What is the 12th term in the sequence?
12, 15, 18, 21, ...
a) 38
b) 45
c) 42
d) 48

Answer:

(3 x - 2) (4 x + 3)

Step-by-step explanation:

Factor the following:

12 x^2 + x - 6

Factor the quadratic 12 x^2 + x - 6.

The coefficient of x^2 is 12 and the constant term is -6.

The product of 12 and -6 is -72. The factors of -72 which sum to 1 are -8 and 9.

So 12 x^2 + x - 6 = 12 x^2 + 9 x - 8 x - 6 = 3 (3 x - 2) + 4 x (3 x - 2):

3 (3 x - 2) + 4 x (3 x - 2)

Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2):

Answer:  (3 x - 2) (4 x + 3)

The answer is (3 x - 2) (4 x + 3).

Polynomial exists an algebraic expression with terms divided utilizing the operators "+" and "-" in which the exponents of variables exist always nonnegative integers.

Factor the following:

[tex]$$12x^{2}+x-6$$[/tex]

Factor the quadratic

[tex]$12x^{2} +x-6$[/tex]

The coefficient  [tex]x^{2}[/tex] is 12 and the constant term is -6.

The product of 12 and -6 is -72.

The factors of -72 which sum to 1 exist at -8 and 9.

So

[tex]$12 x^{2} +x-6=12 x^{2} +9 x-8 x-6[/tex]

[tex]=3(3 x-2)+4 x(3 x-2)$[/tex]

[tex]$3(3 x-2)+4 x(3 x-2)$[/tex]

Factor 3 x - 2 from 3 (3 x - 2) + 4 x (3 x - 2)

Hence, The answer is (3 x - 2) (4 x + 3).

To learn more about Polynomials refer to:

https://brainly.com/question/13769924

#SPJ2

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\sqrt[3]{y}=4\qquad\text{cube of both sides}\\\\(\sqrt[3]{y})^3=4^3\\\\y=64\\\\\bold{METHOD\ 2:}\\\\\text{Use the de}\text{finition of cube root}:\\\\\sqrt[3]{a}=b\iff b^3=a\\\\\sqrt[3]{y}=4\iff 4^3=y\to y=64[/tex]

Answer:

The cotangent of 61.6° is .5407.

Step-by-step explanation:

Refer to the sketch attached.

61.6° + 28.4° = 90°. In other words, 61.6° is the complementary angle of 28.4°.

Consider a right triangle OAB with a 61.6° angle [tex]\rm O\hat{A}B[/tex]. The other acute angle [tex]\rm O\hat{B}A[/tex] will be 28.4°.

[tex]\displaystyle \tan{61.6\textdegree{}}=\tan{\rm O\hat{A}B} = \frac{\text{Opposite of }\rm O\hat{A}B}{\text{Adjacent of }\rm O\hat{A}B} = \frac{a}{b}[/tex].

The cotangent of an angle is the reciprocal of its tangent.

[tex]\displaystyle \cot{61.6^{\circ}}=\frac{1}{\tan{\rm O\hat{B}A}} = \frac{\text{Adjacent of }\rm O\hat{B}A}{\text{Opposite of }\rm O\hat{B}A} = \frac{a}{b} = \tan{\rm O\hat{A}B} = \tan{28.4^{\circ}}[/tex].

In other words,

[tex]\cot{61.6^{\circ}} = \tan{28.4^{\circ}} \approx 0.5407[/tex].

[tex]x^2-5\leq0\\x^2\leq5\\x\leq \sqrt5 \wedge x\geq-\sqrt5\\x\in\left\langle-\sqrt5,\sqrt5\right\rangle[/tex]

For this case we must indicate the solution of the following inequality:

[tex]x ^ 2-5 \leq0[/tex]

Adding 5 to both sides of the inequality:

[tex]x ^ 2\leq5[/tex]

We apply square root on both sides of the inequality to eliminate the exponent:

[tex]x \leq\pm \sqrt {5}[/tex]

So, we have two solutions:

[tex]x\leq \sqrt {5}[/tex]

Since it is an inequality, the sign for the negative portion is changed:

[tex]x\geq- \sqrt {5}[/tex]

Answer:

[tex]x\leq \sqrt {5}\\x\geq-\sqrt {5}[/tex]

Answer:

[tex]\large\boxed{\dfrac{50}{3}}[/tex]

Step-by-step explanation:

If the polygons are similar, then the corresponding sides are in proportion:

[tex]\dfrac{z}{10}=\dfrac{20}{12}[/tex]        cross multiply

[tex]12z=(10)(20)[/tex]

[tex]12z=200[/tex]         divide both sides by 12

[tex]z=\dfrac{200}{12}\\\\z=\dfrac{200:4}{12:4}\\\\z=\dfrac{50}{3}[/tex]

Answer:

24x - 20

Step-by-step explanation:

4(6x-5)

= 4(6x) - 4(5).............. (Distributive property)

= 24x - 20 (Ans)

Hello There!

