Twenty times a square of a positive integer, plus 50 equals negative 40 times the square of the positive integer, plus one-hundred and ten times the positive integer. Which equation could be used to solve for the unknown positive integer.
A) 60x2 + 110x + 50 = 0
B) 60x2 + 110x − 50 = 0
C) 60x2 − 110x + 50 = 0
D) 60x2 − 110x − 50 = 0

Answer:K=5D/f

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

810

Step-by-step explanation:

-21 + d = 789

d = 789+21

d= 810

[tex]\frac{1}{2}[/tex] of the grandmother's lawn Dan can mow per gallon.

Option C

Solution:

Given that, mowing [tex]\frac{1}{4}[/tex] uses [tex]\frac{1}{2}[/tex] gallon of gas.

To find: The fraction of the lawn can Dan mow per gallon

According to unitary method,

[tex]\frac{1}{2}[/tex] gallon of gas is required to mow [tex]\frac{1}{4}[/tex] of lawn that is [tex]\frac{1}{2}\rightarrow \frac{1}{4}[/tex]

Therefore, 1 gallon of gas will be required to mow [tex]\frac{1}{2}\times2\rightarrow \frac{1}{4}\frac2[/tex]

[tex]\Rightarrow1 \text{ gallon }\rightarrow \frac{1}{2} \text{ of lawn}[/tex]

Therefore, one gallon will be enough to mow [tex]\frac{1}{2}[/tex] of lawn.

Unitary method:

The unitary method is a technique to solve a problem by finding the value of a single unit first, and then finding the required value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.

Answer:

Step-by-step explanation:

D.

Answer:

The present age of Michael is 33 years .

Step-by-step explanation:

Given as :

Michael is 17 years older than Brandon

And 17 years ago the age of Michael was 4 times as old as Brandon

Now,

Let the age of Michael = M years

And The age of Brandon = B years

So , According to question

M = B + 12                             .........A

And ( M - 17 ) = 4 × ( B - 17 )

Or, M - 17 = 4 B - 68

Or, 4 B - M = 68 - 17

or, 4 B - M = 51               ...........B

Solving Eq A and B

I.e 4 B - ( B + 12 )= 51

or, 4 B - B = 51 + 12

or, 3 B = 63

∴  B = [tex]\frac{63}{3}[/tex]

I.e B = 21 years

So, Now the age of Brandon = B = 21 years

Put the value of B in eq A

So, M = B + 12

∴   M = 21 + 12

I.e M = 33 years

So, Now the age of Michael = M = 33 years

Hence The present age of Michael is 33 years . Answer

Answer:

[tex]m\angle B=54^{\circ}[/tex]

[tex]m\angle BAD=36^{\circ}[/tex]

[tex]m\angle CDA=90^{\circ}[/tex]

[tex]BAC=72^{\circ}[/tex]

Step-by-step explanation:

Given:

[tex]\overline{AB}\cong \overline{AC},[/tex]

[tex]\overline{AD}[/tex] bisects angle BAC

[tex]m\angle C=54^{\circ}[/tex]

Triangle ABC is isosceles triangle, because [tex]\overline{AB}\cong \overline{AC}.[/tex] Angles adjacent to the base of isosceles triangle ABC are congruent.

Hence,

[tex]m\angle C=m\angle B=54^{\circ}[/tex]

The sum of the measures of all interior angles is 180°, so,

[tex]m\angle B+m\angle C+m\angle BAC=180^{\circ}\\ \\m\angle BAC=180^{\circ}-2\cdot 54^{\circ}=72^{\circ}[/tex]

Since [tex]\overline{AD}[/tex] bisects angle BAC, angles BAD and CAD are congruent by definition of angle bisector. So,

[tex]m\angle BAD=m\angle CAD=\dfrac{1}{2}m\angle BAC=\dfrac{1}{2}\cdot 72^{\circ}=36^{\circ}[/tex]

AD ia angle bisector in isosceles triangle drawn to the base, so it is the height. Thus, AD and BC are perpendicular. So,

[tex]m\angle CDA=90^{\circ}[/tex]

Answer:

B) (3/10)/(7/9)=(3/10)(9/7)

Step-by-step explanation:

Answer:

The ordered pair

(−4, 0)

is a solution to the system because it makes both equations true.

The ordered pair

(−4, 0)

is a solution to the first equation because it makes the first equation true.

The ordered pair

(−4, 0)

is a solution to the second equation because it makes the second equation true.

Step-by-step explanation:

Answer:

The needed quadratic equation is : [tex]p(x) = x^2 -3x + 10[/tex]

Step-by-step explanation:

The given equation is of the form [tex]p(x) = ax^2 + bx + c[/tex]

The given solutions of the equations are:

x = 3 +i, x = 3 - i

Now, if x = a is the zero of the polynomial p(x)

⇒(x -a ) is the root of the given polynomial.

⇒ (x - ( 3+i)) and (x - ( 3+i)) are the given roots for p(x)

P(X) = PRODUCT OF ALL ROOTS

⇒ p(x) = (x - ( 3+i))(x - ( 3-i))  = ( x-3 -i)(x -3+i)

Now, [tex](a-b)(a +b) = a^2 - b^2\\\implies ( (x-3)-i)((x-3)+i) = (x-3)^2 - (i)^2 = x^2 +9 - 3x -(-1)\\= x^2 +10 - 3x\\\implies p(x) = x^2- 3x + 10[/tex]

Hence, the needed quadratic equation is : [tex]p(x) = x^2 -3x + 10[/tex]

Answer:

see explanation

Step-by-step explanation:

Note the common difference d between consecutive terms of the sequence

8 - 6 = 10 - 8 = 2

This indicates that the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 6 and d = 2, thus

[tex]a_{n}[/tex] = 6 + 2(n - 1) = 6 + 2n - 2 = 2n + 4 ← explicit formula

Hence

[tex]a_{130}[/tex] = (2 × 130) + 4 = 260 + 4 = 264

Answer:

The aquarium can be made by 83 sq. ft. of glass.

Step-by-step explanation:

The public library aquarium is in the shape of a hollow cuboid.

The dimensions of the hollow cuboid are 6 ft by 2.5 ft. by 4 ft.

Now, the total surface area of the aquarium will be given by 2(LW + WH + HL)

Where, L = length = 6 ft, W = width = 2.5 ft and H = height = 4 ft.

If the top of the aquarium is open, then the total surface area will be

= 2(WH + HL) + LW

= 2(2.5 × 4 + 4 × 6) + 6 × 2.5

= 83 sq. ft.

Therefore, the aquarium can be made by 83 sq. ft. of glass. (Answer)

To calculate the square feet of glass used for the aquarium, we find the total surface area of the rectangular prism excluding the top. The total surface area is 83 square feet.

To find out how many square feet of glass were used to build the aquarium, we need to calculate the surface area of the rectangular prism minus the top since it is open.

The surface area of a rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height.

Given the dimensions of the aquarium:

First, we calculate the areas of the sides:

Total surface area excluding the top is:

Total Surface Area = 2lw + 2lh + 2wh - (length * width)

Total Surface Area = 30 + 48 + 20 - (6 * 2.5) = 98 - 15 = 83 square feet

So, 83 square feet of glass were used to build the aquarium.

Answer:

9/10

Step-by-step explanation:

Final answer:

The improper fraction [tex]\frac{19}{10}[/tex] is equal to the mixed number [tex]1\frac{9}{10}[/tex], where 1 is the whole number and [tex]\frac{9}{10}[/tex] is the proper fraction remainder after division.

Explanation:

The improper fraction [tex]\frac{19}{10}[/tex] can be converted into a mixed number by dividing the numerator by the denominator. The division [tex]\frac{19}{10}[/tex] equals 1 with a remainder of 9. Therefore, the mixed number is [tex]1\frac{9}{10}[/tex]. This illustrates that any improper fraction can be expressed as a combination of a whole number and a proper fraction, where the numerator is smaller than the denominator.

Answer:

-17

Step-by-step explanation:

3 + 4(-5)

= 3-20

= -17

Hope this helps!

Answer:

-17.

Step-by-step explanation:

3 + 4 x (-5)

= 3 + -20

= 3 - 20

= -17.

Answer:

Step-by-step explanation:

-(8x-9)/3 +6>=9

-(8x -9)/3 +18>=27

-8x +9 +18 >=27

-8x >= 27-9-18

-8x >=0

x>=0

Answer:

11

Step-by-step explanation:

Using the order of operations, that is multiplication before addition/ subtraction.

Given

6 + 2 × 3 - 1 ← evaluate multiplication

= 6 + 6 - 1 ← evaluate from left to right

= 12 - 1

= 11

Answer:

576

Step-by-step explanation:

8*8 = 64

If dimensions are tripled, you get 24. 24*24 = 576

Answer:

576

Step-by-step explanation:

A=L*W

8*8=64

8*3=24

24*24=576

Answer:

Approximately 4, exactly 3.786 liters.

Step-by-step explanation:

128/33.8=3.786

There are approximately 3.8 litres in a gallon.

There are 33.8 fluid ounces in a litre. Therefore,

33.8 fluid ounces = 1 litre

128 fluid ounces = ? litre

cross multiply

amount = 128 / 33.8

amount = 3.78698224852

amount ≈ 3.8 litres

There are 128 fluid ounces in a gallon. Therefore,

128 fluid ounces = 1 gallon

Since, 128 fluid ounces = 3.8 litre

Therefore,

Approximately 3.8 litres are in a gallon

read more: https://brainly.com/question/11997116?referrer=searchResults

Answer:

3

Step-by-step explanation:

Greatest Common Factor is the highest number that divides exactly into two or more numbers. It is the "greatest" thing for simplifying fractions.

3 is divisible by 9, 15, and 36.

Because of the answers that you gave I'm going to assume the radians were 3pi/4. That would be A, 135 degrees.

If this is the wrong amount of radians please let me know.

The radian measures of the given degree measures are 3π / 4 Rad, π Rad, 3π / 2 Rad and 2π

One radian is the measure of a central angle subtended by an arc that is equal in length to the radius of the circle. When no symbol is used, radians are assumed. When degrees are the unit of angular measure, the symbol "°" is written. Note that the radian is a derived unit in the International System of Units (SI).

Given are some degree measurements, 135° 180° 270° 360°, we need to convert them into radians.

Since, we know that,

1 Rad = 1 Deg × π / 180

Therefore,

1) 135° = 135 × π / 180

= 3π / 4 Rad

2) 180° = 180 × π / 180

= π Rad

3) 270° = 270 × π / 180

= 3π / 2 Rad

4) 360° = 360 × π / 180

= 2π

Hence, the radian measures are 3π / 4 Rad, π Rad, 3π / 2 Rad and 2π

Learn more about radians, click;

https://brainly.com/question/7721249

#SPJ2

The ratio of Han's measurements and Tyler's measurements corresponds with polenta measurement

Given:

Polenta:

Cups of water = 5

Cornmeal = 2

Ratio of cups of water to cornmeal = 5 : 2

= 5/2

= 2.5

Han:

Cups of water = 3

Cornmeal = 1 1/5

= 6/5

Ratio of cups of water to cornmeal = 3 : 6/5

= 3 ÷ 6/5

= 3 × 5/6

= 15/6

= 2.5

Tyler:

Cups of water = 7 1/2

= 15/2

Cornmeal = 3

Ratio of cups of water to cornmeal = 15/2 : 3

= 15/2 × 1/3

= 15/6

= 2.5

Therefore, the ratio of Han's measurements and Tyler's measurements corresponds with polenta measurement.

Read more:

https://brainly.com/question/3796978

Final answer:

The question involves mathematical ratios to determine the correct proportions for a polenta recipe. By setting up proper proportions, we confirm that Han's and Tyler's calculations for the amount of cornmeal and water needed are correct.

Explanation:

The question discusses proportions used in a recipe which relates to mathematical ratios. Han and Tyler are trying to determine how much cornmeal and water they need for polenta based on a recipe that calls for a specific ratio of these ingredients. To solve this, we must set up a proportion that maintains the constant ratio given by the recipe.

For Han's statement, since the recipe calls for 5 cups of water for every 2 cups of cornmeal, we can set up the following proportion:

5 cups water / 2 cups cornmeal = 3 cups water / x cups cornmeal

Multiply across the equal fractions (5 * x = 2 * 3)

x = 6/5 or 1.2 cups cornmeal, which confirms Han's statement as correct.

For Tyler's statement, using the same ratio:

2 cups cornmeal / 5 cups water = 3 cups cornmeal / x cups water

Multiply across the equal fractions (5 * 3 = 2 * x)

x = 15/2 or 7.5 cups water, which confirms Tyler's statement as correct as well.

Answer:

A- Overall, students are less interested in reading magazines than comics.

Answer:

Option A

Step-by-step explanation:

The minimum possible area of the rectangle is 19.25 m² and the maximum possible area is 29.25 m².

To find the minimum and maximum possible areas of the rectangle, we need to consider the possible values that the length and width can take.

Given that the measured dimensions are 6 m by 4 m to the nearest whole unit, the minimum possible length would be 5.5 m (6 m - 0.5 m) and the minimum possible width would be 3.5 m (4 m - 0.5 m).

Similarly, the maximum possible length would be 6.5 m (6 m + 0.5 m) and the maximum possible width would be 4.5 m (4 m + 0.5 m).

To calculate the minimum and maximum possible areas, we multiply the minimum and maximum possible lengths by the minimum and maximum possible widths respectively. The minimum possible area would be 5.5 m x 3.5 m = 19.25 m² and the maximum possible area would be 6.5 m x 4.5 m = 29.25 m².

Answer:

1/6

Step-by-step explanation:

1/2*1/3

1*1/2*3

1/6

Answer:

1/6

Step-by-step explanation:

1/3*1/2 = 1/6

1/3 = 0.33333333  = 3/9 =1/3

1/6 = 0.1666666   = 15/90=1/6  

Answer:

[tex]\displaystyle 161[/tex]

Step-by-step explanation:

[tex]\displaystyle 159 = \frac{477}{3} \\ \\ 318 = 157 + 161 \\ \\ 161, 159, 157[/tex]

I am joyous to assist you anytime.

Answer:

the answer is D

Step-by-step explanation:

i did it on EDG

Answer:

14

Step-by-step explanation:

13.65 is rounded to 14

Answer:

14

Step-by-step explanation:

since your looking for the nearest whole number the first number behind the decimal is what determines if it goes to 14 or 13. because the number is 6 and is higher than 5 the number would be 14 but if the number was 4 than it would be 13. any number above 5 goes and 4 and below makes the number go down.

Answer:

The average of this pie chart is 33 1/3.

Step-by-step explanation:

To find the average (or mean) of this pie chart, we simply add all the numbers together then divide the sum by however many numbers there are:

71.4 + 14.3 + 14.3 = 100

100  ÷ 3 = 33.333... or 33 1/3

Hope this helps,

❤A.W.E.S.W.A.N.❤

Answer:

joe mama

Step-by-step explanation:

joemama