Find the value of x for which the lines l and m are parallel.

A) 13

B) 10

C) 4.7

D) 5

Answer:

50313.28

See the below process

Step-by-step explanation:

Important formulae

A=Total Amount

P=Principal or amount of money deposit

R=Annual interest rate

N=Number of Times compounded per year

T=Time in years

For the formula:

[tex]a \: is \: equals \: to \: p(1 + \frac{r}{n}) \: n - t \\ p \: is \: equals \: to \: 5000 \: dollars \: comma \: r \: s \: equals \: to \: 8\% \: comma \: n \: is \: equals \: to \: 1 \: and \: t \: is \:equals \: to \: 30 \: years \: [/tex]

Solution:

A=5000(1+0.08 /1) to the power 1.30

5000×10.062657

Answer= 50313.28

-Thank You By MrIshaan

Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

[tex]\sf P =\dfrac{F}{1+r\div n}^{(nt)[/tex]

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

[tex]\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}[/tex]

[tex]\sf P = \dfrac{1000}{(1.0375)^{10}}[/tex]

[tex]\sf P = \dfrac{1000}{1.4450}[/tex]

[tex]\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)[/tex]

Therefore, the price of the zero coupon bond is $692.04.

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1. The product of the matrix MG would be [tex]\left[\begin{array}{ccc}1&k_1+9&4k_2+36\\2t_1&k_1t_1-17&3k_2-19t_1-11\\t_2+1&k_1-4t_2+5&k_2t_2-8\end{array}\right][/tex]

2. The values of k₁ = -9;  k₂ = -9; t₁ = 0; t₂ = -1

The values of the matrix M and G are;

M = [1, 4, 5;                       G = [2, k₁, -19;

      t₁, 3, -1;                             1, -4, k₂;

      1, t₂, 1]                              -1, 5, 11]

The product MG will be row 1

1×2 + 4×1 + 5×-1     1k₁+4×-4+ 5×5       1×-19+4k₂+5×11 ⇒1    k₁+9    4k₂+36

Row 2

t₁×2+3×1+-1×-1    t₁k₁+3×-4+-1×5       t₁×-19+3k₂+-1×11  ⇒ 2t₁    k₁t₁-17 3k₂-19t₁-11

Row 3

1×2+t₂×1+1×-1      1k₁+t₂×-4+-1×5      1×-19+t₂k₂+1×11 ⇒ t₂+1   k₁-4t₂+5    k₂t₂-8

Therefore MG =

1     k₁+9   4k₂+36

2t₁    k₁t₁-17    3k₂-19t₁-11

t₂+1   k₁-4t₂+5      k₂t₂-8

G = M⁻¹  should be an identity matrix which looks like

IM = [ 1 0 0

         0 1 0

        0 0 1 ]

MG and I to find the values of t₁, t₂, k₁, and k₂:

1 = 1,         k₁+9 = 0,       4k₂+36 = 0

2t₁ = 0     k₁t₁-17 = 1        3k₂-19t₁-11 = 0

t₂+1 = 0     k₁-4t₂+5 = 0   k₂t₂-8 = 1

k₁+9 = 0 ⇒k₁ = -9          

4k₂+36 = 0  ⇒  k₂ = -9          

2t₁ = 0 ⇒   t₁ = 0          

t₂+1 = 0 ⇒    t₂ = -1

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Answer:

80 points

Step-by-step explanation:

If score in English is x points and score in math is 5% higher then score in math

y = x + 0.05x

where 0.05 = 5% expressed as decimal

0.05x refers to the 5% increase in score

y = math score

y = x(1 + 0.05)

y = 1.05x

Given score in math = 84 this becomes

84 = 1.05x

x = 84/1.05

x = 80

So Emily's score in English was 80 points

Answer:

x = 78°

Step-by-step explanation:

Line q pass through the parallel line of s and r so their alternet interior angles are equal. the alternet interior angles of 135° is 57°+ x so they are equal .

57° + x = 135°

x = 135° - 57°

x = 78°

So the answer is D, 78°

The matrix after the row operation is:

[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]

We have,

We use the operation R1 → R1/9.

