An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
Which best describes the range of possible values for the third side of the triangle?
< 12.5, x > 18.9
12.5 < x < 18.9
x < 6, X > 26
6
26

Answer:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. [tex]42^\circ[/tex]

5. 16.73 m

Step-by-step explanation:

Solution 1.

Reading of map scale = 1cm:5km

i.e. 1 cm is equivalent to 5 km

Measurement of map  = 7 cm

Actual distance = Measurement of map [tex]\times 5[/tex]

Actual distance = 7 [tex]\times 5[/tex] = 35 km

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Solution 2.

Length of dining hall = 35 m

Measurement of map = 7 cm

Scale = Measurement of map : Length of dining hall (i.e. ratio)

Scale = 7 cm :35 m = 1 cm : 5 m

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Solution 3.

Length of building = 30 m

Scale = 1 cm to 5m

5 m is equivalent to 1 cm on scale

1 m is equivalent to [tex]\frac{1}{5}[/tex] cm on scale

30m is equivalent to [tex]\frac{1}{5} \times 30[/tex] = 6 cm on scale

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Solution 4.

Angle of elevation of A from B = [tex]42^\circ[/tex]

Angle of depression of B from A = ?

Please refer to the image attached, we can clearly observe that both the angles (i.e. angle of elevation from A to B and angle of depression from B to A )will be equal.

Angle of depression of B from A = [tex]42^\circ[/tex]

-------------------

Solution 5.

Given that:

String length, or hypotenuse of triangle BC= 25 m

Angle of string with horizontal, [tex]\angle B = 42^\circ[/tex]

Please refer to the attached image for the clear understanding of the situation.

To find:

Height, AC = ?

We can use trigonometric identity:

[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}[/tex]

OR

[tex]sinB = \dfrac{AC}{BC}\\\Rightarrow sin42^\circ = \dfrac{AC}{25}\\\Rightarrow AC = 25 \times 0.67\\\Rightarrow AC = 16.73 m[/tex]

============

So, the answers are:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. [tex]42^\circ[/tex]

5. 16.73 m

Answer:3hrs 59min

Step-by-step explanation:

πd=perimeter

(113÷3.14)

=35.99

9yards=1hr

35.99yards=?

35.99÷9=3hrs 59min

Answer:

$2.00

Step-by-step explanation:

The grocer bought the oranges for $15.00

15x12= 180 To find the number of oranges he bought

180-20=160 To find the rest of the remaining oranges

160/8= 20 To find how many packs he has

20x.85= 17 To find how much he made from selling the remaining oranges

17-15=2 To find the profit

Answer:

Since it's increasing add 3.5% to 100%

= 103.5% of £16470.45

= 103.5/100 × 16470.45

= 17046.92

= £17046.92

Hope this helps.

Answer:

Ratio of sandwiches with white bread and brown bread is 10:3. Of the white sandwiches 2/3 are vegetarian, of the sandwiches that are brown half are vegetarian. What fraction of the sandwiches are vegetarian?

Step-by-step explanation:

Givens

The ratio between white bread and brown bread is 10:3, that is, for every 10 white bread, there are 3 brown bread.

2/3 of white sandwiches are vegetarian.

1/2 of brown sandwiches are vegetarian.

We know that white bread is represented by 10, and brown bread is represents by 3. So, 2/3 of 10 are vegetarians, and 1/2 of 3 are vegetarians. The sum of them is

2/3 of 10 are vegetarians = [tex]\frac{2}{3} \times 10 = \frac{20}{3}[/tex]

1/2 of 3 are vegetarians = [tex]\frac{1}{2} \times 3 = \frac{3}{2}[/tex]

[tex]=\frac{20}{3}+\frac{3}{2}\\\\=\frac{40+9}{6}\\\\=\frac{49}{6}[/tex]

Therefore, 49/6 represents all the sandwiches which are vegetarian.

Step-by-step explanation:

Nearest thousandth is the third digit after the decimal point.

Or in other words :writing this number till reaching the third digit after the point (3rd digit in decimal part)

48.175

19.926

5.572

Hope this helps you.. Good Luck!

