HELP! URGENT!
Alice wrote three consecutive even numbers. The sum of these numbers was 252.

Pat wrote three consecutive odd numbers. Pat's numbers were larger than Alice's numbers.

The difference between the largest of Pat's numbers and the largest of Alice's numbers was 25.

What was the sum of Pat's numbers?

Answers

Answer 1

Answer:

333

Step-by-step explanation:

Let a represent Alice's numbers and p represent Pat's numbers.

Alice wrote three consecutive even numbers. The sum of the three is 252. This means:

[tex]a+(a+2)+(a+4)=252[/tex]

The first term is even. Each consecutive even term is two more than the previous term. Simplify:

[tex]3a+6=252\\3a=246\\a=84[/tex]

In other words, Alice's first number was 84.

Pat wrote three consecutive odd numbers. His numbers were larger than Alice's numbers. Similar to Alice, we can write:

[tex](p+1)+(p+3)+(p+5)=x[/tex]

The first term is odd. Each consecutive odd term will be 1 more, then 3 more, then 5, etc. We want to find Pat's sum, or x.

We are told that the difference between the largest of Pat's and Alice's  numbers is 25. Therefore:

[tex](p+5)-(a+4)=25[/tex]

Simplify. Substitute a. Solve for p:

[tex]p-a+1=25\\p-84=24\\p=108[/tex]

Therefore, Pat's sum is:

[tex](108+1)+(108+3)+(108+5)=333[/tex]


Related Questions

Statement Reason
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Answer:

Question?

Step-by-step explanation:

Please help ASAP !!!☹️

Answers

Answer: quit

Step-by-step explanation:

it’s really easy .

Sam ran 63,756 feet in 70 minutes. What is Sam's rate in
miles per hour? (There are 5,280 feet in one mile.)
Step 1: What is Sam's rate as stated?
63,756 feet
63, 756 ft
70 min
70 minutes
Step 2: What factor is used to convert feet per minute into
miles per minute?
Step 3: what factor is used to convert miles per minute to miles per hour

Answers

Answer:

10.35 miles per hour

Sam's rate as stated is 63,756 feet per 70 minutes

Divide by 5,280 feet

Divide by 60 minutes

Step-by-step explanation:

1. Find how many feet Sam ran in one minute

63,756 ÷ 70 = 910.8 ft.

2. Find how many feet he ran in one hour

910.8 · 60 = 54,648 ft.

3. Convert the feet to miles

54,648 ÷ 5280 = 10.35

Step 2: There are 5280 feet in one mile. Therefore, you would divide by 5280 feet to convert feet per minute into miles per minute.

Step 3: There are 60 minutes in one hour. Therefore, you would divide by 60 minutes to convert miles per minute to miles per hour.

Answer:

1: 63,756 and 70 mins

2: 1 mile and 5,280 feet

3: 60 mins and 1 hour

4: 10.35

Find the following measure for this figure.
12
10

Answers

Answer:

13 units

Step-by-step explanation:

Using the right triangle formed by the 2 legs and the slant height s

The legs are 12 and 10 ÷ 2 = 5, with hypotenuse s

Using Pythagoras' identity in the right triangle, then

s² = 12² + 5² = 144 + 25 = 169 ( take the square root of both sides )

s = [tex]\sqrt{169}[/tex] = 13

A grocer purchased 200 eggs at rs.9each. 20 of them were broken and he/she sold the rest at rs.9.50 each.Find his /her profit or loss percent.​

Answers

Answer:

5.55%

Step-by-step explanation:

Hope this helped you

If this helped you, plz mark me as brainiliest

Sorry for bad handwriting.

Thank you

A bag contains twelve marbles, which includes seven red marbles and five blue marbles. Roja reaches into the bag and pulls out four marbles. a) How many different sets of four marbles can be pulled from this bag? b) How many of these sets contain two red marbles and two blue marbles? c) How many of these sets contain all red marbles? d) How many of these sets contain all red marbles or all blue marbles?

Answers

Answer:

a) 495

b) 210

c) 35

d) 40

Step-by-step explanation:

Given a total of 12 marbles.

n = 12

Number of red marbles = 7

Number of blue marbles = 5

a) Number of different sets of 4 marbles that can be made from this bag ?

This is a simple combination problem.

where n = 12 and r = 4.

So, answer will be:

[tex]_{12}C_4[/tex]

Formula:

[tex]_{n}C_r = \dfrac{n!}{(n-r)!r!}[/tex]

[tex]_{12}C_4 = \dfrac{12!}{(8)!4!} = \dfrac{12\times 11\times 10\times 9}{4 \times 3\times 2} =\bold{495}[/tex]

b) Two red and two blue marbles:

The answer will be:

[tex]_{7}C_2 \times _{5}C_2 = \dfrac{7\times 6}{2} \times \dfrac{5\times 4}{2} =\bold{210}[/tex]

c) all red marbles.(4 chosen out of 7 red and 0 chosen out of 5 blue marbles)

[tex]_{7}C_4 \times _{5}C_0 = \dfrac{7\times 6\times 5\times 4}{4\times 3\times 2} =\bold{35}[/tex]

d) all red or all blue.(all red marbles plus all blue marbles)

All red marbles:

[tex]_{7}C_4 \times _{5}C_0 = \dfrac{7\times 6\times 5\times 4}{4\times 3\times 2} \times 1=\bold{35}[/tex]

All blue marbles:

[tex]_{7}C_0 \times _{5}C_4 = 1 \times \dfrac{5\times 4\times 3\times 2}{4\times 3\times 2} =\bold{5}[/tex]

So, answer is 40.

what is the change in each term of the sequence? 0.8, 1, 1.2, 1.4, 1.6​

Answers

Begin by studying the pattern.

Notice that the difference between 0.8 and 1 is 0.2.

In other words, 0.8 + 0.2 is 1.

In the same way, 1 + 0.2 is 1.2.

1.2 + 0.2 is 1.4 and 1.4 + 0.2 is 1.6.

So we can see that the difference

between each of the terms is 0.2.

Answer:

+.2

Step-by-step explanation:

To find the common difference, take the second term and subtract the first term

1 - .8 = .2

Check by subtracting the second term from the third term

1.2 - 1 = .2

The common difference is .2

please i need help lol The amount of clay students used for their last art project is weighed. The line plot displays the amounts of clay. How much more clay did the students who used of a pound use than the students who used of a pound?

Answers

Answer:

2  1/4

Step-by-step explanation:

We need to see how much clay they used if each person in that group used 3/4 clay. There are 4 people in the group.

=> 3/4 x 4 = 12/4 =    3

Now, we need to see how much clay they used if each person in that group used 1/4 clay. There are 3 people in the group

=> 1/4 x 3 =   3/4

Now, we need to see how much more clay was used.

=>3 - 3/4

=> 3/1 - 3/4

=> Take the LCM of the denominators and make the denominators equal.

=> 12/4 - 3/4

=> 9/4

They used 9/4 more clay.

Since there are no options with 9/4, we need to make this improper fraction into a proper fraction.

=> 9/4 = 2  1/4

They used 2  1/4 more clay.

f(x) = -7x^2+8x+2f(x)=−7x 2 +8x+2

Answers

Answer:5

Step-by-step explanation:

solve this question .....​

Answers

It’s a bit blurry, I’m not sure if I got the question right..

compare the values of the 7s in the number 4,877,034

Answers

Answer:

4,877,034=70,000

4,877,034=7,000

Explanation:

Place value is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000. It is important that children understand that whilst a digit can be the same, its value depends on where it is in the number.

Hope this helps <3

Need thanks? Comment /hearthelp

Which graph has a slope of 4/5?

Answers

Answer:

[tex]\boxed{ Graph. B}[/tex]

Step-by-step explanation:

Hey there!

Well slope is aka rise/run,

so starting at the red dot and rising 4 units an ruing to the right 5 units,

graph b is the correct answer.

Hope this helps :)

Graph B has a slope of 4/5.

How is a slope calculated?

Slope is calculated with the aid of finding the ratio of the "vertical change" to the "horizontal alternate" among (any) distinct factors on a line.

What is a slope in a straight line?

Typically, the slope of a line offers the measure of its steepness and path. The slope of an instant line among two factors says (x1,y1) and (x2,y2) may be without problems decided by finding the difference between the coordinates of the points. The slope is commonly represented by using the letter 'm'.

Learn more about slope here https://brainly.com/question/1884491

#SPJ2

The sum of three consecutive multiples of 7 is 777 find these multiples

Answers

let the consecutive multiples be 7(n-1) , 7n and 7(n+1)

so 7(n-1)+7n+7(n+1)=777

or 3n=111,

n=37

252,259,266

[tex]7n+7n+7+7n+14=777\\21n=756\\n=36\\\\7n=252\\7n+7=259\\7n+14=266[/tex]

252,259,266

Geometry - Triangle d) In the given figure, BE = EC and CE is the bisector of ZACB. Prove that ZBEC = ZACD. E B D С​

Answers

Answer:

Let m∠BCE = x

Then m∠ACE = x as well since CE is bisecting ∠ACB.

m∠ACD + x + x = 180° ⇒ m∠ACD = 180° - 2x

Consider ΔBEC

Since BE = EC, the opposite angles are congruent:

∠BCE ≅ ∠CBE

Then:

m∠CBE = m∠BCE = x

Find the angle BEC:

m∠BEC = 180° - (x + x) = 180° - 2x

Comparing the above we see that:

m∠BEC = m∠ACDproved


5 3/4 - (-3 7/8) = H
What is H ?​

Answers

Answer:

Step-by-step explanation:

convert mixed fraction into improper fraction

[tex]5\frac{3}{4}=\frac{23}{4}\\\\\\3\frac{7}{8}=\frac{31}{8}\\\\5\frac{3}{4}-[-3\frac{7}{8}]=\frac{23}{4}+\frac{31}{8}\\\\=\frac{23*2}{4*2}+\frac{31}{8}\\\\=\frac{46}{8}+\frac{31}{8}\\\\=\frac{46+31}{8}\\\\\\=\frac{77}{8}\\\\=9\frac{5}{8}[/tex]

Answer:

9 5/8.

Step-by-step explanation:

5 3/4 - (-3 7/8)

= 5 3/4 + 3 7/8

= 5 + 3 + 3/4 + 7/8

= 8 + 3/4 + 7/8    

The LCD of 4 and 8 is 8 so we get

8 + 6/8 + 7/8

= 8 + 13/8

= 8 + 1 5/8

= 9 5/8.

Solve for x. PLZ ANSWER FAST

Answers

Answer:

No solutions.

Step-by-step explanation:

7(2) + 39 > 53 and 16(2) + 15 > 31

14 + 39 > 53 and 32 + 15 > 31

53 >_ 53 but, 47 > 31 :/

So even with one the first equation is smaller.

if 13 minute video played for 6 minutes what is the amount of percent played

Answers

Answer: 46.15%

Step-by-step explanation:

From the question, we are informed that a 13 minute video played for 6 minutes. The amount of percent played will be:

= 6/13 × 100

= 0.4615 × 100

= 46.15%

how many quarts make 5 gallons

Answers

Answer:

4 quarts

Hope it helps!

Step-by-step explanation:

Answer: 5 gallons= 20 quarts

              1 gallon = 4 quarts

someone please help me with this question​

Answers

Answer:

Step-by-step explanation:

The diagram is given to you below. I could not change <C so that it was theta. So C = theta.

So C is the reference angle. Call it theta when you think of it. The diagram shows you how cos(C) must be set up.

The adjacent side is 7

The hypotenuse is 18

theta = C = cos-1(7/18) = 67.11

To the nearest degree 67.11 = 67

*PLEASE* PLEASE PLEASE HELP ME SOMEBODY !3RD! TIME POSTING THIS AND I REALLY BADLY NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Are the two triangles similar? If so, state the reason and the similarity statement. Question options: A) Impossible to determine. B) Yes; SAS; ΔVWX ∼ ΔYZX C) Yes; SSS; ΔVWX ∼ ΔYZX D) The triangles are not similar.

Answers

Answer:I think its not similar

Step-by-step explanation:

they dnot look the same

there are 25 children in the class 3/5 of the children in the class are boys. how many girls are their?
PLZZZ

Answers

There are 10 girls in the class. You want to multiply (3/5)x25, once product is found, you subtract it from 25, the product is 15, so 25-15=10girls

Answer:

10 girls

Step-by-step explanation:

If 3/5 of the class consists of boys, (5/5 - 3/5 = 2/5) : 2/5 are girls

3/5 x 25 = 15

2/5 (girls) = 25 - 15

Therefore, 10 girls in total

A radioactive substance decays exponentially. A scientist begins with 350 milligrams of a radioactive substance. After 14 hours, 175 mg of the substance remains. How many milligrams will remain after 20 hours

Answers

Answer:

N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg

therefore, N(t)=130∗.545/24=35.44mg

Step-by-step explanation:

N(t)=N∗.5t/h where n(t) is amount of substance left, N = initial amount, t = current time, and h = half-life time.h = 24 hours t= 45 hours, N = 130mg

therefore, N(t)=130∗.545/24=35.44mg

Answer:

≈ 130 mg

Step-by-step explanation:

This is about the half-life of the substance.

There is a formula for this kind of calculations:

N(t)= N₀*(0.5)^(t/T), where

N(t) = substance left after time period of t,t = time passed,N₀ = initial amount of the substance,T = hal-life time of the given substance.

In our case, we have:

N₀ = 350 mg,t= 20 hours,T = 14 hours  as half of substance decays during this time period,

And the calculation:

N(20)= 350*(0.5)^(20/14)N(20) ≈ 130 mg

Answer: about 130 mg of substance remains after 20 hours

which of the following is NOT true about a parallelogram?

Answers

Answer:

Any two consecutive angles are complementary.

--------------------

Opposite sides of a parallelogram are parallel, Opposite sides are congruent. Opposite angles are congruent.

