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2 years ago

Which expressions are equivalent to 3(6+b)-(2b + 1)?

Mathematics

1 answer:

Anna [14]2 years ago

7 0

Answer:

18+3b-2b-1

b+17

Step-by-step explanation:

$\mathrm{Using\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b$

$-\left(2b+1\right)=-2b-1$

$=3\left(6+b\right)-2b-1$

$=18+3b-2b-1$

$\mathrm{Group\:like\:terms}$

$=3b-2b+18-1$

$\mathrm{Subtract\:the\:numbers:}\:18-1=17$

$=3b-2b+17$

$\mathrm{Add\:similar\:terms:}\:3b-2b=b$

$=b+17$

[RevyBreeze]

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Find the value of x

marin [14]

Answer:

$x=14$

Step-by-step explanation:

The given triangle is a right triangle, meaning it is a triangle with a right angle, this is indicated by the box around one of the angles. When given a right triangle, one can use the right triangle trigonometric ratios. These ratios describe the relationship between an angle in a right triangle, and the sides in a right triangle. Such ratios are as follows,

$sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}$

Bear in mind that the way one names the sides, in the sense of (opposite or adjacent) will change based on the angle one uses to describe the triangle. However, the hypotenuse is the same no matter the angle, as the hypotenuse is the side opposite the right angle.

In this case, one is given one of the angles, and the side opposite the angle. One is asked to find the hypotenuse of the triangle. One can use the sine (sin) ratio to achieve this.

$sin(\theta)=\frac{opposite}{hypotenuse}$

Substitute,

$sin(30)=\frac{7}{x}$

Inverse operations,

$x=\frac{7}{sin(30)}$

Simplify,

$x=14$

5 0

3 years ago

Problem: Match each value on the left with the number on the right that includes that value.

Anestetic [448]

Answer:

5 Thousands ⇒ 45,089

8 Hundreds ⇒ 958,823

3 millions ⇒ 3,072,700

2 Ten thousands ⇒ 7,426,580

7 Hundred Thousands ⇒ 752,671

Step-by-step explanation:

Solution:

We need match the numbers with given set of numbers.

Now,

5 thousands ⇒

So we can say that from given set of the numbers we need to find the number 5 belongs in thousands place.

So we can say that the number 5 in thousands place from given of number is ;

5 Thousands ⇒ 45,089

8 Hundreds ⇒

So we can say that from given set of the numbers we need to find the number 8 belongs in hundred place.

So we can say that the number 8 in Hundred place from given of number is ;

8 Hundreds ⇒ 958,823

3 Millions ⇒

So we can say that from given set of the numbers we need to find the number 3 belongs in millions place.

So we can say that the number 3 in Millions place from given of number is ;

3 millions ⇒ 3,072,700

2 Ten thousands ⇒

So we can say that from given set of the numbers we need to find the number 2 belongs in Ten thousands place.

So we can say that the number 3 in Ten Thousands place from given of number is ;

2 Ten thousands ⇒ 7,426,580

7 Hundred thousands ⇒

So we can say that from given set of the numbers we need to find the number 7 belongs in Hundred thousands place.

So we can say that the number 7 in Hundred Thousands place from given of number is ;

7 Hundred Thousands ⇒ 752,671

Hence the matching numbers are

5 Thousands ⇒ 45,089

8 Hundreds ⇒ 958,823

3 millions ⇒ 3,072,700

2 Ten thousands ⇒ 7,426,580

7 Hundred Thousands ⇒ 752,671

6 0

3 years ago

helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. she also needs 0.75 cup of sugar pe

tatuchka [14]

The <em><u>correct answer</u></em> is:

She can make 2 loaves of bread and 4 batches of muffins.

Explanation:

Let b represent bread and m represent muffins.

The equation for the amount of flour she needs is 3.5b+2.5m=17.

The equation for the amount of sugar she needs is 0.75b+0.75m=4.5.

To solve this, we will want to eliminate one of the variables. To do this, we will make the coefficients of one of the variables the same. If we multiply 2.5 by 0.3, we get 0.75; this is what we will do to the first equation:

$\left \{ {{0.3(3.5b+2.5m=17)} \atop {0.75b+0.75m=4.5}} \right. \\ \\\left \{ {{1.05b+0.75m=17} \atop {-(0.75b+0.75m=4.5)}} \right. \\ \\0.3b=0.6 \\ \\\frac{0.3b}{0.3}=\frac{0.6}{0.3} \\ \\b=2$

She can bake two loaves of bread.

Substituting 2 for b in the first equation, we have

3.5(2)+2.5m=17

7+2.5m=17

Subtract 7 from each side:

7+2.5m-7=17-7

2.5m=10

Divide both sides by 2.5:

2.5m/2.5 = 10/2.5

m = 4

She can bake 4 batches of muffins.

6 0

4 years ago

Read 2 more answers

A three-dimensional figure with one circular or elliptical base and a curved surface that joins the base to the vertex is called

babunello [35]

Answer:

a cone

Step-by-step explanation:

If the base is circular, then the cone is said to be a "regular" or "circular" cone, much like an ice cream cone.

If the base is elliptical, then it becomes an "elliptical" cone.

Both shapes can be right (where the perpendicular line dropping from the vertex lands on the exact center of the base) or oblique (when the line dropping from the vertex doesn't land on the center of the base)

3 0

3 years ago

Solve for x.4(2x + 3) = 3x + 3 + 2x

ElenaW [278]

Answer:

The value of x is -3.

Explanation:

Given the equation: