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3 years ago

Question 4 of 10

Mathematics

2 answers:

Tatiana [17]3 years ago

8 0

Answer: x=-4
-8=32
=-4

natima [27]3 years ago

5 0

Answer:

The answer is B, -4

Step-by-step explanation:

Subtract 4 on both sides

$-8x=32\\$

Divide both sides by -8

$x=-4$

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At a basketball game, a vender sold a combined total of 200 sodas and hot dogs. The number of sodas sold was three times the num

Nataliya [291]

Answer:

50 hot dogs

150 sodas

Step-by-step explanation:

set up a system of equations where 'h' = # hot dogs sold and '3h' = # sodas sold

h + s = 200

s = 3h

h + 3h = 200

4h = 200

h = 50

s = 200-50 or 150

4 0

3 years ago

Topic: Integrals

Tpy6a [65]

9514 1404 393

Answer:

11 7/16

Step-by-step explanation:

The integration resolves into finding the area of two triangles. The left has a height of (-3/8(-2/3)+2) = 2 1/4, and a width of (16/3-(-2/3)) = 6. Then its area is ...

A = (1/2)bh = (1/2)(6)(2 1/4) = 6 3/4

The right triangle has a height of |(-3/8)(31/3) +2| = |-31/8+16/8| = 15/8. Its width is (31/3) -(16/3) = 5, so its area is ...

A = (1/2)(5)(15/8) = 75/16 = 4 11/16

Then the total area, the value of the integral, is ...

6 3/4 +4 11/16 = 10 23/16 = 11 7/16 . . . the value of the integral

6 0

3 years ago

9. Two points in the plane, A(−3,8) and ????(17,8), represent the endpoints of the diameter of a circle.

kherson [118]

Answer:

a) (7,8)

b) r = 10

c) $(x-7)^2+(y-8)^2=100$

Step-by-step explanation:

a) Given the endpoints the diameter of the circle as A(-3,8) and B(17,8)

we should realize that the center of the circle lies exactly at the midpoint of these two points. let's denote the midpoint as $(x_m,y_m)$

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{-3+17}{2},\dfrac{8+8}{2}\right)$

$(x_m, y_m) = (7,8)$

this is the coordinate of the center of the circle.

b) The radius of the circle can be easily found by using the distance formula between the center point and either of the two endpoints of the diameter.

the general distance formula is:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

in our case the equation changes to: (selecting the centre and point B)

$r = \sqrt{(x_m-x_2)^2+(y_m-y_2)^2}$

$r = \sqrt{(7-17)^2+(8-8)^2}$

$r = 10$

side note: there are more alternate ways to find the radius for e.g (you can use the distance formula between the points A and B and that'll give you the length of the diameter which you can divide by 2 to get the radius) OR (you don't need to use the distance formula at all <u>since in this particular case</u> all the coordinates lie on the same horizontal line, so by simply subtracting the two x-coordinates of the center and either of A or B)

c) the ingredients needed to make the equation of the circle are the

coordinates of the center: $(x_m,y_m) = (7,8)$
radius of the circle: $r = 10$

we can put this in the formula of the circle:

$(x-a)^2+(y-b)^2=r^2$

in our case the equation changes to:

$(x-x_m)^2+(y-y_m)^2=r^2$

$(x-7)^2+(y-8)^2=(10)^2$

$(x-7)^2+(y-8)^2=100$

this is the equation of the circle!

6 0

3 years ago

what solid 3D object is produced by rotating the triangle about line m with a height of 8 and radius 4

Oksi-84 [34.3K]

Answer:

The diagram of the question is missing, I found a matching diagram, and it is attached to this answer

The 3D object produced is a cone with height 8 and diameter 8 (radius 4)

Step-by-step explanation:

A 3 dimensional solid figure can be formed when a 2 dimensional object is rotated about a line without displacing the object.

when the object in the diagram is rotated about line m, the rotation forms an object with a circular base of diameter 8 units (radius 4) from the base of the triangle and height 8 units, and the 3D object formed is called a cone.

3 0

3 years ago

Write each binomial square as a trinomial. <img src="https://tex.z-dn.net/?f=%28x-6%29%5E2" id="TexFormula1" title="(x-6)^2" alt

bogdanovich [222]

The answer is: X^2 - 12x + 36 hope that helps

7 0

3 years ago