Which expression is equivalent to...? Assume... screenshots attached, please help!

Answer:

The domain is all real numbers or (-infinity, +infinity)

The range is all numbers greater than or equal to 4 or (4,+infinity)

Hope this helped! :)

ANSWER

[tex](-∞,+∞)[/tex]

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 4[/tex]

This is a polynomial function.

Polynomial functions are defined for all real values of x.

For every x-value, there is a corresponding y-value.

Therefore the domain of the given function is all real numbers.

We can rewrite this as:

(-∞,+∞).

Final answer:

The equation [x-1]=[x] suggests two possible values for x, which are 0 and 0.5. These are specific values rather than a continuous range or a broad set like all integers or all real numbers.

Explanation:

The equation [x-1]=[x] compares the absolute values of two expressions: x-1 and x. Absolute values are always non-negative, leading to two possible scenarios. First, if x is non-negative, x will be equal to x-1, which only happens when x is zero. Second, if x is negative, then -x is equal to x-1, which is true when x = 0.5. No other values of x will satisfy the equation, as the increment on one side of the equation will not match the decrement on the other. Therefore, the correct set of numbers that describes the possible values of x is neither integers, all real numbers, only negatives, nor only fractions. Instead, it includes specific values, which are 0 and 0.5.

Final answer:

The equation [x-1]=[x] is not satisfied by any real value of x since attempts to solve it lead to contradictions. Thus, there are no possible values of x for this equation; none of the provided choices are correct.

Explanation:

To determine which set of numbers best describes the possible values of x in the equation [x-1]=[x], where [] denotes the absolute value, we must consider when the absolute values of two expressions would be equal.

If x is a non-negative number, then [x] = x and [x-1] = x-1. Thus, the equation implies x = x - 1, which is impossible for any real number.

If x is negative, then [x] = -x and [x-1] = 1-x. The equation becomes -x = 1 - x, which simplifies to 0 = 1, which is also impossible.

Therefore, there are no values of x that can satisfy this equation since we always end up with a contradiction when we attempt to solve it. This means the correct answer is that there are no possible values of x that will satisfy the given equation, which isn't one of the provided choices.

Answer:

Odds are 3 to 7

Step-by-step explanation:

The odds are defined as the probability that the event will occur divided by the probability that the event will not occur.

Let's find:

Probability of blue marble = 3/10 [ 3 blue and 10 in total]

Probabilty of NOT blue marble = 7/10 [7 marbles are red and green (not blue) and 10 in total]

Hence,

Odds of drawing a blue marble = [tex]\frac{\frac{3}{10}}{\frac{7}{10}}=\frac{3}{10}*\frac{10}{7}=\frac{3}{7}[/tex]

The odds are 3 to 7

Answer:

x = 56

y = 32

Step-by-step explanation:

x: y

7:4 = 11

multiply by 8 to make a total of 88

x = 7 × 8 = 56

y = 4 × 8 = 32

For the proportions X: Y = 7:4 and X: Y = 88, we first find that X = 154 and Y = 88. Subsequently, we can determine that X-Y is equal to 66.

The given conditions are X: Y = 7:4 and X: Y = 88. This means X/Y = 7/4 and X/Y = 88. Since both conditions have to be true, it implies 7/4 = 88. Taking the cross product, we find that X = 7*88/4 = 154.

To find Y, we substitute X = 154 into X: Y = 7:4, rearrange the equation to solve for Y, and get Y = 154 * 4 / 7 = 88. Now, we can calculate X-Y = 154-88 = 66. Hence, X-Y is equal to 66.

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The calculated expected value for the private investigator's job is -$2,000, suggesting an expected loss. Therefore, the detective should not take the job based solely on the provided financial information.

To determine whether the private investigator should take the job, we need to calculate the expected value of the job based on the probabilities and payoffs provided.

Here is the calculation:

The expected value (EV) is thus calculated as:

EV = (Probability of Success) × (Gain) + (Probability of Failure) × (Loss)

EV = (0.1) × $70,000 + (0.9) × (-$10,000)

EV = $7,000 - $9,000

EV = -$2,000

Since the expected value is negative, the detective should not take the job based on this information alone, as it represents an expected loss.

Answer:

The answer is 1,550

Step-by-step explanation:

First you find the area of the rectangle 1

Area = ab

=(21 in) (17in)

=357 sq in.

this will be the same for rectangle 3 = 357 sq. in.

next find the area of rectangle 2

area=ac

=(21 in) (11 in)

=231 sq in.

this will be the same for rectangle 4 = 231 sq. in.

next find the area of rectangle 5

area = bc

=(17 in) (11 in.)

=187 sq. in

this will be the same for rectangle 6 = 187 sq. in.

Next add all areas together

Total surface area = 2(ac) + 2(ab) + 2(bc)

= 2(231) sq in. + 2(357) sq in. + 2(187) sq. in

= 462 + 174+ 374

= 1550 sq. in

Answer:

x = 3/5, -3/5

Step-by-step explanation:

Answer:

x = ± [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Given

25x² + 1 = 10 ← subtract 10 from both sides

25x² - 9 = 0 ← in standard form

note that 25x² - 9 is a difference of squares and factors as

(5x - 3)(5x + 3) = 0

Equate each factor to zero and solve for x

5x - 3 = 0 ⇒ 5x = 3 ⇒ x = [tex]\frac{3}{5}[/tex]

5x + 3 = 0 ⇒ 5x = - 3 ⇒ x = - [tex]\frac{3}{5}[/tex]

Answer:

168 units cubed

Step-by-step explanation:

so we know it's base times height right

so like identifying the base doesn't matter as long as you're smart enough to figure how to calculate then whatever lol

so like the base let's just say it's the triangle because that's probably what you're struggling on

so the base of the triangle is like what lol 6 * 8 / 2 = 48 / 2 = 24 so then you have the base multiply by the third dimension

24 * 7 = 140 + 28 = 168 so yeaaaaaaa and it's cubed because it's three dimensional

Answer:

See attached diagram

Step-by-step explanation:

You are given the equation of hyperbola

[tex]\dfrac{(x-1)^2}{49}-\dfrac{(y+3)^2}{9}=1[/tex]

From this equation,

Draw two parallel lines x=1 and y=-3 (they intersect at the center of hyperbola), then on horizontal line match two hyperbola's vertices (7 units to the left and 7 units to the right from the center). Then draw two branches of hyperbola (one in negative direction and one in positive direction).

Answer:

Step-by-step explanation:

(2+2i)(5+3i)

(2)5+(2)3i=10+6i

(2i)5+(2i)3i=10i+6i^2

10+6i+10i+6i^2

6i^2+6i+10i+10

6i^2+16i+10

To find the product of (2+2i)(5+3i), apply the distributive property to multiply each part. The result is 10 (real*real), 6i (real*imaginary), 10i (imaginary*real), and -6 (imaginary*imaginary, since i^2=-1), which are summed to give 4 + 16i.

The product of two complex numbers, such as (2+2i)(5+3i), can be found by using the distributive property (also known as foil - first, outer, inner, laters). In this case:

Sum these results together: 10 + 6i + 10i - 6. Thus, (2+2i)(5+3i)= 4 + 16i.

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Answer:

ohh tough one let me figure this out

Step-by-step explanation:

brb

afk

The arc is equal to the half of circumference.

The formula for circumference is [tex]C=2\pi r=2\pi 11=22\pi\approx69.11[/tex]. Now divide that by 2 and you get [tex]69.11\div2\approx\boxed{34.56}[/tex]

Semicircular arc has a length of approximately 34.56

Hope this helps.

r3t40

here is the answer and solution

Answer:

92 ft^2

Step-by-step explanation:

You have the top part correct. Don't let the multitude of numbers fool you.

The bottom rectangle is 5 high by 10 wide

Area = 10 * 5 = 50 ft^2

Your top part was 6*7 = 42 ft^2

The total area is 50 + 42 = 92 ft^2

Answer:

25

Step-by-step explanation:

I'm not in 8th grade... but I am quite smart.

Look at the graph. Each point goes up 25. It starts at the origin, then 25, 50, 75, 100. In other words, 50 = 25 + 25, 75 = 25 + 25 + 25, and 100 = 25 + 25 + 25 + 25.

9 (boxes a day) x 3 (shipping labels per box)= 27 labels per day

Answer: 27

Step-by-step explanation:

Given : The number of boxes warehouse worker ships = 9

The number of shipping labels contained in box = 3

Then the number of shipping labels the worker need each day is given by :-

[tex]9\times3=27[/tex]

Hence, the number of shipping labels the worker need each day =27

Answer:

a(n) = 64 * (1/4)^(n-1)

Step-by-step explanation:

64/16 = 4

16/4 = 4

and so on

so r = 1/4

Geometric sequence:

a(n) = a1 r^(n-1)

a(n) = 64 * (1/4)^(n-1)

Final answer:

The explicit formula for the geometric sequence 64, 16, 4, 1 is an = 64 times (1/4)(n-1), where 'an' is the nth term of the sequence.

Explanation:

The explicit formula for a geometric sequence is given by an = a1 times r(n-1), where a1 is the first term and r is the common ratio. To find the explicit formula for the geometric sequence 64, 16, 4, 1, we need to firstly identify the common ratio r. We can find this by dividing any term by the previous term, so r = 16 / 64 = 1 / 4. The first term a1 is 64. Thus, the explicit formula for the given sequence would be an = 64 times (1/4)(n-1).

Rotation is a type of transformation that turns a figure around a given point called the center of rotation

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Rotation is a type of transformation that turns a figure around a given point called the center of rotation.

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Final answer:

A rotation is a transformation that involves a figure turning around a fixed point called the center of rotation, with all other points moving in circular paths around this central point.

Explanation:

A rotation is a transformation that turns a figure around a given point called the center of rotation. In geometry, when objects undergo rotation, such as a compact disc (CD) spinning, each point on the object moves along a circular arc. The rotation is planar, meaning the object stays within a single plane as it turns around a central point. The axis of rotation can be thought of as a line passing through this central point, remaining fixed while the rest of the figure rotates around it. For example, Earth's rotation on its imaginary axis, stretching between the North and South Poles, causes the daily cycle of night and day.

When we consider an individual object rotating in a fixed location, the axis of rotation is the line about which the rotation occurs. Points on this axis do not move, and every other point in the object follows a path around this axis. If we were to visualize the motion of a rotating rod, for instance, we would see that a rod rotated around an axis through its center perpendicular to its length exhibits this rotational motion. In all cases, the center of rotation acts as a pivotal point around which the figure rotates.

Answer:

The lines intersected by a transversal must be parallel.

Answer:

10

Step-by-step explanation:

the sum of interior angle and exterior angle = 180°

ext + 108 + ext = 180

2 ext + 108 = 180 (subtract 108 from both sides )

2 ext = 72 (divide both sides by 2 )

ext = 36

The sum of the exterior angles of a polygon = 360°, hence

number of sides = [tex]\frac{360}{36}[/tex] = 10

Answer:

96 is the measure of 3 angles. It has 3 sides since its a regular polygon.

Step-by-step explanation:

Sorry for taking so much time, I had to go AFK. But, here's the explanation:

Each exterior angles always measures 360 degrees and interior angles measure 180. Always.

The sides of a regular polygon is 3.

Now, they asked us to add 108+180 which gives us 288 degrees.

we divide 288÷3(the sides of the polygon) and we get 96 is the measure of three angles.

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Answer:

D

Step-by-step explanation:

Try to remember this formula.

[tex]y=a|b(x-c)|+d[/tex]

Where a is the vertical multiplier, b is the horizontal multiplier, c is the x coordinate of the vertex, and d is the y coordinate of the vertex.

Since the vertex on the graph is (2,3), c and d have to be 2 and 3.

Also, there are no vertical/horizontal stretches so the a and b values stay at 1.

The final equation would come out to [tex]y=|x-2|+3[/tex]

Answer:

18 sq. units

Step-by-step explanation:

Height would be 6 and Length would be 3

6 x 3 = 18

For further help, use a coordinate grid and plot the points

Answer:

9 units

Step-by-step explanation:

We need to find the last point. This is a rectangle. We already have 3 corners. We need the opposite corner to (0,0). One corner has an x of 3 and a y of 0, another corner has a x of 0 and a y of 6.

We therefore know the fourth corner/point is (3, 6)

Now we can properly visualize the rectangle. If the rectangle has a corner at the origin, we can just use a formula and the other corner to find the area.

Area (rectangle) = 1/2 x length x width

The length will be the difference between the two x points (0 and 3) and the width will be the difference between the two y points (0 and 6).

Length = 3

Width = 6

Area = 1/2 x 3 x 6

Area =  9 units

Answer:

Step-by-step explanation:

By showing that 0.20 is greater than 0.18 by doing 0.20-0.18 which gives a positive 0.02, thich means that its greater.

0.2 is greater than 0.18.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

We have to Compare 0.2 and 0.18.

First we have two digits in 0.18 after decimal.

Then, make 0.2 with two digits after decimal as 0.20.

Now, compare the after decimal value

20 > 18

So, 0.2 is greater than 0.18.

Learn more about Inequality here:

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Answer:

X = 20.6 inches

Step-by-step explanation:

Pythagorean Theorem: [tex]A^{2} =B^{2} +C^{2}[/tex]

A = 41.2 in, while B = 35.7 in and we are solving for C.

[tex]41.2^{2} = 35.7^{2} +C^{2}[/tex]

[tex]1697.44 = 1274.49 + C^{2}[/tex]

Now solve for C

[tex]422.95 = C^{2}[/tex]

Take the square root

[tex]20.5657482237 = C[/tex]

Answer:

Step-by-step explanation:

Actually, none of these represent direct proportion, because each one involves adding or subtracting an offset.

The last answer is closest to being a proportional relationship:

$1.75 per pound → Total cost = ($1.75/lb)x, where x is the number of pounds.  This line would go through the origin, as it must, for the relationship to be proportional.  But as soon as we add in or subtract that $1 coupon, this is no longer a proportional relationship.

ANSWER

The constant of variation is 6.

EXPLANATION

The inverse variation equation is:

[tex]xy = k[/tex]

We want to find the constant of variation, when x=-3 and y=-2.

We substitute the values for x and y to get,

[tex] - 3 \times - 2 = k[/tex]

Multiply out the left hand keeping in mind that negative times negative yields a positive result.

This implies that;

[tex]k= 6[/tex]

Hence the constant of variation is 6.

Answer:

The constant of variation k is 6.

Step-by-step explanation:

Given that there is inverse variation between x and y with equation

[tex]xy=k[/tex]

we have to find the constant of variation k when x=-3 and y=-2

The inverse variation equation is:

[tex]xy = k[/tex]

To find constant of variation we substitute the values of x and y

Put x=-3 and y=-2

[tex](-3)\times (-2)=k[/tex]

Solve LHS by multiplying

This implies

[tex]k= 6[/tex]

Hence the constant of variation is 6.

y=9.64

—————

cos21=9/y

Cross Multiply

ycos21=9

Divide both sides by cos21 to isolate y

9/cos21 = 9.640304943

y=9.64

Final answer:

By completing the square, the quadratic function x² + 8x + 6 can be rewritten as (x + 4)² - 10. The minimum value of the function is at -10, corresponding to option D.

Explanation:

To determine the maximum or minimum value of the quadratic function represented by the expression [tex]x^2 + 8x + 6[/tex], we should complete the square. This method involves creating a perfect square trinomial from the given quadratic expression, which allows for easy identification of the vertex of the parabola that represents the function graphically.

We start by taking the coefficient of the x-term (which is 8), dividing it by 2, and then squaring it to get 16. Then we add and subtract this value within our expression, which gives us:

[tex]x^2 + 8x + 16 - 16 + 6[/tex]

The expression now becomes:

( [tex]x^2 + 8x + 6[/tex]) - 10

This simplifies to:

(x + 4)2 - 10

Now that we have a perfect square, we can see that the vertex is at (-4, -10), which represents the minimum value of the function since the coefficient of the [tex]x^2[/tex] term is positive, indicating a parabola that opens upward.

Therefore, the correct answer is:

D) minimum value at − 10

Answer: C. R

Step-by-step explanation:

R changes depending what m is. (It is also the y variable which is always dependent)

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