If it takes me 20 minutes to get to work while traveling at an average speed of 60 mph, but it took me 17 minutes to get to work today, what was my average speed today?​

The length of the vinyl must be 10.2ft

We know that two of the angles of the triangle measure 45°, then we have a right triangle of 45°, 45°, 90°.

We know that the catheti measure 3 ft, using the pithagorean theorem, we know that the length of the hypotenuse is given by:

[tex]H^2 = (3ft)^2 + (3ft)^2[/tex]

[tex]H = \sqrt{2*(3ft)^2} = 4.2ft[/tex]

Then the perimeter of the triangle is:

P = 3ft + 3ft + 4.2ft = 10.2ft

The length of the vinyl must be 10.2ft

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Answer:

See below

Step-by-step explanation:

P = 4pir^2 l     divide both sides by  4 pi r^2

l  =  P /(4pir^2)

25

The angle sum theory says that the sum of all the interior angles in a triangle is 180 degrees.

Finding X

To solve for y, we must first find x. This way we know 2 of the interior angles. Luckily, angle x is a part of a linear pair.

Angle x and the angle with a measurement of 115 form a linear pair. Thus, we can create an equation to find x.

By subtracting 115 from both sides we know that x = 65.

Solving for Y

Now that we know x, we can find y. We know that one of the interior angles is 65 and that the other is 90 degrees. The square marking the bottom angles in the middle show that they are right angles.

Lastly, we can create a formula to find y with the angle sum theory.

Combine like terms

Subtract 155 from both sides

This means that the angle y is 25 degrees.

Answer:

D

Step-by-step explanation:

If you substitute the radius, 10, and the center of the circle, the origin (also known as (0,0) into the equation of a circle, you should get: [tex](x - 0)^{2} + (y - 0)^{2} = 10 ^{2} [/tex]

Multiplying this out should leave you with D as your answer.

The numerator for the following rational expression is 13

The rational expression is given as:

6/t + 7/t

Take the LCM of the denominator;

The LCM of t and t is t

So, we have:

6/t + 7/t = (6 + 7)/t

Evaluate the sum

6/t + 7/t = 13/t

13 is the numerator, while t is the denominator

Hence, the numerator for the following rational expression is 13

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If the square pyramid has side length 9 inches and volume of 270 inches cube then by putting the values within the formula of volume height are going to be 10 inches.

Given Length and volume of a square pyramid are 9 inches and 270 inches cube. Square pyramid is the pyramid having square base. It is a right square pyramid.

We know that the amount of square pyramid is 1/3 *[tex]l^{2} *h[/tex]

Put the values in formula to induce the values oh h.

Volume=1/3*[tex]9^{2}*h[/tex]

270=1/3* 81*h

h=(270*3)/81

h=810/81

h=10

Hence the peak of the square pyramid having length 9 inches and volume of 270 inches cube is 10 inches.

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The weight of each bag is 0.545 lb .

Weight in maths is the value of the mass of an object on a measuring scale , It is measured in pound , ounce , kilogram etc.

It is given that

Total weight of green grapes = 5.65 lb

Total weight of red grapes = 3.07lb

Total weight = 5.65 +3.07 = 8.72   lb

Total number of bags = 16

the weight of each bag

= 8.72 / 16

= 0.545 lb

Therefore the weight of each bag is 0.545 lb .

The complete question is

Emilio bought 5.65lb  of green grapes and  3.07lb of red grapes. He divided the grapes equally into 16 bags. If each bag of grapes has the same weight, how much does each bag weigh?

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The difference of two squares expression is (c) (5x + 3y)(5x - 3y)

The difference of two squares expression is represented as:

a^2 - b^2 = (a + b)(a - b)

Using the above as a guide, we have the following expression in option (c)

(5x + 3y)(5x - 3y)

Hence, the difference of two squares expression is (c) (5x + 3y)(5x - 3y)

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Answer:

52m

Step-by-step explanation:

rhombus

its like a slanted square

all its 4 sides are equal like a square

both pairs of opposite sides are parallel

when the diagonals criss cross they make 4 triangles inside

the sides of the rhombus become the hypotenuse of a triangles inside

if the diagonal is 24 and 10 then

its radius is 12 and 5

the sides of the rhombus become the hypotenuse of a triangle that have the sides 12 and 5

hypotenuse of a triangle that has the sides 12 and 5 is

13

(its a special triangle: its a 5, 12, 13 right triangle)

