What is the equation of the line, in slope-intercept form, that passes through the point (6,−1) and is perpendicular to the line y=2x−7?

A)y=2x+13
B)y=−12x+2
C)y=12x−4
D)y=12x+132

The area of the triangle with points Q(-1,1),R(2,-3), and S(-1,-3) is equal to 6 square units.

In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):

Area of triangle, A = 1/2 × b × h

Where:

By substituting the given vertices into the formula for the area of a triangle with coordinates, we have the following;

[tex]A=\frac{1}{2} \times |x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|\\\\A=\frac{1}{2} \times |-1(-3 + 3) + 2(-3 - 1) + (-1)(1 +3)|\\\\A=\frac{1}{2} \times |0 -8 - 4|\\\\A=\frac{1}{2} \times |-12|[/tex]

Area of triangle = 1/2 × 12

Area of triangle = 6 square units.

Answer:

i think the answer is c.) which is square root

Step-by-step explanation:

Answer:

C. Square root.

Step-by-step explanation:

We have been given 4 choices. We are asked to determine, which of the given functions has a domain of x ≥ 0.

A. linear.

We know that linear function is in form [tex]y=mx+b[/tex], which is defined for all values of x, therefore, option A is not a correct choice.

B. Square

We know that a square function is in form [tex]y=x^2[/tex], which is defined for all values of x, therefore, option B is not a correct choice.

C. Square root.

We know that a square root function is in form [tex]y=\sqrt{x}[/tex]. We also know that a square root function is not defined for negative values of x, so a square root function is defined for all values of [tex]x\geq 0[/tex]. Therefore, option C is the correct choice.

D. Cube

We know that a cube function is in form [tex]y=x^3[/tex], which is defined for all values of x, therefore, option D is not a correct choice.

The expression to compute the quartic root of a number x is sqrt(sqrt(x)).

To compute the quartic root of a number x, you can use the sqrt() function twice. The first call to sqrt() will find the square root of x, and the second call will find the square root of the result from the first call. This can be expressed as sqrt(sqrt(x)). This expression will return the quartic root of x if x is a positive number.

https://brainly.com/question/32892267

#SPJ3

Answer:

3xy^4+y-2/x

Step-by-step explanation:

12x^3y^4 + 4x^2y -8x

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

4x^2

We can break this fraction into pieces

12x^3y^4      4x^2y        8x

-------------- +    ---------   -  ------------

4x^2                4x^2          4x^2

Taking the first piece

12/4 =3

x^3/x^2 =x

y^4/1 =y^4

3xy^4

Taking the second fractions

4/4=1

x^2/x^2 =1

y=y

y

Taking the third fraction

8/4=2

x/x^2 = 1/x

2/x

Adding them back together

3xy^4+y-2/x

To find the blank number to be a perfect square, divide the middle number inside parenthesis by 2 and square it.

The middle value is 6.

6/2 = 3

3^2 = 9

The missing number is 9.

The number needed to complete the square in the function f(x) = 4(x² − 6x + ____) + 20 is 9, as (-3)² = 9 leads to forming a perfect square trinomial (x - 3)².

The question asks for the number required to complete the square for the quadratic expression within the function f(x) = 4(x² − 6x + ____) + 20.

To complete the square, we must find a value that, when added to the expression x² − 6x, forms a perfect square trinomial. This involves taking half of the coefficient of the x term, which is -6, and squaring it. The coefficient half is -3, and (-3)² equals 9.

Therefore, the answer for the blank is 9. When substituting into the expression, it transforms to (x - 3)², which is the required perfect square trinomial.

It differs because dilation changes the shape but not the orientation or place the shape is located.

Answer:

I'm assuming the difference is that it changes the size of the original image.

Step-by-step explanation:

Transforming, Rotating, and Reflecting never change the size of the original image but Dilution does. In other words, dilution makes it so that the new image and original image are no longer congruent.

do you mean theta not 0

Final answer:

To solve for q in the equation k = 4pq², divide both sides of the equation by 4p and take the square root of both sides. Simplify to get q = ±(√k)/(2√p).

Explanation:

To solve for q in the equation k = 4pq², we need to isolate the variable q. Here are the steps:

Divide both sides of the equation by 4p to get q² = k/(4p).

Take the square root of both sides to get q = ±√(k/(4p)).

Simplify the square root to q = ±(√k)/(√(4p)).

Simplify further to q = ±(√k)/(2√p).

Therefore, the correct answer is q = ±(√k)/(2√p). This corresponds to option C.

Answer:

Sean's collection was 250 times greater than Jeremy's.

