the diagonals of a rhombus are in the ratio 3 :4 if the longer diagonals is of 12 cm then find the area of rhombus.​

Answer:

y=2x+14

Step-by-step explanation:

y=2x+2.3+8=2x+14

Irene has 49 Books, and Alejandro has 24 books.

Let's assume that Irene has x books, and Alejandro has y books. According to the given information, we can form the following equations:

1. Irene has twice as many books as Alejandro plus 1:

  x = 2y + 1

2. The total number of books between Irene and Alejandro is 73:

  x + y = 73

We can now solve this system of equations to find the values of x and y.

Substituting the value of x from equation (1) into equation (2), we have:

(2y + 1) + y = 73

3y + 1 = 73

3y = 72

y = 24

Now, we can substitute the value of y into equation (1) to find x:

x = 2(24) + 1

x = 49

Therefore, Irene has 49 books, and Alejandro has 24 books.

To verify our solution, we can check if the sum of their books equals 73:

49 + 24 = 7

So, our solution is correct.

In conclusion, Irene has 49 books, and Alejandro has 24 books.

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Answer:

Solution : Option A

Step-by-step explanation:

What we want to do here is eliminate the parameter t. In order to do that, we can isolate t in our first equation x = t + 6 ----- ( 1 ) and then plug that value for t in the second equation y = 3t - 1. Our solution will be an equation that is not present with t.

( 1 ) x = t + 6, t = x - 6

( 2 ) y = 3( x - 6 ) - 1 ( Distribute the " 3 " in 3( x - 6 ) )

y = 3x - 18 - 1 ( Combine like terms )

y = 3x - 19

As you can see our result will be option a, y = 3x - 19.

Answer:

perimeter: 2

Step-by-step explanation:

8x-3 = 6x

8x – 6x = 3

2x = 3

x = 3/2

The required algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The difference between the perimeter of Tamara's suitcase and Anna's suitcase can be found by subtracting the expression for the perimeter of Anna's suitcase from the expression for the perimeter of Tamara's suitcase:

(8x - 3) - (3x + 2)

Simplifying the expression by removing the parentheses and combining like terms, we get:

8x - 3 - 3x - 2

= 5x - 5

Therefore, the algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

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$108.50

1 bottle collected= $1.50 + $2.00 + $2.50 = $6.00

2 bottles " = $5.00

3 bottles " = $5.50 + $6.00 = $11.50

4 bottles " = $7.00 + $8.00 = $15.00

5 bottles " = $6.00 + $9.00 + $10.00 = $25.00

6 bottles " = $2.00 + $8.00 + $11.00 + $13.00 = $34.00

7 bottles " = $12.00

Then you add up all the answers to get the final amount Eric earned.

$6.00 + $5.00 + $11.50 + $15.00 + $25.00 + $34.00 + $12.00 = $108.50.

Answers:

a) See the table below

b) The equation is \(y = 32000(1.01125)^x\)

c) $40,024.02

d) See the graph below

=========================================================

Explanations:

a)

Start with part (b) where I detail how to get the equation.

Once the equation is found, plug in x = 0 to get

\(y = 32000(1.01125)^x\\\\y = 32000(1.01125)^0\\\\y = 32000\\\\\)

Repeat for x = 1

\(y = 32000(1.01125)^x\\\\y = 32000(1.01125)^1\\\\y = 32360\\\\\)

Repeat for x = 2, x = 3, x = 4 and x = 20 to get the table shown below.

-----------------------

b)

The template for any exponential equation is \(y = a(b)^x\)

a = starting amount = 32000

b = growth factor

The annual interest rate is 4.5%

We compound quarterly, so the quarterly rate is (4.5%)/4 = 1.125% which converts to the decimal form 0.01125; adding one to this leads to the growth factor of b = 1.01125

We go from \(y = a(b)^x\) to \(y = 32000(1.01125)^x\)

-----------------------

c)

Plug in x = 20 to represent 20 quarters have elapsed (aka 20/4 = 5 years)

\(y = 32000(1.01125)^x\\\\y = 32000(1.01125)^{20}\\\\y \approx 32000(1.25075052084381)\\\\y \approx 40024.016667002\\\\y \approx 40024.02\\\\\)

The investment would be worth $40,024.02 after five years, aka twenty quarters.

-----------------------

d)

See below for the graph. I'm using GeoGebra to make the graph. Another option is Desmos. It's preferable to use technology than to graph by hand. If you wanted to graph by hand, then you'd plot each of the points found in the table. Then draw a curve through all those points.

Answer:

Compound interest formula

\(\sf A=P(1+\frac{r}{n})^{nt}\)

where:

Given:

\(\implies y=32000(1+\frac{0.045}{4})^{4 \times 0.25x}\)

\(\implies y=32000(1.01125)^x\)

\(\begin{tabular}{|c | c |}\cline{1-2} \bf Quarterly & \bf \$ \\\cline{1-2} 0 & 32000.00\\\cline{1-2} 1 & 32360.00\\\cline{1-2} 2 & 32724.05\\\cline{1-2} 3 & 33092.20\\\cline{1-2} 4 & 33464.48\\\cline{1-2} --- & --- \\\cline{1-2} 20 & 40024.02\\\cline{1-2}\end{tabular}\)

\(y=32000(1.01125)^x\)  (where x is the number of quarterly periods)

$40,024.02

see attached

The polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5 is P(x) = x^3 - 4x^2 - 17x + 60.  

To construct a polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5, we can use the fact that the polynomial can be written as a product of linear factors corresponding to each zero.

The factor corresponding to x = 3 is (x - 3).

The factor corresponding to x = -4 is (x + 4).

The factor corresponding to x = 5 is (x - 5).

To obtain the polynomial, we multiply these factors together:

P(x) = (x - 3)(x + 4)(x - 5)

Expanding this expression gives us:

\(P(x) = (x^2 - 3x + 4x - 12)(x - 5)\)

\(= (x^2 + x - 12)(x - 5)\)

\(= x^3 - 5x^2 + x^2 - 5x - 12x + 60\)

\(= x^3 - 4x^2 - 17x + 60\).

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Answer:

r=10

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(3r = 30 \\ \frac{3r}{3} = \frac{30}{3} \\ r = 10 \\ \)

Answer:

15.12

Step-by-step explanation:

8% of 14 = 1.12

14 + 1.12 = 15.12

Answer:

Step-by-step explanation:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?

Answer:

1. <AEB and <BEC    2. <AED and <CED

Step-by-step explanation:

Supplementary angles are 2 angles that add up to 180 degrees. 180 degrees is also a line. So I picked angles that form a line.

Answer:

47°

Step-by-step explanation:

If angles are complementary, that means those angles are added up to 90°.

Therefore,

43 + x = 90

Take 43 to the right side to make x as the subject.

x = 90 - 43

x = 47°

Note that a complementary angle adds up to 90 degrees.

In this problem, we get the equation:

43° + x = 90°

So, we need to find the value of x by doing:

90° – 43° = 47°

x = 47°

43° + 47° = 90°

We get the final result as:

x = 47°

Hope this helps :)

The equation will be t = 3s where t is total cost and s is number of snow cones. this can be find out be relationship of number of snow cones and total cost in table .

In given table :

Number of snow cones               Total cost

2                                                      6

6                                                      12

5                                                      15

From above table, we can relate

1st case :
number of snow cones = 2 and total cost = 6

i.e. 3 times of number of cones.

2nd case:

number of cones = 4 and total cost = 12

i.e. 3 times the number of cones.

3rd case :

number of cones = 5 and total cost = 15

i.e. 3 times the number of cones.

So, we see same pattern is repeated in all.

Then equation will be t = 3s where t = total cost , s = number of snow cones.

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The surface area of a rectangular prism is 490 in² by the area of each face and then add them up.

We refer to the prism as a rectangular prism since each face is shaped like a rectangle. A cuboid, which has six rectangular faces, and each opposite rectangular face is equal to and parallel to another rectangular face is known to have a similar shape.

To find the surface area of the right rectangular prism, we need to find the area of each face and then add them up.

Looking at the net, we can see that there are 6 faces, each with its own dimensions:

The top and bottom faces are both rectangles with dimensions 10 in by 13 in, so each has an area of 10 in × 13 in = 130 in².

The front and back faces are both rectangles with dimensions 10 in by 5 in, so each has an area of 10 in × 5 in = 50 in².

The left and right faces are both rectangles with dimensions 13 in by 5 in, so each has an area of 13 in × 5 in = 65 in².

Therefore, the total surface area of the right rectangular prism is:

2(130 in²) + 2(50 in²) + 2(65 in²) = 260 in² + 100 in² + 130 in² = 490 in²

So, the surface area of the right rectangular prism is 490 square inches.

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Answer:

660.4 Millimeters

Step-by-step explanation:

The conversion for inches to millimeters is 25.4, therefore to get the answer. I multiplied 26 by 25.4

25 8 25.4 = 660.4 Millimeters

Answer:

Step-by-step explanation:

At least 9 means more than 9 and includes 9

x ≥ 9     and    [9,  +∞)

At most 9 means numbers less than 9

x≤9       and  (-∞, 9]

more than 9 means bigger than 9 but not including 9

x > 9     and    (9,  +∞)

fewer than 9 means less than 9 but not including 9

x<9       and  (-∞, 9)

strictly between 7 and 9   means between 7 and 9 but not including

7<x<9      and    (7,9)       (This is the only one I'm unsure of.  Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)

between 7 and 7 inclusive.   means it's just =7  There's no boundaries

x=7

no more than 7 means less than 7 and includes 7

x ≤ 7   and   (-∞, 7]

The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

We have,

The volume of the can = The volume of the cylinder - The volume of the three tennis balls.

The volume of the cylinder.

V(cylinder) = πr²h

where r is the radius and h is the height of the cylinder.

Since the can holds three tennis balls snugly, the height of the cylinder is equal to three times the diameter of a tennis ball.

= 3 × 2(3.5 cm)

= 21 cm.

V(cylinder)

= π (3.5 cm)² (21 cm)

= 2709.38 cm³

The volume of one tennis ball.

V (ball) = (4/3)πr³

where r is the radius of the tennis ball. Thus,

V(ball) = (4/3)π(3.5 cm)³ = 179.594 cm³

The total volume of the three tennis balls is:

V(3balls) = 3 V(ball)

= 3(4/3) π (3.5 cm)³

= 538.782 cm³

The volume of the can not be occupied by tennis balls.

V(not occupied) = V(cylinder) - V(3 balls)

= 2709.38 - 538.782

= 2170.598 cm³

The percentage of the can that is not occupied by tennis balls.

percentage = (V(not occupied / V(cylinder)) × 100%

= (2170.598 cm^3/2709.38 cm^3) × 100%

= 80.14%

Therefore,

The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

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The expression for a in terms of c is \(a^{2}= \sqrt{c^{2} -9}\). The correct option is the third option \(a^{2}= \sqrt{c^{2} -9}\)

From the question, we are to determine the expression for a in terms of c

In the given right triangle, we can write that

\(c^{2} = a^{2} +3^{2}\) (Pythagorean theorem)

Thus,

\(c^{2} = a^{2} +9\)

\(a^{2}= c^{2} -9\)

\(a^{2}= \sqrt{c^{2} -9}\)

Hence, the expression for a in terms of c is \(a^{2}= \sqrt{c^{2} -9}\). The correct option is the third option \(a^{2}= \sqrt{c^{2} -9}\)

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Answer:

13.25

Step-by-step explanation:

1. you have to subract the cost of the drink:

94.25-1.50=92.75

2.you have to divide to get the individual cost of pizzas by doing

92.75÷7=13.25

so therefore your answer is 13.25 per pizza

Answer: y=x−2 y = x − 2

Step-by-step explanation:

Answer:

B) in the modern art section of an art museum

Step-by-step explanation:

Hope it helps! =D

Answer:

The angle ACX equals 51 degrees. The angle ACB equals 129 degrees.

