Marc has 45 books on his bookshelf, and Corinna has 61. If Marc buys 4 new books each month and Corinna buys 2 new books each month, after how many months will Marc and Corinna have the same number of books?

Define the variable:_________________________________________



Write the equation: _________________________________________


Solve the equation in the space below. Show your work

Answers

Answer 1
Call x as the number of months that Marc and Corinna have the same number of book.
45 +4x= 61 +2x
4x- 2x= 61-45
2x= 16
x= 8

Related Questions

Linda has 28 jackets 7 of them so it have a cap write 2 ratios that compare the number of jackets without caps to the number of jackets with caps?​

Answers

Answer: (5/12)m

Step-by-step explanation: hope this helps (~﹃~)~zZ

(x + y) (x -y) simplfied and showing work

Answers

Answer:

(x+y) + (x-y) = x + y + x - y =2x

(x+y)(x-y)=x^2 + yx - xy - y^2 = x^2 - y^2

(x+y) ( x-y)

x^2 - y^2

Step-by-step explanation:

help, please i cant do this

Answers

Answer:   x = 3.95

============================================================

Explanation:

Use the pythagorean theorem to tie together the three sides of the right triangle.

[tex]a = x-3 = \text{horizontal leg}\\b = x+5 = \text{vertical leg}\\c = 9 = \text{hypotenuse}[/tex]

[tex]a^2 + b^2 = c^2\\(x-3)^2 + (x+5)^2 = 9^2\\x^2-6x+9 + x^2+10x+25 = 81\\2x^2+4x+34 = 81\\2x^2+4x+34-81=0\\2x^2+4x-47=0\\[/tex]

From here, we use the quadratic formula to solve for x.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(4)\pm\sqrt{(4)^2-4(2)(-47)}}{2(2)}\\\\x = \frac{-4\pm\sqrt{392}}{4}\\\\x \approx \frac{-4\pm19.79898987}{4}\\\\x \approx \frac{-4+19.79898987}{4} \ \text{ or } \ x \approx \frac{-4-19.79898987}{4}\\\\x \approx \frac{15.79898987}{4} \ \text{ or } \ x \approx \frac{-23.79898987}{4}\\\\x \approx 3.94974747 \ \text{ or } \ x \approx -5.94974745\\\\[/tex]

We'll ignore the negative x value because it makes the sides x+5 and x-3 to be negative numbers. Negative side lengths make no sense.

The only practical solution is roughly x = 3.94974747; rounding to 3 sig figs leads to the final answer of x = 3.95

In this case, 3 sig figs means that we're rounding to 2 decimal places.

Some spiders, dragonflies, and houseflies are kept in three separate enclosures. They have a total of 20 heads, 136 legs, and 19 pairs of wings.
Given that...
a spider has 8 legs and 0 pairs of wings
a dragonfly has 6 legs and 2 pairs of wings
a housefly has 6 legs and 1 pair of wings
Find the number of spiders, the number of dragonflies, and the number of houseflies.

Answers

Answer:

Number of Spiders: 8

Number of Dragonflies: 7

Number of Houseflies: 5

Step-by-step explanation:

s= spider

d= dragonfly

h= housefly

Heads:

20= s+d+h

Legs:

136= 8s+6d+6h

Wings:

19= 0s+2d+1h

Solve with substitution.

Divide the second equation by 2.

136= 8s+6d+6h

68= 3d+3h+4s

Set the last equation in terms of d.

19= 0s+2d+1h

d= [tex]\frac{19}{2} -\frac{1}{2}h[/tex]

Substitute what we just found (d) into the first and our new second equation. Simplify.

20= s+d+h

20= s+[tex]\frac{19}{2} -\frac{1}{2}h[/tex]+h

h+2s=21

68= 3d+3h+4s

68= 3([tex]\frac{19}{2} -\frac{1}{2}h[/tex])+3h+4s

3h+8s=79

Take both simplified equations and solve with elimination. Do this by multiplying the top equation by negative 3.

h+2s=21

3h+8s=79

-3h-6s=-63

3h+8s=79

2s=16

s=8

Plug in s=8 into the other equation.

h+2s=21

h+2(8)=21

h=5

Plug in h=5 into the last equation we rewritten.

[tex]d= \frac{19}{2} -\frac{1}{2} h[/tex]

[tex]d=\frac{19}{2} -\frac{1}{2}(5)[/tex]

d=7

(d,h,s)= (7,5,8)

What is more important: to formulate a believable, testable hypothesis or to develop a good strategy to test the hypothesis accurately

Answers

Answer:

It's a matter of opinion. In my opinion you can hypothesize all you want, when  you get to do it in practice it's almost 100% garantee of failure or incomplete hypothesis. So testing is way more important IMO.

Step-by-step explanation:

4,505 in expanded form​

Answers

Expanded: 4000+ 500+ 00+ 5

If tan^2 = 1-a^2, then the value of sec+tan^3 cosec is

Pls explain fast

Answers

Answer:

for example okk then you will try

Answer: (1) (2 – e2)3/2

Solution:

Given,

tan2θ = 1 – e2

sec θ + tan3θ cosec θ

= sec θ + (sin3θ/cos3θ) (1/sin θ)

= sec θ + tan2θ sec θ

= sec θ(1 + tan2θ)

= √(1 + tan2θ) (1 + tan2θ)

= (1 + tan2θ)3/2

= (1 + 1 – e2)3/2

= (2 – e2)3/2

the following are polynomials EXPECT

Answers

Answer:

where the numbers at???

Step-by-step explanation:

Which equation represents a line that is perpendicular to y=3x−4?

Answers

Answer:

- 1/3x + 2

Step-by-step explanation:

Given line:

y = 3x - 4

Perpendicular lines have negative-reciprocal slopes:

m₁*m₂ = - 1

Since m₁ = 3, we can find m₂:

3*m₂ = - 1m₂ = - 1/3

Given choices:

-1/3x + 2 or 1/3x - 4

Correct choice is the first one

suppose that prices of a certain model of new homes are normally distributed with a mean of 150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid between 150,000 and 154,200, if the standard deviation is 1,400. a.) 49.85% b.) 47.5% c.) 34% d.) 99.7%

Answers

49.85% of buyers paid between 150,000 and 154,200

The empirical rule states that for a normal distribution, 68% are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are are within three standard deviation from the mean.

Given that mean (μ) = 150000, standard deviation σ = 1400

68% are within one standard deviation = μ ± σ = 150000 ± 1400 = (148600, 151400)

95% are within two standard deviation = μ ± 2σ = 150000 ± 2 * 1400 = (147200, 152800)

99.7% are within three standard deviation = μ ± 3σ = 150000 ± 3 * 1400 = (145800, 154200)

The buyers who paid between 150,000 and 154,200 = 99.7%/2 = 49.85%

Hence 49.85% of buyers paid between 150,000 and 154,200

Find out more at: https://brainly.com/question/12660012

answer and explain briefly

Answers

Answer:

Step-by-step explanation:

251 divided by something has to equal to a number it will divide by...

2 3 = 2x 2 x 2 = 8

x

p 2 = pxp

251 divided by 25 x8

/49 x8

/100x8

/4x 8

so I would say  5

What is the answer to the first one?

Answers

Answer:

8

Step-by-step explanation:

2(-2)^2 =10 +-2 =8

Points A,B,C are collinear. explain what is wrong with this picture. Use the linear pair theorem in your explanation

Answers

Answer:

hey can u help me with my work i posted i promise ill help u back

can someone please do this? nit the mini task though, number 8

Answers

1 is C

2 is D

3 is C

4 is A

5 is D

5 is A

7 is B

Help pls

Which statement correctly describes the picture?

Answers

Answer:

D

Step-by-step explanation:  The line GH has an arrow, so is designated as GH with an arrow over it.  The line EF has no direction (no arrow), so it is represented simply as EF with a line, with no arrow.  The point P is, well, just point P.

PLEASE HELP!!
100 POINTS
5^a = 2^b = 10, what is a^-1 +b^-1

Answers

Answer:

1.

Step-by-step explanation:

5^a = 10

a log 5 = log 10

a log 5 = 1

a = 1 /log 5

a^-1 = log 5

In the same way:

b = 1 / log 2

b^-1 = log 2,

So a^1 + b^-1 = log5 + log 2 = log (2*5)  

= log 10

= 1.

Match the following equation to the correct situation.

Answers

Answer:

D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

hope it can help you lovelots

What is the slope of the line ( part 2 )

Answers

Answer:

[tex]m=-\frac{1}{2}[/tex]

Step-by-step explanation:

Same as last time, take any 2 points you want:

(0, 3) and (4, 1)

Use the slope formula to calculate the slope:

[tex]m=\frac{1-3}{4-0}\\m=\frac{-2}{4}\\m=-\frac{1}{2}[/tex]

On small problems like these, you don't really even need to calculate it like that. You can just look at the graph, see that it goes down 1 and over 2 from one point to the next, and have your slope that way. Again, rise over run. It "rises" by -1, and runs by 2. -1 over 2, there's your slope.

A water pipe can fill an empty pool in 3 hours. When the pool is full, an open drain can empty the pool in 4 hours. Using the water pipe with the drain open, how many hours will it take to fill the empty pool? I give brainliest

Answers

Answer:

Step-by-step explanation:

Even though this seems like a crazy trick question it isn’t. An empty pool with a closed drain takes 3 hours to fill. A full pool with and open drain takes 4 hours to empty. So to fill and empty pool with an open drain, i’d say in my opinion it’d either take 7 hours or you wouldnt be able to fill it at all. I mean it’s an open drain

hope this helped :3

:3 byeeeeeeeeeeeeeeeee


If m<8= x°, which angles have a measure of 180º – xº? Select all that apply.
<3
<4
<6
<10

Answers

Answer:

  ∠6, ∠10

Step-by-step explanation:

Apparently, we are to assume that the avenues are parallel.

The angles that form a linear pair with ∠8 will be supplementary: ∠6 and ∠7. The angles that correspond to those will also be supplementary to angle 8: ∠10 and ∠11.

Among the answer choices ∠3, ∠4, ∠6, ∠10, only ∠6 and ∠10 are equal to 180° -x.

_____

Additional comment

It appears we are to assume that 1st Ave is parallel to 2nd Ave. If that is the case, then we might also assume that D Street is perpendicular to those avenues. In that case, all of angles 5, 6, 7, 9, 10, 11, 12 are equal to 180° -x, because x and all of those are all 90°.

Two friends, Gabriel and Hudson, had just bought their first cars. Gabriel uses 10 gallons of gas to drive 339 miles in his car. The table below represents the number of miles, yy, that Hudson can drive his car for every xx gallons of gas.

How much farther can Gabriel's car travel on one gallon of gas than Hudson's car?

Answers

Answer- 15.8 Miles

Explanation photo was given above.

a
Lucy has a coin collection. She keeps 3 of the coins in her box, which is 25% of the
collection. How many total coins are in her collection?
Multiply/scale up to solve.
coins
3
25
100
percent

Answers

Answer:

3x4=12

12 coins in her collection

Step-by-step explanation:

25x4=100%

-1/3(2p-9) what does p equal

Answers

Answer:

-2p/3+3

Step-by-step explanation:

3. One leg of a right triangle measures 10 inches while the other leg measures 21 inches. What is the length of the hypotenuse?




A) c = 9in



B) c = 11in



C) c = 12in



D) c = 7in




4. If the length of the hypotenuse is 10m and its base leg is 6m, what is the length of its remaining leg?




A) a = 8m



B) a = 9m



C) a = 12m



D) a = 10m




5. The altitudes of a right triangle has a length of 32cm. It’s hypotenuse measures 9cm. How long is its base leg?




A) b = 5cm



B) b = 7cm



C) b = 6cm



D) b = 9cm




6. Ben pushes a stick in the ground next to a flag pole so that its measure from the ground is 1 foot. The stick casts a shadow of 4 feet while the flag pole casts a parallel shadow of 60 feet. How tall is the

Answers

Step-by-step explanation:

Pythagoras formula for the relation of the side lengths in a right-angled triangle :

c² = a² + b²

c is the Hypotenuse, the side opposite of the 90 degree angle.

a and b are the "legs".

3.

c² = 10² + 21² = 100 + 441 = 541

c = sqrt(541) = 23.2594066...in

so, none of the provided answers. are you sure you put the right numbers ? maybe the second leg is sqrt(21) instead of 21 ? because then it would be

c² = 10² + sqrt(21)² = 100 + 21 = 121

c = 11in

4.

10² = a² + 6²

100 = a² + 36

64 = a²

a = 8 m

5.

again, there must be something wrong. the height of the triangle cannot be longer than the legs of the triangle.

given the answer options of 5 - 9 cm it cannot be 32cm. maybe you mean 3.2 cm ?

also interesting that it says "attitudes" - plural. what do you mean by that ?

because there is something else missing. like how long are the segments of the Hypotenuse where the height (or altitude) is touching the Hypotenuse ?

with just the Hypotenuse length and the height length we cannot calculate the other parts of the triangle, because we can move the height freely along the Hypotenuse and draw fitting right-angled triangles on that "skeleton".

6.

similar triangles. that means the lengths of corresponding lines (like sides or heights) are all in relation with the same scaling factor.

so, the small triangle has its "height" side of 1 ft, and multiplying with the scaling factor would then give us the height of the flag pole.

what is the scaling factor ? we get that from the pair of corresponding sides we already know : the shadows.

going from the small to the large triangle we have to transform 4ft into 60ft.

what do I have to multiply 4 with to get 60 ?

4 × x = 60

x = 60/4 = 15

so, the flag pole is

15×1 = 15ft tall.

IF F(x) is ax + x² – 152-18
as show that F(3)=0
(
b) Find the factors of F(x).

Answers

[tex]x = 3[/tex]

[tex]a(3) \: + \: 3 {}^{2} - 152 - 18[/tex]

[tex]3a \: + \: 9 \: - 134[/tex]

[tex]3a \: - 134 + 9[/tex]

[tex]3a - 143[/tex]

Step-by-step explanation:

Hope this helps you XD ✌️Carry on learning !!

A sandwich store charges a $10 delivery fee,and $4.50 for each sandwich.

a. Graph the total cost of sandwiches and delivery based on the number of sandwiches ordered. let x represent the number of sandwiches and y represent the total cost. Be sure to label your axes and scale them by labeling each grid line with a number.

PLEASE PLEASE PLEASE answer this i need to get a good grade on my test its worth 70% of my grade.

Answers

Y- intercept form y=Mx+b
Y is total sales
M is price per sandwich
X is number of sandwiches
B delivery Fee


Y = 4.50x + 10

The required graph shows equation y = 10 + 4.50x which represents the total cost of sandwiches and delivery based on the number of sandwiches ordered.

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Let x represent the number of sandwiches and y represent the total cost.

Here is a graph of this equation:

y = 10 + 4.50x

This graph shows that the total cost of sandwiches and delivery is a straight line that increases by $4.50 for each additional sandwich ordered. The $10 delivery fee is the y-intercept of the line, which is the point where the line crosses the y-axis (when x = 0).

The slope of the line is 4.50, which indicates the change in the total cost for each unit change in the number of sandwiches.

Learn more about the graphs here:

brainly.com/question/16608196

#SPJ2

Given: \overline{AE} \parallel \overline{FD},

AE



FD

, \overline{BF} \parallel \overline{EC}

BF



EC

and \overline{AC} \cong \overline{BD}.

AC



BD

.


Prove: \triangle AEC \cong \triangle DFB△AEC≅△DFB.
needed 3 prove (angle/slide)

Answers

Answer:

See below for answer.

Step-by-step explanation:

∠ECB ≅ ∠FBC    Parallel lines cut by a transversal form congruent alternate  

                             interior angle  

Δ AEC ≅ Δ DFB   ASA                

Tute Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating. 15% tip on a bill of $53.67 The amount of the tip is approximately $ Submit​

Answers

Answer:

$68.53. 67%

Step-by-step explanation:

$68. 58 I think I'm not sure

24 pens in 2 boxes How many pens in 1 box?__________

find unit rate

Answers

24 pens divided by 2 boxes equals 12 pens per box.

The formula for the area of a rhombus with diagonals of lengths c and d is A= 1/2 cd.
a. Solve the formula for c.

b. The area of a rhombus is 35 square feet. The length of one of the diagonals is 10 feet. What is the length of the other diagonal?

c. In a square (which is a rhombus), the lengths of the diagonals are the same. If a square has an area of 32 square feet, then what is the length of each diagonal

Answers

Answer:

I think it's A

Step-by-step explanation:

i apologize if I'm wrong

Other Questions
mark is paid $12.45 and hour at his job.he works a shift of 4 hours and 20minutes. how much does john earn for this shift? The moment the teacher announced the scores of the competition, the students celebrated. Substitute The moment with No sooner.1 pointa. Their teacher announced.b. Had their teacher announced.c. Than their teacher was announcing.d. Was their teacher announcing. candidate for the man booker prize or newbery medal PLS HELP ASAP ILL GIVE BRAINLKEST what is in the build back better reconciliation bill? I lived in Africa around 15 mya. I had bilophodont molars ad a frugivorous diet. I had some adaptations for terrestrial quadrupedalism. What fossil primate am I the urinary bladder is composed of ________ epithelium. plz hurryc. Describe one example of a human right that you think is essential for everyone to have throughout the world. Why is this right essential? (5 points) A car's velocity is modeled by V(t)=0.5t^2 -8t +24 ,where the velocity is in feet per second and time is in seconds. When does the car come to a complete stop12 seconds8 seconds4 seconds2 seconds you lose one quarter, two dimes, and two nickels.a. Write the amount as a decimal.The amount as a decimal is ____.b. Write the amount as a fraction in the simplest form.The amount as a fraction is ____. Find the perimeter.Simplify your answer. AYUDAAA PORFAVOOOOOOR!! If we wanted to know what grade we needed to get on the final in this class based on our expected performance before the final, we would call that _____________ analysis What is the algebraic expression for the following word phrase: the product of 7 and the difference of x and y? Which unemployment rate do most economists consider to be acceptable in the United States?0 percent5 percent10 percent20 percent Why does the preacher live outside the settlement? Which part of the executive branch does Mr. F say the Krakatoans have more wealth than or comparable to?From Twenty one balloons. what is the coordinates of the point? 3/4 + 1/2 + 1/3 sum to infinity HI I REALLY NEED HEP PLEASEE