Find x in this right triangle.

Answer:

The length is 10 inches and the width is 7 inches.

Step-by-step explanation:

A rectangle is shape with 4 sides where 2 pairs of sides are equal and form 4 perpendicular angles. 1 pair of sides is the width and is distance w. 1 pair of sides id the length and is 3 inches more than the width or 3 + w. The total distance around the shape is the perimeter. We know the perimeter is 34 inches. Add each side together and set it equal to 34. Then solve for w.

P = l + l + w + w

34 = 3 + w + 3 + w + w + w

34 = 6 + 4w

28 = 4w

7 = w

This means its length which is 3 inches longer is 7 + 3 = 10.

you want to take 3×1/4 which would equal 0.75. but if you want to change it into a fraction it would be 3/4

Answer:

The correct answer is F (false)

Step-by-step explanation:

Points to remember

Sin θ = Opposite side/Hypotenuse

Tan θ = Opposite side/Adjacent side

Sec θ = Hypotenuse/Adjacent side

To find Sin 45, Sec 45 and Tan 45

We have Sin 45 = 1/√2

Sec 45 = 1/Cos 45 = 1/(1/√2) = √2

Tan 45 = 1

To find Sec θ/Tan θ

Here  θ = 45

Sec (45)/Tan (45) = √2/1 = √2 ≠ Sinθ

Therefore the correct answer is False(F)

Answer:

The answer is ellipse; 3x² + y² + 6x - 6y + 3 = 0

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* 3x² + y² = 9

∵ A = 3 , B = 0 , C = 1

∴ B² - 4 AC = (0)² - 4(3)(1) = -12

∴ B² - 4AC < 0

∴ The graph is ellipse or circle

* If A and C are nonzero, have the same sign, and are not

 equal to each other, then the graph is an ellipse.

* If A and C are equal and nonzero and have the same

 sign, then the graph is a circle.

∵ A and C have same signs with different values

∴ It is an ellipse

* Now lets study T(-1 , 3), that means the graph will translate

 1 unit to the left and 3 units up

∴ x will be (x - -1) = (x + 1) and y will be (y - 3)

* Lets substitute the x by ( x + 1) and y by (y - 3) in the equation

∴ 3(x + 1)² + (y - 3)² = 9

* Use the foil method

∴ 3(x² + 2x + 1) + (y² - 6y + 9) = 9

* Open the brackets

∴ 3x² + 6x + 3 + y² - 6y + 9 = 9

* Collect the like terms

∴ 3x² + y² + 6x - 6y + 12 = 9

∴ 3x² + y² + 6x - 6y + 12 - 9 = 0

∴ 3x² + y² + 6x - 6y + 3 = 0

* The answer is ellipse of equation 3x² + y² + 6x - 6y + 3 = 0

Final answer:

The system of equations has infinitely many solutions because they represent the same line. The solution can be written in terms of the parameter t as (x, y) = ((3 + 6t)/5, t).

Explanation:

The student's question involves determining the type of solution a system of two linear equations has and finding the solution if it exists. The given system of equations is:

5x - 6y = 3

10x - 12y = 6

Notice that the second equation is just the first equation multiplied by 2. This means the system has infinitely many solutions because the two equations are actually the same line. To find these solutions in terms of a parameter t, we can solve the first equation for x as follows:

Choose t to represent y (i.e., let y = t).

Substitute y = t into the first equation to get 5x - 6t = 3.

Solve for x to find x = (3 + 6t)/5.

Therefore, the solutions to the system can be expressed as (x, y) = ((3 + 6t)/5, t), where t is any real number.

Answer:

The problem that is getting solved is 40 divided by zero

Answer:

Step-by-step explanation:

This is a faulty way of showing it. What you are solving here is

40 - 10*4 which is 0. What is transcribed is not equivalent to any division that I can see.

Perhaps 0/40

If you have answers, please list them.

Answer:

12 miles per (1/3) hour equals

36 miles per hour

Step-by-step explanation:

Answer: option d.

Step-by-step explanation:

 To solve this problem you must keep on mind the properties of logarithms:

[tex]log(b)-log(a)=log(\frac{b}{a})\\\\log(b)+log(a)=log(ba)\\\\a*log(b)=log(b)^a[/tex]

Therefore, knowing the properties, you can write the expression gven in the problem as shown below:

[tex]5logx+6log(x+7)=logx^5+log(x+7)^6=logx^5(x+7)^6[/tex]

Then, the answer is the option d.

