[tex]2(x+5)=3x+1[/tex]

Answer:

Line 1

Step-by-step explanation:

Slope = (y₂ - y₁)/(x₂ - x₁)

Now, in line 1, all the y coordinates are equal, meaning, that y₂ - y₁ = 0 no matter what. Hence, line 1 is the answer.

Cheers!

The total cost of the candy excluding tax is  $19.2

From the question we have that

The cost of the candy per pound is $5.00

And a coupon that gives a discount of $0..20 per pound

hence 4 pounds of candy without discount is

= 4 * 5

= $20

the discount is solved to be

= 4 * 0.2

= 0.8

subtracting the discount

= 20 - 0.8

= $19.2

So the amount to be paid for the candy is $19.2

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The image will be formed 23.31 cm along the +x direction of the lens. The height of the image is h{i} = 7 cm.

The magnification produced by a lens is defined as ratio of the height of the image to the height of the object. It is denoted by 'm'.

Given is that a 2.8 cm object is placed 35mm in front of a converging lens. The magnification of the lens is 2.5.

Given is that -

m = h{i}/h{o}

h{i} = 2.8 x 2.5

h{i} = 7 cm

f = {object distance} / {(1 / Magnification) + 1)} × 1000

f = {3.5} / {(1/2.5) + 1} x 1000

f = 2.5 cm

Using the lens formula -

1/d(o) + 1/d(i) = 1/(f)

1/d(i) = 1/2.5 - 1/2.8

1/d(i) = 0.0429

d(i) = 1/0.0429

d(i) = + 23.31 cm

Therefore, the image will be formed 23.31 cm along the +x direction of the lens. The height of the image is h{i} = 7 cm.

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Answer:

250

Step-by-step explanation:

AX² is the standard form of a quadratic equation, where A is a coefficient and X is a variable.

In mathematics, a quadratic equation is a polynomial equation of the form ax2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to zero. A quadratic equation can have either one, two, or no real solutions, depending on the value of the discriminant, b2 - 4ac. The discriminant determines the nature of the roots of the equation: if it is positive, the equation has two distinct real solutions; if it is zero, the equation has one repeated real solution; and if it is negative, the equation has two complex conjugate solutions.

The standard form of a quadratic equation is ax2 + bx + c = 0, where a is the coefficient of the x2 term, b is the coefficient of the x term, and c is the constant or free term. AX2 is the standard form of the equation, where A is the coefficient of the x2 term and X is the variable. If the coefficient A is not equal to 1, the equation can be simplified by dividing both sides of the equation by A. Solving a quadratic equation requires the use of the quadratic formula, which is used to find the roots of the equation. The quadratic formula states that the roots of the equation are x = [-b ± √(b2 - 4ac)]/2a.

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Answer:

[tex]l = \dfrac{4x^4y^7}{z}[/tex]

Step-by-step explanation:

[tex]A = l\cdot w[/tex]

We can divide both sides of this formula by width to solve for length.

[tex]\dfrac{A}{w} = l[/tex]

Then, we can plug in the given values for width and area.

[tex]\dfrac{12x^6y^7}{3x^2z} = l[/tex]

Finally, we can solve for length by applying the quotient exponent rule.

[tex]\dfrac{x^a}{x^b} = x^{(a-b)}[/tex]

[tex]\dfrac{12x^6y^7}{3x^2z} = l[/tex]

[tex]4\cdot x^{(6-2)} \cdot \dfrac{y^7}{z} = l[/tex]

[tex]l = \dfrac{4x^4y^7}{z}[/tex]

The solution to the equations are as follows:

x = 0

r = -4

b = -8

n = -3

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

The equation can be solved by find the values of the variables as follows:

Hence,

5.

1 - 3x = 3x + 1

-3x - 3x = 1 - 1

-6x = 0

x = 0

6.

4r + 8 + 5 = -15 - 3r

4r + 13 = -15 -3r

13 + 15 = -3r - 4r

28 = -7r

r = 28 / -7

r = -4

7.

-12 - 4b = 4 - 2b

-12 - 4  = -2b + 4b

-16 = 2b

b = -8

8.

