the gold bar has a trapezium cross-sectional area.
gold has a density of 19.3 grams per cm^3
work out the mass of the gold bar in kg

Answer:

5

Step-by-step explanation:

use formula a^2+b^2=c^2

so 4^2+3^2=25

then we square root 25 to get the length

square root of 25 equals 5

so the length is 5

hope this helps!

Answer:

T = 2

Step-by-step explanation:

5 + 2T - 3 = 6

2 + 2T = 6

2T = 4

T = 2

Answer:

T=2

Step-by-step explanation:

first you're going to subtract the numbers 5-3=2

then you're going to move the constant to the right and change its sign(-2 now)

then you're going to do 6-2=4

divide both sides of the equation by 2

T=2

Answer:to determine if a solution is extraneous, we simply plug the solution into the original equation.

Step-by-step explanation:

hope this helps!

Answer:

to determine if a solution is extraneous, we simply plug the solution into the original equation.

Step-by-step explanation:

Answer: 230cm²

Step-by-step explanation:

>We can do this by splitting the figure into 2 trapeziums.

>Additionally, you can see that both trapeziums bear the same lengths a and b. Hence, we can use this formula: [tex]\frac{1}{2} * (a+b) * (total height)[/tex].

>Thus,

Area = [tex]\frac{1}{2} *(7+16)*20=230[/tex]

Answer:

115 sq cm

Step-by-step explanation:

the shared side (16 cm) separates these two shapes into two trapezoids

the formula for the area of a trapezoid is:

A = 1/2h(sum of bases)

the bases for the left trapezoid are 7 and 16 because they are parallel

the bases for the right trapezoid are also 7 and 16 because they are parallel

the height for one could be 'x' and for the other could be '20-x-'

Area of 1st trapezoid:

A = 1/2x(23)

   = 23x/2

Area of 2nd trapezoid:

A = 1/2(20-x)·(23)

   = 10-x/2·(23)

   = (230-23x)/2

If you add the areas together you get the following:

23x/2 + (230-23x)/2

= 230/2

= 115

Slope = (y2-y1) / (x2-x1)

9) (7 - -6)/(-11- 17) = 13/-28

10) (-5-4)/(-4-3)= -9/-7

11) (15-14)/(17- -20) = 1/37

12) (-7 - -18) /(-1 -11) = 11/-12

Answer:

3.106

Step-by-step explanation: hope this helps

Answer:

Step-by-step explanation:

[tex]Sin \ 15 =\dfrac{opposite \ side}{hypotneuse}\\\\\\0.2588=\dfrac{x}{12}\\\\\\0.2588*12=x[/tex]

x = 3.1056

x = 3.1

Answer:

D. y = 9x + 30.

Eric has thirty dollars when he starts, so he would be adding 30, and since he makes 9 dollars an hour, it would be 9x. therefore the answer is 9x + 30

Answer:

60º

Step-by-step explanation:

The interior angles of a triangle equals 180º. And 60+60+60=180, that is your answer.

Answer:

Because the side w is [tex]\frac{1}{2}[/tex]  the side opposite the right angle (the hypotenuse) + [tex]\sqrt{3\\}\\[/tex] (because of the 30-60-90 triangle), we just need to divide by the hypotenuse by 2 and then add three. Knowing this, our answer will come out to be 2 + [tex]\sqrt{3\\}\\[/tex] .

Step-by-step explanation:

Answer:

α = 44°

Step-by-step explanation:

For angle α, y is the opposite leg.

z is the hypotenuse.

sin α = opp/hyp

sin α = y/z

sin α = 0.7

α = sin-1 0.7

α = 44°

Answer:

Slope = -[tex]\frac{7}{3}[/tex]

Y-intercept = 4

Step-by-step explanation:

-> See attached

-> This equation is in slope-intercept form.

         [] When we use y = mx + b, the m is the slope and the b is our y-intercept.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

Answer:

248 tickets were students and 124 were adults! 372 ÷ 3 = 124 and 124 × 2 = 248 and 248 + 124 = 372 so

124 tickets for adults

and 284 tickets for students

91 customers

Step-by-step explanation:

(140x65)/100=91

Answer:

Step-by-step explanation:

The scale factor for each side is

12/7 = 1.714

What that means is that if you multiply the side length of the small square by the scale factor, you get the side length of the large square.

7 * 1.714 = 11.998 which is not exactly 12, but it is close enough.

