A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum height of 16 mm halfway across a horizontal distance of 80 mm.

Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)

Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)

Answer:   x = 2

Work Shown:

x+5 = 7

x+5-5 = 7-5

x = 2

Subtract 5 from both sides to isolate x. This is to undo the plus 5.

Answer: 5

Step-by-step explanation:

[tex]\sqrt{(5-2)^2 +(-2-2)^2}=5[/tex]

Answer:225 jeans.

Step-by-step explanation: What we need to do here is convert the number of jeans to a percentage. There were 25 jeans when 50 customers were surveyed and 25 is half of 50 or 50%. This means that if 450 pairs of pants are ordered half of them should be jeans. 450/2 = 225.

Answer:

a = 3

b = -9

c = -3

d = 22

e = 49 - 9

f = a^2 -3

Step-by-step explanation:

Please no more questions :(

Answer:

x > -10

Step-by-step explanation:

2 + x > -8

x > -8 - 2

x > -10

Answer:

x>-10

Step-by-step explanation:

2+x-2>-8-2

x>-10

Step-by-step explanation:

if we are taking in terms of domain.. is d set of number that we can put to the function with get division by zero .. squaroot of negative number,log of zero e.t.c

A) p(x)/m(x)= 1/squaroot(x) ÷ x²-4 which we know that x²-4 must not be equal to zero

because if is equal to zero we will have division by zero, which have contradicted the hypothesis of law of domain

x²-4 =! 0

(x-2)(x+2)=!0

x=!2 or x=!-2 because if is equal to that it's has contradicted d hypothesis

the answer is all real number except -2 and -

2

B)p(m(x))=p(x²-4) =1/squaroot of x²-4

note they are two things involve we must not get division by zero and root of negative number

we have all real number expect from -2 to 2

C)m(p(x))=m(1/root of (x))=(1/root of (x))²_4)

we have 1/x-4

so the answer is all real number expect zero

Answer:

31

Step-by-step explanation:

The numbers in the sequence increase by (n+1)^2. So the sequence is (1, 1+1^2 (which is 2), 2+2^2 , 6+3^2, 15+4^2, 31+5^2, 56+6^2) and the fifth term of that sequence is 15+4^2, which is 31

The unknown number(x) in the series is 31.

The given series 1, 2, 6, 15, x, 56, 92.

We need to find the value of x.

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, and mathematical analysis.

The numbers in the series increase by (n+1)².

So the sequence is 1, 1+1² (which is 2), 2+2², 6+3², 15+4², 31+5², 56+6² and the fifth term of that sequence is x=15+4²=31.

Therefore, the unknown number(x) in the series is 31.

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Answer:

the answer is 2880

Step-by-step explanation:

because you would use the formula (n - 2) x 180 which equals the sum interior angles of any polygon .

The letter n stands for number of sides so in this case you would do (18 - 2) x 180 so 16 × 180 = 2880

hope this helped :) pls ask if you need any more explanation .

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Answer: C

Step-by-step explanation:

The line [tex]y=x+2[/tex] is shaded below and is solid.

This eliminates all the options except for C.

The insinuation of calling the volume of a solid 3-dimentional shape 10in³ is that the product of all of its dimensions as measured in units is; 10 in.³.

It follows from the task content that the shape in discuss is a solid shape and consequently, one of it's measures is its volume which describes the space it occupies.

On this note, the meaning of a solid having a volume of 10in³ as indicated is that it's volume is; 10 times as large as the volume occupied by an object with unit dimensions 1“ x 1“ x 1“ in which case, the volume is; 1 in³.

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No graph for the polar equation because here sin 0 is 0.

According to the statement

we have given that a polar equation and we have to represent in the graph.

So, For this purpose, we know that the

The expression of a point as an ordered pair. is known as polar notation, the equation of a curve expressed in polar coordinates is known as a polar equation.

