€-grade10
mathematics ​

The numbers 2 2 2 2 can be arranged to make the equation true as follows

The numbers arranged by applying the rule which had acronym of PEMDAS

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

applying the sequence the problem is solved as follows

= (2 + 2/2)²

solving the parenthesis first we solve the problem inside the parenthesis. Inside the parenthesis we start with division

= (2 + 2/2)²

= (2 + 1)²

Then addition

= (3)²

having completed the parenthesis, we solve for the exponents

= 9

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For the given system of equations, the answers are of the given choices (A), (B) and (D).

A group of two or more equations with shared variables is referred to as a system of linear equations. Finding the value of the unknown variables employed in the equations that must satisfy both equations is necessary to solve a system of equations.

Given equations are -

y - 10 = 2x ⇒ y = 2x + 10

1/2y = x + 5 ⇒ y = 2x + 10

We can observe from the equation, that both the lines are same,

So any pair of values (x, y) that satisfy the equation y = 2x + 10 is a solution to the system. For example:

(0, 10) is a solution, since y = 2(0) + 10 = 10 and (1/2).10 = 0 + 5 =

(1, 12) is a solution, since y = 2(1) + 10 = 12 and (1/2).12 = 6 = 1 + 5

(2, -6) is a not solution, since y = 2(2) + 10 = 14 and (1/2)(-6) = 7 = 2 + 5

(-5, 0) is a solution, since y = 2(-5) + 10 = 0 and (1/2)(0) = 0

Therefore, the answer is of the given choices are (A), (B), (D).

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Answer:

D.  3√5

Step-by-step explanation:

The distance between points F and C is the hypotenuse of a right triangle.   Therefore we can use Pythagoras Theorem to calculate the distance between these points.

From inspection of the given graph the coordinates of the two points are:

The horizontal difference between the x-coordinates is:

[tex]x_C-x_F=2-(-4)=6\; \sf units[/tex]

The vertical difference between the y-coordinates:

[tex]y_C-y_F=2-(-1)=3\; \sf units[/tex]

Therefore, we have a right triangle with the following dimensions:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

To calculate the length of the hypotenuse, and therefore the distance between points C and F, substitute the values into the Pythagoras Theorem formula and solve for CF:

[tex]\implies a^2+b^2=c^2[/tex]

[tex]\implies 3^2+6^2=CF^2[/tex]

[tex]\implies 9+36=CF^2[/tex]

[tex]\implies CF^2=45[/tex]

[tex]\implies \sqrt{CF^2}=\sqrt{45}[/tex]

[tex]\implies CF=\sqrt{9 \cdot 5}[/tex]

[tex]\implies CF=\sqrt{9} \sqrt{5}[/tex]

[tex]\implies CF=3\sqrt{5}[/tex]

Therefore, the distance between points F and C is 3√5.

To draw a centroid for ΔABC, follow the steps below.

The intersection point of line segments CD and XY is the centroid of the ΔABC. Label this point as G.

See the sample attached. Note that this is not constructed to scale.

The centroid is the point where the three medians of a triangle intersect.

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. In this case, line segment CD is one of the medians of triangle ABC because it connects the midpoint of AB (which is also the midpoint of CD) to vertex C. The other two medians connect the midpoints of the other two sides to their opposite vertices.

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The slope on the line containing the points (14,-42) is 1.06, as stated in the preceding sentence (-48,24).

The % slope is calculated by multiplying the distance between two locations by the differences in elevation above them. The difference in height between two places is referred to as "rise." The distance between it sites is known as the run. Therefore, the formula for percent slope is (rise / run) x 100.

The slope's formula is as follows:

m = (y₂-y₁)/x₂-x₁)

In the formula, replace the point values as follows:

m = (24-(-42))/(-48-14)

Make the fraction simpler:

m = (24-(-42))/(-48-14)

m = 66/-62

m = 1.06

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The surface area of the net is 108 squate feet

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

A net that has the following shapes

The area of the net is the sum of the individual areas

So, we have

Area = 8 * 12 + 2 * 0.5 * 3 * 4

Evaluate

Area = 108

Hence, teh area is 108 squate feet

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The surface area of the sphere is 113.2 ft².

