The cost 3 kg of apples and 2 kg of orange is $3. Consider x and y as the cost per kgI oranges, respectively and draw the graph

Since the ABCD rectangle's vertex coordinates are A(1, -2), B(4, -2), C(4, -4), and D(3, 1), option c is accurate (1,-4)

You may also refer to it as a quadrilateral that is equiangular, meaning that each of its angles is equal. Another possibility for the parallelogram is a straight angle. Four of the sides of a square are of identical length. Four 90-degree vertices and equal parallel sides make up a rectangle-shaped quadrilateral. This leads to the term "equirectangular rectangle" occasionally being used to describe it. A rectangle is also referred to as a parallelogram due to the equal and parallel lengths of its opposite sides.

given

To find the coordinates, first subtract 1 from 4 to get 3 and then add 3 to -2 to get 1.

Since the ABCD rectangle's vertex coordinates are A(1, -2), B(4, -2), C(4, -4), and D(3, 1), option c is accurate (1,-4)

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The measure of angle MTU m∠MTU is 114 degree.

From the figure in the diagram:

Measure of angle STU is 145 degrees and measure of angle STM is 31 degree.

Since, angle STU composes or is the sum of angle STM and angle MTU.

To find angle MTU, simply subract angle STM from angle STU.

m∠STU = m∠STM + m∠MTU

Hence:

m∠MTU = m∠STU - m∠STM

Plug in the given values and simplify

m∠MTU = 145° - 31°

Subtract 31 from 145

m∠MTU = 114°

Therefore, angle MTU measure 114°.

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Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x+3)/8 = (x+6)/10

x+3 = 8(x+6)/10

x+3 = 4(x+6)/5

x+3 = (4x+24)/5

x +3 = 4x/5  + 24/5

x - 4x/5 =  (24/5)-3

x/5 = 9/5

x = 9

The differentiation of the given function f(x) = eˣ+6 is eˣ

The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given is function f(x) = eˣ+6, we need to find the derivative of this function,

f(x) = eˣ+6

f'(x) = d / dx (eˣ+6)

= d(eˣ)/dx + d(6)/dx

Since, 6 is a constant and derivative of a constant is zero,

d(eˣ)/dx + d(6)/dx = d(eˣ)/dx + 0

Now, when we differentiate eˣ, we get eˣ itself,

Therefore,

d(eˣ)/dx = eˣ

Therefore, the differentiation of the given function f(x) = eˣ+6 is eˣ

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Answer:

Perpendicular lines

Step-by-step explanation:

Parallel lines have the same slope.  In contrast, perpendicular lines have negative reciprocal slopes, in which the product of the slopes of two lines result in -1.

Given the two linear equations, y = -5x + 1 and x - 5y = 30:

Transform x - 5y = 30 into its slope-intercept form, y = mx + b:

x - 5y = 30

x - x - 5y = - x + 30

-5y = -x + 30

Divide both sides by -5:

\(\frac{-5y}{-5} = \frac{-x + 30}{-5}\)

\(y = \frac{1}{5}x - 6\)  (This is the slope-intercept form of the second equation, x - 5y = 30).

Now that we have both equations, it is easier to see that they have negative reciprocal slopes:

y = -5x + 1  ⇒ slope = -5

\(y = \frac{1}{5}x - 6\)   ⇒ slope =  1/5

Multiplying their slopes together:  -5 × 1/5 = -1. Therefore, these equations represent perpendicular lines.

Answer:

Perpendicular lines

Step-by-step explanation:

The maximum height at the moment is 191.0625 ft.

What is the projectile's height?

Let's find out the projectile's maximum height now that we know what it is. The highest vertical location along the object's flight is considered to be its maximum height. The range of the bullet is defined as its horizontal displacement.

Here, we have

Given: The equation for a projectile's height versus time is h(t)=-16t²+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second.

