Mathematics High School

Which equation demonstrates the distributive property?
A) 3 (2 + 8) = 3 (8 + 2)
B) 3 (2 + 8) = 3 × 2 + 3 × 8
C) (3 × 2) × 8 = 3 × (2 × 8)
D) 3 × (2 × 8) = 3 × (8 × 2)

Answers

Answer 1
The distributive property takes a number outside the parentheses and multiplies it by every term inside the parentheses.

The answer is:
B) 3(2+8) = 3x2 + 3x8

Hope this helps! :)

Related Questions

what is area of a parallelogram that has a base of 12 3/4 in. and a height 2 1/2in.?

Answers

The area is Base * Height
Area = b * h
b =12 3/4 in
h = 2 1/2 in

Area = 12.75 * 2.5 = 31.875 or 31 7/8 square inches.

What metric unit would be appropriate to measure a length of two cities?

Answers

Miles or kilometers.

Which of the following is a polynomial function in factored form with zeros at 0, –3, and 4?

A. f(x) = x^3 + x^2 – 12x
B. f(x) = x(x – 3)(x + 4)
C. f(x) = x^3 – x^2 – 12x
D. f(x) = x(x + 3)(x – 4)

Answers

The answer is D.

Explanation:
You can find the zeroes of a polynomial function in factored form by setting each factor equal to zero and solve for [tex]x[/tex].

The polynomial function of answer A is not even factored, so we can rule that one out.

Lets set each one of the factors of answer B equal to zero, solve for [tex]x[/tex] and see what happens:
- [tex]x=0[/tex]
- [tex]x-3=0[/tex]
  [tex]x=3[/tex]
- [tex]x+4=0[/tex]
  [tex]x=-4[/tex]
As you can see, our zeroes are 0,3, and -4, so this is not the correct answer either.

The polynomial function of answer C is not even factored, so we can rule that one out as well.

Lets apply what we just learned to the factored polynomial of answer D:
- [tex]x=0[/tex]
- [tex]x+3=0[/tex]
  [tex]x=-3[/tex]
- [tex]x-4=0[/tex]
  [tex]x=4[/tex]
This time our zeroes are, 0, -3, and 4; therefore we can conclude that D is the correct answer.

Find the lateral area of the square pyramid.

Answers

lateral area = 8 *4 = 32 x 22 = 704/2 = 352 square meters

The cross products property states that the product of the ___ equals the products of the ___

Answers

The product of the ___means___ equals the products of the ___extremes___

For example:
3/6 = 4/8
Cross multiplying we get
3*8 = 6*4
24 = 24
The "means" are the middle values 6 and 4. The extremes are the outer edge values 3 and 8

Find the height of the top of the goal post, rounded to the nearest tenth of a foot

Answers

Final answer:

Due to insufficient and irrelevant information, the height of the goal post can't be determined.

Explanation:

Unfortunately, the provided information does not allow us to ascertain the height of the goal post. The information presented primarily consists of measurements and heights of trees and people. Without any relevant information specific to the height of the goal post on which the question is based, it's not possible to provide a thorough answer. If further details were provided, such as the angle of the viewer's line of sight toward the top of the post and their distance from the post, then we could use trigonometric principles to resolve the answer.

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Can someone please help me

Answers

Answer:

Convert to inches to solve and then convert back. The first solution is 1 foot 10 inches.

Step-by-step explanation:

To solve convert feet inches into inches by multiplying the number of feet by 12 and adding it to the inches. Then subtract and convert back.

For example: 5 feet is 5*12=60 inches. So 5 feet 7 inches is 60+7=67.

3 feet is 3*12=36 inches. So 3 feet 9 inches is 36+9=45 inches.

Subtract the two.

67-45= 22 inches.

22 inches is 12+10. 12 inches is 1 foot. This is 1 foot 10 inches.

Triangle ABC is congruent to triangle XYZ. Angle A measures 50 degrees, angle B measure 2x+40 degrees, and angle Z measures 4x+8 degrees. Find the value of x.

20.5

13.67

16

10.5

Answers

angle Z is congruent to angle C, so angle C measures 4x+8
the sum of the three angles of a triangle is 180, so 
50+2x+40+4x+8=180
6x++98=180
6x=82
x≈13.67

Final answer:

To find the value of x, we use the fact that the angles of a triangle sum up to 180 degrees. By setting an equation with the given angle measurements and solving for x, we find the value of x to be 13.67.