13 times 4 is 52

Answer:yes

15x times 2=30x

15x times 3= 45x

3y tines 2 =6y

3y times 3=9y

Step-by-step explanation:

Answer:

14x^7-56x^6=9

Step-by-step explanation:

distribute

(7x^2)(2x^3 +6)(x^2 -4 * 9=x)

(2x^3+6)(x^2 -4 * 9=x)=2x^5-8x^4=9

(7x^2)(2x^5-8x^4=9)

14x^7-56x^6=9

The function is an exponential function; the initial value is -6.1 and the base is 3

The equation of the function is given as:

y = -6.1 *(3^x)

An exponential function is represented as:

y = ab^x

Where:

Initial value = a

base = b

By comparison, we have

a = -6.1 and b = 3

Hence, the function is an exponential function; the initial value is -6.1 and the base is 3

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Answer: 105

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so

[tex]\frac{x}{14}=\frac{97.5}{13}\\\\=\frac{x}{14}=7.5\\\\x=\boxed{105}[/tex]

The value of the probability P(S or T) is 39%

The probability values are given as:

P(S) = 12% P(T) =27%

For mutually exclusive events,

P(S or T) = P(S) + P(T)

This gives

P(S or T) = 12% + 27%

Evaluate the sum

P(S or T) = 39%

Hence, the value of the probability P(S or T) is 39%

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Answer: 132 million

Exponential growth formula: [tex]P=A e^{rt}[/tex]

[P is final amount, A is initial amount, r is growth rate, x is time intervals]

To find growth rate:

[tex]112 = 107 e^{r(3)}[/tex]

[tex]3r= ln(112/107)[/tex]

[tex]r= ln(112/107)/3 = 0.01522334561[/tex]

Population in 2008:

[tex]P_{2008}=107 e^{(0.01522334561(14))}[/tex]

[tex]P_{2008}=132.4169522[/tex]

[tex]P_{2008}=132\:million \quad (rounded \:to\:nearest\:million)[/tex]

Answer:

The formula of volume of cube is l*b*h

45*25*10=11250 cubic cm

Step-by-step explanation:

volume =length×width ×height

given:

length:45 cm

width:25 cm

height(depth):10 cm

according to the question

45 cm×25cm ×10cm

11250 cubic cm

The solution to the quadratic equation by completing the square is x = -1 + √3, x = -1 - √3

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

x² + 2x - 2 = 0

x² + 2x + 1 - 1 - 2 = 0

(x + 1)² - 3 = 0

(x + 1)² = 3

x + 1 = ± √3

x = -1 ± √3

Thus, the solution to the quadratic equation by completing the square is x = -1 + √3, x = -1 - √3

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Answer:

See below

Step-by-step explanation:

density = mass/volume

   re-arrange to    density * volume = mass

                                 20 * 64 = 1280 gm

Density = mass/volume    

   re-arrange to      volume = mass / density

                                                 560 / 14 = 40 cm^3

The match of the multiplication problem with the simplified expressions is as follows:

The process involved in multiplying polynomial expression requires using all the parameters in parentheses to multiply each other.

From the given information:

[tex]\mathbf{4x(4x^2-x+3)}[/tex]

By using distributive law m(a+b+c) = ma + mb + mc

[tex]\mathbf{=4x(4x^2)+4x(-x)+4x(3))}[/tex]

= 16x³ - 4x² + 12x

(8x + 1)(2x -3)

By applying FOIL method: (a+b)(c+d) = ac + ad + bc + bd

= (8x (2x)) + (8x(-3)) + (1 × 2x) + (1 × (-3))

= 16x² - 22x - 3

4x² (4x)

Applying exponent rule; [tex]\mathbf{a^b*a^c = a^{b+c}}[/tex]

[tex]\mathbf{= 4x^2 (4x)= x^2*4^{1+1}x}[/tex]

[tex]\mathbf{= x^2*4^{2}x}[/tex]

[tex]\mathbf{= 4^{2}x^{2+1}}[/tex]

[tex]\mathbf{= 4^{2}x^{3}}[/tex]

[tex]\mathbf{= 16x^{3}}[/tex]

(2x + 3) (8x² - 4x + 3)

Using distributive parentheses:

= 2x(8x² - 4x + 3) + 3(8x² - 4x + 3)

= 16x³ + 16x² - 6x + 9

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The area of the figure is 11. 27 cm²

The figure given is a parallelogram

The formula for the area of a parallelogram is given thus;

Area = base × height

From the figure, we have that

base = 2. 3 cm

height = 4. 9 cm

Substitute into the formula

Area = 2. 3 × 4. 9

Area = 11. 27 cm²

Thus, the area of the figure is 11. 27 cm²

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The shaded region shown in the graph of the normal distribution corresponds to P(x < 92.5).

An equation is an expression that shows the relationship between two or more numbers and variables.

The z score shows by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean)/standard deviation

The diagram represents z < 1.5 mean = 100, standard dev = 5 hence:

-1.5 = (x - 100)/5

x = 92.5

The shaded region shown in the graph of the normal distribution corresponds to P(x < 92.5).

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The value of a and b are 5.5 and 11.0.

The sides a and b of the triangle can be found as follows:

∠B = 29°

c = 11

∠C = 75°

∠A = 180 - 75 - 29 = 76°

Using sine ratio,

b / sin 29° = 11 / sin 75

b sin 75 = 11 sin 29

b =  11 sin 29 / sin 75

b = 5.33290582271 / 0.96592582628

b = 5.51816958277

b = 5.5

Let's find a,

a / sin 76 = 11 / sin 75

a sin 75 = 11 sin 76

a = 11 sin 76 / sin 75

a = 10.673252989 / 0.96592582628

a = 11.0466922042

a = 11.0

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Answer:

If a numbed substitutes x in f (x), you must substitute that number in the function for x.

Step-by-step explanation:

f(5) = 3(5) + 2

f(5 )= 17

Answer:

The speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

Step-by-step explanation:

Let’s assume the speed of the plane =x miles/hr

And let the speed of wind =y miles/hr

So, the speed of the aeroplane in the direction of wind =(x+y) miles/hr

Speed of the aeroplane in the opposite direction of wind =(x–y) miles/hr

We know that, distance=speed×time

Then according to the given conditions, we have

3300=(x+y)×(3+(18/60))

here convert 18mins to hour by dividing by 60 and add to 3hrs.

⇒x+y= 3300/3.3

⇒x+y=1000 … (i)

And,

3300=(x-y)×(4+(24/60))

here convert 24mins to hour by dividing by 60 and add to 4hrs.

⇒x-y= 3300/4.4

⇒x-y=750 … (ii)

Adding equation (i) and (ii), we get

2x=1750

⇒x= 1750/2

=875

Substituting the value of x in equation (ii), we get

875−y=750

⇒y=875-750

⇒y=125

Therefore, the speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.

The answer is : True

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The value of m and n to show the solution of the equation x² + 6x - 5 = 0 is m = -3 and n = ± √14

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

x² + 6x - 5 = 0

x² + 6x = 5

x² + 6x + 9 = 5 + 9

(x + 3)² = 14

x + 3 = ±√14

x = -3 ± √14

The value of m and n to show the solution of the equation x² + 6x - 5 = 0 is m = -3 and n = ± √14

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Answer:

  1,16,00,000

Step-by-step explanation:

To round to the nearest lakh, identify the digit that is to the right of the number place representing 1 lakh. If it is 5 or greater, round up.

The value 1,15,78,995 is 115.78995 lakh. The digit to the right of the decimal point in this number is 7, which is greater than 4. Hence the nearest lakh is 116 lakh, or ...

  1,16,00,000

Answer:

[tex]y=-\frac{3}{2}x-3[/tex]

Step-by-step explanation:

The slope-intercept form is written as y= mx +c, where m is the slope and c is the y-intercept.

For the equation to be in the slope-intercept form, first leave the y term on the left-hand side of the equation and bring the rest to the right-hand side.

2y= -3x -6

Ensure that the coefficient of y is 1. In this question, we can divide both sides of the equation by 2 to achieve the slope-intercept form.

[tex]y=\frac{-3x}{2}-\frac{6}{2}[/tex]

Simplify:

[tex]\bf{y=-\frac{3}{2}x-3 }[/tex]

Additional:

For more questions on slope-intercept form, do check out the following!