Two students wrote the equations shown below.




Erica Aliyah


y = -0.5x y = 2.5x - 8




Which statement is true?

A Graphs of both equations will pass through the origin.

B Only Erica’s equation is proportional.

C Both equations have a negative slope.

D Only Aliyah's is proportional

0.27 is the experimental probability of selecting a green marble.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that Michael has a bag of marbles.

The frequency of selecting each color is recorded  

Outcome Frequency

Green 4

Black 6

Orange 5

The total number of marbles are 4+6+5=15 marbles.

We need to find the experimental probability of selecting a green marble.

We need to select green marbles (4) from total marbles (15).

Probability=4/15=0.266=0.27

Hence, 0.27 is the experimental probability of selecting a green marble.

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Answer:

13/4 as an improper fraction

3 1/4 as a mixed number fraction

Step-by-step explanation:

Turn 3 1/2 into an improper fraction

7/2 - 1/4

To write 7/2 as a fraction with a common denominator, multiply by 2/2

7/2 x 2/2 = 14/4

14/4 - 1/4 = 13/4

Answer:

  7 hours 35 minutes

Step-by-step explanation:

You want to know the length of the time period between 1:29 pm and 9:04 pm.

Remembering that an hour is 60 minutes, we can rewrite the ending time before we subtract the beginning time.

  9:04 -1:29

  = 8:64 -1:29 = (8-1):(64-29) = 7:35

The movie marathon lasted 7 hours 35 minutes.

The scale factor of the two rectangles is 1.5

According to Euclidean Plane Geometry, a rectangle is a quadrilateral with equal opposed sides and four right angles. In other words, a rectangle is a parallelogram with a right angle of 90 degrees or an equiangular quadrilateral (i.e., 360°/4 = 90°). A rectangle is referred to as a square if its four sides are all the same length.

The ratio of the matching side lengths of two comparable figures is known as the scale factor. We know that the ratio of the respective side lengths of the two rectangles equals equivalent to r since Rectangle A and Rectangle B are similar to one another by the scale factor r.

We can set up the following ratio to determine the scale factor if the lengths of rectangles A and B are 1.5r+2.25 units and 3 units, respectively.

(1.5r+2.25) / 3 = r

Solving for r, we get:

r = (1.5r + 2.25) / 3

multiply both sides of the equation by 3

3r = 1.5r + 2.25

Subtract 1.5r from both sides

1.5r = 2.25

divide both sides by 1.5

r = 2.25/1.5

r = 1.5

Therefore, the scale factor of the two rectangles is 1.5.

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Answer:

I have graphed a line with a slope of 3/5 and attached a screenshot in the explanation.

Step-by-step explanation:

A grocer makes a display of cans in which there are 10 rows.

The top row has one can and each lower row has two more cans than the row above it.

We can write it as sequence:

1, 3, 5, 7, . . .

We can observe that it's an arithmetic sequence: 1, 3, 5, 7, . . . , 2n-1

We know that the formula for the sum of n-terms of arithmetic sequence:

S(n) = (n/2)(1 + 2n-1)

Here, Sn = 100

So, (n/2)[1 + 2n-1] = 100

n(1 + 2n + 1)

n(2n) = 200

2n^2 = 200

n^2 = 100

n = 10

Hence, the number of rows = 10

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Answer:

Step-by-step explanation:

Since you already know that one of the angles is 21 degrees, this helps you A LOT. In total the line is 180 degrees so to find x you just do 180-21 which equals 159

x+ 159 degrees

The measure of x = 5, in the given diagram of a trapezoid.

A trapezoid is a four-sided shape with one parallel pair of sides. It is essentially a two-dimensional shape or figure similar to a square, rectangle, or parallelogram. As a result, this shape, like other shapes, has a perimeter and an area.

When two parallel lines are intersected by a transversal, the pair of interior angles on the same side of the transversal are supplementary.

Therefore, ∠D + ∠E = 180°

17x - 10 + 21x = 180°

38x − 10 = 180°

38x = 180° + 10

38x = 190

x = 190/38

x = 5

Thus, The measure of x = 5, in the given diagram of a trapezoid.

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Answer:

approximately 248 miles per hour if we are taking average speed

Step-by-step explanation:

The process of finding the horizontal asymptote and y intercept is explained below.

In order to find the steps, we must know that what is meant by asymptote and intercept.

The process of finding the asymptote is defined as the horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.

If the degree of numerator is less than degree of denominator then horizontal asymptote at y = 0

Where as if the degree of numerator is greater than degree of denominator by one then there is no horizontal asymptote

Finally if the degree of numerator is equal to degree of denominator then the horizontal asymptote at ratio of leading coefficients.

As per the definition of intercept we have identified that the point that will intersect at the y axis is referred as the y intercept.

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The stated statement states that 139 of said animals Margie counted had two legs, mostly two-legged birds.

An arithmetic value used to compute and portray a quantity would be a number. In writing, numerical symbols like "3" are used to represent numbers. A decoder is a logical approach the portray a number using digits or symbols.

Assume that there are x two-legged birds and y four-legged animals. Now, we can employ equation systems to find a solution to this issue.

Enter two equations here:

2x + 4y = 522

x + y = 200

Add two to the latter equation now.

2x + 4y = 522

2x + 2y = 400

We discover that; by deducting the following equations from the first equation.

2y = 122

y = 61

There were 139 two-legged birds due to the 200 heads, which indicated a total of 200 animals.

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The complete question is-

The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?

A). 61

B). 122

C). 139

D). 150

E). 161

The range between 3/16 & 3/8 is where the line plot with the difference of daily mileage logged by each racer in a group is still most obvious.

A line graph, liner plot, or line chart is a graph that uses lines to link the individual data points. For a specific time period, quantitative values are displayed as a line graph. Line graphs are widely used in finance to depict the past market movements of a securities or asset.

Here,

calculation

The number line indicates that there's more than or equal to 3 marks when there are 7 markings either on or to the right of 3. The fraction must first have the same denominators.

=> 3/8 x 2 = 6/16

=> 1/2 x 8 = 8/16, 3/8 x 2 = 6/16

=> 5/8 x 2 = 10/16, 1/2 x 8 = 8/16

Since they all have the same numerator, we can now compare them.

=> 3/16 - 1/16 = 2/16

=> 6/16 - 3/16 = 3/16

=> 8/16 - 6/16 - 2/16

=> 10/16 - 8/16 = 2/16

The largest distinction is between 3/16 and 3/8 (6/16 vs. 3/16).

The range between 3/16 and 3/8 is where the line plot with the difference in daily mileage logged by each runner in a group is most obvious.

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The complete question is " Coach Taylor asked his team to record the distance they ran during practice The line plot shows the number of miles the individual members in a group of runners run each day. How many runners run at least 3 miles per day?."

The two angles measure 90 degrees are called as complementary angles.

What are  complementary angles?

In geometry, complementary angles are defined as two angles whose sum is 90 degrees.

The two angles' complement and supplement are determined by the sum of their measurements. The two angles are said to be complimentary if their combined measurement equals that of a straight angle.

In other words, a right angle results from the combination of two complimentary angles (90 degrees). Angles 1 and 2 are said to be complementary if their sum of angles equals 90 degrees (i.e., 1 + 2 = 90°), and as a result, they are referred to as each other's partners.

two angles that add up to 90 degrees are known as complementary angles. For example, 60° and 30°.

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Answer:

Step-by-step explanation: The answer will be D isolate the variable x by dividing by the factors.

Answer:

Step-by-step explanation:

Let AB = 3 units , BC = 1 unit and AC = ? (TO BE CALCULATED)

By Pythagoras theorem:

(AC)²=(AB)²+(BC)²

therefore, (AC)²= 3²+1²

(AC)²=9+1

(AC)²=10

(AC) = √10 = 3.03 cm

The value of all four numbers will be 91, 98, 105, 112 respectively.

Let the first multiple be 7x

As the multiple of any number can be determined by simply multiplying the given number by the natural number or the counting numbers.

So, the value of the second multiple of 7 will be 7(x+1)

The value of third multiple of 7 will be = 7(x+2)

The value of fourth multiple of 7 will be = 7(x+3)

As all the multiple are consecutive so we have taken the multiplying factor as x, (x+1), (x+2) and (x+3)

From the data given in the question:

Sum = 7x+7x+7+7x+14+7x+21 = 406

=>28x+42=406

=>28x=364

=>x=(364/28)=13

So, the value of first multiple = 7x = (7*13) =91

So, the value of the second multiple of 7 will be 7(13+1)=98

The value of third multiple of 7 will be = 7(x+2)=7(13+2)=105

The value of fourth multiple of 7 will be = 7(x+3)=7(13+3)=112

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Speed of the given object in centimeters per hour

= 0.23 cm / hour

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.

Like 1 yard = 91.44 cm

1 month = 730 hrs.

Given,

Distance covered by the object = 11 yards

Distance covered in cm = 11 × 91.44 = 1005.84 cm

Time taken to cover 11 yards = 6 months

Time taken in hours = 6 × 730 = 4380 hrs.

Speed of the object = distance covered by the object / Time taken

Speed of the object = 1005.84/4380 = 0.2296 ≈ 0.23 cm per hour

Hence,  in centimeters per hour,

the speed of the object is 0.23 cm / hour.

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The area of the semicircle is, 6.28 unit².

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

BC is the diameter of the semicircle.

And, The area of rectangle ABCD is 20 and the length of line AB is 5.

Now, We have;

The area of rectangle ABCD is 20 and the length of line AB is 5.

Let the width of rectangle = x

So, We can formulate;

⇒ 20 = x × 5

⇒ x = 4

Here, the width of rectangle is the diameter of the semicircle.

So, The radius of semicircle = 4 / 2

                                            = 2 units

We know that;

Area of semicircle = π r

Where, 'r' is radius of semicircle.

Hence, We get;

⇒ Area of semicircle = π r

⇒ Area of semicircle = 3.14 × 2

                                 = 6.28 unit²

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \: 4x - 6 = x + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - x = 9 + 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x = 15[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 15 \div 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 5[/tex]

Answer:

Step-by-step explanation:

4x-6=x+9

4x-x=9+6

3x=15

Final answer: x = 5

To Solve the inequalities , we take the variables on a side and the numbers on the other side and then apply mathematical operations to solve it .

What is Inequality ?

The Inequality is defined as a relationship between two values that are not equal to each other .

The method of solving the inequalities is a little different than solving equations.

To solve the inequalities, some simple rules should be followed .

(i) The inequality does not change if any number or variable is added or subtracted from both sides.

Similarly, the value of inequality is not affected if the same number is multiplied on both the sides.

(ii) If the inequality is divided by a negative variable or number on both  sides, then the inequality sign gets reversed.

(iii) On dividing inequality by a positive number, there is no change.

For Example : Solve the inequality [tex]4x+6 > 3x+7[/tex] ;

subtracting [tex]3x[/tex] from both the sides ,

we get ;

[tex]x+6 > 7[/tex],

Now subtracting [tex]6[/tex] from both sides of the inequality;

we get ;

[tex]x > 1[/tex] .

Therefore , the solution of the inequality [tex]4x+6 > 3x+7[/tex] is [tex]x > 1[/tex] .

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Answer:

D

Step-by-step explanation:

I think it would be D hope this helps!

The best definition of a decimal is decimals are whole counting numbers.

Suppose that the number is abcdefg and belongs to the decimal numerical system.

Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.

Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.

Thus, we write abcd.efg as:

[tex]a \times 10^3 + b \times 10^2 + c \times 10^1 + d \times 10^{0} + e \times 10^{-1} + f \times 10^{-2} + g \times 10^{-3}[/tex]

We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.

We call e as digit at 10th place (division by 10), f as digit at hundredth place and so on.

Therefore, the definition will be Decimals are whole counting numbers,

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Definition of a rectangle

Explanation:

A rectangle has two sets of parallel sides, and those opposite sides are the same length. This is simply the definition of what it means to be a rectangle. Because ABCD is a rectangle, we have these two pairs of congruent opposite sides:

Answer:

1.centre

2.chord

3.chord

4.radius

5.diameter

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The domain of a function with two variables is the set of all possible inputs (x-values and y-values) that make the function defined. To find the domain, first identify all of the restrictions on the x-values and y-values, then combine them into a single set of restrictions.

