5. What is the largest natural number less than 1000 that is equal to the sum of 4 natural consecutive
numbers?
A) 995
B) 996
999
C) 997
D) 998
E) 999

Answer:

Step-by-step explanation:

To find the instantaneous rate of change function for the given function p = 2 - 3q², we need to find the derivative of the function with respect to q. The derivative gives us the slope of the tangent line to the curve at any point, which is the instantaneous rate of change at that point.

So, we can start by taking the derivative of the given function:

dp/dq = d/dq(2 - 3q²)

dp/dq = 0 - 3(2q)

dp/dq = -6q

Therefore, the instantaneous rate of change function for p = 2 - 3q² is given by:

dp/dq = -6q

This means that the instantaneous rate of change (slope of the tangent line) of the function p with respect to q is -6q at any given point.

As $sqrt-40$ cannot be further simplified in terms of real numbers, the answer is given in simplified form.

A right triangle's hypotenuse (the side that faces the right angle) has a square length that, according to Pythagoras' Theorem, is equal to the sum of the squares of the lengths of the other two sides (the legs). Formally, Pythagoras' theorem asserts that if a right triangle has legs of lengths a, b, and c, and a hypotenuse of length c, then:

[tex]a^2 + b^2 = c^2[/tex]

Pythagoras, an ancient Greek mathematician, is credited with discovering and proving this theorem, therefore it bears his name.

given

The Pythagorean theorem can be used to determine the length of the omitted side. Let x be the length of the side that is missing. The right triangle that results has a hypotenuse that is top-bottom in length and legs that are x and slant in length. This can be expressed as:

x2 + slant2 = (top - bottom)2

$$

To put it simply, we have:

\begin{align*} \s(top - bottom) (top - bottom)

2 &= x 2 + slant 2, top 2 - 2top "cdot bottom + bottom 2 - slant 2," x 2 &= "sqrt" top 2 - 2top "cdot bottom + bottom 2 - slant 2," and "end align"

begin-aligning* x = sqrt((5),2,5,8,and(8),2,-7,2). sqrt = 25 - 80 + 64 - 49; sqrt = 40; sqrt = boxed 2i sqrt 10; end align;

As $sqrt-40$ cannot be further simplified in terms of real numbers, the answer is given in simplified form.

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Answer:

x ≈ 13,6; y ≈ 15,7; z ≈ 26,7

Step-by-step explanation:

I added a photo of my solution

Answer: Answer is below <3

Step-by-step explanation:

The absolute value equations in the form of  |x-b|= c(where b is a number and c can be either a number or an expression) that has the following solution set

all numbers such that x ≤ 5 and all numbers such that x ≥ -1.3 will be x -5 ≤ 0 and x + 1.3 ≥ 0.

Isolate the absolute number on one side of the equation to solve an equation containing the absolute value.

Then, resolve both equations by changing their respective contents to the positive and negative values of the variable on the other side of the equation.

In another word, the absolute value equation is the equation that has a real absolute value not imaginary and not binary.

In the mode function, it could be two values if the mode is going negative or positive.

Given that the equation |x-b| = c and the constraint is

all numbers such that x ≤ 5

all numbers such that x ≥ -1.3

so by substituting we will get x -5 ≤ 0 and x + 1.3 ≥ 0.

The complete question is-

Write the absolute value equations in the form |x-b|=c (where b is a number and c can be either a number or an expression) that has the following solution set

all numbers such that x ≤ 5

all numbers such that x ≥ -1.3

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Answer:

(-infinity, -11) U (-11, 9) U (9, infinity)

Step-by-step explanation:

we have to restrict this so that the denominator isn't 0

to find this, we can factor the denominator to (x+11)(x-9). the zeroes, then, are x=-11 and x=9.

so, the domain must exclude these values, and we get (-infinity, -11) U (-11, 9) U (9, infinity)

Answer: approximately 41.96 yards

Step-by-step explanation:

If a square property contains 1,758.1066 square yards, then the area of the square is equal to this value.