The equation for a projectile's height versus time is

h(t) = -16t²+Vt+h

h = 2

V = 110

Substitute these values into the function

h(t) = -16t²+110t+2

Take the first derivative

h'(t) = -32t + 110

Equate the derivative with zero h'(t) = 0

0 = -32t + 110

110 = 32t

t = 110/32

t = 3.4375

Find the maximum height at the moment

t = 3.4375 (s)

h(3.4375) = -16(3.4375)² + 110(3.4375) + 2

h(3.4375) = -189.0625 + 378.125 + 2

h(3.4375) = 191.0625 ft

Hence, the maximum height at the moment is 191.0625 ft.

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The value of x in the figure is 6

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal

The two opposite sides of the parallelogram that bear x are

2x-3 = 5x-21

Collecting similar terms we have

2x-5x = -21 +3

2x-5x = -21 +3

-3x = -18

Making x the subject of the formula

Hence x = 6

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The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

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\( {7x}^{4} + {12x}^{2} + 3x\)

Answer:

$305

Step-by-step explanation:

4 tickets = $122     <-- divide by 4

1 ticket = $30.5       <-- multiply by 10

10 tickets = $305

Answer:

305

Step-by-step explanation:

122 +122=244

122 divided by 2=61

244+61=305

Answer:

6 more girls than boys

Step-by-step explanation:

7+5=12

36 divided by 12 = 3

3x7=21

3x5=15

The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression

Given data ,

Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.

So , on simplifying the equation , we get

= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²

= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²

= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²

Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.

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Answer:

1711

Step-by-step explanation:

\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)

Make sure to follow order of operations!

Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

On solving the provided question we can say that - the inequality equation which will be formed is 290x \(\geq\) -23 + y

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.

here,

we have 290x

so the inequality equation which will be formed is

-y + 290x \(\geq\) -23

290x \(\geq\) -23 + y

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Fast food menus have increased in portion size and calories, driven by consumer demand and competitive pricing.

Two very much upheld perceptions about changes in the size and calories of cheap food menu things over the beyond 30 or more years are:

The piece sizes of inexpensive food things have altogether expanded. For instance, a burger today is a lot bigger than it was quite a while back. This pattern towards bigger piece sizes has been driven by the business' longing to offer more benefit for cash and to fulfill buyer needs.

The caloric substance of cheap food things has additionally expanded altogether. Cheap food is currently a significant supporter of the typical individual's day to day calorie consumption.

The expansion in calories is because of a mix of bigger part measures, the expansion of fatty fixings like cheddar and sauces, and the multiplication of unhealthy menu things like southern style chicken and burgers.

Cheap food fastens have been persuaded to expand the calorie content of their items to make them more attractive and interesting to buyers.

By and large, these progressions in cheap food menu things have added to the ascent in stoutness rates and related medical conditions.

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Answer:

This is your answer ☺️☺️☺️

Answer:

2^3=2^6

Step-by-step explanation:

well 2×2×2=16

and 2×2×2×2×2×2=64

The ratio of the area of the large rectangle to the area of the small rectangle is 9 : 1.

The area of rectangle is -

A = Length x breadth

Given is that Jacques and Faye are investigating relationships between two similar rectangles. Jacques finds that the first rectangle has a length of 12 units and a width of 6 units. Faye finds that the second rectangle has a length of 4 units and a width of 2 units.

We can write the ratio of the area of the rectangles as -

r = A{L}/A{S}

r = (12 x 6)/(4 x 2)

r = 9/1

Therefore, the ratio of the area of the large rectangle to the area of the small rectangle is 9 : 1.

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150 Inches... NEEERRRD

Answer:

5log5(1)-3*4log4(3)=-12log4(3)

Step-by-step explanation:

5log5(1) = 0 this is a log rule.

Any log to the 1 is zero.

So it will just be

0-3*4log4(3) = -12log_4(3)

Answer:

(1) protein in hot dog = ¼ * protein in 3 ounces of hamburger

(2) protein in hot dog + protein in 3 ounces of hamburger = 25

So we need to re-arrange (1) and (2) to solve for the protein in 3 ounces of hamburger!

(re-arrange (1)): 4 * protein in hot dog = protein in 3 ounces of hamburger

(re-arrange (2)): protein in hot dog = 25 - protein in 3 ounces of hamburger

(plugging re-arranged (2) into re-arranged (1)):

4 * (25 - protein in 3 ounces of hamburger) = protein in 3 ounces of hamburger ( multiplying )

100- 4 protein in 3 ounces of hamburger = protein in 3 ounces of hamburger

solving for the protein in 3 ounces of hamburger:

5 * protein in 3 ounces of hamburger = 100

protein in 3 ounces of hamburger = 20 gram

Answer:

220

Step-by-step explanation: a p e x

There are 220 ways to choose the paintings.

"Combination  determines the number of possible arrangements in a collection of items where the order of the selection does not matter."

\(^{n}C_r=\frac{n!}{r!(n-r)!}\)

For given example,

There are 12 paintings at an art show.

⇒ n = 12

Three of them are chosen randomly to display in the gallery window.

⇒ r = 3

So, using the formula for combination, the number of possible ways to choose the paintings would be,

\(\Rightarrow~ ^{n}C_r=\frac{n!}{r!(n-r)!}\\\\\Rightarrow~ ^{12}C_3=\frac{12!}{3!(12-3)!}\\\\\Rightarrow~ ^{12}C_3=\frac{12!}{3!\times 9!}\\\\\Rightarrow~^{12}C_3=220\)

Therefore, there are 220 ways to choose the paintings.

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Considering the definition of equation, for a value of n of 10 the cost and revenue are equal.

A first degree equation is a mathematical equality with one or more unknowns.

Solving an equation consists of finding the value that the unknown must take so that equality is fulfilled.

The steps to solve an equation are as follows:

The cost C in dollars of producing a certain item is represented by the equation C = \(\frac{n}{2}\)+ 20, where n represents the number of items produced.

The revenue R, in dollars, from selling n items is represented by the equation R=2n+ 5.

The cost and revenue are equal. Then:

\(\frac{n}{2}\)+ 20= 2n+ 5

Solving:

When a term passes to the other side of equality, its sign changes (if it is positive it becomes negative and vice versa):

20 -5= 2n - \(\frac{n}{2}\)

15= \(\frac{3}{2}n\)

The X is cleared. Since the term in front of it is multiplying, it goes to the other side of the equation by dividing.

15 ÷\(\frac{3}{2}\)= n

10= n

Finally, for a value of n of 10 the cost and revenue are equal.

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Answer:

12

Step-by-step explanation:

We can conclude that the equation of the circle is (x - 3)² + (y + 6)² = 32, where (3, -6) is the center and 4√2 is the radius. Option 3 and 6 are correct  options.

Based on the information given, we know that circle has its center at the point (3, -6) and a radius of 4√2. We also know that the point (-1, -2) and (4, -0.5) are on the circle.

Using the distance formula, we can confirm that the distance between the center of the circle and each of these points is indeed 4√2.

This equation can be simplified to x² - 6x + y² + 12y + 1 = 0 by expanding and combining like terms. This is the equation of circle , and any point that satisfies this equation will be on the circle. Option 3 and 6 are correct  options.

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Answer:

1. False

2. True

3. False

4. True

5. True

6. False

7. True

8. False

9. True

10. False

#SahreYourKnowledge!

The linear function for the total cost C is:

A function is an expression, rule, or law that defines a relationship between one variable.

Example:

\(f(\text{x}) = 2\text{x} + 1\)

\(f(1) = 2 + 1 = 3\)

\(f(2) = 2 \times 2 + 1 = 4 + 1 = 5\)

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The total cost for x cubic yards.

\(\bold{C = 28 + 48x}\)

Thus, the function is C = 28 + 48x.

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Answer:

Step-by-step explanation:

Given:

Simplify equation for perimeter and solve for W:

Find L: