Find the 52nd term of the arithmetic sequence —24, –7, 10, ...

Answer:

b

Step-by-step explanation:

Δ QRP and Δ XRY are similar, thus ratios of corresponding sides are equal, that is

[tex]\frac{XY}{QP}[/tex] = [tex]\frac{RY}{RP}[/tex] , substitute values

[tex]\frac{XY}{4}[/tex] = [tex]\frac{4}{8}[/tex] ( cross- multiply )

8XY = 16 ( divide both sides by 8 )

XY = 2

Answer:

Step-by-step explanation:

Answer: Graph D

Step-by-step explanation:

The slope is 2

x goes after the slope in graph functions

The line goes through 3 on the y-axis so that’s where + 3 comes in.

2x + 3

Answer:

2x^2 - 11x + 15

Step-by-step explanation:

Expand 2x - 5 and x - 3 means that the algebraic expressions be multiplied.

(2x - 5)(x - 3)

x(2x - 5) -3(2x - 5)

2x^2 - 5x - 6x +15 = 2x^2 - 11x + 15

Answer:

x=50

Step-by-step explanation:

note that 40% is 2/5

Therefore, 30 tomatoes is 1- 2/5 = 3/5

3/5 of the tomatoes last year is 30

lets say tomatoes = x

3/5 x = 30

divide by 3 on both sides

1/5 x = 10

multiply by 5 on both sides

x=50

:D

hope it helped :D

Answer:

Solution,

Norman produces 30 tomatoes this year.

40% less tomatoes than the last year.

Let the last year's tomatoes be 'x'.

Then,

40% of X

[tex]40 \div 100 \times x[/tex]

[tex]0.4x[/tex]

This year=30

[tex]x - 0.4x= 30 \\ or \: 0.6x = 30 \\ or \: x = \frac{60}{0.6} \\ x = 50[/tex]

Therefore, His garden produced 50 tomatoes last year.

Hope this helps...

Good luck on your assignment...

Answer:

Option B

Step-by-step explanation:

Here we have to apply " combination and permutation. " It is given that the drama club had to choose three booths from a selection of 9, considering the possible ways to choose so. This is a perfect example of combination. In nCr, n corresponds to 9, respectively r corresponds to 3.

[tex]\mathrm{n\:choose\:r},\\nCr=\frac{n!}{r!\left(n-r\right)!},\\\\\frac{9!}{3!\left(9-3\right)!} =\\\frac{9!}{3!\cdot \:6!} =\\\\\frac{9\cdot \:8\cdot \:7}{3!} =\\\frac{504}{6} =\\\\84\\\\Solution = Option B[/tex]

Hope that helps!

Answer:

B. 84 is correct.

I did the quiz.

Answer:

976 cm^2.

Step-by-step explanation:

The surface area consists of 2 congruent triangles + 2 congruent sloping rectangles  + a rectangular base.

Area of the 3 triangles 1/2*base*height * 2

= base * height

= 14*24 cm^2

Area of the 2 rectangles = 2*25 * 10

= 20*25 cm^2

Area of the base = 14 * 10 cm^2

So total surface area = 14*24 + 20*25 + 14*10

= 976 cm^2.

Answer:

Answer choice A) About 38.47 square units

Step-by-step explanation:

Since all four sides of a square have the same length, the perimeter of a square is just 4 times one of the side lengths. The perimeter of the square and therefore the circumference of the circle is 5.5*4=22. The circumference of a circle is 2 times the radius multiplied by pi. The radius of this circle is therefore:

[tex]\dfrac{22}{2\pi}\approx 3.503[/tex]

Since the area of a circle is [tex]\pi r^2[/tex], the area of this circle is:

[tex]\pi \cdot 3.503^2= 3.14\cdot 12.271\approx 38.47[/tex]

Hope this helps!

The area of a circle with a circumference that equals the perimeter of the square is  about 38.47 square units

Since all four sides of a square have the same length, the perimeter of a square is just 4 times one of the side lengths.

The perimeter of the square and therefore the circumference of the circle is [tex]5.5*4=22.[/tex]

The circumference of a circle is 2 times the radius multiplied by pi. The radius of this circle is, therefore

[tex]22/2\pi=3.503[/tex]

The area of a circle is [tex]\pi r^2[/tex],

the area of this circle is:

=[tex]\pi \times 3.305^2[/tex]

[tex]=3.14(12.27)[/tex]

=38.47 unit^2

Thus, The area of a circle with a circumference that equals the perimeter of the square is about 38.47 square units.

To learn more about the circle visit:

https://brainly.com/question/24375372

#SPJ2

Answer:

The Seccond One

Answer:

The fact that the first marble was replaced.

