Mathematics College

express the following equation in standard form and indicate the values of a,b and c 5x =y-14

step by step pls

Answers

Answer 1

Answer:a=5

b= -1

c= -14

The standard equation is

ax + by = c .........(i)

given equation

5x = y - 14

or, 5x - y = - 14

or, 5x + (-1 × y) = - 14 ........(ii)

comparing equation (ii) with (i)

a= 5

b= -1

c = -14

Related Questions

pls help asap

An administrative assistant can type 100 words in 90 seconds. What is the assistants rate of typing in word per minute

Answers

66 because you divide 100 by 90 that multiply that number by 60

Find the first six terms of the sequence defined by each of these recurrence relations and initial conditions.
a) an=6an-1, a0=2
b) an=a2n-1, a1=2
c) an=an-1+3an-2, a0=1 , a1=2
d) an=nan-1+n2 an-2 a0=1 ,a1=1
e) an= an-1+an-3 , a0=1, a1=2 , a2=0

Answers

Answer:

See explanation

Step-by-step explanation:

Solving (a):

$a_n = 6a_{n-1}$ where $a_0 = 2$

n = 1

$a_n = 6a_{n-1}$

$a_1 = 6a_{1-1}$

$a_1 = 6a_{0}$

Substitute 2 for $a_0$

$a_1= 6 * 2$

$a_1= 12$

n = 2

$a_n = 6a_{n-1}$

$a_2 = 6a_{2-1}$

$a_2 = 6a_{1}$

Substitute 12 for $a_1$

$a_2= 6 * 12$

$a_2= 72$

n = 3

$a_n = 6a_{n-1}$

$a_3 = 6a_{3-1}$

$a_3 = 6a_2$

Substitute 72 for $a_2$

$a_3= 6 * 72$

$a_3= 432$

n = 4

$a_n = 6a_{n-1}$

$a_4 = 6a_{4-1}$

$a_4 = 6a_{3}$

Substitute 432 for $a_3$

$a_4 = 6 * 432$

$a_4 = 2592$

n = 5

$a_n = 6a_{n-1}$

$a_5 = 6a_{5-1}$

$a_5 = 6a_4$

Substitute 2592 for $a_4$

$a_5 = 6 * 2592$

$a_5 = 15552$

n = 6

$a_n = 6a_{n-1}$

$a_6 = 6a_{6-1}$

$a_6 = 6a_{5}$

Substitute 15552 for $a_5$

$a_6 = 6 * 15552$

$a_6 = 93312$

$a_1= 12$ $a_2= 72$ $a_3= 432$ $a_4 = 2592$ $a_5 = 15552$ $a_6 = 93312$

Solving (b):

$a_n = a^2_{n - 1$ where $a_1 = 2$

We have

$a_1 = 2$ which serves as the first term

n =2

$a_n = a^2_{n - 1$

$a_2 = a^2_{2-1}$

$a_2 = a^2_{1}$

Substitute 2 for $a_1$

$a_2 = 2^2$

$a_2 = 4$

n = 3

$a_3 = a^2_{3-1}$

$a_3 = a^2_{2}$

$a_3 = 4^2$

$a_3 = 16$

n = 4

$a_4 = a^2_{4-1}$

$a_4 = a^2_3$

$a_4 = 16^2$

$a_4 = 256$

n =5

$a_5 = a^2_{5-1$

$a_5 = a^2_4$

$a_5 = 256^2$

$a_5 = 65536$

n = 6

$a_6 = a^2_{6-1$

$a_6 = a^2_{5$

$a_6 = 65536^2$

$a_6 = 4294967296$

$a_1 = 2$ $a_2 = 4$ $a_3 = 16$ $a_4 = 256$ $a_5 = 65536$ $a_6 = 4294967296$

Solving (c):

