Find The Slope Of The Line That Passes Through ( 7,1 ) And (10,3) Simplify Your Answer And Write It As (2024)

The ascending order of the given numbers is 2×[tex]10^{-4}[/tex] <0.004< 4×[tex]10^{-2}[/tex] < 0.042 < 0.24

The first number = 0.24

The second number = 4×[tex]10^{-2}[/tex]

The second number is the form of scientific notation. To compare the numbers, all the numbers should be in same form. So we have to convert the scientific notation to the decimal form

4×[tex]10^{-2}[/tex] = 0.04

The third number = 0.042

Third number is decimal form

The fourth number = 2×[tex]10^{-4}[/tex]

Convert the scientific notation to the decimal form

2×[tex]10^{-4}[/tex] = 0.0002

The fifth number = 0.004

The order of the numbers from least to greatest

= 2×[tex]10^{-4}[/tex] <0.004< 4×[tex]10^{-2}[/tex] < 0.042 < 0.24

Hence, the order of the given numbers from least to greatest is 2×[tex]10^{-4}[/tex] <0.004< 4×[tex]10^{-2}[/tex] < 0.042 < 0.24

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Answer:2.04x10 to the 4th

Step-by-step explanation:

multiply 20.4 x 1000

Then write the answer like this: 20,400

now make a decimal under ten countaining all #s that arent 0: 2.04

count the decimal places between the end of the 2 and the last 0 in the number 20,400

There are 4 places so thats 10 the power of 4

Now just put it all together

The roots of the function f(x) = [tex]x^2+2x-1[/tex] are

x = [tex]-1+\sqrt{2}[/tex]

x = [tex]-1-\sqrt{2}[/tex]

The function is given f(x)= [tex]x^2+2x-1[/tex]

The roots of given function will be at f(x) = 0

Substitute the value in the equation

[tex]x^2+2x-1[/tex] =0

Here to find the roots of the function, we have to use the quadratic formula in the given function

Roots of the function = [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

From the given function the values of

a = 1

b = 2

c = -1

Substitute the values in the quadratic formula and find the roots of the function

= [tex]\frac{-2+/-\sqrt{2^2-4(1)(-1)} }{2(1)}[/tex]

= [tex]\frac{-2+/-\sqrt{4+4} }{2}[/tex]

= [tex]\frac{-2+/-2\sqrt{2} }{2}[/tex]

The roots of the given functions are

x = [tex]-1+\sqrt{2}[/tex]

x = [tex]-1-\sqrt{2}[/tex]
Hence, the roots of the function f(x) = [tex]x^2+2x-1[/tex] are

x = [tex]-1+\sqrt{2}[/tex]

x = [tex]-1-\sqrt{2}[/tex]

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Answer:

the x = 0 and y = 1

so start off at the zero on the x-axis, and move up to the 1 on the y- axis

The value of c in the equation cx+4y=12 would give the equation a slope of 8 would be 32.

What is the slope of a straight line?

A straight line of the form y = MX + c has its slope as 'm'

It is constant for a line. The more the slope is, the steeper the line is.

Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have a negative slope. The horizontal line has 0 slopes and the vertical line has an infinite slope, as it is now at maximum steepness.

We have been given the equation cx+4y=12 which has a slope of 8.

Also cx+4y=12

4y = 12 - cx

y = 12/4 - cx/4

y = 3 - cx/4

Then we know that straight line of the form y = mx + c

By comparing the formula;

y = 3 - cx/4

Slope = c/4 = 8

c/4 = 8

c = 8(4)

c = 32

Therefore, the value of c in the equation cx+4y=12 would give the equation a slope of 8 would be 32.

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Semicircle is the best figure to use to estimate the volume of the punch bowl.

What is meant by volume?Every three-dimensional object requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an object within the boundaries of three-dimensional space. It is also known as the object's capacity. The liquid state has a definite volume but no definite shape. A solid state has a definite volume and a definite shape. Even if the containers are changed, the solid's shape and volume remain constant. Volume is a measurement of an object's capacity. For example, the volume of a cup is 100 ml if it can hold 100 ml of water up to the brim.

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Answer:

0.3,1/2,26%

Step-by-step explanation:

ascending order if arranging from smallest to highest .In this case, 0.3 Is the smallest followed by 1/2 and then 26%.

In order to calculate the composite function (gow)(x), that is, g(w(x)), we need to use w(x) as the input (value of x) in the function g(x).