The answer would be (24x-20)

We use order of operations so first we would multiply 4 by 6 and get 24x

then, we would multiply 4 by -5 and get -20

Your answer would be 24x - 20

ANSWER

The radius is 4

EXPLANATION

The given equation is:

[tex] {x}^{2} + {y}^{2} - 10y + 6x + 18 = 0[/tex]

We complete the square to get the expression in standard form:

[tex]{x}^{2} + 6x + {y}^{2} - 10y + 18 = 0[/tex]

[tex]{x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25[/tex]

We factor using perfect squares to get:

[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = 16[/tex]

This implies that,

[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2} [/tex]

Comparing to

[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

The radius is r=4

Answer:

Δ TUW ≅ ΔVWU ⇒ by AAS case

Step-by-step explanation:

* Lets revise the cases of congruent for triangles

- SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and  

 including angle in the 2nd Δ  

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ  

 ≅ 2 angles and the side whose joining them in the 2nd Δ  

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles

 and one side in the 2ndΔ

- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse

 leg of the 2nd right angle Δ

* Lets solve the problem

- There are two triangles TUW and VWU

- ∠T and ∠V are right angles

- LINE TW is parallel to line VU

∵ TW // VU and UW is a transversal

∴ m∠VUW = m∠TWU ⇒ alternate angles (Z shape)

- Now we have in the two triangles two pairs of angle equal each

 other and one common side, so we can use the case AAS

- In Δ TUW and ΔVWU

∵ m∠T = m∠V ⇒ given (right angles)

∵ m∠TWU = m∠VUW ⇒ proved

∵ UW = WU ⇒ (common side in the 2 Δ)

∴ Δ TUW ≅ ΔVWU ⇒ by AAS case

Answer:

Step-by-step explanation:

Given ∠T and ∠V are right angles.

TW ║ UV

To prove ⇒ ΔTUW ≅ ΔVWU

Proof ⇒ In ΔTUW and ΔVUW,

∠T ≅ ∠ V ≅ 90° (given)

Side UW ≅ UW ( Common in both the triangles )

TW ║ UV

and UW is a transverse.

So ∠TWU ≅ ∠WUV [alternate interior angles]

Since Angle = Angle = side are equal

Therefore, ΔTUW ≅ ΔVWU

[tex]19 + 6 = 25 \div 2 = 12.5[/tex]

Answer:

12.5

Step-by-step explanation:

19+6=25 , 25÷2= 12.5

Answer:

Slope is 1

Step-by-step explanation:

Rise over Run.  Delta y over Delta x.  -8-2/-5-5 = -10/-10 = 1

Check the picture below.

let's notice those two corresponding angles of 90° - 2x, and also recall that the sum of all interior angles in a triangle is 180°.

[tex]\bf 60+3x+(90-2x)=180\implies x+150=180\implies x=30[/tex]

Answer:

Step-by-step explanation:

the nth term of the geometric sequence  is :  An =A1 × r^(n-1)

A1 = -10

r= -40/20=20/-10=-2

n =11

A11 = -10× (-2)^(11-1)

A11 = -10× (-2)^(10)

A11 = - 10240

Answer:

-10,240.

Step-by-step explanation:

This is a geometric sequence with common ratio 20/-10 = -40/20 = -2.

The nth term = a1r^(n-1)   where a1 = the first term and r = the common ratio, so the 11th term = -10 * (-2)^ (11-1)

= -10 * 1024

= -10,240.

Answer:

25

Step-by-step explanation:

look B=C

so,

A+B+C=180 Sum of all <s of Tri

x+5+3x+3x=180

7x=175

x=175÷7

x=25

Answer: A or 25

Step-by-step explanation:

did the exam on edge 2020

Answer:

15 ounces

Step-by-step explanation:

If there is 165 ounces in 11 boxes then divide the ounces by the boxes to get the amount of ounces in one box.

Answer:

15

Step-by-step explanation:

Answer: [tex]945\ pixels[/tex]

Step-by-step explanation:

We know  that the original photo was 800 pixels wide and the new photo will be 1,260 pixels wide. Therefore,  we can find the scale factor.

