The sum of 5 consecutive integers is 265. What is the fifth number in this sequence?

Answers

Answer 1

Final answer:

To find the fifth number in a sequence of 5 consecutive integers with a sum of 265, you can use the formula for the sum of an arithmetic series. The fifth number is 53.

Explanation:

To find the fifth number in a sequence of 5 consecutive integers where the sum is 265, we can use the formula for the sum of an arithmetic series. The formula is: Sum = (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference. In this case, we have n = 5, so:

265 = (5/2)(2a + 4d)265 = 2.5a + 10da + 4d = 53

Since we are looking for the fifth term, we can use the formula a + (n-1)d = 53 to solve for the fifth number:

a + 4d = 53a + 4(a+d) = 532a + 4d = 532a + 8d = 1062a + 8d - 2a - 4d = 106 - 534d = 53d = 13.25

Substituting the value of d back into the equation a + 4d = 53, we can find the value of a:

a + 4(13.25) = 53a + 53 = 53a = 53 - 53a = 0

Therefore, the fifth number in the sequence is a + 4d = 0 + 4(13.25) = 53.

Related Questions

Tony started a blanket business. He purchased a sewing machine and some fabric to get started, and then sold each blanket for the same price. The expression −450+12x−450+12x represents the profit that Tony has earned based on the number of blankets sold.

Which expression represents the total amount Tony earns from selling blankets?

x
12x
-450+12x
12

Answers

The answer is 12x My dude

12x meh friend and here is something you might find funny horsepower is how fast you hit the wall torque is how far you take the wall

What are the characteristics of a gas?
A. a definite shape but no definite volume
B. no definite shape but a definite volume
C. a definite volume and definite shape
D. no definite shape or definite volume

Answers

D. no definite shape or definite volume

Answer:

Step-by-step explanation:

Andrea is shopping for items for her pet sitting business because the store is having a sale where everything in the store is 5% off. Andrea buys a cat carrier for $39.99 and a cat tower for $19.99. She has a coupon for an additional 15% off on the cat tower. Before tax, Andrea estimates that her total, after discounts, will be about $54. Determine if Andrea has estimated correctly.
a. Yes. Andrea has estimated correctly.
b. No. Andrea has taken 20% of the total, which is not correct..
c. No. Andrea has taken successive discounts on the total, but the coupon is just on the cat tower.
d. No. Andrea has only taken the 5% discount on the cat tower and not on the carrier

Answers

C is the answer you are looking for!

Turner has 6 pounds of pasta.Each Time he makes dinner he uses 3/4 pound of pasta.How many dinners can he make?

Answers

3/4 is equal to 0.75

So, 6 divided by 0.75 which gives you 8
or it could also be written as 6 divided by 3/4 which is also 8..

SO in summary, Turner can make 8 dinners

Hello! I would be happy to help you! So all you are doing is seeing how many times 3/4 can fit into 6 pounds

Final Answer: 8 times or 8 dinners

1. simplify

9 x 5 + 2 / 8 - 3

by the way " / " means division.

Answers

the answer would be 42.25 because first you multiply 9 and 5, then divide 2 and 8 and add that to 45, then you subtract 3 from that.

Your answer will be 46. Remember PEMDAS. Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. These are the steps you would do a problem like this in. First you would multiply 9x5, because there is no parentheses or exponents. Next, divide. This will leave you with 45+4-3. Next, do your addition and subtraction. There's your answer Hope this helps :)

If p||q, solve for x.

Answers

x=10 because both of the angles when added equal 180

The two angles are supplementary because they are corresponding angles(not sure i the term is actually corresponding... i could be something else). Thus 7x-1+13x-19=180 so 20x-20=180 so x=10

according to the rational root theorem, which is a factor of the polynomial f(x) = 3x^3 - 5x^2 - 12x + 20?

Answers

They are: +-(1,2,4,5,10,20)/+1(1,3)

If I set a goal of signing up 30% of customers to receive emails. that means that if I speak to 130 customers today I need to collect email addresses from ?

Answers

130*.3 people
^^^^^^^^^

Answer:39

Step-by-step explanation:

130+30%=39

Which expression is equivalent to 4 -(-7)? A 7+4, B 4-7, C -7-4, D -4+7

Answers

Hi there! You are subtracting a negative number, which is basically the same thing as adding, because two negatives make a positive. B and C is out, because they do not fit the expression. You are actually adding both numbers and anytime you have to subtract a negative number, you add. When you do basic math, 4 + 7 is 11. Both numbers are negative and D does not work, because you're adding from a negative number. The only answer choice that has the expression is A. The answer is A.

The diagram shows triangle MNP. Which term describes point Q?

Answers

Answer:

(B) Incenter

Step-by-step explanation:

From the given figure, it can be seen that PMN is a triangle where MQ is the angle bisector of ∠NMP, PQ is the angle bisector of∠NPM and NQ is the angle bisector of ∠MNP.

Also, It is equally distant from the three line segments forming the sides of the triangle. Thus, By the definition of incenter, Q can be named as the incedntre of the given triangle PMN.

Since, the centroid, circumcenter and orthocenter does not satisfy the conditions given in the figure, thus Q can not be considered as centroid, circumcenter and orthocenter.

Hence, option B is correct.

Answer:

the answer is incenter

Step-by-step explanation:

took the apex quiz got it correct !

PLEASE HELP ASAP- solve the equation :
9x^2+64=0 . i need work to be shown for credit ....

Answers

In this quadratic equation a=9 b=0 c=64, you could use the Quadratic Formula:
x = [-b +-sqrt (b^2 -4*a*c)] / 2*a
x = 0 +- sqrt (0 -4*9*64) / 2*9
x = +- sqrt(-2,304) / 18

x = + 48 i / 18
x = -48 i /18

Where "i" is the square root of minus 1.

Jared wants to purchase his favorite barbeque sauce. The barbeque sauce comes in two different size bottles. The 32 ounce bottle is on sale for $4.59. The 18 ounce bottle is priced at $3.06. Jared has a coupon for 60 cents off if you buy two 18 ounce bottles. Determine if Jared gets the better buy when he buys one 32 ounce bottle or when he buys two 18 ounce bottles. a. Jared will get the same deal on either purchase. b. Jared will get the better deal buying one 32 ounce bottle. c. Jared will get the better deal buying two 18 ounce bottles. d. Jared doesn’t need the coupon, he will get the best deal on one 18 ounce bottle.

Answers

Answer:

b. Jared will get the better deal buying one 32 ounce bottle.

Step-by-step explanation:

The midpoint of 2004-06-02-01-00_files/i0130000.jpg is (5, 4). One endpoint of 2004-06-02-01-00_files/i0130001.jpg is T(2, 9). What are the coordinates of endpoint U? A. (–1, 8) B. (3.5, 6.5) C. (6, 1) D. (8, –1)

Answers

I think you misplaced a file in the question...

its is d becuase there was a show me video when i had to answer the question. hope i helped please give me brainliest

Find an equation of the line containing the point (3,3) and parallel to y = 2 x − 1 y=2x-1.

Answers

y=mx+b
y=2x+b
then substitute x and y
3=2(3) + b
3= 6 + b
b=-3
y=2x-3

If 5 ounces is equal to 140 grams, then 2 pounds of pizza dough is equal to how many grams?

Answers

907.18 grams are in 2 pounds.

Which equation can be used to solve for b?

A) tan(30°) = 5/b
B) tan(30°) = b/5
C) tan(30°) = 10/b
D) tan(30°) = b/10

Answers

SOH CAH TOA
tan(x) = opposite / adjacent

the hypotenuse is the longest side of 10, so C and D are not correct.

Side b is adjacent to the 30° angle
Side 5 is opposite of the 30° angle

tan(30) = 5/b

In this exercise we want to calculate the value of angle B, so we have to:

Letter A

So knowing the tangent formula as:

[tex]tan(x) = opposite / adjacent[/tex]

Knowing some information given in the exercise such as:

the hypotenuse is the longest side of 10Side b is adjacent to the 30° angleSide 5 is opposite of the 30° angle

So we have:

[tex]tan(30)=5/b[/tex]

See more about triangles at brainly.com/question/25813512

Without solving the equation, determine the nature of the roots of x2 - 2 x - 8 = 0.

