ten times the sum of half a number and 6 is 8

Given points (-4, -113) (5,-293) and (-1,7)

We frame 3 equations using the given points

[tex]y=ax^2+bx+c[/tex]

Plug in (-4, -113)

[tex]-113=a(-4)^2+b(-4)+c[/tex]

-113 = 16a -4b + c -------> first equation

Plug in (5,-293)

[tex]-293=a(5)^2+b(5)+c[/tex]

-293 = 25a +5b + c----> second equation

Plug in  (-1,7)

[tex]7=a(-1)^2+b(-1)+c[/tex]

7 = 1a -1b + c -----> third equation

Now we use the three equation and solve for a,b,c

Use first and second equation and subtract it

-113 = 16a -4b + c

+293 = -25a -5b - c

----------------------------------

180 = -9a + -9b (divide the whole equation by 9)

20= -1a -1b --------------> fourth equation

Subtract third equation from first equation

-113 = 16a -4b + c

-7 = -1a +1b - c  

----------------------------------

-120 = 15a - 3b (divide by -3 on both sides)

40 = -5a +b --------------> fifth equation

Use fourth and fifth equation

20= -1a -1b

40 = -5a +b

Add both equations

60 = -6a

so a= -10

Now we use the fourth equation

20= -1a -1b

20 = -1(-10) -1b

20 = 10 - 1b

-1b = 10

so b =-10

Now plug in the values in third equation

7 = 1a -1b + c

7 = 1(-10) -1(-10) + c

7 = c

We got a=-10, b=-10  and c=7

So equation becomes [tex]y=-10x^2-10x+7[/tex]

If 98 - 32 = 66,

then x = 66°

A) the Johnson family will travel 300 miles in 5 hours

Assuming 5, represents the amount of hours & 300 representing miles

IQ scores and GPAs are positively correlated with a strong relationship. Similarly, IQ and SAT scores are positively correlated with a strong relationship. Because the variable IQ is in both sets, there is likely to be a relationship between the other two variables, GPAs and SAT scores.

Correlation is a measure which describes if an association or relationship exists between two variables. Since there is a positive relationship between IQ and both GPA and SAT score, then GPA and SAT should correlate.

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In A, traveled hours will be increased if the distance traveled is increased and hence it is in direct variation.

In B, both x and y represent the length of a table and the difference is in units only. So, it is also in direct variation.

In C, more number of $1-off coupons used, more money will be saved and hence it is also in direct variation.

In D, if the speed is increased, then the time to travel 60 miles will be decreased. Hence it is not in direct variation.

Answer:

x = time it takes to travel 60 miles, and y = speed traveled

Step-by-step explanation:

First, you need to add 367 and 863. That should equal 1230. Then, subtract 8631 from 1230. That should get you -7401. So, there’s you’re answer. To check it, add them together. Hope this helps :)

Answer: The another number should be -7401.

Step-by-step explanation:

Since we have given that

sum of 367 and 863 is equal to sum of 8631 and another number.

Let the another number be 'x'.

According to question, it becomes,

[tex]367+863=8631+x\\\\230=8631+x\\\\1230-8631=x\\\\-7401=x[/tex]

Hence, the another number should be -7401.

2 and 5 8th   Convert  to improper fraction.

so, after you convert it. It should be like this

11/12 divided by 21/8

then use reciprocal so it will be

11/12 multiply by 8/21

then you got 88/252

then simplify it, 88 divided 4, and 252 divided 4

so the answer is 22/63.

The division of 11/12 by 2 and 5/8 (or 21/8) results in the fraction 22/63 after simplification.

To solve this problem, we first need to express everything as a fraction. So, '2 and 5/8' can be written as 21/8 (that is 2 whole and 5/8).

The question is asking us to divide 11/12 by 21/8. To perform division with fractions, we multiply by the reciprocal of the divisor. So, we rewrite this as 11/12 multiplied by 8/21.

Performing this multiplication gives us 88/252. This can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4, to get 22/63.

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(6, 2 )

substitute x = 5 into the equation and solve for y

6y + 8 = 20 ( subtract 8 from both sides )

6y = 12 ( divide both sides by 6 )

y = [tex]\frac{12}{6}[/tex] = 2

the ordered pair is (5, 2 )

plug in 5

4(5)=6y+8

20=6y+8

12=6y

2=y

(5,2)

Solution-

A school has 1800 students and 1800 light bulbs, each with a pull cord and all in a row.

As all the lights start out off, in the first pass all bulbs will be turned on.

In the second pass all the multiples of 2 will be off and rest will be turned on.

In the third pass all the multiples of 3 will be off, but the common multiple of 2 and 3 will be on along with the rest. i.e all the multiples of 6 will be turned on along with the rest.