$a_n=a_{n-1}+3a_{n-2};$ $a_0=1$ ; ; $a_1=2$

$a_1=2$ ---- First term

n = 2

$a_n=a_{n-1}+3a_{n-2};$ becomes

$a_2=a_{2-1}+3a_{2-2}$

$a_2=a_1+3a_0$

Substitute values for a1 and a0

$a_2=2+3 * 1$

$a_2=2+3$

$a_2=5$

n = 3

$a_n=a_{n-1}+3a_{n-2};$ becomes

$a_3=a_{3-1}+3a_{3-2}$

$a_3=a_{2}+3a_{1}$

$a_3=5+3 * 2$

$a_3=5+6$

$a_3=11$

n = 4

$a_n=a_{n-1}+3a_{n-2};$ becomes

$a_4=a_{4-1}+3a_{4-2}$

$a_4=a_{3}+3a_{2}$

$a_4=11+3 * 5$

$a_4=11+15$

$a_4=26$

n = 5

$a_n=a_{n-1}+3a_{n-2};$ becomes

$a_5=a_{5-1}+3a_{5-2};$

$a_5=a_{4}+3a_3$

$a_5=26+3 * 11$

$a_5=26+33$

$a_5=59$

n = 6

$a_n=a_{n-1}+3a_{n-2};$ becomes

$a_6=a_{6-1}+3a_{6-2}$

$a_6=a_{5}+3a_4$

$a_6=59+3*26$

$a_6=59+78$

$a_6=137$

$a_1=2$ $a_2=5$ $a_3=11$ $a_4=26$ $a_5=59$ $a_6=137$

Solving (d):

$a_n=na_{n-1}+n^2a_{n-2}$; $a_0=1$; $a_1=1$

$a_1=1$ --- First term

n = 2

$a_n=na_{n-1}+n^2a_{n-2}$ becomes

$a_2=2 * a_{2-1}+2^2a_{2-2}$

$a_2=2 * a_1+4*a_0$

$a_2=2 * 1+4*1$

$a_2=2 +4$

$a_2=6$

n = 3

$a_n=na_{n-1}+n^2a_{n-2}$ becomes

$a_3=3 * a_{3-1}+3^2 * a_{3-2}$

$a_3=3 * a_{2}+9 * a_{1}$

$a_3=3 * 6+9 * 1$

$a_3=18+9$

$a_3=27$

n = 4

$a_n=na_{n-1}+n^2a_{n-2}$ becomes

$a_4=4*a_{4-1}+4^2*a_{4-2}$

$a_4=4*a_{3}+16*a_{2}$

$a_4=4*27+16*6$

$a_4=204$

n = 5

$a_n=na_{n-1}+n^2a_{n-2}$ becomes

$a_5=5 * a_{5-1}+5^2 * a_{5-2}$

$a_5=5 * a_{4}+25 * a_{3}$

$a_5=5 * 204+25 *27$

$a_5=1695$

n = 6

$a_n=na_{n-1}+n^2a_{n-2}$ becomes

$a_6=6 * a_{6-1}+6^2*a_{6-2}$

$a_6=6 * a_{5}+36*a_{4}$

$a_6=6 * 1695+36*204$

$a_6=17514$

$a_1=1$ $a_2=6$ $a_3=27$ $a_4=204$ $a_5=1695$ $a_6=17514$

Solving (e):

$a_n= a_{n-1}+a_{n-3};\ a_0=1; a_1=2; a_2=0$

First term: $a_1=2$

Second Term: $a_2=0$

n = 3

$a_n= a_{n-1}+a_{n-3}$ becomes

$a_3= a_{3-1}+a_{3-3}$

$a_3= a_{2}+a_0$

$a_3= 0+1$

$a_3= 1$

n = 4

$a_n= a_{n-1}+a_{n-3}$ becomes

$a_4= a_{4-1}+a_{4-3}$

$a_4= a_{3}+a_{1}$

$a_4= 1+2$

$a_4=3$

n = 5

$a_n= a_{n-1}+a_{n-3}$ becomes

$a_5= a_{5-1}+a_{5-3}$

$a_5= a_{4}+a_{2}$

$a_5= 3 + 0$

$a_5= 3$

n = 6

$a_n= a_{n-1}+a_{n-3}$ becomes

$a_6= a_{6-1}+a_{6-3}$

$a_6= a_{5}+a_{3}$

$a_6= 3 + 1$

$a_6= 4$

$a_1=2$ $a_2=0$ $a_3= 1$ $a_4=3$ $a_5= 3$ $a_6= 4$

Helppppppppppppppppppppppppppppppppppppppppp

Answers

X=4 if i assume the sides are the same length, therefore side AD is equal to 32

Smoking males in a given area have a mean life expectancy of 68.5 years, with a standard deviation of 5.3 years. The distribution of life expectancy is not assumed to be symmetric.

Between what two life expectancies does Chebyshev's Theorem guarantee that we will find at least 89% of smoking males?

Round your answers to the nearest tenth. Enter the bounds in ascending order.

Answers

Answer:

52.6, 84.4

Step-by-step explanation:

Smoking males in a given area have a mean life expectancy of 68.5 years, with a standard deviation of

Chebyshev's Theorem guarantee that we will find at least 89% of smoking males in the life expectancy range [52.6, 84.4].

What is Chebyshev's inequality?

In probability theory, Chebyshev’s inequality guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean.

Let X be a random variable with mean μ with a finite variance σ², then for any real number k > 0, P(|X-μ| < kσ) ≥ 1-1/k².

Given,

Mean life expectancy = μ = 68.5 years

Standard deviation = σ = 5.3 years

P(|X-μ| < kσ) ≥ 1-1/k²

P(|X-68.5| < 5.3k) ≥ 1-1/k²

P(|X-68.5| < 5.3k) ≥ 0.89

$1 - \frac{1}{k^{2} } = 0.89$

$\frac{1}{k^{2} } = 0.11\\ \\\frac{1}{k^{2} } = \frac{1}{9} \\\\k = 3$

Between the following two life expectancies does Chebyshev's Theorem guarantee that we will find at least 89% of smoking males:

= [μ - 3σ, μ + 3σ]

= [68.5 - 3*5.3, 68.5 + 3*5.3]

= [52.6, 84.4]

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if S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Answers

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$, which agrees with the initial value S₁ = 1.

• Assume the closed form is correct for all n up to n = k. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for n = k + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

If a wheel rotates by 1888 degrees, how many complete revolutions has it made?

Answers

The number of revolutions made by the wheel is 5.24 ≅ 5.

Finding number of revolutions:

One complete revolution is equal to 360 degrees, so to find the number of complete revolutions the wheel has made, we can divide the total number of degrees rotated by 360.

Here we have

A wheel rotated by 1888°

As we know One complete revolution is equal to 360 degrees

Hence, the angle can be rotated by the wheel in 1 rotate = 360°

Let the wheel make 'x' revolution to make 1888°

=> 360(x) = 1888

=> x = 1888/360

=> x = 5.24

Therefore,

The number of revolutions made by the wheel is 5.24 ≅ 5.

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Isabel’s competition who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0. Graph the function in part e. Is your graph discrete or continuous? Explain.

Answers

Answer:

x= 1.99

f(x) = 1.99x + 3

Step-by-step explanation:

Hope this helps! (;

Property taxes are placed on the tax roll based on a property's assessed value. If a tax district has a tax rate of 0.35%, then what is the tax owed on a house with an assessed value of $230,000?
A.
$805
B.
$80,500
C.
$8,050
D.
$80.5

Answers

Answer:

Your answer is A

Step-by-step explanation:

please help it’s due!

Answers

Answer:

Step-by-step explanation:

Answer:

the triangulation trajectory is undefied

Step-by-step explanation:

If an independent-measures design is being used to compare two treatment conditions, then how many different groups of participants would be needed and how many scores would there be for each participant

Answers

Answer:

2 groups and 1 score for each participant

Step-by-step explanation:

An independent measures design is a defined as a research method whereby multiple experimental groups are examined and the participants will only be in one group. Now, each participant will only be affected by one condition of the independent variable during the experiment.

In the question given, we want to use the method I just described to compare two treatment conditions.

This means that there will be two groups and each participant in both groups will be assigned one score.

What is true about the net of a pyramid?It will always contain exactly 1 triangle.It will always contain exactly 2 triangles.It can contain any number of triangles greater than or equal to 3.It can contain any number of triangles greater than or equal to 4.

Answers

Answer:

Step-by-step explanation:

it can contain ≥ 3 triangles.

Answer:c

Step-by-step explanati

Using tan(A+B), find the exact value of tan(105).

Answers

Answer:

-2-√3

Step-by-step explanation:

The sum of angles formula for tangent is ...

tan(A+B) = (tan(A) +tan(B))/(1 -tan(A)tan(B))

For the desired angle, we can use A=45°, B=60°. Then we have ...

tan(105°) = (tan(45°) +tan(60°))/(1 -tan(45°)tan(60°))

The tangent values we need are ...

tan(45°) = 1

tan(60°) = √3

Then our tangent is ...

tan(105°) = (1 +√3)/(1 -1·√3) = (1 +√3)²/((1 -√3)(1 +√3)) = (4+2√3)/(-2)

tan(105°) = -(2+√3)

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answers

The scale factor and the value of x for each figure is given as follows:

A) Scale factor of 1/3, x = 7 m.

B) Scale factor 0.4747, x = 4.5 in.

How to obtain the scale factor and the value of x?

For Figure A, we have that the ratio between the areas is given as follows:

510/4590 = 1/9.

As the area is measured in square units, while the side lengths are measured in units, the scale factor is the square root of 1/9, hence it is given as follows:

1/3.

Then the value of x is obtained as follows:

x = 21 x 1/3

x = 7 m.

For Figure B, we have that the ratio between the areas is given as follows:

16/71 = 0.22535.

The scale factor is then the square root of 0.22535, which is given as follows:

0.4747.

Then the value of x is given as follows:

x = 9.5 x 0.4747

x = 4.5 in.

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What is the slope of the line that passes through the points (-10, -8) and
(-8, -16)? Write your answer in simplest form.

Answers

Answer:

Equation: y = -4x + 32

Slope: -4

Step-by-step explanation:

Given : (-10,-8) and (-8, -16)

Slope Formula: $\frac{y_1 - y_2}{x_1-x_2}$

Solve For Slope, Input Given Points:

$\frac{-8 - (-16)}{-10 - (-8)}$$\frac{8}{-2}$$-4$

Solve for y-intercept:

Input the slope into the equation y = mx + b. Plugin x and y values for the x and y variables to find b.

y = -4x + b-8 = -10(4) + b-8 = -40 + bb = 32

Equation of LIne: y = -4x + 32

-Chetan K

Answer:

(1,-4)

Step-by-step explanation:

Remember this formula:

y2 - y1/x2-x1

Your two cordinates:

(-10,-8) and (-8,-16)

First do -16-(-8)

That should equal -8

Note: This is for the Y

Next do -8-(-10)

That should equal 2

Note: This is for the X

So now our slope is (2,-8)

If you want the simplest form:

Divide by (2,2)

So the answer shall be (1,-4).

Cassie is going to dinner and a movie with some friends. The movie starts at 7:30 p.m. The restaurant
is 15 minutes from the theater, and dinner will take one hour. If Cassie
lives 20 minutes from the restaurant, what time should she leave her house?

Answers

Answer:5:55pm

Step-by-step explanation:

7:30-0:20=7:10-1:00=6:10-0:15=5:55pm

Look at the graph. What is ?

Answers

Answer:

no picture.

Step-by-step explanation:

no picture

The 2 in 1,703,298 has _______________ the value of the 2 in 3,932,574.

Answers

Answer:

1/10

Step-by-step explanation:

The value of 2 in 1,703,298 is 200.

The value of 2 in 3,932,574 is 2,000.

2,000 divided by 200 is 10.

Therefore, the 2 in 1,703,298 has 1/10 the value of the 2 in 3,932,574.

Answer:

1 tenth or 10%

Step-by-step explanation:

The 2 in the first number is in the hundreds place (200) but the 2 in the second number is thousands place(2000)

200/2000=0.1 or 10%

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How many schools have fewer than 50 classrooms

Answers

Answer:

7 schools have fewer than 50 classrooms.

QUESTION IN PICTURE

Please explain your answer in steps, thank you.

Answers

We can complete the blanks with the following ratios:

(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags

Since we do not need a flag at the starting line, then 32 flags will be required in total.

How to obtain the number of flags

To solve the problem, we would first convert 400 yds to feet and miles.

To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.

To convert to miles, we would have 0.227 miles.

Now, we divide the entire race distance by the number of miles divisions.

This gives us:

7.5 mi /0.227 mi

= 33 flags

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Paula is buying a watermelon that cost $0.50 per pound the watermelon weighs 5 lb and 3/5 pounds what is the cost of the watermelon in dollars.

Answers

Answer: 2.80

Step-by-step explanation:

There is 5 pounds of watermelon and each pound is worth 0.50 cents so

5 x 0.50 = 2.50. So now we need to find the amount 3/5 pounds costs and 5/5 = 0.50 so 1/5 = 0.10 And 3 x 0.10 = 0.30. So 0.30 + 2.50= 2.80

PLEASE HELP WITH MY HOMEWORK!!

Explain how you can make 5 1/5 - 3 7/10 a simpler problem. Then subtract.

Answers

5 1/5 - 3 7/10 simplified and subtracted equals 3/2.

what is improper fraction?

An improper fraction is a fraction in which the numerator (the top number) is greater than or equal to the denominator (the bottom number). For example, 7/4 is an improper fraction because the numerator (7) is greater than the denominator (4).

To make 5 1/5 - 3 7/10 a simpler problem, we need to convert the mixed numbers into improper fractions, which will make it easier to subtract them.

To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator of the fraction and then add the numerator.

So, we have:

5 1/5 = (5 x 5 + 1)/5 = 26/5

3 7/10 = (3 x 10 + 7)/10 = 37/10

Now, we can subtract the two improper fractions:

26/5 - 37/10

To subtract fractions, we need to have a common denominator. The smallest number that both 5 and 10 divide into is 10, so we can convert both fractions to have a denominator of 10:

(26/5) x (2/2) = 52/10

37/10

Now we can subtract the fractions:

52/10 - 37/10 = 15/10

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 5:

15/10 = (15/5) / (10/5) = 3/2

Therefore, 5 1/5 - 3 7/10 simplified and subtracted equals 3/2 or 1 1/2.

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can somebody PLEASE help me with this question i’m begging and i’ll give brainlist

Answers

The missing values are:

angle DGE = 45 degrees

angle EDG = 85 degrees

FD = 10

GD = 10√2

EG = (20 + 13√3) / 2

How to find the missing sides

The missing sides in the figure is solved as follows

angle DGE = angle BAG = 45 degrees (alternate angles are equal)

angle EDG = angle ADC (vertical angles are equal)

angle ADC + 45 + 50 = 180 (sum of angles in a triangle)

angle ADC = 180 - 50 - 45

angle ADC = 85 degrees

Since DGE = 45 degrees and FG = 10

tan 45 = FD / FG

tan 45 = FD / 10

FD = 10

solving for GD

GD² = FD² + FG² = 10² + 10² = 200

GD = 10√2

solving for EG

EG = EF + FG

cos 50 = EF / 13

EF = 13 cos 50 = 13√3 / 2

EG = EF + FG = 13√3 / 2 + 10 = (20 + 13√3) / 2

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What is 17/40 written as a decimal?

Answers

Answer:

0.425

Step-by-step explanation:

division of 17/40

The answer for this is .425

What is the midpoint of the line segment graphed below?

Answers

Answer:

(4, 7/2)

Step-by-step explanation:

midpoint = x values/2, y values/2

what is the answer-3x+14-11+11x

Answers

Answer:

-3x+14

Step-by-step explanation:

Construct the 99% confidence interval estimate of the mean wake time for a population with the treatment
m
(Round to one decimal place as needed)
ample Get more help-
HW Score: 39.53%, 17 of 43 points
O Points: 0 of 6
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 14 subjects had a mean wake time of 105 0 min After treatment, the 14 subjects had a
mean wake time of 782 min and a standard deviation of 24 1 min Assume that the 14 sample values appear to be from a normally distributed population and construct a 99% confidence interval estimate of the
mean wake time for a population with drug treatments What does the result suggest about the mean wake time of 105 0 min before the treatment? Does the drug appear to be effective?

Answers

The result suggests that the mean wake time might have really reduced since the values barely fall above 100 min as in before treatment with a high degree of confidence. thus , the drug is effective.

Confidence interval is written in the form as;

(Sample mean - margin of error, sample mean + margin of error)

The sample mean represent x , it is the point estimate for the population mean.

Margin of error = z × s/√n

Where s = sample standard deviation = 21.8

n = number of samples = 17

Now the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

then the degree of freedom, df for the sample.

df = n - 1 = 17 - 1 = 16

Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01

α/2 = 0.01/2 = 0.005

Therefore the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995

the t distribution table, z = 2.921

Margin of error = 2.921 × 21.8/√17

= 15.44

The confidence interval for the mean wake time for a population with drug treatments will be; 90.3 ± 15.44

The upper limit is 90.3 + 15.44 = 105.74 mins

The lower limit is 90.3 - 15.44 = 74.86 mins

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an excise tax is a tax on what?

Answers

Answer:

excise taxes are taxes on specific goods like gasoline

Step-by-step explanation:

An excise tax is a legislated tax on specific goods or services at purchase such as fuel, tobacco, and alcohol.

I'll Give brainliest too! I need help with these.

Answers

This is not seeing me clearly so that's why I can't able to help u.

| -1/2 + 1’1/2 |
| -5 + (-1)|

find the sum 51.2 x 9.08

Answers

Answer:

465.804

Step-by-step explanation:

465.804hdidjdjdjjssnsnsns

Mr. Carter is making a dessert using 9/10 pound of peach and 5/10 pound of raspberries. How much more peaches than raspberries is he using

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Answer: 4/10
Explanation: 9/10 - 5/10 = 4/10
The denominator is already both 10 so u can subtract the numerator without worry

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