The Williard family was saving up for their summer vacation. Mrs. Williard had $475.88 in their savings account for the trip. Mr. Williard received a bonus at work for $609.00 that he is saving for the trip. If the trip will cost the Warren's a total of $1675.98, how much more money do they need for their vacation

[tex]m = m \\ \frac{97 - 68}{2 - 1} = \frac{134 - 97}{3 - 2} \\ 29 = 37 \\ this \: function \: is \: non \: linear[/tex]

[tex]f(1) = 68 \: \: \: f(2) = 97 \: \: \: \: f(3) = 134 \\ f(x) = ax {}^{2} + bx + c[/tex]

[tex]f(1) = 68 \\ 7.8(1) {}^{2} - 2.9(1) + 67.1 = 68 \\ 7.8 - 2.9 + 67.1 = 68 \\ 72 = 68 \\ this \: is \: false[/tex]

The Jacobian for this transformation is

[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}[/tex]

with determinant [tex]|J| = 12[/tex], hence the area element becomes

[tex]dA = dx\,dy = 12 \, du\,dv[/tex]

Then the integral becomes

[tex]\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv[/tex]

where [tex]R'[/tex] is the unit circle,

[tex]\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1[/tex]

so that

[tex]\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv[/tex]

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

[tex]\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}[/tex]

Then

[tex]\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}[/tex]

The addition equation to represent how their charges combine to make the overall charge of the atom is + 1 + - 1 = 0

A hydrogen atom has one positively charged proton and one negatively charged electron.

An atom of every elements has an electron(negatively charged) and positively charge(proton) part.

An atom as a whole is electrically neutral if the number of proton and electron are equal. They will cancel each other to make the atom neutral.

Therefore, the addition equation to represent how their charges combine to make the overall charge of the atom is as follows;

+ 1 + - 1 = 0

1 positively charged proton plus single negatively charged electron  = zero(neutral)

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The value of function f(x) over g(x) is [tex]2x^{2} +4x-1-\frac{9}{4x+1}[/tex]

Given functions are:

f(x)=8[tex]x^{3}[/tex]+18[tex]x^{2}[/tex]-10

g(x)=4x+1

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions exist everywhere, and they are crucial for constructing physical links in the sciences.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. A function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

[tex]\frac{f(x)}{g(x)}=\frac{8x^{3}+18x^{2} -10 }{4x+1}[/tex]

      = [tex]2x^{2} +4x-1-\frac{9}{4x+1}[/tex]

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Considering the graph of the velocity of the car, it is found that the interval in which it was stopped at a traffic light was:

Between 3 and 4 minutes.

When a car is stopped at a traffic light, the car is not moving, that is, it's velocity is of zero.

In this problem, the graph gives the velocity as a function of time, and it is at zero between 3 and 4 minutes, hence the interval in which it was stopped at a traffic light was:

Between 3 and 4 minutes.

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Answer:

A. (3x + 4)(x-7)

Step-by-step explanation:

3x times x = 3x^2

3x times -7 = -21x

4 times x = 4x

4 times -7 = -28

-21x + 4x = -17x

3x^2 - 17x - 28

Answer:

Week 4

Step-by-step explanation:

Victoria has $250 and saves $150 each week, hence have increments $150 each week

250+150 (first week)

= 400

second week = 400 + 150 = 550

third week = 550 + 150 = 700

fourth week = 700 + 150 = $850

Felicia on the other hand has $1,650 and spends $200 each week, hence has decrements of $200 each week.

1650+200 (first week)

= 1450

second week = 1450 - 200 = 1250

third week = 1250 - 200 = 1050

fourth week = 1050 + 200 = $850

One can prove congruence through transformation if they have the same shape and size.

The congruency postulates include:

In geometry, it should be noted that two figures are congruent if they have the same shape and size.

In this case, if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

One can prove triangle congruence using congruency postulates by using the SSS theorem( side side side theorem).

It should be noted that the congruence postulate is used to illustrate that the triangles are equal.

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Answer:

14cm.

Step-by-step explanation:

X is the hypotenus, 7√3 is the opposite and the other side is the adjacent. Choose sin from (soh, cah, toa) because you have to find 'H' (hyp) and opposite is given. Hence, sin 60= 7√3 over x. Cross multiply and you'll get x * sin 60= 7√3. Make x the subject of formula and 14 will be the answer.

The value of the vector will be -53. The correct option is C.

In mathematics and physics, the term "vector" is used informally to describe certain quantities that cannot be described by a single number or by a set of vector space elements.

