3x + 5y = 4
16x + 10y = 4
How can one number in the second equation be changed so the system has only one solution? Explain.

Answer:

B.

Step-by-step explanation:

Answer:

y = 1/8 x - 9/2

Step-by-step explanation:

slope of line q = 1/8

y-(-2)= 1/8(x-2)

y+2 = 1/8 x - 1/4

y = 1/8 x - 1/4 - 2

y = 1/8 x + (-1-8)/2

y = 1/8 x -9/2

The error was made in the Step 1 as Distributive property of multiplication was not used correctly  .

In the question ,

it is given that

the equation is 2x -(1/4)(12x+4)= 3

Step 1 : by using the distributive property of multiplication ,

we get

2x - (1/4)*12x -(1/4)*4 = 3

2x - 3x - 1 = 3

So , after the first step the equation should be 2x - 3x - 1 = 3

we see that the  Distributive property of multiplication , was not used properly as the negative sign was not distributed to both the terms .

So ,  Step 1 is wrong.

Step 2 : Adding like terms

we get ,

-x - 1 = 3

Step 3 : Adding 1 to both the sides ,

we get

-x - 1 [tex]+[/tex] 1 = 3 + 1

Step 4:

-x = 4

x = -4

Therefore ,The error was made in the Step 1 as Distributive property of multiplication was not used correctly  .

The given question is incomplete , the complete question is

An equation and the steps to solve it are shown below:

2x -(1/4)(12x+4)= 3

Step 1: 2x + 3x + 1 = 3

Step 2: 5x+1=3

Step 3: 5x+1-1=3-1

Step 4: 5x = 2

In which step was the error made and why?

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Answer:

Step-by-step explanation:

The line perpendicular to y = 4 will be a vertical line through the point (−2, 1). The equation of the vertical line is x = −2.

the number of Red sweets=14

Let the probability of getting a red sweet be = P(R)

Let the probability of getting a Blue sweet be = P(B)

Let the probability of getting an orange sweet be = P(O)

Let the probability of getting a yellow sweet be = P(Y)

Let the number of Red sweets be represented as = n(R)

Let the number of Yellow sweets be represented as = n(Y)

Let the number of Orange sweets be represented as = n(O)

Let the number of Blue sweets be represented as = n(B)

Let the total number of sweets in the jar be represented as = n(T)

P(B) = 0.5

P(E) = 0.2

P(R) = 2 x P(O)

The formula of probability =

Number of the Sweets of a color/Total number of sweets in the jar

then,

P(B)=n(B)/ n(T)

P(B)=0.5 (Given in question)

n(B)=20 (Given in question)

So,

0.5 = 20/n(T)

5/10 = 20/n(T)

5/10 x 1/20 = 1/n(T)

cross multiplying

n(T)=10/5 x 20

dividing 10 by 5 =2

n(T) = 2 x 20

n(T) = 40

P(Y)=0.2 (Given in question)

Applying the formula of probability

P(Y) = n(Y)/n(T)

putting values

0.2=n(Y)/40

2/10=n(Y)/40

2/10 x 40 =n(Y)

Dividing 40 by 10 = 4

n(Y)= 2 x 4

n(Y)= 8

P(R)=2P(O)

Applying the formula of probability

n(R)/n(T)=2n(O)/n(T)

Cancelling out n(T) with n(T)

So,

n(R)=2 x n(O) -(i)

n(T) = n(O)+n(R)+n(B)+n(Y)

putting values

40=n(O)+n(R)+20+8

40=n(O)+n(R)+28

40-18=n(O)+n(R)

From -(i)

22=2n(O)+n(O)  

22=3n(O)

n(O)=22/3

Since,

n(R)=2xn(O)

n(R)=2x22/3

n(R)=44/3

n(R)=14.6

the number of Red sweets=14.6

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The required value of g(-4) = 1 in the given function is represented in the shown graph.

A graph can be defined as a visual representation or a diagram that represents data or values.

The function is given in the represented graph of g(x)

We have to determine the value of g(-4) of the given function in the graph

According to the given graph, we can see that the value of the domain of the given function g(x) when the value of variable x is -4 when the value of the variable y is 1. this means the value of g(-4) = 1.

Therefore, the required value of g(-4) = 1 in the given function is represented in the shown graph.

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The length and width of a rectangle that maximises the enclosed area are 800 yards. The maximum area is 640,000 square yards.

In the given question we have to find the maximum area of the rectangular area.

Liana has 3200 yards of fencing to enclose a rectangle.

As we know that the perimeter of rectangle

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 3200

Divide by 2 on both side we get

x+y = 1600................(1)

From the area of rectangle is

A = xy

From the equation the value of y is 1600-x.

Now putting the value of y

A = x(1600-x)

A = 1600x-x^2

On differentiating

dA/dx = 1600-2x

Putting dA/dx=0

1600-2x=0

Subtract 1600 on both side we get

-2x= -1600

Divide by -2 on both side we get

x = 800 yards

Now putting the value of x in the y=1600-x

y=1600-800

y=800 yards

So the maximum area is

A= 800*800

A= 640,000 square yards

Hence, the length and width of a rectangle that maximises the enclosed area are 800 yards. 640,000 square yards is the maximum area.

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Step-by-step explanation:

3 units right = x + 3

12 units down = y - 12

E = (-5, 4) -> E' (-2, -8)

F = (-5, 9) -> F' (-2, -3)

G = (1, 9) -> G' (4, -3)

H = (1, 4) -> G' (4, -8)

Answer: 9/3

Step-by-step explanation: the trriangles proportion is three and 9/3=3

The 95% confidence interval for the population proportion of members who vote yes is (0.782, 0.818).

A choice that is made at random (purely by chance, with no predictability). They tapes of samples are:

Convenient: Sample taken from a pool that is easily accessible.

Random: Put all the possibilities into a hat, then pull some of them at random. Every kth element is taken in a systematic manner. If you wanted to survey anything on the street, for instance, you may interview every fifth person.

Cluster: The population is divided into groupings, or clusters, and every component of each cluster is surveyed.

Stratified: Additionally stratifies the people into several groupings. But only a small portion of the group is questioned after that.

Now, finding the sample proportion,

[tex]p=\frac{x}{n} \\\\=\frac{1600}{2000}\\\\ =0.8[/tex]

The confidence level is given as,

[tex]C=p\pm[z(\frac{\alpha}{2})\times\sqrt{\frac{p(1-p)}{n} } ][/tex]

The value of [tex]z(\frac{\alpha}{2})[/tex] is 1.96

Putting the values, we get

[tex]C=0.8\pm[1.96\times\sqrt{\frac{0.8(1-0.8)}{2000} } ]\\\\C=0.8\pm[1.96\times\sqrt{\frac{0.8(0.2)}{2000} } ]\\\\C=0.8\pm0.018\\\\C=(0.782,0.818)[/tex]

Therefore, the 95% confidence interval is (0.782,0.818).

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The given question is incomplete. Here is the complete question.

a random sample of 2,000 members of a union reveals that 1,600 would vote yes on a merger proposal. what is the 95% confidence interval for the population proportion of members who would vote yes?

a) 0.782 to 0.818

b) 0.754 to 0.799

c) 0.690 to 0.713

d) 0.799 to 0.951

With the help of permutanions and combinations we can conclude the answer.

acc to our question-

Hence ,permutanions and combinations concept helped us to reach our solution.

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The day which has the least change in temperature is Wednesday.

The day which has the least change in temperature can be calculated by finding the change in temperature:

Monday = High temperature - low temperature

= 82° - 58°

= 24°

Tuesday = High temperature - low temperature

= 85° - 60°

= 25°

Wednesday = High temperature - low temperature

= 77° - 62°

= 15°

Thursday = High temperature - low temperature

= 68° - 50°

= 18°

Friday = High temperature - low temperature

= 75° - 48°

= 27°

Saturday = High temperature - low temperature

= 70° - 52°

= 22°

Sunday = High temperature - low temperature

= 84° - 56°

= 28°

The day which has the least change in temperature is Wednesday

Which two consecutive days which showed a drop in temperature: Wednesday and Thursday with 77° and 68° respectively.

Unlike line graph, table graph is the graph that is easier to read.

Therefore, the graph which best illustrate the graph is table graph because it represent the data in a clearer way.

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Answer:

  23346

Step-by-step explanation:

You want to know the number of hits on Grace's website 7 weeks from now if she gets 38,800 now and the number decreases 7% per week.

The growth factor per week is ...

  growth factor = 1 + growth rate

The growth rate of hits is -7% per week, so this is ...

  growth factor = 1 -7% = 0.93

The exponential function describing the number of hits can be written ...

  hits = (initial value)(growth factor)^weeks

  hits = 38,800(0.93^weeks)

Then in 7 weeks, the number of hits is expected to be ...

  hits = 38,800(0.93^7) ≈ 23,346

Grace can expect to get about 23,346 hits in 7 weeks.

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Answer:

f = 3cm g = 16cm

Step-by-step explanation:

Area of ABCE = 60cm²

Area of ABCD = 48cm²

60 - 48 = 12

Area of ADE = 12cm²

A to D = 3cm

f = 3cm

g = 16cm

Answer:

Step-by-step explanation: 7w-12+(-15w+60)= 7w-12-15w-60= -8w-72

-8w-72 is the answer or -8(w+9) if you take out a -8

The required simplified solution of the sum of the expressions is -8w + 48

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
To add 7w-12 and -15w+60
According to the question,
= 7w - 12 - 15w + 60
= 7w - 15w + 60 - 12
= -8w + 48

Thus, the required simplified solution of the sum of the expressions is -8w + 48

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The population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

All these elements are taken into account when formulating the population growth formula.

r = [(b + i) - (d + e)]/1000

Put the values in the formula.

r =  [(2,000 + 100) - (500 + 200)]/1000

r = 2100 - 700/ 1000

r = 1.4

Thus, the population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

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The weight of the salad at the cost of $7.28 will be 31.9 ounces.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that at Sascha's Salad Bar, customers make their own salads and pay by ounce. Jenny paid $6.16 for a 22-ounce salad. Seth spent $7.28 on a salad.

$6.16 ⇒ 22 ounces

$1 ⇒ 22 / $6.16

$7.28 ⇒ ( 22 x 7.28 ) / $6.16

$7.18 ⇒ 31.9 ounces

Therefore, the weight of the salad at the cost of $7.28 will be 31.9 ounces.

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The length AC of the triangle will be 10.6 units

The trigonometric functions (also called circular functions, angle functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given is a right angled ΔABC as shown in the figure.

We have the image as shown in the figure. In the right angled triangle -

Sin(62°) = CA/CB

Sin(62°) = CA/12

CA = 12 x Sin(62°)

CA = 12 x 0.88

CA = 10.6

Therefore, the length AC of the triangle will be 10.6 units

Therefore, by following the steps above, we can plot the graph of →

y = 5 cos(2x + π/3) - 1

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[Refer to image attached for full question]

Dario cuts the lasagna into 15 equal slices.

Given,

Quantity of Parmesan cheese = 2/3 pounds

Quantity of Ricotta cheese = 1 3/4 = 7/4 pounds

Quantity of Mozzarella cheese = 1 1/3 = 4/3 pounds

The quantity of cheese in each pieces when the lasagna is cut = 1/4 pounds

We have to find the number of slices of cheese.

Here,

Total quantity of cheese;

2/3 + 7/4 + 4/3 = 2 + 7/4 = 15/4 pounds

Number of slices = total cheese / quantity of cheese in pieces

= (15/4) / (1/4) = 15 slices

That is,

Dario cuts the lasagna into 15 equal slices.

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The slopes of the given lines are:

1. 2/5.

2. -1.

If a line passes through points on a graph, [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], the formula that can be employed to find the slope of a line is given as:

Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

1. Using two points on the line, (3, 1) and (-2, -1):

Slope of the line = m = (-1 - 1)/(-2 - 3)

Slope of the line (m) = -2/-5

Slope of the line (m) = 2/5

The slope of the graph is 2/5.

2. Using two points on the line, (-3, 2) and (2, -3):

Slope of the line = m = (-3 - 2)/(2 -(-3))

Slope of the line (m) = -5/5

Slope of the line (m) = -1

The slope of the graph is -1.

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Answer:

x=-5/2

Step-by-step explanation:

x=-5/2

Answer:

12x+4=20x+24

Add negative 4 to both sides

6x+9=4x-3

Add -9 to both sides

-5x/4=4 Multiply both sides by 04

-4(5x-7)=-18 Distribute -4 on the left side

Step-by-step explanation:

12x+4=20x+24

Add negative 4 to both sides

6x+9=4x-3

Add -9 to both sides

-5x/4=4 Multiply both sides by 04

-4(5x-7)=-18 Distribute -4 on the left side

21 is  missing  length of parallel lines.

What is an example of parallel lines?

Because lines are parallel

so they cut into equal proportion

 then ,         4/10  = x/15

                  4 * 15/10 = x

                     x = 6

length of line  = 15 + 6 = 21

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The equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

Given:

(1,-5) with slope m = -1

The standard slope intercept form is y = mx + c.

substitute m = -1 and (1,-5)

-5 = -1(1) + c

-5 = -1 + c

c = -4.

y = mx + c

y = -1(x) + (-4)

y = -x - 4.

Therefore the equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

Therefore equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.

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0.57 mi²  = 15,890,688 ft² after converting square miles in square foot.

The given conversion in question is-

0.57 mi²  = __ ft²

We know that

1 mi²  = 27,878,400 ft²

Then, multiply both sides by 0.57

1 x 0.57 mi²  = 27,878,400 x 0.57 ft²

0.57 mi²  = 15,890,688 ft²

Thus, the conversion of 0.57 mi²  = 15,890,688 ft².

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The system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.

For the stated data;

Standard car license plates in a nation typically have 3 digits, 2 letters, and 2 numbers.

There are total 9 digits (0 - 9).

There are total 26 letter (A - Z)

Repetitions of letters and numbers given allowed.

Thus, numbers and the letters ca be arranged as;

1st place = 9 ways.

2nd place = 9 ways.

3nd place = 9 ways.

4th place = 26 ways.

6th place = 26 ways.

7th place = 9 ways.

8th place = 9 ways.

Total ways = 9×9×9×26×26×9×9

Total ways = 39917124

Thus, the system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.

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Answer:

yes, you did it right!

Step-by-step explanation:

You firsth calculate how much 15% of £600 are.
You did it exactly right. It's £90.
And to work out rhe value of the shares one week later, you add the £90 to the £600.

Find the degree of the equation to determine if linear.

Linear