​3 + 10x+ 4x as an algebradic expression

144x² - 24x + 1 = 12²x² - 24x + 1 = (12x)² - 2(12x) + 1² = (12x - 1)²

The Big Ideas or Focal Points in the mathematics curriculum in grades 4 are as follows:

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The angle LZW, given that angles Izw and Wzo are supplementary, would be an Obtuse angle.

If the angles Izw and Wzo are supplementary, then their sum is equal to 180 degrees.

Since Wzo is an acute angle (meaning it measures less than 90 degrees), we know that Izw must be an obtuse angle, so that their sum is 180 degrees. An obtuse angle is an angle that measures greater than 90 degrees and less than 180 degrees. It is "obtuse" because it is more than a right angle (90 degrees), which is considered "sharp" or "acute".

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The value of x in the sequence notation is 27/4

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

[tex]\sum\limits^4_{j=-2} {2x(-\frac{3}{2})^j = \frac{1389}{32}[/tex]

When the above expression is expanded, we have the following equation

2x[(-3/2)⁻² + (-3/2)⁻¹ + (-3/2)⁰ + (-3/2)¹ + (-3/2)² + (-3/2)³ + (-3/2)⁴] = 1389/32

Evaluate the exponents the expressions

So, we have

2x[4/9 - 2/3 + 1 - 3/2 + 9/4 - 27/8 + 81/16] = 1389/32

Evaluate the fractions

2x * 463/144 = 1389/32

Evaluate the products

x * 463/72 = 1389/32

Solve for x

x = 72/463 * 1389/32

Evaluate

x = 27/4

Hence, the value of x is 27/4

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The elevation of the gun will the projectile hit the missile will be 62.18°.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

Let 't' be the time. And 'θ' be the angle. Then the measure of the angle is given as,

688t / sin 35° = 548 / sin θ

sin θ = 0.4568

θ = 27.18°

The angle from the base is calculated as,

⇒ 27.18° + 35°

⇒ 62.18°

The elevation of the gun will the projectile hit the missile will be 62.18°.

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Using the circumference formula of the circle, we know that the area of the shaded region is 2,375 in.

The circumference of a circle is the distance encircling its edge.

The diameter of a circle is the distance measured through its center.

The radius of a circle is the distance from the center to any point on the edge.

The circumference of a circle or ellipse in geometry is its perimeter.

That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.

The curve length around any closed figure is more often referred to as the perimeter.

So, the circumference of the inner circle is 125.6 inches.

Then, the radius would be:

C = 2πr

125.6 = 2πr

125.6 = 6.28r

r = 125.6/6.28

r = 20 in

r for the outer circle: r will be 20 + 14 = 34 in

Area of the inner circle:

A = πr²

A = π20²

A = 1256.63706

A = 1257 in

Area of the outer circle:

A = πr²

A = π34²

A = 3631.68111

A = 3632 in

Area of the shaded region:

3632 in - 1257 in = 2,375 in

Therefore, using the circumference formula of the circle, we know that the area of the shaded region is 2,375 in.

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The rate of interest per annum will be 3.6%.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

Given, Isabelle takes out a loan that gathers compound interest.

At the start, the loan amount is £5500

after the 1-year loan amount is £5698.00

After the 2-year loan amount is £5903.13

thus,

P = 5500

For t = 1 year A = 5698.00

since interest is annually thus, the value of n is 1

So, from the formula

5698 =  5500( 1 + r)

5500r = 5698 -5500

r = 198/5500

r = 0.036

or

rate of interest, r = 3.6%

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The functions that represent a horizontal dilation of the function y = log x are A and C.

Horizontal dilation, also known as horizontal stretching or compression, is a transformation of a function that changes the shape of its graph by scaling the independent variable (x-axis).

When a function is horizontally dilated, it is stretched or compressed horizontally without changing its vertical position. If the function is stretched horizontally, it becomes flatter and wider, while if it is compressed horizontally, it becomes steeper and narrower.

Horizontal dilation is achieved by multiplying the independent variable x in the function by a positive constant a. If a > 1, the function is horizontally compressed, and if 0 < a < 1, the function is horizontally stretched. If a = 1, the function is not affected by horizontal dilation.

The function that represents a horizontal dilation of the function y = log x is a function of the form y = log(ax), where a is a positive constant. This is because changing the value of a will stretch or compress the graph horizontally.

A. h(x) = log(2x) + 1 represents a horizontal compression by a factor of 2, followed by a vertical translation upward by 1 unit.

