Horizontal Method For Numbers 3 - 4,PLS HELP 100 POINTS


1. ( 3 x − 3 ) ( 8 x + 1 )

= ( ) ( 8 x ) + ( ) ( 1 ) − ( 8 x ) − 3 ( )

= ( ) x ^2 + 3 x − ( ) x − 3

= ( ) x ^2 − ( ) x − 3


2. ( x − 4 ) ( 3 x − y + 3 )

= x ( ) + x ( ) + x ( ) − 4 ( ) − 4 ( ) − 4 ( )

= 3 x ^2 − ( ) + ( ) − ( ) + ( ) + ( )

= 3 x ^2 − x y − 9 x + 4 y + 12

PLS HELP GIVING 100 POINTS

The round-off of the number 216,777777 to 2 decimal places​ is 216.78.

When a number is rounded off, its value is preserved while it is moved closer to the next number. simplifying the number. It is done for whole numbers as well as decimals at different places of hundreds, tens, tenths, and so on.

A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. If the number after it is between 5 and 9, it will be rounded up to its higher value.

To round 216,777777 to 2 decimal places, we look at the third decimal place, which is 7. Since 7 is greater than or equal to 5, we round up the second decimal place, which is 7. Therefore, 216,777777 rounded to 2 decimal places is 216,78.

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Answer:

Let q be the number of quarters in the jar and d be the number of dimes in the jar.

The total number of coins in the jar is given as 54, so we can write:

q + d = 54

The total value of the coins is $16.85. We can express this as the sum of the values of the quarters and the dimes in the jar:

0.25q + 0.10d = 16.85

Therefore, the system of equations that can be used to determine the number of quarters and dimes in the jar is:

q + d = 54

0.25q + 0.10d = 16.85

The final answers are:

Example 4. 45: 1

46: 1

47: \( \frac{17}{12} \)

To evaluate each expression, we can use the identities for sine and cosine, and then simplify.

For example 4. 45, we have:

\( \sin ^{2} 120^{\circ}+\cos ^{2} 120^{\circ} \)

= \( (\frac{\sqrt{3}}{2})^{2}+(-\frac{1}{2})^{2} \)

= \( \frac{3}{4}+\frac{1}{4} \)

= 1

For 46. \( \sin ^{2} 225^{\circ}+\cos ^{2} 225^{\circ} \), we have:

= \( (-\frac{\sqrt{2}}{2})^{2}+(-\frac{\sqrt{2}}{2})^{2} \)

= \( \frac{2}{4}+\frac{2}{4} \)

= 1

For 47. \( 2 \tan ^{2} 120^{\circ}+3 \sin ^{2} 150^{\circ} \), we have:

= \( 2(\frac{\sqrt{3}}{3})^{2}+3(\frac{1}{2})^{2} \)

= \( 2(\frac{1}{3})+3(\frac{1}{4}) \)

= \( \frac{2}{3}+\frac{3}{4} \)

= \( \frac{8}{12}+\frac{9}{12} \)

= \( \frac{17}{12} \)

So the final answers are:

Example 4. 45: 1

46: 1

47: \( \frac{17}{12} \)

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Answer:

2 tangents

with common points p and O touching both the circles only 2 tangets can be drawn

The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.

The function for this given problem is defined as follows:

y = 1.5x² + 4x - 2.

a 1.5, b 4, c -2.

By Solving the equation we get these values,

x = -3.09, hence function passes through the point (-3.09, 0).

x = 0.43, hence function passes through the point (0.43, 0).

The y-intercept of this function is given by coefficient c = -2, hence the function also passes through the point (0, -2).

The x-coordinate vertex is given as follows:

x = -b/2a = -4/3 = -1.33.

Hence the y-coordinate vertex is of:

y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.

Missing Information

The problem asks for the graph of the following function is given below:

y = 1.5x² + 4x - 2.

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Answer:

mAngle EFG = 139°

mAngle IFH = 49°

Step-by-step explanation:

First, just look at the top half of the diagram. Straight across D, F, G is a straight line. That's 180° We can write an equation with the two marked angles added up, equal to 180° to solve for x and to solve for those two angles. See image.

Then look for two crossing lines that makes a giant x (not a variable, on the image) That's EH and DG. The angles that are across from each other are called Vertical angles and they are equal to each other. See image.

Last, see the bottom part of the image where an angle is marked with a little tiny square. That means its a right angle and is 90°. We can subtract to find the second angle that we're being asked to find. See image.

The coefficient of the first term is 80, and the degree is 9; the coefficient of the second term is -6, and the degree is 4; the coefficient of the third term is -8, and the degree is 0. The polynomial is 80x^(9)y^(2)-6x^(4)yz-8.