The area that a sphere's outer surface covers in three dimensions is known as the surface area of the Sphere. A sphere is a three-dimensional solid that resembles a circle in shape and is round.

The formula for a sphere's total surface area is given by

Here we have

The formula for the radius of a sphere r = 1/2 [√S/π]    

Diameter of the Moeraki boulder radius = 3 feet

=> 3 feet =  1/2 [√S/π]    

=> 6 = [√S/π]

Squaring on both sides

=> 36 = [√S/π]²  

=> S/π = 36

=> S = 36π  

=> S = 113.2  

Therefore,

The surface area of the sphere is 113.2 ft².

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The amount of extra meals that Taryn needs to feed her dog today is given by the inequality expression; x > 2

The parameters given in the question are;

Weight of dog = 40 pounds

Average amount of calories required per day = 1215 calories

Amount of calories already eaten = 729 calories

Amount of calories fed per meal = 243 calories

The inequality that represents the given word problem is;

243x + 729 > 1215

Subtract 729 from both sides to get;

243x > 486

divide both sides by 243 to get;

x > 2

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Answer:

Step-by-step explanation:

If the product of two rational numbers is 4/25, we can write the equation:

(x) * (-6/5) = 4/25

where x is the other number.

Expanding the equation:

x * -6/5 = 4/25

Multiplying both sides by 5 to get rid of the fraction on the right-hand side:

5 * x * -6/5 = 5 * 4/25

x * -6 = 4

Dividing both sides by -6:

x = -4/-6

x = 4/6

So, the other number is 4/6.

Answer:

So the other number is -[tex]\frac{4}{3}[/tex].

Step-by-step explanation:

Let x be the number.

We know,

(-[tex]\frac{6}{5}[/tex]) × x = [tex]\frac{4}{25}[/tex]

-[tex]\frac{6}{5}[/tex] × x =  [tex]\frac{4}{25}[/tex]          (By expanding the left side of the equation)

Dividing both sides by -[tex]\frac{6}{5}[/tex]

x = - [tex]\frac{4}{25}[/tex]  × -[tex]\frac{6}{5}[/tex]

After simplifying the equation ,

x = -[tex]\frac{4}{3}[/tex]

So the number is -[tex]\frac{4}{3}[/tex].

Kathy should take 4 trips if the price of a round-trip ticket is 230.

Point A on the graph would be placed at (230, 4). This demonstrates that Kathy should take 4 trips if the price of a round-trip ticket is 230. This can be calculated as follows:

Kathy has a budget of 1,000. Therefore, she can afford 4 round-trip tickets at the price of 230 each. This can be calculated by dividing 1000 by 230, which gives 4. Therefore, Kathy should take 4 trips if the price of a round-trip ticket is 230.

It is important to note that Kathy should also consider other factors such as the cost of other expenses, such as accommodation and food, when deciding how many trips to take. Additionally, Kathy may also want to consider whether the benefits of taking more trips are worth the additional cost.

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The required, there is no highest common factor between 4454 and 121j²k. None of the options are correct.

The highest common factor (HCF) of two or more numbers is the largest number that divides all of the numbers exactly.

Here,
To find the greatest common factor (GCF) of 4454 and 121j²k, we need to factor both numbers into their prime factors and then identify the common factors.

Since 4454 is an even number and 121 is an odd number so there is no prime highest common factor between the given number.

Thus, none of the options are correct.

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(a) The angle measurement of first unknown angle is c = 80 degrees

(b) The angle measurement of second unknown angle is y = 110 degrees

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees

The angle measurement of first unknown angle will be:

a + b + c = 180  (sum of angles in a triangle is 180 degrees)

c = 180 - a - b

c = 180 - 30 - 70

c = 80 degrees

(b) The angle measurement of second unknown angle will be:

y = 180 - b  (sum of angles on a straight line is 180 degrees)

y = 180 - 70

y = 110 degrees

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The student must she score on the fourth test in order to raise her test average 4 points is 4 points.

An average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.

Given that, a student has completed 3 tests in biology class, we need to find that how many points above her present test average must she score on the fourth test in order to raise her test average 4 points,

Let the required point be x,

According to question,

x+4×3 / (3+1) = 4

x+12 = 16

x = 4

Hence, the student must she score on the fourth test in order to raise her test average 4 points is 4 points.

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There are 11/3 pounds of cherries at Johnson's Farm in order to pay the same amount as picking 6 pounds of cherries at Mood's Farm.

In general, the unitary method is a useful tool for solving problems like this where we need to compare the cost of two different scenarios. We can set up equations based on the rates or costs involved, and then use algebra to solve for the unknown variables.

To begin, let's use a unitary method to find the total cost of picking cherries at Johnson's Farm. We know the entry fee is $26, so we can start with that. Then, for each pound of cherries picked, the cost is $6. So, if we let x be the number of pounds of cherries picked, the total cost at Johnson's Farm would be:

Total Cost = $26 + $6x

Now, let's use a unitary method to find the total cost of picking cherries at Mood's Farm. We know that there is no entry fee, so we can start with just the per-pound cost of $8. If we let y be the number of pounds of cherries picked, the total cost at Mood's Farm would be:

Total Cost = $8y

To find how many pounds of cherries you would need to pick at each farm in order to pay the same amount, we need to set these two total costs equal to each other and solve for x:

$26 + $6x = $8y

$6x = $8y - $26

x = (8/6)y - 13/3

x = (4/3)y - 13/3

So, if you picked 6 pounds of cherries at Mood's Farm (y = 6), the equivalent cost at Johnson's Farm would be:

x = (4/3)(6) - 13/3

x = 8 - 13/3

x = 11/3

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Answer:

61.25

Step-by-step explanation:

brainlest pls and I hope this helped u :)

The Selling price of a book with a retail of R 100 and R 88 will be 99.625 and 87.625 respectively.

The selling price of a good or service is the final cost to the seller, or what the buyer actually pays. A commodity or service in a specific amount, weight, or measurement can be exchanged.

It is one of the most crucial things for a business to decide. It is significant since it determines whether or not it will survive. Sales of a product are directly impacted by its price.

According to the question,

Discount = 3/8 of the retail price.

Now,

When retail price is 100,

Selling price [tex]= 100-3/8[/tex]

[tex]=99.625[/tex]

When retail price is 88.

Selling price [tex]= 88-3/8[/tex]

[tex]=87.625[/tex]

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Answer: 1067/10000 is a fraction in simplest form. where, 0.1067 is a decimal, 10.67% is a percentage.

Step-by-step explanation:

The value of m <2 is C. 120°

In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.

In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.

Therefore,

m<2 = m<6

This is because they are corresponding angles

With this in mind, m<6 = 120°

Therefore, m<2 = 120°

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The statement that " t-value changes depending on the number of data points collected" is (b) False because t-value is a statistic that is used in hypothesis testing to determine the difference between 2 sample means is significant or not.

The t-value does depend on the sample size (number of data points) as well as the sample mean and standard deviation, but it does not change "depending on" the number of data points in the sense that the same data set will always produce the same t-value for a given statistical test.  

So , it is important to note that the t-value is a fixed value for a given set of data, regardless of the number of data points collected.

Therefore, if the same data set is used to perform a t-test multiple times, the resulting t-value will always be the same.

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The two major properties of similar shapes include the following:

In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied because it would either enlarge (increase) or reduce (decrease) them.

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The equation in standard form representing the scenario where Briana has $3 in her piggy bank and has all quarters and dimes, using x for the number of quarters and y for the number of dimes, is [tex]25x + 10y = 300[/tex].

Let x be the number of quarters and y be the number of dimes Briana has in her piggy bank.

The value of each quarter is 25 cents or 0.25 dollars, and the value of each dime is 10 cents or 0.10 dollars. Therefore, the total value of the coins in Briana's piggy bank can be expressed as:

[tex]0.25x + 0.10y[/tex]

Since Briana has $3 in her piggy bank, we can set up the following equation:

[tex]0.25x + 0.10y = 3.00[/tex]

To write this equation in standard form ([tex]Ax + By = C[/tex]), we need to clear the decimals by multiplying both sides of the equation by 100:

[tex]25x + 10y = 300[/tex]

Therefore, the equation in standard form that represents this scenario is:

[tex]25x + 10y = 300[/tex]

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Answer: Musical preferences

A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely your musical preferences affect mortality or how much sweetener you consume.