In the fourth pass 4th light bulb will be turned on and so does all the multiples of 4.

But, in the sixth pass the 6th light bulb will be turned off as it was on after the third pass.

This pattern can observed that when a number has odd number of factors then only it can stay on till the last pass.

1 = 1

2 = 1, 2

3 = 1, 3

4 = 1, 2, 4

5 = 1, 5

6 = 1, 2, 3, 6

7 = 1, 7

8 = 1, 2, 4, 8

9 = 1, 3, 9

10 = 1, 2, 5, 10

11 = 1, 11

12 = 1, 2, 3, 4, 6, 12

13 = 1, 13

14 = 1, 2, 7, 14

15 = 1, 3, 5, 15

16 = 1, 2, 4, 8, 16

so on.....

The numbers who have odd number of factors are the perfect squares.

So calculating the number of perfect squares upto 1800 will give the number of light bulbs that will stay on.

As,  [tex]\sqrt{1800} =42.42[/tex]  , so 42 perfect squared numbers are there which are less than 1800.

∴ 42 light bulbs will end up in the on position. And there position is given in the attached table.

Old holiday light strings with bulbs that act as open switches will go out entirely if one bulb fails, while new versions with bulbs that short circuit will keep the remaining bulbs lit. Each bulb in an old 40-bulb series string on 120 V would be 3 V, while in a new 39-bulb series string it would be approximately 3.08 V per bulb. In a series circuit, a 60 W bulb would be brighter than a 100 W bulb.

When holiday lights wired in series have a bulb that burns out, in the old versions with bulbs that act like an open switch, the entire string of lights will go out. This is because the electrical circuit is broken, and current cannot flow through the circuit anymore. If the string operates on 120 V with 40 identical bulbs, the normal operating voltage of each bulb when all are functioning is 120 V / 40 bulbs = 3 V per bulb.

In contrast, newer versions are designed so that when a bulb burns out, it acts like a closed switch. This means the rest of the bulbs will stay lit because the circuit remains closed, allowing current to continue flowing. If one bulb short circuits and there are 39 remaining bulbs, each bulb will have an operating voltage of 120 V / 39 bulbs ≈ 3.08 V per bulb.

Regarding two household lightbulbs rated 60 W and 100 W connected in series, the one with the higher resistance (which is typically the lower-wattage bulb) will be brighter because it drops more voltage across it compared to the higher-wattage bulb with lower resistance.

Answer:  

Part A:  The function  [tex]f(x)[/tex] has greater slope than function [tex]g(x)[/tex]

Part B:  [tex]g(x)[/tex] has a greater y-intercept than [tex]f(x)[/tex].

Step-by-step explanation:

Part A:

For finding the slope of [tex]f(x)[/tex], first we need to pick any two order pairs from the given table in form of [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] and then use the formula of slope:  [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Lets choose two points as [tex](-1, -15)[/tex] and [tex](0, -10)[/tex]

So,  [tex]m= \frac{-10-(-15)}{0-(-1)}= \frac{-10+15}{0+1}= 5[/tex]

Thus, the slope of the function [tex]f(x)[/tex] is 5.

Another function is:  [tex]g(x)=2x+8[/tex]

The function [tex]g(x)[/tex] is given in standard slope intercept form [tex]y= mx+b[/tex]. So, we will get  [tex]m=2[/tex]

Thus, the slope of the function [tex]g(x)[/tex] is 2.

So, the function  [tex]f(x)[/tex] has greater slope than function [tex]g(x)[/tex]

Part B:

For function [tex]f(x)[/tex], there is one ordered pair as [tex](0, -10)[/tex]. This point is lying on the y-axis. So, the y-intercept of [tex]f(x)[/tex] is -10.

Now, in [tex]y= mx+b[/tex] form, [tex]'b'[/tex] is represented as the y-intercept. So, for function [tex]g(x)=2x+8[/tex], the value of [tex]'b'[/tex] will be 8.

Thus, the y-intercept of [tex]g(x)[/tex] is 8.

As  [tex]8>-10[/tex],

So, [tex]g(x)[/tex] has a greater y-intercept than [tex]f(x)[/tex].

5w + 9z = 2z + 3w

Subtract 2Z from each side:

5w + 7z = 3w

Subtract 5w from each side:

7z = -2w

Divide both sides by -2:

w = 7z / -2

We have been given an equation  and we are asked to find value of w from our given equation.

[tex]5w+9z=2z+3w[/tex]

First of all we will subtract 3w from both sides of our equation.

[tex]5w-3w+9z=2z+3w-3w[/tex]

[tex]5w-3w+9z=2z[/tex]

Now let us subtract 9z from both sides of our equation.

