Which of the following shows that polynomials are closed under subtraction when two polynomials, (5x2 + 3x + 4) − (2x2 + 5x − 1), are subtracted?
A. 3x2 − 2x + 5; will be a polynomial
B. 3x2 − 2x + 5; may or may not be a polynomial
C. 3x2 + 8x + 3; will be a polynomial
D. 3x2 + 8x + 3; may or may not be a polynomial

Answer:

[tex]-6x+15< 10-5x[/tex]

Step-by-step explanation:

we have

[tex]-3(2x-5) < 5(2-x)[/tex]

solve for x

eliminate the parenthesis (apply the distributive property)

[tex]-3*2x+3*5 < 5*2-5*x[/tex]

[tex]-6x+15< 10-5x[/tex] ---> correct representation of the inequality

Adds (5x-15) both sides

[tex]-6x+15+5x-15< 10-5x+5x-15[/tex]

[tex]-x< -5[/tex]

Multiply by -1 both sides

[tex]x>5[/tex]

(q+8)(2n^2-1)

I think this is the correct form.

Answer:

Third graph

Step-by-step explanation:

We are determine whether which of the given graphs is that of the linear inequality [tex]2y>x-2[/tex].

We know that, on the graph the greater than sign ([tex]>[/tex]) represents the shaded part above the line and less than sign ([tex]<[/tex]) represents the shaded region below the line.

While the signs [tex]\leq[/tex] or [tex]\geq[/tex] is denoted by a solid line on the graph.

Therefore, the third graph represents the given inequality.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

2y > x-2

The solution of this inequality is the shaded area above the dotted line 2y=x-2

The graph in the attached figure

Answer:

12π

Step-by-step explanation:

The area of a circle is π*r^2, where r is the radius. Therefore, given that the area is π*36, the radius is 6.

The circumference of a circle is 2πr, which in this case is 2*6*π=12π.

Answer:

12 is the best estimate

Answer:

option A.

Step-by-step explanation:

We have to find the circumference of the given circle with radius 2 units.

Since formula to calculate circumference of a circle is = 2πr

Where r = radius of the circle.

Circumference = 2 × (3.14) × (2)

                        =  4 × 3.14

                        = 12.56

So approximate value will be option A.

Answer:

Option C is correct.

Step-by-step explanation:

[tex]\theta=\frac{5\pi }{6}[/tex]

We need to find reference angle and signs of sinФ, cosФ and tanФ

We know that [tex]\theta=\frac{5\pi }{6}radians[/tex] is equal to 150°

and 150° is in 2nd quadrant.

So, Ф is in 2nd quadrant.

And In 2nd quadrant sine is positive, while cos and tan are negative

The reference angle Ф' is found by: π - Ф

=> Ф = 5π/6

so, Reference angle Ф' = π - 5π/6

Ф' = 6π - 5π/6

Ф' = π/6

So, Option C Θ' = pi over 6; sine is positive, cosine and tangent are negative is correct.

Answer:

f(x) = 4.5x + 3/8

Answer: Third Option

[tex]f(x) = \frac{3}{8}x + 54[/tex]

Step-by-step explanation:

We want to propose an equation that models the distance traveled by the caterpillar as a function of time, we have a constant initial quantity of 4.5 feet and then we know that every minute the caterpillar advances 3/8 of an inch

Then the distance that the caterpillar to advanced after x minutes is:

[tex]f(x) = \frac{3}{8}x[/tex]

Then we know that initially the caterpillar was at a distance of 4.5 feet or 54 inch

Then the equation for the distance in inch is:

[tex]f(x) = \frac{3}{8}x + 54[/tex]

The value of sin n depends on the angle n and represents the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle.

The value of sin n depends on the angle n. In mathematics, sine is a trigonometric function that represents the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. It is a periodic function that oscillates between -1 and 1 as the angle increases or decreases.

For example, if n is 0 degrees, then sin n is 0. If n is 90 degrees, then sin n is 1. If n is 180 degrees, then sin n is 0 again. The values of sin n for angles in between can be determined using a calculator or trigonometric tables.

It's important to note that in mathematics, the angle n is typically measured in radians rather than degrees. In radians, a full circle is equal to 2π, so an angle of 360 degrees is equal to 2π radians.

Answer:

The correct option is C

Step-by-step explanation:

x2 - 12x + 36

The coefficient of 1st term will be multiplied by the constant:

1*36 = 36

Now find two numbers whose product is 36 and whose addition is 12.

6*6 = 36

6+6 =12

Now break the middle term:

x^2-6x-6x+36 = 0

Now group the terms:

(x^2-6x) - (6x-36) = 0

Now take common of each group:

x(x-6)-6(x-6) = 0

(x-6) (x-6) =0

(x-6)=0    ,  (x-6) =0

x-6=0       , x-6=0

x=0+6      , x=0+6

x=6        ,   x=6

Thus the correct option is C. x=6 only....

Answer:

a. _ √20 , about 4.472136

b - (-3, 8)

c- Slope of 2

Step-by-step explanation:

Calculator

Answer:

a. [tex]AB=2\sqrt{5}[/tex]

b. [tex](-3,8)[/tex]

c. [tex]2[/tex]

Step-by-step explanation:

You have the points:

A(-2,10)

where i will call: [tex]x_{1}=-2[/tex] and [tex]y_{1}=10[/tex]

B(-4,6)

where i will call: [tex]x_{2}=-4[/tex] and [tex]y_{2}=6[/tex]

for our calculations we are going to need the distance in x between the points ([tex]\Delta x[/tex] )and the distance in y between the points ([tex]\Delta y[/tex]):

[tex]\Delta x =|x_{2}-x_{1}|=|-4-(-2)|=|-4+2|=|-2|=2\\\Delta y =|y_{2}-y_{1}|=|6-10|=|-4|=4[/tex]

a. To find AB (the distance between point A and point B) you need The Pythagorean Theorem:

[tex](AB)^2=(\Delta x)^2+(\Delta y)^2\\(AB)^2=(2)^2+(4)^2\\(AB)^2=4+16\\\\AB=\sqrt{20}\\ AB=2\sqrt{5}[/tex]

b. to find the coordinates of the midpoint we average the x-coordinates and the y coordinates

[tex]x_{mid}=\frac{x_{1}+x_{2}}{2} =\frac{-2-4}{2}=\frac{-6}{2} =-3\\y_{mid}=\frac{y_{1}+y_{2}}{2} =\frac{10+6}{2}=\frac{16}{2} =8\\[/tex]

so the midpoint [tex](x_{mid},y_{mid})[/tex] is at: [tex](-3,8)[/tex]

c. For the slope we use the slope formula:

[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{6-10}{-4-(-2)}=\frac{-4}{-2}=2[/tex]

The slope is equal to 2.

Answer:

Width=4.7 ft

Length=16.1 ft

Step-by-step explanation:

Let the width of the table to be x ft

Then the length should be two more than three times the width= 2+3x ft

The area of the serving table should be 75 ft²

But you know the area of this table is calculated by multiplying the length by the width of the table

Hence, Area= length× width

Length=x ft  and width =2+3x ft

75ft²= (x ft) × (2+3x ft)

[tex]75=x*(2+3x)\\\\75=2x+3x^2\\\\3x^2+2x-75=0[/tex]

Apply the quadratic formula to solve this quadratic equation

The formula is ;

x= (-b ±√b²-4ac)÷2ac

where a=3, b=2 and c=-75

x= (-2 ± √2²-4×3×-75)÷(2×3)

x=(-2±√4+900)÷6

x=(-2±√904)÷6

x=(-2±30.1)÷6

x=(-2+30.1)÷6=4.683⇒4.7(nearest tenth)

or

x=(-2-30.1)÷6= -32.1÷6=-5.35⇒ -5.4

Taking the positive value

x=width =4.7 ft

2+3x= length= 2+3(4.7)=16.1 ft

Answer:

Step-by-step explanation:

Next time, please share the answer choices.

(4/5)^6 is equivalent to:

 4^6         4096

---------- = -----------

  5^6        15625

Answer:

4^6/5^6

Step-by-step explanation:

Answer:

60% growth, 40% decay, 20% decay, 80% decay, 40% growth. In that order :)

Step-by-step explanation:

The number inside the parenthesis is always 1+a number. So for every .1 up or down, that's 10% growth or decay(up being growth, down being decay).

Answer:

Step-by-step explanation:

A). In exponential equation [tex]80(1.6)^{t}=20[/tex], 1.6 is the common ratio which represents [(1 + 60% of 1) = 1.6] a growth of 60%.

B). In [tex]20(0.6)^{t}=1.2[/tex] common ratio is 0.6 [(1 - 40% of 1)] which represents 40% decay.

C). In [tex]60(0.8)^{t}=1.4[/tex] common ratio is 0.8 [(1 - 20% of 1)] which represents 20% decay.

D). In [tex]40(0.2)^{t}=1.6[/tex] common ratio is 0.2 [(1 - 80% of 1)] which represents 80% decay.