Explanation:

The student asks about determining the value of x in two congruent triangles, ABC and XYZ, given the measurements of the angles. If triangles are congruent, their corresponding angles are equal. Using the fact that the sum of the angles in a triangle is 180 degrees, and given Angle A is 50 degrees, Angle B is 2x+40 degrees, and Angle Z is 4x+8 degrees, we can set up an equation because Angle B corresponds to Angle Z in congruent triangles:

50 + (2x + 40) + (4x + 8) = 180

Combine like terms:

50 + 2x + 40 + 4x + 8 = 180

6x + 98 = 180

Subtract 98 from both sides:

6x = 82

Divide both sides by 6:

x = 13.67

Therefore, the value of x is 13.67.

1. Real numbers that cannot represent as a quotient of two integers are ____ numbers.
2. The sum of a number and it’s ____ equals zero.
3. You can simplify an expression by combining it’s ____.
4. ____ is a numbers distance from zero on a number line.
5. when you make conclusions based on patterns you observe, you use ____.

Answers

1. Irrational  
2. Additive inverse
 3. Like terms
 4. Absolute value
 5. Inductive reasoning

PLEASE HELP
6.02B

Respond to the following prompt in a word processing document.

Describe, in detail, when to use the law of cosines, the law of sines, and the law of sines with the ambiguous case. Provide general guidelines, in your own words, for each law that can be applied to any triangle situation with which you are presented. To aid in your explanation, you may refer to specific problems from the text.

Your response must include:
A discussion of
The law of cosines
The law of sines
The ambiguous case (law of sines)
General guidelines in your own words that can be applied to any triangle.

Answers

Law of cosines :

The law of cosines establishes:

[tex] c ^ 2 = a ^ 2 + b ^ 2 - 2*a*b*cosC.
[/tex]

general guidelines:

The law of cosines is used to find the missing parts of an oblique triangle (not rectangle) when either the two-sided measurements and the included angle measure are known (SAS) or the lengths of the three sides (SSS) are known.


Law of the sines:


In ΔABC is an oblique triangle with sides a, b, and c, then:

[tex] \frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC} [/tex]

The law of the sines is the relation between the sides and angles of triangles not rectangles (obliques). It simply states that the ratio of the length of one side of a triangle to the sine of the angle opposite to that side is equal for all sides and angles in a given triangle.

General guidelines:

To use the law of the sines you need to know either two angles and one side of the triangle (AAS or ASA) or two sides and an opposite angle of one of them (SSA).


The ambiguous case :


If two sides and an angle opposite one of them is given, three possibilities may occur.


(1) The triangle does not exist.


(2) Two different triangles exist.


(3) Exactly a triangle exists.


If we are given two sides and an included angle of a triangle or if we are given 3 sides of a triangle, we can not use the law of the sines because we can not establish any proportion where sufficient information is known. In these two cases we must use the law of cosines

Final answer:

The Law of Sines, Law of Cosines, and the Ambiguous Case are used to solve triangles depending on the given information. The Law of Sines is used when you have angles and sides but no right angle, the Law of Cosines is used when you have at least one side and angles, and the Ambiguous Case is used when you have one angle and two sides with two possible triangles. General guidelines are provided for each law.

Explanation:

The Law of Sines:

The law of sines is used to solve triangles when you have information about the measures of angles and sides, but do not have a right angle. It relates the ratios of the lengths of the sides of a triangle to the sines of its angles.

The Law of Cosines:

The law of cosines is used to solve triangles when you have information about the measures of angles and sides, and at least one side is known. It relates the lengths of the sides of a triangle to the cosine of one of its angles.

The Ambiguous Case:

The ambiguous case, also known as the law of sines with the ambiguous case, is used to solve triangles when you have information about the measures of angles and sides, and want to find all possible solutions. It occurs when you have one angle and two sides given, but there are two possible triangles that can be formed.

General Guidelines:

Use the law of sines when you have the measure of an angle and the length of its opposite side, or two pairs of an angle and its opposite side.Use the law of cosines when you have the length of one side and the measures of the other two sides or when you have two sides and the included angle.Use the law of sines with the ambiguous case when you have the measure of an angle and the length of its opposite side, and there are two possible triangles that can be formed.

