One number is three less than a second number. Four times the first is 10 more than 6 times the second. Find the
numbers.
***

By using the concepts of line segment and collinearity of line segments, the numerical length of the line segment JK within the line segment IK is 21 units.

In this problem we find two collinear line segments IJ and JK, two line segments are collinear if they are contained by the same line. The mathematical expression that represents the two collinear line segments are shown below:

IJ + JK = IK

If we know that JK = x + 6, IJ = 9 and IK = 2 · x, then the numerical length of JK is:

9 + (x + 6) = 2 · x

x + 15 = 2 · x

15 = 2 · x - x

15 = x

x = 15

JK = x + 6

JK = 15 + 6

JK = 21

The length of the line segment JK is 21 units.

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The figure with these coordinates are R'(0, -4), S'(2, 0), T'(3, 0) and U' (4, -1) given below. Therefore, option A is the correct answer.

Given that, the translation is 3 units right and 4 units down.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions. Since it is just moving the shape from one place to other, there is no change in the shape.

The coordinates of the given figure are R(-3, 0), S(-1, 4), T(0, 4) and U(1, 3).

If the translation is 3 units right and 4 units down, then the coordinates become (x+3, y-4).

That is, R'(-3+3, 0-4)=(0, -4)

S'(-1+3, 4-4)=S'(2, 0)

T'(0+3, 4-4)=T'(3, 0)

U'(1+3, 3-4)=U' (4, -1)

So, the coordinates are R'(0, -4), S'(2, 0), T'(3, 0) and U' (4, -1)

The figure with these coordinates are R'(0, -4), S'(2, 0), T'(3, 0) and U' (4, -1) given below. Therefore, option A is the correct answer.

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Answer:

64,222=60,000

526,193=530,000

168,055=170,000

584,629=580,000

Step-by-step explanation:

I would suggest watching a math antics video to better understand these questions. if the first number to the right is a 5 or above the number goes up  of its 4 or below it stays the same.

The numbers given illustrates that the nth term will be:

1. n² + 1

2. n²

1. It should be noted that from the information given, the numbers are 2, 5, 10 and 17. It should be noted that the nth term will be:

n² + 1.

Therefore, the 5th term will be:

n² + 1 = 5² + 1 = 26

2. The numbers given are 0, 1, 4, 9. The nth term is n². In this case, the 4th number will be:

n² = 4² = 16

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Answer:

Answer:

17. 9a^2/16

18. 25c^2/9

19. 49m^2/64

20. 16x^4/25

Step-by-step explanation:

:)

Answer: a = 15

Step-by-step explanation:

first distribute the 5 and 3 to the parenthesis

5a-5-15=3a+6+4

then add the numbers on each side together

5a-20=3a+10

then add 20 to both sides to move that over and subtract 3a from both sides to move that over

2a=30

divide by 2

a=15

The graph of a function f(x) is translated up when a positive number is added to the y-value of the function by 3 units that is the graph g(x) that is g(x) = f(x) + 3.

The correct option that illustrate the transformation that gives g(x) that has a y-intercept at 3, is the option B;

g(x) = f(x) + 3

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

The graph of the function f(x) = x, as an illustration is attached

The transformation of linear functions are:

Horizontal shifts;

f(x + h); A shift of h units left

f(x - h); A shift of h units right

Vertical shifts;

f(x) + m; A shift of m units up

f(x) - m; A shift of m units down

Whereby the y-intercept of f(x) is 0, we have;

Let f(x) = x, therefore;

g(x) = f(x) + 3

      = x + 3

The graph has to be shifted 3 places up to get g(x), therefore;

The function that gives g(x) from f(x) is the option;

B. g(x) = f(x) + 3

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Answer:

983/300 or 3 83/300

Step-by-step explanation:

Multiply to move the decimal, therefore giving you a whole number.

The number of ways to select a chair person, a vice chairperson, a secretary, and a 4-person advisory committee is 303600 ways.

It should be noted that from the information, the engineering department of a large company has 25 members and the members must select a chair person, a vice chairperson, a secretary, and a 4-person advisory committee.

Therefore, the number of different ways that this can be done will be:

= 25P4

= 25! / (25 - 4)!

= 25! / 21!

= 25 × 24 × 23 × 22

= 303600 ways

Therefore, there are 303600 ways.

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Answer: The multiplication of $.79 and 3.7 should be 2.923.

Given that,

The number is 0.79 and 3.7

We have to multiply both the numbers.

Based on the above information

$0.79

× 3.7

--------

5.53

+2.370

---------

2.923

Here the decimal should be moved three times to the left hand side as it tells the number of spaces that should be written in the real equation till the coming decimal.

In this way, the multiplication could be done of these two numbers.

Answer:

6 m/s²

Step-by-step explanation:

[tex]\frac{27 \text{ m/s}}{4.5 \text{ s}}=6 \text{ m/s}^2[/tex]

Answer:

AB and CD are congruent.

Step-by-step explanation:

Given points:

After plotting the given points (see attachment), we can easily determine that AB is 7 units and CD is 7 units.  Therefore, AB and CD are congruent.

Alternatively, as points A and B share the same x-coordinate, the length of AB is the difference between the y-coordinates:

⇒ AB = 8 - 1 = 7 units

Similarly, as points C and D share the same y-coordinate, the length of CD is the difference between the x-coordinates:

⇒ CD = 5 - (-2) = 7 units

Finally, we can prove that AB and CD are congruent by calculating their lengths using the distance formula.

[tex]\boxed{\begin{minipage}{7.8 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]

[tex]\begin{aligned}\implies AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(-4-(-4))^2+(8-1)^2}\\& =\sqrt{(0)^2+(7)^2}\\& =\sqrt{0+49}\\& =\sqrt{49}\\& =7\end{aligned}[/tex]

[tex]\begin{aligned}\implies CD & =\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\ & =\sqrt{(5-(-2))^2+(-5-(-5))^2}\\ & =\sqrt{(7)^2+(0)^2}\\ & =\sqrt{49+0}\\ & =\sqrt{49}\\ & =7\end{aligned}[/tex]

Therefore, as AB = CD, this proves that AB and CD are congruent.

Answers in bold:

======================================================

Explanation:

Part (a)

Pick any two points on line p. I'll go for points A and V. They lead to the name "line AV". The order doesn't matter so we could say "line VA"

Or you could pick points A and R to get line AR, and so on.

There are 6 different ways to name this line. We found 2 so far, and I'll let you find the other four.

-------------------------------

Part (b)

To name a plane, we need 3 points that reside in it. Points R, S and Z are in the vertical plane W. So we could call it "Plane SRZ". The order of the points doesn't matter.

-------------------------------

Part (c)

The term "collinear" means the points are on the same straight line. This applies to points S, R and Q. Also, it applies to points A, R, and V.

We cannot say something like "points S, R, and V are collinear" since they are on different lines. The points need to be on the same straight line.

-------------------------------

Part (d)

Coplanar points are part of the same plane. Pick your four favorite points in plane W that is shaded. You cannot select W since it's not a point.

-------------------------------

Part (e)

A line segment has a fixed length. Neither endpoint goes on forever. Technically there aren't any segments shown on this diagram since we have lines only. Though if we focus on a subset of say line AV, then segment RV is one possible line segment.

-------------------------------

Part (f)

Like with part (e), there are technically only lines here and nothing else. But we could break the line apart to get 2 rays.

A ray has one fixed endpoint and it points forever in one direction only. Think of a ray of light. An example of a ray is to start at point R and go forever toward point V. This forms ray RV. A similar situation happens with ray RA.

The order is important. The notation Ray RV is different from Ray VR since the first letter tells us the fixed endpoint that doesn't go on forever.

Notice how rays RV and RA, when joined together, form a straight line. They point in opposite directions. You could think of it like one is pointing north and the other points south.

Answer:

[tex]\textsf{a.} \quad \overleftrightarrow{AV} \; \textsf{and} \; \overleftrightarrow{RV}[/tex]

[tex]\textsf{b.} \quad STZ, \; RTZ, \;QTZ[/tex]

[tex]\textsf{c.} \quad A, R\; \textsf{and}\; V[/tex]

[tex]\textsf{d.} \quad Q,S,T \; \textsf{and}\; Z[/tex]

[tex]\textsf{e.} \quad \overline{AR}[/tex]

[tex]\textsf{f.} \quad \overrightarrow{RA} \; \textsf{and} \; \overrightarrow{RV}[/tex]

Step-by-step explanation:

A line can be named by using two points on the line or by a (lowercase) letter.

Therefore, two other names for line p are:

A plane can be named by using three non-collinear points in the plane or by a (capital script) letter.

Therefore, three other names for plane W are:

Collinear points are points that lie on the same line.

The collinear points on the given diagram are: A, R & V, and S, R & Q.

Therefore, three points that are collinear are:

Coplanar points are three or more points that lie in the same plane.

The coplanar points on the given diagram are: Q, R, S, T and Z

Therefore, four points that are coplanar are:

A line segment is part of a line that has two endpoints, and is named by its two endpoints.

The line segments on the given diagram are:

[tex]\overline{AR}, \;\overline{RV}, \; \overline{AV}, \; \overline{SR}, \; \overline{RQ} \; \textsf{and}\; \overline{SQ}.[/tex]

Therefore, a line segment is:

A ray is a part of a line that has one endpoint (so continues infinitely in the direction without an endpoint).  

Opposite rays are two rays that have a common endpoint and form a line.  They are named by the common endpoint followed by any other point on each ray.

The pairs of opposite rays on the given diagram are:

[tex]\overrightarrow{RA} \; \textsf{and} \; \overrightarrow{RV}, \quad \overrightarrow{RS} \; \textsf{and} \; \overrightarrow{RQ}[/tex]

Therefore, a pair of opposite rays are:

The point which could represent the player catching the ball is: C. (4, 25).

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.

By critically observing the graph (see attachment) which models the given data, we can reasonably infer and logically deduce that the point (4, 45) where the "Distance from Goal" on the y-axis intersect with the "Time after Throw" on the x-axis represents the player catching the ball.

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Answer: 4, 25

Step-by-step explanation:

The numbers are 6 and 7.

Let the values be x and x + 1.

Therefore, the equation will be:

4x + (x + 1)² = 73

4x + x² + 2x + 1 = 73

x² + 6x + 1 - 73 = 0

x² + 6x - 72 = 0

x² + 12x - 6x - 72

x(x + 12) - 6(x + 12)

Therefore, x - 6 = 0

x = 0 + 6 = 6

Therefore, the numbers are 6 and 7

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The required solution of the scaled factored figure is,
B. Figure B has the same number of edges as Figure A.
E. Figure B has angles with the same measures as Figure A.

Given that,
Figure B is a scaled copy of Figure A. We have to select all of the statements that must be true.

Here,
Figure B is similar to figure A but smaller than figure A.
So, Options A, C, and D are false
since the figure is similar, and the number of edges and angles are also equal.
So, Options B and E are correct.

Thus, the required solution of the scaled factored figure is,
B. Figure B has the same number of edges as Figure A.
E. Figure B has angles with the same measures as Figure A.

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Answer: When a substance melts, it is changing from a solid to a liquid state. When a substance is set on fire, it is changing from a solid to a gaseous state.

Answer:

When a substance melts, it is changing from a solid to a liquid state. When a substance is set on fire, it is changing from a solid to a gaseous state.

Answer:

complementary angles

Step-by-step explanation:

∠ XVY and ∠ ZVY form angle XVZ

∠ XVZ is a right angle = 90° , then

∠ XVY + ∠ ZVY = 90°

2 angles whose sum is 90° are complementary angles

10 is the correct answer

Answer:

Step-by-step explanation:

let weight of DVD & packing material=x lb

8.50x+1.10=2.50x+2.25

8.50 x-2.50 x=2.25-1.10

6 x=1.15

x=1.15/6=0.19166... lb

The expression that represents the perimeter of the triangle in the image is: 7a - 2.

To find the perimeter of a triangle, add the lengths of the three sides of the triangle together. The sum of the three sides of the triangle is the perimeter of the triangle.

The triangle in the image has the following as the lengths of its sides:

Therefore:

The perimeter of the triangle = 2a - 3 + 2a + 3a + 1

Combine like terms

The perimeter of the triangle = (2a + 2a + 3a) + (- 3 + 1)

The perimeter of the triangle = 7a - 2

Therefore, the expression that represents the perimeter of the triangle in the image is: 7a - 2.

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Answer:

45%

Step-by-step explanation:

27/60 x 100

.45 x 100

45

The measure of the angle of the straight line is equal to 180 degrees. the measure of the ∠HLI and ∠ILM is equal to the which is 30 degrees. Thus option 4 is the correct option.

An endlessly long row of evenly spaced dots that spans in both directions makes up a line. Its length is the only dimension it has. A geometry called an angle is created when two line segments, lines, or rays intersect.

Given information-

The measure of the angle KLH is 120 degrees.

The image is attached below for the given problem.

The angle of the straight line

The measure of the angle of the straight line is equal to 180 degrees.

The line KLM is a straight line thus the angle of the line KLM is equal to 180 degrees.

The value of the angle ILH is 30 degrees given in the figure.

The value of the angle KLH is given in the question which is equal to 120 degrees. Thus,

∠KLM = ∠ILM + ∠KLH + ∠ILH

Take the angle KLH and the angle ILH on the other side,

∠ILM = ∠KLM - ∠KLH - ∠ILH

∠ILM = 180 - 120 - 30

∠ILM = 30

Thus the measure of the is 30 degrees.

As the measure of the is equal to the which is 30 degrees. Thus option 4 is the correct option.

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Answer:

d. mAngleHLI = mAngleILM

Step-by-step explanation:

trust

Answer:

Correct

Step-by-step explanation:

Answer: yessir

Step-by-step explanation:

The algebraic expression for "three more than twice a number" is translated as: 2n + 3.

An algebraic expression is a mathematical statement that is written to represent a phrase, using alphabets as variables of the algebraic expression, operation signs and numbers.

Given the phrase "three more than twice a number", we can represent the number using the variable, x.

Therefore:

Twice the number, n, would be: 2n

3 more than 2n would be translated as: 2n + 3.

The whole phrase, translated into algebraic expression is expressed as: 2n + 3.

Conclusively, the algebraic expression for "three more than twice a number" is translated as: 2n + 3.

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Answer:

20km

Step-by-step explanation:

rounding down because it's not over five

Step-by-step explanation:

the area of any triangle is

baseline × height / 2

so, in our case

12 × height / 2 = 48

6 × height = 48

height = 48/6 = 8 units

m with the height and half of the baseline creates a right-angled triangle. and we can use Pythagoras to get m.

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle), which is m for this right-angled triangle.

a and b are the legs, which are in our case the height of the main triangle and half of the baseline of the main triangle.

so we get

m² = 8² + (12/2)² = 8² + 6² = 64 + 36 = 100

m = 10 units