Answer:

x=4.47

Step-by-step explanation:

this is the answer

Step-by-step explanation:

we can find the value of c by Pythagoras theorem

according to Pythagoras theorem

h² = a² + b²

where

h = hypotenuse (i.e. longest side of a right angled triangle)

a = side

b = base

so, we have to find h or hypotenuse here

h² = (24)² + (18)²

h = 576 + 324 = 900

h² = √900 = 30

c = 30

therefore, value of c is 30.

Hope this answer helps you dear!

Answer:

a = 3   b = -18   c = 11   d = 0

Step-by-step explanation:

The table tells you what value the function will product (y) if you input the corresponding value of x.

So, for example, if you input the value of x = 1 into the function, you will get y = -4.

If we substitute x = 0 and y = 0 into the function we can find the value of d immediately:

0 = a(0)³ + b(0)² +c(0) + d

0 = 0 + 0 + 0 + d

0 = d

As d = 0, we can now eliminate d and write the function as:

y = ax³ + bx² + cx

Now substitute the remaining pairs of values into y = ax³ + bx² + cx to create 3 equations:

1) When x = 1, y = -4

⇒ a(1)³ + b(1)² + c(1) = -4

⇒ a + b + c = -4

2) When x = 2, y = -26

⇒ a(2)³ + b(2)² + c(2) = -26

⇒  8a + 4b + 2c = -26

⇒  4a + 2b + c = -13

3) When x = 3, y = -48

⇒ a(3)³ + b(3)² + c(3) = -48

⇒ 27a + 9b + 3c = -48

⇒ 9a + 3b + c = -16

Now solve the system of 3 equations simultaneously to find the value of a, b and c.  To do this, reduce this to 2 equations with 2 unknowns by eliminating one of the unknowns from two pairs of equations:

Eliminate c by subtracting equation 1) from equation 2) to create equation 4):

2)  4a + 2b + c = -13

1)   a + b + c = -4

4)  3a + b = -9

Eliminate c by subtracting equation 2) from equation 3) to create equation 5):

3)  9a + 3b + c = -16

2)  4a + 2b + c = -13

5)  5a + b = -3

Now use equations 4) and 5) to find a and b, by subtracting equation 4) from equation 5) to find a:

5)  5a + b = -3

4)  3a + b = -9

6)  2a = 6

  ⇒  a = 6 ÷ 2 = 3

and substituting the found value of a into equation 4) or 5) to find b:

5)  5(3) + b = -3

      15 + b = -3

         ⇒ b = -18

Now substitute the found values for a and b into one of the original 3 equations to find c:

1)   a + b + c = -4

    3 - 18 + c = -4

              ⇒ c = 11

Therefore,  the function is   y = 3x³ - 18x² + 11x

Answer:

x=7

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

A line with undefined slope is a vertical line. A vertical line has the equation

x = anumber

The point you were given has an x and a y...(x,y) The first number is the x.

x = 7

That's it, thats the equation of a line with undefined slope that goes through (7, -3).

<<<Fun fact: Lines with 0 slope are horizontal lines and have the equation

y = anumber >>>

Answer:

3/20

Step-by-step explanation:

15% = [tex]\dfrac{15}{100}[/tex]

Divide the numerator and denominator by 5

       = [tex]\dfrac{3}{20}[/tex]

Answer:

3/20

15%/100% = 3/20 by dividing top and bottom by 5

15/5=3

100/5 =20

Hope this helps!

Answer:

3 egg for each cupcake

Step-by-step explanation:

60-24=36

36/12=3

Answer:

Where are the statements?

Step-by-step explanation:

Answer:

x=2 , y=6

Step-by-step explanation:

        3 x + 2 y =    18

        3 x +     y =   12

     (-)       (-)         (-)

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

                     y =    6

3x+6=12

=>3x=12-6

=>3x=6

=>x=6/3

=>x=2

Answer:

expression no make sense'

Step-by-step explanation:

Check the picture below.

Answer:

x < -7 or x > 13

Step-by-step explanation:

3 - x < -10 or 3 - x > 10

-x < -13      or    -x > 7

x > 13         or    x < -7

Answer: x < -7 or x > 13

Answer:

x < -7 or x > 13

Step-by-step explanation:

Solving Absolute Value

Possibility 1:

Step 1: Subtract 3 from both sides.

Step 2: Divide both sides by -1.

Possibility 2:

Step 1: Subtract 3 from both sides.

Step 2: Divide both sides by -1.

Therefore, the answer is x < -7 or x > 13.