B. K(x) = log(x + 1) represents a horizontal translation to the left by 1 unit.

C. f(x) = log(0.3x) represents a horizontal compression by a factor of 1/0.3 = 3.33.

D. g(x) = 5 log(x) represents vertical stretching by a factor of 5.

Therefore, the functions that represent a horizontal dilation of the function y = log x are A and C.

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Answer:

Below

Step-by-step explanation:

Volume of a cylinder is given by the formula

V = pir^2 h     SUbstitute in the values given for  r , h

V = pi * (17/2)^2 * 42 = 9533 ft^3 =  353 yd^3  

The solutions for the given equations are:

31. x = 4 or x = -2

32. x = 2+√13 or x = 2-√13

33. x = -3+√5 or x = -3-√5

34. x = -0.5+√4.25 or x = -0.5-√4.25

35. x = 1.5+√1.25 or x = 1.5-√1.25

To solve the equations by completing the square, we will use the following steps:

Step 1: Move the constant term to the right side of the equation.

Step 2: Take half of the coefficient of the x term and square it.

Step 3: Add this value to both sides of the equation.

Step 4: Factor the left side of the equation.

Step 5: Take the square root of both sides of the equation.

Step 6: Solve for x.

Let's apply these steps to the given equations:

31. x^2-2x-8 = 0

Step 1: x^2-2x = 8

Step 2: (-2/2)^2 = 1

Step 3: x^2-2x+1 = 9

Step 4: (x-1)^2 = 9

Step 5: x-1 = ±3

Step 6: x = 4 or x = -2

32. x^2-4x-9 = 0

Step 1: x^2-4x = 9

Step 2: (-4/2)^2 = 4

Step 3: x^2-4x+4 = 13

Step 4: (x-2)^2 = 13

Step 5: x-2 = ±√13

Step 6: x = 2+√13 or x = 2-√13

33. x^2+6x+4 = 0

Step 1: x^2+6x = -4

Step 2: (6/2)^2 = 9

Step 3: x^2+6x+9 = 5

Step 4: (x+3)^2 = 5

Step 5: x+3 = ±√5

Step 6: x = -3+√5 or x = -3-√5

34. x^2+x-4 = 0

Step 1: x^2+x = 4

Step 2: (1/2)^2 = 0.25

Step 3: x^2+x+0.25 = 4.25

Step 4: (x+0.5)^2 = 4.25

Step 5: x+0.5 = ±√4.25

Step 6: x = -0.5+√4.25 or x = -0.5-√4.25

35. x^2-3x+1 = 0

Step 1: x^2-3x = -1

Step 2: (-3/2)^2 = 2.25

Step 3: x^2-3x+2.25 = 1.25

Step 4: (x-1.5)^2 = 1.25

Step 5: x-1.5 = ±√1.25

Step 6: x = 1.5+√1.25 or x = 1.5-√1.25

Therefore, the solutions for the given equations are:

31. x = 4 or x = -2

32. x = 2+√13 or x = 2-√13

33. x = -3+√5 or x = -3-√5

34. x = -0.5+√4.25 or x = -0.5-√4.25

35. x = 1.5+√1.25 or x = 1.5-√1.25

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Answer:

D is the answer trust me

Using some rules for interior angles, we will see that:

x = 22.5

y = 22.5

Remember that the sum of the interior angles of any triangle is 180°.

Now, we can see that :

3x + k = 180°

Where k is the missing angle in the left triangle.

k = 180° - 3x

if we add the 3 interior angles, we will get:

2x + y + 180° - 3x = 180°

y - x = 0°

So x and y have the same value.

If now use the top triangle, we can write:

(90 - y) + 3x + 2x = 180

And we know that y = x

90 -x  + 3x + 2x = 180

90 + 4x = 180

4x = 180 - 90  =90

x = 90/4 = 22.5

Then:

x = 22.5

y = 22.5

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The side of the unknown side of this right angled triangle is 14cm

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given two sides of the triangle are 17cm and 9cm.

We have to find the unknow side of the triangle.

By Pythagoras theorem we find the length of unknown side.

The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

17²=9²+x²

289-81=x²

208=x²

Take square root on both sides

x=√208

x=14.42 cm

Hence, the side of the unknown side of this right angled triangle is 14cm

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The correct options are A, D, and E. Option B is not a valid ordinal number ending, and option C does not match any of the given cardinal numbers.

What is cardinal number ?

