The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.

piecewise function defines the function graphed between y=2x+3 and y=-1/3x+3.

How to compare linear equations?

The comparison method, a procedure for solving systems of independent equations, starts by rewriting each equation with the same variable as the subject. Any of the variables may be chosen as the first variable to isolate. Each equation is now an isolated-subject equation, and equation where one variable is isolated.

Given:

y = 2x+3

y = -1/3x+3

The left portion of the blue curve is y = 2x+3 but it is only graphed when x < 0 (we could argue that  but I'll set that aside for the other portion).

The right portion is the line y = -1/3x + 3 and it's only graphed when

Both lines have y-intercept 3.

The slopes are 2 and -1/3.

The equations are

y = 2x + 3; y = -1/3 x + 3e could have this piecewise function

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Answer:

C. No real factors

Step-by-step explanation:

Not factorable

Answer:

The answer is 112ft

Step-by-step explanation:

32+16+8+8+16+8+8+16 = 112ft

Answer:

112ft

Step-by-step explanation:

The length of the little rectangle jutting out is the only unmarked length, so once we find that we can just add up all the sides to find the perimeter.

We see the overall length of the shape is 24ft and the length of the top of the shape, minus the unmarked length, is 16ft. This means the unmarked length is 24ft-16ft=8ft

Now add up each side to get to the perimeter:

32ft + 16ft + 16ft + 8ft +8ft +8ft +8ft +16ft = 112ft

Answer:The answer is 2.5 pints.

Answer:B costs less than A

Step-by-step explanation:

i am not quite sure but i think,

A)8----2,89

  1------x

x=0.38

B)12----4,19

1---------y

y=0.35

Answer:

(-9)×(-7/3)=9×7/3=3×7=21

Answer:

21

Step-by-step explanation:

-9 is equal to -9/1

the negative sign on the -7/3 can be put on the top or bottom

-9 -7 63

--- x --- = ---

1 3 3

63 divided by 3 equals 21 and is therefore in the simplest form

Answer:

Step-by-step explanation:

To solve this system of two equations with two variables (x and y), we'll use the substitution method. Here's how:

Solve one of the equations for either x or y, in terms of the other variable. Let's solve the first equation, 2x - 5y = 4, for x:

x = (4 + 5y)/2

Substitute the expression for x from step 1 into the second equation, 4x = 8 + 10y:

4(4 + 5y)/2 = 8 + 10y

Simplify the equation from step 2:

8 + 10y = 8 + 10y

Solve for y by subtracting 8 from both sides:

10y = 10y

Divide both sides by 10 to find the value of y:

y = y

Now that we have the value of y, we can substitute it back into the expression for x from step 1:

x = (4 + 5 *y)/2

So the solution to the system of equations is (x, y) = ((4 + 5 *y)/2, y=y).

Answer:

(3) 3

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which each of them can be defined by adding a common difference to a term to find the next term.

So for example, let the first term, or number be expressed as: [tex]a_1[/tex] and the common difference be expressed as: [tex]d[/tex] That means the second term, or number can be defined as: [tex]a_2=a_1+d[/tex]. If we now add the common difference to the second term, we would get the third term, and so on.

An arithmetic sequence can be compared to that of a linear equation, except it's a sequence of numbers... and also it's restricted to integers greater than zero (starts at first term, second term.... and so on)

So the common difference can be compared to the slope, and we can actually just use the slope formula! The "x" value being the term number, and the "y" value being the term. So the first term in the sequence is 5 can be expressed as: (1, 5) and the fifth term is 17 can be expressed as (5, 17). Now using the slope formula we would get: [tex]d=\frac{17-5}{5-1}=\frac{12}{4}=3[/tex]

Another way to think of it is the first term is 5, and if we add "d" or the common difference to it, we get the second term, if we add another "d" we get the third term, if we another "d" we get the fourth term and if add yet another "d" we get the fifth term. We add a total of four "d's" which can be expressed as: [tex]5+4d[/tex] and this equals the fifth term, but we also know this to be equal to 17, so we can set them equal to each other: [tex]5+4d=17[/tex] now just subtract 5 and divide by 4 to get: [tex]d=3[/tex]

Answer:

-$48.39

Step-by-step explanation:

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

A graph of the solution to this inequality 2.45 < x ≥ 4.6 is shown in the image attached below.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would translate the word problem into an algebraic equation as follows;

2.45 < x ≥ 4.6

By splitting, we have the following compound inequality:

x > 2.45

x ≥ 4.6

In this scenario, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the graph contains a dashed line because of the greater than (>) symbol.