The given polar equation is

r = 1-3 sin 0

here the value of r is 0.

so, No graph is possible for the given statement

because here the value of r is 0 and for zero value there is a no graph possible.

So, No graph for the polar equation because here sin 0 is 0.

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Answer: Moderate negative association

Step-by-step explanation:

A quadrilateral PQRS is a parallelogram. PQ and RS are opposite sides then the answer of this particular question is , x = 4, the parallelogram PQRS is a rhombus, QR = 31, The opposite angles are congruent. Thus, more than one answer is correct.

According to the question,

PQ = 7x+12; RS = 5x -20 and QR = 31

Solving PQ and RS we get x = 4. Thus, PQ = 40 and RS = 40.

A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and congruent.  A quadrilateral that has all sides equal and opposite sides parallel is called Rhombus.

Thus, the parallelogram PQRS is a rhombus.

Hence,  a quadrilateral PQRS is a parallelogram. PQ and RS are opposite sides then the answer of this particular question is , x = 4, the parallelogram PQRS is a rhombus, QR = 31, The opposite angles are congruent. Thus, more than one answer is correct.

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The function that could be represented by Rebecca’s graph is f(x) =-2(5/4)^x+3

The properties are given as:

For an exponential function to keep decreasing, one or more the following must be true:

For the left end of an exponential function to approach a constant, the following must be true:

The equation that has the above properties is f(x) =-2(5/4)^x+3

Hence, the function that could be represented by Rebecca’s graph is f(x) =-2(5/4)^x+3

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Answer:

-2n -32

Step-by-step explanation:

Acc. to BODMAS

we multiply first

⇒-6n - -8 x [(+4) (n)]

⇒ 6n  - 8n x -32

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

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{6n - 8(n + 4)}[/tex]

[tex]\huge\textbf{Solve: }[/tex]

[tex]\mathsf{6n - 8(n + 4)}[/tex]

[tex]\huge\textbf{Distribute \boxed{\bf -8} within the parenthesis:}[/tex]

[tex]\mathsf{= 6n - 8(n) - 8(4)}[/tex]

[tex]\mathsf{= 6n - 8n - 32}[/tex]

[tex]\huge\textbf{Combine the like terms: }[/tex]

[tex]\mathsf{= (6n - 8n) - (32)}[/tex]

[tex]\mathsf{= 6n - 8n - 32}[/tex]

[tex]\mathsf{= -2n - 32}[/tex]

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

[tex]\huge\boxed{\frak{{ -2n - 32}}}\huge\checkmark[/tex]

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

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

Considerando la definición de triángulo rectángulo y sus propiedades, el valor del ángulo que falta de un triángulo rectángulo es 65°.

Un triángulo es un polígono conformado por tres lados, así como por tres vértices y tres ángulos interiores.

Una de las propiedades de cualquier triángulo indica que la suma de los ángulos interiores es igual a 180°.

El triángulo rectángulo es una figura geométrica que se considera como un polígono formado por tres lados que forman un ángulo interior recto (es decir, mide 90°) y dos ángulos interiores agudos.

En este caso, sabes que:

Entonces, el valor del ángulo faltante se puede calcular mediante:

90° + 25° + ángulo faltante= 180°

Resolviendo:

115° + ángulo faltante= 180°

ángulo faltante= 180° - 115°

ángulo faltante= 65°

Finalmente, el valor del ángulo que falta de un triángulo rectángulo es 65°.

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[tex]\stackrel{\textit{\LARGE Line A}}{(\stackrel{x_1}{-8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{4})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{(-8)}}} \implies \cfrac{4 -5}{-5 +8}\implies -\cfrac{1}{3} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\LARGE Line B}}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1})} ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{-1 -1}{4 +0}\implies -\cfrac{1}{2}[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes, and that parallel lines have equal slopes, well, those two slopes above aren't either, so since they're neither, and they're different, that means that lines A and B intersect.

Answer:

.8849   or   88.49% have score ess than 123

Step-by-step explanation:

Answer:

88.49 %  have less than 123   (or .8849)

Step-by-step explanation:

123 is    18/15 = 1.2   S.D. ABOVE the mean    z-score +1.2

   from z- score table    +1.2    this is .8849   or 88.49 %

Answer:

t = 1.75(s)

Step-by-step explanation:

I gotchu

Answer:

x = 1/3

Step-by-step explanation:

1/2 + X = 5/6

collecting the like terms

X = 5/6 - 1/2

making one fraction on the left side by taking the common denominator

X = (5 - 3)/6

X = 2/6

devide the numerator and denominator by 2, you get

X = 1/3

Answer:

Area = 33 inches squared

Step-by-step explanation:

The formula for the area of a kite is:

Area = ½ × (d)1 × (d)2

To find the first diagonal (d1):

d1 = 7 in + 4 in = 11 in

To find the second diagonal (d2):

The triangles on the right of the kite must be 3 4 5 triangle since it is a right triangle with a hypotenuse of 5 and a side of 4, we know half of a diagonal would be 3 inches.

d2 = 3 in + 3 in = 6 in

Now we can plug the diagonals into the area formula.

Area = ½ × 11 × 6 = 33 inches squared

Answer: A = 33 in²

Step-by-step explanation:

Given information:

Longer side = 7 in

Shorter side = 4 in

Shorter Hypotenuse = 5 in

Given formula:

A = (1/2) × (d₁) × (d₂)

Please refer to the attachment below for a graphical understanding

Determine the length of the shorter side (vertical) through the Pythagorean theorem

a² + b² = c² (Pythagorean theorem)

(4)² + b² = (5)² (Substitute values into the equation)

16 + b² = 25

b² = 25 - 16

b² = 9

b = 3  or b = -3 (rej)

Substitute values into the given formula

A = (1/2) × d₁ × d₂

A = (1/2) × (7 + 4) × (3 + 3)

Simplify values in the parenthesis

A = (1/2) × 11 × 6

Simplify by multiplication

A = (11/2) × 6

[tex]\Large\boxed{A=33}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

All real numbers greater than or equal to 5

Step-by-step explanation:

The range of y=|x| is all real numbers greater than or equal to 0. Adding 5 to this makes the range all real numbers greater than or equal to 5.

Trigonometry functions are functions that relate two sides of a given triangle with one of its included angles.

The expression that shows the distance that he walked = x + y + 100

                                                                 = 87 + 50 + 100

                                                                 = 237 yards

Trigonometry functions are functions that relate two sides of a given triangle with one of its included angles. The required function may be a sine function, a cosine function, or a tangent function.

Such that;

The given question can be solved by applying the appropriate trigonometric function.

So that to determine the value of x, we have:

Cos θ = [tex]\frac{Adjacent}{Hypotenuse}[/tex]

Cos 30 = [tex]\frac{x}{100}[/tex]

⇒ x = 100 cos 30

      = 100 x 0.866

x = 86.60

Thus, the start of the sidewalk is approximately 87 yards.

To determine the value of sidewalk y, we have:

Sin θ = [tex]\frac{Opposite}{Hypotenuse}[/tex]

Sin 30 = [tex]\frac{y}{100}[/tex]

⇒ y = 100 x Sin 30

      = 100 x 0.5

   y = 50

Thus the sidewalk which represents the end of the path is 50 yards.

Therefore, the total distance that he walked = 100 + 87 + 50

                                                                 = 237 yards

The expression that shows the distance that he walked = x + y + 100

                                                                 = 87 + 50 + 100

                                                                 = 237 yards

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Answer:

  2800

Step-by-step explanation:

The choice at any node (except the edges) is to go right or go down.

To get from A to B requires a total of 4 choices to go down, and 4 choices to go right. Those can occur in any order. Locating the "right" choices in the list of "all" choices is effectively choosing 4 of 8. The number of ways those choices can be made is ...

