what of the plane is a transformation which shifts all the points in a plane figures without altering the shape of the figure

Answer:

Option 1.

Step-by-step explanation:

The given equation of the line is 10x + 5y = 20

Now we will convert this equation into y-intercept form

10x + 5y = 20

5y = 20 - 10x

y = [tex]\frac{1}{5}[/tex] (20 _ 10x)

= -2x + 4

y-intercept of the line is 4 which gives us hint that graph (1) or (2) may be the correct option.

Since slope is (-2)

So from graph (1) slope of the line passing through (0,4) and (-2,0)  = [tex]\frac{4.0}{0+2}[/tex] = 2

Therefore, graph A is not the answer.

For graph (2) slope of the graphed line passing through (0,4) and (2,0)  = [tex]\frac{4-0}{0-2}[/tex] = (-2)

So graph (2) is representing the line y = -2x +4

Option 1. is the answer.

The length of DP is:

                      DP=14 units

It is given that:

Point P is the midpoint of DE.

DP =3x + 2 and DE = 10x - 12.

We know that a midpoint divides the given line segment into two equal parts (i.e. it bisects a line segment)

Hence, we have:

DP+PE=DE

Also, DP=PE

This means that:

2DP=DE

2(3x+2)=10x-12

2×(3x)+2×2=10x-12

6x+4=10x-12

10x-6x=4+12

4x=16

x=16/4

x=4

Hence,

DP=3x+2=3×4+2

i.e.

DP=14

Answer:

88  14/16

Step-by-step explanation:

I call these mixed numbers, a mixed number is written as a b/c and it means

[tex]a+\frac{b}{c}[/tex]

So, we can use the above to re arrange our expression to a more convenient presentation.

we have>

[tex]20+\frac{9}{16} + 24+\frac{5}{8} + 21+\frac{5}{16}+23+\frac{3}{8}\\  \\88+\frac{14}{16} +\frac{8}{8} \\\\89+\frac{14}{16}[/tex]

88  14/16, we tend to no simplify this expression anymore since, the number 14/16 usually means something in real life, like the diameter for a construction pipe

Answer:

the value of h is, -8.75

Step-by-step explanation:

The distributive property says that:

[tex]x \cdot (y+z) = x\cdot y+ x\cdot z[/tex]

Given the equation:

[tex]-110=13+3(4h-6)[/tex]

Apply the distributive property we have;

[tex]-110=13+12h-18[/tex]

Combine like terms;

[tex]-110=12h-5[/tex]

Add 5 to both sides we get;

[tex]-105=12h[/tex]

Divide both sides by 12 we get;

-8.75 = h

or

h = -8.75

Therefore, the value of h is, -8.75

2^4 x 2^-7 = 0.125

2^3 = 8, 1 /8 = 0.125

 answer is B

2^4 x 2^-7 = 0.125

2^3 = 8, 1 /8 = 0.125

answer is B

To approximate the square root of 39 to the nearest whole number, we can use the method of estimation. The estimated value of the square root of 39 is a little less than 6.

To approximate the square root of 39 to the nearest whole number, we can use the method of estimation. We know that the square root of 36 is 6, and the square root of 49 is 7. Since 39 is closer to 36, we can estimate the square root of 39 to be a little less than 6.

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0.7x-1.4 =-3.5

 add 1.4 to each side

0.7x = -2.1

 x = -2.1 / 0.7

x = -3

 Answer is B -3

[tex]-3[/tex] is the value of x in the equation [tex]0.7x -1.4 = -3.5[/tex]

What is equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

According to question, we have to find the value of  x in the equation [tex]0.7x -1.4 = -3.5[/tex]

Now,[tex]0.7x -1.4 = -3.5[/tex]

⇒[tex]x=\frac{-2.1}{0.7} \\[/tex]

⇒[tex]x=-3[/tex]

So,-[tex]3[/tex] is the  value of x in the equation [tex]0.7x -1.4 = -3.5[/tex]

Hence, Option(B) is correct.

Learn more about equation here:

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1kg = 2.20462 pounds

1kg = 35.274 ounces

1kg = 1000  grams

Answer: 8/10

Step-by-step explanation: Using the place value chart, we can see that 0.8 means eight-tenths which can be written as the fraction 8/10. Since 8/10 is not in lowest terms, we need to divide both the numerator and denominator by the greatest common factor of 8 and 10 which is 2 to get 4/5.

Therefore, 0.8 can be written as the fraction 8/10.

The perfect cubes from the given options are 64x^16, 8x^3, 81x^6, and 125x^9 as they can all be expressed as the cube of an integer or a product of an integer and variable raised to an exponent that is a multiple of three.

The question is asking us to identify which expressions are perfect cubes. A perfect cube is a number that can be expressed as the cube of an integer. The expression for a perfect cube with variables is x3n, where n is a non-negative integer. We apply this principle to the options given:

Therefore, the perfect cubes from the options given are 64x16, 8x3, 81x6, and 125x9.

Answer: [tex]\dfrac{3}{8}[/tex]

Step-by-step explanation:

Let x denotes the total pocket money Josh has.

As per given , we have

Saved pocket money = [tex]\dfrac{1}{4}x[/tex]

Money Remains = [tex]x-\dfrac{x}{4}=\dfrac{3x}{4}[/tex]

Money he spent = [tex]\dfrac{1}{2}[/tex] of (Money Remains)

=  [tex]\dfrac{1}{2}\times\dfrac{3x}{4}[/tex]

[tex]=[/tex][tex]\dfrac{3x}{8}[/tex]

Hence, the fraction of money he spent = [tex]\dfrac{3}{8}[/tex]

An absolute value equation with solutions -10 and -5 is |x + 7.5| = 2.5. This is determined by finding the midpoint between -10 and -5, and then expressing the equation to reflect that distance.

To write an absolute value equation that has the solutions x=-10 and x=-5, you must consider the midpoint between these two solutions. The midpoint or average is found by adding the values together and dividing by 2, which we can write as (x + 10 + x + 5)/2. Simplifying, we get (2x + 15)/2 = x + 7.5 as the midpoint. Now an absolute value equation that holds the given solutions will have its vertex (the point where the absolute value expression equals zero) at this midpoint and the same distance from both -10 and -5, which is 2.5 units. So, the equation looks like |x + 7.5| = 2.5.

Answer:

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Step-by-step explanation: