Find the range of the following
function given that
ƒ(x) = x² − 1
Domain: -2

When a scale factor of 1 inch to 6 feet is used, the length is 9 inches.

From the information illustrated, a scale factor of 1 inch to 6 feet is used. In this situation, an object in real life is 55 feet long.

The number of inches that should be in the scale drawing will be:

= Number of feet / Scale used

= 55 / 6

= 9.17 inches

The length that should be in the scale is 9 inches.

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A scale factor of 1 inch to 6 feet is used. An object in real life is 55 feet long. How many inches long should it be in the scale drawing?

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

126 = 5n + 1;

125 = 5n

25 = n

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)

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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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:

y=-3x-2

Step-by-step explanation:

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

The ratio of consonants to vowels is 21:5.

What is ratio?

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4), while the ratio of oranges to overall fruit is 8:14. (or 4:7).

No. of consonants = 21

No. of vowels = 5

(A) Ratio of consonant to vowels = 21/5 = 21:5

(B) Fraction of vowels = 5/26

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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)

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

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:If 104 items were sold and 32 if these are cookies, to get number of brownies sold subtract 32 from 104.  This gives 72 brownies sold.  

A ratio is a fraction.  If we want the ratio of brownies to cookies it would look like

    brownies            72

   ________     =  _____

     cookies             32

This ratio could be reduced by dividing both parts of the fraction by the greatest common factor of 8.

This gives a reduced ratio of     9

                                             _____

                                                4

Step-by-step explanation:

Answer:I think 82 or 56

Step-by-step explanation:

Answer:

92 men

Step-by-step explanation:

First, since they give you the total employees, you need to add the ratios together to get a total.

4 + 7 = 11

Next, setup a proportion using men to total employees.

[tex]\frac{4}{11}=\frac{m}{253}[/tex]

The left side is the ratio and the right side is the actual. m will represent the total number of men employed.

Cross multiply then divide.

4 x 253 = 1012

11 x m = 11m

11m = 1012

11m/11 = 1012/11

m = 92

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 < ∞

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 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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There are thing we must already know:

From this, we must know that:

The scientis needs 0.25kilograms. From this we calculate:

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:

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

Answer:

70 square units

Step-by-step explanation:

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

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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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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Answer: Corresponding angles

Step-by-step explanation:

True by the definition of corresponding angles.

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.

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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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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On average, the bear's weight change per month was 8.6 pounds.

The average is the mean value in a data set.

We compute the average by adding the data values and dividing by the number of items in the data set.

In this scenario, the average weight loss per month offers an idea of the weight change the bear experienced during the 7¹/₂ months.

The number of months during hibernation = 7¹/₂ or 7.5 months

The total weight loss = 64.5 pounds

The average weight change per month = 8.6 pounds (64.5/7.5)

Thus, we can conclude that, on average, the bear experienced a weight loss of 8.6 pounds per month and reduced by a total of 64.5 pounds in 7¹/₂ months.

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During 7 1/2months of hibernation, a black bear experienced a weight loss of 64.5 pounds.

Answer:

35/7

Step-by-step explanation:

$7.99 is the constant of proportionality in this relationship.

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.

Given Data

The cost for 6 months is $47.94.

x = number of months

x = 6

y =  total amount of money they have paid for the subscription

y = 47.94

Constant of proportionality = [tex]\frac{47.94}{6}[/tex]

Constant of proportionality = 7.99

$7.99 is the constant of proportionality in this relationship.

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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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