The polynomial p(x) = x3 + 3x2 - 4 has a known factor of (1 - 1).
Rewrite p(x) as a product of linear factors.​

Step-by-step explanation:

In circle with centre O.

[tex]OA \cong OB.. (Radii\: of \:same \:circle) \\

\therefore m\angle OAB = m\angle OBA =28°\\

(m \angle 's \:opposite \:to \:congruent \:sides \:\\are \:equal) [/tex]

[tex] m \angle AOB = 180°-(m\angle OAB + m\angle OBA)\\

\therefore\: m \angle AOB = 180°-(28° + 28°)\\

\therefore\: m \angle AOB = 180°-56°\\

\therefore\: m \angle AOB = 124°\\

m \angle ACB = \frac{1}{2} \times m \angle AOB[/tex]

[tex](m\angle\: formed\: on\: the \:circle \:\\is\: half\: the\:\angle\: formed\: at\: the \:center\: \\of \:the \:circle)[/tex]

[tex] \therefore\: m \angle ACB = \frac{1}{2} \times 124°\\

\therefore\: m \angle ACB = 62°\\[/tex]

Answer:

4,000

Step-by-step explanation:

Answer:

  1

Step-by-step explanation:

Three side lengths uniquely specify one triangle.

__

Additional comment

All triangles formed with the same three specific side lengths are considered to be congruent. However, the sides can be arranged smallest-to-largest in CW or CCW order. If the triangle is scalene, the different ordering will result in congruent triangles that will not overlay one another.

Only one unique triangle can be formed

Triangle

A triangle is a three-sided polygon with three vertices and three edges. It is a fundamental geometric shape.

How many unique triangle with given side lengths of 8 inches, 10.3 inches, and 13 inches?

only one unique triangle can be formed with sides length of 8 inches, 10.3 inches, and 13 inches

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Answer:

-1    i hope this helps!    :)

Step-by-step explanation:

you are given both 10b + 19    and b = -2

lets plug in the value of b

10b(-2) + 19

multiply the 10b and the -2

-20b + 19

-20 + 19 = -1

-1

Answer:

To calculate the volume of a sphere, use the formula v = ⁴⁄₃πr³, where r is the radius of the sphere. If you don't have the radius, you can find it by dividing the diameter by 2. Once you have the radius, plug it into the formula and solve to find the volume.

Step-by-step explanation:

To find the volume of a soccer ball,the formula is V=4/3 πr^3,where r is the radius and π=3.14. A regulation soccer ball has a radius of 35cm. find the volume of a soccer ball to the nearest cubic centimeter. This is just some to keep in mind.

Says shouldn’t  Say 18 inches because that is  1 ft 6 inches

Answer: slope = -3/2

Y intercept = -2

Step-by-step explanation:

Final answer:

The maximum volume of paint required is 2 liters.

Explanation:

To calculate the maximum volume of paint needed to paint the wall, we need to first determine the area of the wall. The wall measures 2.1 m by 5.2 m, so the area is:

Area = Length × Width = 2.1 m × 5.2 m = 10.92 m²

Now, we know that one tin of paint covers 3.5 m² and contains 0.5 liters of paint. To find the number of tins needed, we divide the total area by the area covered by one tin:

Tins needed = Total area / Area per tin = 10.92 m² / 3.5 m²

Tins needed = 3.12

Since we cannot buy a fraction of a tin, we need to round up to the nearest whole number, which means Max needs 4 tins of paint. To find the total volume of paint, we multiply the number of tins by the volume of one tin:

Total volume = Tins needed × Volume per tin = 4 × 0.5 L = 2 L

Therefore, the maximum volume of paint Max will need is 2 liters.

To simplify the expression 15/1+4 + 6+3/3, we perform the division operations first, followed by addition, which results in the simplified expression of 26.