A cardinal number is a type of number used to represent the size or quantity of a set or collection of objects. It is a number that expresses how many objects are in a particular set or group, and is used to answer questions like "how many?"

For example, the cardinal number of the set {1, 2, 3} is 3, because there are three objects in the set. The cardinal number of a set can be finite or infinite, depending on whether the set has a definite number of elements or not.

The ordinal numbers corresponding to the cardinal numbers are:

183: 183rd

201: 201st

82: 82nd

Therefore, the correct options are A, D, and E. Option B is not a valid ordinal number ending, and option C does not match any of the given cardinal numbers.

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If Lin's sister dοes nοt make any depοsits οr withdrawals, the balance in her accοunt after 22 days will be -$133.57.

The balance is the sum οwing οn an accοunt in banking and accοunting. The term "balance" in bοοkkeeping refers tο the difference between the tοtal οf debit entries and the tοtal οf credit entries made intο an accοunt οver the cοurse οf a certain financial periοd. The accοunt shοws a debit balance when tοtal debits exceed tοtal credits.

Net debt is represented by an accοunt balance that is less than zerο. An accοunt with a minus sign (-) at the end οf the amοunt typically has a negative balance οr is in debt.

Given,

The fee charged when the balance falls belοw zerο = $5.95/day

The current balance in Lin's sister's accοunt = −$2.67

We are asked tο find her accοunt balance after 22 days if nο transactiοns are made.

Since the current balance in her accοunt is belοw zerο, a fee will be charged.

The fee charged fοr 22 days = 5.95 × 22 = $130.9

Then the current balance = -2.67 - 130.9 = -$133.57

Therefοre if Lin's sister dοes nοt make any depοsits οr withdrawals, the balance in her accοunt after 22 days will be -$133.57.

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The exact value of cos(2a) is 7/25 and the exact value of sin a/2 is √10/10. Remember to consider which sign is appropriate when using the trigonometric identities.

Given tan a = 3/4, and sin a = -3/5, we can find the exact value of cos(2a) and sin a/2 by using the appropriate trigonometric identities.

a) cos(2a) = 1 - 2sin^2(a) = 1 - 2(-3/5)^2 = 1 - 18/25 = 7/25

b) sin a/2 = √[(1 - cos a)/2] = √[(1 - (4/5))/2] = √[(1/5)/2] = √(1/10) = 1/√10 = √10/10

Therefore, the exact value of cos(2a) is 7/25 and the exact value of sin a/2 is √10/10. Remember to consider which sign is appropriate when using the trigonometric identities.

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So, the LU-factorization of the given matrix is:

LU = `[1 0 0 0]` `[4 0 1 8]`

`[0.25 1 0 0]` `[0 1 -4.25 6]`

`[0 4.25 1 0]` `[0 0 1.25 -2]`

`[0 0 -1.25 1]` `[0 0 0 1]`

The LU-factorization of a matrix is a method of decomposing a matrix into a lower triangular matrix (L) and an upper triangular matrix (U). The L matrix must have a unit diagonal, meaning that all the entries on the main diagonal are equal to 1.

To find the LU-factorization of the given matrix, we can use the following steps:

1. Begin with the given matrix:

`[4 0 1 8]`

`[1 1 -4 10]`

2. Use Gaussian elimination to transform the matrix into an upper triangular matrix (U):

`[4 0 1 8]` → `[1 1 -4 10]` → `[0 1 -4.25 6]` → U = `[0 0 1.25 -2]`

3. Now, we can use the entries from the Gaussian elimination to create the lower triangular matrix (L):

L = `[1 0 0 0]`

`[0.25 1 0 0]`

`[0 4.25 1 0]`

`[0 0 -1.25 1]`

4. Finally, we can write the LU-factorization as:

LU = `[1 0 0 0]` `[4 0 1 8]`

`[0.25 1 0 0]` `[0 1 -4.25 6]`

`[0 4.25 1 0]` `[0 0 1.25 -2]`

`[0 0 -1.25 1]` `[0 0 0 1]`

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1) 140

2) T2 = ?

3) $13,786.40

4) $835.88

5) x = 3, y=(0, 1.5)

1) To find the number of pounds of grass seed needed to cover an area of 140,000 ft2, you need to write a proportion and solve it. Set up the proportion using the given information:

20 lb/10,000 ft2 = x lb/140,000 ft2

To solve for x, multiply both sides of the equation by 140000:

20 lb * 140000/10,000 ft2 = x lb

x = 2800 lb

You will need 2800 lbs of grass seed to cover an area of 140,000 ft2. To find out how many whole bags of seed you will need to buy, divide the total number of pounds by the number of pounds in a bag, which is 20 lbs. You will need to buy 140 whole bags of seed.