Step-by-step explanation:

1.0 x 10^7 is the same as 10,000,000

4.0 x 10^4 is the same as 40,000

Divide 10,000,000 by 40,000 to get the answer. 10,000,000/40,000 = 250

Answer:

The best estimate of the area of the irregular shape is [tex]19.5\ units^{2}[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

To know an estimate of the area of the figure calculate the area of the rectangle minus the squares marked with x

so

[tex]A=(8*6)-29=19\ units^{2}[/tex]

therefore

The best estimate of the area of the irregular shape is [tex]19.5\ units^{2}[/tex]

Answer:ITS NOT 19.5!!! ITS 15.5

Step-by-step explanation:

Answer:

In the first account was invested [tex]\$3,000[/tex]  at 3%

In the second account was invested [tex]\$4,000[/tex]  at 5%

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

First account

[tex]t=1 years\\ P=\$x\\ r=0.03[/tex]

substitute in the formula above

[tex]I=x(0.03*1)[/tex]

[tex]I=0.03x[/tex]

Second account

[tex]t=1 years\\ P=\$(7,000-x)\\ r=0.05[/tex]

substitute in the formula above

[tex]I=(7,000-x)(0.05*1)[/tex]

[tex]I=350-0.05x[/tex]

Remember that

The interest is equal to [tex]\$290[/tex]

so

Adds the interest of both accounts

[tex]0.03x+350-0.05x=\$290[/tex]

[tex]0.05x-0.03x=350-290[/tex]

[tex]0.02x=60[/tex]

[tex]x=\$3,000[/tex]

therefore

In the first account was invested [tex]\$3,000[/tex]  at 3%

In the second account was invested [tex]\$7,000-\$3,000=\$4,000[/tex]  at 5%

$3000 was invested at 3% and $4000 was invested at 5%.

To determine how much was invested in each account, follow these steps:

1. Define variables:

  - Let [tex]\( x \)[/tex] be the amount invested at 3% interest.

  - Let [tex]\( y \)[/tex] be the amount invested at 5% interest.

2. Set up the equations:

  - The total amount invested is $7000:

    [tex]\[ x + y = 7000 \][/tex]

  - The total interest earned is $290. The interest from each account is [tex]\( 0.03x \)[/tex] and [tex]\( 0.05y \),[/tex] respectively:

   [tex]\[ 0.03x + 0.05y = 290 \][/tex]

3. Solve the system of equations:

  From the first equation:

  [tex]\[ y = 7000 - x \][/tex]

  Substitute [tex]\( y \)[/tex] into the second equation:

  [tex]\[ 0.03x + 0.05(7000 - x) = 290 \][/tex]

  Distribute and simplify:

  [tex]\[ 0.03x + 350 - 0.05x = 290 \][/tex]

  [tex]\[ -0.02x + 350 = 290 \][/tex]

  [tex]\[ -0.02x = 290 - 350 \][/tex]

  [tex]\[ -0.02x = -60 \][/tex]

  [tex]\[ x = \frac{-60}{-0.02} \][/tex]

  [tex]\[ x = 3000 \][/tex]

  Now find [tex]\( y \)[/tex]:

  [tex]\[ y = 7000 - x \][/tex]

 [tex]\[ y = 7000 - 3000 \][/tex]

  [tex]\[ y = 4000 \][/tex]

Answer:

Step-by-step explanation:

f(x) + n - shift the graph of f(x) n units up

f(x) - n - shift the graph of f(x) n units down

f(x - n) - shift the graph of f(x) n units to the right

f(x + n) - shift the graph of f(x) n units to the left

===================================

Look at the picture.

The graph of F(x) shifted 1 unit to the right and 3 units down.

Therefore the equation of the function G(x) is

[tex]G(x)=(x-1)^2-3[/tex]

In the context of this horse racing problem, the weights assigned to horses can range from 53 kg - 4 kg to 53 kg + 4 kg, or 49 kg to 57 kg, thus option a (49 kg–57 kg) is the correct answer.

The question involves the concept of range in mathematics. In this horse racing scenario, we are given that the standard weight carried is 53 kg, and that the weight carried by each horse cannot differ by more than 4 kg from the standard. To find the maximum weight, we need to add 4 kg to the standard weight. So, the maximum weight a horse can carry is 53 kg + 4 kg = 57 kg. Likewise, to find the minimum weight, we subtract 4 kg from the standard. As a result, the minimum weight a horse can carry is 53 kg - 4 kg = 49 kg. Therefore, the maximum and minimum acceptable weights for a horse to carry are 57 kg and 49 kg, respectively, making option a the correct answer.

https://brainly.com/question/29204101

#SPJ3

ANSWER

D. Ellipse;

[tex]3{x}^{2} +{y}^{2} + 6x - 6y + 3= 0[/tex]

EXPLANATION

The given equation is

[tex]3 {x}^{2} + {y}^{2} = 9[/tex]

Dividing through by 9 gives

[tex] \frac{ {x}^{2} }{ 3} + \frac{ {y}^{2} }{9} = 1[/tex]

This is the equation of an ellipse centered at the origin.

