Consider this equation.


The equation has [two valid solutions, one valid solution] and [no extraneous solutions, one extraneous solution]. A valid solution for x is [ 2, 5, 0, 4]

Answer:  The correct answer is x=(-pt+ty)/w

Step-by-step explanation:

Solve the equation for x:

y=xw/t+p

Step 1: Multiply both sides by t:

ty=pt+wx

Step 2: Flip the equation:

pt+wx=ty

Step 3: Add -pt to both sides:

pt+wx+−pt=ty+−pt

wx=−pt+ty

Step 4: Divide both sides by w.

wx/w=(−pt+ty)/w

x=(−pt+ty)/w

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Answer:

[tex]\huge\boxed{\sf x=\frac{ty-tp}{w} }[/tex]

Step-by-step explanation:

[tex]\displaystyle y=\frac{xw}{t} +p\\\\Subtract \ p \ to \ both \ sides\\\\y-p=\frac{xw}{t} \\\\Multiply \ t \ to \ both \ sides\\\\t(y-p)=xw\\\\ty-tp=xw\\\\Divide \ w \ to \ both \ sides\\\\\frac{ty-tp}{w} =x\\\\x=\frac{ty-tp}{w} \\\\\rule[225]{225}{2}[/tex]

Answer:

x = 7

Step-by-step explanation:

8x - 6x = 2 + 12

2x = 14

2/2 x = 14/2

x = 7

Step-by-step explanation:

the x value comes from the slope when graphing. for example, the slope on this problem is just x which means its only one. so you move up one and to the right one. for the second equation, its negative so you move back one or down one. the x value coms from when they are both intercepted when graphed.

Answer:

48 feet

Step-by-step explanation:

Marco has 2 pieces of rope that are each 8 yards long.

2 x 8 = 16 yards.

Marco has a total of 16 yards of rope.

Note that for converting yard to feet, that: 1 yard = 3 feet.

Marco, in this case, has 16 yards. Multiply 16 yards with 3 feet to obtain your answer:

16 yards x (3 feet/1 yard) = 48 feet/16 yards.

Marco has 48 feet worth of rope.

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Answer:

3k/2 - k+3/3=8- k+2/4

(3k/2)x3 - (k+3/3)x2=(8)x4 - k+2/4

9k-2k-6/6 = 32-k-2/4

7k-6/6 = 30-k/4

(7k-6)x4 = (30-k)x6

28k - 24 = 180 - 6k

34k = 204

k = 204/34

k=6

Step-by-step explanation:

First, you multiply both sides by the numbers there to both the numerator and denominator, to get the same denominator. Then, simplify the answers in the second step. Next, cross multiply by multiplying the numerator of the left side to the denominator of the right side; and multiplying the numerator of the right side of the denominator of the left side. When you reach the fifth step, move -6k to the left side it will turn to +6k and add with 28k to get 34k. Move -24 to the right side it will turn +24 and add with 180 to get 204. Lastly, divide 204 by 34 to get k = 6.

Answer:

tan R = [tex]\frac{45}{28}[/tex]; tan S =[tex]\frac{28}{45}[/tex]

Step-by-step explanation:

The tangent proportion is [tex]\frac{opposite}{adjacent}[/tex].

When R is the reference angle TS (45) is the opposite side and TR is the adjacent side (28).

When S is the reference angle, TR is the opposite side (28) and TS is the adjacent side (45).

Answer:9x-3=8

Step-by-step explanation:

3 less means minus 3 from a number

product of 9 and a number is 9 times x

9x-3=8

is eight means = sign

Answer:

-17

Step-by-step explanation:

-7-x=10

+7.   +7

-x=17

/-1 /-1

x= -17

hopes this helps please mark brainliest

Answer:

m=[tex]-\frac{3}{2}[/tex]

Step-by-step explanation:

The slope is found with the equation m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]:

[tex](x_1,y_1)=(3,1)\\(x_2,y_2)=(1,4)\\m=\frac{(4)-(1)}{(1)-(3)}\\m=\frac{3}{-2}[/tex]

The number of terms in the Arithmetic Progression is 20 if the sum is 990.

