Parallel lines, transversal, and algebra really need help

The senate has 4+22 = 26 members this year.

Let x be the number of Democrat members in the senate.

Last year, the number of Republican members was x+20

This year, the number of Republican members is (x+20) - 2 = x+18

This year, the number of members in the senate is 2/3*(x+18) = 2/3*x+12

So the number of members in the senate this year is x+12

To find the value of x, we can use the fact that the number of members in the senate this year is the same as last year.

x + (x + 20) = x + 12

x+x+20 = x + 12

2x = 8

x = 4

So the senate has 4 Democrat members and x+18 = 4+18 = 22 Republican members.

Therefore the senate has 4+22 = 26 members this year.

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The formula of algebraic expression identities is (a – b)2 = a2 – 2ab + b.

What is algebraic expression ?

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). There are 3 main types of algebraic expressions which include: Monomial Expression. Binomial Expression. Polynomial Expression.

Formula of Algebraic Identities ,

[tex](a+b)^{2}[/tex] = a2 + 2ab + b^2

[tex](a-b)^{2}[/tex] = a2 – 2ab + b^2

(a + b) (a – b) = a2 - b^2

(x + a) (x + b) =[tex]x^{2}[/tex]+ (a + b) x + ab.

(x + a) (x – b) =[tex]x^{2}[/tex] + (a – b) x – ab.

(x – a) (x + b) =[tex]x^{2}[/tex] + (b – a) x – ab.

(x – a) (x – b) = [tex]x^{2}[/tex] – (a + b) x + ab.

[tex](a+b)^{3}[/tex] = a3 + b3 + 3ab (a + b)

The formula of algebraic expression identities is (a – b)2 = a2 – 2ab + b.

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Radiometric dating uses a decay curve to estimate the age of a fossil. The X-axis represents the number of years since the fossil was formed. The Y-axis represents the amount of radioactive material remaining in the fossil.

Radioactive elements decay over time, and the rate of decay is used to calculate how long ago the fossil was formed. The decay curve is a graph of the amount of the radioactive element left in the fossil over time, with the X axis showing the amount of time that has passed since the fossil was formed and the Y axis showing the amount of the radioisotope that is left in the fossil. The decay curve is used to estimate the age of the fossil by looking at the rate of decay and the amount of radioisotope that is left in the fossil.

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The expression to represent the amount of canned food collected so far is 5x² + 3xy + 2.

To write an expression that represents the number of cans the friends still need to collect to meet their goal is 2x² - 7xy + 4

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

PART A

To write an expression to represent the amount of canned food collected so far, sum the expressions for the already collected number of cans. That is:

amount collected so far = 2x² + 3x²−4 + 3xy + 6

amount collected so far = 5x² + 3xy + 2

PART B

To write an expression that represents the number of cans the friends still need to collect to meet their goal, subtract amount collected so far from collection goal. That is:

amount left = 7x² − 4xy + 6 - (5x² + 3xy + 2)

amount left = 2x² - 7xy + 4

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Answer: True

Step-by-step explanation:

Because 8-2 is 6 therefore the equation is 6>3 saying that 6 is greater than 3 or 3 is less than 6

Answer: (-4,0)

Step-by-step explanation:

3y = 20 -4x  .multiply by 2

2y = 12 - 3x  .multiply by 3

we get,

6y= 40 - 8x

6y= 36 - 9x

Subtracting both we get,

0 = 4 + x

x= - 4

Answer:

Dilated point coordinates: (-1, -2)

Step-by-step explanation:

For a point (x, y), the dilation of the point by a scale factor of k centered around the origin will result in a point (x', y') where x' = kx and y' = ky

Depending on the value of k, the point will move either closer to the origin(k < 1) or farther away from the origin (k > 1)

Here we have the original point A(-4, -8) and k = [tex]\dfrac{1}{4}[/tex]

So the new point will move closer to the origin

The coordinates of the new point A' will be

[tex]x' = 4\cdot \dfrac{1}{4} = -1\\\\y' = -8\cdot \dfrac{1}{4} = -2\\[/tex]

So the dilated point A' will have coordinates (-1, -2)

The conversion of units shown below.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

1. 25 mi/hr=__m/min

As, 1 m/h = 0.01667 m/min

25 mph = 25 x 0.01667

             = 0.41675 m /min

2. 32 mi/gal=__gt/min

32 mile/ gal = 153721589.8148768 gt/ min

3. 10 m/s=__ft/s

10 m/s= 32.80 ft/s

4. 14 gal/s=__km/l

14 gal/s = 32.93 km/l

5. 3.5 days=__mins

3.5 days = 5040 minutes

6. 100yd=__qt/m

100 yd= 0.0001 qt/m

7. 15 dollars/hr=__cents/min

15 dollars/hr= 25 cents/ min

8. 5L/s =___kL/min

5 L/s = 0.3 Kl/ min

9. 62in.=__m

62in.= 1.5748 m

10. 7 days= __s

7 days=604800 sec

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The angle of depression from the cruiser to the submarine is 63.43 degrees.