3n - 15 = 7n + n

3n - 7n - n = 15

-5n = 15

n = -3

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Answer:

The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.

Step-by-step explanation:

The ratio of the musicians to fashion professionals is 13 : 32

Total number of people on the guest list= 45

Number of musicians= 13

Number of fashion professionals = Total number of people on the guest list - Number of musicians

= 45 - 13

= 32 people

The ratio of the musicians to fashion professionals = 13 : 32

Ultimately, based on the given situation the ratio of musicians to fashion professionals = 13 : 32

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The equation evaluates to -2 when k = 20 and m = -2

What is a linear equation in 2 variables?

A linear equation in two variables is an equation that can be written in the form of

ax + by = c

where a, b, and c are constants and x and y are the variables. This equation represents a straight line in a two-dimensional coordinate system where x and y are the coordinates. The values of x and y that satisfy the equation form the set of solutions of the equation.

0.3k - 4m = 0.3(20) - 4(-2) = 6 - 8 = -2

Explanation:

First substitute the given values of k and m into the equation: 0.3k - 4m = 0.3(20) - 4(-2)

Next, simplify the multiplication: 0.3(20) = 6

Now we can simplify the subtraction of a negative number: 4(-2) = 8

So we have: 6 - 8 = -2

As you can see, the equation evaluates to -2 when k = 20 and m = -2

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In mathematics, a radical is a number or expression that represents the principal value of the square root, cube root, or any other higher-order root of a given number or expression.

sin(30) = opposite/hypotenuse

so, the length of the opposite side = sin(30) * hypotenuse

The hypotenuse is the side opposite the right angle, and has a length of 16 units, so we can substitute this into the equation:

sin(30) = opposite/16

To find the length of the opposite side, we can multiply both sides of the equation by 16:

opposite = (sin(30))*16

opposite = 8

So the length of the other side of the triangle is 8 units.

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Answer:

Step-by-step explanation:

To find the domain and range of a piecewise function, you will need to consider each piece separately and then combine the results. First Identify the domain of each piece, then Identify the range of each piece and Combine the domains and ranges

Note: Sometimes you may find that domain or range of a certain piece is not mentioned in the function, in that case, you can assume it to be the default domain or range of real numbers.

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According to Theorem 6.1C, a quadrilateral's subsequent angles are supplementary if it is a parallelogram.

One of the most fundamental geometric shapes is the square. This particular parallelogram contains four sides that are identical to one another and four right angles. Due to its two sets of parallel sides and four right angles, a square is also a rectangle.

A parallelogram's consecutive angles are congruent. A parallelogram's diagonals cut each other in half. A rhombus has four right-angled angles. A rhombus has consecutive sides that are congruent. Conclusion 6.3C. A parallelogram becomes a rectangle if one of its angles is a right angle.

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The remainder when 2x² - 5x - 1 divided by x - 3 is (2x + 1)

Let p(x) represents a polynomial  2x² − 5x − 1 and m(x) represents a polynomial x - 3

i.e., p(x) =  2x² − 5x − 1

and m(x) = x - 3

we need to find the remainder when 2x² − 5x − 1 divided by x − 3

If we divide a polynomial  p(x) =  2x² − 5x − 1  by m(x) = x - 3 using polynomial long division method, the result is:

p(x) / m(x)

= ( 2x² - 5x - 1 ) ÷ (x - 3)

= [ ( 2x² - 5x - 1 ) × ( 2x + 1)] + 2

This means, the quotient is  ( 2x + 1) and the remainder is 2

(see in attachment)

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Answer:c60

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be height x is 20 m.

Polygons include triangles since they have four sides or more. It has a simple, geometric shape. The letters ABC make up a triangle, which is a square angle. Euclidean geometry results in a single rectangle or square so when sides remain not coincident. Because they have 3 components and three corners, triangles are polygons. A triangle's corners are where its three sides meet. The total of the angles in a triangle is 180 degrees.

