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2 months ago

Two thirds a number plus 4 is 7

2 answers:

5 0

Assign the variable "x" to represent the unknown number.

The equation based on the statement is:
_____________________________________
(⅔)x + 4 = 7.
_____________________________________
To solve for "x":

First, subtract "4" from both sides:

(⅔)x + 4 − 4 = 7 − 4;

which simplifies to:

(⅔)x = 3;

Next, multiply both sides by "3" to eliminate the fraction's denominator:

3 × (⅔)x = 3 × 3;

resulting in: 2x = 9;

Finally, divide both sides by "2" to isolate "x":
__________________________________________________
(2x) / 2 = 9 / 2

x = 9/2 = "4 ½" or "4.5".
_______________________________________

zzz [12.3K]2 months ago

4 0

Let's denote the unknown number as 'n'.
The plus sign represents addition.
The word 'is' corresponds to the equals sign.

So, the expression can be written as: $\frac{2}{3}$ n + 4 = 7

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“The perimeter P of a triangle is equal to the sum of the lengths of sides a,b, and c”

AnnZ [12381]

Answer:

1. Calculate the sum of "a", "b" and "c".

2. The perimeter equation is: $P=a+b+c$

Step-by-step explanation:

In this case, P denotes the triangle's perimeter while a, b, and c are the triangle's sides.

The definition states that the sum results from an addition operation. Thus, the statement "The perimeter P of a triangle equals the total of sides a, b, and c" means that the perimeter is determined by aggregating the lengths of the triangle's sides.

Consequently, you can express this in the following equation:

$P=a+b+c$

5 0

2 months ago

Indicate the general rule for the arithmetic sequence with a3 = 8 and a8 = 33.

lawyer [12517]

Answer:

$u_{n} = -2 + (n-1)5$

Step-by-step explanation:

$u_{n} = a + (n-1)d$

$u_{3} = a + (3-1)d = 8$

$u_{3} = a + 2d = 8$

$u_{8} = a + (8-1)d = 33$

$u_{8} = a + 7d = 33$

Simultaenous Equations

a + 2d = 8

a + 7d = 33

By subtracting one equation from the other

(a + 7d = 33) - (a + 2d = 8)

(a - a) + (7d - 2d) = (33 - 8)

5d = 25

d = 25/5

d = 5

Now replace d in either equation to solve for a

a + 2(5) = 8

a + 10 = 8

a = 8 - 10 = -2

a = -2

a + 7(5) = 33

a + 35 = 33

a = 33 - 35 = -2

a = -2

$u_{n} = -2 + (n-1)5$

6 0

1 month ago

Turkey sandwiches cost $2.50 and veggie wraps cost $3.50 at a snack stand. Ben has sold no more than $30 worth of turkey sandwic

tester [12383]

Answer:

Ben could have sold a maximum of 6 turkey sandwiches.

Step-by-step explanation:

Turkey sandwiches are priced at $2.50, while veggie wraps cost $3.50 at the snack stand.

Our goal is to determine the largest number of turkey sandwiches Ben might have sold.

$2. 5 0 x + 3. 5 0 y \leq 3 0$

4 veggie wraps were sold (y).

Thus, the inequality is: 2.50x + 3.50(4) < 30

2.50x + 14 < 30

- 14 - 14

2.50x < 16

$x$

Ultimately, Ben could sell a maximum of 6 turkey sandwiches.

4 0

2 months ago

Read 2 more answers

Given: <br> AB tangent at D, AD = OD = 4<br> Find: Area of the shaded region

lawyer [12517]

<span>With AB tangent at D, where AD = OD = 4
, triangle OAD forms a right angle with sides measuring 4 and 4.
So, the area of triangle OAD is computed as 1/2 * 4 * 4 = 8

The angles AOD and DAO equal 45 degrees.
Therefore, the area of circular sector OCD is calculated as the area of circle O multiplied by 45/360
= pi * 4 * 4 * 45/360
= 2pi

The shaded area ACD results from the triangle OAD minus the area of circular sector OCD
= 8 - 2pi
= 1.72

</span>

6 0

1 month ago

The volume of a large can of tuna fish can be calculated using the formula V= πr(r)h. Write an equation to find the radius, r, i

Zina [12379]

The formula can be applied to determine the radius. Step-by-step explanation: The volume of the larger can is given by V=πr(r)h or V=πr²h. To isolate r, divide both sides by πh. Then, by applying the square root to both sides and substituting π with 3.14, the resulting equation will yield the radius.

5 0

1 month ago