[tex]5w-3w+9z-9z=2z-9z[/tex]  

[tex]5w-3w=2z-9z[/tex]

[tex](5-3)w=(2-9)z[/tex]

[tex]2w=-7z[/tex]

Now let us divide both sides of our equation by 2.

[tex]\frac{2w}{2}= \frac{-7z}{2}[/tex]

Upon cancelling 2 from left side of our equation we will get,

[tex]w=\frac{-7}{2} z[/tex]

Therefore, we can see that [tex]w=\frac{-7z}{2} [/tex].

Trey is given expression: [tex]\frac{12}{15} +\frac{1}{10}.[/tex].

He got the answer [tex]\frac{13}{25}[/tex].

Solution: The denominators of the given expression are 15 and 10.

Therefore, in order to add the fractions, we need to find common denominator of 15 and 10.

Common denominator is the least common denominator.

Least common denominator of 15 and 10 is 30.

Therefore, Trey need to make both denominator as 30.

12/15 would become 12×2/15×2 = 24/30.

1/10 would become 1 × 3/ 10 × 3 = 3/30.

On adding 24+3, we get 27.

So, 24/30 + 3/30 = 27/30.

And 27/30 could be written in simplest fractions as 9/10.

But Trey got answer 13/25.

Therefore, Trey answer incorrect.

He must find common denominator (LCD) first and then add the fractions.

can be simplified as 5-9+7=-4+7=3

Q: evaluate (+5)-(+9)-(-7

A: if you remember how to add integers correctly, your answer would have been 3

(i added a picture to help you a little bit more)

hope this helps! ❤ from peachimin

I say when she starting to put weight on the trampoline for the first part she making energy you see. Same thing with the second picture she charging up the energy more and more  then when she jumps all that energy is being released making her jump up in the air higher so i say the  3rd picture first then 2nd then first because she preparing the energy to jump then she is adding more energy after that she releases it and jumps high

We are given the results of an election:

Candidate Fraction of votes

Johnson = [tex]\frac{1}{9}[/tex]

Smith  = [tex]\frac{7}{18}[/tex]

Dragovic = [tex]\frac{1}{2}[/tex]

Now, we need to find the difference between the fractions of votes received by Dragovic and Johnson.

Therefore, difference is :

[tex]\frac{1}{2} - \frac{1}{9}[/tex]

Taking common denominator of 2 and 9 is 18.

[tex]=\frac{1\times9}{2\times 9} - \frac{1\times 2}{9\times 2}[/tex]

[tex]=\frac{9}{18} - \frac{2}{18}[/tex]

[tex]=\frac{9-2}{18}[/tex]

[tex]=\frac{7}{18}[/tex]

Therefore, the difference between the fractions of votes received by Dragovic and Johnson is [tex]\frac{7}{18}[/tex].

Answer:

Step-by-step explanation:

7/18

The equation of the line that passes through the points (6,0) and (2,-7) is '7x - 4y = 42' when transformed into the standard form.

In mathematics, especially in linear algebra, the standard form of the line is a way of describing a specific line on the plane. We can get this by using two points through which the line passes. In this case, we have the points (6,0) and (2,-7).

First, we calculate the slope using the formula (y2 - y1) / (x2 - x1). Substituting our values, we have (-7 - 0) / (2 - 6) = -7 / -4 = 7/4. So, the slope is 7/4.

Next, we find the y-intercept (b) by substituting one of the points into the equation y = mx + b. Using the point (6,0), we get 0 = 7/4 * 6 + b. Solving for b, we find that b = -21/2.

The equation is then y = 7/4x - 21/2. To convert this to the standard form, we multiply all parts by 4 to remove the fraction. The equation then becomes 4y = 7x - 42. After arranging, we obtain our final equation: 7x - 4y = 42.

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it would be D x=10 hope this helps.

Answer:x=10

Step-by-step explanation:

Answer:

p^2 + 3p - 10

Step-by-step explanation:

Use the so-called "foil" method of multiplication of binomials:

p^2 -2p + 5p - 10, or p^2 + 3p - 10

Given:-

... ( p+5 )( p-2 )

When we have an equation like,

( a + b ) ( a - c )

... a² + ba - bc - ac

We have,

( p+5 )( p-2 )

... p² - 2p + 5p - 10

... p² + 3p - 10 Is the answer.

Hope it helps!

-1 > -4

3 > 0

1 > -2

3 > -5

I don't understand the second one sorry.

The inequalities should be matched with the graphs that represent them as follows;

6. 4y + 3 ≤ y + 6   ↔ graph C.

7. -2y > 2   ↔ graph A.

8. y/3 < -1   ↔ graph D.

9. 3y ≤ 2y + 3   ↔ graph B.

