3/4+7/12 adding and subtracting fractions with value

[tex]\left\{\begin{array}{ccc}-5x+3y=3\\-4x+y=1&|\text{add 4x to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}-5x+3y=3\\y=4x+1&(*)\end{array}\right\\\\\text{Substitute }\ (*)\ \text{to the first equation}\\\\-5x+3(4x+1)=3\qquad\text{use distributive property}\\\\-5x+(3)(4x)+(3)(1)=3\\\\-5x+12x+3=3\qquad\text{subtract 3 from both sides}\\\\7x=0\qquad\text{divide both sides by (-5)}\\\\\boxed{x=0}\\\\\text{Substitute the value of x to}\ (*):\\\\y=4(0)+1\\y=0+1\\\boxed{y=1}\\\\Answer:\ x=0\ and\ y=1.[/tex]

A) -102 feet

She started at -38 feet. She then went -120 feet, so -38-120= -158. She then went +56 feet. -158+56=-102.

Answer:

The answer is A. -102

Step-by-step explanation:

If she started at 38 feet below sea level, we would describe it as -38. If she descended 120 feet deeper, than we subtract that from -38.

-38-120=-158

She is now 158 feet below sea level, or -158.

Then, if she climbs up 56 feet, we would add that to -158.

-158+56=-102

Answer: The passenger will travel 17 miles.

Step-by-step explanation:

Since we have given that

Cost of a taxicab ride = $2.50

Cost of per mile = $1.10

Total cost of the trip = $21.20

Let number of miles the passenger travel be x

According to equation,

[tex]2.50+1.10x=\$21.20\\\\1.10x=\$21.20-\$2.50\\\\1.1x=18.7\\\\x=\frac{18.7}{1.1}\\\\x=17\ miles[/tex]

Hence, the passenger will travel 17 miles.

The sllope-intercept form:

[tex]y=mx+b[/tex]

[tex]6y-12=14x[/tex]          add 12 to both sides

[tex]6y=14x+12[/tex]      divide both sides by 6

[tex]y=\dfrac{14}{6}x+\dfrac{12}{6}\\\\\boxed{y=\dfrac{7}{3}x+2}[/tex]

To change the equation 14x=6Y-12 into slope-intercept form, first isolate Y by adding 12 to both sides, then dividing by 6. This results in the equation Y = (7/3)x + 2.

The equation provided is 14x=6Y-12 and we need to transform it to slope-intercept form, which has a general format of y = mx + b, where m is the slope and b represents the y-intercept.

Let's start by isolating y in the equation:

So, the slope-intercept form of the given equation is Y = (7/3)x + 2.

Learn more about Slope-Intercept Form

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Answer:

i wanna say 7 days

Step-by-step explanation:

75/12 = 6.25 round up to 7

Answer:

y=12x+75

X=75/12

X=6.25

Answer will be 7

Step-by-step explanation = x=75/12= x 6.25 = technically it’s will be 7 days

Answer:

19.2 million.  

Step-by-step explanation:

Let us find the amount of savings per center by dividing 2.4 by 2.

[tex]\text{Amount of savings per center}=\frac{2.4\text{ Million}}{2\text{ Center}}[/tex]

[tex]\text{Amount of savings per center}=1.2\frac{\text{ Million}}{\text{ Center}}[/tex]

Hence, the company saved 1.2 million per center.

Let us multiply savings of each center by total number of company's distribution centers to find the total amount of money that the company can be expected to save.    

[tex]\text{Total amount of company's savings}=(1.2\times 16)\text{ million}[/tex]

[tex]\text{Total amount of company's savings}=19.2\text{ million}[/tex]

Therefore, Mr. Ortiz's company will save 19.2 million.

Answer:

-62

Step-by-step explanation:do multiplication 1st then work out problem left to right.

Answer: 33

5x+10x+25x= 1320 or 40x= 1320

Jamie has 33 nickels.

To find out how many nickels Jamie has, we need to set up an equation.

Let's assume Jamie has x nickels. Since Jamie has an equal number of nickels, dimes, and quarters, he also has x dimes and x quarters.

The value of x nickels is 5x cents, the value of x dimes is 10x cents, and the value of x quarters is 25x cents.

According to the problem, the total value of all the coins is $13.20, which is equal to 1320 cents.

So we can write the equation as follows: 5x + 10x + 25x = 1320.

Combining like terms, we get 40x = 1320. Dividing both sides by 40, we find that x = 33.

Therefore, Jamie has 33 nickels.

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Answer:

There are 40 girls and 24 boys in the camp

Step-by-step explanation:

let [tex]b[/tex] be the number of boys and [tex]g[/tex] be the number of girls in the camp, then when know that

[tex]\dfrac{b}{g} = \dfrac{3}{5}[/tex]                                (this says that the ratio of boys to girls is 3: 5)

And since there are a total of 64 campers, we have  

[tex]b+g =64[/tex]            (this says that the total number of boys an girls must 64)

Thus, we have two equations and two unknowns:

[tex](1). \: \: \dfrac{b}{g} = \dfrac{3}{5}[/tex]  

[tex](2). \: \:b+g =64[/tex]  

and we solve this system by first solving for [tex]b[/tex] in equation (1):

[tex]b= \dfrac{3}{5}g,[/tex]

and substituting it into equation (2):

[tex]\dfrac{3}{5}g+g=64[/tex]

solving for [tex]g[/tex] we get:

[tex]\boxed{g=40}[/tex].

Putting [tex]g=40[/tex] into equation (2), we solve for [tex]b[/tex] to get:

[tex]b+40=64[/tex]

[tex]\boxed{b=24}[/tex]

Thus, there are 40 girls and 24 boys in the camp.

Answer:

1430 yards

Step-by-step explanation:

Note that [tex]1\text{ acre}=\dfrac{1}{640}\text{ square mile}.[/tex] Then

[tex]25\text{ acres}=\dfrac{25}{640}\text{ square mile}.[/tex]

If one side of the restangular field measures exactly [tex]\dfrac{1}{4}[/tex] mile, then let the second side be x miles and

[tex]\dfrac{25}{640}=\dfrac{1}{4}\cdot x,\\ \\x=\dfrac{\frac{25}{640}}{\frac{1}{4}}=\dfrac{25}{640}\cdot \dfrac{4}{1}=\dfrac{25}{160}=\dfrac{5}{32}\ mile.[/tex]

The perimeter of the rectangle will be

[tex]P=2\cdot \dfrac{1}{4}+2\cdot \dfrac{5}{32}=\dfrac{2\cdot 8+10}{32}=\dfrac{26}{32}=\dfrac{13}{16}\ mile.[/tex]

Since [tex]1\ mile=1760\ yards,[/tex] then [tex]\dfrac{13}{16}\ mile=\dfrac{13}{16}\cdot 1760=1430\ yards.[/tex]

To fence a 25-acre rectangular field with one side 1430 yards of fencing is needed.

To order fencing for a 25-acre, rectangular field, with one side measuring exactly  1/4 mile, we first need to determine the field's dimensions. Since a mile equals 1760 yards, one side of the field is

1/4 x 1760 = 440 yards.

Now, to find the other side, we use the area formula (Area = length x width).

The field is 25 acres, and 1 acre equals 4840 square yards. So the field has an area of 25 x 4840 square yards.

Let's denote the unknown side as 'width':

= 25 x 4840 = 440 x width

Width =  25 x 4840/ 440

= 275 yards

Now that we have both the length and the width, we can find the perimeter, which is the total length of fencing needed. The perimeter of a rectangle is 2  x (length + width).

Perimeter = 2 x (440 + 275) = 2 x 715

= 1430 yards

Therefore, to enclose the field completely, you would need 1430 yards of fencing.

Answer:

18 divided by 5 is equal to 3 with a remainder of 3 so she can only make 3 T-shirts

Step-by-step explanation:

Answer:

3 shirts

Step-by-step explanation:

She has 18 buttons. 18 divided by 5 is 3.6

so she can make 3 shirts

Answer:

The APY of the saving account is 4.048656%

Step-by-step explanation:

We know the formula for APY which is given by

[tex]APY=(1+\frac{r}{n} )^n-1[/tex]

here, r= interset rate =  3.9886% = 0.039886

n = compounding cycles = 4

On plugging these values in the above formula, we get

[tex]APY=(1+\frac{ 0.039886}{4} )^4-1[/tex]

On simplifying this we get

APY = 0.04048656 =4.048656%

Answer:

APY = 4.0486561%

Step-by-step explanation:

Given is the Annual Percentage Rate (APR) = 3.9886% compounded quarterly.

Suppose Principal amount, P = $1.

time, t = 1 year.

interest rate, r = 3.9886% = 0.039886

period of compounding, n = 4 (for quarterly).

Future value = P * (1 + r/n)^(nt)

FV = 1 * (1 + 0.039886/4)^(1*4) = 1.040486561

Annual Percentage Growth = (FV/P)*100 = (1.040486561 / 1) * 100 = 4.0486561%

Hence, Annual Percentage Yield (APY) = 4.0486561%

Answer:

16 kg of I type and 64 kg of II type should be mixed.

Step-by-step explanation:

Given that a metal alloy in original has 20% copper and 80% other metals.

Another mixture contains 60% copper and 40% other metals.

We have to get a new alloy of 80 kg which has 52% copper.

Let us assume that we mix x kg of I alloy and y kg of second alloy.

Then we have x+y = total weight = 80 kg.

x+y = 80   ... (i)

Next condition is that new alloy has 52% copper in it

When we mix x kg of I, and y kg of II, copper content would be

0.2x+0.6y.  This equals 52% of 80 = 41.6

Or Dividing by 0.2 we get

x+3y =208  ... (ii)

(ii)-(i) gives 2y = 128 or y =64 kg

x = 16 kg

16 kg of I type and 64 kg of II type should be mixed.

Verify:

Copper in new alloy = 16(0.2) + 64(0.6) = 3.2+38.4 = 41.6

= 52% of 80

[tex](2\sqrt7+3\sqrt6)(5\sqrt2+4\sqrt3)\qquad\text{use distributive property}\\\\=(2\sqrt7)(5\sqrt2)+(2\sqrt7)(4\sqrt3)+(3\sqrt6)(5\sqrt2)+(3\sqrt6)(4\sqrt3)\\\\=10\sqrt{14}+8\sqrt{21}+15\sqrt{12}+12\sqrt{18}\\\\=10\sqrt{14}+8\sqrt{21}+15\sqrt{4\cdot3}+12\sqrt{9\cdot2}\\\\=10\sqrt{14}+8\sqrt{21}+15\sqrt4\cdot\sqrt3+12\sqrt9\cdot\sqrt2\\\\=10\sqrt{14}+8\sqrt{21}+(15)(2)\sqrt3+(12)(3)\sqrt2\\\\=\boxed{10\sqrt{14}+8\sqrt{21}+30\sqrt3+36\sqrt2}[/tex]

Answer:  The required product is [tex]10\sqrt{14}+8\sqrt{21}+30\sqrt3+36\sqrt2.[/tex]

Step-by-step explanation:  We are given to find the following product :

P = (2 square root 7+3 square root 6)(5 square root 2+4 square root 3).

We will be using the following property of radicals :

[tex]\sqrt a\times \sqrt b=\sqrt{ab}.[/tex]

The given product can be written and evaluated as follows :

[tex]P\\\\=(2\sqrt7+3\sqrt6)(5\sqrt2+4\sqrt3)\\\\=2\sqrt7(5\sqrt2+4\sqrt3)+3\sqrt6(5\sqrt2+4\sqrt3)\\\\=10\sqrt{7\times2}+8\sqrt{7\times3}+15\sqrt{6\times2}+12\sqrt{6\times3}\\\\=10\sqrt{14}+8\sqrt{21}+15\times2\times\sqrt3+12\times3\sqrt2\\\\=10\sqrt{14}+8\sqrt{21}+30\sqrt3+36\sqrt2.[/tex]

Thus, the required product is [tex]10\sqrt{14}+8\sqrt{21}+30\sqrt3+36\sqrt2.[/tex]

Let's go through the list of values and test the claim

Is 32 divisible by 2? Yes because 16*2 = 32. Is it also divisible by 4? Yes because 8*4 = 32. So we can cross choice A off the list

Is 12 divisible by 2? Yes because 6*2 = 12. Is it also divisible by 4? Yes because 3*4 = 12. So we can cross choice B off the list.

Is 40 divisible by 2? Yes because 2*20 = 40. Is it also divisible by 4? Yes because 4*10 = 40. Choice C is also crossed off the list.

Is 18 divisible by 2? Yes because 2*9 = 18. Is it also divisible by 4? No. We can see that by dividing 18/4 = 4.5 which is not a whole number result. Or you can list out the multiples of 4 which are 4, 8, 12, 16, 20 and we see that 18 is not on the list.

So choice D) 18 is the answer. This is a counter example to show that the claim "if number is divisible by 2, then it is also divisible by 4" is a false statement.

The required counterexample for the conjecture is 18. which is the correct answer that would be an option (D).

The divisibility rule states that " Divisible By, implies that when two numbers are divided, the result would be a whole number.

For example divisibility rule of 3 is that the sum of the digits should be 3.

A counterexample for the conjecture is 18. This is a counterexample because 18 is divisible by 2 (it is an even number), but it is not divisible by 4.

Therefore, the statement "any number that is divisible by 2 is also divisible by 4" is false, because there are some numbers (like 18) that are divisible by 2 but not by 4.

Thus, the required counterexample for the conjecture is 18.

Hence, the correct answer would be an option (D).

Learn more about the divisibility rule here:

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Answer:

False...there's nothing to depend on when you are expecting a random number out of 2 different rolls of the "number cube".

Hope this helps!! (:

Answer:

I think it is D because 9 times 7 equals 63...

Answer:

The answer is c Hope this helps:)

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

l x w = area

(x + 5) (3.4) = 51

x+5=15

x=10

plug back into the equation for length

(10+5) = 15

Answer:

37

Step-by-step explanation:

a + b for a=24 and b=13

plug in

24 + 13

= 37

Answer:

a + b = 37

Step-by-step explanation:

substitute the values a = 24 and b = 13 into the expression

a + b =  24 + 13 = 37

Answer:

MI = -x+16

Step-by-step explanation:

MI + IB = MB

MI + 2x-7 = x+9

Subtract 2x from each side

MI + 2x-7 -2x = x+9-2x

MI -7 = -x+9

Add 7 to  each side

MI -7+7 = -x+9+7

MI = -x+16

The length of segment MI can be found by adding the lengths of segments MB and IB together, resulting in MI = 3x + 2.

This problem relates to the concept of line segments in geometry. Line MB and IB are parts of a straight line where M, I and B are points on the line. Given that MB = x + 9 and IB = 2x - 7, we realize that MB + IB = MI.

To solve this problem, you simply add the equations of the two line segments together because the total length segment MI would be the sum of segments MB and IB:

So, MI = MB + IB = (x + 9) + (2x - 7).

Then, simplify the equation by performing the addition:

MI = 3x + 2.

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Answer:

False that the answer

Proportional relationships occur when the ratio between two quantities is constant. The provided details of the graph suggest a proportional relationship, but there could be an error— the point (8,27) doesn't follow the same ratio. Please double-check this point.

Based on the provided details of the graph, we can infer that we have a proportional relationship, which exists when the ratio of the values of two quantities always remains the same. For example, in the graph, every two 'Bunches of Thyme' corresponds to a $6 increase in the 'Price of Bunches'. This constant ratio (1 bunch: $3) is characteristic of a proportional relationship.

So, the graph indeed represents a proportional relationship. The coordinates of the points (2, 6), (4, 12), (6, 18), and (8, 24), etc., fit the pattern y = 3x, which is another typical sign of a proportional relationship along the axis.

But it looks like there might be a mistake in your graph details because the point (8,27) doesn't fit the pattern y=3x. For x = 8, y should be 24 instead of 27. If that's not a typo, the graph doesn't represent a proportional relationship.

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Answer:

1.5:2.25 because there is 1.5 quarts of juice and 2.25 quarts of ginger ale and the you put that with the to sign and there you have it

Answer:

i think its 5w -2 =6

Step-by-step explanation:

product is 5w and 2 less than product is 5w-2 which is equal to 6

that is 5w - 2 = 6

Answer:

y = -3x  

Step-by-step explanation:

(a) Slope

y = mx + b

Choose points (-3, 9) and (3, -9)

m = (-9 - 9)/(3 – (-3))

m = -18/(3 + 3)

m = -18/6

m = -3

=====

(b) y-intercept

y = mx +b

Choose point (0,0).

0 = 0 + b

b = 0

=====

(c) Equation of line

y = mx + b

y = -3x

Answer:

is a function that is defined on a sequence of intervals

Step-by-step explanation:

next time please just search it up on google.

Answer:

A piecewise function has different rules for different parts of its domain. The following situation can be modeled by a piecewise function.

Step-by-step explanation:

Answer:

0.3101001000......

0.410100100010000....

Step-by-step explanation:

To find irrational number between any two numbers, we first need to understand what a rational and irrational number is.

Rational number is any number that can be expressed in fraction of form [tex]p/q[/tex]. Since q can be 1, all numbers that terminate are rational numbers. Example: 1, 12.34, 123.66663

Irrational number on the other hand can't be expressed as a fraction and do not terminate. Also, there is no pattern in numbers i.e. there is no repetition in numbers after the decimal point.

For example: 3.44444..... can be expressed as rational number 3.45.

But 3.414114111.... is an irrational number as there no pattern observed. Also,it does not terminate.

We can find infinite number of irrational numbers in between two rational numbers.

Irrational numbers in between 0.3 and 0.7:

0.3101001000......

0.410100100010000....

0.51010010001.......

0.6101001000....

There are many others. We can choose any two as answers.

Answer:

5x+5y

Step-by-step explanation:

Answer: There is not error in finding the product. The result is: [tex]=\frac{3}{25}[/tex]

Step-by-step explanation:

1. You have the following multiplication shown in the problem above:

[tex]\frac{2}{5}*\frac{3}{10}[/tex]

2. To solve it you must multiply the numerators and multiply the denominators, as you can see below:

[tex]\frac{2*3}{5*10}=\frac{6}{50}[/tex]

3. When you simplify the product, you obtain the following result:

[tex]=\frac{3}{25}[/tex]