OAmalOHopeO

Plz help me this is probably easy but im just not seeing it plz help me ASAP

Answers

Answer: is attatched to the photo I sent

Step-by-step explanation:

I admit, this is tricky, just remember to think about it as where the shapes are the most similar. I'm not exactly sure how to explain it, but where it reflects like a mirror is the "copy"

The example I'm thinking of attached too, but these over lap so its diffucult

5. In figure 2.9, line AB || line CD and line PQ is transversal. Measure of one of the angles is given Hence find the measures of the following angles (1) LART (ii) ZCTO (iii) ZDTO (iv) ZPRB​

Answers

Voće q no tonto es 2.9. Y también AB ok coprende ??? Ok chao

PLEASE HELP
You have to create 3 functions to make hills on a grap

Requirements are in the photo.
(ignore graphs)

4. Write equations for three hills that do meet the requirements. Sketch them on one axis. (For the
purposes of this exercise, this is a sketch, so the steepness and minimums and maximums of the
graphs do not need to be exact). (6 points: 1 point for each equation, 1 point for each sketched curve)

Answers

Answer:

Hill 1: F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 2: F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 3: F(x) = 4(x - 2)(x + 5)

Step-by-step explanation:

Hill 1

You must go up and down to make a peak, so your function must cross the x-axis six times. You need six zeros.

Also, the end behaviour must have F(x) ⟶ -∞ as x ⟶ -∞ and F(x) ⟶ -∞ as x⟶ ∞. You need a negative sign in front of the binomials.

One possibility is

F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 2

Multiplying the polynomial by -½ makes the slopes shallower. You must multiply by -2 to make them steeper. Of course, flipping the hills converts them into valleys.

Adding 3 to a function shifts it up three units. To shift it three units to the right, you must subtract 3 from each value of x.

The transformed function should be

F(x)  = -2(x +1)(x)(x -2)(x -3)(x - 6)(x - 7)

Hill 3

To make a shallow parabola, you must divide it by a number. The factor should be ¼, not 4.

The zeroes of your picture run from -4 to +7.

One of the zeros of your parabola is +5 (2 less than 7).

Rather than put the other zero at ½, I would put it at (2 more than -4) to make the parabola cover the picture more evenly.

The function could be

F(x) = ¼(x - 2)(x + 5).

In the image below, Hill 1 is red, Hill 2 is blue, and Hill 3 is the shallow black parabola.

what is meant by derivative​

Answers

Answer:

its basically just rate of change or slope. with derivatoves you can find the slope of a tangent line which is a line that touches the curve at a point.

Isabelle bought some stationery.1/3 of them. Were pencils.5/8 of the remainder were erasers and the rest were rulers.The table shows the cost of each stationery,Pencil:$1.20,Eraser:$1,Ruler:$0.50. She spent a total of $169.50 on all the stationery. a)What fraction of the stationery bought was rulers? b)How much more did she spend one erasers than rulers?

Answers

Answer:

1/4 ; $28.25

Step-by-step explanation:

Given the following :

Cost of stationeries:

Pencil:$1.20

Eraser:$1

Ruler:$0.50

Total : $169.50

Let total Stationeries purchased = t

Fraction of pencils = 1/3t

Remainder = t - 1/3 = 2/3t

Fraction of eraser = 5/8 of remainder

Thus ;

Fraction of eraser = 5/8 * (2/3)t= 10/24 = (5/12)t

Rest were ruler ;

(2/3)t - (5/12)t= (8 - 5)/12

= 3 / 12 = 1/4t

Fraction of rulers = 1/4

Amount spent on erasers:

(5/12) of the total cost of stationery

(5/12) * 169.50 = $70.625

B.) How much more did she spend on erasers than rulers

Amount spent on rulers :

(1/4) * $169.50 = $42.375

Take the difference :

$(70.625 - 42.375) = $28.25

x+1=0
Giải hộ em với

Answers

Answer:

x = -1

Step-by-step explanation:

-Subtract 1 from both sides of the equation

x + 1 = 0

x + 1 - 1 = 0 - 1

-simplify

x = -1

12 – 2x= -2(y – x)
-2x = -2(y – x) – 12
x= (y - x) + 6

Answers

Answer:

x=o and y= -6

Step-by-step explanation:

12-2x = - 2(y-x)

or,12-2x = -2y + 2x

or, 12 = - 2y + 4x

or, 12/2= 2x - y

or, 2x - y = 6

• 2x -6= y.....eqn_1

-2x=-2y+2x -12

or,4x +2y= -12

or,4x + 2(2x-6)= -12

or, 4x+4x-12=-12

or, 8x= 0

• x= o

putting the value of x in eqn...3

o=(y-0)+6

or, o= y + 6

•y = -6

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