Let f(x) = 3x² + 1 and g(x) = x +4.

Find (f +g)(x)

and (f -g)(x).

Answer:

our fraction is 33.333333333333/100, which means that 20/60 as a percentage is 33.3333%.

Answer:

y = root under 24 (evaluate it if necessary)

or y = 2 root 6

Step-by-step explanation:

Let the reference angle be x

for the triangle in left,

b = 6-4 = 2

Now,

taking x as refrence angle,

cosx = b/h

or, cosx = 2/h

again,

for the bigger triangle,

taking x as reference angle,

cosx = b/h

or, cosx = b/6

As we can see base of bigger triangle is equal to hypotenuse of triangle at the left,

Let's suppose its a

so, cosx = a/6 = 2/a

now,

a/6 = 2/a

or, a² = 12

now,

for bigger triangle, using pythagoras theorem,

h² = p²+b²

or, 6² = y² + a²

or, 36 = y² + 12

or, y² = 24

so, y = root under 24

Answer:

To enable a set of three numbers to represent three sides of a triangle, sum of smaller two numbers must be greater than the largest number. Hence, only C can represent a triangle.

⚪ The sum of the measures of the interior angles of a triangle in Euclidean space is always 180 degrees

The answer is none

Answer:

no outlier

Step-by-step explanation:

An outlier is basically a number that "different" or "outcast" in a group of numbers.

If we look at this data set, there are no particular outliers that are "different" or an "outcast."

Therefore, the answer is no outliers.

Answer:

24265

Step-by-step explanation:

I think you just need to add the expressions 23000 and 1265

23000 + 1265

= 24265

Answer:

No

Step-by-step explanation:

Exponents are only added when polynomials are multiplied and only applies to like terms. You add the coefficients of the like terms instead.

For example:

[tex](x^2+3x+6)+(2x^2-4x+1)=(1+2)x^2-(3-4)x+(6+1)=3x^2-x+7[/tex]

Answer:

no

Step-by-step explanation:

The exponents are added when the the same coefficient is multiplied:

[tex]x^2(x^3) = x^5[/tex]

If you think about it:

x^2 = x * x    and     x^3 = x * x * x

so you get:

(x^2)(x^3) = x * x * x * x * x = x^5

But, when adding x's of the same power, you add a coefficient:

[tex]x^2 + x^2 = 2x^2[/tex], not [tex]x^2 + x^2 = x^4[/tex]

Always remember to only add exponents when the coefficient/variable is multiplied, not added.

And, when an exponent is put to an exponent, multiply them:

[tex](x^3)^3 = x^3^(^3^) = x^9[/tex]

well, let's take a peek at the pyramid, hmmmm it has a triangular face that has a height of 5 and a base of 4, wait a second! it reallyi has 4 of those, ooook, and then it has a bottom that is a 4x4 square.

[tex]\stackrel{\textit{\large Areas}}{\stackrel{four~triangles}{4\left[ \cfrac{1}{2}(4)(5) \right]}~~ +~~\stackrel{square}{(4\cdot 4)}}\implies 40+16\implies 56[/tex]

The total distance travelled by the car is 80 miles.

Speed is the ratio of total distance to total time. It is given by the formula:

Speed = distance / time

From the graph:

Distance = speed * time

Total distance = 20 mph * 1 hour + (30 mph * (90 - 60)/60 hour) + (50 mph * (120 - 90)/60 hour) + (40 mph * (135 - 120)/60 hour) + (20 mph * (150 - 135)/60 hour) + (10 mph * (180 - 150)/60 hour) = 80 miles

The total distance travelled by the car is 80 miles.

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Answer:

positive numbers show deposits so it'd be A! $126.40

Answer:

53 secs

Step-by-step explanation:

Answer:

The amount of money originally spent and the money made by Stefan is required.

Stefan originally spent $110.

Money Stefan made is $66.

Step-by-step explanation:

Answer:12

Step-by-step explanation:

z=60/5

Answer:

6/7

Step-by-step explanation:

Your first step will be to find the slope of Line C. Using the slope formula of [tex]\frac{y_{2}-y_1 }{x_2-x_1}[/tex], the slope of Line C is [tex]\frac{7-14}{7-1} = \frac{-7}{6}[/tex].

If Line D is perpendicular to C, that means the slope is the negative reciprocal of Line C. So, that means the slope is 6/7.