We should know that Arithmetic Progression is a type of sequence in which the difference between consecutive terms are derived from the addition or subtraction of a common tern known as the common difference (d).

The given parameters are

Sum of the Arithmetic Progression (n)=990

Common difference (d) =5

The common difference is derived as follows:

5*0+2=2

5*1+2=7

5*2+2=12

5*3+2=17

d=7-2=12-7=17-12=5

The formed AP is 2,7,12,17,.....

Using the formula

[tex]S_{n} =[/tex]n/2[{2a+(n-1)d}

Where:

Applying the formula

990=[tex]\frac{n}{2}[/tex][2*2(n-1)5]

1980=n[4+5n-5]

1980=4n+5n²-5n

Rearrange the equation

5n²-n-190=0

Solving the equation

[tex]n=\frac{-b \frac{+}{-}\sqrt{b^{2}-4ac } }{2a}[/tex]

Where

a=5

b=-1

c=-1980

Applying the formula

n=[tex]\frac{1+199}{10} or \frac{1-199}{10} \\[/tex]

200/10   or -198/10

n=20 or n=-19.8

Taking the positive value of n=20

There the number of terms in the AP is 20

In conclusion, the number of terms in the Arithmetic Progression is 20 if the sum is 990.

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Answer:Answer:

The value of f(6) is, 18

Step-by-step explanation:

Given the function:

              .....[1]

We have to find the value of.

Put x = 6 in [1] we have;

⇒

⇒

Simplify:

Therefore, the value of f(6) is, 18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

we fill in where x is and make it 6

And I will use pemdas

f(6)=6^2÷3+6

f(6)=36÷3+6

f(6)=12+6

f(6)=18

Hopes this helps please mark brainliest

Answer:

10,000,000,000

Step-by-step explanation:

[tex]10^{10}[/tex]= 10,000,000,000

rounded to the nearest 10th = 10,000,000,000

Answer:

Step-by-step explanation:

Answer:

y = -8x + 3

Step-by-step explanation:

We are given that a line passes through the point (-0.5,7), and is parallel to y = -8x - 2

We want to write the equation of this line in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name.

Parallel lines have the same slopes.

Therefore, we can start by finding the slope of y = -8x - 2.

It is also written in slope-intercept form. -8 is where m (slope) should be; therefore, the slope of the line is -8.

We can plug in -8 for m in y=mx+b.

y = -8x + b

Now we need to find b.
As the equation passes through the point (-0.5,7), we can use its values to help solve for b.

Substitute -0.5 as x and 7 as y.

7 = -8(-0.5) + b

Multiply

7 = 4 + b

Subtract 4 from both sides

3 = b

Substitute 3 as b in the equation.

y = -8x + 3

Topic: parallel and perpendicular lines

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The sample standard deviation of the 14 measurements is 3.93

The standard deviation = √(variance)

Standard deviation = σ = √[Σ(x - xbar)²/N]

x = each variable

xbar = mean

N = number of variables

For 12 variables,

N = 12

σ = 4.25

xbar = 38

Σ(x - xbar)² = sum of the square of all deviations; let it be equal to D

4.25 = √[Σ(x - xbar)²/12]

4.25 =√(D/12)

4.25² = D/12

D = 216.75.

For 14 measurements,

N = 14

The mean is going to still be 38, because the two new measurements are each 38.

xbar = 38

And the new additions to the sum of deviations, will be (38 - 38)² twice, that is, 0.

Standard deviation for 14 measurements

Standard deviation = σ = √[Σ(x - xbar)²/N]

σ = √(216.75/14) = 3.93

Therefore, the standard deviation is 3.93

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Disclaimer

The question given by you is incomplete, the solution provided is of a similar question, the question is

A sample of 12 measurements has a mean of 38 and a sample standard deviation of 4.25. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 38 each. The sample standard deviation of the 14 measurements is:

Answer:

I think it is true, please let me know if I am wrong:)

Answer: -1.34328358

Step-by-step-explanation;

3(7/5x + 4) - 2(3/2-5/4x) = 0

3·(7/5·x + 4) - 2·(3/2-5/4·x) = 0

134x = -180

x = -180/134 = -1.34328358

Answer:

Explanation vvvvvv

Step-by-step explanation:

2.3

0.8+1.5 = 2.3

Also.. for 0.6, do you also find the sum or could you find the difference?

0.8-0.2 = 0.6

I will answer in comments if this isn't right.

The interval of convergence is given as: ⟹|x|<1

What is Maclaurin series?

Given the values of the function's successive derivatives at zero, a Maclaurin series is a power series that enables one to construct an approximation of a function with input values close to zero.

We will utilize the common power series representation of the functions, such as sine and the logarithmic function, to find the first three non-zero terms of the Maclaurin series representation for the function. We shall multiply the terms of each expression to obtain the final expression.

[tex]sin(x) = x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{2n+1}}{(2n+1)!}[/tex]

[tex]ln(1+x) = x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{n+1}}{(n+1)}[/tex]

The series representation shown above is only accurate when ⇒|x| < 1.

Given that;

f(x) = 4 sin(x) ln(1+x)

We are familiar with how functions are represented by power series:

[tex]sin(x) = x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{2n+1}}{(2n+1)!}[/tex]

[tex]ln(1+x) = x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........= \sum_{n=0}^{\infty} (-1)^n\ \frac{x^{n+1}}{(n+1)}[/tex]

The series representation shown above is only accurate when ⇒|x| < 1.

[tex]sin(x) ln(1+x) = [x -\frac{x^3}{3!}+\frac{x^5}{5!} +\frac{x^7}{7!} +........][x -\frac{x^2}{2}+\frac{x^3}{3} +\frac{x^4}{4} +........][/tex]

[tex]sin(x) ln(1+x) = x^2 -\frac{x^3}{3}+\frac{x^4}{4} +\frac{x^5}{5} +........[/tex]

Finally, the function's power series representation is given as:

⇒ [tex]f(x) = 4 sin(x) ln(1+x) = 4 [x^2 - \frac{x^3}{2}+\frac{x^4}{6} +\frac{x^5}{6}+..... ][/tex]

The interval of convergence is given as: ⟹|x|<1.

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Answer:

10.4 g/cm³

Step-by-step explanation:

Find the volume with formula, l x b x h

Then the formula gram / volume to find density.

The percent of the people had a mild that has an allergic reaction is 0.6%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Given that the company that makes haircare products had 2,000 people try a new shampoo. Of the 2,000 people, 12 had a mild allergic reaction.

It should be noted the percentage will be:

= Allergic people / Total people × 100

= 12/2000 × 100

= 0.6%

The percentage is 0.6%.

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If a credit card has an APR of 32.47%, and its billing cycle is 30 days long. The credit card's periodic interest rate is 2.67%.

A credit card periodic rate can be defined as the interest amount that a person pays on the balance of their credit card.

Given data:

Billing cycle = 30 days long

APR = 32.47%

Using this formula to find the credit card periodic interest rate

Credit card periodic interest rate = APR / (Number of days in a year /Billing cycle)

Where:

Credit card periodic interest rate =?

Annual percentage rate (APR) = 32.47%  

Number of days in a year =365 days

Billing cycle = 30 days

Now let find the credit card periodic interest rate

There is 365 days in a year.

Credit card periodic interest rate = 32.47% ÷ (365 days / 30 days)

Credit card periodic interest rate =32.47% / 12.17

Credit card periodic interest rate = 2.67%

Therefore the  periodic interest rate is 2.67%

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0>1,If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y.

Explanation:

0>1.

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The 200 km, 100 km, and 400 km distances traveled by the airplane at bearings of 335°, 170°, and 288°, respectively, indicates;

a) The displacement of the airplane when it lands is 485.56 kilometers

b) The bearing the airplane could have flown to complete the journey directly is 288.27°

A bearing is the measurement in degrees of an angle from the north direction

a) The path of the airplane can be represented using vectors as follows;

A bearing of 335° = N 25° W

Therefore;

[tex]\vec{d_1}[/tex] = -200·sin(25°)·i + 200·cos(25°)·j

A bearing of 170° = S 10° E

Therefore;

[tex]\vec{d_2}[/tex] =  100·sin(10°)·i - 100·cos(10°)·j

A bearing of 280° = N 80° W

Therefore;

[tex]\vec{d_3}[/tex] = -400·sin(80°)·i + 400·cos(80°)·j

The resultant displacement of the airplane, can be found by adding the above displacement vectors as follows;

R = (100·sin(10°)-200·sin(25°) - 400·sin(80°))·i + ((200·cos(25°) - 100·cos(10°) + 400·cos(80°))·j = -461.08·i + 152.24·j

The distance of the airplane from the start is therefore;

|R| = √((-461.08)² + 152.24²) ≈ 485.56

b) The direction of the airplane obtained from the resultant vector can be presented as follows;

[tex]\theta = arctan\left(\dfrac{152.24}{-461.08\right)}\approx -18.27^{\circ}[/tex]

From the other possible values of the angle, θ, we get;

θ = 180° - 18.27° ≈ 161.73°

The 161.73° is measures from the positive x-axis, and therefore is in Quadrant II

The bearing is therefore 270° + the measure of the 161.73° above the negative x-axis, which indicates;

The bearing = 270° + 180° - 161.73° = 288.27°

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The solution set of the quadratic inequality is (-1,5)

What is Quadratic inequality?

Inequalities can take many various forms, just like equations, one of which is the quadratic inequality.

A second-degree equation with a quadratic inequality substitutes an inequality sign for an equal sign.

The two roots are always provided in the answers to quadratic inequality. Different types of roots may exist, and discriminating between them is possible (b2 – 4ac).

The following are the quadratic inequalities' generic forms:

ax2 + bx + c < 0

ax2 + bx + c ≤ 0

ax2 + bx + c > 0

ax2 + bx + c >= 0

According to the given question

-a^2 + 4a + 7 > 2

-a^2 + 4a + 5 >0

multiplying with - 1

a^2 -4a -5 < 0

a^2 - 5a + a - 5 < 0

a(a-5) + 1(a-5) < 0

(a+1)(a-5) < 0

a<-1 & a< 5

a is in between -1 and 5

(-1,5)

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Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after

Answer:

Yes

Step-by-step explanation:

Plug in x and y:

17(-9)+12(8)<8

-153+96<8

-57<8

This is true so the point must satisfy the inequality.

Answer:

Step-by-step explanation:

1. 0

2. 3

3. 18

4. 33

5. 48

6. 198

Answer:

800(1+7/100)

800(1.7)

1360

Step-by-step explanation:

formula isp(1+r/100)power t

The exponential or the future value with interest is A = $ 856

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the future value be represented as A

To calculate the future value of $800 after one year with an interest rate of 7%, we can use the formula for simple interest:

The future value = present value x (1 + (interest rate x time))

So , the exponential equation is

x ( t ) = x₀ × ( 1 + r )ⁿ

Plugging in the values we have:

The future value = $800 * (1 + (0.07 * 1))

The future value = $800 * 1.07

The future value = $856

Hence , the future value of $800 one year from today with a 7% interest rate would be $ 856

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The distance between the two points (5,5) and(-1,-3) is 10 from the distance formula.

Given that,

The points area (5,5) and (-1,-3)

We have to find the distance between the two points.

We know that,

The distance between two points is the length of the line segment spanning those two points on the plane.

d=√((x₂ - x₁)² + (y₂ - y₁)²) is a common formula to calculate the distance between two points.

Any two points on an x-y plane or coordinate plane can have their separation between them determined using this equation.

We get,

(5,5) and (-1,-3)

Distance= [tex]\sqrt{(-1-5)^{2}+(-3-5)^{2} }[/tex]

Distance= √(-6)²+((-8)²

Distance= √36+64

Distance= √100

Distance =10

Therefore, The distance between the two points (5,5) and(-1,-3) is 10 from the distance formula.

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