3. Find the values of a and b. 36° 113° O​

The volume of a right square pyramid PABCD is 50.91 cubic units

Let l be the side length of right squared pyramid and h be the height.

We know that the formula for the volume of the right squared pyramid.

V = a²h / 3

And the formula for the height of right squared pyramid.

h = (1/√2)a

Here, the side length (a) = 6 units

So, using above formula of height,

h = (1/√2) × 6

h = 6/√2

h = 3√2 units

Now using the formula for the volume of the right squared pyramid, the volume of pyramid PABCD would be,

V = (6² × 3√2) / 3

V = 6² × √2

V = 36√2

V = 50.91 cubic units

Therefore, the volume of PABCD is 50.91 cubic units

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The solution of the equation is x = -1 and y = -3.

And the intersection point is (-1, -3).

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation.

And simultaneous equation is the system of equation.

Given system of equations:

y = x-2      ...... equation 1

y = −3x−6  ...... equation 2

To solve the system of equations:

Substitute the value of y from the equation 1 to equation 2,

we get,

x - 2 = -3x - 6

x + 3x = -6 + 2

4x = -4

x = -1

Then y = -1 -2 = -3.

By graphically:

1). Draw the linear equation on the graph.

2). And the intersection point of the lines is a solution of the equation.

3). The solution is x = -1 and y = -3.

The complete graph is given in the attached image.

Therefore, the solution is x = -1 and y = -3.

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Answer:

156km

Step-by-step explanation:

Given data

The red Maserati traveled at a speed of 120km/h for 5 hours one day.

Distance = speed*time

Distance= 120*5

Distance= 600km

The green Ford Pickup traveled at a speed of 74km/h for 6 hours

Distance = speed*time

Distance= 74*6

Distance= 444km

Hence the difference is

=600-444

=156km

Answer:

Incomplete Question. Send Full question pls.

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

Explanation:

Let x be the number of gallons used up. It's some positive real number.

We'll use the formula

miles = (mpg)*(number of gallons)

to help figure out how much fuel is used. The trip is 432 miles, and the mpg rating is 31

So,

miles = (mpg)*(number of gallons)

432 = 31*x

31x = 432

x = 432/31

x = 13.9354838709678  which is approximate.

Multiply that with the 2.79 to get the final answer.

2.79*x = 2.79*13.9354838709678 = 38.8800000000001

The 1 at the very end is probably due to some rounding error, but then again it may be accurate. Either way, that value rounds to 38.88

Side note: The 31 mpg rating is very likely an average value and not the same throughout the trip. This is due to the car changing speeds at different points of the journey. In reality, the true answer will vary slightly from the 38.88 figure we just calculated (but it should be fairly close).

The total amount of money that Tom and his friend would spend on gas during the trip is $38.88.

The first step is to determine the total amount of gas that would be needed during the trip.

Gas that would be needed = 432 / 31 = 13.94

The second step is to multiply the gas that would be needed by the cost of gasoline: $2.79 x 13.94= $38.88

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Answer:

Step-by-step explanation:

Remark

The angle formed by the intersection of a tangent to a circle and an intersecting secant is 1/2 (Arc PS - arc PR)

PS = 208

PR = 74

Solution

x = 1/2 (208 - 74)

x = 1/2 (134)

x = 67

Answer:

58 gold tiles

Step-by-step explanation:

Let silver = s ; purple = p ; gold = g

Number of silver Tiles = 79

44 more silver tiles than purple tiles

Purple tiles = silver tiles - 44

Purple tiles = 79 - 44 = 35

23 more gold tiles than purple tiles:

Number of gold tiles = purples Tiles + 23

Number of gold tiles = 35 + 23 = 58 tiles

Answer:

i think it's C

Step-by-step explanation:

Answer:B

Step-by-step explanation: Because it right

The number √2 is called an irrational number because the value of √2 = 1.41421356... and the the value is non terminating and non repeating .

What are Irrational Numbers ?

The Numbers whose vales are Non Repeating and Non Terminating are called as Irrational Numbers ,

also the numbers that cannot be expressed on the form of [tex]\frac{p}{q}[/tex] are called as Irrational Numbers .

the number is given as √2 ;

we know that the values of √2 is = 1.41421356... ,

we see that the the value is non terminating and the numbers after decimal point are non repeating ,

Therefore  , the number √2 is an irrational number .

The given question is incomplete , the complete question is

Why the number √2 is called a Irrational Number ?

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Answer:

The first one 3^7 *1/3-4

Step-by-step explanation:

Step-by-step explanation:

ok so first use this formula. V= 4/3 * 3.14 * 9 to the power of 3. so multiply 4/3 and 3.14 and then multiply 9 and 9 and 9 and then multiply that all together

Answer:

3 and 3/20

Step-by-step explanation:

If Lin is solving the inequality [tex]15-x < 14[/tex] and she know the solution is x = 1 , then the solution of  inequality is [tex]x > 1[/tex] .