E). In [tex]1.2(1.4)^{t}=80[/tex] common ratio is 1.4 [(1 + 40% of 1)] which represents 40% growth.

Answer:

5 large frames

16 small frames

Step-by-step explanation:

$13 times 5 large frames = $65

$9 times 16 small frames = $144

144+65=209

Answer as a fraction: 4/15

Answer as a decimal: 0.267

The decimal version is approximate rounded to three decimal places.

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

Explanation:

6 apples, 4 peaches

6+4 = 10 pieces of fruit total

The probability of picking an apple is 6/10 = 3/5

After you pick and eat the apple, there are 10-1 = 9 pieces of fruit left. Also, the probability of picking a peach is 4/9, as there are 4 peaches out of 9 fruit left over.

Multiply out 3/5 and 4/9 to get (3/5)*(4/9) = (3*4)/(5*9) = 12/45 = 4/15

Using a calculator, 4/15 = 0.267 approximately.

Answer:

Fraction: [tex]\frac{4}{15}[/tex]

Decimal: [tex]0.2667[/tex]

Percent: 26.67%

Step-by-step explanation:

If the basket contains six apples and four peaches then the Total amount of fruit in the basket is (6+4) 10 pieces of fruit.

You reach in and randomly pick out an apple. Since there are only 4 apples, the probability of this happening was [tex]\frac{4}{10}[/tex] , and now there are only 9 pieces of fruit in the basket.

Now you reach in and randomly pick out a peach. Since there are 6 peaches, the probability of this happening is [tex]\frac{6}{9}[/tex]. Now we can find the probability of both of these things happening one after another by multiplying both probabilities together

[tex]\frac{4}{10} * \frac{6}{9}  = \frac{24}{90}[/tex]

[tex]\frac{24}{90} = \frac{4}{15}[/tex] ...... simplified

So we can see that the probability of you picking out an apple and a peach in sequence is [tex]\frac{4}{15}[/tex] or [tex]0.2667[/tex]

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

-10.2n - 1

Step-by-step explanation:

−2.4n − 3 + (−7.8n + 2) =

= -2.4n - 7.8n - 3 + 2

= -10.2n - 1

Answer:

-10.2n -1

Step-by-step explanation:

−2.4n−3 + −7.8n+2

Combine like terms

−2.4n −7.8n -3+2

-10.2n -1

Answer: 5.

Step-by-step explanation:

6+9 = 15

10 + x = 15

-10 -10

x = 5

Answer:

x=5

Step-by-step explanation:

6+9=10+x

15=10+x

x=15-10

x=5

Answer:

y=0.01179/w

Step-by-step explanation:

First understand that the fuel consumption in miles per gallon is inversely proportional to the weight of a car.

If y is the fuel consumption in miles per gallon and w is weight of car in pounds . you can write the first statement as;

y∝1/w

Introduce a constant value for proportionality, k

y=k/w....................make k subject of the formula by multiplying both sides by 1/w

k=y/w

Given in the question that ;

w=2800

y=33

k=?

To find k , apply the formula that you derived above

k=y/w

k=33/2800 =0.011785⇒0.01178(4 significant figures)

Rewrite the formula as

y=k/w  ⇒ y=0.01179/w

The equation that relates y and w is;

y=0.01179/w

The fuel consumption in miles per gallon for a car varies inversely with its weight and can be represented mathematically by the inverse proportionality relationship y = k/w. Substituting the given values gives us the constant k = 92400, so the final equation is y = 92400/w.

This problem can be defined mathematically by an inverse proportionality relationship, expressed as y = k/w, where k is a constant, y is the fuel consumption in miles per gallon, and w is the weight of the car in pounds.

To find the value of k, we can substitute the given values into the equation. This gives us 33 = k/2800, which simplifies to k = 33 * 2800, or k = 92400.

So, the equation that relates the mileage per gallon, y, to the weight of the car, w, is y = 92400/w. This means the fuel efficiency of a car decreases as its weight increases, thus heavier cars tend to have lower miles per gallon.

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Answer:

4.   2x^2 - 2x.

Step-by-step explanation:

Adding the 2 functions:

Area of the 2 triangles = x^2 + x + x^2 - 3x

= .2x^2 - 2x

Answer:

OPTION 4

Step-by-step explanation:

Let be f(x) the function that represents the area of Triangle A:

[tex]f(x)=x^2 + x[/tex]

Let be g(x) the function that represents the area of Triangle B:

[tex]g(x)=x^2 - 3x[/tex]

Then, you need to add the area of Triangle A and the area of Triangle B in order to find the sum of the areas (Let be h(x) the function that represents the sum of the the areas of triangles A and B):

Therefore, this is:

[tex]h(x)=(x^2 + x)+(x^2 - 3x)=x^2 + x+x^2 - 3x=2x^2-2x[/tex]

You can notice that this matches with the option 4.

