5a - 26 = -10
6a + 46 = 36

If (a,b) is the solution to the system of equations shown above, what is the value of a?

(a) The height after t years is given by

h(t) = 0.6t² + 3t + 11

(b) The shrubs are 38 centimetres tall when they are sold.

The growth rate of the shrubs during the first year of growth can be determined by setting t = 1 in the given differential equation dh/dt = 1.2t + 3. This gives us dh/dt = 1.2(1) + 3 = 4.2 centimeters per year.

Therefore, during the first year of growth, the shrubs will grow at a rate of 4.2 centimeters per year. This rate of growth is expected to increase as the shrubs age and reach the end of the 5-year growth period before they are sold by the nursery.

(a) To find the height after t years, we integrate the growth rate function with respect to t:

∫dh/dt dt = ∫(1.2t + 3) dt

h(t) = 0.6t² + 3t + 11

(b) The shrubs are sold after 5 years, so we plug in t = 5 into the function we found in part (a):

h(5) = 0.6(5)² + 3(5) + 11

= 38 cm

Therefore, the shrubs are 38 centimetres tall when they are sold.

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Answer:

Step-by-step explanation:

hello

Step-by-step explanation:

we all know that development is positive change in society and fidelity is a process of fertilization of human in society that explain us development and fertilization are the process of positive changes in our environment and province

The ratio table is given below:-

Oranges      3         4       8     10     12  

Cost( in $)   3.75   5       10     12.5   15

Fractions are frequently used to describe ratios and proportions. A ratio is shown when a fraction is stated as a:b, whereas a proportion implies that two ratios are equal. a and b can be any two numbers in this situation. The ratio and proportion are two fundamental ideas that lay the groundwork for comprehending other concepts in mathematics and science.

We use the concept of ratio and proportion in our daily lives, such as in business when dealing with money or in cooking.

As a result, the ratio defines the relationship between two values, such as a:b when b is higher than zero. For example, the 2:4 ratio is expressed as 2:4 = 1:2. And in this instance, the comment is deemed proportionate.

Now,

As given no. of oranges = 8

Cost of 8 oranges = 10

cost of 1 orange=10/8=1.25 rs/orange

then

The table will be as follow

Oranges      3         4       8     10     12  

Cost( in $)   3.75   5       10     12.5   15

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You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second,  64.23 feet/second long it will take for the object to hit the ground below. This can be solved using the concept of law of conservation of energy.

Three fundamental quantities all maintain their original values. Energy, momentum, and angular momentum are these. Energy is a conserved quantity, which could surprise you if you've read instances in previous pages, such the kinetic energy of charging elephants. The first law of thermodynamics, generally known as the law of conservation of energy, stipulates that the energy of a closed system must remain constant and cannot rise or fall on its own without external intervention.

Given that,

Height of the cliff, h= 55 Foot

Initial speed of the projectile, u = 85 m/s

Let, the projectile hit the ground with velocity "v"

Applying the law of conservation of energy,

mgh + 1/2 mu² = 1/2 mv²

or, m (gh + 1/2 u²) = 1/2 mv²

or, (gh + 1/2 u²) = 1/2 v²

or, 10 × 55 + (1/2 × (55)²) = 1/2 v²

or, 550 + 1512.5 = 1/2 v²

or, 2062.5 = 1/2 v²

or, 4125 = v²

or, v = 64.23 feet/second

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The equation of the straight line is 2x+5y=340.

The x-intercept point of that line is (170,0).

A straight line has different forms like point-slope form, standard form, slope-intercept form, and others. A specific form is used according to the given data for convenience.

As f(-10)=64 and f(15)=54, two points can be wriiten as (x₁,y₁)=(-10,64) and (x₂,y₂)=(15,54).

Now, use the two-point form of the equation of a line.

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)

(y-64)/(x-(-10))=(54-64)/(15-(-10))

(y-64)/(x-10)=-10/25

25(y-64)=-10(x-10)

5(y-64)=-2(x-10)

5y-320=-2x+20

2x+5y=340

Therefore, the required equation of the line is 2x+5y=340.

To find the x-intercept, substitute y=0 into the equation of the line.

2x+5×0=340

2x=340

x=170

Therefore, the x-intercept point is (170,0).

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The measure of angle ∠T found using the law of sines is about 72°

The law of sines states that the ratio of the of the sine of an angle in a triangle to the length of the opposite side, is the same for the three angles in a triangle.