Here,

Given :

Area of triangle is  120 m².

the base length is 12m

To find the height = x,

=>Area = 1/2 * base * height

=> 120  = 1/2 * 12 * x

=> 120 = 6 *x

=> x = 120/6

=> x =20

Therefore , the solution of the given problem of triangle comes out to be

height x is 20 m.

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Answer: The square root of 36 is expressed by √36, where '√' is the radical symbol and 36 is the radical form.

Step-by-step explanation: √36 is equal to 6, which is a rational number. Since 36 is a perfect square, therefore, it becomes easy for us to find its square root.

Hoped It Helped

The square root of 36 is expressed by √36, where '√' is the radical symbol and 36 is the radical form is 6 .

What is square root ?

Its like abundance (quantity ) of which is called amplitude (quantity) of the particular square .

Give : √36

Now,

Few examples of square root,

√4 = 2

√9 = 3

√16 = 4

√25  = 5

√36 = 6

√36 is equal to 6, which is a rational number. Since 36 is a perfect square, therefore, it becomes easy for us to find its square root.

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The factored form of the quadratic function is f(x) = a(bx + c) (dx + e)

The term quadratic function is defined as a polynomial function with one or more variables in which the highest exponent of the variable is two and the graph of the quadratic equation is always forms the parabola.

Here we have given that we have to find the  the factored form of a quadratic function

As we all know that the general form of the quadratic function is written as,

=>  f(x) = ax² + bx + c

While we factorize the general form then it can be expanded like the following,

=> f(x) = a(bx + c) (dx + e)

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Answer: [tex]4\sqrt{26}[/tex]

Step-by-step explanation:

This is a rather tricky question at first, but it's easy when you figure out the trick.

The key here is using the Pythagorean theorem twice.

We see that the big triangle is divided by its height into two smaller ones.

First, use the Pythagorean theorem on the triangle on the left to find the height.

height = [tex]\sqrt{80-64}=\sqrt{16} =4[/tex]

Now that we know the height is 4, we can use the Pythagorean theorem on the triangle on the right to find x.

x = [tex]\sqrt{20^{2}+4^{2} } =\sqrt{416} = 4\sqrt{26}[/tex]

And there we have our final answer.

The population will reach 700,000 in the year 2044. The equation to calculate this is t = ln(700000/776000)/(-0.015), which gives t = 42.

1. We are given the population of San Francisco in 2002, which is 776,000.

2. We are also given the equation P=776000e^-0.015, which is a model for the population of San Francisco over time.

3. We need to figure out when the population will reach 700,000.

4. To do this, we need to rearrange the equation to solve for t, the number of years since 2002.

5. Rearranging the equation gives us t = ln(700000/776000)/(-0.015).

6. Plugging in our values gives us t = 42.

7. This means that the population of San Francisco will reach 700,000 in the year 2044 (i.e. 42 years since 2002).

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The expression can be used Jake paid each night for the hotel is:

x = d/5 - $50

Now, According to the question:

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

The given data is:

He bought a plane ticket for $250 and stayed in a hotel for 5 nights.

The price d is equal to $250 + 5 prices of staying in a hotel for a night.

If we let "x" be the price per night then we can get the following:

The expression will be:

d = $250 + 5x

5x = d - $250

[tex]x = \frac{d - 250}{5}[/tex]

x = d/5 - $50

Hence, The expression can be used Jake paid each night for the hotel is:

x = d/5 - $50.

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The way to convert the vertex form to factored form is explained below.

The term vertex is defined as  a special point of a mathematical object, and is usually a location where two or more lines or edges meet.

Here we have to write down the steps to convert the vertex form to factored form.

The very first steps is to expand the vertex form into standard quadratic form and then use the quadratic root formula to determine the roots.

Here as we all know that factored term is the product of a constant and two linear terms and they are the roots of the function.

So, now we have to use the quadratic formula to convert them into factor form.

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The additional angles are P and Q. The measure of angle P = 116 if the measure of angle Q is 64º

Additional angles add up to 180.

P+Q = 180

P +64 = 180

Subtract 64 from each side

P = 180-64

P =116

The complete question is:

Angle P and angle Q are supplementary angles. If the measure of angle Q is 64º, find the measure of angle P.

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The solution set of the inequality x 4 5x 2/3 7x 3 5 is x> 7.

To solve this inequality, we need to isolate the x term on one side and all the other terms on the other side. We can do this by subtracting 4 from both sides of the equation, which gives us 5x 2/3 7x 3 - 4 < 0.

Next, we can add 7x 3 to both sides of the equation, giving us 5x 2/3 - 4 + 7x 3 < 7x 3.

Now, since the denominator of the first term is 3, we can multiply both sides of the equation by 3/3. This gives us 5x 2 - 4 3 + 21x 3 < 21x 3.

Next, we can subtract 21x 3 from both sides of the equation, which gives us 5x 2 - 4 3 < 0.

Now, we can divide both sides of the equation by 5, which gives us x 2 - 4/5 < 0.

Finally, we can take the square root of both sides of the equation, which gives us x - 2/√5 < 0.

This means that x > 2/√5 + 2. Since 2/√5 + 2 > 7, the solution of the inequality is x > 7.

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The statement AB + BC = AC is true according to the segment addition postulate.

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

The smaller segments in this problem are given as follows:

AB and BC.

The large segment is given as follows:

AC.

Hence the equation is given as follows:

AB + BC = AC.

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The correct answers are 1, 2, and 5 AB=BC,AD=2AC and BD=CD.

Circle is a two-dimensional shape made up of points that are all the same distance from the center point. This distance is called the radius. Circles are one of the most fundamental shapes in geometry, and can be found in nature in many places, from the sun to the rings of Saturn. Circles can also be used to create other shapes such as ellipses, sectors and arcs.

1. The two circles have the same radius.

2. The two circles intersect at two distinct points.

3. The line segment connecting A and C is the diameter of the larger circle.

4. The line segment connecting A and C is the radius of the smaller circle.

5. The two circles have different radii.

6. The two circles have the same circumference.

The correct answers are 1, 2, and 5.

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Answer:

B and C I think.....

Step-by-step explanation:

it makes sense cuz if u make a line it'll kinda go through.

The answer is c: x+1/x, which is not a polynomial because it contains a fraction (1/x).

This is not a polynomial because it contains a fraction (1/x). A polynomial is an expression consisting of variables, constants, and exponents. It can be of any degree, but it must not contain any fractions. The other three options (a, b, and d) are all polynomials because they only contain variables, constants, and exponents.

For example, option a: √3x^2-2√3x+3, can be written as 3x2-2x+3, which is the standard form of a polynomial. Similarly, option b: 3x3/2-5x2-1/√2x-1, can be written as 3x2-5x+1, and option d: 5x2-3x+√2, can be written as 5x2-3x+2, which are both in the standard form of a polynomial.

Therefore, the answer is c: x+1/x, which is not a polynomial because it contains a fraction (1/x).

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Take the example of a $10,000 savings account earning 2% interest annually. Since the interest rate is 0.02, expressed as a decimal, the following formula would be appropriate:  Interest equals $10,000 divided by 0.02 times one to equal $200.

Interest = P x R x T is the formula for calculating interest.

P is Principal amount

R is the interest rate

T is the quantity of time periods.

Interest is calculated as $10,000 divided by 0.0015 times one.

Interest equals $15.

The Complete Question is interest rate.

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The expression that shows Francine balance after 'm' months is

First bank : 200 + 50m

Second Bank : 100 + 75m

By dividing the account value by the interest rate and the length of time the money has been in the account, you can figure out how much simple interest you'll receive in a savings account. A savings account's interest is money you earn, not money you pay, so keep that in mind.

Simple interest is calculated based on a loan's principle or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principle sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

Interest = P x R x T is the formula for calculating interest.

P is Principal amount

R is the interest rate

T is the quantity of time periods.

For this situation, the computation would be:

In the first bank she deposited $ 200 initially and $50 every month so

The equation will be 200 + 50*m

'm' is the number of months

In the second bank she deposited $ 100 initially and $70 every month so

The equation will be 100 + 75*m

'm' is the number of months

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