Find all real solutions of the equation, approximating when necessary.
x^3+4x^2=10x+15=0

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: 30 degrees

Step-by-step explanation:

well 60 divided by 2

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

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:

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

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.

Answer:

12 miles per (1/3) hour equals

36 miles per hour

Step-by-step explanation:

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:

• 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.

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

6ttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt

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 is 44cm

Step-by-step explanation:

The slant height of a cone with a radius of 3 inches and a surface area of 16.8π square inches is 2.6 inches.

In order to find the slant height of a cone, we need to understand the formula for calculating the surface area of a cone. The formula is πrs + πr². The given surface area is 16.8π and the radius is 3 in. This area consists of the area of the base (which is a circle of radius 3 in, hence area πr² = π(3)² = 9π) and the area of the side, which is πr times the slant height (s).

So, we subtract the base area from the total area to isolate the side area: 16.8π - 9π = 7.8π. This is equal to πrs, so we can set up the equation: 7.8π = 3πs (we replace 'r' with its given value 3). Solving for 's', we divide both sides of the equation by 3π, getting slant height 's' = 7.8π / 3π, which simplifies to 2.6 inches.

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Answer: 20 picks

Step-by-step explanation: because orange is picked 3 out of every 5 picks, and 12 picks are orange, you multiply 3 by 4 to get 12, and 5 by 4 to get 20.

Answer:

I think the answer would be 20 picks. Good luck :)

Answer:

About 7 times

Step-by-step explanation:

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.

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.

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:

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

Step-by-step explanation:

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:

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 :}

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: 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.

The 21 consonants are :

b c d f g h j k l m n p q r s t v w x y z

The 5 vowels are :

a e i o u

Now, to arrange the consonants there are 21! ways.

Now the vowels can be arranged in 22 ways because one vowel can be placed before 'b' and one after 'z' also.

It can be shown like this : (V represents vowels)

V b V c V d V f .......................

Therefor the ways to put vowels will be : [tex]22P5[/tex]

The complete order to place consonants without repeating vowels becomes: [tex]22P5*21![/tex]

There are 22! x 6! x 5! ways to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively.

In order to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively, we can consider the vowels as a single block that needs to be placed in between the consonants. Firstly, let's count the number of ways to arrange the consonants C (21 consonants + 1 y) and the block of vowels V (5 vowels) as separate entities. This can be done in 22! x 6! ways. However, we need to consider that within the V block, the vowels can be rearranged in 5! ways. Therefore, the total number of arrangements is 22! x 6! x 5!.

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Answer:

  No

Step-by-step explanation:

The magnitude of the distance from the origin to the point (8, 17) will be more than 17. That point is not on a circle of radius 9 centered at the origin. It is well outside the circle.

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:

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:

  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.

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]

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:

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)