The inequality that Line is solving is [tex]15-x < 14[/tex] ,

the solution of the equation [tex]15-x = 14[/tex] is given as x = 1 ;

we have to find the value of x for which the given inequality expression is true ,

Case(i) , let us take [tex]x > 1[/tex] ,

So , putting x = 2 , in the inequality ,

we get ; [tex]15-2 < 14[/tex]

= 13 < 14 , that is TRUE .

Case(ii) , let us take [tex]x < 1[/tex] ,

So , putting x  = 0 in the inequality ,

we get ; [tex]15-0 < 14[/tex]

= 15 < 14 , that is FALSE .

Therefore , the solution of the inequality is x > 1 .

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If you double the amount of fluid ounces, the amount of cups also double

There is proportional relationship between the number of fluid ounces and the number of cups. So, the number of cups would change by the same factor as the number of fluid ounces.

The donation is proportional to the dinner bill

The donation for a dinner bill of $50 is $9

If there are 8 fluid ounces in one cup

8 : 1 = 16 : x

8/1 = 16/x

8 × x = 16 × 1

8x = 16

x = 16/8

x = 2

The difference between weight = 1

The difference between cost = $0.68 - $0.47

= $0.21

$0.89 - $0.68

= $0.21

$1.10 - $0.89

= $0.21

Cost of mailing 6-ounce letter

1 : 0.47 = 6 : x

1/0.47 = 6/x

1 × x = 6 × 0.47

x = $2.82

The donation for a dinner bill $50 is

Dinner bill : donation

25 : 4.50 = 50 : x

25/4.50 = 50/x

25 × x = 50 × 4.50

25x = 225

x = 225/25

x =$ 9

Therefore, there is a proportional relationship between two quantities if there is an equal change in the values of both quantities.

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Answer:

[tex] \approx \: 7.33 \: {cm}^{2} [/tex]

Step-by-step explanation:

Area of the blue shaded region

[tex] = \frac{ \theta}{360 \degree} \times \pi r_1^2 - \frac{ \theta}{360 \degree} \times \pi r_2^2 \\ \\ = \frac{ \pi\theta}{360 \degree} ( r_1^2 - r_2^2) \\ \\ ( r_1 = 4 \: cm, \: \: r_2 = 3\: cm, \: \: \theta = 120 \degree) \\ \\ = \frac{ 3.14 \times 120 \degree}{360 \degree} ( 4^2 - 3^2) \\ \\ = \frac{ 3.14 }{3} \times 7 \\ \\ = \frac{21.98}{3} \\ \\ = 7.32666667 \\ \\ \approx \: 7.33 \: {cm}^{2} [/tex]

Answer:

height 14 cm

Step-by-step explanation:

The volume of the cuboid whose dimensions are  l = 22 cm, b = 14 cm, h = 14 cm is 4312 cu. cm.

What is the Volume of Cuboid?

Volume of cuboid is the total space occupied by the cuboid in a three-dimensional space. A cuboid is a three-dimensional structure having six rectangular faces. These six faces of the cuboid exist as a pair of three parallel faces.

Here, length of cuboid = 22 cm

Breadth of cuboid = 14 cm

Height of cuboid = 14 cm

Volume of Cuboid = Length X Breadth X Height

                                = 22 X 14 X 14 cu. cm.

                                = 4312 cu. cm.

Thus, the volume of the cuboid whose dimensions are  l = 22 cm, b = 14 cm, h = 14 cm is 4312 cu. cm.

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Answer:

144 cm

Step-by-step explanation:

Bottom: 4x11 = 44

Side 3x4x1/2 = 6

Other side = 6 (same)

Slant = 3, 4 and the hypotenuse is 5 (pythagroem triple )

5x11 = 55

Back: 3x11= 33

44+6+6+55+33= 144

Answer:

a)  25

b) the square root of 36 should be done

Step-by-step explanation:

x² - 10x = 11

take half of 10 and square it

x² - 10x + 25 = 11 + 25

(x-5)² = 36

x-5 = [tex]\sqrt{36}[/tex]

x - 5 = 6  and  x - 5 = -6

x = 11  and  x = -1

Answer:

chick fil a

Step-by-step explanation:

because chick fil a is always right

Answer:

C)   [tex]\overline {AD}[/tex] ≅ [tex]\overline {AC}[/tex],  [tex]\overline {BD}[/tex] ≅ [tex]\overline {CD}[/tex], [tex]\overline {AD}[/tex] ≅ [tex]\overline {AD}[/tex]

Step-by-step explanation:

From the given diagram, we have;

Segment [tex]\overline {AB}[/tex] in triangle ΔABD is congruent to segment [tex]\overline {AC}[/tex] in triangle ΔACD

Segment [tex]\overline {AD}[/tex] is congruent to segment [tex]\overline {AD}[/tex]  by reflexive property

For ΔABD to be congruent to ΔACD, by the Side-Side-Side, SSS, congruency postulate, all the sides of ΔABD should be congruent to the corresponding side of ΔACD, the required added statement is therefore;

Segment [tex]\overline {BD}[/tex] is congruent to segment [tex]\overline {CD}[/tex]

The correct option is therefore option C;

[tex]\overline {AD}[/tex] ≅ [tex]\overline {AD}[/tex], [tex]\overline {BD}[/tex] ≅ [tex]\overline {CD}[/tex], [tex]\overline {AD}[/tex] ≅ [tex]\overline {AC}[/tex]

Answer:

c

Step-by-step explanation:

If Hermione paid 98 coins and Luna paid 28 coins, Hermione paid for 672 Chocolate Frogs.