To simplify the expression 15/1+4 + 6+3/3 using the order of operations, we must follow specific rules. The order of operations is often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). In the absence of parentheses and exponents in this expression, we'll focus on the multiplication/division and addition/subtraction.

First, let's look at the division and multiplication. Since there's no multiplication, we only need to perform the division operations, and we proceed from left to right:

Now we are left with the addition operations:

15 + 4 + 6 + 1 = 26

Therefore, the simplified expression is 26. To generate accurate answers, always follow the order of operations diligently.

The simplified expression is [tex]\( 26 \).[/tex]

To simplify the expression using the order of operations (PEMDAS/BODMAS), we follow these steps:

1. Parentheses/Brackets

2. Exponents/Orders

3. Multiplication and Division (from left to right)

4. Addition and Subtraction (from left to right)

Given the expression [tex]\( \frac{15}{1} + 4 + 6 + \frac{3}{3} \),[/tex] let's simplify it step by step:

1. Solve the division: [tex]\( \frac{15}{1} = 15 \) and \( \frac{3}{3} = 1 \).[/tex]

2. Now, we have:[tex]\( 15 + 4 + 6 + 1 \).[/tex]

3. Perform addition from left to right: [tex]\( 15 + 4 = 19 \), \( 19 + 6 = 25 \), \( 25 + 1 = 26 \).[/tex]

Therefore, the simplified expression is [tex]\( 26 \).[/tex]

Answer:

x1 = 0.45 and x2 = -1.12

Step-by-step explanation:

To solve the equation 6x2+4x−3=0 using the quadratic formula, we use the following equation:

x = [-b ± √(b2 - 4ac)] / 2a

Where a, b and c are coefficients of the quadratic equantion (in our case, a = 6, b = 4 and c = -3)

So we have that:

x1 = [-4 + √(16 + 72)] / 12 = (-4 + 9.3808) / 12 = 0.4484

x2 = [-4 - √(16 + 72)] / 12 = (-4 - 9.3808) / 12 = -1.1151

Rounding to nearest hundredth, we have x1 = 0.45 and x2 = -1.12

Answer:

1.5 pages per minute.

Step-by-step explanation:

Answer:

Anna Maria reads 0.66 (2/3) page per minute

Step-by-step explanation:

Unit rate (speed)=distance/time, so you would divide 40 by 60. that simplifies to 2/3, or .66

The coefficient for x² in the equation x² - 5x + 6 is 1, as it is the implied coefficient when no numerical coefficient is written before a term in a polynomial.

The coefficient for x2 in the polynomial equation x2 - 5x + 6 is implied to be 1. When a term in a polynomial has no numerical coefficient written, it is understood that the coefficient is 1. In any polynomial equation of the form ax2 + bx + c = 0, the coefficient of x2 is represented by a. In the given expression, since there is no number in front of x2, a is 1. Therefore, the coefficient of x2 in the equation x2 - 5x + 6 is 1.

Answer:

54/25

Step-by-step explanation:

Answer:

[tex]cos(D)=0.51[/tex]

[tex]m\angle D=59.49^o[/tex]

Step-by-step explanation:

we know that

In the right triangle DEF

[tex]cos(D)=\frac{DF}{ED}[/tex] ---> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

[tex]cos(D)=\frac{33}{65}=0.51[/tex]

using a calculator

[tex]m\angle D=cos^{-1}(\frac{33}{65})=59.49^o[/tex]

To find the value of the cosine of angle ∠D in triangle ΔDEF, use the cosine formula with the given side lengths which is 59.49 degrees.

In the given triangle ΔDEF, the measure of angle ∠F is 90°. We are given the lengths of the sides DF, FE, and ED as 33, 56, and 65 units respectively. To find the value of the cosine of angle ∠D, we need to use the cosine formula:

cos(D) = (DF2 + DE2 - EF2) / (2 * DF * DE)

Substituting the known values, we have:

cos(D) = (332 + 652 - 562) / (2 * 33 * 65)

= 59.49

Simplifying this expression gives us the value of the cosine of angle ∠D.

