Find the value of y for the following system of equations. -x - y = 7 x - y = 9

Answer:

5.65 cm

Step-by-step explanation:

We are given that the length of each leg of an isosceles right triangle is 4 cm and we are to find the length of the hypotenuse.

For this, we will use the Pythagoras Theorem:

[tex] a ^ 2 = b ^ 2 + c ^ 2 [/tex]

where [tex]a[/tex] is the hypotenuse.

[tex] a ^ 2 = 4 ^ 2 + 4 ^ 2 [/tex]

[tex] \sqrt { a ^ 2} = \sqrt { 3 2 } [/tex]

[tex] a = 5 . 6 5 [/tex]

Therefore, the length of the hypotenuse is 5.65 cm.

Answer:

hypotenuse = 4√2

Step-by-step explanation:

It is given that, the  length of each leg of an isosceles right triangle is 4 cm

To find the hypotenuse

From the given information we get the given triangle is a right triangle with angles 45°, 45° and 90°

Therefore the side are in the ration 1 : 1 : √2

Here two legs are give

leg1 : leg2 : hypotenuse = 4 : 4 : 4√2

Therefore hypotenuse = 4√2

Answer:

Domain: All Real Numbers

Range: All real numbers

Step-by-step explanation:

The given function is:

[tex]f(x) = 2(x-4)[/tex]

Domain:

The given function will not be undefined on any value of x as there is no denominator involved in the function.

So, the domain of the function is all real numbers

Range:

Similarly the range of the function is also all real numbers.

In finance, the buyer pays more when choosing to finance the boat rather than paying cash upfront due to additional fees included in the payments.

The subject area of the question is Mathematics, specifically Financial Mathematics. The question is asking about the total cost Ken will pay for the boat if he chooses to finance it. The down payment is $3000 and he will make 48 monthly payments of $300, totaling $14,400. Therefore, Ken will pay a total of $17,400 when financing the boat, which is $2,400 more than the cash purchase price.

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To find the total amount paid for the boat, add the down payment to the product of the monthly payments and the number of payments.

To find the total amount paid for the boat, we need to calculate the total future amount. The down payment is $3,000 and there are 48 monthly payments of $300 each.

The total future amount can be calculated using the formula:

Total Future Amount = Down Payment + Monthly Payments * Number of Payments

Plugging in the values, we get:

Total Future Amount = $3,000 + $300 * 48 = $17,400

Therefore, Ken will pay a total of $17,400 for the boat.

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Answer:

Step-by-step explanation:

[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}\\\\f(x)=2x^2-7x\\\\\text{Put the values of x = 2 and x = 6 to the equation of the function:}\\\\f(2)=2(2^2)-7(2)=2(4)-14=8-14=-6\\f(6)=2(6^2)-7(6)=2(36)-42=72-42=-30\\\\\dfrac{f(6)-f(2)}{6-2}=\dfrac{-30-(-6)}{4}=\dfrac{-24}{4}=-6[/tex]

Answer:

64.21

Step-by-step explanation:

Here we are given with the a number in decimals and need to find its product with 10.

please note the rule of multiplication in decimals . When we multiply any decimal with 10, 100, 1000 , 10000 and so on.. the position of decimal in the number given to us shifts to its right by the number of places as we have the number of 0 in the multiplier

6.421 X 10

here we have only one 0 in the multiplier , hence the position of decimal in 6.421 will be shifted to one place towards right

6.421 x 10 = 64.21

Answer:

64.21

Step-by-step explanation:

For this case we have the following functions:

[tex]f (x) = 4x ^ 2 + 1\\g (x) = x ^ 2-5[/tex]

We must find[tex](f-g) (x):[/tex]

By definition of operations with functions we have:

[tex](f-g) (x) = f (x) -g (x)[/tex]

So:

[tex](f-g) (x) = f (x) -g (x) = 4x ^ 2 + 1- (x ^ 2-5) = 4x ^ 2 + 1-x ^ 2 + 5 = 3x ^ 2 + 6[/tex]

Answer:

Option A

[tex]3x ^ 2 + 6[/tex]

Answer:

x = 21

Step-by-step explanation:

x- 12 = 9

Add 12 to each side

x- 12+12 = 9+12

x = 21

Answer:

[tex]\huge \boxed{x=21}[/tex]

Step-by-step explanation:

[tex]\Huge\textnormal{Add 12 from both sides of the equation.}[/tex]

[tex]\displaystyle x-12+12=9+12[/tex]

[tex]\Huge \textnormal{Simplify and solve to find the answer.}[/tex]

[tex]\displaystyle 9+12=21[/tex]

[tex]\huge \boxed{x=21}[/tex], which is our answer.

Answer:

The graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex] is a vertical stretch of 5 units and a horizontal stretch by 2 units of the parent graph

Step-by-step explanation:

We want to find out how the graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex] compare with the graph of the parent function [tex]g(x)=\cos (x)[/tex].

We can observe that the transformation applied to the basic cosine function is of the form:

[tex]y=A \cos Bx[/tex]

The [tex]A=5[/tex] is a vertical stretch by a factor of 5 units.

[tex]B=\frac{1}{2}[/tex] is a horizontal stretch by a factor of 2 units.

Therefore the graph of [tex]f(x)=5\cos(\frac{1}{2}x)[/tex]  will stretch vertically by a factor of 5 units and stretch horizontally by a factor of 2 units as compared to  [tex]g(x)=\cos (x)[/tex].

See attachment

Answer:

It is A i believe.

Step-by-step explanation:

Because, 15/100 = 0.15 and y is your regular price so;

y - 0.15

Sorry had to rewrite what i did, but i hope my answer has helped you.

Check the picture below.

Answer:

i think its d

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=√(-x-3) - 3

y exisit : - x -3 ≥ 0

- x  ≥ 3

x ≤ - 3    the domain is :  D=] -∞,-3 ]

y=√(-x-3) - 3

y + 3 = √(-x-3)

x exisit :  y + 3  ≥ 0   ; y ≥ -3

the range is : w = [- 3,+ ∞ [

look the graph

Let your age = X

Now you have 500 - 3x = 278

Subtract 500 from each side:

-3x = -222

Divide both sides by -3:

x = -222 / -3

x = 74

You are 74 years old.

The age of an old man is 74 years old.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Let the age of an old man be x.

500 reduced by 3 times my age is 278 can be expressed as

⇒ [tex]500-3x=278[/tex]

⇒ [tex]500-278=3x[/tex]

⇒ [tex]222=3x[/tex]

⇒ [tex]x=\frac{222}{3}[/tex]

⇒ [tex]x=74[/tex]

Hence we can conclude that the age of an old man is 74 years old.

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Answer:

105 frames

Step-by-step explanation:

Given that 25 frames are played per second

25 frames= 1 sec

The video already played 3 and 2/5 seconds before the player started to count 0

Write 3 and 2/5 seconds as an improper fraction

=(5*3)+2 / 5 = 17/5 seconds

Multiply by 25 frames

17/5 *25 =85 frames

So according to the video counter,after 17/5 seconds,it should count 85 frames.However,at 0 seconds,it indicated a count of 190 frames.Thus,to get the number of frames that were already in count you subtract 85 frames from the 190 frames.

190-85=105 frames.

The video had played 275 frames when the timer showed [tex]-3\frac{2}{5}[/tex]    seconds.

To determine how many frames had been played when the timer showed [tex]-3\frac{2}{5}[/tex] seconds, we first need to convert [tex]-3\frac{2}{5}[/tex] seconds to an improper fraction or decimal. We have [tex]-3\frac{2}{5}[/tex] = [tex]-\frac{17}{5}[/tex] seconds.

Since the video plays at a rate of 25 frames per second, we can calculate the number of frames played during [tex]-\frac{17}{5}[/tex] seconds as follows:

Total frames = 25 frames/second × [tex]-\frac{17}{5}[/tex] seconds = -85 frames.

This means that 85 frames had been played before the timer started counting (since negative time indicates frames played before the recorded start time).

Since at 0 seconds, the video had already played 190 frames, we add the frames played during the negative time interval:

Total frames = 190 frames (initial) + 85 frames = 275 frames.

Answer:

180 in

Step-by-step explanation:

The perimeter is just the sum of the lengths of the sides of the shape.

