a+b-2c=5 2a+2b-4c=1 2a-b+2c=3

By using the fact that the triangles are similar, we can write and solve an equation to find that t = 11.

Here we know that K is the midpoint of GJ and I is the midpoint of HJ, this means that triangle JKI is similar to JHG, but dilated by a factor 1/2.

That means that we can write:

(1/2)HG = IK

We know that:

GH = t + 47

IK = -5t + 84

Replacing these in the equation above, we will get:

(1/2)*(t + 47) = -5t + 84

t + 47 = 2*(-5t + 84)

t + 47 = -10*t + 168

t + 10t = 168 - 47

11t = 121

t = 121/11 = 11

The value of t is 11.

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Nata was using the partial products method to solve the multiplication problem 42 × 15. She likely wrote 20 because she was finding the product of 42 and 10, which is 420. Writing 20 was likely a shorthand for the digit 2 in 420.

In the partial product method, each digit of one number is multiplied by each digit of another number, keeping each digit in its original place. Place value is typically used to calculate the partial product. To get the product of two-digit numbers, we employ the partial product method.

The partial products method involves breaking down one factor into its place value components and multiplying each component separately, then adding the products together to get the final answer.

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Answer:

82+54=136°

Step-by-step explanation:

the value of the extreior angle in a tringle equals to the sum of the further two angles in the tringle

Graph y=-7 by plotting y-intercept (0,-7) and all points have y=-7, it is a horizontal line.

What is graph ?

A graph is a mathematical structure used to represent relationships between objects. In a graph, objects are represented by vertices (or nodes) and relationships are represented by edges (or arcs). Graphs can be used to model a wide variety of real-world systems, including networks of roads, social networks, and the internet.

To graph y = -7, you can start by plotting the y-intercept, which is the point at which the line crosses the y-axis. In this case, the y-intercept is (0, -7) because when x = 0, y = -7.

To graph the line, you can then pick any other x-value, substitute it into the equation, and find the corresponding y-value. For example, if you pick x = 1, then y = -7. So, you can plot the point (1,-7) on the graph.

You can repeat this process with different x-values and plot more points on the graph.

Graph y=-7 by plotting y-intercept (0,-7) and all points have y=-7, it is a horizontal line.

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Answer:

112 chocolate bars

Step-by-step explanation:

Given that the chocolatier made 16 batches of salted caramel chocolate bars, each batch consisted of 42 bars and he sent an equal number of bars to each of its 6 stores,

What is asked: To determine how many bars did each store receive.

Method of solving: Using elementary operations as multiplication and division.

Start considering each batch as the following box:

So it suggests that to find the total number of chocolates produced is equal to the product

Before multiplying, now see that the chocolatier is equally dividing them to its 6 stores, which means that he will take this quantity and divide equally into 6 boxes.

Therefore, this process is the same as dividing by 6, therefore

Is the expression that gives the result desired.

Simplifying the fraction and multiplying the terms gives

This is the amount of chocolate bars each store received.

Answer: 11 1/4

Step-by-step explanation:

4 1/2 * 2 1/2

= 9/2 * 5/2

= 45 / 4

= 11 1/4

the equation that can be used to determine the value of the artwork in "x" year is A = 1500(1 + 0.0128)^x.

An equation that can be used to determine the value of the artwork in "x" years is a compound interest equation. This type of equation is used to calculate the value of an investment over time, taking into account the initial investment amount and the interest rate.

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It can be contrasted with simple interest, which is calculated only on the principal amount.

Compound interest is considered to be more beneficial for savers and investors, as it allows for interest to be earned on previously earned interest, leading to faster growth of the principal.

In this case, the artwork appreciates by 1.28% in value every year and was purchased for $1500. The formula for compound interest is:

A = P(1 + r)^n

Where:

A = the future value of the artwork

P = the initial investment (the purchase price of $1500)

r = the interest rate (1.28% per year)

n = the number of years

To use this equation, we need to convert the interest rate from a percentage to a decimal. We do this by dividing the interest rate by 100. So, 1.28% as a decimal is 0.0128.

Now we can substitute the values into the equation:

A = 1500(1 + 0.0128)^x

Therefore, the equation that can be used to determine the value of the artwork in "x" year is A = 1500(1 + 0.0128)^x.

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Answer: (A) 16

must be less than 19

and more than 5

Step-by-step explanation:

The value of the length of side UX for the right triangle formed by sides tangent to the circle is equal to 3.4 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

The side XV is perpendicular to the side UV tangent to the circle, which makes the triangle a right triangle.

so by evaluation we derive the value for the hypotenuse UX as follows;

UX = √(3² + 1.6²)

UX = √(9 + 2.56)

UX = √11.56

UX = 3.4

Therefore, the length of side UX for the right triangle is equal to 3.4 using the Pythagoras rule.

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An average mean of 1.72 children can be found on every house

One method for making data more comprehensible is to put it in a frequency distribution table. Consider having a list of IQ results for a talented class at a certain elementary school. The frequency of a value in a set of data is how frequently it appears.

Victor, for instance, made nine attempts to obtain a red gumball. The quantity of gumballs in each hue that were produced would be the frequency in this situation. The distribution of observations based on a variable's possible values is displayed in a frequency table.

frequency = 10 + 4 + 2 + 3 + 4 + 2

= 25

Sum of children

= (10 × 0)+(4 ×1)+(2 × 2)+(3 × 3)+(4 × 4)+(2 × 5)

= 43

Mean =  43/25

= 1.72

Thus, An average mean of 1.72 children can be found on every house.

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The perimeter, in units, of the parallelogram exists 48.

Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the other number line, which is vertical. At a place known as the origin, the two axes collide. The coordinate plane allows us to graph points, lines, and more.

A coordinate plane is a framework for describing and graphing points and lines. The coordinate plane is composed of two axes, one vertical (y) and one horizontal (x). The coordinate plane has four quadrants. The origin is the location where these lines converge (0, 0).

Therefore, the correct answer is option C) 48.

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Answer: The friends who shared 2 chocolate chip cookies.

Step-by-step explanation: 3/2= 1.5  and 4/3= 1.3

1.5>1.3

Answer:

3. (-4/5, -3) 6. (4, 12/-5)

Step-by-step explanation:

3. so first we have

-5x - 10y = 20

-5x - 8y = 14

so first we have to have the x's be opposite so we multiply the top one by -1 which gets us

5x + 10y = -20

-5x - 8y = 14

then we cancel out the x's and subtract 10 by 8 and -20 by 14 so it's now

2y = -6

then we divide by 2 on both sides so it's

y = -3

but now we have to solve for x so we substitute y in on the bottom equation so now it is

-5x - 8(-3) = 20

now we multiply

-5x + 24 = 20

subtract 24 from both sides

-5x = -4

divide by -5

x = -4/5

then put it in coordinates

(-4/5, -3)

6. so we have

x = 4

-4x - 5y = 4

so first we have to substitute the top in for the bottom so now we have

-4(4) - 5y = 4

distribute

-8 - 5y = 4

add 8 to both sides

-5y = 12

divide

y = 12/-5

coordinates

(4, 12/-5)

For given equation of circle radius is 6 unit and center is at (-2,1).

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

Now,

As shown in graph the graph by taking two points on graph

(-2,7) and (-2,-5)

Center will be at (-2-2)/2, (7-5)/2

i.e. (-2,1)

And for radius take magnitude of points from y-coordinate

(7+5)/2=6 unit

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The range of integer value in C is: -2,147,483,647 to 2,147,483,647

We know that the range  of data types means the maximum and minimum value that can be stored inside the variable of a given type.

In C programming, the primitive data types are:

char – this data type hold a single character

float –  this data type hold single-precision types of floating-point.

int –  this data type hold integers

double  - this data type hold double-precision types of floating-point

The int i.e., integer data type holds whole numbers that range from -2,147,483,647 to 2,147,483,647.

The number 2,147,483,648 cannot be used.

The integer value is stored as a signed binary integer.

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The cannonball will be at a height of 640 feet for the first time after 6.5 seconds.

Acceleration, is a rate at which velocity changes with time, in terms of both speed and direction.

The time it will take for the cannonball to reach a height of 640 feet for the first time can be found using the equation:

t = (vf - vi) / a

where:

t = time (in seconds)

vf = final velocity (in feet per second) = 0 (at the top)

vi = initial velocity (in feet per second) = 208

a = acceleration (in feet per second squared) = -32 (upwards)

Plugging in the values:

t = (0 - 208) / (-32) = 6.5 seconds.

So, the cannonball will be at a height of 640 feet for the first time after 6.5 seconds.

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The probability that the counter removed is red is given as follows:

18/55.

A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.

The probabilities of a red counter being removed from Bag B is obtained considering these following scenarios:

Hence the probability that the counter removed is red is calculated as follows:

p = 4/11 x 6/10 + 3/11 x 4/10 = 36/110 = 18/55.

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Answer:

9/6=12/x-4

Step-by-step explanation:

The missing value for x is 7.

The inverse variation relationship between two variables x and y is described by the equation y = k/x,

where k is a constant.

We can use this equation to find the missing value, using the information given.

First, we'll use the first set of points to find the constant k:

y = k/x

16 = k/3.5

16 * 3.5 = k

56 = k

Next, we'll use the constant k and the second set of points to find the missing x value:

y = k/x

8 = 56/x

8 * x = 56

x = 56/8

x = 7

hence x is 7

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Based on the information provided, the length of the rope for the goat to graze over half of the field is 0.5 units.

The radius of a circle can be defined as a straight line that goes from any of the borders of the circle to its center of it.

The radius and the proportion of the field that the goat can graze is proportional. In this case if the length is 1 unit the goat can graze all the field; therefore, if we cut the graze to 0.5 the goat will graze only half of the field.

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The distance remained to be covered by amrita to attend a function is 2950 meters or 2.95 kilometers.

Given,

  Total distance to be covered by Amrita = 20 KM = 20000 m

  Distance covered by her car before broken = 17 Km 50 meter = 17050m

We know that,

                        1 Kilometer = 1000 meter

Remaining Distance = (20000 - 17050)m

                                  = 2950 m

                                  = 2.95 KM

Therefore, the distance remaining to be covered by amrita is 2950 meters or 2.95 Kilometers.

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If a circular mulch bed has a radius of 1.6 feet. A bag of mulch contains 2 cubic feet of mulch. The mulch's depth to an appropriate number of significant digits is: C. 0.25 foot.

The volume of the mulch bed is given by the formula for the volume of a cylinder:

V = π * r^2 * h

Where:

r = radius (1.6 feet)

h=  the height (the depth of the mulch).

Since we have 2 cubic feet of mulch, and want to spread it evenly over the bed, we can set 2 = π * r^2 * h and solve for h:

h = 2 / (π * r^2) = 2 / (π * 1.6^2)

h ≈ 0.25 feet

Therefore the depth of the mulch is approximately 0.25 feet.

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The polynomial, so d can be any value less than b.

A polynomial is an expression made up of multiple terms, each of which is a number, a variable, or the product of a number and one or more variables. Polynomials are typically used to model real-world scenarios including, but not limited to, population growth, force and acceleration, and angles of elevation. Each term of the polynomial is separated from the others by an addition or subtraction sign.

Given the polynomial 4x^3 + ax^2 + bx + c,
a = 4, b = -3, c = 5, d = -2.
To find the values of a, b, c, and d, we need to compare the coefficients of the polynomial to the given values.
The coefficient of the term with the highest degree (x^3) is 4, so a = 4.
The coefficient of the next degree (x^2) is a, so a = -3.
The coefficient of the next degree (x) is b, so b = 5. The coefficient of the constant term is c, so c = -2. Finally, d is not given in the polynomial, so d can be any value less than b.

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[tex]( \frac{3}{5} ){}^{2} + 4 \times 3 - 2[/tex]

[tex] \frac{9}{25} {}^{} + 12- 2[/tex]

[tex] \frac{9}{25} {}^{} + 10[/tex]

[tex] \frac{9 + 10(25)}{25} [/tex]

[tex] \frac{9 + 250}{25} [/tex]

[tex] \frac{259}{25} [/tex]

The vertices of the triangle DEF after the 90º counterclockwise rotation about the point (5,2) are given as follows:

D'(-11, -2), E'(-10, 1) and F'(-6, -3).

The five more known rotation rules are given as follows:

Considering the 90º counterclockwise rotation about the point (5,2), the rule is given as follows:

(x,y) -> (-y - 5, x - 2).

Hence the vertices are given as follows:

D'(-11, -2), E'(-10, 1) and F'(-6, -3).

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The value of {p} is equivalent to 1.68.

Given is the expression -

43p = 72

The given equation is -

43p = 72

{p} = 72/43

{p} = 1.68

Therefore, the value of {p} is equivalent to 1.68.

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The solutions of the quadratic equation are:

m = 1  ± i*√(5)/2

The correct option is b.

Here we want to solve the quadratic equation:

4m² - 8m +9 = 0

Replacing the coefficients on the quadratic formula, we will see that the solutions are:

[tex]m = \frac{8 \pm \sqrt{(-8)^2 - 4*4*9} }{2*4} \\\\m = \frac{8 \pm \sqrt{-80} }{8}\\\\m = 1 \pm\sqrt{-80/64} \\\\m = 1 \pm\sqrt{-5/4} \\\\m = 1 \pm\sqrt{-5}/2\\\\m = 1 \pm\sqrt{5}i/2[/tex]

These are the solutions.

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