What is the equation of the line that has a slope of -4 and goes through (-1,6)

The solution of this system of linear equations is [tex](x,y,z) = (1,2,4)[/tex]. (Correct choice: C)

The system of equations is represented by the following augmented matrix:

[tex]\left[\begin{array}{cccc}2&1&4&16\\5&-2&2&-1\\1&2&-3& -9\end{array}\right][/tex] (1)

Where the fourth column represents the vector column of independent coefficients. After making some operations, we find that the reduced row-echelon form of the augmented matrix is:

[tex]\left[\begin{array}{cccc}1&0&0&1\\0&1&0&2\\0&0&1& 4\end{array}\right][/tex]

The solution of this system of linear equations is [tex](x,y,z) = (1,2,4)[/tex]. (Correct choice: C) [tex]\blacksquare[/tex]

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Final answer:

To solve the system of equations, we need to find the reduced row-echelon form of the augmented matrix. Applying row operations, we can reduce the matrix to row-echelon form. Then, using backward substitution, we can find the values of x, y, and z. The solution to the system of equations is (-10, 2, 8.5).

Explanation:

To solve the system of equations, we can represent it as an augmented matrix and find its reduced row-echelon form. The augmented matrix for the given system of equations is:

[2 1 4 | 16]
[5 -2 2 | -1]
[1 2 -3 | -9]

Next, we need to apply row operations to reduce the matrix to its row-echelon form. Following the Gaussian elimination method, we perform the row operations:

R2 → R2 - 5R1, and
R3 → R3 - R1

The resulting matrix in row-echelon form is:

[2 1 4 | 16]
[0 -7 -18 | -81]
[0 0 0 | 0]

Now, we can apply backward substitution to find the values of x, y, and z. From the last row of the row-echelon form, we know that 0z=0. We can assign any value to z, such as 1, and then solve for x and y. Plugging in z=1, we get:

2x + 1y + 4(1) = 16

x + 2y - 3(1) = -9

Simplifying these equations, we get:

2x + y + 4 = 16 → 2x + y = 16 - 4 → 2x + y = 12

x + 2y - 3 = -9 → x + 2y = -9 + 3 → x + 2y = -6

Using these equations, we can solve for x and y by setting up a system of linear equations:

2x + y = 12
x + 2y = -6

Solving this system, we can find the values of x and y: x = -10 and y = 2. Finally, substituting these values back into one of the original equations, we can find z:

2(-10) + 1(2) + 4z = 16 → -20 + 2 + 4z = 16 → 4z = 34 → z = 8.5

So, the solution to the system of equations is (-10, 2, 8.5).

Answer:

X=89.4

Step-by-step explanation:

Answer:

270 miles

Step-by-step explanation:

Let the total distance be d.

Then (2/3)d = 180 miles.

Solve for d by multipying both sides by (3/2):

(3/2)(2/3)d  = (3/2)(180 miles) = 270 miles

The total distance is 270 miles.

Answer:

12x-8y

Step-by-step explanation:

10x+2x=12x

-5y-3y=-8y

Answer: 12x-8y

Step-by-step explanation: add like terms 10x and 2x, and -3-5= 8 so 8y

Answer:

[tex]2\frac{1}{6}\ frames[/tex]

Step-by-step explanation:

we know that

To find out how many frames she can  make with the exiting material, divide 1 5/8 by 3/4

so

[tex]1\frac{5}{8}:\frac{3}{4}[/tex]

Convert mixed number to an improper fraction

[tex]1\frac{5}{8}=\frac{1*8+5}{8}=\frac{13}{8}[/tex]

substitute

[tex]\frac{13}{8}:\frac{3}{4}=\frac{52}{24}\ frames[/tex]

Simplify

[tex]\frac{13}{6}\ frames[/tex]

Convert to mixed number

[tex]\frac{13}{6}\ frames=\frac{12}{6}+\frac{1}{6}=2\frac{1}{6}\ frames[/tex]

Answer:

The total cost for 8 skiers=316 dollars

Step-by-step explanation:

Given that the expression 15n+12n+100 represents the total cost in dollars for skis,boots and a lesson for n skiers.

To simplify the given expression :

15n+12n+100=27n+100

27n=-100

Therefore [tex]n=\frac{-100}{27}[/tex]

Now to find the total cost for 8 skiers.

The total cost for 8 skiers can be written as below

Put n=8 in the given expression 15n+12n+100

15(8)+12(8)+100

=120+96+100

=316

Therefore the total cost for 8 skiers is 316 dollars

The total cost for 8 skiers=316 dollars

Answer:

10 liters of solution should be drained off  and replaced with water.

Step-by-step explanation:

As forty liters of a 60% salt solution are being reduced to a 45% solution, and we have to determine the amount in liters that must be drained and replaced with distilled water so that the resulting solution will  contain only 45% salt solution.

So, the equation becomes

[tex]0.60(40-x) = 0.45(40)[/tex]

[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]

[tex]0.6\left(40-x\right)=0.45\cdot \:40[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:0.45\cdot \:40=18[/tex]

[tex]0.6\left(40-x\right)=18[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}10[/tex]

[tex]0.6\left(40-x\right)\cdot \:10=18\cdot \:10[/tex]

[tex]\mathrm{Refine}[/tex]

[tex]6\left(40-x\right)=180[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}6[/tex]

[tex]\frac{6\left(40-x\right)}{6}=\frac{180}{6}[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]40-x=30[/tex]

[tex]\mathrm{Subtract\:}40\mathrm{\:from\:both\:sides}[/tex]

[tex]40-x-40=30-40[/tex]

[tex]-x=-10[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]

[tex]\frac{-x}{-1}=\frac{-10}{-1}[/tex]

[tex]x=10[/tex]

Therefore, 10 liters of solution should be drained off  and replaced with water.

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Answer:

10 liters of solution should be drained off  and replaced with water.

Step-by-step explanation:

;) brainliest???????

Answer:

Step-by-step explanation:

For example, apply the distributive property to the expression 3 (2 + ) to produce the equivalent expression 6 + 3; apply the distributive property to the expression 24 + 18 to produce the equivalent expression 6 (4 + 3); apply properties of operations to + + to produce the equivalent expression 3.

Answer:

1/8

Step-by-step explanation:

If we divide both the top and the bottom by 5 since we know 125 is a multiple of 5, we get 25/200. Divide both by 5 again to get 5/40. Divide by 5 one more time to get 1/8, and since the numerator is 1, the fraction cannot be simplified any further. Therefore, the answer in its simplest form is 1/8.

Answer:

If we divide both the top and the bottom by 5 since we know 125 is a multiple of 5, we get 25/200. Divide both by 5 again to get 5/40. Divide by 5 one more time to get 1/8, and since the numerator is 1, the fraction cannot be simplified any further. Therefore, the answer in its simplest form is 1/8.

Step-by-step explanation:

Answer:

15.68

Step-by-step explanation:

22/15=23/x

cross product

15*23=22*x

345=22x

x=345/22

x=15.68

Answer:

Step-by-step explanation:

breadth = x

length = 2x

Perimeter = 540m

2*( length + breadth ) = 540

2 *(2x + x) = 540

3x = 540/2

3x = 270

x = 270/3

x = 90 m

Breadth = 90m = 90 *100 = 9000 cm

Length = 2*90 = 180 m = 180 * 100 = 18000 cm

No.of bricks = Area of room/ area of one brick

= 9000 * 18000 / 20 * 12

= 675000 bricks

Answer:

80.4

Step-by-step explanation:

To remember all of the ratios for trigonometry, using the acronym "SohCahToa". You always divide two sides for trig. ratios.

'S' is sine or sin for short.

'C' is cosine or cos for short.

'T' is tangent, or tan for short.

'h' means hypotenuse, the longest side in the triangle.

'o' means the side that's opposite, or not touching the angle of reference.

'a' means the side that's adjacent, or touching the angle of reference.

The angle of reference means the angle you are talking about (use the symbol θ to mean angle). In this question, the angle of reference is 15°.

We have the adjacent side, 300, and we need to find the opposite side, x.

The trig. ratio that has the side adjacent and opposite is tangent or 'tan'.

tanθ = opposite / adjacent     Trig. ratio for tangent

tan15° = x / 300     Substitute what we know. Isolate 'x'.

x = 300tan15°     This means 300 times tan15°. Use a calculator.

x = 80.3847..... Exact decimal answer on your calculator

x ≈ 80.4       Answer rounded to nearest tenth (first decimal)

When rounding, you decide to round up or down using the decimal place after where you will cut off.

In 80.3847..... '8' tells us to round up because it is 5 or greater.

If  the second decimal place was 4 or less, we round down (the answer would be 80.3).

Answer:

Step-by-step explanation:

a hole 8 ft deep.....would be -8 because it is -8 below ground level

u earn $ 8....thats +8

a temp of 8 F....thats a +8

an 8 yd pass....thats a + 8

Answer:

a hole 8 ft deep.....would be -8 because it is -8 below ground level

If the given function is h(x)=5x-1 then  h(1)h(1) would be equal to 16.

Function is a type of relation, or rule, that maps one input to specific single output.

Given;

h(x)=5x-1

In order to find the  h(1)h(1)

substitute x = 1 in the function h(x)

h(x)=5x-1

h(1) = 5(1) - 1

h(1) = 5 -1 = 4

So, h(1)h(1) = 4 x 4 = 16

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Answer:

18.7 feet far

Step-by-step explanation:

Based on the information given we can conclude that our set up will be a Right triangle (i.e. one angle is 90°), where the hypotenuse will be denoted by the guy wire of [tex]20ft[/tex]  and angle of 21° is the angle formed between then hypotenuse and the base (i.e. ground).

Thus we want to find the base length (lets call it [tex]x[/tex] ) of this triangle, so we can use trigonometry as we have one angle and the hypotenuse, as follow:

[tex]cos(21)=\frac{adjacent side}{hypotenuse}=\frac{baselength}{guywire}\\\\ cos(21)=\frac{x}{20} \\x=20cos(21)\\x=18.671\\x=18.7ft[/tex]

So the base is approximately 18.7 feet far from the tree of the anchored wire.

The distance from the base of the tree to the stake anchoring a guy wire that is 20 ft long and makes a 21-degree angle with the ground is approximately 18.8 ft, found using the cosine function of trigonometry.

The student asked for help in determining the distance from the base of the tree to the stake anchoring a guy wire that is 20 ft long and makes a 21-degree angle with the ground. To solve this problem, we need to employ trigonometry, specifically the cosine function which relates the adjacent side of a right triangle (the distance we're looking for) to the hypotenuse (the length of the guy wire) and the angle between them.

Using the formula cosine(angle) = adjacent/hypotenuse, we can set up our equation as cos(21°) = distance/20 ft. Rearranging the equation to solve for the distance, we get distance = 20 ft * cos(21°). After calculating, we find that the distance from the base of the tree to the stake is approximately 18.8 ft.

Answer:

Any U

Step-by-step explanation:

Hey there. Here isbyour solution:

2.7-2.8=0

0/u=0

Statement is always true. So u[tex]\in[/tex]R

Answer:

I think it is option B. and option C.

Step-by-step explanation:

an instance of a form of reasoning in which a conclusion is drawn from two given or assumed propositions. a common or middle term is present in the two premises but not in the conclusion, which may be invalid.

Brady bought items totaling $42.13 from the hardware store. After giving a hundred-dollar bill, he received $57.87 in change.

To calculate the change Brady gets back from the hardware store, we need to add up the cost of the items he purchased and then subtract this total from the amount of the hundred-dollar bill he provided to the owner. First, we add the cost of the wrench ($9.63), the nail gun ($28.01), and the dozen nails ($4.49) to find the total spending. Once we have the total, we subtract it from $100 to find out how much change Brady should receive.

Let's calculate:

Brady will receive $57.87 in change from the hardware store.

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Answer:80

Step-by-step explanation:

Answer:

Number of cars=3

Number of buses=4

Step-by-step explanation:

Let the number of cars be x, and the number of buses be y.

x+y=7 (total number of vehicles) ---①

5x+45y=195 (total number of students) ---②

*each car holds 5 students, whereas each bus holds 45, which equals to 5x and 45y

From equation ①,

x=7-y ---③

Substitute ③ into ②

5(7-y)+45y=195

35-5y+45y=195

40y=195-35

40y=160

y=4

Therefore,

x+y=7

x=7-y

x=7-4

x=3

Answer:

The slope to the given points A at (2,6) and B at (4,10) is 2

Therefore slope m=2

Step-by-step explanation:

Given points are A at (2,6) and B at (4,10)

To find the slope of the given two points :

Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the given points A at (2,6) and B at (4,10) respectively

Slope m[tex]=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now substitute the points in the above equation we get

m[tex]=\frac{10-6}{4-2}[/tex]

[tex]=\frac{4}{2}[/tex]

[tex]=2[/tex]

Therefore m=2

The slope to the given points A at (2,6) and B at (4,10) is 2

Therefore slope m=2

Answer: 23x305 = n , n = 7,015 square feet

Step-by-step explanation:

1 office = 305 square feet

If we want to calculate the area of 23 offices, we just need to multiply the area of one office, by the number of total offices.

That's 305 square feet * 23 = 7015 square feet

The correct answer is 23x305 = n , n = 7,015 square feet

Hope I helped!

The correct answer is The graph stretches because 7 is bigger than 1.

The graph of [tex]\( f(x) = 7|x-5|+9 \)[/tex] experiences a vertical stretch, not a shrink, despite the coefficient ( 7 ) being greater than 1.

The absolute value function ( |x| ) reflects any negative values of ( x ) to their positive counterparts, essentially mirroring the negative portion of the graph onto the positive side.

When you apply a coefficient greater than 1 to [tex]\( |x| \), as in \( 7|x| \),[/tex] it vertically stretches the graph.

This means that the graph of ( f(x) ) will be vertically stretched by a factor of 7 compared to the graph of ( |x| ).

In this case, since [tex]\( |x-5| \)[/tex] is the argument of the absolute value, it implies a horizontal shift of the graph of [tex]\( |x| \)[/tex] by 5 units to the right.

So, the absolute value graph [tex]\( |x| \)[/tex] gets shifted 5 units to the right before it is stretched vertically by a factor of 7.

The ( +9 ) at the end of the function only moves the entire graph up by 9 units.

Thus, the graph of [tex]\( f(x) = 7|x-5|+9 \)[/tex] experiences a vertical stretch by a factor of 7.

Therefore, the correct statement is: "The graph stretches because 7 is bigger than 1."

Question

Does the absolute value graph below stretch or shrink? Support your answer. F(x) = 7|x-5|+9

The graph shrinks because 7 is between 0 and 1.

The graph stretches because 7 is bigger than 1.

The graph shrinks because 7 is bigger than 1.

The graph stretches because 7 is between 0 and 1.

Answer:

f(x)=(x+2)(x−(−1+i2√))(x−(−1−i2√))

Sorry if its wrong!

The required completely factored form is f(x) = (x + 2)(x−(−1+i2√))(x−(−1−i2√)).

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original. For example, the number 21 factors into primes as 3 × 7, and the polynomial x² − 9 factors as (x+3)(x-3).

The function is given in the question following as:

f(x) = x³ + 4x² + 7x + 6

We have to determine the completely factored form of the given function

As per the given question, we have

⇒ f(x) = x³ + 4x² + 7x + 6

Common factor as (x + 2) out in the above expression,

⇒ f(x) = (x + 2)(x² + 2x + 3)

⇒ f(x) = (x + 2)(x−(−1+i√2))(x−(−1−i√2))

Therefore, the required completely factored form is f(x) = (x + 2)(x−(−1+i2√))(x−(−1−i2√)).

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Answer:

Explanation:

First, you must find the y-value returned by the line in the graph for a time (x) of five minutes, and then use the deviation of 3º to conclude the range of the real temperature.

1. y- value at x = 5 min.

The trend line (blue line in the graph) passes through the point (5,15), which means that it predicts a temperature of 15ºF when the time (x) is 5 minutes, or five minutes after the freezer was turned on.

2. Actual temperature value

It is stated that the temperature was actually three degrees from what the trend line shows, that means that the actual temperature could be 3ºF more or 3ºF less than the predicted temperature of 15ºF.

Mathematically:

The values that the actual temperature could be after the freezer was on for five minutes are 12°F or 18°F.

A trendline is sometimes referred to as a line of best fit and it is a statistical tool which is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any form of correlation (either positive or negative) between a given data.

By critically observing the scatter plot, we can logically deduce that the trend line passes through the point (5, 15), which implies that the temperature is 15°F, 5 minutes after the freezer was turned on.

Since the actual temperature deviates by 3°F from what the trend line shows, we have:

Actual temperature = 15 ± 3

Actual temperature = 15 - 3 = 12°F

Actual temperature = 15 + 3 = 18°F

Answer:

The rule of translation (x,y) → (x+6 , y-8)

Step-by-step explanation:

The rest of the question is the coordinates of the ΔABC and ΔA'B'C'

The coordinates of the ΔABC: A(-6,2) , B(-5,5) , C(-1,3)

The coordinates of the ΔA'B'C': A'(0,-6) , B'(1,-3) , C'(5,-5)

It is required the rule of translation.

By Comparing between any of the points and its image

For example between A and A'

Let A(-6,2) = (x,y)  and  A'(0,-6) = (x+h , y+k)

So, x = -6 and y = 2

And x+h = 0 , y+k = -6

Substitute with x and y to find h and k

So, -6 + h = 0 ⇒ h = 6

And 2 + k = -6 ⇒ k = -8

So, the rule of translation (x,y) → (x+6 , y-8)

Answer:

487887

Step-by-step explanation:

The nth term of the quadratic sequence 1, 12, 29, 52, 81 is T(n) = 2n² - n - 2.

1. Check for a Quadratic Sequence:

To determine if a sequence is quadratic, we look at the differences between consecutive terms, and then the differences between those differences (second differences).

First differences: 11, 17, 23, 29

Second differences: 6, 6, 6

The sequence is quadratic since the second differences are constant.

2. General Form of a Quadratic Sequence:

The quadratic sequence formula in general is:

T(n) = an² + bn + c

Where:

T(n) is the nth term

a, b, and c are constants to be determined

3. Forming Equations:

We can use the first three terms of the sequence to create three equations:

For n = 1: a(1)² + b(1) + c = 1

For n = 2: a(2)² + b(2) + c = 12

For n = 3: a(3)² + b(3) + c = 29

Simplifying these equations, we get:

a + b + c = 1

4a + 2b + c = 12

9a + 3b + c = 29

4. Solving the Equations:

By concurrently solving this set of equations, we arrive at:

a = 2

b = -1

c = -2

5. Finding the nth Term:

Substituting the values of a, b, and c into the general formula, we get: T(n) = 2n² - n - 2

Answer:

23 over 3 will give you a mixed number / whole number of 8

Step-by-step explanation:

your answer is 8

Answer:

the answer to this is

24/3= 8 ( edited again as I TOOK THE wrong values )