Answer:

C The distance around the circle is the circumference

Step-by-step explanation:

For information:

A is the diameter

B is the radius

I am prertty sure it is the third opption. if not then I think you are right about the one you already chose. Super sorry if wrong

Answer:

x=40

Step-by-step explanation:

Looking at this problem, we can see that 3x+9=129

Subtract 9 on both sides:

3x=120

Divide by 3 on both sides:

x=40

Answer:

x + 4y

Step-by-step explanation:

Hey there! First, we have to recall back laws of exponent.

[tex]\displaystyle \large{a^{\frac{m}{n}} = \sqrt[n]{a^m} }[/tex]

Now simplify the expressions in surds form.

[tex]\displaystyle \large{\sqrt[3]{x^2+8xy+16y^2} \cdot \sqrt[3]{x+4y} }[/tex]

From x²+8xy+16y², we can convert the expression to perfect square.

Perfect Square

[tex]\displaystyle \large{x^2+2xb+b^2 = (x+b)^2}[/tex]

Therefore, from the expression.

[tex]\displaystyle \large{x^2+8xy+16y^2 = (x+4y)^2}[/tex]

Thus:

[tex]\displaystyle \large{\sqrt[3]{(x+4y)^2} \cdot \sqrt[3]{x+4y}[/tex]

Because both have same surds, multiply them in one.

Surd Property I

[tex]\displaystyle \large{\sqrt[n]{x} \cdot \sqrt[n]{y} =\sqrt[n]{xy} }[/tex]

Therefore:

[tex]\displaystyle \large{\sqrt[3]{(x+4y)^2(x+4y)}[/tex]

Since both are like-terms and multiplying each other, we can apply one of exponent laws.

Exponent Laws II

[tex]\displaystyle \large{a^m \cdot a^n = a^{m+n}}[/tex]

Therefore, we have [tex]\displaystyle \large{\sqrt[3]{(x+4y)^{2+1} } \to \sqrt[3]{(x+4y)^3} }[/tex]

Simplify the expression, we have cube expression inside the cube root. Therefore, we simplify as x+4y as we cancel cube and cube root.

Let me know if you have any questions through comments!

[tex]\bold{x + 4y}[/tex]

Explanation :-

[tex]{(x^{2} +8xy+16y^{2})^{\frac{1}{3} } (x+4y)}^{\frac{1}{3} }[/tex]

Rewriting it into the expression of [tex]a^{2} + 2ab + {b}^{2} [/tex],

[tex]x^{2} + 2x \times 4y + (4y)^{2})^{\frac{1}{3} }(x + 4y)^{ \frac{1}{3} }[/tex]

[tex] = > ((x + 4y)^{2})^{ \frac{1}{3} }(x + 4y)^{ \frac{1}{3} }[/tex]

Now multiplying the fractions as,

[tex] = > ((x + 4y))^{ \frac{2}{3} }(x + 4y)^{ \frac{1}{3} }[/tex]

Now as the bases of the fractions are same, we can multiply directly,

[tex] = > (x + 4y)^{ \frac{2}{3} + \frac{1}{3} }[/tex]

[tex] = > (x + 4y)^{ \frac{3}{3} }[/tex]

As when same numerator and denominator of a fraction is 1, so,

[tex] = > (x + 4y)^1[/tex]

As 1 can be neglected (since it has no specific need in the equation), so,

[tex] = > x + 4y[/tex]

Hence, the answer is [tex]\bold{x + 4y}[/tex]

From the equation solved, it can be deduced that the value of x will be -5.

From the information given, the equation is 4x/7 - 6 = -20. The step to solve it is given below:

4x/7 - 6 = -20

Cross multiply

4x = -20(7 - 6)

4x = -20(1)

4x = -20

Divide both side by 4

4x/4 = -20/4

x = -5

In conclusion, the value of x is -5.

Learn more about equations on:

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Answer:

Given

addition property of equality

multiplication property of equality

division property of equality

Step-by-step explanation:

I took the test

Answer:

To take the question as it is written, the question is how much would it be to buy 9 pens. Long one to believe that they are wanting to buy nine and not just a total of 9. If each of us $1.50, to buy 9 pens would be $13.50. At this point they would have bought 9 pens and have received 4 free, for a total of 13 pens.

Step-by-step explanation:

The slope of the linear equation is 20 and the y-intercept is 150

Slope measures how steep a straight line is. It is described as rise over run.