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By using the substitution method, the value of x is equal to -1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

2y - 4x = 8                 .......equation 1.

3(x + 4) - 2y = 5          .......equation 2.

From equation 1, we have:

y = 2x + 4         .......equation 3.

By using the substitution method to substitute equation 3 into equation 2, we have the following:

3(x + 4) - 2(2x + 4) = 5

3x + 12 - 4x - 8 = 5

-x + 4 = 5

x = 4 - 5

x = -1.

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The slope of the line on the graph will be a negative one. Then the correct option is A.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

From the graph, the two points are (-2, 2) and (2, -2). Then the slope is given as,

m = (- 2 - 2) / (2 + 2)

m = - 4 / 4

m = - 1

The slope of the line on the graph will be a negative one. Then the correct option is A.

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The complete question is attached below.

Answer:

Base: 8. Height: 3.

Step-by-step explanation:

Let the height be x. Then the base would be 2x+2. The formula for the area of a triangle is 1/2*base*height. We know the area, and we know the base and height in terms of x. Now you just solve for x. 1/2*x*(2x+2) = 12. x(2x+2) = 24. You could plug in factors of 24, but I used the quadratic formula to solve this equation. 2x^2 +2x -24 = 0. Plugging in these values into the quadratic formula, we get that x = 3. This means that the height is 3. Since the base is 2x+2 and x is 3, then the base is 8.

The correlation coefficient of the data-set in this problem is given as follows:

C. r² = 0.931.

The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.

The points from the table in this problem are given as follows:

(3,2), (4,4), (5,5), (7,6), (10,20).

Inserting these points into a calculator, the correlation coefficient is obtained as follows:

r² = 0.931.

Meaning that the correct option is given by option C.

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The measure of the first angle is 128. 5 degrees

From the information given, we have that;

Let the second angle be x

We have the representation as;

3x - 26 + x = 180

collect the like terms, we get;

3x + x = 180 + 26

Add or subtract the like terms

4x = 206

Make 'x' the subject of formula by dividing by the coefficient of x, we get;

x = 206/4

divide the values

x = 51.5 degrees

Then, the angle is 128 .5 degrees

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place g(x) as the value x, into p(x)

to gain p(g(x)) = (1 / SqrRt(x) )² - 4

simplify = ( 1 / x ) - 4

find domain

x =/= 0 (undefined) & (1/4)

The combined volume of a 4-foot cube and a 6-foot cube is not equal to the volume of a 10-foot cube.

The volume of a cube is calculated by cubing the length of its side.

here,

Let's denote the length of the sides of the 4-foot and 6-foot cubes as "a" and "b", respectively. Then the length of the side of the 10-foot cube is "c", and we know that:

a³ + b³ = c³

We want to confirm if the combined volume of a 4-foot cube and a 6-foot cube is equal to the volume of a 10-foot cube. We can calculate the volumes of the cubes as follows:

Volume of 4-foot cube: a³ = 4³ = 64 cubic feet

Volume of 6-foot cube: b³ = 6³ = 216 cubic feet

Volume of 10-foot cube: c³ = 10³ = 1000 cubic feet

The sum of the volumes of the 4-foot and 6-foot cubes is:

64 + 216 = 280

Therefore, the combined volume of a 4-foot cube and a 6-foot cube is not equal to the volume of a 10-foot cube.

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The new tuition 4 years from now is $6962.68.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Given that, principal =$6691, rate of interest=1% and time period=4 years.

Now, A=6691(1+1/100)⁴

=6691(1+0.01)⁴

=6691(1.01)⁴

= 6691×1.04060401

= $6962.68

Therefore, the new tuition 4 years from now is $6962.68.

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Answer:

Step-by-step explanation:

You want an inequality and its solution for finding the cost of goggles that put Winston over his $150 budget when combined with the purchase of a $90.50 helmet.

If x represents the cost of the goggles, then Winston's total spending is ...

  90.50 + x

If that is over is $150 budget, the relation is described by ...

  90.50 +x > 150

Subtracting 90.50 from both sides gives ...

  x > 59.50

This tells us the goggles cost more than $59.50.

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The battery level after two hours of constant use unplugged is found replacing the instance of x on the line of best fit by 2.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The variables for this problem are given as follows:

Hence after a time of two hours the battery level is found as the numeric value at x = 2.

The problem is incomplete, hence the general procedure to solve the problem is presented.

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The width of the rectangle is [tex]4x^8y^6[/tex]inches.

Option A is correct.

What is the area of the rectangle?

A rectangle is a four-sided polygon with two pairs of parallel sides, and all four angles are right angles (90 degrees). The area of a rectangle is the amount of two-dimensional space that it occupies and is given by the product of its length and width. In other words, the area A of a rectangle with length l and width w is given by the formula:

A = l x w

To find the width of the rectangle, we can use the formula for the area of a rectangle, which is:

Area = length x width

In this case, we are given the area and the length of the rectangle, so we can rearrange the formula to solve for the width:

width = Area / length

Substituting the given values, we have:

width = [tex]\frac{(32x^{12}y^{9})}{(8x^4y^3)}[/tex]

Simplifying the expression, we get:

width = [tex]4x^{8}y^{6}[/tex]

Therefore, the width of the rectangle is[tex]4x^8y^6[/tex]inches.

Option A is correct.

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The equations that explains the process to find the number of square yards of fabric she will use and the number of square yards of fabric she will have left, using the addition of fractions are;

(3/8) + (2/8) = 5/8 square yards of fabric will be used

1 - 5/8 = 3/8 square yard of fabric will be left

A fraction is a representation of a part of a whole, consisting of a number in the numerator divided by another number in the denominator expressed as a quotient.

The amount of fabric Diana has = 1 square yard

Amount of fabric to make one pillow = 3/8 square yard

Amount of fabric required to make the other pillow = 2/8 square yard

Therefore, the amount of fabric Diana will use can be found by adding the fractions of the areas of the fabric she uses for each pillow as follows;

The number of square yard of fabric Diana will have left can be found from the difference between the initial number of square yards of fabric Diana has and the amount of square yards of fabric she will use.

Initial number of square yards of fabric = 1

Number of square yards of fabric she will use = 5/8

Therefore;

Number of square yard of fabric Diana has left = (Initial number of square yards of fabric) - (Number of square yards of fabric she will use)

Number of square yard of fabric Diana has left = 1 - 5/8 = (8 - 5)/8 = 3/8

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The x-intercepts are (-2, 0), (-1, 0), (1, 0), and (2, 0).

What is meant by the x-intercept?

The value of the x coordinate at the point where the graph intersects the x-axis, or alternatively, the value of the x coordinate at the point where the value of the y coordinate equals zero, is the x-intercept for any curve.

The x-intercepts are the points where the graph meets the x-axis.

Which means that the coordinate of y will be zero.

It is given in the question that the graphed function will meet the x-axis at 4 points which are (-2, 0), (-1, 0), (1, 0), and (2, 0)

Therefore the x-intercepts of the function will be: (-2, 0), (-1, 0), (1, 0), and (2, 0).

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Answer: B)  (-1,0)

Step-by-step explanation:

Just took the test on edge

Answer:

2.9375

Step-by-step explanation:

7 5/6 / 2 2/3 = 47/16 = 2 15/16 = 2.9375

The solutions of the quadratic equation are;

1) x = 1 or -1/2

2) x = 11 or -1

We know that the quadratic formula is one of the ways that we can use to solve for the variables that we have in a quadratic equation. We can be able to obtain x by using the formula;

x = -b ±√b^2 - 4ac/2a

To use the discriminant;

√b^2 - 4ac

√(-5)^2 - (4 * 4 * 10)

√-135

The roots are imaginary

√18^2 - 4(1 * 81)

= 0

The roots are equal

√(-4)^2 - (4 * 4 * -24)

=20

The equation roots are real and different

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Answer: 54.54 mph

Step-by-step explanation: To calculate the average speed of a car that traveled 300 miles in 5.5 hours, you can divide the total distance traveled by the total time taken: Average speed = Total distance / Total time-average speed = 300 miles / 5.5 hours = 54.55 miles per hour (mph)So, the average speed of the car is 54.55 mph.

An equation in point-slope form for this line is y=6x+5.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Given that;

Point on a line (-1,-1)

Slope of the line 6

Now, substituting the values in the general formula of line

y+1=6(x+1)

y+1=6x+6

y=6x+5

Therefore, the equation with the given slope will be y=6x+5.

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The best way to figure out if there is a solution to the equation:

 --> solve this whole thing algebraically

Let's solve:

 [tex]-4x+7x=4(x+2)-(x+8)\\3x=4x+8-x-8\\3x=3x[/tex]

If we get this kind of circumstance:

 --> where the left/right part of the equation are equal and cannot be

      solved further

     ---> the solution is all real numbers

Answer: solution is all real numbers