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Answer:

[tex]x=4[/tex]

Step-by-step explanation:

Step 1:  Make an equation

[tex]\frac{12}{6} = \frac{x}{2}[/tex]

Step 2:  Cross multiply

[tex]\frac{12}{6} = \frac{x}{2}[/tex]

[tex]x * 6 = 12 * 2[/tex]

[tex]6x = 24[/tex]

Step 3:  Divide both sides by 6

[tex]6x / 6 = 24 / 6[/tex]

[tex]x=4[/tex]

Answer:  [tex]x=4[/tex]

Answer:32

Step-by-step explanation:

then the ratio belonging to apple is four

so u divide 4 by 5 then multiply to the total no of fruit

and that will give u 32

A ratio shows us the number of times a number contains another number. The number of apples in the basket is 32.

A ratio shows us the number of times a number contains another number.

Let the number of apples and oranges in the basket be represented by 4x and x respectively.

Given the total number of fruits in the basket is 40. Therefore, the sum of the number of fruits can be written as,

[tex]4x+x=40\\5x=40\\x=8[/tex]

The number of apples = 4x = 4(8) = 32

Hence, the number of apples in the basket is 32.

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Hope this will help u....:)

Look at the attached picture ⤴⤴

The composite function -3 x f(-8) +7 x g(2) has a value of 53

How to evaluate the composite function

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x + 3 and g(x) = x

Calculating f(-8) and g(2), we have

f(-8) = 2 * -8 + 3 and g(2) = 2

Evaluate

f(-8) = -13 and g(2) = 2

Using the above as a guide, we have the following:

-3 x f(-8) +7 x g(2) = -3 * -13 + 7 * 2

Evaluate

-3 x f(-8) +7 x g(2) = 53

Hence, the composite function has a value of 53

Question

Evaluate the expression -3 x f(-8) +7 x g(2) if f(x) = 2x + 3 and g(x) = x

Answer:

It should be

A

F

D

Step-by-step explanation:

Just do A^2+B^2=C^2 and plug in what the three given numbers are, if A^2+B^2=C^2 and it comes out as correct meaning the sum of A and B is equal to C than boom you have a triple

Answer would be option(A){6, 8, 10}, (D) {12, 16, 20} and (F) {15, 20, 25} are examples of Pythagorean Triples

What is Pythagoras theorem?

Pythagoras theorem states that, a right-angled triangle, the square of the one side is equal to the sum of the squares of the other two sides.

{6, 8, 10}, {12, 16, 20} and {15, 20, 25} is the three Pythagorean Triples where any 2 side the sum of the squares adds up to be equal the other side.

We can test this:

6²+ 8² = 10² ⇒ 100=100

12²+16²= 20² ⇒ 400=400

15²+ 20²= 25²⇒ 625=625

Hence, {6, 8, 10}, {12, 16, 20} and {15, 20, 25} is the three Pythagorean Triples

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Answer:

36 degrees

Step-by-step explanation:

Answer:

a.p/100

b.56

Step-by-step explanation:

2% of p=k

2/100 ×p=k

2p/100=k

Cross multiply 2p=100k

P=100k/2

p=50k

Let's make k the subject of formula

k=p/50

So 50% of k in terms of p

50/100×k

And k=p/50

So let's substitute

50/100×p/50

P/100

Therefore 50%of k=p/100

Let the unknown number be x

10% of x is 7

10/100×x=7

10x/100=7

Cross multiply

10x=(100)(7)

10x=700

Divide both sides by 10

X=70

So 80% of 70

80/100×70

5600/100

=56

Therefore 80% of 70=56

The student solved the system of equations by substitution. He substituted y = x - 1 into the first equation and solved for x. He then substituted the value of x into the second equation to find the value of y.