Answer:

x=5

Step-by-step explanation:

2(x+4)+2x+3=3x+16

One solution was found :

                  x = 5

Answer:

2x+8+2x+3=3x+16=

2x+2x-3x=-8-3+16=

4x-3x=-11+16=

x=5

Answer:

x= -3,      x = 1

Step-by-step explanation:

Zeros are values of x, when f(x) = 0.

0=(x+3)(x-1)

x+3 = 0,  x - 1=0

x= -3,      x = 1

Answer:

x = -3, x = 1

Step-by-step explanation:

To determine the zeroes of the factored quadratic equation, we need to look back at its definition. The zeroes are a function are specific x-values that result in a y-value of 0.

In this case, we want the numbers inside of the parantheses to equal 0. If we substitute in x = -3, we get (0)(x - 1), and we know that is just 0. Similarly, if we substitute in x = 1, we get (x + 3)(0), and we know that is just 0.

As such, these are your solutions.

Answer:

-1458

Step-by-step explanation:

Let's find the rule of the sequence. It seems that each term is -3 times the previous term.

Let's continue the sequence.

486, -1458

-1458 is the 7th term

Answer:

$ 21

Step-by-step explanation:

Money spent = (2/5) * 60 + (1/4) * 60

                      = 2*12 + 1*15

                      = 24 + 15

                      = $ 39

Money save = 60 - 39 = $ 21

Answer:

2

Factored out:

2 ( 2 − n )

Answer:

2

Step-by-step explanation:

The GCF (greatest common factor), is 2 because 2 can go into both numbers.

original: 4-2n

with GCF factored out: 2(2-n)

Answer:

(2, 4)

x = 2

y = 4.

Step-by-step explanation:

To find the solution to the system of equations, we can simply set the two equations equal to each other as shown:

x + 2 = 3x - 2

Subtract 'x' from both sides:

2 = 2x - 2

Add '2' to both sides:

4 = 2x

x = 2.

Plug this value for 'x' into an equation to solve for 'y':

y = (2) + 2

y = 4.

Therefore, the solution to the system is (2, 4).

Answer:

Y=4

Step-by-step explanation:

How I did this.

y=x+2 y=3x-2

Moved around (you can do this)

y=2+2 y= 3x-x

y=4 y=2x

y=4.

Not sure if this is right. please check other answers

Answer:

91.99%

Step-by-step explanation:

To find what percentage of $7599 is $6990, we simply need to divide $7599 by $6990 and multiply by 100:

6990 / 7599 * 100 = 91.99%

Therefore, they paid 91.99% of the original price.

Answer:

The answer is C, 60 degrees.

Step-by-step explanation:

Answer:

[tex] \boxed{Number \: that \: give \: average \: of \: 27 \: with \: 12 \: is \: 42} [/tex]

Step-by-step explanation:

Let the number be 'x'

[tex] = > \frac{x + 12}{2} = 27 \\ \\ = > x + 12 = 27 \times 2 \\ \\ = > x + 12 = 54 \\ \\ = > x = 54 - 12 \\ \\ = > x = 42[/tex]

Answer:

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.

Step-by-step explanation:

hope this helps you :)

Answer

Go 6 across to the right and 8 up from there

Step-by-step explanation:

Answer:

This is a coordinate, and it tells you where to plot a point on a set of axis. The first number in the coordinate tells you the x-value and the second one tells you the y-value. X-values go across the horizontal axis, known as the x-axis. Y-values go up and down the vertical axis, known as the y-axis.

In this case, to plot the point, you would start at the very center of the axis, where y and x both equal 0. You'd go 6 to the right, because they gave you a positive x-value. The you'd go up 8, because they gave you a positive y-value.

If they give you a negative x-value, you'd go to the left, and if they give you a negative y-value, you'd go down.