The coefficient of a term in a polynomial is the number that is multiplied by the variable(s) in the term. The degree of a term is the sum of the exponents of the variables in the term.

In the first term, 80x^(9)y^(2), the coefficient is 80 and the degree is 9 + 2 = 11.

In the second term, -6x^(4)yz, the coefficient is -6 and the degree is 4 + 1 + 1 = 6.

In the third term, -8, the coefficient is -8 and the degree is 0 since there are no variables.

The polynomial is already in standard form, so there is no need to find the polynomial. It is simply 80x^(9)y^(2)-6x^(4)yz-8.

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The measures of the two interior angles are:

x = 62°

y = 118°

We can see a cuadrilateral, if the sides are parallel like in this case, opposite interior angles have the same measure, then:

x = 62°

And we know that adjacent angles should add up to 180°, then:

y+ 62° = 180°

y = 180° - 62° = 118°

These are the measures of the two interior angles.

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The polynomial in factored form as a product can be found by using the factor theorem and synthetic division. The factor theorem states that if f(a) = 0, then (x-a) is a factor of f(x). We can use synthetic division to find the factors of f(x)=12x^(5)+5x^(4)-39x^(3)+9x^(2)+19x-6.

First, we need to find a value of x that makes f(x) = 0. We can use the rational root theorem to find possible rational roots. The possible rational roots are ±1, ±2, ±3, ±6. We can use synthetic division to test these possible roots.

Using synthetic division with x = 1, we get a remainder of -1, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of f(x).

Now we can divide f(x) by (x+1) using synthetic division to get the quotient 12x^(4)-7x^(3)-32x^(2)+41x-6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this quotient.

The possible rational roots of the quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of 8, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of the quotient.

We can divide the quotient by (x+1) using synthetic division to get the new quotient 12x^(3)-19x^(2)-13x+6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this new quotient.

The possible rational roots of the new quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of -14, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of the new quotient.

We can divide the new quotient by (x+1) using synthetic division to get the new quotient 12x^(2)-31x+6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this new quotient.

The possible rational roots of the new quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of -13, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 49, so x = -1 is not a root. Using synthetic division with x = 2, we get a remainder of 0, so x = 2 is a root and (x-2) is a factor of the new quotient.

We can divide the new quotient by (x-2) using synthetic division to get the new quotient 12x-3. This quotient cannot be factored further, so the factors of f(x) are (x+1)(x+1)(x+1)(x-2)(12x-3).

Therefore, the polynomial in factored form as a product is f(x) = (x+1)(x+1)(x+1)(x-2)(12x-3).

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Answer:

CD = 22

Step-by-step explanation:

You would double the side lengths given since this is a rectangle and set them equal to 80 cause that is the perimeter. So the equation would be 6z + 6 + 8z + 4 = 80. You would use the PEDMAS rule and subtract 6 from both sides which gives you:

6z + 8z +4 = 74

Subtract 4 from both sides

6z + 8z = 70

Add 6z + 8z

14z = 70

Divide 70 and 14z

z = 5.

AB and CD is equal in length so all you have to do is plug in 5 to z in the AB equation.

4(5) + 2

= 22

The principal amount lent out at simple interest is RS.690 in 3 years and RS.750 at the end of the second year RS.738.

To calculate the amount of money that needs to be lent out, use the following formula:

Amount = Principal * (1 + (Rate * Time))

Where:
Principal = 690
Rate = 0.05 (5% simple interest rate)
Time = 2 years

Therefore, the amount to be lent out is:
Amount = 690 * (1 + (0.05 * 2)) = 738

Therefore, the amount to be lent out is RS.738.

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Answer:

48 cups

Step-by-step explanation:

‐-------------------

Answer:

13

Step-by-step explanation:

First drop the line.

How many units is it from Point [tex]r[/tex] to the x axis?

12.

How many units is it from Point [tex]r[/tex] to the y axis?

5.

Now we can use the Pythagorean Theorem.

[tex]12^5+5^2=c^2[/tex]

[tex]144+25=c^2[/tex]

[tex]c^2=169[/tex]

[tex]c=13[/tex]

The trigonometric ratios of sine and cosines indicates that we get;

Trigonometric ratios specify the relationship between two sides of a right triangle and the acute angle in the right triangle.

