Mathematics High School

I need more math help, the!

Cement truck A can pour 200 cubic ft of concrete in 20 minutes. It only takes truck B 15 minutes to do the same job. If they both work together,how long will it take them to pour the 200 cubic feet?

I need help setting up the problem and solving it, thank you!

Answers

Answer 1
Track A takes 20 minutes
Track B takes 15 minutes
In 1 minute track be will do a fraction of 1/20, while track B will do 1/15
Both tracks in a minute = 1/20+1/15
                                      = 35/300
Therefore the two tracks will take 300/35 minutes to fill the 200 cubic feet
That is 300/35
           = 8.57  minutes
           ≈ 9 minutes

Related Questions

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

Answers

Miles or kilometers.

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.

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

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.

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.

Blueberry bushes are planted in a field in the year 2009. The blueberry bushes start to grow and cover the field in such a way that the area covered by the bushes doubles every year. If they continue to grow in this way, the field will be entirely covered with blueberry bushes by the year 2016.

When will the field be covered 25% of the way

Answers

about halfway into 2011
Well, Let's see.
They are planted in 2009, and the field will be covered by 2016. 2016-2009= 7. They will be growing for 7 years.
If it's covered 1.5625% in the first year, 
Then 3.125% second year,
6.25% 3rd year,
12.5% 4th year,
25% 5th year,
50% 6th year,
100% 7th year.
So the 5th year? Maybe... I don't know. Please tell me if it's wrong!

Find the lateral area of the square pyramid.

Answers

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

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~

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.

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


a. True
b. False: the fixed manipulator causes a number to be displayed in scientific notation.

Answers

a. True i hope that help

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.

What is the solution of the system? Use the elimination method. {4x+3y=62x+2y=5 The only solution is (−32,  4) .

The only solution is (0, 2) .

There are an infinite number of solutions.

There is no solution.

Answers

The only solution is (−3/2,  4) 

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

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.

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.

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:

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.

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)

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]


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.

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.

Learn more about height of goal post here:

https://brainly.com/question/38223980

#SPJ12

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

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.

Learn more about radius here: https://brainly.com/question/24375372

#SPJ2

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

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).

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

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.

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.

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.
Other Questions
I need help with #13 please Every time we use scarce resources in one way, we give up the opportunity to use them in other ways. true false In three to four sentences, describe how legal contracts provide incentives for people to exchange goods and services Because consumers in the same neighborhoods tend to buy the same types of cars, appliances, and apparel and shop at the same types of retailers, _______ segmentation can help retailers to tailor each store's assortment to the preferences of the local community. paul is in charge of the egg toss at the world egg day fair. there are 48 people participating in teams of 8 people. each team needs 1 egg. paul is buying eggs in cartons that each have 6 eggs. how many cartons does paul need? Which column and row references are updated when you copy the formula: =SUM($B5:D$15)? why is manuscript writing not taught formally in the preschool setting Which substance produced in the laboratory is used as a post exposure preventative measure against rabies? Marcus saves $13 each week.in how many weeks will he saved at least $100 Read the following passage from "The Happy Man.""Inside him, he felt a boundless power, an imperishable energy, an ability to achieve anything with confidence, precision, and obvious success. His heart was overflowing with love for people, animals, and things and with an all-engulfing sense of optimism and joy. It was as if he were no longer troubled or bothered by fear, anxiety, sickness, death, argument, or the question of earning a living. Even more important than that, and something he could not analyze, it was a feeling which penetrated to every cell of his body and soul; it played a tune full of delight, pleasure, serenity, and peace and hummed in its incredible melodies the whispering sound of the world which is denied to the unhappy."Which of the following stylistic elements is used by the writer in these lines to create humor?A. HyperboleB. IncongruityC. IronyD. Sarcasm What is one advancement women are still striving to achieve? Match the reflexive pronoun to the correct verb. 1. Nos 2. Te3. Se4. Me5. OsA. Cepillo los dientesB. VistesC. MaquillaD. VestimosE. Lavis el peloPLEASE HELP An automobile antifreeze mixture is made by mixing equal volumes of ethylene glycol (d = 1.114 g/ml; = 62.07 g/mol) and water (d = 1.00 g/ml) at 20c. the density of the mixture is 1.070 g/ml. express the concentration of ethylene glycol as: Jonah finished a race in 11.62 seconds. Marco finished the same race in 9.8 seconds. How many seconds faster did Marco finish the race than Jonah? A. 1.82 secondsB. 2.22 secondsC. 10.64 secondsD. 11.36 seconds powers held by both the national and state governments in a federal system are called _________ Your cookie recipe calls for 34 cup of flour. You want to make 3 batches of cookies. Which diagram shows how much flour you need? ... Solver the equation 5= w + 1.5. Leo painted for 2/3 of an hour each day on Monday, Tuesday, Thursday and Friday. How long did Leo paint this week Jacob, age 13, gets a laugh from the whole school orchestra when he imitates the music teacher, who is out of the room. the next day, jacob's friend brad boasts at lunch that "jacob and i really got a laugh out of the orchestra at practice yesterday." brad is identifying with jacob and appropriating jacob's accomplishment as his own. this example illustrates one kind of How does the author uses the character of editha to voice his own opinions