Hope that helped : )

Answer:

dimensions are 2.19 inches by 9.14 inches

Step-by-step explanation:

Here, we are interested in knowing the dimensions of the rectangle

Now, let the width of the rectangle be x, from the question, we can write;

6x-4 as the length

Area of rectangle = l * b

x(6x-4) = 20

6x^2 - 4x = 20

divide through by 2

3x^2-2x = 10

3x^2 -2x -10 = 0

using quadratic formula;

x = -b ± √(b^2 - 4ac)/2a

From the quadratic equation, a = 3, b = -2 and c = -10

substituting these values, we have

x = 2 ± √(-2)^2 -4(3)(-10))/6

x = 2 ± √(124)/6

x = 2 + √(124)/6 or 2 - √(124)/6

x = (2+11.14)/6 or (2-11.14)/6

x = 2.19 or -1.52

Since width cannot be negative, we choose 2.19 alone

So the length is 6(2.19) -4 = 9.14

Answer:

apparently just label each part ( a, b, c, d, so on) and tell the order/ switch em around

Step-by-step explanation:

Answer:

area = 4cm2

Step-by-step explanation:

the area of triangle is gotten by 1/2bh

1/2 × 2 × 4 = 4.

base is 2cm because it has covered 2 grids while the height is the measure from the base to the tip of the triangle, which is 4cm.

area of square is L × L

2 by 2 = 4.

so, the two shapes have same area.

Answer:

A=(1/2)(b)(h)

Step-by-step explanation:

The area of a triangle is 1/2(b)(h), so in this case, A=(1/2)(24)(16)=192

Answer:

([tex]\frac{13}{5}[/tex] , [tex]\frac{6}{5}[/tex] )

Step-by-step explanation:

Given the 2 equations

2x - y - 4 = 0 → (1)

3x + y - 9 = 0 → (2)

Adding the 2 equations term by term will eliminate the term in y, thus

5x - 13 = 0 ( add 13 to both sides )

5x = 13 ( divide both sides by 5 )

x = [tex]\frac{13}{5}[/tex]

Substitute this value into either of the 2 equations and evaluate for y

Substituting into (2)

[tex]\frac{39}{5}[/tex] + y - 9 = 0

- [tex]\frac{6}{5}[/tex] + y = 0 ( add [tex]\frac{6}{5}[/tex] to both sides )

y = [tex]\frac{6}{5}[/tex]

Solution is

([tex]\frac{13}{5}[/tex] , [tex]\frac{6}{5}[/tex] )

Answer:

49

Step-by-step explanation:

Add then subtract

Answer:

150

Step-by-step explanation:

Step 1: Plug in what we know

5x + 10(5) = 800

Step 2: Solve for x (smaller cars)

5x + 50 = 800

5x = 750

x = 150

Answer:

150

Step-by-step explanation:

:)

Answer:

(6, 3)

Step-by-step explanation:

Since, the triangle PQR is rotated 360° around the origin so, Q' will coincide with Q, and in this way their coordinates would be same.

Therefore, Q' (6, 3)

The correct answer is (6,3)

Because if you rotate any coordinate points 360 degrees around the origin, it will always remain the same.

Hope this helps :D

Don't forget to mark the other guy brainliest ;)

Answer:

21%

Step-by-step explanation:

Out of the 25 + 9 + 12 + 21 + 12 + 21 = 100 total rolls, 6 came up 21 times so the percentage is 21/100 = 21%.

Answer:

0.40x=1900

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

All angles = 180

All sides are equal

Therefore, 180/3 = angle degrees = 60

x is an opposite angle of bottom right angle therfore x = 60

Answer:

(a) x = 60°

(b) Angle x is alternate to the right base angle of the equilateral triangle.

Step-by-step explanation:

(a) The triangle in the figure above is an equilateral triangle in which all sides and angles are equal. The sum of angles in a triangle is 180°. Each angle in the equilateral triangle is 60° (180°/3 = 60°)

Therefore, angle x is 60°.

(b) Alternate angles are equal. Angle x and the right base angle of the equilateral triangle are alternate angles. Therefore, angle x is 60°.

Answer:

A) inside the circle

Step-by-step explanation:

equation of the circle is:

[tex](x-a)^{2} + (y-b)^{2} = r^{2}[/tex]

where (a,b) is center of the circle and r is radius so

[tex]x^{2} + y^{2} = r^{2}[/tex] now plug in given point to find the radius

[tex](6)^{2} + (-4)^{2} = r^{2}[/tex]

36 +16 = 52 so

r = [tex]\sqrt{52}[/tex]  ≈ 7.2 or  [tex]r^{2} =52[/tex]

when you plug point (√2 , -7) into equation of the circle

(√2)^2 + (-7)^2 = 2 +49 =51

51 is less than 52 so this is inside of the circle