Simplify the following.
7^1=
4^0=
6^-1=

Answer:

1:3

Step-by-step explanation:

if a + b = 4a then b has to be 3a

(1) + (3) = 4(1)

(2) + (6) = 4(2)

it works no matter what you plug in for a

To find the ratio a:b given that a+b=4a, we rearrange the equation to find b=3a, and then simplify the ratio to get 1:3.

To find the ratio a:b, given that a+b=4a, we first need to express b in terms of a. This can be done by subtracting a from both sides of the equation:

a + b - a = 4a - a

b = 3a

Now that we have b expressed as 3a, we can find the ratio of a to b:

a : b = a : 3a

As we can simplify the ratio by dividing both terms by a (assuming a is not zero):

a : b = 1 : 3

Therefore, the ratio of a to b is 1:3.

Step-by-step explanation:

i) An intersecting system of linear equations

A system of linear equations comprises of two or more linear equations. Linear equations are simply straight line equations with a given slope and a unique y-intercept .

Solutions to systems of linear equations can be determined using a number of techniques among them being;

Elimination method

Substitution method

Graphical method

The graphs of a system of linear equations will intersect at a unique single point if the lines are not parallel.

An example of intersecting system of linear equations;

y = 2x -5 and y =5x + 4

The two lines will intersect at a particular single point since the slopes are not identical. The attachment below demonstrates this aspect.

ii) A parallel system of linear equations

Two lines are said to be parallel if they have an identical slope but unique y-intercepts. Parallel lines never intersect at any given point since the perpendicular distance between them is always constant.

Thus a parallel system of linear equations has no solution. An example of parallel system of linear equations;

y = 3x - 4 and y = 3x + 8

The attachment below demonstrates this aspect.

iii) A coincident system of linear equations

A system of linear equations is said to be coincident if the two straight lines are identical. That is the lines have an identical slope and y-intercept. Basically, we are just looking at the same line. Two parallel lines can also intersect if they are coincident, which means they are the same line and they intersect at every point.

Therefore, this system of linear equations will have an infinite number of solutions.

False. The answer is -4

Answer:

B

Step-by-step explanation:

formula   s =4*pi*r^2

s=4(3.14)(3^2)

s = 12.56(9)s= 113.04

1 degree is [tex]\dfrac\pi{180}[/tex] radians. So 14 degrees is [tex]\dfrac{14\pi}{180}=\dfrac{7\pi}{90}[/tex] rad.

Easy way to remember this: one complete revolution in a circle is 360 degrees. But it's also [tex]2\pi[/tex] radians. So the conversion rate is

[tex]\dfrac{2\pi\,\rm rad}{360^\circ}=\dfrac{\pi\,\rm rad}{180^\circ}[/tex]

i.e. for every [tex]\pi[/tex] radians there are 180º.

Answer:

[tex]\large\boxed{14^o=\dfrac{7\pi}{90}\ radians}[/tex]

Step-by-step explanation:

[tex]\text{The formula for conversion of degrees to radians:}\\\\1^o=\dfrac{\pi}{180^o}\ radians\\\\x^o=\dfrac{x\pi}{180}\ radians\\\\\text{We have}\ x=14^o.\ \text{Substitute:}\\\\14^o=\dfrac{14\pi}{180}=\dfrac{7\pi}{90}[/tex]

Answer:

B.

Step-by-step explanation:

I plugged it into a graphing calculator which got me this.

The equation that this graph represents is B. x²/3² + y²/2² = 1.

It should be noted that a graph simply means a diagram that represents the variation of variables

In this case, it's important to look at the points through which the graph passes. The y-intercept and the slope is also important.

The slope is the change in y over the change in x. By looking at the points, the equation that this graph represents is x²/3² + y²/2² = 1. This satisfies the given relation.

Learn more about graph on:

https://brainly.com/question/19040584

#SPJ2

Answer:

x=5

Step-by-step explanation:

4x-7(x+3)=-36

Distribute

4x-7x-21=-36

Combine like terms

-3x-21 = -36

Add 21 to each side

-3x+21 = -36+21

-3x = -15

Divide by -3

-3x/-3 = -15/-3

x = 5

Answer: use photomath

Step-by-step explanation:

Answer:

[tex]\large\boxed{(3x-7)(3x-5)=9x^2-36x+35}[/tex]

Step-by-step explanation:

[tex]\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(3x-7)(3x-5)\\\\=(3x)(3x)+(3x)(-5)+(-7)(3x)+(-7)(-5)\\\\=9x^2-15x-21x+35\qquad\text{combine like terms}\\\\=9x^2+(-15x-21x)+35\\\\=9x^2-36x+35[/tex]

Answer:

x=√2, x=-√2, x= 3 and x=-3

Step-by-step explanation:

We need to solve the equation x^4 - 11x^2+18=0

We can replace x^4 = u^2 and x^2 = u

So, the equation will become

u^2 -11u+18 = 0

Factorizing the above equation:

u^2 -9u-2u+18 =0

u(u-9)-2(u-9)=0

(u-2)(u-9)=0

u=2, u=9

As, u = x^2, Putting back the value:

x^2 =2 , x^2 =9

taking square roots:

√x^2 =√2 ,√x^2=√9

x=±√2 , x = ±3

so, x=√2, x=-√2, x= 3 and x=-3

Final answer:

The real zeros of the polynomial equation x^4 - 11x^2 + 18 = 0 are found by factoring the equation as a quadratic in x^2, which yields the real zeros x = 3, x = -3, x = √2, and x = -√2.

Explanation:

To find the real zeros of the polynomial equation x4 - 11x2 + 18 = 0, we can attempt to factor it. Notice that the equation resembles a quadratic in form, with x2 taking the place of x. If we let y = x2, our equation becomes y2 - 11y + 18 = 0, which is a quadratic equation.

Factoring the quadratic equation gives us (y - 9)(y - 2) = 0. Thus, the solutions for y are y = 9 and y = 2. Since y = x2, we now solve for x by finding the square roots of these solutions.

For y = 9, the values of x are x = 3 and x = -3. For y = 2, the values of x are x = √2 and x = -√2. Therefore, the real zeros of the original polynomial equation are x = 3, x = -3, x = √2, and x = -√2.

Answer:

the range is 77.

Step-by-step explanation:

the range is 77. you calculate range by subtracting the smallest number from the biggest number.

This is your  answer feel free do double check

Answer:

C

Step-by-step explanation:

Given ΔLMN and ΔPQR are similar, then

∠L, ∠P and ∠M, ∠Q and ∠N, ∠R are congruent

Hence ∠L = ∠P = 80° → C

Answer:

The Answer is C, 80 degrees

Step-by-step explanation:

Answer:

(-15)/3 = -5  

Step-by-step explanation:

(-15)/3

Assume that your positive tiles are yellow, and your negative tiles are red.

The question is asking, "if you take 15 red tiles and split them into three equal groups, how many will you have in each group?"

How can you model the first value of -15?  With 15 red tiles.

Let’s model how to divide the tiles into three equal groups by moving one tile at a time into three separate groups until all 15 tiles have been moved.

Step 1.

Start with 15 red tiles, as in the first picture.

Step 2.

Start by moving tiles one at a time to begin creating three new groups.

The middle picture shows the situation after you have moved the first three tiles.

Step 3.  

Continue moving tiles one at a time from the original group and stacking them evenly in the three new groups until you have no more tiles to move.  

The third picture shows the situation when you have finished.

How many red tiles are in each group?  There are five.

Is the answer positive or negative?  The answer is negative, because there are five red negative tiles in each group.

Conclusion? (-15)/3 = -5

Integers are expressions without decimals.

The result of the quotient of -15 and 3 is: -5

The expression is given as:

[tex]\mathbf{\frac{-15}{3}}[/tex]

To do this using integer tiles, we start by isolating the negative sign

[tex]\mathbf{\frac{-15}{3} = (-)\frac{15}{3}}[/tex]

Then divide 15 by 3 (see attachment for illustration of the division)

From the attached figure, we have:

[tex]\mathbf{\frac{15}{3} = 5}[/tex]

Substitute 5 for 15/3 in [tex]\mathbf{\frac{-15}{3} = (-)\frac{15}{3}}[/tex]

So, we have:

[tex]\mathbf{\frac{-15}{3} = (-)5}[/tex]

Remove bracket

[tex]\mathbf{\frac{-15}{3} = -5}[/tex]

Hence, the result of the expression is: -5

Read more about integer quotients at:

https://brainly.com/question/13733829

To solve the equation (x - 3)(x + 9) = -27, we simplified and set the quadratic equation to zero, which leads to solutions x = 0 or x = -6. We need to cross-verify this with the original equation as the student suggested different solutions.