Let x be the length of each side of the square. Then, the area of the square can be expressed as x^2.

So we have:

x^2 = 1,758.1066 sq. yards

Taking the square root of both sides gives:

x = √1,758.1066

x ≈ 41.96 yards

Therefore, each side of the square is approximately 41.96 yards long.

Each side of the square is approximately 41.9143 yards long.

The answer of the given question based on proofing  Circle M and Circle N are similar  the correct option is  (c) Translate the circle M onto point P and dilate the image with scale factor PQ/MN.

A scale factor is a mathematical ratio that describes how the size of an object or a figure changes between two similar shapes. In geometry, two figures are considered similar if they have the same shape, but not necessarily the same size.

The scale factor is defined as ratio of any two corresponding lengths in  two similar figures. It is usually denoted by letter "k", and can be calculated as:

k = length of corresponding side in the larger figure / length of corresponding side in the smaller figure

The correct answer is (c):

Translate the circle M onto point P and dilate the image with scale factor PQ/MN.

To prove that Circle M and Circle P are similar, we need to show that they have the same shape, which means that corresponding angles are congruent and corresponding sides are proportional.

Translation is a transformation that preserves shape, so we can translate Circle M onto Circle P to make them coincide. Then, we can dilate the image with a scale factor that preserves the ratio of the radii of the circles.

The scale factor that preserves the ratio of the radii is PQ/MN, because PQ is the corresponding radius of Circle P, and MN is the corresponding radius of Circle M. Therefore, dilating the image of Circle M with a scale factor of PQ/MN will result in a circle that is similar to Circle P, with corresponding angles congruent and corresponding sides proportional.

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Answer:

c

Step-by-step explanation:

Graph c is the correct solution of the given inequality.

To solve the inequality 11 <= y - 43, we need to isolate y on one side of the inequality.

Adding 43 to both sides, we get:

11 + 43 <= y - 43 + 43

54 <= y.

Draw a number line and mark any relevant points. For example, if the inequality involves x > 3, mark the point 3 on the number line.

Determine if the inequality is "greater than" (>), "less than" (<), "greater than or equal to" (≥), or "less than or equal to" (≤).

For a "greater than" or "greater than or equal to" inequality, shade the line to the right of the relevant point(s) on the number line. For a "less than" or "less than or equal to" inequality, shade the line to the left of the relevant point(s) on the number line.

If the inequality includes "and," place another shade for the second part of the inequality. The solution is where the two shaded regions overlap.

If the inequality includes "or," draw two separate number lines for each part of the inequality and shade the appropriate regions. The solution is the combination of the two separate shaded regions.

Indicate whether the endpoints are included or excluded, using an open circle for excluded endpoints and a closed circle for included endpoints.

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Answer:

Step-by-step explanation:

4 *  7= 28

Answer:

28

Step-by-step explanation:

hope i help u:)

We can conclude after answering the provided question that Therefore, interest after 19 years, the amount in the account will be $1,418.50.

In mathematics, interest is the sum of money earned but rather owed on an initial investment or loan. You can use either simple or compound interest. Rate of return is computed upon that main fee plus any previously earned interest, whilst simple interest is given as a percent of the initial amt. If you invest $100 at a 5% each year simple interest rate, you will earn $5 through interest every year for four years, for a total of $15.

calculating the future value of an investment is:

[tex]FV = PV x (1 + r)^n\\FV = $500 x (1 + 0.08)^19\\FV = $500 x 2.837\\FV = $1,418.50[/tex]

Therefore, after 19 years, the amount in the account will be $1,418.50.

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In the given question angle a= 60° and b= 120° by exterior angle theorem

When a triangle's side is extended to make an angle outside the triangle, the external angles of the triangle are formed. We can use the formula below to determine the size of an external angle:

Sum of Measurements of Distant Interior Angles = Measure of Exterior Angle

The two interior angles that are not directly close to the external angle being measured are known as the remote interior angles. Remote internal angles are angles at vertices A and B if we extend the side AB to generate an exterior angle at vertex C in a triangle with vertices A, B, and C.

Measure of Interior Angle at Vertex A + Measure of Interior Angle at Vertex B = 180 degrees, where Measure of Exterior Angle at Vertex C = 180 degrees.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Question reads..}[/tex]

[tex]\textsf{Last year 525,398 people walked across the Golden Gate Bridge. This year 650,482}\\\textsf{people walked across the Golden Gate Bridge. How many more people walked}\\\textsf{across the Bridge this year as compared to last year?}[/tex]

[tex]\huge\text{Well when we come across..}[/tex]

[tex]> \textsf{When are comparing two (or more numbers), we are either SUBTRACTING or}\\\textsf{ADDING the numbers, it all depends on how you read the word problem. That is}\\\textsf{we have to read the word problem CAREFULLY so we can know what operation }\\\mathsf{(+,-, \div, \times)}\textsf{ we are doing}[/tex]

[tex]\huge\text{If that is the case, we are doing in this}\\\\\huge\text{word problem..}[/tex]
[tex]> \textsf{We are SUBTRACTING because we are COMPARING \underline{CURRENT year}}\\\textsf{with the \underline{PAST year}}}[/tex]

[tex]\huge\text{What should the equation look like right off the}\\\\\huge\text{top of your head?}[/tex]
[tex]\mathsf{650,482 - 525,398}[/tex]

[tex]\huge\text{Just SOLVE it like a regular basic arithmetic}\\\huge\text{equation}[/tex]
[tex]\mathtt{650,482 - 525,398}[/tex]

[tex]\text{Start with the bigger number (650,482) \& go down however many spaces you} \\\text{have for the smaller number (525,398).}[/tex]

[tex]\rightarrow\mathtt{125,084}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathtt{125,084}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

125,084 more people walked across the Bridge this year, compared to last year.

Step-by-step explanation:

To find how many morepeople walked across the bridge in the current year compared to last year, woth the number of this year being larger than last year's, simply subtract the larger number from the smaller number by hand or using a calculator:

650,482 - 525,398= 125,084.

Therefore, 125,084 more people walked across the Bridge this year, compared to last year.

In case you need to do this subtraction by hand, check the attached image to see the process.

Answer:  I just want points

Step-by-step explanation:

This is not understandable math.

Answer:

5x²-6x+1 this is the answer

Answer: THE ANSWER IS 3 BECAUSE I HAD THIS TEST

RATE BRAINLIEST PLEASE

Step-by-step explanation:

The derivative of the function is (5/2)x² - 2, the critical points are [tex](\frac{2\sqrt{5} }{5}, -\frac{8\sqrt{5} }{15}), (-\frac{2\sqrt{5} }{5}, \frac{8\sqrt{5} }{15})[/tex], the points of inflection of the function is at (0,0)

(a) The derivative of f(x) is f'(x) = (5/2)x² - 2.

(b) The critical points occur where f'(x) = 0 or where f'(x) is undefined.

Setting f'(x) = 0, we get (5/2)x² - 2 = 0,

[tex](\frac{2\sqrt{5} }{5}, -\frac{8\sqrt{5} }{15}), (-\frac{2\sqrt{5} }{5}, \frac{8\sqrt{5} }{15}[/tex]

(c) f'(x) = (5/2)x² - 2 is positive when x > (2√5)/5 and negative when x < (-2√5)/5. Therefore, f(x) is increasing on the interval

[tex](-\infty, -\frac{2\sqrt{5} }{5}), (\frac{2\sqrt{5} }{5}, \infty)\\[/tex] and it decreases along the interval of

[tex](-\frac{2\sqrt{5} }{5}, \frac{2\sqrt{5} }{5})[/tex]

(d) The second derivative of f(x) is f''(x) = 5x

(e) f''(x) is positive when x > 0 and negative when x < 0. Therefore, f(x) is concave up on the interval (0, infinity) and concave down on the interval (-infinity, 0).

(f) The points of inflection for f(x) are (0,0)

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The ratio of pack A is 3 : 2 [tex]km^{2}[/tex]  and for pack B is 7 : 5 [tex]km^{2}[/tex] . Pack A has more of mountainous territory.

What is ratio?

One can calculate how much of one quantity is included in the other by comparing two amounts of the same unit and obtaining the ratio.

We are given two packs.

Pack A has a territory of 900 [tex]km^{2}[/tex] and of that 600 [tex]km^{2}[/tex]  are mountainous.

So, the ratio in the simplest form is 3 : 2 [tex]km^{2}[/tex] .

Similarly, Pack B has a territory of 700 [tex]km^{2}[/tex]  with 500 [tex]km^{2}[/tex]  being mountainous.

So, the ratio in the simplest form is 7 : 5 [tex]km^{2}[/tex] .

On comparing the ratios, we get that Pack A has more of mountainous territory than Pack B.

Hence, both territories do not have the same ratio of mountains to the total range.

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The value of the given relation of the parallelogram to justified the relation of the given part is x = 7, y = 9 and z = 17.

What about the property of parallelogram?

A parallelogram is a four-sided flat shape that has two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are also equal. The parallel sides of a parallelogram are usually denoted by "a" and "b", while the height or perpendicular distance between the parallel sides is denoted by "h"

Define relation:

A relation is a set of ordered pairs that describe the relationship between two or more variables. Specifically, a relation is a set of ordered pairs (x, y) where x and y belong to some sets of objects, called the domain and range, respectively.

For example, consider the relation R between the set of all real numbers and itself defined by:

R = {(x, y) | y = x²}

This relation is a set of ordered pairs where the second element (y) is equal to the square of the first element (x). In this case, the domain and range of the relation R are both the set of all real numbers.

According to the given information:

As, we know opposite side of parallelogram are equal so,

10x + 14  = x + 77

9x = 63

x = 7

In the same way we also know that in case of parallelogram diagonal bisect equally to each other so,

4y-19 = y + 8

3y = 8 + 19

y = 9

And,

2z + 3 = 37

2z = 34

z  = 17

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The option 2 is correct of given question ''All the powers have a value of 1 because the exponent is zero.''

An exponent is a mathematical notation that indicates the number of times a quantity is multiplied by itself. It is written as a superscript number to the right of the quantity being multiplied.

For example, in the expression 5³, 5 is the base and 3 is the exponent. This means that 5 is being multiplied by itself three times: 5 x 5 x 5, which equals 125.

The statement "All the powers have a value of 1 because the exponent is zero" describes what these four powers have in common.

When the exponent is zero, any number (except for 0) raised to the power of 0 equals 1. Therefore, 10⁰  = 1, (-2)⁰ = 1, and any non-zero number raised to the power of 0 equals 1.

There is no fractional value involved in this case, as raising a number to the power of zero does not involve any division.

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Complete question:

Answer: Option C = 5x^2 + 12x - 7

Step-by-step explanation: First, we need to combine like terms.

-2x^2 + 8x - 9 + 4x + 7x^2 + 2 = (7x^2 - 2x^2) + (4x + 8x) + (-9 + 2) = 5x^2 + 12x - 7

So the expression is equivalent to option C, which is 5x^2 + 12x - 7.

Answer:

ITS THE FIRST ONE

Step-by-step explanation:

-2X2+8

HOPE THIS HELPS

So ΔOAP≅ΔOBQ(by AAS) so OA ≅ OB(CPCTC) and PO ≅ OQ(CPCTC)

The AAS theorem, also known as the angle-angle-side theorem, is a theorem in Euclidean geometry that states: "If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent."