Step-by-step explanation:

Independent means that the second part does not depend on what happens in the first part.  When we put the marble back, we have the same conditions  as before the marble was drawn, so it is independent

Answer:

The answer is 3.125.

Answer:

It's 3.125

Step-by-step explanation:

Hope this help lol

Answer:

(4x^2 +9)(4x^2-9) =0

Step-by-step explanation:

16x^4 - 18 = 0

Rewriting

(4x^2)^2 - 9^2 =0

We notice that this is the difference of squares

a^2 - b^2 = (a-b)(a+b)

(4x^2 -9)(4x^2+9) =0

Answer:

The answer is option 2.

Step-by-step explanation:

In the question, 16 and 81 are perfect squares. So in order to find the equivalent equation, you have to factorize it :

APPLY,

[tex](a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]

So for this question :

[tex]16 {x}^{4} - 81 = 0[/tex]

[tex]{(4 {x}^{2})}^{2} - {(9)}^{2}= 0[/tex]

[tex](4 {x}^{2} + 9)(4 {x}^{2} - 9) = 0[/tex]

Answer:

44.

Step-by-step explanation:

Since the mean of 14, 16, 16, 13, 23, x is 21, then we have 14 + 16 + 16 + 13 + 23 + x is equal to 126. Summing we have 14 + 16 + 16 + 13 + 23 = 82. 82 + x is equal to 126. X = 44.

Answer:

Z=80°

Step-by-step explanation:

If the quadrilaterals are similar, they have the same angle measurements.

∠Z=∠F

Since all interior angles of a quadrilateral add up to 360°, we can subtract ∠E, ∠C, and ∠G's measurements from 360°.

360°-100°-120°-60°=∠Z

260°-120°-60°=∠Z

140°-60°=∠Z

80°=∠Z

∠Z=80°

The measure of angle z in quadrilateral ABCD is 80 degrees.

Two quadrilaterals are similar quadrilaterals when the three corresponding angles are the same.

The sum of interior angles of a quadrilateral is 360 degrees.

According to the given question

We have two quadrilaterals  ABCD and FECG, and they are similar to each other.

Since, ABCD and FECG are similar to each other.

Therefore, ∠BAD = ∠EFG

⇒ z = ∠EFG

Now, In quadrilateral FECG

We have

∠EFG + 100 + 120 + 60  = 360  

( sum of the interior angles of a quadrilateral is 360 degrees)
⇒ ∠EFG + 280 = 360

⇒ ∠EFG = 360 - 280

⇒ ∠EFG = 80 degrees

Therefore, z = 80 degrees

Learn more about the similar quadrilaterals here:

https://brainly.com/question/16919595

#SPJ2

The general form of the equation of the circle will be x² + y² − 8x − 4y + 11 = 0.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

The standard form of the equation of a circle is (x − 4)² + (y−2)² = 9

Then the general form of the equation of the circle will be

x² + 4² − 8x + y² + 2² − 4y = 9

      x² + y² − 8x − 4y + 20 = 9

        x² + y² − 8x − 4y + 11 = 0

Then the correct option is A.

Learn more about the equation of a circle here:

https://brainly.com/question/10165274

#SPJ1

Answer:

[tex]4a^2b^2(ab^3-4a^3+3b)[/tex]

This is the answer,the option C

Step-by-step explanation:

Answer: [tex]3\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{\left(5-2\right)^2+\left(5-2\right)^2}[/tex]

= [tex]3\sqrt{2}[/tex]

Answer & Step-by-step explanation:

First, we must know the formula for finding the distance between two given points.

[tex]Distance(d)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We will plug in (2,2) for (x1,y1) and we will plug in (5,5) for (y2,y1).

[tex]Distance(d)=\sqrt{(5-2)^2+(5-2)^2}[/tex]

Subtract 2 from 5 in both parentheses.

[tex]Distance(d)=\sqrt{(3)^2+(3)^2}[/tex]

Simplify the exponents.

[tex]Distance(d)=\sqrt{9+9}[/tex]

Add 9 and 9 together.

[tex]Distance(d)=\sqrt{18}[/tex]

Simplify the radical.

[tex]Distance(d)=3\sqrt{2}[/tex]

This number can also be simplified into 4.24.

So, the distance between the two points is 3√2 units or 4.24 units.

Answer:

A: y = -2/5x - 1

B: 2x + 5y = -5

E: y - 1 = -2/5(x+5)

Step-by-step explanation:

I only got 2 out of 3 answers, but the ones listed above should be correct :) Hope this helps! :D

The equation of the line is 2x + 5y = -5.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line that is parallel to the line 2x + 5y = 10 will have the same slope as the given line, which is -2/5.

