which equation can be used to solve for x

Answer:

[tex]MN = \sqrt{14[/tex]

Step-by-step explanation:

Given

[tex]NO = 12[/tex]

[tex]OP = 2.5[/tex]

[tex]OQ = 4.5[/tex]

Required

Find MN

First, we calculate QP using Pythagoras theorem

[tex]OQ^2 = OP^2 + QP^2[/tex]

[tex]4.5^2 = 2.5^2 + QP^2[/tex]

[tex]20.25 = 6.25 + QP^2[/tex]

Collect like terms

[tex]QP^2 = 20.25 - 6.25[/tex]

[tex]QP^2 = 14[/tex]

Take square roots

[tex]QP = \sqrt{14[/tex]

To solve MN, we have:

[tex]MN = OP[/tex]

So:

[tex]MN = \sqrt{14[/tex]

Answer: 70ft

Step-by-step explanation:

ht= (-3)^2 + 15(3) + 16

ht= 9 + 45 + 16

ht= 70

Answer:

Equation: 180 = 127.50 + 3.5x

Angle 1: 135.45°

Angle 2: 44.55°

Step-by-step explanation:

The two angles form a straight line so they add to 180 degrees

9/4x + 101.7 + 1 1/4x +25.8 = 180

Change the mixed number to an improper fraction

9/4x + 101.7 + 5/4x +25.8 = 180

Combine like terms

14/4x +127.5 = 180

Subtract 127.5 from each side

14/4x = 180-127.5

14/4x = 52.5

Multiply each side by 4/14 to isolate x

x =52.5 * 4/14

x = 15

Angle 1 = 9/4x +101.7 = 9/4*15 + 101.7 = 33.75+101.7=135.45

Angle 2 = 1 1/4x +25.8 = 5/4 (15) +25.8 =18.75+25.8=44.55

Answer: Choice D

[tex]\frac{9\sqrt{2}}{2}[/tex]

=============================================

Explanation:

We have a 45-45-90 triangle. If x is the leg length, then y = x*sqrt(2) is the hypotenuse.

Solving for y gets us [tex]x= \frac{y}{\sqrt{2}} = \frac{y\sqrt{2}}{2}[/tex]

In this case, y = 9 is the hypotenuse which then leads to choice D.

------------

Another way to find the answer is to use the pythagorean theorem

a = x and b = x are the two congruent legs

c = 9 is the hypotenuse

Solving a^2+b^2 = c^2, aka x^2+x^2 = 9^2, will lead to [tex]x = \frac{9\sqrt{2}}{2}[/tex]

Answer:

a. 4

b. 5

Step-by-step explanation:

a. r = √(112/7) =√16 =4

b. 4x+8 = 28

4x = 28-8

4x = 20

x= 5

The value of X algebraically is 5 and the common difference is;4.

There are three parameters which differentiate between which geometric sequence we're talking about.

The first parameter is the initial value of the sequence.

The second parameter is the quantity by which we multiply previous term to get the next term.

We are given that  terms shown below are the first three terms of a geometric sequence whose common ratio is positive.

7, 4x+8, 112

Therefore, the common difference is;

r = √(112/7) =√16

r =4

Now, 4x+8 = 28

4x = 28-8

4x = 20

x= 5

The value of X algebraically is 5.

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Answer:

-2

Step-by-step explanation:

Well since this line is parallel to y=3x-5 they must have the same slope

We are just solving for the y-intercept

We have a point (2,4) lets plug it into

y=3x+ b

4 = 3(2) +b

4= 6 +b

-2 = b

The value of b is -2

Answer:

B-value = -2

Step-by-step explanation:

In the picture below Orange line represents the line of "y = 3x - 5", since we know that the line passing through the point (2,4) is parallel to the given line, the slope of the line would be 3x as well. To find b-value or y-intercept we have to plot the point on the graph where the line passing through the points (2,4) intersects the y-axis, in this case it's at (0,-2), therefore the b-value = -2.

Hope this helps!

Here is the diagram:

Answer:

Volume of Cuboid = 72 cubic feet

Step-by-step explanation:

Using 1 cubic foot as standard

Given:

Length of given cuboid = 6 feet

Width of given cuboid = 3 foot

Height of given cuboid = 4 foot

Find:

Volume of Cuboid

Computation:

Volume of Cuboid = Length of cuboid x Width of cuboid x Height of cuboid

Volume of Cuboid = (6)(3)(4)

Volume of Cuboid = 72 cubic feet

Given:

The figure of two triangles.

To find:

The similarity statement for the given triangles.

Solution:

The corresponding sides of similar triangles are proportional.

In the given triangles,

[tex]\dfrac{XY}{AB}=\dfrac{6}{12}[/tex]

[tex]\dfrac{XY}{AB}=0.5[/tex]

Similarly,

[tex]\dfrac{YZ}{BC}=\dfrac{3}{6}[/tex]

[tex]\dfrac{YZ}{BC}=0.5[/tex]

And,

[tex]\dfrac{XZ}{AC}=\dfrac{7}{14}[/tex]

[tex]\dfrac{XZ}{AC}=0.5[/tex]

Since [tex]\dfrac{XY}{AB}=\dfrac{YZ}{BC}=\dfrac{XZ}{AC}[/tex], therefore

[tex]\Delta XYZ\sim \Delta ABC[/tex]

It can be written as:

[tex]\Delta ZYX\sim \Delta CBA[/tex]

Therefore, the correct option is A.

Answer:

a common denominator

Step-by-step explanation:

Answer:

In mathematics, the intersection of two sets A and B, denoted by A ∩ B, is the set containing all elements of A that also belong to B (or equivalently, all elements of B that also belong to A).

Step-by-step explanation:

Answer:

21.42 cloves of garlic

Step-by-step explanation:

50 ÷ 7 = 7.14

7.14 x 3 = 21.42

Answer:

x = -6

Step-by-step explanation:

1/3(x-9)=2x+7

1/3x - 3 = 2x + 7

-5/3x = 10

x = -6

Answer:

1. 1.5 inches

2. 1 inch

3. 1.75 inches

4. 1.25 inches

5. 2 inches

Step-by-step explanation:

im guessing that you're asking what each place is.

Answer:

5894.82 ft^3

Step-by-step explanation:

We have to split the figure into two parts and then find the volume of both and add. The figure is split into a cylinder and hemisphere. The volume of the cylinder is 4823.04 ft^3 because the formula to find the volume of a cylinder is pi(r^2)h. The volume of the hemisphere is 1071.78 ft^3. Now, we have to add those volumes to get our final answer. 4823.04 + 1071.78 = 5894.82.

Answer:

V = 64 cm^3

Step-by-step explanation:

Volume is length times width times height

V = l*w*h

V = 4*4*4

V = 64 cm^3

Answer:

64

Step-by-step explanation:

4x4x4=64

Answer:

6/4

Step-by-step explanation:

Answer:

Exact Form:

3/2

Decimal Form:

1.5

Mixed Number Form:

1 1/2

Step-by-step explanation:

Answer:

12 no .

x+2(4/5)=3(1/6)

x+5*2+4/5=6*3+1/6

x+14/5=19/6

5*x+14/5=19/6(do cross multiplication)

6(x+14)=19*5

6x+84=95

6x=95-84

x=11/6

Step-by-step explanation:

13 no

-0.4a+1.2=3.6

-0.4a=3.6-1.2

a=2.4/-0.4

a=-6

Answer:

5 dogs

1 1/4 cups per bottle

Step-by-step explanation:

10/3 ÷ 2/3 get solved by 10/3 x 3/2, which gives you 30/6 or 5

45/8 ÷ 9/2 is 45/8 x 2/9 which is 5/4 or 1 1/4

Answer:

16 = x

Step-by-step explanation:

A triangle has 180 degrees. Use this to solve for x

180=(9x-8)+(x+2)+(x+10)

180 = 9x + x + x - 8 + 2 +10

180 + 8 -2 - 10 = 11 x

176 = 11x

176/11 = x

16 = x

Answer:

x = 16

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

x + (3x - 4) = 5 - (-7 - 3x)

Step 2: Solve for x

Answer:

About 64 Miles

Step-by-step explanation:

I think you just divide the miles by minutes which is about 1.06 then x 60 = 64

Humans knowingly create environmental disasters.

Step-by-step explanation:

Step-by-step explanation:

would you still like me to help you with this question

Angle of depression of the slope is 24. degree.

Angle of depression is equal to the angle of elevation.

sine = the vertical drop/ the ski slope

sine = 100/250

      = 2/5 = 0.4.

sine - 1 (0.4) = 23.57 which is about 24 degree.

Therefore, the correct angle of depression of the slope is approximately 24 degree.

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Answer:

It would be "a sentence that includes two independent clauses connected by a conjunction" which is Choice B.

Choice A wouldn't work as there needs to be two or more independent clauses for it to be a Compound Sentence.

Choice B would work, as it follows the definition of a Compound Sentence.

Choice C wouldn't work, that would be a Complex Sentence

Choice D wouldn't, that would be a Simple Sentence.

Also, note that this question is something for the Language Arts section.

Answer:

B. A sentence that includes two independent clauses connected by a conjunction.

Step-by-step explanation:

Compound sentences can make your writing very rich as you can connect two distinct independent clauses (no dependent clauses) using coordinating conjunctions such as for, and, nor etc (FANBOYS).

Example would be:

Juan likes to hunt, and he is going hunting on Sunday.

"Juan likes to hunt" is an independent clause where "Juan" is the subject, "likes" is the action, and a complete thought is expressed because we know what he likes to do now.

"He is going hunting on Sunday" is an independent clause where "He" is the subject, "is going" is the action, and a complete thought is expressed as we now know where he is going Sunday and what action he is doing.

The conjunction "and" is used, and a comma is correctly placed before "and."

The number of coloured papers as per the given problem is 18.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

Given that,

The ratio of coloured papers to white papers is 3/8.

And, the number of white papers is 48.

Suppose, the number of coloured papers be x.

Then, as per the question the following equation can be obtained,

3/8 = x/48

=> x = 3/8 × 48

=> x = 18

Hence, the number of coloured papers is 18.

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Answer:

[tex]1017.9ft ^{3} [/tex]

Step-by-step explanation:

[tex]volume \: of \: cylinder \\ v = \pi \times r {}^{2} \times h \\ = \pi \times 9^2 \times 4 \\ = 1017.9[/tex]