The number of soft drink brands available for purchase is not a lurking variable in this scenario. Correct option is C.

The statement is asking which of the given variables is not a lurking variable in the scenario where Shawna is considering the correlation between the calories of sweeteners consumed and the mortality rates among women, and is trying to determine whether drinking more soft drinks will lead to a higher chance of her dying.

A lurking variable is a variable that is not included in the analysis, but has an effect on the relationship between the variables being studied. In this case, the variables being studied are the calories of sweeteners consumed and the mortality rates among women, and the effect of drinking more soft drinks on the chances of dying.

Out of the given variables, the number of soft drink brands available for purchase would not be a lurking variable, as it does not have an effect on the relationship being studied.

Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could all potentially have an effect on the relationship being studied, either as confounding variables or moderators.

For example, Shawna's weight could be a confounding variable, as it is associated with both sweetener consumption and mortality rates. The time of day she exercises could be a moderator, as exercise may affect the metabolism of sweeteners and caffeine, which could in turn affect mortality rates.

The amount of caffeine available in soft drinks could be a confounding variable, as caffeine consumption is associated with both sweetener consumption and mortality rates.

In summary, the number of soft drink brands available for purchase is not a lurking variable in this scenario, while Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could potentially be confounding variables or moderators that need to be accounted for in the analysis.

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It took Bunolo 100 minutes (or 1 hour and 40 minutes) to complete the 10 km race at an average speed of 6 km/h.

To find out how long it took Bunolo to complete a 10 km race with an average speed of 6 km/h, we can use the formula:

time = distance / speed

where "distance" is the distance of the race and "speed" is the average speed at which Bunolo ran. We can convert the speed to km/minute to get the time in minutes.

To do this, we can divide the speed in km/hour by 60 (the number of minutes in an hour) to get the speed in km/minute:

6 km/hour ÷ 60 minutes/hour = 0.1 km/minute

Now, we can substitute the distance and speed values into the formula to get the time in minutes:

time = 10 km / 0.1 km/minute = 100 minutes

Therefore, To complete the 10 km race with the average speed of 6 km/h, it took Bunolo 100 minutes.

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Points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.

What are points, lines, and planes?

Point: A point is a basic geometric object that represents a specific location in space.

Line: A line is a straight path that extends infinitely in both directions. It is made up of an infinite number of points that are all collinear, or lie on the same straight path.

Plane: A plane is a two-dimensional flat surface that extends infinitely in all directions.

Navigation: Points and lines are essential for navigation, both on land and in the air. For example, on a map, points represent specific locations, while lines represent roads, highways, and other paths that can be taken to get from one point to another.

Architecture and Design: Points, lines, and planes are critical for architecture and design. Architects use points to specify the locations of walls, columns, and other structural elements, while lines are used to create the edges of rooms and buildings. Planes are used to define the surfaces of walls, floors, and ceilings.

Art: Artists often use points, lines, and planes to create visual effects in their work. Points can be used to create texture, while lines can be used to create movement and depth. Planes can be used to create shapes and form.

Engineering: Points, lines, and planes are fundamental to engineering, which involves the design and construction of structures and machines. Engineers use points to specify the locations of components, while lines are used to create the edges of parts. Planes are used to define the surfaces of structures, such as the wings of an airplane.

Hence, points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.

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Answer:

A

Step-by-step explanation:

The line has a negative slope, with a y-intercept of (0,-3), and an x-intercept of (-2,0)

Answer: 55+p

Step-by-step explanation: Since p is in unlike terms as 55, you can just write that as is an the expression to represent the dog's weight.

Answer:

hundredths

Step-by-step explanation:

The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The number which is divisible by 15, 20, or 30 will be given as,

LCM of the numbers 15, 20, and 30 will be given as,

2  |    15,       20,       30

2  |    15,        10,       15

3  |    15,         5,       15

5  |     5,          1,        5

          1,          1,         1

LCM = 2 x 2 x 3 x 5

LCM = 60

The number whose remainder is always 8 is given as,

⇒ 60 + 8

⇒ 68

The number when divided by 15, 20, and 30 and the remainder is always 8 will be 68.

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Answer:

25 minutes

Step-by-step explanation:

The time difference between 1:25 and 1:50 is 25 min