Answers

Evaluate using the discriminant (the part of the quadratic equation under the square root sign) b²-4ac
In your equation, a=1, b=(-2), and c=(-8)...substitute their values into the discriminant:
(-2)²-4(1)(-8)
4+32 = 36

The value is positive, therefore the equation has two real roots.
It's a perfect square (√36=6) so the roots are rational
Answer: two real, rational roots

(If the result was a negative number, the system would have two irrational roots. If the result was zero, the system would have a double root (one value repeated twice - when graphed, the vertex of the parabola falls on the x-axis)∨

Final answer:

The equation x² - 2x - 8 = 0 has two real and distinct roots.

Explanation:

A quadratic equation is an equation of the form ax² + bx + c = 0. In this equation, the coefficient of the x² term is 1, so a = 1, b = -2, and c = -8. We can determine the nature of the roots without solving the equation by looking at the discriminant, which is the term inside the square root of the quadratic formula. The discriminant is given by b² - 4ac. If the discriminant is positive, the equation has two real and distinct roots. If the discriminant is zero, the equation has two real and identical roots. If the discriminant is negative, the equation has two complex roots.

In this case, we have b = -2 and a = 1, so the discriminant is (-2)² - 4(1)(-8) = 4 + 32 = 36. Since the discriminant is positive, the equation has two real and distinct roots.

Kim was walking down a rocky path for 4 minutes the election dropped steadily altogether it dropped 8 feet what was the chance in elevation per minute for the 4 minutes?

Answers

in 4 minutes it changed 8 feet

so 8/4 =2 feet per minute change

and since it dropped it would be a negative change so -2 feet per minute

You want to embroider a square design. You have an embroidery hoop with a 6 inch diameter. Find the largest value of x so that the entire square will fit in the hoop. Round to the nearest tenth

Answers

Final answer:

The largest size of the square that can be embroidered within the 6 inch hoop is 4.2 inches per side (rounded to the nearest tenth). This is found using geometry principles involving squares and circles.

Explanation:

This question is asking for the side length of a square that will fit within a circle, or in this case, an embroidery hoop, with a certain diameter. This is a concept from geometry that involves the relationship between squares and circles. Essentially, the diameter of the circle becomes the diagonal of the square.

To calculate the side length (x) of the square, we'll use the formula for the diagonal (d) of a square divided by the square root of 2 (d = √2 * x). Since the diameter of the hoop is 6 inches, rearranging the equation gives us x = d / √2 which results in x = 6 / √2 = 4.2 inches (rounded to the nearest tenth)

Learn more about Geometry here:

https://brainly.com/question/31408211

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9
Angela is buying a dress that is on sale for 20% off. If the original price of the dress is $60.00, how much money is Angela saving on the dress?

Answers

convert 20% into a decimal like this >> 20/100 =0.2 now 0.2 x 60.00 =12 the answer hope it works.

Angela is Saving $12 on the dress.

What is Percentage?

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Original Price of Dress = $60

Discount = 20% off

So, the Price of Dress after discount

= 60- 20% of 60

= 60- 12

= $48

Hence, Angela saving $12.

Learn more about Percentage here:

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Prove the Converse of the Pythagorean Theorem using similar triangles. The Converse of the Pythagorean Theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures.

Answers

The Pythagorean Theorem tells us that in a right angle, the sum of the squares lengths of the legs of the triangle equal the squared length of the hypotenuse.

By angle similarity of triangles we know that if we have three triangles △ADB △ABC △BDC triangles are similar then the sides of the triangles are proportional. AD:AB=AB:AC=AC::BC= BC:DC
AD/AB=AB/AC AC/BC=BC/DC
Now we cross multiply
AD*AC=AB*ABAC*DC=BC*BC
This is the same as
AD*AC=AB2AC*DC=BC2
AD*AC+AC*DC=AB2+BC2
Distributive property
AC(AD+DC)=AB2+BC2
But by construction
AD+DC=AC
Substituting
AC*AC=AB2+BC2
So we have
AB2+BC2=AC2
This proves that the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse.

Answer:

To prove the Converse of Pythagorean Theorem:

Step-by-step explanation:

1. Draw a right triangle (Triangle ABC)

2. Draw an altitude from and A to the hypotenuse creating 2 new triangles

3. The part that intersects the hypotenuse will be point D, this makes a right angle

Triangle DBA and triangle ABC both have right angles and share angle B, this means that triangle ABC and triangle DBA are congruent by the AA postulate. Since triangle DAC and triangle ABC both have right angles(angle D and angle A) and they share angle C, triangle DAC and ABC are congruent by the AA postulate as well.