Please help asap! lots of points

Answers

Hello there! I can help you! Let's start solving this by solving for the slope. In case you forgot, the formula for finding slope is y2 - y1 / x2 - x1. The points represent each values. Here's what each value would be:

y2: -5
y1: -9
x2: 10
x1: 9

Fill in the numbers for the equation and solve. -5 - (-9) is 4. 10 - 9 is 1. 4/1 is just simply 4. There. The slope is 4, but we're not done. We'll use one of the points as x and y.  Point-slope form is in the form of y - y1 = m(x - x1). y1 is -9. Because that is a negative number, we will be adding, so that part is y + 9, which eliminates answer choices A and B. x1 is 9. The other part will be 4(x - 9). That eliminates answer choice C. That leaves D, with the problem in point-slope form being y + 9 = 4(x - 9). When you subtract 4x from both sides, subtract 9 to isolate the y, multiply -10 and 4 together to get -40, and subtract 5 from -40 to get -45, the equation becomes -4x + y = -45. You use the values of the second point to find the value on the x-side. There. The answer is D.

Answer:

The answer is D.

Hope I helped :)

Have a blessed day <3

~Michael~

Too many nutrients is not good for bodies of water. This man-made is called what?

A. Cultural eutrophication

B. Point-source pollution

C. Eutrophication

Answers

I think the answer is a
I think this is more of a health or biology question, but that's okay...

I believe the answer is most likely Cultural eutrophication because it's the process that speeds up natural eutrophication because of human activity.

a flyer on a reconnaissance flight has 4 hours for a round trip. his blade can fly 200 mph in still air. he flies out from his base against a 20 mph wind and immediately returns to his base, flying with the same wind. how many hours did he take for his fight out?

Answers

When flying with the wind, the effective plane speed is 200 + 20 = 220 mph.
When flying against the wind, the effective plane speed is 200 - 10 = 180 mph.

Let d =  the distance (miles) from his base to the destination.
The time (hours) to travel with the wind is
t₁ = d/220  
The time (hours) to travel against the wind is
t₂ = d/180

The total time taken is 4 hours, therefore
t₁ + t₂ = 4
d/220 + d/180 = 4
d(1/220 + 1/180) = 4
0.010101d = 4
d = 396 miles

Therefore
t₁ = 396/220 = 1.8 hours = 1 hour, 48 minutes (floght in)
t₂ = 396/180 = 2.2 hours = 2 hours, 12 minutes (flight out)

Answer: 2.2 hours

A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 6/5 .



What is the volume of the dilated prism?

Enter your answer, as a decimal, in the box.

Answers

First we need to find the volume of the prism without the dilated factor:

The volume would be:
Volume of the prism(without dilated) = (area of the base) * (height)
Since,
Area of base = 5[tex]ft^{2}[/tex]
Height of the prism = 10f

Volume(without dilated) = 5*10 = 50[tex]ft^{3}[/tex]

Now let us apply the dilated factor! For that you need to multiply for factor with the volume of the prism without dilation.

Volume of the dilated prism = [tex]d^{3}[/tex] * (Volume of the prism without dilation)

Where d = dilated factor. Therefore,

[tex]v = (\frac{6}{5} )^{3} * 50[/tex]


v = 86.4[tex]ft^{3}[/tex]

So the correct answer: 86.4[tex]ft^{3}[/tex]


Maxine picked 7 1/4 pounds of blueberries and kodi picked 3 3/4 pounds of blueberries thy want to package into 1 1/2 to sell at their family what is the greatest number of 1 1/2 bags of blueberries they can make?

Answers

7.25+3.75=11 pounds total
11/1.5= 7 plus .5 pounds left
So the greatest number they can make is 7

I need 21 centimeters but i need to translate that into millimeters wht is the answer in milli eters

Answers

1cm = 10mm

21cm = 10 x 21 = 210 mm

Solve the system of equations using the substitution method.

{2x+8y=4
x=−3y+5

Enter your answers in the boxes.

x=

y=

Answers

Answer:


Step-by-step explanation:

X=14

y=-3

Answer:

(14,-3)

Step-by-step explanation:

Find (fxf)(0)

F(x)+3x-2

Answers

Final answer:

To find (fxf)(0), substitute 0 into the given function f(x) = x + 3x - 2. The resulting value is -2.

Explanation:

To find (fxf)(0), we need to substitute 0 into the given function. The function is f(x) = x + 3x - 2. Substituting 0 for x, we get f(0) = 0 + 3(0) - 2 = -2. Therefore, (fxf)(0) = f(f(0)) = f(-2).

16 POINTS. Find the x and y intercepts of number 8 show work. I think my points are wrong.

Answers

Again, I'd try graphing this thing and get your point this way. Go to Wolframalpha dot com Put
y = 2x^4 + 3x^3 - 16x - 24 into the input line.
According to wolframalpha there are 2 real roots and 2 imaginary ones.

there are places on the internet that will solve quartics for you and likely those solutions will show all 4 roots. You were right to be a little suspicious, but the question is a bit unreasonable.

Note to Moderator. Wolframalpha dot com is just a tool. the work is my own.

This figure is made up of a triangle and a semicircle.

What is the area of this figure?

Use 3.14 for pi. Round only your final answer to the nearest tenth.

Enter your answer as a decimal

Answers

Given is a composite figure where we have a semicircle and a triangle.


To find the area of the semicircle, we need diameter of the circle which is the distance between two given points (2,4) and (2,-3). So the diameter is 4-(-3) = 7 and radius would be 3.5 units.

Area of circle = π·r² = 3.14 × (3.5)² = 38.465 squared units.

So, area of semicircle = 38.465 ÷ 2 = 19.2325 squared units.

To find the area of the triangle, we need base and height of the triangle. The base is same as diameter = 7 and the height would be distance between given point (5,0) and (2,0), so height is 5-2 = 3.

Area of triangle [tex] =\frac{1}{2} bh = \frac{1}{2} (7)(3) = 10.5 [/tex] 1/2 * 7 * 3 = 10.5 squared units.

Total area = Area of triangle + Area of semicircle = 10.5 + 19.2325 = 29.7325 squared units.

So, final answer is 29.7325 squared units.

A mortgage broker charges $4000 plus 1.8% of the mortgage amount. What is the mortgage broker fee for a $309,000 mortgage?

Answers

The answer is 9,562. Thank you very much.

Final answer:

The mortgage broker fee for a $309,000 mortgage is calculated by multiplying the mortgage amount by 1.8% and then adding a fixed charge of $4000, resulting in a total fee of $9,562.

Explanation:

The mortgage broker fee for a $309,000 mortgage can be calculated by taking 1.8% of the mortgage amount and adding the fixed charge of $4000. To find 1.8% of $309,000, we multiply 0.018 by 309,000.

0.018 \( \times \) $309,000 = $5,562.

Then we add the fixed charge:

$5,562 + $4,000 = $9,562.

So, the mortgage broker fee for a $309,000 mortgage is $9,562.

4/5 are girls. Today 3/5 brought there lunch. What fraction of the students are girls who brought there lunch today?

Answers

4/5 * 3/5 =12/25 i think

The radius r of a circle can be written as a function of the area A with the following equation:

[tex]r= \frac{A}{ \pi } [/tex]

What is the domain of this function? Explain why it makes sense in this context.

Answers

The real formula of the radius is r = √(A/pi)

 In this context, it makes sense as the radius cannot have a negative value. 

Thus, the domain of the function is [0,∞)

This means that the Area can have any positive value starting from zero.


The width of a rectangle is 6 less than twice its length. if the area of the rectangle is 110 cm^2, what is the length of the diagonal?

Answers

 the answer is: 9.16485485837795, -6.16485485837795. but if you need the work here it is
Step 2. Let 2L-6 be the width since the width of a rectangle is 6 less than twice its length. 

Step 3. Area A=113=L*(2L-6) 

Step 4. Solving for L yields the following steps 

 

Subtract 113 from both sides of the equation to get a quadratic equation 

 

 

To solve for L, we can use the quadratic formula given as 

 

where a=2, b=-6 and c=-113 

Solved by pluggable solver: SOLVE quadratic equation with variableQuadratic equation  (in our case ) has the following solutons:



For these solutions to exist, the discriminant  should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=940 is greater than zero. That means that there are two solutions: .




Final answer:

The length of the rectangle is 10 cm and the width is 11 cm. Using the Pythagorean theorem, the length of the diagonal can be calculated to be √221 cm.

Explanation:

The length of the rectangle is 10 cm and the width is 11 cm.

To find the length of the diagonal, we can use the Pythagorean theorem:

Diagonal2 = Length2 + Width2

Diagonal = √(102 + 112) = √(100 + 121) = √221 cm.

The length of the rectangle is 10 cm and the width is 11 cm. Using the Pythagorean theorem, the length of the diagonal can be calculated to be √221 cm.

If two quantities are added and the sum is zero, what do you know about the quantities?

Answers

The two values must be opposites or both 0's

The formula for the volume of a cone is v=1/3pir^2h. Find the radius, to the nearest hundredth, of a cone with a height of 3 in. and a volume of 12in.^3.Show your steps to finding the radius to receive credit.

Answers

The radius of the cone with a height of 3 in and a volume of 12 in is 1.95 in.

What is radius?

Radius is the line that connects any point of the circumference of a circle to the center of that circle.

Given:

V = 1/3(πr²h)............... Equation 1

Where:

V = Volume of the coner = radius of the coneh = height of the cone

Make r the subject of the equation

r = √(3V/πh)................ Equation 2

From the question,

Given:

V = 12 in³h = 3 in

Substitute these values into equation 2

r = √[(3×12)/(3.14×3)]r = √(12/3.14)r = √(3.82)r = 1.95 in.

Hence, the radius of the cone with a height of 3 in and a volume of 12 in is 1.95 in.

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Final answer:

The radius to the nearest hundredth is 1.38

Explanation:

To find the radius of a cone with a given height and volume, use the formula [tex]V = 1/3 * \pi * r^2 * h[/tex], where V is the volume, r is the radius, and h is the height.

In this case, the volume is given as 12 in^3 and the height is given as 3 in.

Substituting these values into the formula:

[tex]12 = 1/3 * \pi * r^2 * 3[/tex]

Multiply both sides of the equation by 3:

[tex]36 = \pi * r^2 * 3[/tex]

Divide both sides of the equation by 3π:

[tex]12/\pi = r^2[/tex]

Take the square root of both sides of the equation:

[tex]r = \sqrt{(12/\pi )[/tex]

Approximating it to nearest hundredth -

r ≈ 1.38

When Marsha went shopping, she decided to buy some nuts to take home. She bought 1 3/4 lbs. of cashews, 5/8 lbs. of almonds, and 2 1/2 lbs. of peanuts. How many pounds of nuts did she buy?

Answers

Let
x-------------> lbs. of cashews-------> 1 3/4 lbs------> (4+3)/4-----> 7/4 lbs
y-------------> lbs. of almonds-------> 5/8 lbs
z-------------> lbs. of peanuts-------> 2 1/2 lbs--------> (2*2+1)/2-----> 5/2 lbs
T-------------> total pounds of nuts

we know that
T=x+y+z
T=[(7/4)+(5/8)+(5/2)]--------> (1/8)*[14+5+20]-----> (1/8)*[39]=39/8 lbs

T=39/8=4.875 lbs----------> 4 7/8 lbs

the answer is  4 7/8 lbs

Answer: 4 7/8

Step-by-step explanation:

i just took the test

One base angle of an isosceles triangle measures 33 degrees. What is the number of degrees in the vertex angle?

Answers

keeping in mind that an isosceles triangle has two twin sides, and those twin sides make twin angles on the other end, namely the base, check the picture below.

Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After running for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable. Which equation can be used to represent k, the number of kilometers Julissa runs in t minutes? k – 2 = 1/9(t – 18) k – 18 = 1/9(t – 2) k – 2 = 9(t – 18) k – 18 = 9(t – 2)

Answers

Answer:

the answer is C

Step-by-step explanation:

using her first part 2 kilometers in 18 minutes

total kilometers - 2

and total time - 18

so you would get:

k – 2 = (t – 18)

PLEASE HELP, 40 points, absurd answers will be reported, good answers will get brainliest
8.03b

(PART 1)
Find at least three examples of conic sections in the real world (marketing, architecture, nature, etc.). Make sure your collage demonstrates at least two of the conic categories you have learned. You may use circles, ellipses, parabolas, or hyperbolas. Arrange your images on paper or in a document.


(PART 2)
Respond to each of the following prompts in a word processing document.

Write a brief description about one of the conics from your collage.
Write the equation that represents your conic in its standard form. To do this either find the measurements of your conic example to create the equation or guess the measurements of the conic.
Your assignment must include:

Your conics collage.
A description about one conic from your collage.
The standard form equation of one of the conics.
An explanation of how the equation for the conic was found.

Answers

Part 1) There are a lot of examples. The Colliseum in Rome is an example of an ellipse in architecture. Tires of cars are in a very good approximation a circle.  The Arch of triumph is an example of a parabola in the real world, as are many bridges, such as the golden gate bridge.
Part 2) The Golden Gate Bridge is a suspension Bridge spanning the Golden Gate, a short strait in San Francisco. It is one of the wonders of the Modern World and it was opened in 1937. It cost around 500 million dollars in today's currency and it is one of the longest suspension bridges in the world and from land to land the distance is 1280 m. The height of the suspensions is 230 m.
Part 3) We can think of a parabola of the form y=ax^2 where we need to substitute the values to find a.
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