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xxTIMURxx [149]
2 years ago
7

The table shows expressions to represent the number of students involved in different activities. The number of students involve

d in sports and student council is equal to the number of students involved in band and drama club. Model the situation with an equation. Select the correct expression for each box. Then solve the equation.​

Mathematics
1 answer:
Maurinko [17]2 years ago
6 0

Answer:

6n + 7 = 7n

Step-by-step explanation:

Number of students involved in sports = 5n + 7

Number of students involved in student council = n

Number of students involved in sports and student council = (5n + 7) + n = 5n + 7 + n = 6n + 7

Number of students involved in band = 3n - 2

Number of students involved in drama club = 2(2n + 1)

Number of students involved in band and drama club = (3n - 2) + 2(2n + 1) = 3n - 2 + 4n + 2 = 7n

Equation to model number of students involved in sports and student council which equal number of students involved in band and drama club:

6n + 7 = 7n

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What is the distance between (3, 5.25) and (3, –8.75)? 6 units 8.25 units 11.75 units 14 units
evablogger [386]
By using distance formula :


\text{Distance formula,}  \bold{  \boxed{ Distance = \sqrt{( x_{2} -x_{1})^{2}+(y_{2} -   y_{1})^{2}) }}}





Given points = ( 3 , 5.25 ) and ( 3 , - 8.75 )


\bold{Taking \:  \:  \:  x_{1}=3 \:   \: , \: \:   x_{2}= 3  \:  \: , \:   \:  y_{1}= 5.25 \:   \: ,  \:  \: y_{2}= -8.75}




On applying formula, we get


Distance = \sqrt{ ( x_{2}-x_{1})^{2}+(y_{2}-y_{1})^2} \\  \\  \\ Distance = \sqrt{ ( 3 - 3 )^{2} + ( - 8.75 - 5.25 )^{2}}  \\ \\ \\ Distance = \sqrt{ ( 0 )^{2}  + ( - 14)^{2}}  \\ \\ \\ Distance = \sqrt{ ( - 14 )^{2}} \\ \\ \\ Distance = \sqrt{ 14^{2}} \:\:\:\:\:\:\:\:\:\:\: \:  \:  \:  \:  \:  \:  \:  \:  | \bold{ ( - 14 )^{2} = 14^{2}}  \\  \\  \\ Distance =  {14}^{2 \times  \frac{1}{2} }  \\  \\  \\  Distance =  {14}^{1}  \\  \\  \\  Distance = 14 \: units








Hence, Option D is correct.
4 0
2 years ago
Read 2 more answers
Venita is factoring the expression 32 a b minus 8 b. She determines the GCF and writes the factored expression as 8 b (4 a minus
never [62]

Answer:

She subtracted the GCF from the second term in the expression instead of dividing.

Step-by-step explanation:

Given the expression 32ab-8b, to find the common greatest factor, we will bring out a function that us common to both terms 32ab and 8b. To do that, we need to first find their individual factors as shown:

32ab = (2×2×2)×2×2×a×(b)

8b = (2×2×2×b)

From both factors, the common terms are the values in parenthesis i.e 2×2×2×b = 8b

Hence the GCF of the expression 32ab - 8b is 8b. On factoring out 8b from the expression we will have;

= 32ab - 8b

= 8b(32ab/8b - 8b/8b)

= 8b(4a-1)

Comparing the gotten equation with Venita's own, 8b(4a-0), we can say that she correctly factored out the GCF but her error was that she subtracted 8b from the second term of the expression instead of dividing by 8b. 8b-8b is what gives her 0 making her expression wrong. She should have divided her second term also by 8b to have 8b/8b which results in 1 instead of 0 that venita got.

7 0
1 year ago
Read 2 more answers
It costs 20 cents to receive a photo and 30 cents to send a photo from a cellphone. C is the cost of one photo (either sent or r
ddd [48]

Answer:

(a) PC(C)=     \left \{ {{0.6 \ \ \ \ x=20} \atop 0.4 \ \ \ \ {x=30}} \right. \\\ 0 \ \ \ \ \ \ \ else

(b) E[C] = 24 cents

Step-by-step explanation:

Given:

Cost to receive a photo = 20 cents

Cost to send a photo = 30 cents

Probability of receiving a photo = 0.6

Probability of sending a photo = 0.4

We need to find

(a) PC(c)

(b) E[C]

Solution:

(a)

PC(C)=     \left \{ {{0.6 \ \ \ \ c=20} \atop 0.4 \ \ \ \ {c=30}} \right. \\\ 0 \ \ \ \ \ \ \ else

(b)

Expected value can be calculated by multiplying probability with cost.

E[C] = Probability × cost

E[C] = 0.6\times20 +0.4 \times 30 = 12 + 12 = 24\  cents

3 0
1 year ago
Given circle X with radius 10 units and chord AB with length 12 units, what is the length of segment CX, which bisects the chord
andrew-mc [135]
Consider the circle with center X, as shown in the figure. 

Draw the diameter of the circle which is parallel to cherd AB, as shown in the figure.

Since the diameter and AB are parallel, then the line segment XC which bisects AB at C, will be perpendicular to AB.

SO triangle XCB is a right triangle. Thus the length of CX, by the Pythagorean theorem is  

\sqrt{ XB^{2}- CB^{2}} = \sqrt{ 10^{2}- CB^{6}}= \sqrt{100-36}= \sqrt{64}=8 units.


Answer: 8 units

7 0
2 years ago
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Irina-Kira [14]

Answer:

11/13

Step-by-step explanation:

198/234

(198/18)/(234/18)

11/13

4 0
2 years ago
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