This will give us,

Row 1 values will change to 9/9, 4/9, -9/9

So,

1, 4/9, -1

Now,

[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]

Thus,

The matrix after the row operation is:

[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]

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The x value in the linear expression 6x - 2y = -17 is -13/6 when y = 0

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

The linear expression 6x - 2y = -17

To determine the value of x in the linear expression, we set y to any value say y = 2 and then calculate the value of x

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

6x - 2(2) = -17

Evaluate

6x = -13

Divide both sides by 6

x = -13/6

This means that the value of x is equal to -13/6

So, we have (-13/6, 0)

Hence, the ordered pairs of the linear expression is (-13/6, 0)

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(A) The preimage is ABC.

(B) The image is A'B'C'.

(C) The coordinates of the output are:

A(0,9) reflects over the line of reflection to A'(0,-9).

B(-4,4) reflects over the line of reflection to B'(4,-4).

C(0,4) reflects over the line of reflection to C'(0,-4).

In geometry, a reflection is a type of transformation where a figure is flipped over a line, called the line of reflection. In this problem, ABC-A'B'C' is a reflection, which means that it is a transformation of a figure where each point of the original figure has a corresponding point in the reflected figure such that the line of reflection is the perpendicular bisector of the line segment joining each point to its corresponding point.

A) The preimage is the original figure, which is ABC.

B) The image is the reflected figure, which is A'B'C'.

C) The coordinates of the output are:

A(0,9) reflects over the line of reflection to A'(0,-9).

B(-4,4) reflects over the line of reflection to B'(4,-4).

C(0,4) reflects over the line of reflection to C'(0,-4).

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Answer:

cos(45°) = √2/2

B is correct.

The regular admission price for one adult is $17.50.

We have,

Let's first determine the total cost of admission after the coupons have been applied.

Since each person has a coupon for $5 off, the total discount for the group is $5 x 6 = $30.

The total cost of admission after the discount.

$105 - $30

= $75.

Let A be the regular admission price.

Since each person paid the same price after the discount, we can set up the following equation:

6(A - $5) = $75

We subtract $5 from the regular price A because that is the amount of the coupon discount.

We can simplify the equation as follows:

6A - $30 = $75

6A = $105

A = $17.50

Therefore,

The regular admission price for one adult is $17.50.

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Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

Just add the powers while it is multiply

-1+(-3)

= -1 - 3

= -4

So it is [tex]2^{-4}[/tex]

We can expect a student to guess 17 correct answers on a test with 68 four-choice multiple choice questions with probability 0.25.

Since the probability of guessing the correct answer to a four-choice multiple choice question is 0.25, the probability of guessing an incorrect answer is 1 - 0.25 = 0.75.

We can model the number of correct guesses as a binomial distribution with n = 68 (the number of trials) and p = 0.25 (the probability of success, i.e., guessing correctly).

The expected value of a binomial distribution is given by the formula:

E(X) = n * p

So, in this case, the expected number of correct answers that a student should guess on the test is:

E(X) = 68 * 0.25 = 17

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Answer:

25% probability

Step-by-step explanation:

2x2=4

1x1=1

1 out 4 is shaded red

1 out of 4 is 1/4 which is 25%

The maximum number of toothbrushes the dentist can purchase is 50.

Let's denote the number of toothbrushes the dentist orders by "x".

If the dentist orders less than 50 toothbrushes, then the cost of the toothbrushes will be 2.58x.

If the dentist orders 50 or more toothbrushes, then the cost of the toothbrushes will be 1.24x.

There is a base cost of [tex]$48[/tex] for printing the dentist's name and address on the toothbrushes.

The total cost of the order can be expressed as:

Total cost = 48 + (2.58x) for x < 50

Total cost = 48 + (1.24x) for x ≥ 50

The maximum number of toothbrushes the dentist can purchase, given that the budget is [tex]$110[/tex].

So we can set up an equation:

Total cost = 110

For x < 50:

48 + 2.58x = 110

2.58x = 62

x ≈ 24.03

For x ≥ 50:

48 + 1.24x = 110

1.24x = 62

x ≈ 50

The maximize number of toothbrushes, we choose the larger value of x, which is x ≈ 50.

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Based on the calculations, Helen needs to buy 60 feet of fence panels for her rectangular garden in the backyard

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

This means that

Perimeter = 20 yards

By metrric unit of conversion, we have

1 yard = 3 feet

So, we have

Perimeter = 20 * 3 feet

Evaluate

Perimeter = 60 feet

Hence, she needs to buy 60 feet of fence panels

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The constraint of x for the function g(x) = -40(2x + 7)(x - 10) is given by, 0 [tex]\le[/tex] x [tex]\le[/tex]6.

