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2 years ago

which of the following expressions is equivalent to 3a-2ax4a+6a? (a) 4a^2+6a (b)3a-20a^2 (c) 9a-8a^2 (d) a^2

Mathematics

1 answer:

lianna [129]2 years ago

4 0

Answer:

$\boxed{\sf (c) \ 9a - 8 {a}^{2}}$

Step-by-step explanation:

$\sf Simplify \: the \: following: \\ \sf \implies 3a - 2a \times 4a + 6a \\ \\ \sf - 2a \times 4a = - 2 {a}^{2} \times 4 : \\ \sf \implies \boxed{ \sf - 2 {a}^{2} \times 4} + 3a + 6a \\ \\ \sf - 2 \times 4 = - 8 : \\ \sf \implies \boxed{ \sf- 8} {a}^{2} + 3a + 6a \\ \\ \sf 3a + 6a = 9a : \\ \sf \implies 9a - 8 {a}^{2}$

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HJ is twice JK. J is between H and K. If HJ= 4x and HK=78, find Jk.

ss7ja [257]

You'll find it easier to understand if you illustrate the problem as what is shown in the attached picture. From the illustration and the problem description, two equations can be formulated:

HJ = 2JK
HJ + JK = HK

2JK + JK = 78
3JK = 78
JK = 78/3
JK = 26

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2 years ago

The table shows some values of a function of the form y = ax2 + bx + c.

natali 33 [55]

Answer:

Value of constant term c is (-4)

Step-by-step explanation:

The given table represents a function which is in the form of a quadratic equation,

y = ax² + bx + c

We choose three points (3, -10), (4, -16) and (5, -24) from the table and satisfy the equation to get the values of a, b, and c.

For point (3, -10)

-10 = a(3)² + 3b + c

9a + 3b + c = -10 -------(1)

For point (4, -16)

-16 = a(4)² + 4b + c

16a + 4b + c = -16 ------(2)

For point (5, -24)

-24 = a(5)² + 5b + c

25a + 5b + c = -24 -----(3)

Equation (1) - equation (2)

(9a + 3b + c) - (16a + 4b + c) = -10 + 16

-7a - b = 6

7a + b = -6 ------(4)

Equation (2) - equation (3)

(16a + 4b + c) - (25a + 5b + c) = -16 + 24

-9a - b = 8

9a + b = -8 -------(5)

Equation (4) - Equation (5)

(7a + b) - (9a + b) = -6 + 8

-2a = 2

a = -1

From equation (4),

-7(1) + b = -6

b = -6 + 7

b = 1

From equation (1)

9(-1) + 3(1) + c = -10

-9 + 3 + c = -10

c = -10 + 6

c = -4

Therefore, the value of constant term c is (-4).

5 0

2 years ago

A formula for 6 gallon of light green paint use 3/8 gallons of white paint. Liam has 9/16 gallon of white paint. Does liam have

FromTheMoon [43]

Answer:

Yes he have enough white paint.

Step-by-step explanation:

We are given

6 gallons of light green paint use → $\frac{3}{8}$ gallons of white paint

using the unitary method

1 gallons of white paint → 6*8/3 gallons of light green paint

→ 16 gallons of light green paint

but Liam have 9/16 gallons of white paint

9/16 gallons of white paint → 16* 9/16 gallons of light green paint

→ 9 gallons of light green paint

Yes Liam have enough white paint to make 8 gallons of light green paint.

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2 years ago

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sp2606 [1]

Lets take Gregs weight as “x”. This means that Justins weight is x-15, and x/2 = (x-15)-75.

If we take that last equation, lets combine like terms:

x/2 = x - 15 - 75
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Now multiply both sides by 2 to get rid of the fraction
x = 2x - 180
Subtract 2x from both sides
x - 2x = -180
-x = -180
x = 180 — this is Gregs weight

Justins weight is x-15, so 180-15, which is 165 pounds. Hope this helped.

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1 year ago

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notka56 [123]

Answer:

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The response variable is the one for which measurements are desired and that depends on other variables.

In this case, family size, household income, and household neighborhood are independent variables, while the response variable is the monthly household expenditures on groceries.

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2 years ago