The specified equations are presented as follows;

1. sin(55) = cos(θ)

The sine of an angle is the ratio of the opposite side to the angle in a right to the hypotenuse side of the right triangle

The trigonometric ratio of the cosine of an angle is the ratio of the adjacent side to the angle to the hypotenuse side in a right triangle

The acute angles in a right triangle are complementary

Let A and B represent the acute angles of a right triangle, we get;

The adjacent side to the angle A is the opposite side to the angle B

The hypotenuse side remains the same, therefore;

cos(A) = sin(B), and sin(A) = cos(A)

Which indicates; sin(55) = cos(90 - 55) = cos(35)

sin(55) = cos(θ) = cos(35)

2. cos (28) = sin(90 - 28) = sin(62)

cos(28) = sin(62)

sin(θ) = sin(62) = cos(28)

3. cos(y) = sin(θ)

cos(y) = sin(90 - y)

cos(y) = sin(90 - y) = sin(θ)

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a. The equation "(a) x2+3​=x+4" gives the solution as x = 1.

b. The equation "(b) 2x-1​-x-4=2" gives the solution as x = -1.

To solve these radical equations, we will need to isolate the radical on one side of the equation and then square both sides to get rid of the radical. After that, we can solve for x using standard algebraic methods.

(a) x2+3​=x+4

First, we will isolate the radical on one side of the equation:
x2+3​=x+4
x2=x+4-3
x2=x+1

Now, we will square both sides of the equation to get rid of the radical:
(x2)2=(x+1)2
x4=x2+2x+1

Next, we will rearrange the equation and set it equal to zero:
x4-x2-2x-1=0

Now, we can use the quadratic formula to solve for x:
x=(-(-2)±√((-2)2-4(1)(-1)))/(2(1))
x=(2±√(4+4))/(2)
x=(2±√8)/(2)
x=(2±2√2)/(2)
x=1±√2

So, the solutions for x are 1+√2 and 1-√2.

(b) 2x−1​−x−4​=2

First, we will isolate the radical on one side of the equation:
2x−1​=x−4+2
2x−1​=x−2

Now, we will square both sides of the equation to get rid of the radical:
(2x−1)2=(x−2)2
4x2-4x+1=x2-4x+4

Next, we will rearrange the equation and set it equal to zero:
3x2=3

Now, we can solve for x by dividing both sides of the equation by 3 and taking the square root:
x2=1
x=±√1
x=±1

So, the solutions for x are 1 and -1.

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The following function can be used to find b:

b= 7d

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

7 boxes per day

=> For d days , the number  boxes will be 7d

total number of boxes

b= 7d

when b=  3,500 ,

3500= 7d

=> d= 3500/7 = 500 days

The following function can be used to find b:

b= 7d

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The second smallest number that has 1, 2, 3, 4, and 5 as factors is 360.

What is factorization?

A number or other mathematical object is factorization or factored when it is written as the product of numerous factors, often smaller or simpler things of the same sort.

To find the smallest number that has 1, 2, 3, 4, and 5 as factors, we can simply multiply these numbers together, since they are all factors of their product:

1 × 2 × 3 × 4 × 5 = 120

Now we need to find the second smallest number with these factors. One way to approach this is to list out the multiples of 120 until we find a number that also has the factors 1, 2, 3, 4, and 5, and is larger than 120.

Multiplying 120 by 2, 3, 4, 5, and 6 gives us the multiples:

240, 360, 480, 600, 720

Checking each of these multiples, we see that only 360 has all the factors 1, 2, 3, 4, and 5. Therefore, the second smallest number that has 1, 2, 3, 4, and 5 as factors is 360.

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The solution set is {6, 7, 8, …} for x ∈ N and the value of a number substituted for x is greater than 6.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Here, we have

Given: Inequality:

12+11/6x ≤  5+3x

We have to determine the statement(s) and number line(s) that can represent the inequality.

12+11/6x ≤  5+3x

12(6x) + 11 ≤  6x(5+3x)

72x +132 ≤ 30x + 18x²

42x + 132 ≤ 18x²

7x + 22x ≤  3x²

we concluded that the value of a number substituted for x is greater than 6.; b. The solution set is {6, 7, 8, …} for x ∈ N." These are the statements and number lines that can represent inequality.

Hence, the solution set is {6, 7, 8, …} for x ∈ N, and the value of a number substituted for x is greater than 6.

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Answer:

Step-by-step explanation:

The llsab have to be divided by the number quotient and then once your sllab get hot then you answer.

READ THIS BACKWARDS

Answer:  39

Step-by-step explanation:   9 = ? - 30, add 30 on both sides you get 39=?

2x+7y+2z+10=0 is the equation of the plane passing through A(-2, 0, -3) and B(1, -2, 1) that lies parallel to the line through C(-2, -13/5, 26/5) and D(16/5, -13/5, 0).

The equation of the plane passing through a point (a,b,c) can be written as A(x-a) + B(y-b) + C(z-c) = 0, where A, B and C are the coefficients of the normal vector to the plane.