Given that,

AP ≅ BQ

AP ⊥ AB and BQ ⊥ AB

so ∠A = 90° and ∠B = 90°

To prove that

AO ≅ BO and PO ≅ OQ

In ΔOAP AND ΔOBQ

AB ≅ BQ (given)

∠A = ∠B = 90°

∠AOP = ∠BOQ (vertically opposite angle theorem)

Therefore,Δ OAP ≅ Δ OBQ

∴ OA ≅ OB (CPCT)

PO ≅ OQ (CPCT)

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Answer: 2 7/8 = 23/8

Step-by-step explanation:

1/8+1/8 = 2/8 = 1/4  (add w/ other 3) (This is not added to the final equation since added at the one below this)

1/4+1/4+1/4+1/4=1

3/8+3/8+3/8= 9/8 = 1 1/8

3/4 = 6/8

Add them

1 + 1 1/8 + 6/8 = 2 7/8

Answer:

120 ft / sec

Step-by-step explanation:

to know how many yards in 1 sec

120 yd ÷3 = 40 yd

so 40 yd/sec

to make them in feet per sec

1 yd= 3 ft

40 yd ×3 ft = 120 ft

so, 120 ft/sec

the value οf f(h(-1)) will be ∛2.

A unique kind οf relatiοn called a functiοn is οne in which each input has precisely οne οutput. In οther wοrds, the functiοn prοduces exactly οne value fοr each input value. The graphic abοve shοws a relatiοn rather than a functiοn because οne is mapped tο twο different values. The relatiοn abοve wοuld turn intο a functiοn, thοugh, if οne were instead mapped tο a single value. Additiοnally, οutput values can be equal tο input values.

The x-values are input intο the functiοn machine. The functiοn machine then perfοrms its οperatiοns and οutputs the y-values. The functiοn within can be any functiοn.

f(x) = ∛x+3

g(x)= 8x³-3

h(x)= 2x+1

f((h(-1))= f(-1) = ∛2

Hence the value οf f(h(-1)) will be ∛2.

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The area of the segment formed by a side of the hexagon and the circle is (3π - 9 √(3)) / 4 square inches.

A regular hexagon ABCDEF inscribed in a circle with center O. Let's consider the segment bounded by side AB and the arc ACB. We want to find the area of this segment.

First, find the central angle of the sector AOC. Since the hexagon is regular, the central angle of each sector is 60 degrees. Therefore, the central angle of AOC is 120 degrees.

Next, find the area of sector AOC by using the formula for the area of a sector:

Area of sector AOC = (central angle / 360) × π × radius²

= (120 / 360) × π × (3 / 2)²

= (1 / 3) × π × 9 / 4

= (3 / 4) × π

Now, find the area of triangle AOB. Since the hexagon is regular, triangle AOB is equilateral with side length 3". Therefore, use the formula for the area of an equilateral triangle:

Area of triangle AOB = (1 / 4) × (3)² × √(3)

= (9 / 4) × √(3)

Finally, find the area of the segment by subtracting the area of triangle AOB from the area of sector AOC:

Area of segment AB = Area of sector AOC - Area of triangle AOB

= (3 / 4) × π - (9 / 4) × √(3)

= (3 π - 9 √(3)) / 4

Therefore, the area of the segment formed by side AB and the circle is (3 π - 9 × √(3)) / 4 square inches.

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The answer would be 228.295489891

Rounded to the nearest tenth it would 228.3

The diagonal of the Rhombus intersect at point M and thus, m<IMJ is 90 degrees

It is important to note the properties of a Rhombus, they are;

From the diagram shown, we can see that the diagonals are;

Diagonal 1: JL

Diagonal 2: IK

These diagonals intersect at point M and since diagonals in a Rhombus intersect at right angles, that is , 90 degrees.

Then, m< IMJ is 90 degrees

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The final price Carson paid was $75.99.

The original cost of the item is $149.

Carson bought the item for 40% off the original price, which means he paid:

$149 x 0.6 = $89.40

Carson paid only $89.40 after he got a 40% discount.

Now, Carson receives an additional discount of 15% off the discounted price. This means he pays:

$89.40 x 0.85 = $75.99

After getting an additional discount of 15% Carson paid $75.99 only.

Therefore, Carson's final sale price for the item was $75.99 after getting 40% and additional 15% discount.

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