The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of integers of equal length and outputs a single number.

The given vectors are u=2i-9j and v=-5i+7j, the dot product of the vectors will be calculated as below:-

u.v = ( 2i-9j ).( -5i+7j)

u.v = -10i² + 17 (i.j) -45(i.j) -63j²

Substitute i² = 1, j² = 1 and (i.j) = 0 in the above equation.

u.v = -10 + 63

u.v = 53

Therefore, the value of the vector will be -53. The correct option is C.

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Answer:

x=3

y = -2

Step-by-step explanation:

2x+5y = -4

y = x-5

We want to use substitution

In the first equation, every time we see y, substitute x-5

2x + 5( x-5) = -4

Distribute

2x + 5x -25 = -4

Combine like terms

7x -25 = -4

Add 25 to each side

7x -25+25 = -5+25

7x = 21

Divide each side by 7

7x/7 = 21/7

x=3

Now we can find y

y = x-5

y = 3-5

y = -2

The answer is x = 3, y = -2 or (3, -2).

We are given that :

Let us substitute the 2nd equation's value of y in the 1st equation.

Now, substitute for x in the 2nd equation.

Answer:

6

Step-by-step explanation:

Given an isosceles triangle the two sides opposite of congruent angles are equal to eachother, so you can create an equation setting the two sides equal to eachother and solve for x.

[tex]x+4=3x-8\\x=3x-12\\-2x=-12\\x=6[/tex]

The length of AC is simply x, therefore 6

Answer:

5 line of symmetry

Step-by-step explanation:

Answer:

7+21+15+19+.....+79

Here 21 be replaced by 11.

Now., common diffrence btw terms , d = 11-7 = 4

first term , a = 7

Last term , l = 79

number of terms = ( a + l ) ÷ d

=( 7 + 79 ) ÷ 4 = 86 ÷ 4 = 21.5 { It cannot be in decimal }

There's some mistake in the terms you provided please check your question again...

Pick 2 coordinates:

I choose first & last one (0,15) & (8-9)

Change in y is 24

(15--9 = 24)

Change in x is 8

(0 - 8) = - 8

24/-8 = - 3

So, slope = - 3

Hope this helps!

Answer:

-3

Step-by-step explanation:

The formula to find the slope is (change in y)/(change in x). In other words, rise over run.

If we look at the data, we can see that the x and y value changes.

x value: 0 --> 2 --> 4 --> 6 --> 8

y value: 15 --> 9 --> 3 --> -3 --> -9

When y changed from 15 to 9, the x changed from 0 to 2.

y: 15 --> 9

x: 0 --> 2

There was a difference of -6 in the y and a difference of 2 in the x.

At the top, I wrote that the slope was (change in y)/(change in x)

With -6 and 2 we found, we can say that the slope is -6/2.

If we simplify this answer, we end up with -3.

So -3 is the slope of the data.

Answer:

  5.09 years

Step-by-step explanation:

The formula for the future value of an investment can be filled with the given values and solved for time.

The future value of a one-time investment P earning interest at annual rate r compounded n times per year for t years is ...

  FV = P(1 +r/n)^(nt)

Using this formula with the given values, we have an expression for t:

  7300 = 5000(1 +0.075/4)^(4t)

Dividing by 5000, we have ...

  1.46 = 1.01875^(4t)

Taking logarithms gives the linear equation ...

  log(1.46) = 4t·log(1.01875)

Dividing by the coefficient of t, we find ...

  t = log(1.46)/(4·log(1.01875)) ≈ 5.0929

The time required for the value to reach $7300 is about 5.09 years.

__

Additional comment

The attachments show different calculator solutions. They give the same value for t.

The TVM Solver uses P/Y = 1 so the value of N is in years.

The graphical solution recasts the problem to f(x) = 0. It finds the value of t that makes the difference between the investment value and $7300 be zero.

Answer:

the answer to "2 times what equals 25?" is 12.5.

Step-by-step explanation:

proof from r.h.s to l.h.s

(cot(a)-tan(a))(cot(a)+tan(a))

cot(a)=cos(a)/sin(a)

tan(a)=sin(a)/cos(a)

(cot(a)-tan(a))=cos(a)/sin(a) - sin(a)/cos(a)

=cos²(a)-sin²(a)/sin(a)cos(a)

from trigonometry identity cos²(a)-sin²(a)=cos2(a)

so we have cos2(a)/sin(a)cos(a)

(cot(a)+tan(a))=cos(a)/sin(a) +sin(a)/cos(a)

=cos²(a)+sin²(a)/cos(a)sin(a)

from trigonometry identity cos²(a)+sin²(a)=so we have 1/cos(a)sin(a)

(cot(a)-tan(a)) ÷(cot(a)+tan(a))

=cos2(a)/cos(a)sin(a) ÷ 1/cos(a)sin(a)

=cos2(a)/cos(a)sin(a) * cos(a)sin(a)

=cos2(a)

proved

Answer:

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=-4^x+5\\g(x)=x^3+x^2-4x+5 \end{cases}[/tex]

This is an exponential function.

An exponential function includes a real number with an exponent containing a variable.

x-intercept (when y = 0):

[tex]\begin{aligned}f(x) & = 0\\\implies -4^x+5 & =0\\ 4^x &=5\\\ln 4^x &= \ln 5\\x \ln 4 &= \ln 5\\x&=\dfrac{ \ln 5}{\ln 4}\\x&=1.16\:\: \sf(2\:d.p.)\end{aligned}[/tex]

Therefore, the x-intercept of f(x) is (1.16, 0).

y-intercept (when x = 0):

[tex]\begin{aligned}f(0) & = -4^{0}+5\\& = 1+5\\& = 6\end{aligned}[/tex]

Therefore, the y-intercept of f(x) is (0, 6).

End behavior

[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]

[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow 5[/tex]

Therefore, there is a horizontal asymptote at y = 5 which means the curve gets close to y = 5 but never touches it.  Therefore:

This is a polynomial function of degree 3 (since the greatest exponent of the function is 3).

A polynomial function is made up of variables, constants and exponents that are combined using mathematical operations.

x-intercept (when y = 0):

There is only one x-intercept of function g(x).  It can be found algebraically using the Newton Raphson numerical method, or by using a calculator.

From a calculator, the x-intercept of g(x) is (-2.94, 0) to 2 decimal places.

y-intercept (when x = 0):

[tex]\begin{aligned}g(0) & = (0)^3+(0)^2-4(0)+5\\& = 0+0+0+5\\& = 5 \end{aligned}[/tex]

Therefore, the y-intercept of g(x) is (0, 5).

End behavior

[tex]\textsf{As }x \rightarrow \infty, \: f(x) \rightarrow \infty[/tex]

[tex]\textsf{As }x \rightarrow -\infty, \: f(x) \rightarrow - \infty[/tex]

Therefore:

Conclusion

Key features both functions have in common:

The vertical asymptote of f(x) is (A) x = 0, –9.

To find the vertical asymptote of f(x):

The vertical asymptotes of a function are the zeroes of the denominator of a rational function

The function is given as: [tex]f(x) = \frac{(x-9)}{(x^{3} -81x)}[/tex]

Set the denominator to 0:

Factor out x:

Express 81 as 9^2:

Express the difference between the two squares:

Split, [tex]x=0[/tex] or [tex]x=-9[/tex] or [tex]x+9=0[/tex].

Solve for x:

Therefore, the vertical asymptote of f(x) is (A) x = 0, –9.

(See attachment for the graph of f(x))

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The complete question is given below:

Consider the function f(x)=(x-9)/(x^3-81x) . find the vertical asymptote(s) of f(x).

A) x = 0, –9

B) x = –9

C) x = 0, 9

D) x = 9

The mean of the given data is 206.5.

To find the mean of the given data:

Sum of values = 211 + 226 + 186 + 221 + 181 + 228 + 207 + 215 + 203 + 203 + 204 + 196 + 226 + 212 + 212 + 201 + 219 + 191 + 191 + 185 + 193 + 231 = 4,542

Number of values = 22

Mean = 4,542 ÷ 22 = 206.5

Therefore, the mean of the given data is 206.5.

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Answer:

Step-by-step explanation:

Using it's concept, the probability a person tests positive who does not actually have Tuberculosis is:

c. 49/148.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 198 + 98 = 296 people who test positive, which is the number of total outcomes, and of those, 98 do not have the disease, which is the number of desired outcomes. Hence the probability is given by:

p = 98/296 = 49/148.

Which means that option c is correct.

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The probability a person tests positive who does not actually have Tuberculosis is 1/100

The probability is given as:

The probability a person tests positive who does not actually have Tuberculosis.

This is a conditional probability, and it can be calculated using

P = n(Tests positive | Does not have Tuberculosis)/n(Does not have Tuberculosis)

Using the given table of values, we have:

P = 98/9800

Evaluate the quotient

P = 1/100

Hence, the probability a person tests positive who does not actually have Tuberculosis is 1/100

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5. m∠C = 95°

6. m∠C = 70°

7. The other acute angle in the right triangle = 70°

8. m∠C = 70°

9. m∠C = 60° [equilateral triangle]

10. Measure of the exterior angle at ∠C = 110°

11. m∠B = 70°

12. m∠Z = 70°

A triangle is a 3-sided polygon with three sides and three angles. The sum of all its interior angles is 180 degrees. Some special triangles are:

5. m∠C = 180 - 50 - 35 [triangle sum theorem]

m∠C = 95°

6. m∠C = 180 - 25 - 85 [triangle sum theorem]

m∠C = 70°

7. The other acute angle in the right triangle = 180 - 90 - 25 [triangle sum theorem]

The other acute angle = 70°

8.  m∠C = 180 - 55 - 55 [isosceles triangle]

m∠C = 70°

9. m∠C = 60° [equilateral triangle]

10. Measure of the exterior angle at ∠C = 50 + 60

Measure of the exterior angle at ∠C = 110°

11. m∠B = 115 - 45

m∠B = 70°

12. m∠Z = 180 - 35 - 75

m∠Z = 70°

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There are 59 integer solutions

Such questions are best solved by writing cases and calculating the total number of cases. So beginning with

1)  x = -3. The possible combinations are as follows:-

-3 2 13

-3 3 12

-3 4 11

-3 5 10

-3 6 9

-3 7 8

-3 8 7

-3 9 6

-3 10 5

-3 11 4

10 combinations

2) x = -2

-2 2 12

through

-2 11 3

10 combinations

3) x = -1

-1 2 11

through

-1 10 3

9 combinations

4) x = 0

0 2 10

through

0 9 3

8 combinations

as we can see from the pattern at x =1  we get 7 combinations, at x =2  we get 6 combinations, at x=3 we get 5 combinations and at x =4  we get 5 combinations.

Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.

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Answer:

10 shelves

Step-by-step explanation:

out of the other choices, 10 is most suitable to divide with 80

The height of the basketball at 0.5 seconds will be = 26.5

A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation.

Example of a polynomial equation is: 2x2 + 3x + 1 = 0, where 2x2 + 3x + 1 is basically a polynomial expression which has been set equal to zero, to form a polynomial equation.

According to the given equation if we put value in it we will follow the following steps -

[tex]h(t) = - 16t^{2} + 35t+ 5\\ h(0.5) = -16(0.5)^{2} + 35(0.5) + 5\\h(0.5) = -16(0.25) + 17.5 + 5\\h(0.5) = 4 + 17.5 + 5\\h(0.5) = 26.5\\[/tex]

Therefore, the height of the basketball at 0.5 s will be 26.5

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Answer:

Is the question supposed to be (1.5), if so then the answer would be 21.5

Step-by-step explanation:

ht=-16t^2+35t+5

h(1.5)=-16(1.5)^2+35(1.5)+5

=21.5

Two or more equations using the same variable are referred to mathematically as a "system of linear equations." These equations' solutions serve as a representation of the intersection of the lines.

Two equations are presented here:

1) x + 3y = 7

2) 2x + 4y = 8

First, in the first equation, we want to isolate x:

x + 3y = 7

x = 7 -3y

In order to create an equation that depends just on the variable y, we must now b) swap it out in the second equation.

2x + 4y = 8

2(7 - 3y) + 4y = 8

The value of y is now determined by solving this equation in step (c).

14 - 6y + 4y = 8

14 - 2y = 8

-2y = 8 - 14 = -6

y= 6/2= 3

d) With the value of y now available, we can change the equation we obtained in step a) by substituting it.

x = 7 - 3y

x = 7 - 3*3 = 7 - 9 = -2

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I understand that the question you are looking for is:

Find the solution to the system of equations, x + 3y = 7 and 2x + 4y = 8.

1. Isolate x in the first equation: x = 7 − 3y

2. Substitute the value for x into the second equation: 2(7 − 3y) + 4y = 8

3. Solve for y:

14 − 6y + 4y = 8

14 − 2y = 8

−2y = −6

y = 3

4. Substitute y into either original equation: x = 7 − 3(3)

5. Write the solution as an ordered pair:

Answer:

division

Step-by-step explanation:

ratio compares 2 numbers by dividing them

example

2 out of 3 dentists like gum

2 ÷ 3 = .67 = 67%

so you can say

67% of dentists like gum

A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.