So, the equation of the plane passing through a point (-2,0,-3) can be written as A(x+2) + B(y) + C(z+3) = 0,...i)

Now the plane also passes through the point (1,-2,1) so A(1+2) + B(-2) + C(1+3) = 0,

So, 3A-2B+4C=0.........ii)

Now, the direction cosines of CD is

l= 16/5 +2= 26/5

m= -13/5+13/5 = 0

n= 0-26/5 = -26/5

For a plane and line to be perpendicular Dot product of the direction cosines must be zero

or A*26/5 +  B*0 + C*-26/5=0

or, A=C.....iii)

Putting this in i) 7A-2B=0 or, A=2B/7....iv)

putting iii) and iv)

A(x+2) + B(y) + C(z+3) = 0

or, A(x+2) + B(y) + A(z+3) = 0

or, 2*B*(x+2)/7 + B(y) + 2*B*(z+3) /7= 0

or 2*(x+2)/7 + y + 2*(z+3) /7= 0

or 2x+7y+2z+10=0

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The values of k that make the system inconsistent are k = 0 and k = 2.

The system obtained from the given augmented matrix is:
```
1 2 -1 | 4
0 -1 1 | 3
0 0 k^2-2k | -3k-3
```
For the system to be inconsistent, the last equation must be a contradiction, meaning that the coefficients of the variables are all zero but the constant term is nonzero. In other words, we need `k^2-2k = 0` and `-3k-3 ≠ 0`.

Solving for k in the first equation, we get:
```
k^2-2k = 0
k(k-2) = 0
```
So k = 0 or k = 2.

However, we also need `-3k-3 ≠ 0`, which means that k ≠ -1. Therefore, the values of k that make the system inconsistent are k = 0 and k = 2.

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Answer: Let's use the trigonometric ratio of sine to find the measure of the larger acute angle of the right triangle. We have:

sin(theta) = opposite / hypotenuse

where theta is the measure of the larger acute angle, and opposite is the length of the shorter leg of the right triangle. Substituting the given values, we get:

sin(theta) = 2sqrt(6) / 2sqrt(15)

          = sqrt(2/5)

Using a calculator, we can find the value of theta to the nearest tenth of a degree:

theta = arcsin(sqrt(2/5))

     ≈ 38.2°

Therefore, the measure of the larger acute angle of the right triangle is approximately 38.2 degrees.

Step-by-step explanation:

The sum of the digits of the number which when added to 2000 makes the resulting number divisible by 12,16,18 and 21 is 7

The smallest number which when added to 2000 makes the resulting number divisible by 12, 16, 18, and 21 is 312. The sum of the digits of x is 3 + 1 + 2 = 6.

To find the smallest number x that can be added to 2000 to make the resulting number divisible by 12, 16, 18, and 21, we need to find the least common multiple (LCM) of these numbers.

The LCM of 12, 16, 18, and 21 is 1008. Then we need to find the smallest multiple of 1008 that is greater than 2000. This is 1008 * 3 = 3024. The difference between 3024 and 2000 is 1024, so x = 1024.The sum of the digits of x is 1 + 0 + 2 + 4 = 7. Therefore, the sum of the digits of x is 7.

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The difference in interest earned between the twο investments is R5 118.08.

There are twο main types οf interest: simple interest and cοmpοund interest. Simple interest is calculated οnly οn the principal amοunt, while cοmpοund interest is calculated οn bοth the principal amοunt and any accumulated interest frοm previοus periοds.

Interest rates can be fixed οr variable. A fixed interest rate remains the same thrοughοut the lοan οr investment periοd, while a variable interest rate can change οver time depending οn market cοnditiοns.

Interest is an impοrtant cοncept in finance and ecοnοmics, and it plays a key rοle in bοrrοwing and lending, investments, and savings.

Investment A:

Simple interest = P × r × t

Where P = R5 500, r = 8% = 0.08 and t = 4 years

Simple interest = 5500 × 0.08 × 4

Simple interest = 1760

Investment B:

Cοmpοund interest = [tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

Where P = R5 500, r = 7.5% = 0.075, n = 1 (as it is cοmpοunded annually) and t = 3 years

Cοmpοund interest = [tex]$5500 \times (1 + \frac{0.075}{1} )^{(1 \times 3)} - 5500[/tex]

Cοmpοund interest = 1332.63

The difference between the interest earned οn the twο investments is:

Difference = Investment A - Investment B

Difference = 1760 - 1332.63

Difference = 427.37

Therefοre, the difference in interest earned between the twο investments is R5 118.08.

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Step-by-step explanation:

the error happened in line 2 :

(2x - 3)(6x + 2)

= 2x6x + 2×2x - 3×6x - 3×2 (instead of +3×2)

the error was using the wrong sign for the term 3×2. it was created by -3 multiplied by +2 = -3×2.