The domain of a function with two variables is the set of all possible inputs (x-values and y-values) that make the function defined. To find the domain, first identify all of the restrictions on the x-values and y-values. These restrictions may come from the function itself, such as any values that would make the function undefined, or from outside sources, such as boundaries placed on the function’s input. Once all of the restrictions are identified, they must be combined into a single set of restrictions. This set of restrictions defines the domain. For example, if the function is defined for all x-values between 1 and 5 and all y-values between -3 and 7, then the domain is all x-values between 1 and 5 and all y-values between -3 and 7. The domain of a function with two variables is an important part of understanding how the function behaves, as it defines the range of inputs for which the function is valid.

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The side length of each square represent for the rectangle to correctly represent (0, 3) · (0, 5) is 1 units.

A rectangle represented by (0, 3) · (0, 5) has length 3 units and breadth 5 units. To represent that rectangles with minimum number of squares of same size, we calculate the highest common factor.

Highest Common Factor is a mathematical concept used to find the greatest number that divides two or more numbers without leaving a remainder. It is also known as the greatest common divisor (GCD) or the greatest common factor (GCF).

Highest common factor of 3 and 5 is 1 as both are prime numbers. So squares with side length 1 unit best represent the rectangle to correctly represent (0, 3) · (0, 5).

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The planes that contain point W from the given image are;

Plane V

Plane VWY

Plane RYV

A coordinate plane is a graphing and description system for points and lines. A vertical y-axis and a horizontal x-axis make up the coordinate plane.

From the attached image, we see that the planes whose name contains V also contains W.

The plane B contains the line XR and the Line YV as well as the W at the line YV.

Finally, the plane m also contains line YV and obviously the same as plane RYU.

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If you know two angles and one side of a triangle, you can use the Law of Cosines to find the length of the other two sides.

The Law of Cosines states that for a triangle with sides a, b, and c, and angles A, B, and C opposite to those sides, the following formula holds:

c² = a² + b² - 2ab cos(C)

Where C is the angle opposite to side c.

So, if you know the measures of two angles (A and B) and the length of one side (c), you can use the Law of Cosines to find the lengths of the other two sides (a and b) by using the following formulas:

a = √(c² + b² - 2bc cos(A))

b = √(c² + a² - 2ac cos(B))

You can use the above equations to find the sides of the triangle, if you have the measures of two angles and one side.

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Just re dot the points like mirror it on where ever on the graph

Use the same x-coordinate and the y-opposite coordinate's to reflect a point on the x-axis. Use the same y-coordinate and the x-opposite coordinate's to reflect a point on the y-axis.

A point can be reflected in the x-axis, y-axis, or both axes.

Due to identical x-coordinates and opposing y-coordinates, the red spots on the x-axis are mirror reflections of one another. Thus, in opposing directions and 3 units away from the x-axis, are the red spots. A reflection in the x-axis is shown by the red spots.

Due to the identical y-coordinates and opposing x-coordinates, the blue spots on the y-axis are mirror reflections of one another. the blue points are thus

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Answer:Yes

?=6



Step-by-step explanation:

they sare the same angle 55 and angle

Answer:

Triangle ABC is similar to triangle CDE

?=8

Step-by-step explanation:

We can set up a proportion: x/12=8/12. We can use cross multiplication to get 12x=96 which would x=8.

The triangles are similar since both of them have 55 degrees as one of the angle measures.

The dy for the given values of x and dx is dy = 0.5632, and their difference to the nearest thousandth is 0.0005.

The difference between dy and Δy can be determined by subtracting dy from Δy and taking the absolute value. In this case, dy approximates Δy to the nearest thousandth with a difference of 0.0005. This is a very small difference, indicating that dy is an accurate approximation for Δy.

The accuracy of dy can be attributed to the fact that the function f(x) = ln(1 + x^2) is a smooth function, meaning that the rate of change at a point (i.e., the derivative) is nearly constant. This allows dy to accurately approximate the change in y, Δy, over a small interval of x. Furthermore, the choice of dx = 0.2 is a small enough value that it does not significantly affect the accuracy of the approximation.

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