Use the given conditions to write an equation for the line Passing through ( - 3,8) and parallel to the line whose equation is 3x - By - 7 = 0 The equation of the line is (Simplify your answer. Type an equation using x and y as the variables.

Answer:

5

Step-by-step explanation:

23 - 10 = 13

13 - 8 = 5

Answer:

5

Step-by-step explanation:

p = a + b + c

23 = 8 + 10 + c

23 = 18 + c

5 = c

The pairs of table are(y=2x+3)

y inetercept of the graph is (0,3)

Hence the solution is (0,3)

Answer:

A = 13 1/2 sq units

Step-by-step explanation:

A(trapezoid) = 1/2·h·(b₁ + b₂)

b₁ = one of the bases

b₂ = the other base

the bases are the sides parallel to each other

the height is the number of units connecting the bases

A = 1/2(3)(3+6)

A = 3/2(9)

A = 27/2 or 13 1/2 sq units

Answer:

Step-by-step explanation:

6=2(y+2)

6=2y+4

2=2y

y=1

Answer:

1

Step-by-step explanation:

1+2=3

2(3)= 2x3=6

There ya go

Discrete variables are those that can take on only specific values, such as integers, whereas continuous variables can take on any value within a range or interval. Here are the classifications of the given variables:Discrete variables:1. Number of students who make appointments with a math tutor2.

Number of days required for a product to be shipped3. Lifetime of batteries in a tape recorder4. Weights of newborn infants at a certain hospital5. Number of pizzas sold last year in Kuala Lumpur6. Times required to complete a chess game7. Ages of children in a daycare center8. Weights of lobsters in a tank in a restaurant9. Number of bananas in a local supermarket10. Blood pressure of runners in a marathon11. Number of loaves of bread baked at a local bakery12. Number of students in a class13. Number of clinics at Kelana JayaContinuous variables:1. The water temperature of the saunas at the spa2. Incomes of single parents who attend a community college3. Monthly allowance of a student4. CGPA of a student The total number of variables is 17.

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Answer:3y/(4y+6)-6y/(2y+3)

3y(2(2y+3))-6y/(2y+3)

(3y-6×2y)/(2(2y+3))

-9y/4y+6

1.st one is your answer. hope this helps

we have

5/x=15/24

solve for x

Multiply in cross

15*x=24*5

x=24*5/15

x=8

The original purchase price of the car before any of the discounts and taxes is,

⇒  $15,024

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

There is a 12% discount because of the Happy Easter Sale and another 5% discount because the purchaser is a valued customer. After these discounts the GST increases the price by 10%.

Here, the customer paid $14 000.

Now, Let the original price = x

Hence, We can formulate;

⇒ x - (12% of x) - 5% of x + 10% of x = 14,000

⇒ x - 12x/100 - 5x/100 + 10x/100 = 14,000

⇒ (100x - 12x - 5x + 10x) / 100 = 14,000

⇒ 93x/100 = 14,000

⇒ 93x = 1400000

⇒ x = $15,024

Thus, The original purchase price of the car before any of the discounts and taxes is,

⇒  $15,024

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Answer:

37.437

Step-by-step explanation:

Answer:

37.437

Hope it helps

Answer:

11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Answer: 3.57 years

Step-by-step explanation:

Based on the question given, the interest is the difference between the amount and the principal which will be:

= $19800 - $16800

= $3000

The formula for Simple interest is given as:

Interest = Principal × Rate × Time

3000 = 16800 × 5% × Time

3000 = 16800 × 0.05 × Time

3000 = 840 × Time

Time = 3000 / 840

Time = 3.57

The time taken to grow the investment is 3.57 years

The missing angle D is 55 degrees, and the lengths of DE and DF are approximately 8.40 units and 14.65 units, respectively. Therefore, the correct option is (B) m∠D = 55°, DE ≈ 8. 40 units, DF ≈ 14. 65 units