Based on the information provided, we would determine the solution set for each of the given inequality by simplifying as follows;

4y + 3 ≤ y + 6

By rearranging and collecting like terms, we have the following;

4y - y ≤ 6 - 3

3y ≤ 3

By dividing both sides of the inequality by 3, we have;

y ≤ 1 (solid dot at point 1 and it decreases to the left).

Part 7.

-2y > 2

By dividing both sides of the inequality by -2, we would flip (reverse) the inequality symbol;

-2y/-2 > 2/-2

y < -1 (hollow dot at point -1 and it decreases to the left).

Part 8.

y/3 < -1

By cross-multiplying, we have;

y < -3 (hollow dot at point -3 and it decreases to the left).

Part 9.

3y ≤ 2y + 3

By rearranging and collecting like terms, we have the following;

3y - 2y ≤ 3

y ≤ 3 (solid dot at point 3 and it decreases to the left).

yes it is, -4x+9=13, subtract 9 from both sides, -4x=4, divide by negative 4 from both sides, x= -1. Hope I helped!

-4x + 9 =  13

-4x =  4

 x = -1

Answer is Yes

x = - 1 is  a solution

So for example 11/3 is 3 2/3 because you divide 11 by 3 and how you do it is that 3 goes into 11 3 times so you would write three on top of the 11 and then subtract 11-9 which is 2 so it is 3 2/3

The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.

a. 3 2/3

b. 3 3/8

c. 5

d. 4 1/5

Hey there!!

Given equation :

... ( x - 3 ) ( 3x - 4 )

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

... 3x² - 4x - 9x + 12

... 3x² - 13x + 12

Hope my answer helps!!

By setting up and solving the proportion, we can determine that 90 hamburgers will be sold when 63 hot dogs are sold.

To find out how many hamburgers will be sold if 63 hot dogs are sold, we need to use the given ratio of 7 hot dogs to 10 hamburgers.

First, we can set up a proportion: 7/10 = 63/x.

Cross-multiplying, we get 7x = 10 * 63.

Solve for x by dividing both sides by 7, x = (10 * 63) / 7.

Simplifying further, x = 630 / 7. Performing the division, x = 90.

So, if 63 hot dogs are sold, 90 hamburgers will be sold using the given ratio.

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Based on the sample inspection of 200 tires with 16 being defective, one would expect approximately 1,600 tires to be defective out of the 20,000 tires produced, using proportional reasoning.

In the case where a tire maker produces 20,000 tires and inspects 200 of them, finding 16 to be defective, we can use proportional reasoning to estimate the number of defective tires in the entire lot. The ratio of defective to inspected tires is 16 / 200. We can set up a proportional relationship to find the expected number of defective tires (D) out of the 20,000 total tires:

(16 defective) / (200 inspected) = (D defective) / (20,000 total)

Now, we solve for D:

16 / 200 = D / 20,000

Multiplied both sides by 20,000:

20,000 * 16 / 200 = D

This simplifies to:

1600 = D

Therefore, one would expect about 1,600 tires to be defective out of the 20,000 tires made, this is based on the sample inspection results.

Answer:

The Answer is 2852.1

Step-by-step explanation:

Rounding off means simplifying the number while keeping it close to its true value. The "tenth" position is the 1st number to the right after decimal place. The number in the tenth position is 1, and there are no numbers to the right after that.

If there were any numbers to the right of the tenth position we will have to follow the following rules to round off to the nearest tenth.

If the number to the right of tenth place is less than 5 then keep the same number in the tenth place.

If the number to the right of the tenth place is 5 or more than 5 add one to the number in the tenth position.

In here as there is 0 after tenth position we can keep the same number, that is 1.

So 2852.1 rounded off to the tenth position is 2852.1.

( - ∞, ∞ )

h(x) is a polynomial and is defined for all real values of x thus domain ∈ R

or ( - ∞, ∞ ) ← in interval notation

Answer:

3x - y + 5

Step-by-step explanation:

4x - 3y + 10 - x + 2y - 5

To simplify, you need to combine like terms. Like terms are terms that have the same variable part. All terms with x are like terms and can be combined. All terms with y are like terms and can be combined. All terms with no variable are like terms and can be combined. A term with x and a term with y are not like terms and cannot be combined.

It may be helpful at first, to move the like terms together to combine them.

4x - 3y + 10 - x + 2y - 5 =

= 4x - x - 3y + 2y + 10 - 5

= 3x - y + 5

Answer:

3 x  −  y  +  5

Step-by-step explanation:

4x - 3y + 10 - x + 2y - 5

add/ subtract all the x values

4x - x = 3x

add/ subtract all y values

-3y + 2y = 1y or y

add/ subtract all real numbers

10 - 5 = 5

3x - y + 5

The x- intercept would be (3,0) or 3

The y-intercept would be (0,-4) or -4

C would be your answer.