To find a solution to the equation (x - 3)(x + 9) = -27, we can start by simplifying the left side of the equation. We'll distribute the terms:

x² + 9x - 3x - 27 = -27

Then we combine like terms:

x² + 6x - 27 = -27

To make it easier to solve, we want to set the equation to zero:

x² + 6x - 27 + 27 = 0

x² + 6x = 0

We factor out an x:

x(x + 6) = 0

Now, we can use the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero:

x = 0 or x + 6 = 0

Which gives us the solutions:

x = 0 or x = -6

But the student has mentioned that the solutions are x = 3 or x = -7. To double-check, we substitute these values back into the original equation:

(3 - 3)(3 + 9) and (-7 - 3)(-7 + 9)

Both expressions simplify to an identity. Thus, there may be a mistake in our initial simplification, and we should review it to ensure accuracy.

Answer:

Step-by-step explanation:

Put z = 5 to the expression (10 + 25) ÷ z:

(10 + 25) ÷ 5 = 35 ÷ 5 = 7

Answer:

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

and i² = -1

[tex](3+i)(4+2i)\\\\=(3)(4)+(3)(2i)+(i)(4)+(i)(2i)\\\\=12+6i+4i+2i^2\qquad\text{combine like terms}\\\\=(12-2)+(6i+4i)\\\\=10+10i[/tex]

Answer:

11 + 10i

Step-by-step explanation:

Note that we're multiplying two binomials here, and thus may use the FOIL method.  This requires four multiplications, as follows:

3*4 + 3*2i + 4i - 1               (The last term is 1 because i(i) = i^2 = -1.)

Simplifying, we get:

12 + 6i + 4i -1, or:

11 + 10i

Answer:

9.2 gallons

Step-by-step explanation:

18.4/2 = 9.2 gallons

15/2.0=7.5. The average velocity of the person is 7.5.

The formula for area of a sector is...

A = [tex]\frac{1}{2} r^{2}[/tex]θ

NOTE θ is converted from degree to radian

θ = 167 × [tex]\frac{\pi }{180}[/tex]

θ = [tex]\frac{167\pi }{180}[/tex]

so...

A = [tex]\frac{1}{2}(17.8)^{2} (\frac{167\pi }{180})[/tex]

A = (1/2)(316.84)(2.9146)

A = 158.42 * 2.9146

A = 461.7

Hope this helped!

The area of the shaded sector is A = 461.7

The formula for area of a sector is...

[tex]A = (1)/(2) r^(2)θ[/tex]

θ is converted from degree to radian

[tex]θ = 167 × (\pi )/(180)[/tex]

[tex]θ = (167\pi )/(180)[/tex]

so...

[tex]A = (1)/(2)(17.8)^(2) ((167\pi )/(180))[/tex]

A = (1/2)(316.84)(2.9146)

A = 158.42 x  2.9146

A = 461.7

Area of a triangle= base • height/2;

A=17•4/2= 17•2=34 ft^2

Answer: im not even joking im trying to answer the same question rn because i have a math test tomorrow and havent done any of the unit yet

Step-by-step explanation:

For this case we must find the value of the variable "x" of the following equation:

[tex]12 = x + 3[/tex]

So, we follow the steps:

Subtracting 3 from both sides of the equation we have:

[tex]12-3=x+3-3[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]9 = x\\x = 9[/tex]

Thus, the value of x is 9.

Answer:

[tex]x = 9[/tex]

You can use this equation to find the axis of symmetry or the vertex of the quadratic equation as long as it is in standard form

X= (-b/2a)

The answer is x=2

Answer:

The answer will be x = 2.

Step-by-step explanation:

Answer:

(4,4), (2,8)  (4,8)  and all points in the shaded region as attached below

Step-by-step explanation:

This question is on solutions for inequalities equations

Give the equation as;

x+2y ≥ 10.......................................rewrite the equation for graphing purposes

x+ 2y = 10.............................................compose a table for values of x with corresponding values of y

x  -2    0   2  

y   6    5    4

Plot and shade the wanted region as show in the attached graph

For example point (4,4)  or point (2,6) will satisfy the  inequality  x+2y ≥ 10 as;

(4,4)........ x+2y ≥ 10------4+2(4)  ≥ 10

20 ≥ 10 ,,,,,,,,,,,,,,,,,,which is okay

Answer:

-2p² − 11p − 35

Step-by-step explanation:

Simplifying:

-2(p + 4)² − 3 + 5p

-2(p² + 8p + 16) − 3 + 5p

-2p² − 16p − 32 − 3 + 5p

-2p² − 11p − 35

This is also the standard form.

Answer:

-2p^2 - 11 p - 35

Step-by-step explanation:

Please, use " ^ " to indicate exponentiation.  Thus:

–2(p + 4)^2 – 3 + 5p

Now perform the exponentiation first, obtaining:

-2(p^2 + 8p + 16) - 3 + 5p, or

-2p^2 - 16 p - 32  - 3 + 5p

Now rearrange these terms in descending order by powers of p:

-2p^2 - 11 p - 32  - 3, or

-2p^2 - 11 p - 35

Answer:

The rational function that is graphed is B

The rational function which is graphed below is:

                                Option: B

           B.   [tex]F(x)=\dfrac{x}{(x-1)(x+1)}[/tex]

From the graph of the function we see that the graph has vertical asymptote at x=1 and x= -1

The function in which above two property hold true is:

         B.   [tex]F(x)=\dfrac{x}{(x-1)(x+1)}[/tex]

( since in option: A

If denominator equal to 0 then x=0 and -1

This means that the vertical asymptotes are 0 and -1 .

In option: C

If denominator is equal to zero.

Then x=0 and 1

This means that the vertical asymptotes are 0 and 1

In option: D

When denominator=0

then x=0

This means that the vertical asymptote is at x=0

which is false )

The answer is:

The sixth option,

[-6,6]

To solve the problem, we need to find which of the given options match with the solution to the inequality. As we know, solving inequalities is almost the same that solving equalities, we need to isolate the variable and then, find where it satisfies the given condition (inequality)

So, solving the inequality we have:

[tex]-3x^{2} +1\leq -107\\-3x^{2}\leq -107-1\\-3x^{2} \leq -108\\3x^{2} \leq 108\\x^{2} \leq \frac{108}{3}\\\sqrt{x^{2} } \leq \sqrt{36}\\ x^{2\leq } +-36\\(x-6)(x+6)\leq 0[/tex]

Therefore, we have that the solutions to the inequality are:

First solution:

[tex]x-6\leq 0\\x\leq 6[/tex]

Second solution:

[tex]x+6\leq 0\\x\leq-6[/tex]

Hence, the correct option is the sixth option, the solution is described by the following solution set :

[-6,6]

Have a nice day!

Answer:

28 grams

Step-by-step explanation:

1 cup is 8 grams of fiber, since a half a cup is 4 you times it by 2

then 8x3 because you're multiplying the fiber of one cup by 3. which equals 24, but you still have a half of cup of oats left. and since 4 grams equal a half a cup you just simply add 4 onto 24 which equals 28

Answer:

28 grams

Step-by-step explanation:

because i a mulpitplyed the numbers to get my answer

Answer:

D

Step-by-step explanation:

This is called "implication". So if A (is true), then B MUST be true. If B is false, the implication is false. In all other cases, the implication is true. Suppose A is false, then it doesn't matter what B is, the implication is true, since we don't care what B is.

It's a bit confusing I suppose. Below is a truth table using P and Q in stead of A and B.

Final answer:

The correct answer is D: If A is true, then B must be true. This represents a logical conditional where the statement is true unless the antecedent A is true and the consequent B is false.

Explanation:

The statement "If A, then B" is a logical conditional, which can be represented as A
ightarrow B in logical notation. This statement best matches option D: If A is true, then B must be true. In logic, the only time a conditional statement is false is when the first part (the antecedent A) is true and the second part (the consequent B) is false. Otherwise, the statement is considered true, regardless of the individual truth values of A or B. This includes when A is false; the truth value of B does not affect the truth value of the conditional in this case. Therefore, if A is true, the conditional obliges B to also be true for the statement to remain true.

let's notice that the center of the circle is at the orgin, and that the distance from the center to an endpoint B is its radius.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ O(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]

[tex]\bf \stackrel{radius}{r}=\sqrt{(4-0)^2+(5-0)^2}\implies r=\sqrt{4^2+5^2} \\\\\\ r=\sqrt{16+25}\implies r=\sqrt{41} \\\\[-0.35em] ~\dotfill\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{0}{ k})\qquad \qquad radius=\stackrel{\sqrt{41}}{ r} \\\\\\ (x-0)^2+(y-0)^2=(\sqrt{41})^2\implies x^2+y^2=41[/tex]

Answer:

The correct answer is option B

Step-by-step explanation:

B.  x2 + y2 − 41 = 0

Answer:

I need some more information

Step-by-step explanation:

..........

Answer:

Can you provide a picture/

Step-by-step explanation: