pythagoras theorem.

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Answer:

  20

Step-by-step explanation:

To find the value at the blue dot, you must identify the scale of the markings of the number line.

__

12 is 2 marks to the right of 8, so we know 2 marks has a value of 12-8 = 4.

That means the second mark to the right of 12 will be 12+4 = 16.

The second mark to the right of that is 16+4 = 20, which is where the blue dot is.

The value at the blue dot is 20.

The recursive formula is f(n+1)= f(n)-5.

Given sequence :

f(1)= 6, n≥1.

Let f(n) denote the nth term of the given sequence.

f(1)= 6

f(2)= 1 = f(1)-5

f(3)= -4 = 1-5= f(2) -5

f(4)= -9 = 1-10 = f(2)-10

and so on

Hence, the recursive formula is f(n+1)= f(n)-5.

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The distance between point A to point B is 115.91 ft if the boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water. Luis measures an angle of depression to the boat at point A to be 10 degrees.

From the above information, we can draw a right-angle triangle.

Let's suppose the distance between point A and point B is x

In right-angle triangle, BCD

tan31 = DC/BC = 107/BC

BC = 107/tan31

BC = 178.07 ft

In right-angle triangle, ACD

tan20 = DC/AC

tan20 = 107/(x + BC)

Plug the value of BC

tan20 = 107/(x+178.07)

x + 178.07 = 293.980

x = 115.91 ft

Thus, the distance between point A to point B is 115.91 ft if the boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water.

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Answer:

i) Her claim is incorrect

ii) see below

iii)  44 cm

Step-by-step explanation:

Given:

If the picture is enlarged by a scale factor of 3 to form a poster, then the dimensions of the poster will be:

Area of rectangle = width × length

⇒ Area of poster = (3x) × 3(x + 4)

                             = 9x(x + 4)

                             = 9x² + 36x  cm²

Inputting x = 31 into the area of poster formula found above:

⇒ 9(31)² + 36(31)

= 8649 + 1116

= 9765 cm²

Therefore, as 9765 ≠ 1053 her claim in incorrect.

Using the formula for the area of poster found in part (i).

Area of poster = 1053 cm²

⇒ 9x² + 36x = 1053

⇒ 9x² + 36x - 1053 = 0

⇒ 9(x² + 4x - 117) = 0

⇒ x² + 4x - 117 = 0

First find x by solving the equation from part (ii):

⇒ x² + 4x - 117 = 0

⇒ x² + 13x - 9x - 117 = 0

⇒ x(x + 13) - 9(x + 13) = 0

⇒ (x - 9)(x + 13) = 0

⇒ x = 9,  x = -13

As width cannot be negative, x = 9 only

Perimeter of picture = 2(width + length)

                                 = 2(x + x + 4)

                                 = 2(2x + 4)

                                 = 4x + 8

Input found value of x into the expression for the perimeter:

⇒ Perimeter of picture = 4(9) + 8

                                      = 36 + 8

                                      = 44 cm

Answer:

Step-by-step explanation:

P(A∪B) = 1/6 + 1/2 = 2/3

By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.

The three sides of a triangle are consecutive if and only if they are represented by three consecutive natural numbers. The perimeter is the sum of the three side lengths, whose formula is presented below:

x + (x + 1) + (x + 2) = 141

3 · x + 3 = 141

3 · (x + 1) = 141

x + 1 = 47

x = 46

By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.

The statement is complete, the correct statement is the following:

The triangle has three consecutive sides and its perimeter is 141 centimeters. Work out the value of each side.

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Answer: -10

Step-by-step explanation:

10 x 4 is 40 so with 2 negatives, it turns positive, and 40 plus 10 = 50

Answer:

x=-10

Step-by-step explanation:

-4x+10=50

10=50+4x

-50+10=4x

-40=4x

4x=-40

x=-40÷4

x=-10

Answer:

$69

Step-by-step explanation:

He ows Josue $69 because $158-$89 = $69

What is the sentence and what are the questions. Until I know I can't help. But I should be able to answer if you can tell me

Answer:

(a,b)

Step-by-step explanation:

Using the Midpoint formula,

[tex]\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]

you will get

[tex]\left(\frac{2a+0}{2},\:\frac{0+2b}{2}\right)[/tex]

which is

(a,b)

The ratio of the days it rained to number of days is 3 : 7

The proportion of the number of days it rained is given as:

Proportion = 3/7

This means that:

Proportion = Days it rained/Total number of days.

So, we have:

Days it rained/Total number of days = 3/7

Express as ratio

Days it rained : Total number of days = 3 : 7

Hence, the ratio is 3 : 7

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answer to this is 24cm2

Step-by-step explanation:

area of square is 4x4=16 and area of triangle is 6x4=32 add the both together (32+16) and you have 40cm2

Answer:

363.22

Step-by-step explanation:

Method 1:

You could find the whole figure surface area than divided by 1/2

Method 2: (the one I'm going to personally be doing)

Break the figure into two rectangular figures

Formula for surface area of rectangular prism:

A = 2(width x length + height x length + height x width)

Figure 1:

A = 2(width x length + height x length + height x width)

height = 3.8 yd

length = 10.1 yd

width = 4.3 yd

A = 2((4.3) x (10.1) + (3.8) x (10.1) + (3.8) x (4.3))

A = 2(98.15)

A = 196.3

Figure 2:

A = 2(width x length + height x length + height x width)

height = 8.4 yd

length = 10.1 yd

width = 2 yd

A = 2((2) x (10.1) + (8.4) x (10.1) + (8.4) x (2))

A = 2(121.84)

A = 243.68

There is overlapping surface area that shouldnt be include so we need to subtract it...

For one face of figure 1

3.8 x 10.1 = 38.38

Total:

Figure 1 + Figure 2 - 2(one face)

196.3 - 38.38 = 157.92

243.68 - 38.38 = 205.3

205.3 + 157.92 = 363.22

Answer: number 4 (43º, 62º, 75º)

Step-by-step explanation:

26 + 42 + 106 ≠ 180 so number 1 is not a triangle.

34 + 63 + 79 ≠ 180 so number 2 is not a triangle.

62 + 34 +80 ≠ 180 so number 3 is not a triangle.

43 + 62 + 75 = 180 so number 4 is a triangle.

Because only the angles are given and not the sides, there is an infinite number of triangles. The answer is number 4 (43º, 62º, 75º).

The units on a base area calculations is  known to be cm² or  m² while units on your volume calculations is known to be m³ or cm³.

The unit above is used because in base area calculation, only 2 sides are calculated while in volume calculation, 3 sides are involved.

Note that in base area, square unit is often used in its calculations via the use of two dimensions length and breadth (cm² or  m² ).

In terms of volume, cubic unit is used in its calculations through the use of three dimensions length, breadth and height ( m³ or cm³.).

Note also that Area is seen as the space taken by a two dimensional flat object while volume is seen as the space taken by the three-dimensional object and as such The units on a base area calculations is  known to be cm² or  m² while units on your volume calculations is known to be m³ or cm³.

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Answer:

t = 6

∠BAC = ∠EAD = 6°

∠BCA = ∠ABC = ∠AED = ∠EDA = 87°

Step-by-step explanation:

From inspection of the diagram, we can see that there are 2 triangles inside a circle.  One of the vertices of both triangles is at the center of the circle. The other vertices of both triangles are on the circumference of the circle.

The dashes on the line segments (chord) mean they are equal in length.

⇒ BC = DE

The legs of both triangles are the radius of the circle.

Therefore, ΔABC = ΔAED

This means the ∠BAC = ∠EAD, therefore:

⇒ 6t - 12 = 18 - 4t

⇒ 10t - 12 = 18

⇒ 10t = 30

⇒ t = 3

Substituting the found value of t into one of the expressions to find ∠BAC and ∠EAD:

⇒ ∠BAC = ∠EAD = 6(3) - 12 = 6°

Triangles ΔABC and ΔAED are both isosceles triangles (as they have 2 sides of equal length: the radii).

Therefore, the remaining 2 angles in each triangle will be equal.

The sum of interior angles of a triangle = 180°

⇒∠BAC + 2(∠BCA) = 180°

⇒ 6° + 2(∠BCA) = 180°

⇒ 2(∠BCA) = 174°

⇒ ∠BCA = 87°

Therefore, as ∠BCA = ∠ABC = ∠AED = ∠EDA

all the other angles are 87°

If j represent the number of jelly beans in each box, then the equation that models the problem is; 6j = 324

We are told that the principal used 6 small boxes of jelly beans to fill a large glass jar.

Now, each box had the same number of jelly beans, for a total of 324 jelly beans.

If j represent the number of jelly beans in each box, then the equation that models the problem is; 6j = 324

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