Divide the width of the new photo by the width of the original photo. Then the scale factor is:

[tex]scale\ factor=\frac{1,260\ pixels}{800\ pixels}\\\\scale\ factor=\frac{63}{40}[/tex]

The final step is to multiply the height of the original photo by the scale factor calculated.

Therefore the height of the new photo will be:

[tex]h_{new}=(600\ pixels)(\frac{63}{40})\\\\h_{new}=945\ pixels[/tex]

Answer:

Step-by-step explanation:

Givens

First, we need to find the scale factor by dividing

[tex]s=\frac{1260}{800}=1.575[/tex]

Then, we multiply the height by the scale factor

[tex]600 \times 1.575 = 945[/tex]

Therefore, the new height is 945 pixels.

Answer:

7/2

Step-by-step explanation:

Round 6 3/4 to 7

Round 1 1/2 to 2

7 divided by 2

=7/2

Answer:

B and E

Step-by-step explanation:

By looking at the discriminant, which is [tex]b^2-4ac[/tex], you get that [tex]5^2-4*1*7=25-28=-3[/tex]. Therefore, the only two answers with a -3 inside the square root are B and E.

Answer:

B & E

Step-by-step explanation:

see attached

9 x 5 = 45 -> total $ on Friday

99 - 45 = 54 -> total $ on Saturday

54 ÷ 9 = 6 hours

Answer:

A, B.

Step-by-step explanation:

If Matt charges $9 an hour, and he worked for 5hrs on Friday night, then that means we have to do multiplication.

So, $9x5=$45.

And then it says he babysat again on Saturday, and in TOTAL, he earned $99.

So, if he already made $45, and he has a total of $99, then we need to work backwards to figure out how much he made on Saturday.

$99-$45=$54

So, he made $45 on Friday and $54 on Saturday.

Now, we continue to work backwards and divide how much he made on Saturday ($54), by how much he charges per hour.

$54/9=6

So, Matt worked a total of 6hrs on Saturday.

Answer:

They would be perpendicular because the lines intersect at a ninety degree angle. Hope this helps! Please mark brainliest!

Step-by-step explanation:

Follow below steps:

The term that describes lines that intersect at 90-degree angles is perpendicular. Lines that are perpendicular to each other form four angles at the point of intersection. Each of these angles is a right angle, which measures 90 degrees. This is a fundamental concept in geometry, which is a branch of mathematics dealing with properties and relations of points, lines, surfaces, solids, and higher dimensional analogues.

For example, in the context of a coordinate plane, the x-axis and y-axis are perpendicular to each other. Moreover, theorems in geometry further explain the properties of perpendicular lines, such as the fact that if a line segment is drawn joining the extremities of two equal lines which are perpendicular to a given line, the joining segment is bisected at right angles by a third perpendicular line.

Answer:

(x-8) (x+5)

Step-by-step explanation:

x^2-3x-40

What 2 numbers multiply to -40 and add to -3

-8 *5 = -40

-8+5 = -3

(x-8) (x+5)

Answer:

i think the answer is undefined

Step-by-step explanation:

Answer: 1. inconsistent, 2. infinite, 3. (4, -1), 4. exactly two solutions.

Step-by-step explanation: HOPE THIS HELPS. ;))))

Answer:

The solution of the inequality is a < 0.2870

Step-by-step explanation:

* Lets talk about the exponential function

- the exponential function is f(x) = ab^x , where b is a constant and x

 is a variable

- To solve this equation use ㏒ or ㏑

- The important rule ㏒(a^n) = n ㏒(a) OR ㏑(a^n) = n ㏑(a)

* Lets solve the problem

∵ 13^4a < 19

- To solve this inequality insert ㏑ in both sides of inequality

∴ ㏑(13^4a) < ㏑(19)

∵ ㏑(a^n) = n ㏑(a)

∴ 4a ㏑(13) < ㏑(19)

- Divide both sides by ㏑(13)

∴ 4a < ㏑(19)/㏑(13)

- To find the value of a divide both sides by 4

∴ a < [㏑(19)/㏑(13)] ÷ 4

∴ a < 0.2870

* The solution of the inequality is a < 0.2870

Answer:

a < 0.2870

Step-by-step explanation:

We are given the following inequality which we are to solve, rounding it to four decimal places:

[tex] 1 3 ^ { 4 a } < 1 9 [/tex]

To solve this, we will apply the following exponent rule:

[tex] a = b ^ { l o g _ b ( a ) } [/tex]

[tex]19=13^{log_{13}(19)}[/tex]

Changing it back to an inequality:

[tex]13^{4a}<13^{log_{13}(19)}[/tex]

If [tex]a > 1[/tex] then [tex]a^{f(x)}<a^{g(x)}[/tex] is equivalent to [tex]f(x)}< g(x)[/tex].