We can start by using the trigonometric ratios of the angles in a right triangle. In particular, we can use the tangent function to find the measure of angle D

tan(D) = DE / FE

tan(D) = DE / 12

We know that angle F is 35 degrees, so angle D must be

D = 90 - F

D = 90 - 35

D = 55 degrees

Now that we know the measure of angle D, we can use the sine and cosine functions to find the lengths of DE and DF, respectively. We know that

sin(F) = DE / DF

cos(F) = FE / DF

Substituting the given values

sin(35) = DE / DF

cos(35) = 12 / DF

Solving for DE and DF

DE = DF × sin(35)

DE = DF × 0.574

DE ≈ 0.574 × DF

DF = 12 / cos(35)

DF ≈ 14.65 units

DE ≈ 0.574 × 14.65

Multiply the numbers

DE ≈ 8.40 units

Therefore, the correct option is (B) m∠D = 55°, DE ≈ 8. 40 units, DF ≈ 14. 65 units

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The given question is incomplete, the complete question is:

Solve the given right triangle for its missing angle and side measures

A. m∠D = 55°, DE ≈ 4. 40 units, DF ≈ 13. 65 units

B. m∠D = 55°, DE ≈ 8. 40 units, DF ≈ 14. 65 units

C. m∠D = 35°, DE ≈ 8. 40 units, DF ≈ 13. 65 units

D. m∠D = 35°, DE ≈ 8. 40 units, DF ≈ 14. 65 units

Answer:

D C B A is the answer kid now pay up

(a) `T1:0 = [cos150 sin150 0 0; -sin150 cos150 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cos150 sin150 0; 0 -sin150 cos150 0; 0 0 0 1]`

(c) `T1:0 = [cos150 0 -sin150 0; 0 1 0 0; sin150 0 cos150 0; 0 0 0 1]`

Given that Frame zero, F0 is the fixed global frame.

For each of the cases below find T1

Case (a)

F1 is rotated by an angle θ about zo.

Let O be the origin of the fixed frame F0, A be the origin of the frame F1 and α be the angle between the x-axis of the frame F0 and the projection of the x-axis of the frame F1 on the xy plane of the frame F0.

Let l, m, n be the direction cosines of the vector from O to A, expressed in F0.

The content-loaded frame zero F0 is the fixed global frame, which means that the vectors i, j, k representing the x, y, and z-axis of F0 are fixed and cannot be transformed.

Therefore, the transformation matrix T1:0

in this case is:

`T1:0 = [l1 m1 n1 0; l2 m2 n2 0; l3 m3 n3 0; 0 0 0 1]`

Case (b)

F1 is rotated by θ about xo.

Let β be the angle between the y-axis of F0 and the projection of the y-axis of F1 on the yz plane of F0.

Let γ be the angle between the z-axis of F0 and the projection of the z-axis of F1 on the zx plane of F0.

The transformation matrix T1:0

in this case is given by:

`T1:0 = [1 0 0 0; 0 cosθ sinθ 0; 0 -sinθ cosθ 0; 0 0 0 1]`

Case (c)

F1 is rotated by θ about yo.

Let β be the angle between the y-axis of F0 and the projection of the y-axis of F1 on the yz plane of F0.

Let γ be the angle between the z-axis of F0 and the projection of the z-axis of F1 on the zx plane of F0.

The transformation matrix T1:0

in this case is given by:

`T1:0 = [cosθ 0 -sinθ 0; 0 1 0 0; sinθ 0 cosθ 0; 0 0 0 1]`

Thus, the transformation matrix T1:0

for the three cases (a), (b), and (c) are given as follows:

(a) `T1:0 = [cosθ sinθ 0 0; -sinθ cosθ 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cosθ sinθ 0; 0 -sinθ cosθ 0; 0 0 0 1]`

(c) `T1:0 = [cosθ 0 -sinθ 0; 0 1 0 0; sinθ 0 cosθ 0; 0 0 0 1]`

Given θ = 150,

T1:0 for the three cases are:

(a) `T1:0 = [cos150 sin150 0 0; -sin150 cos150 0 0; 0 0 1 0; 0 0 0 1]`

(b) `T1:0 = [1 0 0 0; 0 cos150 sin150 0; 0 -sin150 cos150 0; 0 0 0 1]`

(c) `T1:0 = [cos150 0 -sin150 0; 0 1 0 0; sin150 0 cos150 0; 0 0 0 1]`

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Check the picture below.

so the triangle with the 35° angle is an isosceles, namely a triangle with twin sides stemming from the center of the circle, well, twin sides make twin angles, and since the center of the circle makes a central angle, well, any arc will get its degrees from that.

Answer: D) 46

3x+1+3x+1+x-5+x-5=360

8x=368

x=46

Answer:

1. \(\frac{x}{15}\) = 0.85

2. x = 12.75

Step-by-step explanation:

First, we do 12 divided by 15, which is 0.80 (80%). The question is asking how much consecutive free throws is needed to raise it to 85%.

So, and equation we make is:

\(\frac{x}{15}\) = 0.85, where x represents the number of free throws.

Now, we solve.

Multiply each side by 15 to solve for x.

x = 12.75

12.75 consecutive free throws is needed to raise the percent to 85%.

Answer:

-0.45

Step-by-step explanation:

oof

Relative to Stacy's goal, her average aerobics time over the last five weeks will be 0.09.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

Stacy likes to do heart-stimulating exercises 10 hours every week to remain in shape. She tracks how much time she does heart-stimulating exercise every week compared with her goal. The table shows the information throughout the previous five weeks.

The table is given below.

Week                                          1              2            3              4            5

Aerobics time (hours)              2.8          −2           1 ³/₄          0           −3

Then relative to Stacy's goal, her average aerobics time over the last five weeks will be given as

⇒ (2.8 − 2 + 1 ³/₄ + 0 − 3) / 5

⇒ (0.45) / 5

⇒ 0.09

Relative to Stacy's goal, her average aerobics time over the last five weeks will be 0.09.

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Answer:

The angle is 35 degrees.

Step-by-step explanation:

180-20-40= 120

180-120-25= 35

Answer:

b) 5.8

Step-by-step explanation:

Explanation

Given diagram the angles are (9 x + 6)°, (10 x + 7)°, (10 x - 1)°

we know that the sum of the angles of the triangle is equal to 180°

∠A +∠B +∠C = 180°

(9 x + 6)°+(10 x + 7)°+ (10 x - 1)° = 180°

On simplification , we get

29 x + 12 = 180

29 x = 180 -12

29 x = 168

x = 5.79 ≅ 5.8

Answer:

b

Step-by-step explanation:

Part A: The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: The point (8, 2) is not included in the solution area.

Part C: The point (3, 1) represents one feasible solution that meets the constraints of the problem.

Part A: The graph of the system of inequalities consists of two lines and a shaded region. The line x + 3y = 8 is a solid line because it includes the equality symbol, indicating that points on the line are included in the solution set. The line x + y = 2 is also a solid line. The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: To determine if the point (8, 2) is included in the solution area, we substitute the x and y values into the inequalities:

8 + 3(2) ≤ 8

8 + 6 ≤ 8

14 ≤ 8 (False)

Since the inequality is not satisfied, the point (8, 2) is not included in the solution area.

Part C: Let's choose a point in the solution set, such as (3, 1). This point satisfies both inequalities: x + 3y ≤ 8 and x + y ≥ 2. In the context of the real-world scenario, this means that Michelle can buy 3 servings of dry food (x = 3) and 1 serving of wet food (y = 1) with her $8 budget. This combination of dog food allows her to feed at least two dogs at the animal shelter while staying within her budget. The point (3, 1) represents one feasible solution that meets the constraints of the problem.

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Answer:

1000

Step-by-step explanation:

20,000 divided by 20 is 1,000!

Answer:

the customer should pay Rs.6780 including VAT.

Step-by-step explanation:

here,

Marked price(MP)=7500

Discount(D)=20%

VAT=13%

now,

selling price(SP)=MP-D%of MP

=7500-20×7500/100

= 7500-1500

= Rs 6000

again,

SP with VAT = SP +VAT of SP

= 6000+13×6000/100

=6000+780

=Rs.6780

hence,

the customer should pay Rs. 6780 including VAT.

9 block rhombuses would create 3 hexagons.

In order to increase the total number by three, a hexagon can be divided into a minimum of three rhombuses, each of which can be further divided into four rhombuses. With n being a positive integer, the result is 3n. The top two hexagons in this image are each divided into 8 and 10 rhombuses. The total number of rhombuses that can fit in a hexagon is not limited to multiples of three, given that the total number of rhombuses dividing a hexagon can be raised by three by quartering a single component rhombus. The amount might actually be any integer larger than 7.

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Answer:

I think it's B

Step-by-step explanation:

x = -2

2 + x > -8

2 + -2 > -8

0 > -8

Using the given function, we can plug in x=3 and t=5 to find the concentration of the drug in the blood:

C = f(x,t) = 26te^-(5-x)
C = f(3,5) = 26(5)e^-(5-3)
C = f(3,5) = 130e^-2

Using a calculator, we can simplify this to:

C = f(3,5) ≈ 32.22 mg/liter

Therefore, the concentration of the drug in the blood 3 hours after injection with a dosage of 5 mg is approximately 32.22 mg/liter.
Hi! To find the concentration C at f(3,5), you'll need to plug in the values for x and t into the given function f(x,t) = 26te^-(5-x).

So, f(3,5) = 26(5)e^-(5-3) = 130e^(-2).

Now, calculate the exponential value: e^(-2) ≈ 0.1353.

Finally, multiply this value by 130: 130 * 0.1353 ≈ 17.589.

Thus, f(3,5) = 17.589 mg/liter (rounded to 3 decimal places).

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a) The R11 component of the Ricci tensor is \(c^{-2}(a(t) + 2a(t)^2).\)

b) Using the above result, the component R11 of the Ricci tensor is \(c^{-2}(a(t)+ 2a(t)^2)\).

To determine the R11 component of the Ricci tensor using the given metric tensor, we need to substitute the appropriate indices into the formula for the Ricci tensor:

\(R11 = g^mn R1mn\)

where \(g^{m}n\) represents the components of the inverse metric tensor and R1mn represents the components of the full Riemann tensor.

Given:

Metric tensor (gmn):

9μν:

1 0 0

0 \(a(t)^2\) 0

0 0 \(a(t)^2\)

Ricci tensor (Rmn):

Rμν:

0 0 0

0 \(c^{-2} (a(t)\) + \(2a(t)^2)\) 0

0 0 \(c^{-2}(a(t) + 2a(t)^2)\)

a) To determine the R11 component, we need to substitute m = 1 and n = 1 into the formula:

\(R11 = g^mn R1mn\)

The inverse metric tensor (\(g^mn\)) is obtained by taking the reciprocal of the corresponding components of the metric tensor (gmn). In this case, the reciprocal of the diagonal components is simply the inverse value:

\(g^11 = 1/1 = 1\)

Substituting m = 1, n = 1, and the appropriate components of the Ricci tensor, we have:

\(R11 = (1)(0) + (1)(c^{-2}(a(t) + 2a(t)^2))(1) + (1)(0)\)

      \(= c^{-2}(a(t) + 2a(t)^2)\)

Therefore, the R11 component of the Ricci tensor is \(c^{-2}(a(t) + 2a(t)^2).\)

b) Using the above result, the component R11 of the Ricci tensor is \(c^{-2}(a(t) + 2a(t)^2)\).

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The value of the infinite series as n tends to 0 is: 0

Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.

From the infinite series, we want to find the value of the series as n tends to 0.

We are given the series as:

x/2ˣ

At x = 0, we have:

0/2⁰ = 0/1 = 0

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The interquartile range approximately remains the same.

When all individuals are arranged in ascending order, first 10 include 5-6 year old and the 11th person is 30 year old mother.

Original,

which would again be 5 or 6.

New,

which would again be 5 or 6.

Hence, would approximately remain the same.

When all individuals are arranged in ascending order, first 10 include 5-6 year old and the 11th person is 30 year old mother.

Original Median was either 5 or 6.

New Median = \frac{n+1}{2}^{th}term=\frac{11+1}{2}^{th}term=6^{th}term which would again be 5 or 6.

Hence, Median would approximately remain the same.

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