We can start the problem by using algebra. Let x be the number of Chocolate Frogs that Hermione paid for. Then we know that:

x + (2016 - x) = 2016 (the total number of Chocolate Frogs)

Also, we know that the cost of the Chocolate Frogs Hermione paid is 98 coins, and the cost of the Chocolate Frogs Luna paid is 28 coins. Let's assume the cost of each Chocolate Frog is y. Then we can write:

x * y = 98 and (2016 - x) * y = 28

Now we have a system of two equations with two variables (x and y). To find the value of x, we can use any method to solve the system of equations, such as substitution or elimination.

Using substitution, we can solve for y in the second equation and substitute it into the first equation:

(2016 - x) * y = 28

y = 28 / (2016 - x)

x * (28 / (2016 - x)) = 98

x * (28 / (2016 - x)) = 98

x = 98 * (2016 - x) / 28

Solving for x, we get:

x = 2016/3

So Hermione paid for 2016/3 = 672 Chocolate Frogs.

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Answer:

Hermione paid for 1,568 frogs.

Step-by-step explanation:

First, do 98 + 28. That will give you 126. Then do 2,016 / 126. That gives you 16. 16 x 98 = 1568 frogs.

Let's do Luna's to check our work.

28 x 16 = 448 frogs. 448 + 1568 = 2,016. So, Hermione paid for 1,568 frogs.

Answer:

The common divisor that leaves a reminder of 6 is 324

Step-by-step explanation:

Given

1626, 1950 and 2274

Required

Common divisor that leaves a remainder of 6

First, we subtract 6 from each number

[tex]1626 - 6 = 1620[/tex]

[tex]1950 - 6 =1944[/tex]

[tex]2274 - 6 = 2268[/tex]

Next, we find the common divisor of 1620, 1944, 2268

[tex]1620 \to 2 * 2 *3 * 3*3*3*5[/tex]

[tex]1944 \to 2 * 2 * 2 * 3 * 3 * 3 * 3 * 3[/tex]

[tex]2268 \to 2 * 2 * 3 * 3 * 3 * 3 * 7[/tex]

The common factors are:

[tex]Common = 2 * 2 * 3 * 3 * 3 * 3[/tex]

[tex]Common = 324[/tex]

Answer:

Step-by-step explanation:

There are 100 cm in 1 meter. the dimensions are 400cm by 250cm. depending on which way you turn them, they will fit better. if you take 400 divided by 16, you will have a row of 25 wide and if you divide 250 by 10, you will have a length of 25. you now have 25 rows of 25. 25x25 is 625 tiles.

Hope this helps

Straight line has the equation is, y = 5x - 4.

An endless number of points that are connected on both sides of the point make up a straight line.

The slope of a straight line, "m," is determined by:

m = y2 - y1 / x2 - x1

A linear equation has the expression y = mx + b in slope-intercept form. X and Y are the variables in the equation. The numbers m and b stand for the line's slope (m) and the value of y at x = 0.

The graph's acquired points are (0,-4) and (1,1)

The slope is ,

m = 1-(-4) / 1-0

  = 5/1

  = 5

The line's equation will be as follows since it crosses the y-axis at its intersection point, where C = -4.

⇒ y = mx + c

⇒ y = 5x + (-4)

⇒ y = 5x - 4

As a result, y = 5x - 4 is the equation for the straight line depicted below.

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Answer:

1. y = -2x - 4

2. y = 3x + 2

3. Horizontal

Hello there!

Answer:

[tex]36 - 25x^{2}y^{2}[/tex]

Step-by-step explanation:

We can use the special formula:

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

If a = 6 and b = 5xy then:

[tex](6 - 5xy)(6 + 5xy) = 6^{2} - (5xy)^{2} = 36 - 25x^{2}y^{2}[/tex]

This is the final answer

But if we don't know this formula, we can solve it other way:

[tex](6 - 5xy)(6 + 5xy) = 6^{2} + 5xy * 6 - 5xy * 6 - (5xy)^{2} = \\\\= 6^{2} - (5xy)^{2} = 36 - 25x^{2}y^{2}[/tex]

An example of x-intercept is (3,0).

Here x=3 is the x-intercept in this line.

By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.

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270 mins - 10 laps

xmins -5 laps

(cross multiply)

270*5=10x

10x=1350

x= 1350/10

x=135 mins