Here, [tex]a=13[/tex], [tex]f(x)=4a[/tex] and [tex]g(x)= log_{13}(19)[/tex].

[tex]4a<log_{13}(19)[/tex]

[tex]a<\frac{log_{13}(19)}{4}[/tex]

a < 0.2870

Answer:

[tex]\large\boxed{f(x)=x+4}[/tex]

Step-by-step explanation:

[tex]y-8=(x-4)\\\\y-8=x-4\qquad\text{add 8 to both sides}\\\\y-8+8=x-4+8\\\\y=x+4\to f(x)=x+4[/tex]

Answer:

a = sqrt(33)

Step-by-step explanation:

a^2 + 4^2 = 7^2

a^2 + 16 = 49

a^2 = 33

a = sqrt(33)

Answer:

The distance from B to B’ is [tex]5\ units[/tex]

Step-by-step explanation:

we know that

In a translation the shape and dimensions of the figure are not going to change.

therefore

AA'=BB'=CC'=DD'

Find the distance AA'

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

[tex]A(1,5)\\A'(-2.1)[/tex]  

substitute the values

[tex]AA'=\sqrt{(1-5)^{2}+(-2-1)^{2}}[/tex]

[tex]AA'=\sqrt{(-4)^{2}+(-3)^{2}}[/tex]

[tex]AA'=\sqrt{25}[/tex]

[tex]AA'=5\ units[/tex]

therefore

[tex]BB'=5\ units[/tex]

Mapping A shows x--->y. A is the answer. Exactly one x value is matched to exactly one y value.

Answer:

Step-by-step explanation:

Remember, a sphere is defined as a three-dimensional object where all points on its surface are equidistant form its center.

According to its definition, all point on the boundaries can be called a point on the sphere.

So, among the options, only point B is on the sphere, because J and S are inside.

Therefore, the right answer is Point B.

You are on the right tracks.

Since angle ABC is a right angle, that means lines AB and BC are perpendicular.

Therefore the gradient of BC = the negative reciprocal of the gradient of AB. We can use this to form an equation to find what K is.

You have already worked out the gradient of AB ( 1/2)  (note it's easier to leave it as a fraction)

Now lets get the gradient of BC:

[tex]\frac{5-k}{6-4}= \frac{5-k}{2}[/tex]

Remember: The gradient of BC = the negative reciprocal of the gradient of AB. So:

[tex]\frac{5-k}{2} =negative..reciprocal..of..\frac{1}{2}[/tex]

So:

[tex]\frac{5-k}{2}=-2[/tex]           (Now just solve for k)

[tex]5-k=-4[/tex]

[tex]-k=-9[/tex]                          (now just multiply both sides by -1)

[tex]k = 9[/tex]

That means the coordinates of C are: (4, 9)

We can now use this to work out the gradient of line AC, and thus the equation:

Gradient of AC:

[tex]\frac{1-9}{-2-4} =\frac{-8}{-6} = \frac{4}{3}[/tex]

Now to get the equation of the line, we use the equation:

y - y₁ = m( x - x₁)                            

Let's use the coordinates for A (-2, 1), and substitute them for y₁  and x₁  and lets substitute the gradient in for m:

y - y₁ = m( x - x₁)    

[tex]y - 1=\frac{4}{3}(x +2)[/tex]           (note: x - - 2 = x + 2)

Now lets multiply both sides by 3, to get rid of the fraction:

[tex]3y - 3 = 4(x+2)[/tex]             (now expand the brackets)

[tex]3y - 3 = 4x+8)[/tex]              

Finally, we just rearrange this to get the format: ay + bx = c

[tex]3y - 3 = 4x+8[/tex]              

[tex]3y = 4x+11[/tex]

[tex]3y - 4x = 11[/tex]          

And done!:

________________________________

Answer:

The equation of a line that passes through point A and C is:

[tex]3y - 4x = 11[/tex]        

Answer:

Step-by-step explanation:

6,-5 ON APEXXXXX

Answer: (6, -5)

Step-by-step explanation:

The general equation of a circle is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is center and r is radius of the circle.

Given : The equation of a circle : [tex](x-6)^2+(y+5)^2=15^2[/tex]

[tex]\Rightarrow\ (x-6)^2+(y-(-5))^2=15^2[/tex]

Comparing to the general equation of circle , we get

[tex](h,k)=(6, -5)[/tex]

Hence, the coordinates of the center of the circle = (6, -5)