The correct statement could be that Vince substituted the equation y = x - 1 into the first equation -5x + y = -21. Next, he solved for x. Once he found the value for x, he substituted that into the equation y = x - 1 to find the value of y, providing the solution to the system of equations.

Step-by-step:

So, the solution to the system is x = 5, y = 4.

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Answer:

The area of the sector is  [tex]\frac{\pi}{2}\ units^2[/tex]

Step-by-step explanation:

step 1

Find the area of complete circle

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

we have

[tex]r=3\ units[/tex]

substitute

[tex]A=\pi 3^2\\A=9\pi\ units^2[/tex]

step 2

Find the area of the sector

we know that

The area of complete circle subtends a central angle of 2π radians

so

using proportion

Find out the area of a sector by a central angle of 1/9 pi radians

[tex]\frac{9\pi}{2\pi}=\frac{x}{\frac{1}{9}\pi} \\\\x=9\pi(\frac{1}{9}\pi})/2\pi\\\\x=\frac{\pi}{2}\ units^2[/tex]

Answer:

80 dollar tip

Step-by-step explanation:

16 percent of 500=80

Answer: That would be $580.

Step-by-step explanation: The tip is equal to $80 itself self you add the original amount ($500) to the tip (16%=$80) the total will be $580.

Answer:

The two polynomial CAN be [tex]5x^4+5x^3+8x^2+x+6[/tex] and [tex]5x^4+5x^3+8x^2+2x+13[/tex].

Step-by-step explanation:

Step 1: Simplify the expression:

[tex]2*2 + x + 3[/tex]

[tex]4+x+3[/tex]

[tex]x+7[/tex]

Step 2: Think of a random polynomial:

[tex]5x^4+5x^3+8x^2+x+6[/tex]

Step 3: Either add your "random polynomial" by [tex]x+7[/tex] or subtract it.

I want to add it so...

[tex]5x^4+5x^3+8x^2+x+6+x+7[/tex]

= [tex]5x^4+5x^3+8x^2+2x+13[/tex]

 Check by subtracting  [tex]5x^4+5x^3+8x^2+x+6[/tex] and [tex]5x^4+5x^3+8x^2+2x+13[/tex].

         [tex]5x^4+5x^3+8x^2+2x+13[/tex]

   -      [tex]5x^4+5x^3+8x^2+x+6[/tex]

        _____________________

         [tex]0x^4 - 0x^3 -0x^2 +x +7[/tex] or  [tex]x+7[/tex]

Answer:

16/3 or 5 1/3

Step-by-step explanation:

Plugging in 2 for n, you get(2/3*6)+(2/3*2)=4+4/3=16/3= 5 1/3. Hope this helps!

Answer:

6 ounces

Step-by-step explanation:

So set your equation up as

12(x)+20(6)=16(x+6)

You set it up this way because with the first number you know the percet but not the ounces so your ounces would be x. The second set you know percet and ounces (the percent will alway go outside the parenthesis). then the last number is waht it wil equal; again we know the percent but not the product. We put x+6 in the parenthesis because you are adding the ounces your don't know(x) wiht the ones you do (6).

To solve distribute

12x+120=16x+96

Now all you have to do is solve for x. Subtract the 96 over then subtract the 12x over, so it would look like this.

12x+120=16x+96

      -96         -96

12x+24=16x

-12x       -12x

24=4x    Now simply divide by 4 and you get 6=x

There should be 6 ounces mixed in order to get the required solution.

Let the number of ounces be represented by x.

Based on the equation, the equation to use will be:

12(x) + 20(6) = 16(x + 6)

Expand the equation

12x + 120 = 16x + 96

Collect like terms

16x - 12x = 120 - 96

4x = 24

Divide both side by 4

4x/4 = 24/4

x = 6

Therefore, the number of ounces will be 6 ounces.

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Answer:

1.08 ⋅ 10 ^8 km

Step-by-step explanation:

Answer:

198

Step-by-step explanation:

(6-3) x 66 subtract

3x66 multiply

198