Mathematically, where the side lengths of the triangle are; a, b, c, and the corresponding opposite angles are ∠A, ∠B, and ∠C, we get;

[tex]\frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}[/tex]

The parameters in the question are;

AT = 28

AD = 37

m∠D = 46°

DT = a

Therefore, according to the law of sines, we get;

37/(sin∠T) = 28/(sin(46°))

Inverting both sides, we get;

(sin∠T)/37 = (sin(46°))/28

(sin∠T) = 37 × (sin(46°))/28

∠T = arcsine(37 × (sin(46°))/28) ≈ 72°

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{v = \dfrac{1}{3}(3.14) (5^2) \times 10}\\\\\mathsf{v = \dfrac{1}{3}(\dfrac{3.14}{1})(5\times5)(10)}\\\\\mathsf{v = \dfrac{1\times3.14}{3\times1}(25)(10)}\\\\\mathsf{v = \dfrac{3.14}{3}(25)(10)}\\\\\mathsf{v = 1.046667(25)(10)}\\\\\mathsf{v = 26.166667(10)}\\\\\mathsf{v = \dfrac{785}{3}}\\\\\mathsf{v = 261 \dfrac{2}{3}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{v = \dfrac{785}{3} \ or \ v = 261 \dfrac{2}{3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

1,755 cm² icings are needed for one cake.

The correct option is (C).

What is the area of the circle?

The area of a circle is the amount of space enclosed within the circle. It is a measure of the size of the circle, and it is determined by the distance from the center of the circle to its edge (which is the radius). The formula for the area of a circle is:

A = πr²

The surface area of the circular top of the cake can be found using the formula for the area of a circle:

A = πr^2

where A is the area of the circle, and r is the radius. For the red velvet cake, the radius is 13 cm, so the area of the circular top of the cake is:

A = 3.14 x 13^2 = 530.66 cm^2 (rounded to two decimal places)

To find the surface area of the curved side of the cake, we need to find the circumference of the circular base and multiply it by the height of the cake. The circumference can be found using the formula:

C = 2πr

where C is the circumference and r is the radius. For the red velvet cake, the circumference of the circular base is:

C = 2 x 3.14 x 13 = 81.64 cm (rounded to two decimal places)

So, the surface area of the curved side of the cake is:

A = C x h = 81.64 x 15 = 1224.60 cm^2 (rounded to two decimal places)

Therefore, the total surface area of the cake that needs to be iced (excluding the circular bottom) is:

530.66 + 1224.60 = 1755.26 cm^2 (rounded to two decimal places)

Rounding to the nearest square centimeter, we get that approximately 1755 cm^2 of icing is needed for one red velvet cake at the Bisecting Bakery.

Therefore, 1,755 cm² icings are needed for one cake.

The correct option is (C).

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Answer:

1531 pesos

Step-by-step explanation:

The profit when x=10 is calculated as follows:

P(10) = 10^3 + 5(10^2) + 3(10) + 1 = 1000 + 500 + 30 + 1 = 1531 pesos.

Based on the given information,

only one triangle is possible.

The correct option is C.

It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.

Given:

The angle measure of B = π/6 = 30°.

a = 20, and b = 10

That means,

m∠A = 2∠B = 2 x 30 = 60°.

Now, there is only one possibility of a triangle, and that triangle is 30-60-90 triangle.

Hence, only one triangle is possible.

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The expression which is equivalent to the expression 14x+3−13x+(−2) is:

x +1

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,

14x+3−13x+(−2)

Now it can be simplify in the following way:

⇒ 14x - 13x + 3 - 2

the variable and constant terms can be clubbed together,

⇒ x + 1

Hence, the equivalent expression is x + 1

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Answer:

4 I think

Step-by-step explanation:

4+36=40, 10x4=40

Answer: 12

Step-by-step explanation:

1) Create an equation. Lets call the missing number x. 36 is added to x or 36+x and when 36 is added to x it is 4 times of x or 4x, so our equation is 36+x=4x.

2) Bring the variable to one side by subtracting x on both sides. Our new equation is 36=3x.

36) Get rid off the coefficient 3 by dividing 3 on both sides to get x=12

The volume of the cylinder is  

Using the volume of cone given by the formula

= π r² h/3

In the problem the volume is given by  222 and volume of cylinder is equal to

= π r² h

comparing the two volumes and taking proportions

volume of cone / volume of cylinder

π r² h/3 / π r² h = 222 / volume of cylinder

π r² h / 3 π r² h = 222 / volume of cylinder

1 / 3  = 222 / volume of cylinder

volume of cylinder = 3 * 222

volume of cylinder =  666

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The volume of the rectangular prism is 42 cubic inches

The volume of a rectangular prism is calculated as the product of its length, width, and height.

The formula is:

V = l x w x h

Where,

V is the volume

l is the length

w is the width

h is the height.

The volume of this figure is calculated using the formula given above as;

V = l * w * h

We can divide the figure into two rectangular prism and calculate the volume.

v = (8 * 3 * 1) + (6 * 3 * 1)

v = 42 in³

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Answer:

Step-by-step explanation:13x6

The closest answer choice is 0.76, which corresponds to 0.1934. So the answer is 0.1934.

We can calculate the variance of the hotel's star rating by using the formula:

variance = sum[(xi - mean)^2 * pi]

where xi is the rating (1, 2, 3, or 4), mean is the expected value of the rating, and pi is the proportion of the population that left that rating. Since we know the proportions of the population that left each rating, we can calculate the expected value of the rating as:

mean = 1(0.3) + 2(0.2) + 3(0.2) + 4(0.3) = 2.9

Then, we can calculate the variance as:

variance = (1 - 2.9)^2 * 0.3 + (2 - 2.9)^2 * 0.2 + (3 - 2.9)^2 * 0.2 + (4 - 2.9)^2 * 0.3

variance ≈ 0.57

Finally, the standard deviation is the square root of the variance:

standard deviation = sqrt(0.57) ≈ 0.756

Therefore, the closest answer choice is 0.76, which corresponds to 0.1934.

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The solution is Option B.

The area of the rectangle is given by the equation A = 4 4/5 feet²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the equation will be

Let the length of the rectangle be L = 8 feet

Let the width of the rectangle be W = ( 3/5 ) feet

Now , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of Rectangle = ( 3/5 ) x 8

On simplifying the equation , we get

Area of Rectangle = 24/5 feet²

Area of Rectangle = 4 4/5 feet²

Hence , the area of the rectangle is 4 4/5 feet²

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In the xy-plane, the point (2,10) lies on the graph of the function f(x) = 2x^2 + bx - 8.  The value of b is 4.

What is linear equation?

A linear equation is an equation that describes a straight line in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope of a line is the measure of how steeply the line rises or falls, and the y-intercept is the point at which the line crosses the y-axis.

In a two-dimensional coordinate system, a linear equation represents a straight line that can be graphed by plotting pairs of x and y values that satisfy the equation. The line passes through all points that satisfy the equation and no others.

We can find the value of b by using the point-slope form of a linear equation, which states that the equation of a line with slope m that passes through the point (x1, y1) is given by y - y1 = m(x - x1).

In this case, the slope of the line is equal to 4x, and the point (x1, y1) is (2, 10), so we have:

y - 10 = 4x * (x - 2)

Expanding the right-hand side, we get:

y - 10 = 4x^2 - 8x

Matching this equation with the given function f(x) = 2x^2 + bx - 8, we see that b = 4.

So the value of b is 4.

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The first equation is:

(5 1/5)^5 = 25x

To solve for x, we need to simplify the left side of the equation first.

(5 1/5)^5 = (5 + 1/5)^5 = 6^5 = 7776

So,

7776 = 25x

Therefore,

x = 7776/25 = 311.04

For the second equation:

If (8 1/3)^2 = 4x, then x =

We need to simplify the left side of the equation first.

(8 1/3)^2 = (8 + 1/3)^2 = 9^2 = 81

So,

81 = 4x

Therefore,

x = 81/4 = 20.25

So the values of x that make each sentence true are 311.04 and 20.25, respectively.

CJ's plan to construct a square inscribed in a circle is through 7 steps.

step 1:

First, draw a circle using a compass (any size).

Step 2:

Using a ruler, draw a diameter or straight line along the length of the circle and pass through its center.

Step 3:

Then open the compass through the circle. Then bring the compass tip to one end of the diameter and swing the compass over the circle to draw an arc.

Step 4:

Keeping the compass the same length, move it to the other side of the diameter, swing it over the circle again, and create another arc until the two arcs intersect. Step 5:

Repeat steps 3 and 4, this time using the same compass size to create an arc under the circle.

Step 6:

Connect the top and bottom intersections of the circle with a ruler or ruler. This creates a perpendicular bisector that bisects the diameter and forms a 90 degree angle.

Step 7:

Finally, use a ruler to connect each corner point to create a square. 

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Based on the information, it can be inferred that the area of the figure is 310 yards²

To calculate the surface area of this figure we must find the area of all the faces of the figure:

Then we must multiply the area of each face by the number of faces with that area.

Finally we must add the areas of the faces

According to the above, the total surface area of this figure is 310 yards ²

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The required volume of the given rectangular prism is given as 240 in ³.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
From the data we have,
Length of the rectangle prism = 12 in
Width of the rectangle prism = 2 in
Height of the rectangle prism = 10 in

The volume of the rectangular prism = length × width × height
                                                 = 12 × 2 × 10
                                                 = 240 in ³

Thus, the required volume of the given rectangular prism is given as 240 in ³.

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The question is incomplete.
Complete question is," Calculate the volume of the prism of dimensions length, width and height are 12, 2, and 10 respectively. "

Answer:

Set up the equation ... 60 + 40X = total charges... where X is the number of hours (6.5)

60 + 40(6.5) = ?

60 + 260 = ?

320 = total charges

25+25=50,4+4=8;50+8=58

Using matrix inversion, the value of x and y are 1.104 and 39.704 respectively

The system of equations can be written in matrix form as:

|  -650    1 |   | x |   |  175    |

|  120     1 |   | y |   |  25,080 |

To solve for x and y, we can use matrix inversion to get:

| x |   |  -650    1 |^-1   |  175    |

| y | = |  120     1 |     |  25,080 |

Using matrix inversion, we get:

| x |   |  -0.00016  0.00875 |   |  175    |    | 1.104 |

| y | = |  0.00476   0.00004 |   |  25,080 | =  | 39.704 |

Therefore, the solution to the system of equations is x = 1.104 and y = 39.704.

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