4 times a number cubed decreased by 7

Choose the answer to complete each statement

NeTakaya

Answer:

1. The slope of the line is 7/3

2. y intercept is -3

3. y= 7/3x -3

Step-by-step explanation:

To find the slope of the line you use the equation y2-y1/x2-x1

y2 and y1 are y coordinates of the 2 coordinates on the same line that you want to find the slope of and the same with x2 and x1

The y-intercept is the point where the line crosses the y axis and x= 0

the equation of a line is y= mx+b

m= slope

b= y intercept

7 0

1 year ago

Javier has four cylindrical models. The heights, radii, and diagonals of the vertical cross-sections of the models are shown in

Sever21 [200]

Given the heights, radii, and diagonals of the vertical cross-sections of the models, the model in which the lateral surface meet the base at a right angle is the model in which the height, the diameter and the diagonal of the vertical cross-section forms a right triangle.

i.e. the sum of the squares of the height (h) and the diameter (d) gives the square of the diagonal vertical cross-section (l).

For model 1:

radius: 14 cm, thus diameter = 2(14) = 28 cm
height: 48 cm
diagonal: 50 cm

 $d^2+h^2=28^2+48^2 \\ \\ =784+2,304=3,090\neq50^2=l^2$

Thus, the lateral surface of model 1 does not meets the base at right angle.

For model 2:

radius: 6 cm, thus diameter = 2(6) = 12 cm
height: 35 cm
diagonal: 37 cm

[tex]d^2+h^2=12^2+35^2 \\ \\ =144+1,225=1,369=37^2=l^2[/tex]

Thus, the lateral surface of model 2 meets the base at right angle.

For model 3:

radius: 20 cm, thus, diameter = 2(20) = 40 cm
height: 40 cm
diagonal: 60 cm

 $d^2+h^2=40^2+40^2 \\ \\ =1,600+1,600=3,200\neq60^2=l^2$

Thus, the lateral surface of model 3 does not meets the base at right angle.

For model 4:

radius: 24 cm, thus, diameter = 2(24) = 48 cm
height: 9 cm
diagonal: 30 cm

 $d^2+h^2=48^2+9^2 \\ \\ =2,304+81=2,385\neq30^2=l^2$

Thus, the lateral surface of model 3 does not meets the base at right angle.

Therefore, the model in which the lateral surface meets the base at a right angle is model 2 (option b)

8 0

2 years ago

Read 2 more answers

How can you use the quotients to determine similarity ?

Gekata [30.6K]

Answer:

See below

Step-by-step explanation:

When two triangles are similar, all of their corresponding angles are the same, as well as a constant ratio of side lengths. This means that the quotient of the length of one of the triangles sides to the length of the other triangle's corresponding sides is the exact same as the quotient between any other pair of corresponding sides on the two triangles.

Hope this helps!

4 0

1 year ago

Read 2 more answers

Interest centers around the life of an electronic component. Suppose it is known that the probability that the component survive

astraxan [27]

Answer:

a) The probability that the life of the component is less than or equal to 6000 hours is 58%

b) The probability that the life is greater than 4000 hours is 96%

Step-by-step explanation:

Let's define the variable time as $t$ , which is measured in hours. Then, according to the problem:

The probability that the component survives for more than 6000 hours is 0.42 $\rightarrow P(t> 6000) = 0.42$
The probability that the component survives no longer than 4000 hours is 0.04 $\rightarrow P(t\leq 4000) =0.04$

a) The probability that the life of the component is less than or equal to 6000 needs to be equal to $1-P(t>6000)$ .

To see this, think of a full set, whose elements can be separate in two categories, the ones that survive more than 6000 hours (let's call them A and number of elements of this type Na) and the ones that survive less than or equal to 6000 (let's call them B and number of elements of this type Nb). Thus, the total number of elements can be calculate as $Na+Nb$ , which represents the unit.

If you want to calculate the proportion of elements of type A, you need to divide the number of element of type A over the total number of elements, which is $P(A) = Na/(Na+Nb)$ . And the same analysis applies to the proportion of elements of type B: $P(B) = Nb/(Na+Nb)$ . Hence, it is easy to see:

$P(A)+P(B) = \frac{Na}{Na+Nb} + \frac{Nb}{Na+Nb} = 1$

of course this only applies when the elements can be only categorized as one type or the other, which is call in probability, mutually exclusive events.

Using this for:

a) $P(t\leq 6000 )=1-P(t>6000) = 1 - 0.42 =0.58\\P(t\leq 6000 )=58\%$

b) $P(t> 4000 )=1-P(t\leq 4000) = 1 - 0.04 =0.96\\P(t> 4000 )=96\%$

3 0

2 years ago

Sue played four games of golf for these games her modal score was 98 and her mean score was 100 her range of score was 10 what w

earnstyle [38]

Answer : Remaining two observation becomes 97 and 107.

Explanation :

Since we have given that

Mean = 100

Modal value = 98

Range = 10

As we know that ,

Range = Highest-Lowest

Let highest observation be x

Let lowest observation be y

So equation becomes x-y=10 ----equation 1

So, observation becomes

x,98,98,y

Now, we use the formula of mean i.e.

Mean = $\frac{\text{Sum of observation}}{\text{N.of observaton}}$

So, mean = $\frac{x=98=98+y}{4}=400\\\frac{196+x+y}{4}=100\\x+y=400-196\\x-y=204$

So our 2nd equation becomes

x+y=204

On using elimination method of system of linear equation on these two equation we get,

x=97

and

$x+y=204\\y=204-x\\y=204-97\\y=107$

Hence , remaining two observation becomes 97 and 107.

8 0

1 year ago