Given that the function is,

g(x) = - 40(2x + 7)(x - 10)

where x stands for the number of years since the year 2003

and g(x) stands for the amount of sales of golf equipment in million dollar unit.

The mathematician used the data for the year span of 2003 - 2009.

Min of x = Number of years since 2003 when the year is 2003 = 2003 - 2003 = 0

Max of x = Number of years since 2003 when the year is 2009 = 2009 - 2003 = 6

So the constraint of x is, 0 [tex]\le[/tex] x [tex]\le[/tex] 6.

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30 gallons of 28% butterfat and 30 gallons of 16% butterfat should be combined to create a 60-gallon mixture that is 22 % butterfat.

Let x gallon of 28% butterfat mixed with the y gallon of 16% butterfat to obtain 60 gallons of 22.5% butterfat,

⇒ x + y = 60 ⇒ x = 60 - y ----(1),

Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,

⇒ 28% of x + 16% of y = 22% of 60

⇒ 0.28x + 0.16y = 0.22 × 60

⇒ 0.28x + 0.16y = 13.2

⇒ 28x + 16y = 1320

⇒ 14x + 8y = 660

From equation (1),

14(60-y) + 8y = 660

840 - 14y + 8y = 660

6y = 180

y = 30

Again from equation (1),

x = 60 - y

= 60 - 30

= 30

Hence, 30 gallons of 28% butterfat and 30 gallons of 16% butterfat are combined to create a 60-gallon mixture that is 22%

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The lateral surface area of the pyramid is 112 sq. in.

The correct answer is an option (B)

From the attached figure of the net of a square pyramid, we can observe that the side length of the square base is 8 in and height of the lateral triangular face is 7 in.

The lateral surface area of the pyramid is equal to the area of the four triangular faces of the pyramid.

Using the formula of the area of triangle, the lateral surface area would be,

A = 4 × (1/2 × base × height)

A = 4 × (1/2 × 8 × 7)

A = 4 × (4 × 7)

A = 4 × 28

A = 112 sq. in.

This is the required lateral surface area.

The correct answer is an option (B) 112 in²

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Find the complete question below.

The net below shows a square pyramid. What is the lateral surface area? A. 176 in^2

B. 112 in^2

C. 64 in^2

D. 210 in^2

Step-by-step explanation:

If this is a regular pentagon , it has FIVE sides of equal length

 64 ÷ 5 = 12.8 units = AB

Answer:

10 * 10^10 is equal to 100,000,000,000

The solution of the differential equation y'' + 2y' - y = xe is found to be [tex]y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t} - \frac{4}{3}xe^{x} + Ce^{x}[/tex]

To solve the differential equation y'' + 2y' - y = xeˣ, we first find the complementary solution by solving the characteristic equation,

r² + 2r - 1 = 0

Using the quadratic formula, we get,

r = (-2 ± √(2² + 4(1)(1))) / 2

r = (-2 ± √6) / 2

So the roots are,

r₁ = -1 - √6/2

r₂ = -1 + √6/2

Therefore, the complementary solution is:

[tex]y_c = Ce^{r_{1}t} + C'e^{r_{2}t}\\y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t}[/tex]

To find the particular solution, we use the method of undetermined coefficients. We assume a particular solution of the form,

y_p = Ax²eˣ + Bxeˣ + Ceˣ

Taking the first and second derivatives, we get,

y'_p = (2Ax + B + A)x eˣ + Beˣ + Ceˣ

y''_p = (4A + 2Ax + B + A)x eˣ + (2A + B)eˣ + Ceˣ

Substituting these expressions into the differential equation, we get,

(4A + 2Ax + B + A)x eˣ + (2A + B)eˣ + Ceˣ + 2[(2Ax + B + A)x eˣ + Beˣ + Ceˣ] - (Ax²eˣ + Bxeˣ + Ceˣ) = xeˣ

Simplifying, we get,

(3Ax² + 4Ax + B)x eˣ = xeˣ

Equating coefficients, we get,

3A = 1

4A + B = 0

Solving for A and B, we get,

A = 1/3

B = -4/3

Substituting these values into the assumed particular solution, we get,

y_p = (1/3)x²eˣ - (4/3)xeˣ + Ceˣ

Taking the first and second derivatives, we get,

y'_p = (2/3)x eˣ - 4/3eˣ + Ceˣ

y''_p = (2/3)eˣ + Ceˣ

Substituting the particular solution and its derivatives into the differential equation and simplifying, We get,

(2/3)xeˣ = xeˣ

This equation is true for all x, so there is no restriction on C. Therefore, the general solution is,

y = y_c + y_p

[tex]y = Ce^{(-1-\frac{\sqrt{6}}{2})t} + C'e^{(-1+\frac{\sqrt{6}}{2})t} - \frac{4}{3}xe^{x} + Ce^{x}[/tex]

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Complete question - y'' + 2y' - y = xeˣ solve the differential equation.

Answer:

Right three

Step-by-step explanation:

Because the translation is applied inside the parentheses, we are shifting the function left/right. To determine whether it is shifted left or right, note that shifting right will have a negative number and shifting left will have a positive number. Since we have a negative number -3, it is shifted right.

Answer:

Step-by-step explanation:

Here if we put [tex]x=3[/tex] then then equation will give 0. Hence it will shift right side three unit .

Final answer: right 3

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

To memorize knowledge there are several tips that can help us. Some are: Repeat some knowledge from time to time to memorize them.

To memorize knowledge there are several methods that can be useful when we need to learn something difficult. In this case, we must use some methods that can help us such as:

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The value of x in the quadrilateral is 70 degrees

To find the value of the fourth interior angle, we can use the fact that the sum of all four interior angles is equal to 360 degrees. We can set up an equation:

85 + 150 + 55 + x = 360

where x is the fourth interior angle we want to find. To solve for x, we can first simplify the left side of the equation by adding the known angles:

290 + x = 360

Then, we can isolate x by subtracting 290 from both sides:

x = 360 - 290

x = 70

Therefore, the value of x when the interior angles of the quadrilateral are 85, 150, and 55 degrees is 70 degrees. This means that the four interior angles of the quadrilateral are 85, 150, 55, and 70 degrees, and their sum is indeed equal to 360 degrees.

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Answer:

The answer for x is 2

Step-by-step explanation:

write the equation

log6(36)= x

rewrite the equation as, x = log6(36) [ formula used; logb x=y; x=y^b]

so, x^6=36

     x^6=2^6[ 36=2^6=2*2*2*2*2*2]

thus, x=2

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The partitions coordinate are (7, -2).

We have the coordinates (8, -5) and (4, 7)

Ratio = 1 :3

Using Section Formula

x = ( 4 + 24)/ 4

x = 28/4

x= 7

and, y= (7 - 15)/4

y = -8/4

y= -2

Thus, the partitions coordinate are (7, -2).

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Probability of landing on space with polka dots = 3/8.

Probability of landing on space with stripes = 1/2.

Probability of landing on space with stripes and even numbers = 1/4.

Probability of landing on space with stripes or even numbers = 5/8.

Hence the code is 'AFCH'.

From the definition of Probability we know that,

Probability of event = (Number of Favorable outcomes)/(Total number of outcomes)

Here total number of spaces = 8.

Number of space with polka dots = 3 [space numbered 1, 4, 6]

Number of space with stripes = 4 [space numbered 0, 2, 3, 5, 7]

Number of space with stripes and even numbers = 2 [the space numbered 0 and 2]

Probability of landing on space with polka dots = 3/8 (A)

Probability of landing on space with stripes = 4/8 = 1/2 (F)

Probability of landing on space with stripes and even numbers = 2/8 = 1/4 (C)

So, Probability of landing on space with stripes or even numbers

= Probability of landing on space with polka dots + Probability of landing on space with stripes - Probability of landing on space with stripes and even numbers

= 3/8 + 1/2 - 1/4

= (3 + 4 - 2)/8

= 5/8 (H).

Hence the code will be 'AFCH'.

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The length of the given rectangular cuboid is: 9 cm

In geometry, a rectangular prism is defined as a polyhedron with two congruent as well as parallel bases. It is also referred to as a cuboid. A rectangular prism is one that possesses six faces, and then all the faces are located in a rectangle shape and possess twelve edges. Whenever its cross-section along the length, it is referred to as a prism.

The formula for the volume of a prism is given by the formula:

V = L * W * H

Where:

L is length

W is width

H is height

We have that Volume = 432 cm³

Thus:

6 * L * 8 = 432

48L = 432

L = 432/48

L = 9 cm

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