If this ellipse has been translated, so that its center is now at (-1,3), then the equation of the translated ellipse becomes

[tex]\frac{ {(x + 1) }^{2} }{ 3} + \frac{ {(y - 3)}^{2} }{9} = 1[/tex]

We multiply through by 9 to get,

[tex]3 {(x + 1)}^{2} + {(y - 3)}^{2} = 9[/tex]

Expand to obtain;

[tex]3( {x}^{2} + 2x + 1) + {y}^{2} - 6y + 9 = 9[/tex]

Expand to obtain;

[tex]3{x}^{2} + 6x + 3+ {y}^{2} - 6y + 9 = 9[/tex]

Regroup and equate to zero to obtain;

[tex]3{x}^{2} +{y}^{2} + 6x - 6y + 3= 0[/tex]

Answer:

k = -2

Step-by-step explanation:

x     -1   0   2     5

f(x)  2   0  -4  -10

ƒ(x) = kx

Substitute a pair of values for x and ƒ(x)

-10 = k×5

Divide each side by 5

k = -2

The constant of variation k = -2.

Answer:

The number b is bigger than the number a by [tex]\dfrac{1}{4}[/tex] of a.

Step-by-step explanation:

1. If the number a is smaller than the number b by 1/5 of b, then

[tex]a+\dfrac{1}{5}b=b.[/tex]

Thus,

[tex]a=b-\dfrac{1}{5}b=\dfrac{4}{5}b,\\ \\b=\dfrac{5}{4}a.[/tex]

2. Consider the expression [tex]b=\dfrac{5}{4}a:[/tex]

[tex]b=\dfrac{5}{4}a=\dfrac{4}{4}a+\dfrac{1}{4}a=a+\dfrac{1}{4}a.[/tex]

This gives you that the number b is bigger than the number a by [tex]\dfrac{1}{4}[/tex] of a.

It is found that A is smaller by 1/5 of b.

To analyze the function or expression to make the function uncomplicated or more coherent is called simplifying and the process is called simplification.

We are given that the number a is smaller than the number b by 1/5 of b.

So if we add a and 1/5 of b, we would have b:

a + 1/5b = b

Solving for a we have:

A = b - 1/5b = 4/5b

A = 4/5b

Solving for b divide both sides by 4/5,

B = 5/4a

Since 4/4 = 1, this means b would be bigger than a by 1/4

Learn more about simplification;

https://brainly.com/question/17579585

#SPJ6

Answer:

(0,-5)

Step-by-step explanation:

The vertex form of the equation of a circle is [tex](x-h)^2 + (y-k)^2 = r^2[/tex] where (h,k) is the center of the circle and r is the radius. This means that for the equation [tex]x^2 + (y+5)^2 = 25[/tex] the center is (0,-5).

Answer:

Center:  ( − 5 , 2 )

Radius:  5

Step-by-step explanation:

on edge

Answer:

Step-by-step explanation:

z1 = -3

z2 = 5i

z1·z2 = (-3)(5i) = -15i = 0 + (-15)i

Then the real and imaginary parts are a = 0, b = -15.

Answer:

A line graph

Step-by-step explanation:

A line graph will be the best option because it can show the exact height based on time as a data point. Connecting each data point will then reveal the trend in how the sapling grows and average growth rate among other information can be found.

Final answer:

A line graph is the best choice for displaying the continuous growth of a sapling tree over a period of several weeks, as it shows trends over time effectively.

Explanation:

The best type of graph for showing the height of a sapling tree over several weeks is a line graph. A line graph is designed to show trends over time and is particularly useful when you want to display changes in a variable continuously, such as the growth of a tree's height. The line graph will clearly depict the gradual increase in height with each passing week, allowing for an easy visual interpretation of the data. Other graphs such as a bar graph, circle graph (or pie chart), or a histogram are not as suitable for representing data over time in the same continuous and clear manner as a line graph.

Answer:

(6,8.75)

Step-by-step explanation:

we know that

The distance from the x-axis to the point (7,8.75) is equal to the y-coordinate of the point

so

The distance is 8.75 units

therefore

All ordered pairs that have 8.75 as y coordinate, will be at the same distance from the x axis that the given point

Answer:

-2.4

Step-by-step explanation:

129x40%=51.6

51.6-54=-2.4

hope that helps!!

Answer:

21) Yes; 23) Yes

Step-by-step explanation:

If the lengths form a right triangle, the sum of the squares of the two shorter sides should equal the square of the longest side (Pythagoras).

21)

5² +  12² =  13²

25 + 144 = 169

       169 = 169

The lengths form a right triangle.

23)

3² +  4² =  5²

9  + 16 = 25

      25 = 25

The lengths form a right triangle.

Answer:

$3.6

Step-by-step explanation:

6%=.06

60*.06=3.6

Answer:

  C.  132

Step-by-step explanation:

We assume all angle measures are in degrees. The vertical angles are equal in measure, so ...

  4x = x +36

  3x = 36

  x = 12

  x +36 = 48

  y = 180 -48 = 132

The value of y is 132.

Answer:

35/12 cups

Step-by-step explanation:

Brett's recipe will make [tex]\( \frac{35}{12} \)[/tex] cups of fruit salad, which is approximately 2.92 cups when rounded to two decimal places.

To find the total number of cups of fruit salad Brett's recipe will make, we add the amounts of each fruit together:

1. Apples: 1 1/2 cups

2. Oranges: 3/4 cup

3. Grapes: 2/3 cup

To add these fractions, we need a common denominator. The least common denominator (LCD) of 2, 4, and 3 is 12.

[tex]1. Apples: \(1 \frac{1}{2} = \frac{3}{2}\) cups[/tex]

[tex]2. Oranges: \(\frac{3}{4}\) cup[/tex]

[tex]3. Grapes: \(\frac{2}{3}\) cup[/tex]

Now, we convert each fraction to have a denominator of 12:

[tex]1. Apples: \(\frac{3}{2} \times \frac{6}{6} = \frac{9}{6}\) cups[/tex]

[tex]2. Oranges: \(\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}\) cups[/tex]

[tex]3. Grapes: \(\frac{2}{3} \times \frac{4}{4} = \frac{8}{12}\) cups[/tex]

Now, we add these amounts:

[tex]\(\frac{9}{6} + \frac{9}{12} + \frac{8}{12} = \frac{18}{12} + \frac{9}{12} + \frac{8}{12} = \frac{35}{12}\) cups[/tex]

So, Brett's recipe will make [tex]\( \frac{35}{12} \)[/tex] cups of fruit salad, which is approximately 2.92 cups when rounded to two decimal places.

In order for it to be a rectangle all four angels have to be 90 so:

13x+34+10x+10=90

23x=46

X=2

Answer:

a) The increasing intervals would be from -4 to 0 and 4 to infinity. The decreasing interval would just be from negative infinity to -4 and 0 to 4.

b) The local maximum comes at x = 0. The local minimums would be x = -4 and x = 4

c) The inflection points are x= +/-√16/3

Step-by-step explanation:

To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.

f(x) = x^4 - 32x^2 + 2

f'(x) = 4x^3 - 64x

Now we take the derivative and solve for zero to find the local max and mins.

f'(x) = 4x^3 - 64x

0 = 4x^3 - 64x

0 = 4x(x + 4)(x - 4)

x = -4 OR x = 4 OR 0

Given the shape of a positive 4th power function function, we know that the first and last  would be a minimums and the second would be a maximum.

As for the increasing, we know that a 4th power, positive function starts up and decreases to the local minimum. It also decreases after the local max. The rest of the time it would be increasing.

In order to find the inflection point, we take a derivative of the derivative and then solve for zero.

f'(x) = 4x^3 - 64x

f''(x) = 12x^2 - 64

0 = 12x^2 - 64

64 = 12x^2

16/3 = x^2

+/- √16/3 = x

-3/2 = x

Answer:

This is a problem where we need to analyse the function. To do so, we can recur to the applications of derivatives.

So, we have to derive the function first:

[tex]f(x)=x^{4}-32x^{2}  +3\\f'(x)= 4x^{4-1} -32(2)x^{2-1} + 0\\f'(x) = 4x^{3} -64x[/tex]

To analyse the function, we need to determinate the intervals using critic points, which can be found making the function equal to zero and then factorize:

[tex]f'(x) = 4x^{3} -64x=0\\x(4x^{2} -64)=0\\[/tex]

Applying the null factor property, we can equal to zero both factors:

[tex]x = 0\\4x^{2} -64=0\\4x^{2} =64\\x^{2} = \frac{64}{4}  =16\\x = ± 4[/tex].

So, there are three critic points: -4; 0 ; 4, which give us four intervals.

[tex](- \infty; -4], (-4;0],(0;4],(4;+\infty)\\[/tex].

Now, we have to evaluate each intervals, to know if they are increasing or decreasing. If the result of each evaluation results more than zero, then it's increasing, if results less than zero, it's decreasing.

So, the test values are -5 (1st interval), -1 (2nd interval), 1 (3rd interval), 5 (4th interval). As you can see, each value is included in one interval. The evaluation can be done just by replacing each value:

[tex]f'(-5) = 4(-5)^{3} -64(-5) = -180 <0\\f'(-1) = 4(-1)^{3} -64(-1) = 60>0\\f'(5) = 180>0\\f'(1) = -60<0[/tex]

Therefore, the increasing intervals of the function are [tex](-4;0],(4;+\infty)\\[/tex]. On the other hand, the decreasing intervals are [tex](- \infty; -4],(0;4],\\[/tex].

On the other hand, if the function change from negative to positive in c, then the function has a minimum located in (c ; f(c)). So, in -4 and 4, the function change from negative to positive (from decreasing to increasing), so the are minimums located in (-4;-253) and (4;-253). However, if the function change from positive to negative in c, then the functions has a maximum locate in (c ; f(c)). In this case, 0 changes from positive to negative. So, the maximum is located in (0; 3).

At last, the inflection points can be find using the second derivative criteria. First, we derive again the function, to find the second derivative, and then equal to zero to find inflexion points:

[tex]f"(x) = 12x^{2} -64=0\\12x^{2} =64\\x^{2} =\frac{64}{12} \\x=\sqrt{\frac{64}{12} } =±2.3[/tex]

Therefore, the inflexion points are located in -2.3 and +2.3. Next, we do the same process, we determine the intervals, then we evaluate each of them to find which interval is concave up and which is concave down.

Intervals: [tex](- \infty;-2.3);(-2.3;2.3);(2.3:+\infty)[/tex]

We can use -3, 0 and 3 to evaluate each interval:

Replacing this values in the second derivative expression ([tex]f"(x) = 12x^{2} -64[/tex]), we have:

[tex]f"(-3) = 12(-3)^{2} -64=44>0\\f"(0)=-64<0\\f"(3) = 12(3)^{2} -64=44>0[/tex]

So, positive results mean concave up, negative results mean concave down. Therefore,  [tex](- \infty;-2.3);(2.3:+\infty)[/tex] are concave up, and (-2.3;2.3) is concave down.

Answer:

Step-by-step explanation:

The expected value is the sum of products of payoff and probability of that payoff:

  -$8(37/38) +$288·(1/38) = $(-296 +288)/38 = -$8/38 ≈ -$0.21

In 1000 plays, the expected loss is ...

  -$8000/38 ≈ $210.53

The expected loss per roulette game, when betting $8 on number 33, is approximately $.0526, which equates to an expected loss of about $52.63 after 1000 games.

In the game of roulette, the player takes a risk by placing a bet on a specific outcome, in this case, the metal ball landing on the number 33. For this situation, we need to calculate the Expected Value, which is the long-term average of a random variable.

The player will either win $280 plus the original $8 bet, amounting to $288 or lose the $8 bet. The chance of winning is 1/38 and the chance of losing is 37/38. The expected value can be calculated as follows: (1/38) * $288 + (37/38) * -$8. This calculates to -$.0526. Therefore, each game, on average, the player loses about $.0526.

If you then multiply this average loss per game by the number of games played, in this case, 1000 games, you would find the total expected loss. So, -$. 0526 * 1000 = -$52.63. Therefore, if a player played this game 1000 times, they would expect to lose about $52.63.

https://brainly.com/question/34769376

#SPJ3

Answer: [tex]y=\frac{2}{5}x-8[/tex]

Step-by-step explanation:

By definition, the equation of the line in  slope-intercept form of is:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

Then, given the slope 2/5 and the point, (-10, -5), you can calculate the value of b by susbtituting and solve for it:

[tex]-10=\frac{2}{5}(-5)+b\\ -10=-2+b\\b=-8[/tex]

Substitute this value and the slope into the equation. THerefore, you obtain:

[tex]y=\frac{2}{5}x-8[/tex]

Answer:

45 minutes.

Step-by-step explanation:

d = 40 - 1/5m

When d = 31 we have:

31 = 40 - 1/5 m

1/5 m = 40 - 31 = 9

m = 9*5

= 45 minutes answer.