So all we need to do here is:

40+10+(40-18)+(50-10)+18+50.

I got (40-18) for the bottom of the top rectangle, the part that is poking out.

I got (50-10) for the right side of the rectangle that is poking out towards the bottom.

40+10+(40-18)+(50-10)+18+50

40+10+22       +40       +18+50

50     +62                      +68

50+62+68

112+68

180

180 in

I'm going to post a drawing here to show the lengths I was talking about:

Answer:

[tex]a_n=5n[/tex]

Step-by-step explanation:

They gave us the first two terms in the sequence which is 5,10.

They then tell us the sequence is arithmetic which means all you need to do to get the next term is add/subtract.

To get from 5 to 10, you would need to add 5.

So that is what we are doing every time here.

5,10,15,20,25,... so on...

Now we want to make an equation for this.

When you see arithmetic sequence, you should think linear equations.

x   |    y

-----------

1        5

2       10

3       15

4       20

Can you see the relationship between y and x?

Slope is 5 because that is what the sequence is going up by.

y=5x+b

Maybe you can already see b is 0. If not, you can use a point on the line to find b.

Let's use (1,5).

5=5(1)+b

5=5+b

0=b

So b=0.

The equation is y=5x.

Our since we are talking about sequences maybe you prefer to say [tex]a_n=5n[/tex]

Answer: [tex]8.0*10^{-4}[/tex]

Step-by-step explanation:

You need to remember the Quotient of powers property:

[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]

Then, given the expression:

[tex]\frac{(4.0*10^6)}{(5.0*10^9)}[/tex]

You must divide the coefficients and subtract the exponents. Then:

[tex]=0.8*10^{-3}[/tex]

In order to write this result in Scientific notation form, you need to move the decimal point one place to the right. Therefore, you get:

[tex]=8.0*10^{-4}[/tex]

Answer:

Step-by-step explanation:

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit.

Answer:

The final step in solving inequality is x>3.

Step-by-step explanation:

To solve this problem, first thing to do is switch sides of -2x>-6, and divde -2 from both sides.

-2x>-6

-2x/-2>-6/-2

Divide numbers from left to right.

-6/-2=3

The final step in solving the inequality is x>3, which is our answer.

I hope this helps!

Thank you! for submitting question on Brainly.

[tex]\huge{\boxed{10}}[/tex]

We can rewrite this using an exponent. [tex]\sqrt{10}^2[/tex]

When you square a square root, you basically just cancel out the square root, leaving whatever was inside the square root symbol. In this case, you end up with a final answer of [tex]\boxed{10}[/tex].

Step-by-step explanation:

First, you must find the square root of 10, which is 3.16.

Now, multiply 3.16x3.16, or find 3.16 squared.

This is 9.98

If  angle θ is in quadrant 3 and the value of sin θ = -3/5, then we can say that; cos θ = -4/5

We are told that the angle θ is in quadrant 3.

Now, we are told that; sin θ = -3/5

In the third quadrant, only tan θ is positive.

Thus, cos θ will be negative.

Thus;

cos θ = -4/5

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Answer:

If  angle θ is in 3rd quadrant and the value of [tex]sin\theta =\frac{-3}{5}[/tex], then  [tex]cos\theta =\frac{-4}{5}[/tex]

Step-by-step explanation:

Given that , angle θ is in 3rd quadrant and the value of [tex]sin\theta =\frac{-3}{5}[/tex]

We know that ,

[tex]sin^2\theta + cos^2\theta =1[/tex]

[tex]cos^2\theta =1 - sin^2\theta[/tex]

By replacing the  value of [tex]sin\theta =\frac{-3}{5}[/tex] we get,

[tex]cos^2\theta =1 - (\frac{-3}{5})^2[/tex]

[tex]cos^2\theta =1 - \frac{9}{25} = \frac{16}{25}[/tex]

Taking roots at the end of both sides we get,

[tex]cos\theta = \frac{4}{5}[/tex]  or [tex]cos\theta = \frac{-4}{5}[/tex]

We know that , In third quadrant, only tan θ and cot θ are positive.

Thus, cos θ will be negative.

So [tex]cos\theta = \frac{-4}{5}[/tex]  

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Answer:

14/18 and 49/63

Step-by-step explanation:

14/18 and 49/63 are equivalent to 7/9.

7 x 2 = 14

9 x 2 = 18

Therefore, 14/18

7 x 7 = 49

9 x 7 = 63

Therefore, 49/63

Answer:

21/27 and 42/54

Step-by-step explanation:

therefore, 21/27 and 42/54 are equivalent to 7/9

7 x 3=21

9 x 3= 27

Therefore, 21/27

7 x 6= 42

9 x6 = 54

Therefore, 42/54

Answer:

[tex]\sqrt[5]{y^{3} }[/tex]

Step-by-step explanation:

[tex]y^{\frac{3}{5} } = y^{\frac{1}{5} * 3}[/tex] = [tex]\sqrt[5]{y^{3} }[/tex]

This is true because of the fractional exponent rule.

Answer:

Step-by-step explanation:If  

n

is a positive integer that is greater than  

x

and  

a

is a real number or a factor, then  

a

x

n

=

n

√

a

x

.

a

x

n

=

n

√

a

x

Use the rule to convert  

y

3

5

to a radical, where  

a

=

,  

x

=

, and  

n

=

.

5

√

y

3

The standard equation of a parabola with vertex (0, 0) and focus (-2, 0) is y^2 = -8x. It opens to the left with the directrix x = 2.

To find the standard equation of a parabola with vertex (0, 0) and focus (-2, 0), we can use the definition of a parabola as the set of all points equidistant from a point (the focus) and a line (the directrix).

Since the focus is at (-2, 0), the directrix is a vertical line equidistant from the vertex on the opposite side of the focus, which is x = 2. The distance between the vertex and the focus (or the vertex and the directrix) is 2 units, so q = 2. This means that the parabola opens to the left.

The standard equation for a parabola that opens horizontally is of the form (y - k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus. Here, p = -2 because the parabola opens to the left.

Therefore, the standard equation for the given parabola is y^2 = -4(2)x or y^2 = -8x.

Answer:

50-4h<32

Step-by-step explanation:

If the temperature starts at 50 and the temperature is decreased by 4 per each hour, then:

1) after the first hour, the temperature is 50-4 or 46

1) after the second hour, the temperature is 46-4 or (50-4)-4 or 50-4(2).

So what I'm trying to show you that if I continue this pattern our equation for what happens h hours later is: 50-4h.

We want to know when is the temperature below 32 so less than 32.

Temperature<32

Put in our variable expression for temperature.

50-4h<32

The question is about using algebra to solve a real-life problem of temperature decrease. The correct inequality for the given problem is '50 - 4h < 32', which shows the number of hours it takes for the temperature (50 and decreasing 4 every hour) to be less than 32 degrees.

The subject matter of this question is mathematics, specifically algebra and inequalities. The question provides that the temperature in degrees Fahrenheit is reducing by 4 each hour from a starting point of 50°F and seeks to find the number of hours (h) it takes for the temperature to decrease below 32°F.

We can represent this situation as an inequality: 50 - 4h < 32. In English, this states that the temperature (50, decreasing by 4 each hour) should be less than 32 degrees. So, to answer your question, option B with '50 - 4h < 32' is the correct inequality for this problem.

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Answer:

the answer is c glad i could help

Answer:

i think the answer is choice H

Step-by-step explanation:

the number of girls to total number of members is 12:22, if you simplify this it's 6:11

Answer:

6:11

Step-by-step explanation:

There are 12 girls.

There are 12+10 member in all.

That means there are 22 members in all.

So the ratio of girls to total members is 12 to 22 or 12:22. To reduce this, look for a common factor. 12 and 22 both share 2 as a common factor so divide both by 2 gives you 6:11.

Answer:

All real numbers

Step-by-step explanation:

we have

f(x) = 3x +9

The linear function  has a range of all real numbers -------> (-∞, ∞)

f(x) can take any real value.

Please see attached image below, for more information

Answer:

I think its B because K is = to Y

So if K is 9 then the asymptote would be 9

Limiting the Y to the to be only greater than 9

Step-by-step explanation:

Answer:

The maximum value of C is 15

Step-by-step explanation:

we have

[tex]x\geq 0[/tex] -----> constraint A

[tex]y\geq 0[/tex] -----> constraint B

[tex]2x+y\leq 10[/tex] -----> constraint C

[tex]3x+2y\leq 18[/tex] -----> constraint D

using a graphing tool

The solution area of the constraints in the attached figure

we have the vertices

(0,0),(0,9),(2,6),(5,0)

Substitute the value of x and the value of y  in the objective function

(0,0) -----> [tex]C=3(0)-2(0)=0[/tex]

(0,9) -----> [tex]C=3(0)-2(9)=-18[/tex]

(2,6) -----> [tex]C=3(2)-2(6)=-6[/tex]

(5,0) -----> [tex]C=3(5)-2(0)=15[/tex]

therefore

The maximum value of C is 15

To find the maximum value of the objective function $C = 3x - 2y$ subject to the given constraints, we can use the method of linear programming. We have the given constraints:
1. $x \geq 0$ (x is non-negative)
2. $y \geq 0$ (y is non-negative)
3. $2x + y \leq 10$
4. $3x + 2y \leq 18$
The first two constraints define that our solution must lie in the first quadrant of the Cartesian plane, as both x and y must be non-negative.
The third and fourth constraints define linear inequalities which we will represent graphically to find the feasible solution region.
Let's start by finding the intercepts of the lines represented by constraints 3 and 4:
For the third constraint, $2x + y = 10$:
- If $x = 0$, then $y = 10$.
- If $y = 0$, then $x = 5$.
For the fourth constraint, $3x + 2y = 18$:
- If $x = 0$, then $y = 9$.
- If $y = 0$, then $x = 6$.
Plotting these lines on a graph will give us two lines which intersect with the axes to form their intercepts and bound a certain area on the first quadrant.
The feasible region is the area that satisfies all the inequalities simultaneously, including the non-negativity constraints of x and y.
Next, we find the vertices of the feasible region. The vertices occur where the lines of the constraints intersect each other as well as with the axes. From the graph, we could find that the feasible region is a polygon formed by intersecting the lines corresponding to the constraints. The vertices are:
1. Where $2x + y = 10$ and $3x + 2y = 18$ intersect.
2. Where $2x + y = 10$ and the y-axis intersect.
3. Where $3x + 2y = 18$ and the x-axis intersect.
We solve for each vertex by solving the system of equations corresponding to the constraints that intersect:
For vertex 1, solving $2x + y = 10$ and $3x + 2y = 18$ simultaneously, we could do this by multiplying the first equation by 2 to eliminate y, and then subtract it from the second equation:
$4x + 2y = 20$
$3x + 2y = 18$
Subtracting the second equation from the first gives
$x = 2$
Plug this value of x into one of the original equations:
$2(2) + y = 10$
$4 + y = 10$
$y = 6$
So, vertex 1 is at (2, 6).
Vertex 2 is at the y-intercept of $2x + y = 10$ which is (0, 10).
Vertex 3 is at the x-intercept of $3x + 2y = 18$ which is (6, 0).
Now, we calculate the value of the objective function at each vertex:
For (2, 6):
$C = 3(2) - 2(6) = 6 - 12 = -6$
For (0, 10):
$C = 3(0) - 2(10) = 0 - 20 = -20$
For (6, 0):
$C = 3(6) - 2(0) = 18 - 0 = 18$
The maximum value of C within the feasible region is found at the intersection points of the constraints. Among the calculated values for the objective function $C$ at the vertices, the maximum value is $18$ at the point $(6, 0)$.
Therefore, the maximum value of the objective function $C = 3x - 2y$ given the constraints is 18.

[tex]\dfrac{15(15-1)}{2}=\dfrac{15\cdot14}{2}=15\cdot7=105[/tex]

Answer:

Step-by-step explanation:

He uses (2/3)(12 eggs) = 8 eggs.

He has (12-8), or 4, eggs left.

Answer:

Step-by-step explanation:

Number of eggs = 1 dozen = 12 eggs

Number of used eggs = 2/3 * 12 (Total eggs will be multiplied by used eggs)

2/3*12

2*4

=8 eggs

Number of used eggs= 8 eggs

To find the number of left eggs. Simply subtract the used eggs from total eggs

12-8 = 4eggs

4 eggs were left....