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2 years ago

Part A: Solve the equation 5(x + 2) = 6x + 3x − 14, and show your work. (5 points)

Mathematics

1 answer:

Cerrena [4.2K]2 years ago

8 0

Answer:

x = 6

Step-by-step explanation:

Step 1 - Expand brackets via distributive property:

$5(x + 2) = 6x + 3x - 14\\5(x) + 5(2) = 6x + 3x - 14\\5x + 10 = 6x + 3x - 14$

Step 2 - Combine like terms:

$5x + 10 = 6x + 3x - 14\\5x + 10 = 9x - 14$

Step 3 - Use the addition property of equality to isolate the 9x:

$5x + 10 = 9x - 14\\5x + 10 + 14 = 9x - 14 + 14\\5x + 24 = 9x$

Step 4 - Use the subtraction property of equality to move the 5x over and isolate the 24:

$5x + 24 = 9x\\5x + 24 - 5x = 9x - 5x\\24 = 4x$

Step 5 - Use the division property of equality to simplify:

$4x = 24\\\\\frac{4x}{4} = \frac{24}{4}\\\\x = 6$

Hope this helps!

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Which of these numbers are relatively prime to 51? Select all that apply. da) 84 Ob) 70 Oc) 62 0d) 30

iren2701 [21]

Answer:

b) 70

c) 62

Step-by-step explanation:

Numbers are relatively prime when they have no factors in common.

The factors of 51 are ...

51 = 3×17

The factors of the other numbers are ...

84 = 2²×3×7 . . . . . has a factor of 3 in common with 51

70 = 2×5×7 . . . . . . no factors in common

62 = 2×31 . . . . . . . no factors in common

30 = 2×3×5 . . . . . has a factor of 3 in common with 51

The numbers 70 and 62 are relatively prime to 51.

6 0

1 year ago

Try to find x & y. I need it so much please

kumpel [21]

Answer:

x = 3

y = 5

Step-by-step explanation:

Using theorem of similar triangles, we have,

(6 + x)/6 = (7 + 3.5)/7

(6 + x)/6 = 10.5/7

Cross multiply

7(6 + x) = 10.5(6)

42 + 7x = 63

7x = 63 - 42

7x = 21

x = 21/7

x = 3

Thus:

7.5/y = (7 + 3.5)/7

7.5/y = 10.5/7

Cross multiply

7.5*7 = 10.5*y

52.5 = 10.5*y

Divide both sides by 10.5

52.5/10.5 = y

y = 5

3 0

2 years ago

PLEASE ANSWER I WILL MARK AS BRAINLIEST

Tomtit [17]

Answer:

Six

Step-by-step explanation:

1.Convert all volumes to millilitres

(a) Chlorpheniramine

V = 100 mL

(b) Lidocaine

$V = \text{2 fl oz} \times \dfrac{\text{29.57 mL}}{\text{1 fl oz}} = \textbf{59 mL}$

(c) Banana flavouring

$V = \dfrac{1}{2}\text{ tsp} \times \dfrac{\text{4.928 mL}}{\text{1 tsp}} = \textbf{2.5 mL }$

2. Calculate the total volume

Chlorpheniramine = 100 mL

Lidocaine = 59

Banana flavouring = <u> 2.5 </u>

TOTAL = 162 mL

3. Calculate the number of doses

$\text{Doses} = \text{162 mL} \times \dfrac{\text{1 dose}}{\text{10 mL}} = \text{16.2 doses}\\\\\text{You can't take a fraction of a dose, so the there are $\large \boxed{\textbf{16 doses}}$}$

5 0

2 years ago

At the fair, 2 corn dogs and 3 pretzels cost $13, and 5 corn dogs and 6 pretzels costs $28. How much

NemiM [27]

Let x represent the cost of corn dogs. Let y represent the cost of pretzels.

2x+3y=13
5x+6y=28

Multiply the first equation by two so that we can eliminate y.

Subtract:
4x+6y=26
5x+6y=28

-x=-2
x=2

4(2)+6y=26
8+6y=26
6y=18
y=3

3 x 2 = 6
6+2=8

Therefore, 2 pretzels and a corn dog would cost $8.

5 0

2 years ago

What is the recursive formula for this arithmetic sequence?<br> -7,-1,5, 11, ...

Serhud [2]

Answer:

Step-by-step explanation:

The recursive formula allows us to find any term in a sequence by adding the common difference d to the previous term.

Here d = - 1 - (- 7) = - 1 + 7 = 6 , then

$a_{n}$ = $a_{n-1}$ + 6 ; a₁ = - 7

4 0

2 years ago