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1 year ago

Three times the sum of half Carlita's age and 3 is at least 12. What values represent Carlita's possible age?

Mathematics

2 answers:

a_sh-v [17]1 year ago

7 0

Answer:

Carlita is at least 2 years old

Step-by-step explanation:

Let x = Carlita's age

3[(1/2)x + 3] ≥ 12 Divide both sides by 3.

(1/2)x + 3 ≥ 4

(1/2)x ≥ 1

x ≥ 2

cestrela7 [59]1 year ago

5 0

Answer:

at least 6

Step-by-step explanation:

3(.5x+3)>12

1.5x+9>12

1.5>9

x>6

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It is 4.7 km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73°E. A ship has sailed due west from

Gennadij [26K]

Answer:

correct option is C. 3.7 km

Step-by-step explanation:

given data

A to Port B = 4.7 km

lighthouse = N73°E

lighthouse = N31°E

solution

we get here first $\angle$ B and

here

$\angle$ A = 90 - 73 = 17°

$\angle$ B = 73 - 31 = 42°

and

sum of all angle 180° so

$\angle$ A +

17° + 42° + $\angle$ C = 180°

solve it we get

$\angle$ C = 121°

Now we use here sin law that is

$\frac{b}{sinB} = \frac{c}{sinC}$ ........................2

put here value and we get

$\frac{b}{sin42} = \frac{4.7}{sin121}$

solve it we get

b = 3,7 km

so correct option is C. 3.7 km

7 0

2 years ago

∆ABC is translated 2 units down and 1 unit to the left. Then it is rotated 90° clockwise about the origin to form ∆A′B′C′.

RideAnS [48]

Answer:

The coordinates of image are A'(-2,1), B'(1,0) and C'(-1,0).

Step-by-step explanation:

From the figure it is clear that the coordinates of triangle are A(0,0), B(1,3) and C(1,1).

∆ABC is translated 2 units down and 1 unit to the left.

$(x,y)\rightarrow (x-1,y-2)$

$A(0,0)\rightarrow (0-1,0-2)=(-1,-2)$

$B(1,3)\rightarrow (1-1,3-2)=(0,1)$

$C(1,1)\rightarrow (1-1,1-2)=(0,-1)$

Then it is rotated 90° clockwise about the origin to form ∆A′B′C′.

$(x,y)\rightarrow (y,-x)$

$(-1,-2)\rightarrow A'(-2,1)$

$(0,1)\rightarrow B'(1,0)$

$(0,-1)\rightarrow C'(-1,0)$

Therefore the coordinates of image are A'(-2,1), B'(1,0) and C'(-1,0).

7 0

1 year ago

Which is equivalent toStartRoot 10 EndRoot Superscript three-fourths x ?

DENIUS [597]

Answer:

I THINK its the last one (8 root 10 to the power of 3x)

Step-by-step explanation:

A square root is the same thing as raising something to the 1/2. So the expression we have is (10^1/2)^3/4x.

Due to exponent rules we can multiply to get

10^3/8x which is the same thing as 10^3x/8

The 8 goes to the root and the 3x becomes the exponent

4 0

2 years ago

Jerry makes $40,000 a year working at a nearby factory. He gets two weeks paid vacation per year, plus five other paid holidays.

JulijaS [17]

Answer:

Vacation pays are not included in salaries. Therefore, Jerry's calculation is wrong.

Step-by-step explanation:

Given is :

Jerry makes $40,000 a year working at a nearby factory.

He gets two weeks paid vacation per year, plus five other paid holidays.

So total paid holidays become = $14+5=19$ days

Subtracting 19 from 365 days and assuming that Jerry works for 365 days a year.

We get = $365-19=346$ days

So, his per day salary will be = $\frac{40000}{346}= 115.60$

Vacation pays are not included in salaries. Therefore, Jerry's calculation is wrong.

4 0

2 years ago

Read 2 more answers

Consider this polynomial, where a is an unknown real number.

DENIUS [597]

Answer:

Step-by-step explanation:

Correct steps to find the value of 'a' should be,

Braulio's synthetic division should be,

-1 | 1 5 a -3 11

1 4 (a - 4) (1 - a) (a + 10)

Here remainder is (a + 10).

So (a + 10) = 17 ⇒ a = 7

Braulio Incorrectly found a value of 'a' because he should have used (-1) instead of 1.

Zahra's calculation by remainder theorem should be,

p(x) = x⁴ + 5x³ + ax² - 3x + 11

p(-1) = (-1)⁴ + 5(-1)³ + a(-1)² - 3(-1) + 11

= 1 - 5 + a + 3 + 11

= (a + 10)

Since, remainder of the solution is 17,

(a + 10) = 17 ⇒ a = 7

Zahra incorrectly found the value of 'a' because she incorrectly solved the powers to (-1).

8 0

2 years ago