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Question
Given: 3x−22=5
Prove: x = 4

Select from the drop-down menus to correctly complete the proof.

1; basically the therom states that 90 + 36 = 126 = 5n + 1;

126 = 5n + 1;

125 = 5n

25 = n

There are thing we must already know:

From this, we must know that:

The scientis needs 0.25kilograms. From this we calculate:

Answer:

number is - 2

Step-by-step explanation:

let the number be n then 7 times the number is 7n and 3 times the number is 3n, so

4 - 7n = 12 - 3n ( add 3n to both sides )

4 - 4n = 12 ( subtract 4 from both sides )

- 4n = 8 ( divide both sides by - 4 )

n = - 2

1) The relationship between ∠2 and ∠6 is that they are alternate angles.

2) The relationship between ∠1 and ∠3 is that they are corresponding angles.

Corresponding angles are defined as the angles that are formed in  corresponding corners with the transversal when two parallel lines are intersected by any other line.

Alternate angles are defined as the angles that are formed by the intersection of a transversal and two parallel lines.

This alternate angle could either be interior alternate or exterior alternate.

1) Since we are told that Line 1 is parallel to Line 2, then it means that from definition of alternate angles that ∠2 and ∠6 are alternate angles.

2) Since we are told that Line 1 is parallel to Line 2, then it means that from definition of corresponding angles that ∠1 and ∠3 are corresponding angles.

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Answer:

70 square units

Step-by-step explanation:

Since it is half a big rectangle, (10*14)/2=70

Answer:

35/7

Step-by-step explanation:

All of the translations describes the same inclination for a straight line because the they all have a pitch (slope) of 2/5.

Mathematically, the pitch (slope) of a geometric figure or straight line can be calculated by using this formula:

Pitch (slope) = V/H

Where:

Based on the information provided, the pitch (slope) of this line is given by:

Pitch (slope) = Up 2/Right 5 = 2/5

Pitch (slope) = Up 4/Right 10 = 2/5

Pitch (slope) = Down 42/Left 5 = 2/5

Pitch (slope) = Up 1/Right 5/2 = 2/5

Pitch (slope) = Down 2/5/Left 1 = 2/5

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Yes, a triangle that has sides with lengths of 9 feet, 12 feet, and 15 feet is a right-angled triangle

A right-angled triangle can be defined as a type of triangle, having one of its interior angles equivalent to 90 degrees.

The properties of right angled triangles include;

From the information given, we have;

Hypotenuse side = 15 feet

Opposite side = 12 feet

Adjacent side = 9 feet

We can see that the properties of a right-angles triangle submits to the parameters given.

Hence, it is a right-angled triangle

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The plane was flying at a height of 706.32 m .

The fundamentals of an object's motion, such as its position, velocity, or acceleration over time, are defined by kinematics equations of motion. An object's motion in one, two, and three dimensions is determined by these three equations of motion. One of three equations of motion can be used to calculate components like displacement (s), velocity (initial and final), time (t), and acceleration (a). The following are the three motion equations:

Initial formula: v = u + at

The second formula is s = ut + 0.5at2.

The third formula is v2 = u2 + 2as.

Let t stand for the package's flight time, s for the plane's altitude, and u for the packet's initial vertical velocity since it is simply dropped.

Given: t = 12 seconds for the delivery to arrive to the ground

With t = 12 and u = 0 in the second equation of motion, we so obtain

s = 0*t + 0.5*9.81*12² = 706.32 m

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Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

Answer:

Either A or B.

Step-by-step explanation:

Each number in the sequence is being added by 6.

So you can use the equation: x+6

The ninth term in the sequence would be 36 because 30+6=36

Answer:

Step-by-step explanation:

Find the dividend. ___ ÷ 22 = 1.9

4,180

418

41.8

4.18

x : 22 = 1.9

x = 22 * 1.9

x = 41.8

Answer:

x = 41.8

Step-by-step explanation:

Answer:

y=-3x-2

Step-by-step explanation:

y=mx+b; adjust b value --> y=-3x-2

Sum of APs 2+5+8+........ as far as the 18th term is 495.

Sum of n terms of A.P.

[tex]S_{n} = \frac{n}{2}[2a+(n-1)d][/tex]

where,

[tex]S_{n}[/tex] = sum of n terms of A.P.

a = first term of A.P.

d = Common difference.

Given,

d=5−2=3

a=2

[tex]S_{11}[/tex]=[tex]\frac{18}{2}[/tex][4+(18-1)×3]

=[tex]\frac{18}{2}\\[/tex][4+51]

=[tex]\frac{18}{2}[/tex]×55

=495

An arithmetic progression, or arithmetic sequence, is a sequence of numbers in which the difference between successive members is constant. Here is the AP formula for AP a, a + d, a + 2d, a + 3d, . . . a + (n - 1) d. The formula for finding the nth term is [tex]a_{n}[/tex] = a + (n – 1) × d.

Then the formula for finding the sum of the arithmetic progressions is:[tex]S_{n} = \frac{n}{2}[2a+(n-1)d][/tex] where a = first term in arithmetic progression, n = number of terms in arithmetic progression, and d = total difference.

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Answer:

9

Step-by-step explanation:

So we'll need to add both angles to make it equal to the total angle. Then we can find X by solving an equation.

(4x + 12) + (12x - 8) = 148

16x + 4 = 148

16x = 144

x = 9

The equation of line passing through point (6,0) and having a slope of -5/6 is y = -(5/6)x + 5

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Point: (6,0)

First, we determine the y-intercept by substituting the given values into the equation of line formula and solve for b.

y = mx + b

0 = (-5/6)6 + b

0 = -5 + b

b = 5

Now that the values of slope m ( -5/6 ) and y-intercept b ( 5 ) is known, plug these into y = mx + b to determine the equation of the line.

y = mx + b

y = (-5/6)x + 5

y = -(5/6)x + 5

Therefore, the linear equation of the line is y = -(5/6)x + 5.

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Answer:

Formula for midpoint is given as [(x1+x2)÷2, (y1+y2)÷2] where x and y are the coordinates of the points.

Midpoint = [(3+5)÷2, (-8+(-2.5))÷2]

= (8÷2, -10.5÷2)

= (4, -5.25)

Answer:

60 weeks.

Step-by-step explanation:

10 and 12 both are divisible by 60, thus itll be 60 weeks before she visits them both in the same week again

We can identify vertical lines by seeing if two points that fall on the line have the same x-coordinate.

If they do, then it is a vertical line.

The slope of vertical lines are always undefined.

We're given the following points:

These points have the same x-coordinate, revealing that this is a vertical line. Therefore, it has an undefined slope.

Undefined

Answer: Corresponding angles

Step-by-step explanation:

True by the definition of corresponding angles.

The value of the equation illustrated as 2(x + 3) is 2x + 6.

In Mathematics, an equation simply illustrates the relationship that the variables have. This can be replaced with letters to express the information.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same values.

In this case, it should be noted that the expression for 2(x + 3) will be:

= 2(x + 3)

Open the bracket

= 2x + 6

The value of the expression is 2x + 6.

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The number line (C) represents the solution to the inequality -0.96 ≥ 0.3x option (C) is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The inequality is:

Let the number is x:

-0.96 ≥ 0.3x

0.3x ≤  -0.96

x ≤ -0.96 /0.3

x ≤ -3.2

x ∈ (-∞, -3.2]

As we know, the number line can be defined as the representation of the numbers on a straight line that goes infinitely on both sides.

The number line (C) represents the solution to the inequality -0.96 ≥ 0.3x

Thus, the number line (C) represents the solution to the inequality -0.96 ≥ 0.3x option (C) is correct.

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Answer:

0%

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are 10*9 ways of selecting two biscuits (in order 1,2)

Of these 90 possible orders

2 digestives can be picked in 5*4 ways =20

2 chocolate can be picked in 2*1 ways = 2

2 ginger can be picked in 3*2 ways =6

Digestive then chocolate can be selected 5*2 ways =10

Chocolate then Digestive can be selected 2*5 ways = 10

Digestive then ginger can be selected 5*3 ways ways = 15

Ginger then digestive can be selected 3*5 ways ways = 15

Chocolate then Ginger can be selected 2*3 ways =6

Ginger then chocolate can be selected 3*2 ways = 6

I have done this the ‘long’ way to demonstrate that all 90 possible outcomes are covered. (Double check)

Probability of taking two different is then the total of the last 6 options divided by the total number of options = 2*(10+15+6)/90 = 31/45 = 68.89% (Approx.)

The area of the rectangle will be 512[tex]cm^{2}[/tex] .

let the longer side of the rectangle be "l" and the shorter side of the rectangle be "b".

Hence, the perimeter of rectangle = 2(l+b)

we are given the perimeter =96cm

thus, 2(l+b)=96

l+b = 96/2

l+b =48

also, we are given the condition that the longer side of the rectangle is two times the length of the Shorter side.

Thus, l=2b, substituting this in l+b=48 we get

2b+b=48

3b=48

b=48/3

b=16cm, now substituting this in l=2b,

l=2(16)

l=32cm

area of the rectangle = length x breadth

=l x b

=32 x 16

= 512[tex]cm^{2}[/tex]

What is the difference between perimeter and area?

Area and perimeter are two crucial characteristics of two-dimensional shapes in mathematics. The area of a shape describes the space it occupies, whereas the perimeter describes how far the shape's boundary extends.

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Answer:

1. B

2. D

Step-by-step explanation:

2. 26(2)-2

26(2)=52

52-2=50

There are 10 students in a class, 6 of them wear glasses. If a student is chosen at random from the class, then the probability that they do not wear glass is 2/5

Total number of Students = 10

Students who wear glasses = 6

Students who don't wear glasses = 4

Probability is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,

P(E) = (Number of favorable outcomes) ÷ (Total favorable outcomes).

The probability of a student not wearing glasses is,

Probability = Students who don't wear glasses/Total number of Students

Probability = 4/10 i.e., 2/5

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Answer: move the base and exponent to the other side of the fraction line and change the exponent to positive: 1/(24)

If jimmys saving account makes 0.7% interest every month if he puts 200 in the account 2 months ago, then 202.81  is in therenow round to the nearest cent

Percentage, a relative value indicating hundredth parts of any quantity.

Given

jimmys saving account makes 0.7% interest every month.

The initial deposit is 200 in the account

After two months of time, we need to the find the total amount in account.

0.7% is converted to decimal

0.7/100=0.007

So after two months

A is amount after two months

r is rate of interest

t is time period

[tex]A=P(1+r)^{t}[/tex]

=200(1+0.007)²

=200(1.007)²

=202.8

Hence 202.8  is there now in Jimmys savings accout

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The number which is an irrational number as required to.ve identified among the answer choices given is; Choice B; √19.

What is an irrational number?

An irrational number, as the name implies is any real number that cannot be expressed as the quotient of two integers (fraction). It follows that such a number cannot be expressed , a/b, where a and b are both integers.

On this note, the number which cannot be expressed in such form is; Choice B; √19.

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The range of the function  f(x) = |x| − 5 is −5 ≤ y < ∞.

Given the function is  f(x) = |x| − 5

we know the domain is (−∞,∞)

therefore from the domain we calculate the range as:

−5 ≤ y < ∞.

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.

All real numbers are defined by the function y=|ax+b|. Consequently, the set of all real numbers is the domain of the absolute value function. Every time a number has an absolute value, it has a positive value. The range of an absolute value function with the form y= |ax+b| is hence y R | y 0.

Hence we get the required range if the function.

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Answer:

hello Your answer is down below

Step-by-step explanation:

The Question given "What is the range of f(x) = |x| − 5?"

The answer choices:

−∞ < y ≤ −5

−5 ≤ y < ∞

0 ≤ y < ∞

5 ≤ y < ∞

So what do we know? hmm: The definition of Function range is: "The set of values of the dependent variable for which a function is defined".

So the range of: [tex]\mathrm{Range\:of\:}\left|x\right|-5\\[/tex]  is f(x) ≥ -5.

Which would mean the Interval Notation                Oh yeah btw the answer is −5 ≤ y < ∞

is [-5, [tex]\:\infty[/tex])

So based of that we can infer the answer is gonna have -5 in it.

As a graph it would look like this

SO from the graph we can see the answer is −5 ≤ y < ∞