So we have:

[tex]\begin{gathered} g(x)=7x-4 \\ g(w(x))=7w(x)-4 \\ g(w(x))=7(x^2-7x+3)-4 \\ g(w(x))=7x^2-49x+21-4 \\ g(w(x))=7x^2-49x+17 \end{gathered}[/tex]

Now, calculating (wog)(x), we have:

[tex]\begin{gathered} w(x)=x^2-7x+3 \\ w(g(x))=g(x)^2-7g(x)+3 \\ w(g(x))=(7x-4)^2-7\cdot(7x-4)+3 \\ w(g(x))=49x^2-56x+16-49x+28+3 \\ w(g(x))=49x^2-105x+47 \end{gathered}[/tex]

The values of the equations that are given will be:

17. b + 9 and -b + 7

18. c - 4 and c + 4

19. a + b - c and a + b + c

20. 5 + 2b and 5 - 2b

21. 4 - h - b and -b + h - 4

22. 2 - b - 2h and b - 2

How to express the equation?

Based on the information given, it should be noted that the equations will be expressed thus:

It should be noted that an equation is used to show the relationship between the variables. The equations will be:

17. |b + 1| + 8

= b + 1 + 8

= b + 9

and

|b + 1| + 8

= -b - 1 + 8

= -b + 7

18. 5 - |c + 1|

= 5 - c + 1

= - c + 4

= c - 4

and

5 - |c + 1|

5 + c - 1

= c + 4

19. |a + b|- c

= a + b - c

and

-a - b - c

Multiply through by -

= a + b + c

20. 5 + |2b|

= 5 + 2b

and

5 + |2b|

= 5 - 2b

21. |4 - h| - b

= 4 - h - b

and

-4 + h - b

= -b + h - 4

22. |2 - b - h| - h

= 2 - b - h - h

= 2 - b - 2h

and

-2 + b + h - h

= b - 2

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Answer:

year 7 have 135 students

year 9 have 45 students

Step-by-step explanation:

200=total students

360=value of the whole chart

1/2×360

=180

year 8 have 180students

360-180=180

the students remain are 180

1/4×180

=45

year 9 have 45 students

180-45

=135

year7 have 135 students

Answer: ales revenue = 1,386,000 dollars Increase sales in percent = 10 percent Increase sales in dollars = 1,386,000 dollars * 0,1 = 138,600 dollars New sales goal in dollars = 1,386,000 dollars + 138,600 dollars = 1,524,600 dollars

New sales goal is 1,524,600 dollars.

Step-by-step explanation:

option a , c and d are the correct statement or is a proper interpretation of a 95% confidence interval 95% of the population values will fall within this variable

What is the 95% confidence interval for a population mean?

It means that for any given number of samples, 95% of them will fall within 2 standard errors of the true mean of the population the sample is derived from.

a. In 95% of all samples, the sample mean will fall within 2 standard errors of the true population mean.

c. In 95% of all samples, the true population mean will be within 2 standard errors of the sample mean.

d. 95% of the population values will lie within 2 standard errors of the sample mean.

therefore option a , c and d are correct

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The number of the smaller squares which would be shaded to represent 0.75% as given in the task content is; 75.

The number of squares to correctly represent 245% on the grid is; 245.

What is the number of smaller squares which would be shaded to represent 0.75%?

It follows from the task content that; To represent the percent, Don uses a 10 × 10 grid and divides one of the squares in the grid into 100 smaller squares.

Since each Square in the 10 × 10 grid represents 1%, it follows that on division of one of the squares in the grid into 100 smaller squares;

The percentage, 0.75% can be represented by shading 75 smaller squares.

Also, the number of squares to be shaded on 10 × 10 grids to represent 245% according to the task content is; 245. This follows from the fact that, all 100 squares on the on 10 × 10 grids represent 100%.

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He’ll get the prize of dollar 10000, then the consumption after adding dollar 1500 is: $10000 + $1500 = $11500

a) the derive equation is 50000 + 10000 + x

jack has maximum amount of wealth = $50,000

When he participated in a jujitsu competition then the prize amount = 10,000

Then we will take a variable x for derive the equation which will depend on that he will win and loose :

Here,

the equation is = 50000 + 10000 + x

b) His consumption after not purchasing medical insurance is $15000.

if, he does not purchase medical insurance then he has no coverage of insurance and

He’ll lose the tournament and he’ll have to pay medical expenses dollar 5000 and also the prize amount $10000

So, his consumption after not purchasing medical insurance is:

$10000 + $5000 = $15000

c) when he will purchase medical insurance then his total consumption is $3500

his consumption if he purchase medical insurance, he will give dollar1 for medical insurance and will get in return dollar .3 ,

When he will have to pay for medical insurance $5000, then he’ll get the coverage on medical insurance:

0.3 * 5000 = $1500

Now, subtracting the amount of medical insurance which he’ll have to pay:

$5000 - $1500 = $3500

He’ll get the prize of dollar 10000, then the consumption after adding dollar 1500 is:

$10000 + $1500 = $11500

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The nth term of the arithmetic sequence when the numbers given are 7, 4, 1, -2 is 6 - 3n.

What will the sequence be?

It should be noted that an arithmetic sequence has a common difference. In this case, the values that are given include 7, 4, 1, -2.

First term = 7

The common difference between the numbers include:

= Second term - First term

= 4 - 7

= -3

The nth term will be:

= a + (n - 1)d

where a = 7

d = -3

= a + (n - 1)d

= 7 + (n - 1) -3

= 7 -3n - 1

= 6 - 3n

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The measure of the angle TRS = 46°

The angles given in figure are :

angle QSR = 110°

angle STR = 64°

angle QRS = 2x-10°

We will find the angle TRS using these given angles and some angle properties in a triangle.

We have the fact that sum of three angles of a triangle = 180°

So angle TRS + angle RST + angle STR = 180°

angle QSR and angle RST are supplementary. i.e., their sum = 180°

So angle RST = 180° - 110° = 70°

So angle TRS = 180°- (70°+64°) = 46°

Using angle TRS we can also find angle QRS and thereby, the value of x.

From the figure, angle QRT = 90°.

So angle QRS = 90°-angle TRS

⇒ 2x - 10° = 90° - 46°

⇒ 2x = 44° + 10°

⇒ x = 54°/2

⇒ x = 27°

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We will compute the volume of each figure.

1) Figure A

We have a cone with:

• Ab = base area = 20 cm²,

,

• h = heigh = 5 cm.

The volume of the cone is:

[tex]V_A=\frac{1}{3}\cdot A_b\cdot h=\frac{1}{3}\cdot(20cm^2)\cdot5\operatorname{cm}\cong33.3cm^3\text{.}[/tex]

2) Figure B

We have a cylinder with:

• Ab = base area = 20 cm²,

,

• h = heigh = 6 cm.

The volume of the cylinder is:

[tex]V_B=A_b\cdot h=20cm^2\cdot6\operatorname{cm}=120cm^3.[/tex]

3) Figure C

We have an inclined cylinder with:

• Ab = base area = 20 cm²,

,

• h = heigh = 5 cm.

The volume of the inclined cylinder is:

[tex]V_C=A_b\cdot h=20cm^2\cdot5\operatorname{cm}=100cm^3.[/tex]

4) Figure D

We have a parallelepiped with:

• Ab = base area = 20 cm²,

,

• h = heigh = 5 cm.

The volume of the parallelepiped is:

[tex]V_D=A_b\cdot h=20cm^2\cdot5\operatorname{cm}=100cm^3.[/tex]

5) Figure E

We have an inclined square pyramid with:

• Ab = base area = 20 cm²,

,

• h = heigh = 10 cm.

The volume of the square pyramid is:

[tex]V_E=\frac{1}{3}\cdot A_b\cdot h=\frac{1}{3}\cdot(20cm^2)\cdot10\operatorname{cm}\cong66.67cm^3\text{.}[/tex]

Answer

Among these figures, figure C and figure D have the same volume.

Answer:

See below

Step-by-step explanation:

99.87-71 = 28.81 this is 28.81/12 = z-score = +2.4

corresponding to .9918 ( from z-score table) = a score of 99.18%

Answer: 18.7598

Step-by-step explanation:

4 x 1.50= 6

6+ 3.95=9.95

3x 0.99= 2.97

2.97 + 9.95= 12.92

12.92+ 5= 17.92

6.5% of 12.92= 0.8398

6.5% of 12.92 + 17.92= 18.7598.

[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-10)}}} \implies \cfrac{-9}{2 +10} \implies \cfrac{ -9 }{ 12 }\implies -\cfrac{3}{4}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-\cfrac{3}{4}}(x-\stackrel{x_1}{(-10)}) \implies y -4= -\cfrac{3}{4} (x +10) \\\\\\ y-4=-\cfrac{3}{4}x-\cfrac{15}{2}\implies y=-\cfrac{3}{4}x-\cfrac{15}{2}+4\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-\cfrac{7}{2} \end{array}}[/tex]

Answer:

1.divide

2.minus

3.times

Answer:

-3(-1) + 4 = 3 + 4 = 7

-3(0) + 4 = 0 + 4 = 4

-3(1) + 4 = -3 + 4 = 1

-3(2) + 4 = -6 + 4 = -2

3x - 4 > 11

15 it’s not that hard

answer: D. (5, ♾)

explanation:

first u need to solve for x:

3x - 4 > 11

3x > 15

x > 5

so if x is greater than 5, then the domain is above 5 to infinity, written as (5, ♾) instead of [5, ♾) because the bracket means greater than or equal to, but > is just greater than

Answer: a) $171 b) $729

Step-by-step explanation:

a) 0.19 * $900 = $171

b) net pay = the money one earns after all deductions

$900 (what she earned) - $171 (taxes she had to pay) = $729

The probability that a sum is an even number will be 5/7.

What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The probability is typically defined as the proportion of favorable outcomes to all outcomes in the sample space. The probability of an event P(E) = (Number of favorable outcomes) is how it is stated (Sample space).

So, the first 7 prime numbers:

2,3,5,7,11,13,17

Then,

Even numbers are always produced when two odd numbers are added together.Odd numbers are always created when Even numbers are added to Odd numbers.In the list of 7, there is only one even number. If that is one of the options, then the outcome will only be odd.As the same number cannot be chosen twice, there is a 6/7 chance that it won't be chosen the first time and a 5/6 chance that it won't be chosen the second time.

By multiplying these two probabilities, we can determine the likelihood of an even sum.

5/6 × 6/730/425/7

Therefore, the probability that a sum is an even number will be 5/7.

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The equation of the line that passes through the point (-9, 2) and is perpendicular to the line 10x - 5y = 6 is y = - 1 / 2 x - 5 /2

How to find equation of a line?

The equation of a line can be represented in slope intercept form.

Therefore,

y = mx + b

where

m = slopeb = y-intercept

Therefore, the equation of the line is perpendicular to 10x - 5y = 6.

5y = 10x - 6

y = 2x - 6 / 5

Perpendicular lines follows the rule below:

m₁m₂ = -1

Therefore,

2m₂ = -1

m₂ = -1 / 2

The slope of the line is - 1 / 2. Now, let's find the equation of the line as it passes through (-9, 2)

y = - 1 / 2 x + b

2 = - 1 / 2 (-9) + b

2 = 9 / 2 + b

b = 2 - 9 / 2

b = 4 - 9 / 2

b = - 5 / 2

Therefore, the equation of the line is as follows:

y = - 1 / 2 x - 5 /2

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Answer: The answer is C. You start off by first thinking about your slope equation, being y=Mx+b. Remember b equals your y- intercept. In this case one of your y-intercepts is positive 1 and the other is positive 2. Now you have the “b” part of the equation. Looking for slope or your “mx” part of the equation is next. All this is going to be is the rise over the run from your y intercept. How much did you rise and how much did you run to get to the next point. Both of these slopes are going up therefore both slopes will be positives. For the first one it rises 2 and runs 1 to get to the next point, however you do not need to write the one at the bottom of the 2 and can leave it as “2x+1”, because it is shaded below the red line the inequality will be less than or equal to

. The blue slope rises 1 and runs 2, it is written as

and because it is shaded above the blue one it will be greater than or equal to

.

Step-by-step explanation:

Considering the linear functions on the graph, the inequality that matches the situation is:

B. y ≥ x/2 + 2

y ≤ 2x + 1

What is a linear function?

A linear function is modeled by:

y = mx + b, In which: m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

here, we have,

The lower bound of the interval is a linear function with

y-intercept of b = 2,

that also passes through (2,3), hence the slope is:

m = (3 - 2)/(2 - 0)

= 1/2.

Hence the inequality is:

y ≥ x/2 + 2

The upper bound of the interval is a linear function with y-intercept of b = 1, that also passes through (2,5), hence the slope is:

m = (5 - 1)/(2 - 0) = 2.

Hence the inequality is:

y ≤ 2x + 1

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By taking the 20 percent of £85 and adding that to the base salary, we can see that last week Brett earned £95

How much did Brett make last week?

Here we need to work with percentages. We know that Brett wins a commission of 20% of sales.

So, if he sells a total amount of A (A is in dollars). Then what he gets is:

0.2*A

Where 0.2 is the decimal form of 20%.

Here we know that Brett wins £78 as a base, and last week he sell a total of £85, then the amount he gets by the commission is:

0.2* £85 = £17

Adding that to the base he already earns each week, we get:

£78 + £17 = £95

In this way, we conclude that last week Brett earned £95

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