2) To solve for T2 in the equation ???????????????? ???????? = ???????????????? ????????, divide both sides of the equation by ???????????????? :

T2 = ???????????????? ????????/????????????????

3) To find the cost of the car before the sales tax, subtract the 5% sales tax from the total cost. The formula is:

Cost before tax = Total Cost - (Total Cost * Sales Tax %)

Cost before tax = $14,512 - ($14,512 * 0.05) = $13,786.40

4) To find the list price of the laptop computer, add the 15% off sale to the sale price. The formula is:

List Price = Sale Price + (Sale Price * Discount %)

List Price = $722.50 + ($722.50 * 0.15) = $835.88

5) The x and y intercepts for the equation 3x + 6y = 9 can be found by setting x or y equal to 0 and solving for the other. To find the x intercept, set y = 0:

3x + 6(0) = 9

3x = 9

x = 3

The x intercept is (3, 0). To find the y intercept, set x = 0:

3(0) + 6y = 9

6y = 9

y = 1.5

The y intercept is (0, 1.5).

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The meaning of point J(2,6) on the graph is given as follows:

The cost of 2 ounces of orange juice is $6.00.

The general format of an ordered pair is given by the rule presented as follows:

(x,y).

In which:

The input and output variables for this problem are given as follows:

Hence the point (2,6) represents that the cost of 2 ounces of orange juice is $6.00, meaning that the second option is the correct option in the context of this problem.

The coordinates of the point are (2,6).

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The maximum value of the function z=8x+3y subject to the constraints is 94

The maximum value of the function z=8x+3y subject to the constraints y>=0, x>=4, y<=10, and 5x+2y<=60 can be found using the method of linear programming.

Graph the constraints on a coordinate plane. The constraints y>=0 and x>=4 are vertical and horizontal lines, respectively.

The constraint y<=10 is a horizontal line at y=10, and the constraint 5x+2y<=60 can be rewritten as y<=-5/2x+30 and graphed as a line with a slope of -5/2 and a y-intercept of 30.

Identify the feasible region, which is the area of the graph that satisfies all of the constraints.

In this case, the feasible region is the quadrilateral bounded by the lines x=4, y=0, y=10, and y=-5/2x+30.

Find the vertices of the feasible region. The vertices are the points (4,0), (4,10), (8,10), and (10,5).

Substitute the coordinates of the vertices into the function z=8x+3y to find the maximum value. The maximum value occurs at the vertex (8,10), where z=8(8)+3(10)=94.

Therefore, the maximum value of the function z=8x+3y subject to the constraints y>=0, x>=4, y<=10, and 5x+2y<=60 is 94.

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The bus’s speed on the level road was 72 mph if the bus traveled on a level road for 6 hours at an average speed of 20 miles per hour.

The given data is as follows:

The bus traveled on road time = 6 hours

Average speed = 20 miles/hour

Time spent on the winding road = 3 hours

Entire trip distance =  534 miles

The equation will be written as:

(x+20) * (6) + (x)(2) = 534

Now, "x" is the average speed on the winding road.

solving for x value,

6x + 120 + 2x = 534

8x = 534 -120

x = 414/8

x = 52

Now,  we calculated the average speed for the winding road.

The average speed for the level road is calculated as:

u1 + v1 = 52 + 20 = 72

Therefore we can conclude that the bus’s speed on the level road was 72 mph.

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The properties of real numbers being used in the equations you provided are as follows:

1. 5−8: This equation does not use any specific property of real numbers. It is simply subtraction of two real numbers.

2. 5.3+2x=2x+36: This equation uses the Commutative Property of Addition, which states that the order in which real numbers are added does not affect the sum. This is why 5.3+2x is equal to 2x+5.3.

3. (a+b)(a−b)=(a−b)(a+b): This equation also uses the Commutative Property of Multiplication, which states that the order in which real numbers are multiplied does not affect the product. This is why (a+b)(a−b) is equal to (a−b)(a+b).

4. 7.A(x+y)=Ax+Ay: This equation uses the Distributive Property, which states that multiplying a real number by a sum is the same as multiplying each term in the sum by the real number and then adding the products. This is why A(x+y) is equal to Ax+Ay.

5. (A+1)(x+y)=(A+1)x+(A+1)y: This equation also uses the Distributive Property, as explained in the previous example.

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The percentage of the discount is b) 75%.

Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.

Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.

Here the original price of picture = 120.00

Sale price after discount = 29.99 ≅ 30

Now using discount percent formula,

=> Discount percentage = (original price- sale price)/(original price)*100

=> Discount percentage = [tex]\frac{120-30}{120}\times 100=\frac{90}{120}\times100 = 75\%[/tex]

Hence the percentage of the discount is b)75%.

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The key shows that 1|1 represents the score 11.

The stem-and-leaf plot that depicts the data set accurately is as follows:

Season Points for the 2021 Riverside Red Dragon Football

0 | 0 3

1 | 0 1 7 7 7 7 7

2 | 0 0 2 4 8 8

3 | 1 3

Key: 1|1 = 11

The stems represent the tens digit and the leaves represent the ones digit in this stem-and-leaf plot, which accurately depicts the frequency of each score in the data set. For instance, the stem 2 and the leaves 0 and 0 indicate the two instances of the score 20, which appears twice. The score 11 is represented by the key as 1|1.

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Answer:

Step-by-step explanation:

80*4=320km

Answer:

x = 1
y = 1

Step-by-step explanation:

The number from the least to the greatest is -10, -8, 0, 7.

To order numbers means to arrange them in a particular sequence based on their magnitudes or values. This can be done in ascending order (smallest to largest) or descending order (largest to smallest).

Ascending order refers to arranging a set of numbers or values from the smallest to the largest value. For example, if we have a set of numbers {3, 1, 7, 2, 8}, arranging them in ascending order would give us {1, 2, 3, 7, 8}.

Descending order refers to arranging a set of numbers from the largest value to the smallest value. For example, if we have the numbers 7, 2, 9, 4, and 1, the descending order would be: 9, 7, 4, 2, 1.

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The zeros and their multiplicities are x=-2/3, multiplicity 5 and x=5, multiplicity 1.

To find the zeros of the function f(x)=(3x+2)^(5)(x^(2)-10x+25), we need to set the function equal to zero and solve for x.

0=(3x+2)^(5)(x^(2)-10x+25)

Since the product of two factors is zero, one of the factors must be zero. We can set each factor equal to zero and solve for x.

(3x+2)^(5)=0

3x+2=0

3x=-2

x=-2/3

The other factor is:

x^(2)-10x+25=0

This is a quadratic equation, which we can solve using the quadratic formula:

x=(-b±√(b^(2)-4ac))/(2a)

x=(-(-10)±√((-10)^(2)-4(1)(25)))/(2(1))

x=(10±√(100-100))/2

x=(10±0)/2

x=10/2

x=5

So the zeros of the function are x=-2/3 and x=5.

To find the multiplicity of each zero, we need to look at the exponent of the factor that contains the zero. The zero -2/3 comes from the factor (3x+2)^(5), which has an exponent of 5, so the multiplicity of -2/3 is 5. The zero 5 comes from the factor (x^(2)-10x+25), which has an exponent of 1, so the multiplicity of 5 is 1.

Therefore, the zeros and their multiplicities are:

x=-2/3, multiplicity 5

x=5, multiplicity 1

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The heat associated with roasting 6.00 g of zinc sulfide is 27.1 kJ.

The molar mass of ZnS is 97.45 g/mol, which means that 6.00 g of ZnS is equal to:

6.00 g ZnS × (1 mol ZnS/97.45 g ZnS) = 0.0616 mol ZnS

According to the balanced equation, the roasting of 2 mol of ZnS releases 879 kJ of heat:

2 ZnS (s) + 3 O₂ (g) → 2 ZnO (s) + 2 SO₂ (g) ΔH = -879 kJ/mol

Therefore, the roasting of 0.0616 mol of ZnS releases:

(879 kJ/mol) × (0.0616 mol ZnS / 2 mol ZnS) = 27.1 kJ

Therefore, the heat associated with roasting 6.00 g of zinc sulfide is 27.1 kJ. Rounded to three significant digits, the answer is 27.1 kJ.

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Answer:

[tex]\frac{4}{50fx^{30} } :[/tex][tex]\frac{2}{25f^{30} }[/tex]

Step-by-step explanation:

Factor thenumber:4=2\2

[tex]=\frac{2 . 2}{50fx^{30} }[/tex]

Factor the number 50= 2 x 25

[tex]=\frac{2.2}{2.25f^{30} }[/tex]

Cancel the common factor:2

[tex]=\frac{2}{25f^{30} }[/tex]