Answer:

D

Step-by-step explanation:

We can use 2 properties of logs to write this as single logarithm:

1. [tex]Log(A^B)=BLog A[/tex]

2. Log x + Log y = Log (x*y)

We can use property #1 to write this as:

[tex]5Logx+6Log(x+7)\\=Logx^{5}+Log(x+7)^{6}[/tex]

Now we can use property #2 to write this as:

[tex]Logx^{5}+Log(x+7)^{6}\\=Log((x^5)((x+7)^6)\\=Logx^{5}(x+7)^{6}[/tex]

We see that answer choice D is right.

Answer:

y = 1/3 x + 4

Step-by-step explanation:

The slopes of perpendicular lines are negative reciprocals. The given line is

y = -3x + 7

which is already in the slope-intercept form, y = mx + b, where m is the slope.

The slope of the given line is -3.

The slope of the perpendicular is the negative reciprocal of -3 which is 1/3.

The line we are looking for has an equation of the form

y = 1/3x + b

We need to find b. We use the x- and y-coordinates of the given point as x and y in the equation above, and we solve for b.

y = 1/3x + b

5 = (1/3)(3) + b

5 = 1 + b

4 = b

Now that we know that b = 4, we replace b with 4 in the equation

y = 1/3x + b to get the answer.

Answer: y = 1/3 x + 4

The equation of the line that is perpendicular to y=-3x+7 and passes through the point (3,5) is y = 1/3x + 4.

To find an equation of the line that is perpendicular to the line represented by the equation y = -3x + 7 and also passes through the point (3, 5), we must first find the slope of this new line. In mathematics, the perpendicular line's slope is the negative reciprocal of the original line's slope. Here, the slope of the original line is -3, so our new line's slope will be 1/3. Now we can use the point slope form to find the equation of the line:

y - y1 = m(x - x1)

Substituting our values, it becomes y - 5 = 1/3(x - 3), which simplifies to y = 1/3x + 4. So, the equation of the line is y = 1/3x + 4.

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Answer:

40oz

Step-by-step explanation:

just make it easy 20 quarters is 4 oz multiply that by 10 it would be 200 quarters and 40 oz

the weight of 200 quarters is 40 ounces.

The question asks to find the weight in ounces, w, of 200 quarters, given that a roll of 40 quarters weighs 8 ounces. To solve this problem, we can set up a proportion which is a statement that two ratios are equal. Since we know the weight of 40 quarters, we can compare this to the weight of 200 quarters. The proportion can be set up as follows:

40 quarters / 8 ounces = 200 quarters / w ounces

To find w, simply cross-multiply and divide:

Therefore, the weight of 200 quarters is 40 ounces.

Answer:

[tex]36\ in^{3}[/tex]

Step-by-step explanation:

we know that

If the box is half empty, then the box is half full

therefore

Find the volume of the box and then divide by two to calculate the volume of granola bar left in the box

The volume of the box is

[tex]V=(3)(4)(6)=72\ in^{3}[/tex]

The volume of granola bar left in the box is

[tex]72/2=36\ in^{3}[/tex]

Answer:

5707 tickets

Step-by-step explanation:

We want to sell 439 tickets each day for the next 13 days

439 * 13 =5707

We need to sell a total of 5707 tickets

Answer:

your first Graph :D Hope this helps

The first equation is greater than or equal to, so the line would be solid.

The second equation is less than so the line would be dotted.

Greater than or equal to would be above the solid line, less than would be to the left of the dotted line.

The top left graph is correct.

Answer: 30 degrees

Step-by-step explanation:

well 60 divided by 2

Just do 60 divided by 2 and that would equal 30 degrees.

Answer:

1. f(-1)

2.f(1)

3.f(0)

4.f(8)

5.f(5)

6.f(2)

Step-by-step explanation:

[tex]f(-1)-------------\ \ \ \ -6\\\\f(0)-------------\ \ \ \ \ \ \ -5\\\\f(1)-------------\ \ \ \ \ \ \ -4\\\\f(2)-------------\ \ \ \ \ \ \ -3\\\\f(5)-------------\ \ \ \ \ \ \ \ \ 0\\\\f(8)-------------\ \ \ \ \ \ \ \ \ 3[/tex]

We are given a function f(x) by:

          [tex]f(x)=x-5[/tex]

It is a linear function with positive slope i.e. 1.

Also, now we will calculate the value of the function at different values of x and match the function to it's corresponding value.

a)

[tex]f(-1)[/tex]

[tex]f(-1)=-1-5\\\\i.e.\\\\f(-1)=-6[/tex]

b)

[tex]f(0)[/tex]

Now when x=0 we have:

[tex]f(0)=0-5\\\\i.e.\\\\f(0)=-5[/tex]

c)

[tex]f(1)[/tex]

when x=1

[tex]f(1)=1-5\\\\i.e.\\\\f(1)=-4[/tex]

d)

[tex]f(2)\\\\f(2)=2-5\\\\i.e.\\\\f(2)=-3[/tex]

e)

[tex]f(5)[/tex]

when x=5 we have:

[tex]f(5)=5-5\\\\i.e.\\\\f(5)=0[/tex]

f)

[tex]f(8)[/tex]

Put x=8

[tex]f(8)=8-5\\\\i.e.\\\\f(8)=3[/tex]

Answer:

a:  sample mean: 130.2 pounds

This is not the population mean

Step-by-step explanation:

To find the mean weight of the sample, add up all the values and divide by the total number of values entered.  In this case, 10, so we have...

mean:  (136 + 99 + 118 + 129 + 125 + 170 + 130 + 128 + 120 + 147)/10 =

1302/10 = 130.2

This is not the population mean.  It is the mean of the sample.  We would have to know more information to make a conjecture about the population mean.

Final answer:

The population mean of the students' weights is determined by summing all the weights and dividing by the number of students, resulting in 130.2 pounds.

Explanation:

To find the population mean (denoted as μ), we add up all the weights of the ten students in the population and divide it by the total number of students. Let's do the calculation:

The weights of the students are 136, 99, 118, 129, 125, 170, 130, 128, 120, and 147 pounds.

The sum of these weights is 136 + 99 + 118 + 129 + 125 + 170 + 130 + 128 + 120 + 147 = 1302 pounds.

Since there are 10 students in the population, we divide the total weight by 10 to find the mean:

μ = ΣX / N = 1302 / 10 = 130.2 pounds

Therefore, the population mean (μ) is 130.2 pounds.

The mathematical representation of the expression 'Four less than the quotient of a number x and 5' is 'x/5 - 4'. This involves division and subtraction of the number x.

The subject of this question is Mathematics, particularly algebraic expressions. In this case, you are being asked to express the phrase 'Four less than the quotient of a number x and 5' as an algebraic expression. The 'quotient of a number x and 5' implies division of the number x by 5, which is represented as 'x/5'. 'Four less than' signifies a subtraction of four from the preceding expression. Therefore, the whole expression can be written as 'x/5 - 4'.

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Answer is 44cm

Step-by-step explanation:

Answer:

  a.  sec(x) = √2

Step-by-step explanation:

csc(x)/cot(x) = (1/sin(x))/(cos(x)/sin(x)) = 1/cos(x) = sec(x) = √2

Answer:

The correct answer is a) [tex] \sec(x) = \sqrt{2}[/tex].

Step-by-step explanation:

Here we need to use some trigonometric identities:

Then, substituting the above identities in the given formula we have:

[tex] \frac{\csc(x)}{\cot(x)} = \frac{\frac{1}{\sin(x)}}{\frac{\cos(x)}{\sin(x)}} = \frac{1}{\sin(x)}\frac{\sin(x)}{\cos(x)} [/tex]

Notice that we can simplify the sinus in both fractions. Thus,

[tex]\frac{\csc(x)}{\cot(x)} = \frac{1}{\cos(x)} = \sec{x}[/tex].

From here, the solutions is pretty straightforward.

Answer:

y = 7   x = -11/3

Step-by-step explanation:

3x + 4y = 17

- (3x + 2y = 3)

Distribute the minus sign  and add together

3x + 4y = 17

- 3x - 2y = -3

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

2y    = 14

Divide by 2

2y/2 = 14/2

y = 7

Now find x

3x + 4y = 17

3x +4(7) = 17

3x +28 = 17

Subtract 28 from each side

3x+28 -28 = 17 -28

3x = -11

Divide each side by 3

3x/3 = -11/3

x = -11/3

Answer:

A.2y=14

Step-by-step explanation:

Apex

Hope this helps Have a nice day

⅔x+4≤14

⅔x≤10

2x≤30

x≤15

Max value of x is 15

7x-2≤?

7(15)-2=105-2=103

7x-2≤103

Greatest value for 7x-2 is 103

Answer:

Ben drove faster

Step-by-step explanation:

350 miles / 6.5 hours = 53.84 miles per hour

520 miles / 12.25 hours = 42.44 miles per hour

53.84 is faster than 42.44 therefore Ben is faster.

QUESTION 1

The given logarithmic expression is

[tex]\log_4(\frac{1}{16})[/tex]

We rewrite [tex]\frac{1}{16}[/tex] in the index form to base 4.

This implies that;

[tex]\log_4(\frac{1}{16})=\log_4(4^{-2})[/tex]

We now apply the power rule: [tex]\log_a(m^n)=n\log_a(m^n)[/tex].

[tex]\log_4(\frac{1}{16})=-2\log_4(4)[/tex]

Recall that logarithm of the base is 1.

[tex]\log_4(\frac{1}{16})=-2(1)[/tex]

[tex]\log_4(\frac{1}{16})=-2[/tex]

QUESTION 2

The given logarithm is;

[tex]\log_2(\sqrt[5]{32})[/tex]

[tex]\log_2(\sqrt[5]{2^5})[/tex]

This is the same as;

[tex]\log_2(2^{5\times \frac{1}{5}})[/tex]

[tex]\log_2(2^{1})[/tex]

[tex]\log_2(2)=1[/tex]

Answer:

About 7 times

Step-by-step explanation:

The answer is: There are a total of 16 skits in the video.

From the statement, we know that the total length of the video is 101 minutes and it contains a 5-minute introduction, the rest of the minutes are short skits (which are 6 minutes long each one).

So, we need to write the following equations:

First equation:

[tex]TotalDuration=Introduction+n*Skit[/tex]

Second equation:

[tex]Skit=6Minutes[/tex]

Where,

[tex]TotalDuration=101Minutes\\Introduction=5Minutes\\n=NumberOfSkits\\Skit=6Minutes[/tex]

So, replacing and substituting the second equation into the first equation we have:

[tex]101Minutes=5Minutes+n*6Minutes\\n*6Minutes=101Minutes-5Minutes\\n*6Minutes=96Minutes\\n=\frac{96Minutes}{6Minutes}=16[/tex]

So, there are a total of 16 skits in the video.

Let's prove it substituting "n" into the first equation:

[tex]101Minutes=5Minutes+16*6minutes\\101Minutes=5Minutes+96Minutes\\101Minutes=101Minutes[/tex]

Have a nice day!

34

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Answer:

• changing an interior angle to a reflex angle

Step-by-step explanation:

In order for the outline of the polygon to have a pair of sides that is concave (pointed inward, rather than outward), the corresponding interior angle must be a reflex angle. (It must measure more than 180°.) Draw one; you'll see.

Answer:

24 muffins, each friend gets 4. There are 4 remaining

Step-by-step explanation:

Answer:

House of representatives=h

United states senate= u

h=4u+35

If u=100:

h=4(100)+35

h=400+35

h=435

Hope this helps :}

Answer:

One solution.  It is (2, 1)

Step-by-step explanation:

Clear out all fractions right away by multiplying all terms by 10.  Then:

0.3x − 0.4y = 0.2

−0.2x + 0.5y = 0.1

becomes

3x - 4y = 2

-(2x + 5y = 1)

Multiply the first row by 2 and the second row by 3, which produces:

  6x - 8y = 4

 -6x +15y =  3

Combining like terms results in:         7y = 7.  Then y = 1.

Now subst. 1 for y in the first equation, to calculate x:

3x - 4(1) = 2

3x          = 2 + 4  = 6.  Then x = 2.

The solution is (2, 1).  There is ONLY ONE SOLUTION.

The equation is y =(4/5)x -6

Answer:

[tex]\large\boxed{y=\dfrac{4}{5}x-6}[/tex]

Step-by-step explanation:

The slope-intercept form of the equation of a line:

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

m - slope

b - y-intercept

We have the slope [tex]m=\dfrac{4}{5}[/tex] and the y-intercept [tex]b=-6[/tex].

Substitute:

[tex]y=\dfrac{4}{5}x-6[/tex]