We can use the tangent function to find the angle of depression from the cruiser to the submarine.

The tangent function relates the opposite side (the vertical distance, or the depth) to the adjacent side (the horizontal distance) in a right triangle.

tan(angle of depression) = opposite/adjacent

In this case, the opposite side is the depth, or the vertical distance from the cruiser to the submarine, which is 2100 ft.

The adjacent side is the horizontal distance from the cruiser to the submarine, which is 900 ft.

tan(angle of depression) = 2100/900

Using a calculator we can find that tan(angle of depression) = 2.3333

Now we can use the inverse tangent function (arctan) to find the angle of depression:

the angle of depression = arctan (2100/900)

Using a calculator we can find that angle of depression = 63.43 degrees

Therefore, the angle of depression from the cruiser to the submarine is 63.43 degrees.

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The value of the function f(x) = 3x - 5 when x = 2 is f(2) = 1

A function is a mathematical equation that shows the relationship between two variables.

Given the function f(x) = 3x - 5, we desire to find f(2).

To find f(2), we substitute x = 2 into the equation. So, we have that

f(x) = 3x - 5. So substituting x = 2 into the equation, w ehave

f(2) = 3(2) - 5

f(2) = 6 - 5

f(2) = 1

So, the value of the function f(x) = 3x - 5 when x = 2 is f(2) = 1

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Converting moles to grams is a relatively straightforward process.

To begin, you'll need to know the molecular weight of the substance you're dealing with. This is the sum of the atomic masses of all the atoms in the molecule.

Once you have the molecular weight, you can then use the following equation to convert moles to grams: moles x molecular weight = grams. For example, if you wanted to convert 1 mole of water to grams, you would use the molecular weight of water (18.015 g/mol) to get the answer: 1 mole x 18.015 g/mol = 18.015 g.

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The inverse of log₁₀x is 10ˣ.

Inverse Function[f][y] provides the value of x for which f[x] equals y. Inverse Function[f][y] represents the inverse of the function f. To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y. Another name for exponentiation is finding an antilog, which is the inverse operation of finding a log.

The steps to determine the inverse of a function y = f are listed below (x). Swap out x and y. Solve for y. Change y to f⁻¹ (x).

Let us take,

a = f(x)

f(x) = log₁₀x

Then, a = log₁₀x

⇔ 10ᵃ = x

∴ f⁻¹(x) = 10ˣ

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Answer:

To factorize 21x⁴y⁵ - 7x³y² + 14x³y⁴, we can factor out the greatest common factor (GCF) from all three terms. The GCF of the three terms is x³y².

So we can write:

21x⁴y⁵ - 7x³y² + 14x³y⁴ = x³y²(21x y³ - 7 + 14x²y²)

We can simplify further by combining the constants:

21x y³ - 7 + 14x²y² = 21x y³ + 14x²y² - 7

So the expression can be factorized as:

x³y²(21x y³ + 14x²y² - 7)

This is the factorization of 21x⁴y⁵ - 7x³y² + 14x³y⁴.

Total distance will be 17.69 miles by multiplying average speed to time.

What is a average?

An average of a list of data is the expression of the central value of a set of data. Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list. In terms of statistics, the average of a given set of numerical data is also called mean. For example, the average of 2, 3 and 4 is (2+3+4)/3 = 9/3 =3. So here 3 is the central value of 2,3 and 4.  Thus, the meaning of average is to find the mean value of a group of numbers.

Average = Sum of Values/ Number of values

Suppose, we have given with n number of values such as x1, x2, x3 ,….., xn. The average or the mean of the given data will be equal to:

Average = (x1+x2+x3+…+xn)/n

Now,

Speed=Distance/time

12.2=distance/1.45

Distance=12.2*1.45

=122/10*145/100

Distance=17.69 miles

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Answer:

81

Step-by-step explanation:

37(3)=81

the percentage of change is calculated using a formula, which gives you the solution as 40% of change in this question.

percentage of change = [ (new price - old price)/old price ] *100

= [(70-50)/50 ] *100

= [20/50 ] *100 = 40%

To calculate the percentage change we divide the change in price by the original value of the factor. By subratcting the old price from the new price, you will get either a positive or negative sign. If it is positive, the change is increasing while in case of negative sign, change results in decrease.

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The measure of the angles in the parallelogram are 144 and 36 degrees.

What is a parallelogram?

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are of equal length and the opposite angles are also equal.

Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.

Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle.

Angles in a parallelogram

a + b + c + d = 360

Opposite angles are equal, so

2a + 2(0.25a) = 360

2a + 0.5 = 360

2.5a = 360

a = 360/ 2.5

a = 144

the other angle = 180 - 144 = 36 degrees

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Answer:

hope this helps!

Step-by-step explanation:

The length of the pool is 50 m, width 25 m, and the depth varies: 2.0 m is the minimum, but 3.0 m is the recommended depth. Olympic-size swimming pool contains 2,500,000 L of water, assuming a nominal depth of 2 m. It's around 550,000 imp gal and 660,000 US gal.

Answer:

A. To find a linear equation that models the temperature T when crickets are chirping at x chirps per minute, we need to use two points that are known. In this case, we are given that a cricket produces 120 chirps per minute at 70 degrees F and 168 chirps per minute at 80 degrees F. We can use these two points to find the slope and y-intercept of the line.

The slope of a line can be found using the formula: m = (y2 - y1) / (x2 - x1)

In this case, we can substitute the given values to get:

m = (168 - 120) / (80 - 70) = 48/10 = 4.8

The y-intercept of a line can be found using the formula: b = y - mx

We can use the point (70, 120) and the slope that we found to get:

b = 120 - (4.8 * 70) = -264

So the linear equation that models the temperature T when crickets are chirping at x chirps per minute is:

T = 4.8x - 264

B. If the crickets are chirping at 150 chirps per minute, we can substitute this value for x in the equation we found above to estimate the temperature:

T = 4.8x - 264

T = 4.8(150) - 264 = 720 - 264 = 456

So the estimated temperature is 456 degrees F.

C. The y-intercept of the line is -264, it represents the temperature when x (chirps per minutes) is zero. In this case it represents the temperature when the cricket is not chirping which is impossible, so it doesn't have any physical meaning.

The other root of the polynomial is 1 - √3.

The roots of a polynomial are the values of the independent variable at which the polynomial is zero.

If a polynomial has integral coefficients with 3 + i and 1 + √3  as roots, then what other roots must it have? To find the roots it has, we note that the root of a polynomial with a square root in the root also has the conjugate of the square root as a root.

So, since 1 + √3, the conjugate is also a root.

The conjugate is 1 - √3.

So, the other root is 1 - √3.

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Answer:

The answe should be c=45d+25

So the value of discriminant for √ 2x² − 5x + √ 2 = 0 is b. 17

The discriminant of a quadratic equation is the value of the expression under the square root in the quadratic formula. The quadratic formula is used to find the solutions of the equation of the form ax² + bx + c = 0, where a, b and c are constants. The solutions of the equation are given by x = (-b ± √(b² - 4ac))/ 2a. The value under the square root (b² - 4ac) is called the discriminant.

Given equation is √ 2x² − 5x + √ 2 = 0

The discriminant of the equation is the value of b² - 4ac, which is

b² - 4ac = (-5)² - 4 * (√2) * (√2) = 25 - 8 = 17

So the value of discriminant for √ 2x² − 5x + √ 2 = 0 is b. 17

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The answer you neede is below.

What is Lines square?

Different sorts of lines, including horizontal, vertical, parallel, and perpendicular ones, can be found in geometry. These lines are crucial in the building of many polygonal shapes. For instance, four lines of equal length form a square, whereas three lines joined end to end form a triangle.

Step by step Explaination:

The population size at the end of 2017 is 8775.

The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction.

To add, one must add two or more numbers or values to produce a new number. For instance, if we multiply 2 by 3 we get 5.

2 + 3 = 5

To subtract is to take away from another value in order to obtain the desired value.

For instance, 2 is the result when 3 is subtracted from 5.

5 – 3 = 2

Given that the population at the beginning of the 2017 is 8615.

There were 173 births, 69 deaths, 85 immigrants, and 29 emigrants, thus the new population is:

N = 8615 + 173 - 69 + 85 - 29

N = 8775

Hence, the population size at the end of 2017 is 8775.

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Now, According to the question:

The function of F5 is:

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In order for (x - k) to be a factor of f(x), it must also be a zero of f(x). An integer-coefficient polynomial function's rational zeros are equal to the constant term's factor divided by the leading coefficient's factor.

When exponents, constants, and variables are joined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).

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B) (0, 1), (2, 7), (3, 4), (-4, 1) , (-6, 7)

It's reason can be explain through diagram, just observe & hit the answer.

B) (0, 1), (2, 7), (3, 4), (-4, 1) , (-6, 7)

It's reason can be explain through diagram, just observe & hit the answer.

The answer is B because on the diagram, the left side is all of the x's and the right side is all of the y's

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Answer:

14 cups of flour

Step-by-step explanation:

14 cups of sugar multiplied by 2 is 28 cups of sugar

7 cups of flour multiplied by 2 is 14 cups of flour