The main cable of a suspension bridge forms a
parabola, described by the equation
y = a(x - h)2 + k.
0
27
52.5 105
127
157.6
12
210
27
y = height in feet of the cable above the roadway
x = horizontal distance in feet from the left bridge
support
a = a constant
(h, k) = vertex of the parbola
What is the vertex of the parbola?
DONE

Answer:

Part 1) [tex](x+4)(x-1)(x-2)(x-4)[/tex]

The related polynomial equation has a total of four roots, all four roots are real

Part 2) [tex](x+1)(x-1)(x+2)^{2}[/tex]

The related polynomial equation has a total of four roots, all four roots are real and one root has a multiplicity of 2

Part 3) [tex](x+3)(x-4)(x-(2-i))(x+(2-i))[/tex]

The related polynomial equation has a total of four roots, two roots are complex and two roots are real

Part 4) [tex](x+i)(x-i)(x+2)^{2}[/tex]

The related polynomial equation has a total of four roots, two roots are complex and one root is real  with a a multiplicity of 2

Step-by-step explanation:

we know that

The Fundamental Theorem of Algebra  states that:  Any polynomial of degree n has n roots

so

Part 1) we have

[tex](x+4)(x-1)(x-2)(x-4)[/tex]

The roots of this polynomial are

x=-4, x=1,x=2,x=4

therefore

The related polynomial equation has a total of four roots, all four roots are real

Part 2) we have

[tex](x+1)(x-1)(x+2)^{2}[/tex]

The roots of this polynomial are

x=-1, x=1,x=-2,x=-2

therefore    

The related polynomial equation has a total of four roots, all four roots are real and one root has a multiplicity of 2

Part 3) we have

[tex](x+3)(x-4)(x-(2-i))(x+(2-i))[/tex]

The roots of this polynomial are

x=-3, x=4,x=(2-i),x=-(2-i)

therefore    

The related polynomial equation has a total of four roots, two roots are complex and two roots are real

Part 4) we have

[tex](x+i)(x-i)(x+2)^{2}[/tex]

The roots of this polynomial are

x=-i, x=i,x=-2,x=-2

therefore    

The related polynomial equation has a total of four roots, two roots are complex and one root is real  with a a multiplicity of 2

Answer:

Mean Absolute Deviation = 3.

Step-by-step explanation:

The mean = (2 + 9 + 1 + 7 + 8 + 9) / 6

= 36/6

= 6.

Subtract  6 from each  number:

2 - 6 = -4 Absolute value = 4

9 - 6 = 3

1 - 6 = -5 Absolute value = 5

7 - 6 = 1

8 - 6 = 2

9 - 6 = 3

Total = 4 + 3 + 5 + 1 + 2 + 3 = 18

Mean Absolute Deviation = 18 / 6 = 3.

Answer:

B: 3

Step-by-step explanation:

First you will take the numbers and add them. The equation would be 2 + 9 + 1 + 7 + 8 + 9. That equals 36.

Then, you may divide that by 6 (how many numbers there were) and that is your mean (also 6).

Next, you find the how far each number is from the mean using absolutes. Those values are 4, 3, 5, 1, 2, and 3.

Finally, add those together to get 18, then divide by how many numbers there were (6) that to get the mean absolute deviation (3).

Hope this helped! :)

Answer:

The price of 4 apples is Rs 28

Step-by-step explanation:

The price of 1 dozen apple is Rs 84

12 apples =Rs 84

1 apple = Rs 84÷12

1apple =Rs 7

Again

Price of 4 apples = Rs 7 × 4

= Rs 28 Ans,,

Final answer:

The Pythagorean theorem relates the lengths of the legs and hypotenuse of a right triangle. By substituting the given values into the equation, we can solve for x using the theorem. The rounded value of x is 3.6 (B).

Explanation:

The Pythagorean theorem relates the length of the legs of a right triangle, labeled a and b, with the hypotenuse, labeled c. The relationship is given by: a² + b² = c². This can be rewritten, solving for c: c = √(a² + b²).

In this case, we want to find the value of x using the Pythagorean theorem. Let's say that the lengths of the legs are 3 and x. Substituting these values into the theorem, we have:

3² + x² = c²

Now, we can solve for x by rearranging the equation:

x² = c² - 3²

x = √(c² - 3²)

Rounding to the nearest tenth, we can find the value of x to be approximately 3.6 (B).

Final answer:

The Pythagorean theorem allows us to calculate the length of the hypotenuse of a right triangle by squaring the lengths of the other two sides, adding them together, and then taking the square root. To round to the nearest tenth, we calculate and then round the final result accordingly.

Explanation:

To use the Pythagorean theorem to find x and round to the nearest tenth, we need to establish the components of the equation. The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is written as a² + b² = c².

However, the problem provided does not include the initial lengths to insert into the equation; hence, we cannot compute the value directly. Nonetheless, I can illustrate with a hypothetical example:

If we have a right triangle with legs of lengths 9 (a) and 6 (b), then the hypotenuse (c) can be found as follows:

c = √(9² + 6²)
c = √(81 + 36)
c = √117
c = 10.82, round off to the nearest tenth would be c = 10.8

In this example, we squared the lengths of the legs, added them together, and took the square root of the result to find the hypotenuse to the nearest tenth. The same steps apply to any right-angled triangle where you are given the lengths of the legs and need to find the hypotenuse using the Pythagorean theorem.

Answer:

D. X+5y=7

passes through both coordinates

Answer:

all work is shown and pictured

Answer:

The answer would be option B and option C

∠DEF and ∠FED describe an angle with a vertex at E.

The correct answers are option (B) and option (C)

For given question,

We need to find the correct angle with a vertex at E.

We know that the vertex is the common point of the rays of an angle.

It is always written at the middle in an angle.

So, ∠DEF and ∠FED describe an angle with a vertex at E.

The correct answers are option (B) and option (C)

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(9x^2 + 8x) – (2x^2 + 3x)

Subtract like terms:

9x^2 - 2x^2 = 7x^2

8x - 3x = 5x

The difference is 7x^2 + 5x

Answer:

[tex]x=\frac{10}{13}[/tex] and [tex]y=-\frac{24}{13}[/tex]

Step-by-step explanation:

The given complex number equation is:

[tex]\frac{1-2i}{2+i}+\frac{4-i}{3+2i}=x+yi[/tex]

We simplify the LHS and compare with the RHS

We collect LCD on the left to get:

[tex]\frac{(1-2i)(3+2i)+(4-i)(2+i)}{(2+i)(3+2i)}=x+yi[/tex]

[tex]\frac{3+2i-6i+4+8+4i-2i+1}{6+4i+3i-2}=x+yi[/tex]

Simplify to get:

[tex]\frac{16-2i}{4+7i}=x+yi[/tex]

Rationalize the LHS:

[tex]\frac{(16-2i)(4-7i)}{(4+7i)(4-7i)}=x+yi[/tex]

Expand the numerator using the distributive property and the denominator using difference  of two squares.

[tex]\frac{64-112i-8i-14}{16+49}=x+yi[/tex]

Simplify to get:

[tex]\frac{50-120i}{65}=x+yi[/tex]

[tex]\frac{10-24i}{13}=x+yi[/tex]

[tex]\frac{10}{13}-\frac{24}{13}i=x+yi[/tex]

By comparing real parts and imaginary parts; we have;

[tex]x=\frac{10}{13}[/tex] and [tex]y=-\frac{24}{13}[/tex]

Answer:

101

Step-by-step explanation:

The theorem to use this is the intercepted arc theorem, which tells us that if we take 2 points on the circumference of a circle and create an angle in the opposite side of the circumference, that angle is HALF that of the ARC intercepted.

If we look at 100 degree angle, we see the ARC intercepted is 99 degree and a degrees. According to theorem, we can say:

99 + a = 2(100)

99 + a = 200

a = 200 - 99

a = 101

Answer:

* cos 211.7 not equal the other values

Step-by-step explanation:

* Lets revise the angles in the four quadrant

- If the angle in the first quadrant is Ф, then the equivalent angles to

 it in the other three quadrant are

# 180° - Ф ⇒ 2nd quadrant (sin only +ve)

# 180° + Ф ⇒ 3rd quadrant (tan only +ve)

# 360° - Ф ⇒ 4th quadrant (cos only +ve)

# -Ф ⇒ 4th quadrant (cos only +ve)

# -180 + Ф ⇒ 3rd quadrant (tan only +ve)

# -180 - Ф ⇒ 2nd quadrant (sin only +ve)

# -360 + Ф ⇒ 1st quadrant (all are +ve)

* Lets solve the problem

∵ Ф = 31.7°

∵ cos 31.7 = +ve value

∵ 180° + Ф° = 180° + 31.7° = 211.7°

∵ cos (180° + Ф°) = - cos Ф° ⇒ cos (180° + Ф°) in the 3rd quadrant is

  same value as cos Ф but with -ve sign

∴ cos 211.7° = - cos 31.7°

∴ cos 31.7° ≠ cos 211.7°

∵ 360° - Ф° = 360° - 31.7° = 328.3°

∵ cos (360° - Ф°) = cos Ф° ⇒ cos (360° - Ф°) in the 4th quadrant has the

  same value and sign with cos Ф°

∴ cos 328.3° = cos 31.7°

∴ cos 31.7° = cos 328.3°

∵ -391.7° + 360° = -31.7° ⇒ more then clockwise turn by 31.7°

∵ cos (-Ф°) = cos Ф° ⇒ cos (-Ф°) in the 4th quadrant has the same value

  and sign with cos Ф°

∴ cos (-31.7°) = cos 31.7°

∴ cos 31.7° = cos (-390.7°)

* cos 211.7 not equal the other values

Answer:

-33 or 33

Step-by-step explanation:

The seventh term of an AP is written as:

[tex]a + 6d[/tex]

The eleventh term of an AP is written as:

[tex]a + 10d[/tex]

If the 7th term is 11 times the 11th term, then;

[tex]a + 6d = 11(a + 10d)[/tex]

Expand to get:

[tex]a + 6d = 11a + 110d[/tex]

[tex]11a - a = 6d - 110d[/tex]

[tex]10a = - 104d[/tex]

[tex] \frac{a}{d} = - \frac{104}{10} [/tex]

[tex] \frac{a}{d} = - \frac{52}{5} [/tex]

We must have a=-52 and d=5

Or

a=52 and d=-5

For the first case, the 18th term is :

[tex] - 52 + 5 \times 17 = 33[/tex]

For the second case,

[tex]52 - 5 \times17 = - 33[/tex]

so shes 72 i think

hope i'm right

Answer: 58 would be my guess, but need more info

have you finished this yet? im doing it rn and i need help on some of them. if you havent i can help you with a couple answers

Answer:

[tex]\$420.43[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=7.5\ years\\ P=\$300\\ r=0.045[/tex]  

substitute in the formula above  

[tex]A=300(e)^{0.045*7.5}[/tex]  

[tex]A=\$420.43[/tex]  

Final answer:

To identify which function the graph represents, analyze the shape and pattern of the graph. The correct function could either be a polynomial such as y = x^4, which has a sharply rising curve, or a logarithmic function with a declining curve due to having a base between 0 and 1, like y = log(1/4)x, but not y = log1x as this is not mathematically valid.

Explanation:

The question requires the identification of a function based on its graph. Since the properties of functions are known, such as the logarithmic function increasing as x increases, and the behavior of exponential functions and their inverses, we can analyze the options given. The function y = log1x is not valid as the base of a logarithm cannot be 1. The function y = x4 is a polynomial function with a graph that rises sharply for positive and negative values of x. Lastly, y = log(1/4)x represents a logarithmic function with base 1/4, which is a declining curve because the base is between 0 and 1.

To choose the correct function that a graph represents, one should look for key characteristics such as the shape of the graph, increase or decrease pattern, as well as specific points like asymptotes or intercepts. If the graph is increasing as x increases and resembles a typical logarithmic curve, the correct choice is a logarithmic function. If the given graph is a sharp rising curve for all x-values and looks like a polynomial, then y = x4 would be correct. The given functions need to be analyzed based on their mathematical properties to select the one that best describes the graph in question.

Answer:

Step-by-step explanation:

[tex]16=2^4\\\\8=2^3\\\\16^{2n-3}=8^{4n}\\\\(2^4)^{2n-3}=(2^3)^{4n}\qquad\txt{use}\ (a^n)^m=a^{nm}\\\\2^{(4)(2n-3)}=2^{(3)(4n)}\iff4(2n-3)=12n\qquad\text{use the distributive property}\\\\(4)(2n)+(4)(-3)=12n\\\\8n-12=12n\qquad\text{subtract}\ 8n\ \text{from both sides}\\\\-12=4n\qquad\text{divide both sides by 4}\\\\\dfrac{-12}{4}=\dfrac{4n}{4}\\\\-3=n\to n=-3[/tex]

Answer:

C 8

Step-by-step explanation:

The average rate of change is given by

f(x2) -f(x1)

---------------

x2-x1

x2 = -3  and x1 = -5

Looking at the graph

f(x2) = f(-3) = 1

f(x1)= f(-5) =-15

Substituting these values into the equation

1 - (-15)

---------------

-3 - (-5)

1+15

----------

-3 +5

16

----

2

8

Answer: OPTION C.

Step-by-step explanation:

You need to use this formula:

[tex]averate\ rate\ of\ change=\frac{f(b)-f(a)}{b-a}[/tex]

Knowing that we need to find the average rate of change for the given quadratic function, for the interval from [tex]x=-5[/tex] to [tex]x=-3[/tex], we need to find their corresponding y-coordinates.

We can observe in the graph that:

For [tex]x=b=-5[/tex] →  [tex]y=f(b)=-15[/tex]

For [tex]x=a=-3[/tex] → [tex]y=f(a)=1[/tex]

Therefore, substitituting, we get:

 [tex]averate\ rate\ of\ change=\frac{-15-1}{-5-(-3)}=8[/tex]

Answer:

(f-g)(x) = 4x - x^(-5)

Step-by-step explanation:

Please, enclose that negative exponent inside parentheses:  g(x)=x^(-5).  No need to type in the " + " in f(x)=4x^+1.

g(x) is to be subtracted from f(x).  Write f(x):

f(x)=4x

followed by the negative of g(x):  -g(x) = -x^(-5)

and now combine these two results:

 f(x)=4x

-g(x)= -x^(-5)

---------------------

(f-g)(x) = 4x - x^(-5)

The expression for (f-g)(x) is (f-g)(x) = 4x² + 1 - 1/x⁵

A function is a mathematical formula that describes how the dependent variable and independent variable are related. The dependent variable's value varies in the function together with the independent variable's value.

To find (f-g)(x), we need to subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x)

We are given:

f(x) = 4x² + 1

g(x) = x⁻⁵ = 1/x⁵

Substituting these values into the expression for (f-g)(x), we get:

(f-g)(x) = f(x) - g(x) = (4x² + 1) - (1/x⁵)

Simplifying the expression, we can write:

(f-g)(x) = 4x^2 + 1 - 1/x⁵

Therefore, the expression for (f-g)(x) is:

(f-g)(x) = 4x² + 1 - 1/x⁵

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Answer:

A strong positive correlation

Step-by-step explanation:

A strong correlation when the correlation coefficient is close to 1 or -1. If the correlation coefficient is close to positive 1, then it is a positive strong correlation coefficient. If the correlation coefficient is close to negative 1, then it is a negative strong correlation coefficient.

Answer:

The r-value indicate A strong positive correlation

Step-by -step-explanation:

The following information should be considered:

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Answer:

[tex]\large\boxed{A\ \cup\ B=[-5,\ 10]}[/tex]

Step-by-step explanation:

Look at the picture.

The union of two sets A and B (A ∪ B) is the set of elements which are in A, in B, or in both A and B

Answer: The crop yield increased by 9 pounds per acre from year 1 to year 10.

Step-by-step explanation:

To solve this we are using the average rate of change formula: Av=\frac{f(x_2)-f(x_1)}{x_2-x_1}, where:

x_2 is the second point in the function

x_1 is the first point in the function

f(x_2) is the function evaluated at the second point

f(x_1) is the function evaluated at the first point

We know that the first point is 1 year and the second point is 10 years, so x_1=1 and x_2=10. Replacing values:

Av=\frac{-(10)^2+20(10)+50-[-(1)^2+20(1)+50]}{10-1}

Av=\frac{-100+200+50-[-1+20+50]}{9}

Av=\frac{150-[69]}{9}

Av=\frac{150-69}{9}

Av=\frac{81}{9}

Av=9

Since f(x) represents the number of pounds per acre and x the number of years, we can conclude that the crop yield increased by 9 pounds per acre from year 1 to year 10.

ANSWER

The diagonal of the square is 6 units.

EXPLANATION

A diagonal of a square divides the square into two congruent right isosceles triangles.

Let the sides of the square be 's' units. Then, the Pythagoras Theorem says that, the sum of the squares of the shorter legs will be equal to the square of the hypotenuse.

Let the diagonal which is the hypotenuse be 'd' units.

Then,

[tex] {d}^{2} = {s}^{2} + {s}^{2} [/tex]

[tex] \implies \: {d}^{2} = 2{s}^{2}[/tex]

From the question, the side length of the square is

[tex]s = 3 \sqrt{2} \: units[/tex]

We plug in this value to obtain:

[tex]\implies \: {d}^{2} = 2{(3 \sqrt{2} )}^{2}[/tex]

Or

[tex]\implies \: {d}^{2} = 2 \times { {3}^{2} (\sqrt{2} )}^{2}[/tex]

[tex]\implies \: {d}^{2} = 9 \times 2 \times 2 = 36[/tex]

We take the positive square root of both sides to get:

[tex]d = \sqrt{36} [/tex]

[tex]d = 6 \: units[/tex]

Answer:

B

Step-by-step explanation:

The vertex form of an absolute value function is f(x)=a|x-h|+k where (h,k) is the vertex.

a is positive means the absolute value function will face up.

a is negative means the absolute value function will face down.

So looking at the picture we see the vertex is (2,3) and all of the choices have a is 1.

So plugging in 2 for h and 3 for k and 1 for a into f(x)=a|x-h|+k

f(x)=|x-2|+3.

B.

The correct function represent in the graph are,

⇒ y = |x - 2| + 3

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph of the function shown in image.

Now, Let the parent function is,

⇒ y = |x|

Clearly, the function is move 2unit left and 3 unit up.

Hence, The correct function represent in the graph are,

⇒ y = |x - 2| + 3

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Answer:

The graph intersect the y-axis at (0,4.5)

The graph intersect the x-axis at (-3.6,0)

Step-by-step explanation:

The equation is;

-4y=-5x-18

Dived every term by -4

[tex]\frac{-4y}{-4} =\frac{-5x}{-4} -\frac{18}{-4} \\\\\\y=\frac{5}{4}x+\frac{9}{2}[/tex]

plot using a graph tool to view the liner graph as below

Answer:

C. $6 per hour.

Step-by-step explanation:

Pick a convenient point on the graph. The rate of change  is the

y coordinate /  x coordinate.

So we pick the point near the top right corner where y = 30 and x = 5 which gives us the answer 30/5 = 6.

The rate of change shown in the graph is option B that is $3 per hour.

The rate of change in a line is the difference between vertical values divided by horizontal values. It is also known as slope. It can be calculated as under:

Rate of change= y2-y1/x2-x1

To calculate the rate of change we need to first select two points which are in the given graph are (0,0) and (1,3)

Rate of change is equal to (3-0)/(1-0)

=3/1

means $ 3 is paid for 1 hour.

Hence the rate of change in the given graph is $3 per hour.

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Answer:

The multiplicative inverse is -5/3

Step-by-step explanation:

Multiplicative inverse means we want to end up with 1

-3/5 * what =1

Multiply by 5 to clear the fraction

-3/5 * what *5 = 1*5

-3 * what = 5

Divide by -3 to isolate what

-3*what /-3 = 5/-3

what = -5/3

The multiplicative inverse is -5/3

Answer:

6.5

Step-by-step explanation:

3! = 6

0! = 1

2! = 2

1! = 1

6 + 1/2*1 = 6.5

So all of the given answers are wrong.

Answer:

D. 74°

Step-by-step explanation:

∠XYZ is an inscribed angle, where its vertex is located on the circle and two intersecting chords form the vertex.

An inscribed angle is equal to HALF of the intercepted arc, which is the arc that is between the two points where the chords hit.

In this picture, the intercepted arc is the red part of the outside of the circle.

Since you are given the measurement of the intercepted arc, you can find the measure of the inscribed angle by finding half of 148°.

Therefore, the inscribed angle is 148° divided by 2, giving us 74°.

The measure of the inscribed angle, ∠XYZ, is D. 74°.

Answer:

9*4

Step-by-step explanation:

We can Factor out a 9 from each term

9 + 27

9 (1+3)

9 (4)

9*4

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

[tex]\huge\text{x + 5}\ >\huge\text{ 10}[/tex]

[tex]\huge\text{First you'll need to SUBTRACT by 5}[/tex][tex]\huge\text{on each of your sides!}[/tex]

[tex]\huge\text{x + 5 - 5}>\huge\text{ 10 - 5}[/tex]

[tex]\huge\text{Cancel out: 5 - 5 because it equals to 0}[/tex]

[tex]\huge\text{Keep: 10 - 5 because it gives us the result of 5}[/tex]

[tex]\huge\text{x}>\huge\text{5}[/tex]

[tex]\huge\text{It's an (o)(p)(e)(n)(e)(d) circle} \checkmark[/tex]

[tex]\huge\text{Starts off with \#5}\checkmark[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: A.}}}[/tex] [tex]\huge\checkmark[/tex]

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

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

Answer:

[tex]\Large\textnormal{A. First graph}[/tex]

Step-by-step explanation:

[tex]\Large\textnormal{First, subtract by 5 from both sides of equation.}[/tex]

[tex]\displaystyle x+5-5>10-5[/tex]

[tex]\Large\textnormal{Then, simplify, to find the answer.}[/tex]

[tex]\displaystyle 10-5=5[/tex]

[tex]\Large \boxed{x>5}[/tex], which is our answer.

[tex]\Large\textnormal{The correct answer is A.}[/tex]