The slope of the linear equation can be found as follows;

He opens the account with $150 and he plans to save $20 each week. Therefore,

let

x = number of weeks

Therefore,

where

y = amount in his account after x number of weeks.

Using the slope intercept equation,

where

m = slope

c = y-intercept

Therefore, the slope of the linear equation is 20 and the y-intercept is 150

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Answer:

Factoring

Step-by-step explanation:

[tex]x^2-5x+6=0[/tex]

[tex]x^2-2x-3x+6=0[/tex]

[tex]x(x-2)-3(x-2)[/tex]

[tex](x-3)(x-2)=0[/tex]

[tex]x=2[/tex] and [tex]x=3[/tex]

[tex]f(x)=(1-x^2)^{\frac{2}{3}}\implies \cfrac{df}{dx}=\cfrac{2}{3}(1-x^2)^{-\frac{1}{3}}\implies \cfrac{df}{dx}=\cfrac{2}{3\sqrt[3]{1-x^2}}[/tex]

when it comes to a rational expression, we can get critical points from, zeroing the derivative "and" from zeroing the denominator alone, however the denominator provides critical valid points that are either "asymptotic" or "cuspics", namely that the function is not differentiable or not a "smooth line" at such spot.

if we get the critical points from the denominator on this one, we get x = ±1, both of which are cuspics.  Check the picture below.

Answer:

x=50

Step-by-step explanation:

Since Line AB and Line CD are parallel, Angle AFG is supplementary to Angle CGF. So then x+3x-20=180. Then you just solve for x.

Combine like terms-> 4x-20=180

Add 20 to both sides-> 4x=200

Divide both sides by 4-> x=50

Hope this helps!

Feel free to ask if you still don't understand something

Answer:

x ≥ 14

Step-by-step explanation:

Answer:

x ≥ 14

Step-by-step explanation:

The ≥ sign represents greater than or equal to, so x ≥ 14.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

[tex]A=-3[/tex]

Step-by-step explanation:

[tex]~~4a+ 28 = 10-2a\\+2a~~~~~~~~~~~~+2a\\~~~~6a+ 28 = 10\\~~~~~~~-28~~-28\\~~~~~6a = -18\\~~~~~~/6~~~/6\\~~~~~a=-3[/tex]

If you want to check your answer look below:

[tex]original~equation:\\4a + 28 = 10 - 2a \\\\To~check~your ~answer~plug~in~-3~for ~a:\\4(-3)+28=10-2(-3)\\[4 x -3 = -12] [ -2 x -3 = 6]\\\\\\Then~you~end~up~with:\\-12+28=10-6\\\\[-12+28=4] [ 10-6=4]\\\\Your solution then is:\\4=4\\This means that this is a true statement and that a=-3[/tex]

Hope this helps let me know if you have any questions about my answer

Answer: D: 2/3

Step-by-step explanation: the numbers you can get is 2, 1, 3, or 5, and the chance of rolling a certain number on a die is 1/6, so for 4 numbers it would be 4/6.

Tell me if I’m wrong

Sample space=6

Getting 2 or an odd no

Probability

p(E)

Answer:

[tex]x=1, x=3, x=7[/tex]

Step-by-step explanation:

Start multiplying and adding all together. You get[tex]x^3-11x^2+31x-21 =0[/tex].

At this point we're stuck factoring since there exist a formula for the roots, but it's nowhere easy to remember. We start writing down The List (rational root theorem: it's the divisor of the constant term divided by the divisor of the lead coefficent, with a plus or minus, in our case it's [tex]\pm1, \pm3, \pm7, \pm 21[/tex]) and let's try checking one by one.

Value [tex]+1[/tex] gives a zero on the LHS, it means the polynomial is divisible by [tex](x-1)[/tex]. By doing the division, or writing it as [tex](x-1)(ax^2+bx+c) = x^3-11x^2+31x-21[/tex], multiplying on the LHS and then finding the values of a, b, and c (easiest for me, your mileage may vary) we can write our expression, finally, as

[tex](x-1)(x^2-10x+21) =0[/tex] At this point you can either apply the quadratic formula or decompose again the second factor as

[tex](x-3)(x-7)[/tex] by finding two numbers whose sum is -10 and product is 21, ie -3 and -7. At this point the expression

[tex](x-1)(x-3)(x-7)=0[/tex] is true if [tex]x=1, x=3, x=7[/tex]