Answer:B, C, D, E.

Step-by-step explanation:

The third side of a triangle with two sides measuring 10 and 14 units must be greater than 4 and less than 24 units. This is determined using the Triangle Inequality Theorem.

The possible values for the third side of a triangle with sides of lengths 10 and 14 can be found using the Triangle Inequality Theorem.

Add the two given side lengths: 10 + 14 = 24.

To find the range of possible values for the third side, subtract the two given side lengths from the total: 24 - 10 = 14, and 24 - 14 = 10.

Therefore, the third side of the triangle must have a length greater than 4 but less than 24.

Answer:

5.75

Step-by-step explanation:

[tex]3 + 11 + 4 + 3 + 10 + 6 + 4 + 5 = 46 \\ 46 \div 8 = 5.75[/tex]

The total amount of numbers are : 8

To find the mean, we calculate the sum of all values and divide that sum by the amount of numbers there are.

PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL :)

Answer:

D. G(x) = (x+2)^2

Step-by-step explanation:

We can easily solve this problem by graphing each case with a graphing calculator or any plotting tool.

The equations are

A. G(x) = (x-2)^2

B. G(x) = (x)^2 + 2

C. G(x) = (x)^2 -2

D. G(x) = (x+2)^2

Se attached image.

The correct option is

D. G(x) = (x+2)^2

Answer:

C. G(x)=x²-2

Step-by-step explanation:

The midpoint of the graph has been displaced from x=0 to x=-2. this is a negative displacement.

Therefore the new equation G(x)=x²-2

This is because there is no tilt in the graph so it is a replica of the red graph.

Answer:

i will answer this in 5 mins

Step-by-step explanation:

Answer:

x = 500.

Step-by-step explanation:

log20x^3 - 2logx = 4

By the laws of logs:

log20x^3 - logx^2 = 4

log(20x^3 / x^2) = 4

20x^3 / x^2 = 10^4

20x = 10,000

x = 10,000 / 20

x = 500.

The solution of the given logarithmic equation is x = 500.

Any equation in the variable x that contains a logarithm is called a logarithmic equation.

Given logarithmic equation

[tex]log20x^{3} -2logx=4[/tex]

Using [tex]mloga=loga^{m}[/tex]

[tex]log20x^{3} -logx^{2}=4[/tex]

Using [tex]loga-logb=log(\frac{a}{b})[/tex]

[tex]\frac{log20x^{3} }{x^{2} }=4[/tex]

[tex]log20x=4[/tex]

[tex]20x=10^{4}[/tex]

[tex]x=\frac{10000}{20}[/tex]

[tex]x=500[/tex]

The solution of the given logarithmic equation is x = 500.

Find out more information about logarithmic equation here

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Answer:

439.7.

Step-by-step explanation:

The mean of these number is

(500+372+536+ 328 +369+412+561) / 7

=439.7.

Final answer:

To determine the mean of the numbers 500, 372, 536, 369, 328, 412, and 561, you add them together and divide by the total count, which results in a mean of approximately 439.71.

Explanation:

To find the mean of a set of numbers, you add up all the numbers and then divide by the number of values in the set. The numbers given are 500, 372, 536, 369, 328, 412, and 561. Let's calculate the mean step by step:

The mean (average) of the numbers is approximately 439.71.

Answer:

[tex]\boxed{\text{3; is not}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}p(x) & = & (x - 7)(x^{2} - 2x + 4) + 3\\\\\dfrac{p(x)}{x - 7} & = &x^{2} - 2x + 4 + \dfrac{3 }{x-7 }\\\\\end{array}\\\\\text{The number }\boxed{\mathbf{3}}\text{ is the remainder when $p(x)$ is divided by $(x - 7)$,}\\\\\text{so $(x - 7)$ }\boxed{\textbf{is not}} \text{ a factor of $p(x)$.}[/tex]

Answer:

Step-by-step explanation:

[tex]x^2-2x-3=0\\\\x^2+x-3x-3=0\\\\x(x+1)-3(x+1)=0\\\\(x+1)(x-3)=0\iff x+1=0\ \vee\ x-3=0\\\\x+1=0\qquad\text{subtract 1 from both sides}\\x=-1\\\\x-3=0\qquad\text{add 3 to both sides}\\x=3[/tex]