Step-by-step explanation:

21 + 30 + y = 180

y = 129

129 + x =180

x = 51

Answer:

$0.75

Step-by-step explanation:

Since f(x) is linear, the rate of change is is the coefficient of x

Answer:

---------------------

Formula for area of a rectangle with dimensions l and w is:

Substitute 10 for l and 4 for w:

Answer:

\(\frac{2}{5\\}\) + \(\frac{5}{10}\)= \(\frac{9}{10}\)

Step-by-step explanation:

Because this is not multiplication or diving you must find the same denominator, which is 10. Now, because 5/10 is already 10 I don't need to change that, but if you see that 2/5 does not have the denominator of 10. Then, I need to multiply 2 on the numerator and the denominator because 5(2) equals 10 and whatever is multiplied to the denominator has to be multiplied to the numerator. So. now the numerator is 4. Lastly, what you need to do is add them together. So, (2+5)=7 and the denominator is stays as 10 because it is addition. So, our final answer is 9/10

[ Hope that helped :) ]

Step-by-step explanation:

For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,

b^2 - 4ac must be positive.

b^2 - 4ac > 0

(k - 3)^2 - 4(3 - 2k) > 0

k^2 - 6k + 9 - 12 + 8k > 0

k^2 + 2k - 3 > 0

To show that k satisfies k² + 2k - 3 > 0 ,the discriminant is given as Δ \(= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.\)

To have two distinct real roots, the discriminant of the quadratic equation must be positive. The discriminant is given by;

Δ \(= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.\)

For two distinct real roots, Δ > 0. So, we have k² + 2k - 3 > 0. Thus, k satisfies the inequality k² + 2k - 3 > 0.

In summary, for the quadratic equation x² + (k - 3)x + (3 - 2k) = 0 to have two distinct real roots, the value of k must satisfy the inequality k² + 2k - 3 > 0

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Answer:

\(\displaystyle {y = -\frac{5}{4}x+9}\)

Step-by-step explanation:

We are given two points of a line and asked to find the equation that goes through these points. These are given in the form:

\((x_1, y_1), (x_2, y_2)\)

To do so, we will first determine the slope of the line using the formula for slope:

\(\displaystyle m = \frac{y_2-y_1}{x_2-x_1}\)

Then, we will use the point-slope formula to find the equation of the line in slope-intercept form.

Point-Slope Formula

\(y-y_1=m(x-x_1)\)

Slope-Intercept Form

\(y=mx+b\)

First, use the slope formula to find the slope of the equation:

\(\displaystyle m = \frac{y_2-y_1}{x_2-x_1}\\\\\\\displaystyle m = \frac{-1-14}{8-(-4)}\\\\\\\displaystyle m = \frac{-15}{12} = -\frac{15}{12}\\\\\\\displaystyle m = -\frac{5}{4}\)

Then, use the point-slope formula to substitute values and find the equation of the line in slope-intercept form:

\(y-y_1=m(x-x_1)\\\\\\\displaystyle y-14=-\frac{5}{4}(x-(-4))\\\\\\\displaystyle y-14=-\frac{5}{4}x-5\\\\\\\displaystyle y-14+14=-\frac{5}{4}x-5+14\\\\\\\displaystyle{y = -\frac{5}{4}x+9}\)

The equation of a line passing through the points (-4, 14) and (8, -1) is:

\(\displaystyle \boxed{y = -\frac{5}{4}x+9}\)