The ratios can be set up as:

AC/BC = DC/AC & AB/BC = DB/BA

Once cross multiplied, the result should be:

(AC)² = (BC)(DC) & (AB)² = (BC)(DB)

Now add both sides together to get:

(AC)² + (AB)² = BC(DC) + (BC)(DB)

To make things easier, factor out the like terms:

(AC)² + (AB)² = BC(DC + DB)

When looking at the triangle(must draw to see), it shows that (DC + DB) is actually side BC. This leaves:

(AC)² + (AB)² = BC(BC) → (AC)² + (AB)² = (BC)²

The Pythagorean theorem says that a² + b² = c². Knowing this, on the original triangle, side AB = a, side AC = b, and side BC = c. Knowing this:

(AC)² + (AB)² = (BC)² → a² + b² = c²

This proves the Converse of the Pythagorean Theorem.

Which equation would represent this problem?

Five added to 3 times a number is equal to 8 less than 5 times the number

Answers

5+3n=8-5n should be the could answer how I solve it was adding is a plus sigh=n and less than is a minus sign

What’s the answer pleaseeeeeeeee

Answers

y^2 +6^2 = 12^2

y^2 +36 = 144

y^2 = 108

sqrt(108) = 10.392 = 6sqrt(3)

Answer is B 6sqrt(3)

So the question says...

Suppose you have ∠SMB and m ∠SMB =125.35 °.

Part A: Determine the angle measure that is complement to ∠SMB, if possible. If ∠SMB does not have a complementary angle, then explain why it does not.

Part B: Determine the angle measure of the supplement of ∠SMB.

Part C: Determine the angle measure of the angle complement to ∠SMB’s supplement.

I’m stuck on this question so if anyone can help me with it that would be greatly appreciated. Thanks!

Answers

Part A. Two angles are complementary if their sum is equal to 90°. Since the angle given is more than 90°, there is no possible complement for a 125.35-degree angle.

Part B. Two angles are supplementary if their sum is equal to 180°. So,
Supplementary angle = 180 - 125.35 = 54.65°

Part C. Complementary angle = 90 - 54.65 = 35.35°

Part A: ∠SMB does not have a complementary angle

Part B: The angle measure of the supplement of ∠SMB is 54.65°

Part C: The angle measure of the angle complement to ∠SMB's supplement is 35.35°

The given angle is ∠SMB and m ∠SMB =125.35 °

For Part A

Complementary angles are angles that sum up to 90°.

To determine the angle measure that is complement to ∠SMB, we will find the angles that adds up to ∠SMB to give 90°. Since ∠SMB is already greater than 90°, therefore, ∠SMB does not have a complementary angle.

For Part B.

Supplementary angles are angles that sum up to 180°.

To determine the angle measure of the supplement of ∠SMB, we will find the angle that adds up to ∠SMB to give 180°. Let the measure of the angle be x, that is

x + 125.35° = 180°

∴ x = 180° - 125.35°

x = 54.65°

∴ The angle measure of the supplement of ∠SMB is 54.65°

For Part C

To determine the angle measure of the angle complement to ∠SMB's supplement, we will determine the measure of the angle that adds up to ∠SMB's supplement to give 90°. Let the angle be y

Then,

y + 54.65° = 90°

(NOTE: ∠SMB's supplement is 54.65°)

∴ y = 90° - 54.65°

y = 35.35°

∴ The angle measure of the angle complement to ∠SMB's supplement is 35.35°

Hence,

Part A: ∠SMB does not have a complementary angle

Part B: The angle measure of the supplement of ∠SMB is 54.65°

Part C: The angle measure of the angle complement to ∠SMB's supplement is 35.35°

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Larissa asked 40 students to name their favorite food 10 students said their favorite food was pizza what percent of the students Larissa surveyed said their favorite food was pizza?

Answers

10 out of 40 said pizza =

divide 10 by 40 = 0.25

0.25 = 25% said pizza

Expand and simplify (x-7)(x+3)

Answers

x(x+3)-7(x+3)
x2+3x-7x-21
x^2-4x-21

It is easy. why you didn't do it yourself?.
Anyway here is a tip to get simplified answer.
first write x*x
x^2
then multiply first x with 3 and second x with (-7) then sum up. will get 3x+(-7x) i.e (-4x). so write this.
x^2+(-4x)
and multiply (-7) by 3 i.e (-21)
x^2-4x+(-21)
So the answer will be.
x^2-4x-21

An alloy of tin is 15% tin and weighs 20 pounds. A second alloy is 10% tin. How many pounds of the second alloy must be added to the first to get a 12% mixture? 30 lb 40 lb 60 lb

Answers

so, they alloy is hmmm some piece of metal.

it has tin, among other metals, regardless of what other metals it may have, we know that for the first one, 15% is tin, the rest something else, and we also know that the alloy itself, weights 20 lbs.

now, how much is just the weight of the tin metal in it alone? well, is 15% of 20 lbs, or (15/100) * 20, or 3 lbs, so of all those 20 lbs, only 3 lbs or 15% is tin.

for the second alloy, let's say we'll add "x" lbs, we know the second alloy is 10% tin, how much of that weight is tin? well 10% of x, or (10/100) * x, or 0.10x lbs.

now, we're looking for a mixture, say the resulting lbs of mix will be "y" lbs, and we know the mixture will be 12% of tin, how much is 12% of y? (12/100) * y, or 0.12y.

now, regardless of what "x" and "y" is, we know that 20 + x = y, and that 3 + 0.10x = 0.12y, thus

[tex]\bf \begin{array}{lccclll} &\stackrel{lbs}{amount}&\stackrel{tin~\%}{quantity}&\stackrel{tin~lbs}{quantity}\\ &------&------&------\\ \textit{15\% alloy}&20&0.15&3\\ \textit{10\% alloy}&x&0.10&0.10x\\ ------&------&------&------\\ mixture&y&0.12&0.12y \end{array} \\\\\\ \begin{cases} 20+x=\boxed{y}\\ 3+0.10x=0.12y\\ ----------\\ 3+0.10x=0.12\left( \boxed{20+x} \right) \end{cases} \\\\\\ 3+0.10x=2.4+0.12x\implies 3-2.4=0.12x-0.10x \\\\\\ 0.6=0.02x\implies \cfrac{0.6}{0.02}=x\implies 30=x[/tex]

A number is a multiple of 3 if and only if the number is odd
True or false

Answers

False. 30 is an even number and is a multiple of 3, 3 x 10 = 30. Same with 60, 90, 120, etc. if you keep adding 30.

PLEASE HELP 30 POINTS!!!!!!

Answers

placed them equal to each other.

3x + 6 = 4x - 2

6 (+2) = 4x (-3x)

8 = x

plug in x to both of the expressions

3(8) + 6 = 24 + 6 = 30
4(8) - 2 = 32 - 2 = 30

True

x = 8

hope this helps

B is wrong, because you do not set them equal to 180 ( you set them equal to each other). Next, it is wrong, because they messed up the end too.

hope this helps

Answer: " x = 8 "
_______________________________
By examining the image attached, we notice that:
_______________________________________________
The 2 (two) particular angles with the following measurements:
_________________________________________________
1) 4x - 2 ; and:

2) 3x + 6 ;
_________________________________________________
are equal; since they are "alternate interior angles" ; since the 2 (two) horizontal lines in the figure are parallel; and since alternate interior angles are equal in measurement.
___________________________________________
The question asks to solve for "x" ;

As such:

4x - 2 = 3x + 6 ;

Solve for "x" ;

Subtract "3" from each side of the equation ; & add "2" to each side of the equation ;

4x - 2 = 3x + 6 ;
-3x +2 = -3x + 2 ;
_________________________
1x = 8 ;
_________________________

→ x = 8 .
____________________________________
Now, we can check our answer:
____________________________________
" 4x - 2 = 3x + 6 " ;

→ Plug in "8" for "x" ; to see if both sides of the equation are equal ;

4(8) - 2 =? 3(8) + 6 ??

→ 32 - 2 =? 24 + 6 ??

→ 30 = ? 30 ? Yes!
____________________________________________________

What is the y-intercept of a line that has a slope of 3 and passes through point (–1, –7)?
–10
–4
3
7

Answers

The answer is b, (-4)

To get this answer you would put this information into point-slope form and then solve for the y-intercept
Math Work:
y-y1=m(x-x1) So you would plug in the y1, m and x1
y+7=3(x+1) the negatives cancel out and turn into positives
y+7=3x+3
-7 -7
y=3x-4
negative 4 is your y-intercept (-4)

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