  C(8, 4) = 8!/(4!(8-4)!) = 8·7·6·5/(4·3·2) = 70

Similarly a total of 2 choices must be made, 1 of which is a "right" choice. The number of ways those can be ordered is ...

  C(2, 1) = 2 . . . . . . . that is: (right, down) or (down, right)

A total of 6 choices must be made, of which 3 are "right." The number of possible orderings is ...

  C(6, 3) = 6·5·4/(3·2·1) = 20

Each set of choices is independent of the others, so the total possible number is the product of the numbers of choices on the subpaths:

  total paths = (70)(2)(20) = 2800

There are 2800 possible paths from A to D.

Answer:

54°

Step-by-step explanation:

Opposite angles of a parallelogram are congruent, so;

[tex]9x+9=8x+14 \\ \\ x=5 \\ \\ m\angle S=9(5)+9=54^{\circ}[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

In a Parallelogram, opposite angles are equal, so we infer that :

[tex] \qquad❖ \: \sf \:9x + 9 = 8x + 14 [/tex]

[tex] \qquad❖ \: \sf \:9x - 8x = 14 - 9[/tex]

[tex] \qquad❖ \: \sf \:x = 5 \degree[/tex]

Next,

Measure of Angle S is :

[tex] \qquad❖ \: \sf \:9x + 9[/tex]

[tex] \qquad❖ \: \sf \:9(5) + 9[/tex]

[tex] \qquad❖ \: \sf \:45 + 9[/tex]

[tex] \qquad❖ \: \sf \:54 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]x > \ln(x)[/tex] for all [tex]x[/tex], so

[tex]\displaystyle \lim_{x\to\infty} (\ln(x) - x) = - \lim_{x\to\infty} x = \boxed{-\infty}[/tex]

Similarly, [tex]\displaystyle \lim_{x\to\infty} (x-e^x) = - \lim_{x\to\infty} e^x = \boxed{-\infty}[/tex]

We can of course see the limits are identical by replacing [tex]x\mapsto e^x[/tex], so that

[tex]\displaystyle \lim_{x\to\infty} (\ln(x) - x) = \lim_{x\to\infty} (\ln(e^x) - e^x) = \lim_{x\to\infty} (x - e^x)[/tex]

You can also rewrite the limands to accommodate the application of l'Hôpital's rule. For instance,

[tex]\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\exp\left(\lim_{x\to\infty} (x - e^x)\right)\right) = \ln\left(\lim_{x\to\infty} e^{x-e^x}\right) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right)[/tex]

Using the rule, the limit here is

[tex]\displaystyle \lim_{x\to\infty} \frac{(e^x)'}{\left(e^{e^x}\right)'} = \lim_{x\to\infty} \frac{e^x}{e^x e^{e^x}} = \lim_{x\to\infty} \frac1{e^{e^x}} = 0[/tex]

so the overall limit is

[tex]\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right) = \ln(0) = \lim_{x\to0^+} \ln(x) = -\infty[/tex]

Step-by-step explanation:

Here! ●□●□●□●□● THIS IS THE ANSWER BRO

Answer:

A

Step-by-step explanation:

First we need to solve the inequality: -3b-15>-24

-3b-15>-24

-3b>-9

b<3 (we divided by a negative so we flip the sign)

This means that we have an empty circle and the arrow pointing left

[tex]\boldsymbol{\sf{-3b-15 > -24 }}[/tex]

Add 15 to both sides.

      [tex]\boldsymbol{\sf{-3b > -24+15 \ \longmapsto \ \ \ [Add \ -24+15] }}[/tex]

               [tex]\boldsymbol{\sf{ -3b > -9}}[/tex]

Divide both sides by −3. Since −3 is < 0, the inequality direction is changed.

               [tex]\boldsymbol{\sf{b < \dfrac{-9}{-3} \ \ \longmapsto \ \ [Split] }}[/tex]

                    [tex]\red{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ \ b < 3}}}}[/tex]

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