Using the point-slope form of the equation of a line, we can find the equation of the line passing through the point (-5, 1) with slope -2/5:

y - 1 = (-2/5)(x + 5)

Multiplying both sides by 5.

5y - 5 = -2x - 10

Adding 10 to both sides.

2x + 5y = -5

Now,

2x + 5y = -5

This can be written as,

5y = -2x -5

y = (-2/5)x - 1

Thus,

The equation of the line is 2x + 5y = -5.

Learn more about the equation of a line here:

https://brainly.com/question/23087740

#SPJ5

Answer:

= 73358400 or 7.33584 x 10^7

Step-by-step explanation:

2465(8) x 465(8)

= 2465 x 8^2 x 465

= 2465 + 64 + 465

= 157760 x 465

= 73358400 or 7.33584 x 10^7

Answer:

The intersection of plane R and plane P is line DB.

Point H is not on plane P

CE and DB intersect at point D

Step-by-step explanation:

Answer:

1 piece of UPS

Step-by-step explanation:

Here, we want to know the difference in the number of pieces handled at the different times

In 1995, amount handled = 1.8 * 10 = 18 pieces

In 2000, amount handled = 1.7 * 10 = 17 pieces

The difference between what was handled in the year 2010 and what was handled in 1995 is 18 -17 = 1

Answer:

[tex]1.35 x 10^{12}[/tex]

Step-by-step explanation:

When you multiply exponents together, you add them, so,

1. Simply multiply 6.75 and 0.2 normally to get 1.35

2. Add the exponents (keep bases the same) to get [tex]10^{12}[/tex]

3. Combine them together to get your answer

Answer:

(z-9)(z+2)

Step-by-step explanation:

U have to find numbers which when u multiply u get -18 and subtract u get -7

-18= -9×+2,2-9=-7

Z²+2z-9z-18

Z(z+2)-9(z+2)

(Z-9)(z+2)

Answer: (z+2)(z-9)

Step-by-step explanation:

[tex]z^{2} -7z-18[/tex]  to solve for this you need to find two numbers that if multiplied together they give you negative 18 and at the same time adds up to -7.

Those two numbers could be  -9 and 2 .

now rewrite the expression like this.

[tex]z^{2} +2z - 9z -18[/tex]   Group them  

([tex]( z^{2} +2z) ( -9z- 18)[/tex]    Factor it out z in the first grouping

z(z +2)  -9(z + 2)          factor out  x+2

(z +2 ) (z-9)

A)4πr^2

4π(5)^2

4π(25)

A≈314.2π

B)4πr^2

4π x (3)^2

4π x(9)

A≈113.112π

hope it helps

Answer:

(a)18

(b)1089

(c)Sunday

Step-by-step explanation:

The problem presented is an arithmetic sequence where:

We want to determine the number of Sundays in the 120 days before Christmas.

(a)In an arithmetic sequence:

[tex]\text{The nth term}, T_n=a+(n-1)d\\T_n \leq 120\\$Therefore:$\\1+7(n-1) \leq 120\\1+7n-7\leq 120\\7n-6\leq 120\\7n\leq 120+6\\7n\leq 126\\$Divide both sides by 7$\\n\leq 18[/tex]

Since the result is a whole number, there are 18 Sundays in which Aldsworth advertises.

Therefore, Aldsworth advertised 18 times.

(b)Next, we want to determine the sum of the first 18 terms of the sequence

1,8,15,...

[tex]\text{Sum of a sequence}, S_n=\frac{n}{2}( 2a+(n-1)d)\\S_{18}=\frac{18}{2}( 2*1+(18-1)*7)\\=9(2+17*7)\\=9(2+119)\\=9*121\\S_{18}=1089[/tex]

The sum of the numbers of days published in all the advertisements is 1089.

(c)SInce the 120th day is the 18th Sunday, Christmas is on Sunday.

Answer:

112 square units.

Step-by-step explanation:

Use the formula for the area of a triangle.

[tex]A=bh[/tex]

[tex]b \times h[/tex]

[tex]14 \times 8[/tex]

[tex]=112[/tex]

Answer:

D

Step-by-step explanation:

The y-coordinate will be the average of 5 and -2 which is 3/2. This eliminates options A and B. C doesn't make sense because the x-coordinate (which is -7) of the midpoint can't be larger or smaller than the x-coordinates of the endpoints, so that means that the answer is D.

Answer:

230 cm squared

Step-by-step explanation:

Split the shape into a triangle and a rectangle

The area of a triangle is base x height / 2

20 x 9= 180/2= 90             (9 because you do 16-7 to find height of triangle)

Find the area of the rectangle=

7 x 20= 140

Add them up

140+90= 230cm squared

I hope this helped :)

Answer:

230 cm squared

Step-by-step explanation: