Find two numbers, if Their sum is −7 and their difference is 14

Answers

Answer 1

Let
a------------> first number
b------------> second number

we know that
a+b=-7--------> a=-7-b----------> equation 1
a-b=14--------> equation 2

I substitute 1 in 2

(-7-b)-b=14-------------> -7-b-b=14----------> -7-2b=14-------> 2b=-7-14
2b=-21---------> b=-10.5
a=-7-b-------> a=-7-(-10.5)-----> a=-7+10.5------> a=3.5

the answer is
the two numbers are
a=3.5
and
b=-10.5

Answer 2

Answer:

3.5 and -10.5

Step-by-step explanation:

i checked, its correct

Related Questions

HELP!! 10 POINTS!! 1 EASY PROBLEM!!

Answers

To solve this problem you must apply the proccedure below:

1. You have:

A=3+12=15

B=4x

C=12

D=3x+1

2. Therefore, you have:

A/B=C/D

3. When you susbtitute the values of A,B,C and D, you obtain:

15/4x=12/(3x+1)

4. Now, you must clear the "x" to calculate its value, as below:

15(3x+1)=12(4x)
45x+15=48x
15=48x-45x
15=3x
15/3=x

5. Therefore, the result is:

x=5

3/7b, 5/3c, 11/21bc The LCD is

Answers

21bc would be your least common denominator

WHICH COULD BE THE NAME OF A POINT
A .EF
B. K
C. Q
D. MN

Answers

B) K can be the name of a point.
C) Q can also be the name of a point.

Hope this helps =)

it is c Q hope it helps

The deli scale weighs meat and cheese in hundredths of a pound. Marco put 5/10pound of pepperoni on the deli scale. What weight does the deli scale show?

Answers

Hello!

So, Marco put 5/10 lb of pepperoni on the scale. The deli scale weighs meat in hundredths.

What would 5/10 be in hundredths?

The answer is, quite simply, 50/100.

Since it is weighed in hundredths, the denominator must be 100. To get a denominator of 100, we must multiply both the numerator and the denominator by 10.

5 × 10 = 50

10 × 10 = 100

The deli scale shows 50/100 lb.

Final answer:

The weight shown on the deli scale for 5/10 pound of pepperoni is 0.5 pounds.

Explanation:

When Marco puts 5/10 pound of pepperoni on the deli scale, the scale which measures in hundredths of a pound will show this weight as 0.50 pounds.

This is because 5/10 can be simplified to 1/2, and when expressed as a decimal, 1/2 is equivalent to 0.5.

Therefore, the deli scale that reads to the hundredths place will display the weight as 0.50 pounds.

A dog sled race is 25 miles long.The equation 5/8 k=25 can be used to estimate the race’s length k in kilometers. Approximately how many hours will it take a dog sled team to finish the race if it travels at an average speed of 30 kilometers?

Answers

the distance to be covered in the race is 25 miles
average speed of the team is 30 km/h
30 km/m in miles/hour will be:
1 mile=0.621371 km
thus
30 km/h=(30×0.621371) miles/hour
=18.64113 miles/hour
time taken to complete 25 miles will be:
time=distance/speed
=25/18.64113
=1.3411 hours

Sandy is working with a carpenter to frame a house they are using 8 foot long boards but each board must be cut to be 7 feet 10 3/4 inches long how much is cut off the board

Answers

It is probably easiest to understand if we convert both measurements to inches so we are working with only one measurement instead of two.

1 foot= 12 inches

multiply feet by inches to equal total inches

8 ft * 12 inches= 96 inches

7 ft * 12 inches= 84 + 10 3/4= 94 3/4

Subtract the difference:
= 96 - 94.75
= 1.25 = 1 1/4 inches cut off

ANSWER: 1 1/4 inches were cut off

Hope this helps! :)

A soft drink manufacturer produces 3408 cans in an 8-hour day. Cans are packaged 24 to a case. How many cases are produced each week? each month? (Assume one week is 40 hours, and one month is four weeks.)

Answers

divide total cans by cans per case:
3408 / 24 = 142 cases per 8 hour day

40 hours / 8 = 5 days

142 * 5 = 710 cases per week

710 * 4 = 2840 cases per month

In applied life data analysis (wiley, 1982), wayne nelson presents the breakdown time of an insulating fluid between electrodes at 34 kv. the times, in minutes, are as follows: 0.05, 0.93, 0.92, 1.18, 2.87, 3.30, 4.30, 4.68, 4.78, 6.46, 7.29, 7.88, 8.36, 12.16, 31.66, 32.59, 33.88, 36.80, and 72.89. calculate the sample mean and sample standard deviation. round the answers to 3 decimal places.

Answers

The mean = 14.36736842

The sample standard deviation = 18.882

See the attached figure for the detailed solution.

The correct answers are:
Sample mean = 14.367
Sample standard deviation = 18.882

Explanation:
To find the sample mean, we first find the sum of the data values. This is 272.98. We next divide this by the number of data points, 19:
272.98/19 = 14.367

The first step in finding the sample standard deviation is to subtract the mean from each data point. This gives us the following values:
-14.31, -13.43, -13.44, -13.18, -11.49, -11.06, -10.06, -9.687, -9.587, -7.907, -7.077, -6.487, -6.007, -2.207, 17.293, 18.223, 19.513, 22.433, 58.523.

Next we square these values. This gives us the following list of values:
204.97, 180.55, 180.82, 173.89, 132.18, 122.47, 101.34, 93.837, 91.91, 62.52, 50.083, 42.081, 36.084, 4.8708, 299.04, 332.07, 380.75, 503.23, 3424.9

Next we find the sum of these values. This is 6417.705.

The next step is to divide this sum by n-1, where n is the number of data values:
6417.705/18 = 356.539

The last step is to take the square root:
√356.539 = 18.882

What is the measure of ∠D ?

Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.

m∠D=
°

Answers

the answer is 29.05°

How do you find the first five terms of a sequence defined recursively

Answers

Interesting question. Good to know for computer science.
Suppose you have a function like
an = 3x - 2 Try the first couple
a1 = 3(1) - 2
a1 = 3 - 2
a1 = 1

a2 = 3(2) - 2
a2 = 6 - 2
a2 = 4 So each term differs by 3
a2 - a1 = 3

an = a_(n - 1) + 3
a3 = a2 + 3
a3 = 4 + 3
a3 = 7

a4 = a3 + 3
a4 = 7 + 3
a4 = 10

a5 = a4+ 3
a5 = 10 + 3
a5 = 13

I'll do one more and then check it.
a6 = a5 + 3
a6 = 13 + 3
a6 = 16

a6 = 3x -2
a6 = 3*6 - 2
a6 = 18 - 2
a6 = 16 which checks.

So the general formula is
an = a_(n - 1) * k if you were multiplying or
an = a_(n - 1) + k if you were adding. The key thing is that you are working with the previous term.

two-thirds of the children in the fourth grade class are girls. if there are 14 girls, what is the total number of children in the class

Answers

Let's call the number of children x. Based on the information given, 2/3x = 14. Divide by 2/3 on both sides to get x = 21 children.

Help with this math question pleaseee!!!

Answers

The asymptote of the parent function [tex] 3^{x} [/tex], like any other similar exponential function is y = 0.

But in this case the parent function is transformed. It is shifted vertically upward by 4 units. When an exponential function is shifted vertically up or down its asymptote is also shifted by same number of units.

Hence, the asymptote of [tex]f(x)= 3^{x}+4 [/tex] will be shifted 4 units above as compared to the asymptote of [tex]f(x)= 3^{x} [/tex] .Therefore, the asymptote of [tex]f(x)= 3^{x}+4 [/tex] is y=4

A rectangular prism has a length of 5 cm, a width of 212 cm, and a height of 112 cm. Which expressions can be used to find the volume of the prism? Select each correct answer. A. 5∙212∙112 B. 1212∙112 C, 112(5+212) D. 12(1212∙112)

Answers

Volume is the amount of 3-dimensional space an object occupies

Volume is measured in cubic units.To find Volume Multiply the length, the width, and the height.

The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W.

The rectangular prism has a length of 5 cm, a width of 212 cm, and a height of 112 cm.

Substituting these values in the formula.

Volume = 5∙212∙112

Option A. 5∙212∙112 is the right answer.

Point P' is the image of P(3, 5), under a reflection across the y-axis. What are the coordinates of P'?

Answers

The point (0, 5) on the line of reflection is the midpoint between the original and its image.
.. P' = (-3, 5)

Answer:

P'( -3 ,5).

Step-by-step explanation:

Given : Point P' is the image of P(3, 5), under a reflection across the y-axis.

To find : What are the coordinates of P'

Solution : We have given

Pre image P( 3 ,5 ).

Rule of reflection over y axis : ( x ,y) →→→( -x , y) .

Here , x = 3 ; y = 5

Then , ( 3 ,5) →→→( -3 , 5) .

Therefore, P'( -3 ,5).

1.) A 2600 lb. car travelling downhill has a grade resistance of -130 lbs. Find the angle of the grade to the nearest tenth of a degree.
2.) A car travelling on a 2.7 degree uphill grade has a grade resistance of 120 lbs. Determine the weight of the car to the nearest hundred poulds.

Answers

Answer:

Step-by-step explanation:

Using the formula for Grade Resistance/Force in this case...

!!AND MAKING SURE YOUR CALCULATOR IS IN DEGREE MODE!!

R(or F) = Wsin∅

--> R/F: the Grade Resistance

--> W: Weight of the Vehicle

--> ∅: Angle of the Hill

Because the Grade Resistance in problem 1) is (-)130lbs... we know that the car is traveling DOWNhill. (If it were simply 130lbs, the car would be traveling up the hill)

W: 2600lbs R: -130lbs ∅: ?? (plug in) --> -130lbs = 2600lbs(sin∅)÷ both sides by 2600lbs -130lbs÷2600lbs (lbs cancel) = -0.05-0.05 = sin∅YOU ARE NOT DONE! DO NOT BE FOOLED when you get to this point.we have just found SIN∅.... but we were asked to find ∅

to do this, we must take the INVERSE of sin.... (because we cannot simply divide both sides by 'sin' by itself... we must instead...

---> sin[tex]^{-1}[/tex](-0.05) = ?

∅ ≅ -2.866 ..... (you can then divide 866 by 60' if necessary, to find degree and minute answer)...

∅ ≅ -2° 14'

Hope this will help you and others with the 2nd question as well! ^_^

DONT GIVE UP! You got this '_^

The angle of the grade to the nearest tenth of a degree will be ∅ ≅ -2° 14'.

What is mechanics?

The branch of mathematics and physics known as mechanics is concerned with the interactions between matter, force, and motion in physical objects.

Using the formula for Grade Resistance/Force in this case...

R(or F) = Wsin∅

R/F: the Grade Resistance

W: Weight of the Vehicle

∅: Angle of the Hill

Because the grade resistance in problem 1) is (-)130lbs... we know that the car is traveling downhill. (If it were simply 130lbs, the car would be traveling up the hill)

W: 2600lbs R: -130lbs ∅: ??

(plugin) --> -130lbs = 2600lbs(sin∅)

÷ both sides by 2600lbs

-130lbs÷2600lbs (lbs cancel) = -0.05

-0.05 = sin∅

When you get to this point. We have just found SIN∅.... but we were asked to find it ∅. To do this, we must take the inverse of sin.... (because we cannot simply divide both sides by 'sin' by itself... we must instead...

sin(-0.05) = ?

∅ ≅ -2.866 ..... (you can then divide 866 by 60' if necessary, to find the degree and minute answer)...

∅ ≅ -2° 14'

Therefore, the angle of the grade to the nearest tenth of a degree will be ∅ ≅ -2° 14'.

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The data in the table below were obtained for the reaction: a + b → p experiment number [a] (m) [b] (m) initial rate (m/s) 1 0.273 0.763 2.83 2 0.273 1.526 2.83 3 0.819 0.763 25.47 the magnitude of the rate constant is ________.

Answers

if we tabulate the data given, we obtain the following table;
Exp [a](m) [b] (m) Initial rate (m/s)
1 0.273 0.763 2.83
2 0.273 1.526 2.83
3 0.819 0.763 25.47
the rate equation
rate = k [a]ˣ[b]ⁿ
where k = rate constant
x and n are order of reaction with respect to a and b respectively
lets take experiment 1 and 2 where [a] is constant so we can find the order of reaction with respect to b

2.83 m/s = k[0.273 m]ˣ[0.763 m]ⁿ ---> 1)

2.83 m/s = k [0.273 m]ˣ[1.526 m]ⁿ ----> 2)
2)/1)
1 = [1.526/0.763]ⁿ
1 = 2ⁿ
n = 0
next we have to find out x, we have to take experiment 1 and 3 where [b] remains constant
25.47 m/s =k [0.819]ˣ[0.763]ⁿ --3)
2.83 m/s = k[0.273 m]ˣ[0.763 m]ⁿ ---> 1)

3)/1)
25.47/2.83 = [0.819/0.273 m]ˣ
9 = 3ˣ
x = 2
therefore order with respect to a = 2 and order with respect to b = 0
rate = k[a]²[b]⁰
to find k lets substitute 1st experiment values
2.83 m/s = k [0.273 m]² [0.763]⁰
k = 2.83/0.0745
k = 37.98 m⁻¹s⁻¹

In this exercise we will use the knowledge of statistics to calculate the value of the constant, so we have to:

[tex]k = 37.98 m^{-1}s^{-1}[/tex]

Recalling how the form of the rate equation is written, we have:

[tex]rate = k [a]^x[b]^n[/tex]

where:

k = rate constant x and n are order of reaction with respect to a and b respectively

Putting the already known values into the given equation:

[tex]2.83 = k[0.273 m]*[0.763 m]^n \\2.83 = k [0.273 m]*[1.526 m]^n \\1 = [1.526/0.763]^n\\1 = 2^n\\n = 0[/tex]

Now trying to find the value of X in the given equation:

[tex]25.47 =k [0.819]*[0.763]^n\\2.83 = k[0.273]*[0.763]^n\\25.47/2.83 = [0.819/0.273 m]^x\\9 = 3^x\\x = 2[/tex]

Now it will be possible to find the value of the constant as:

[tex]2.83 = k [0.273 m]^2 [0.763]^0\\k = 2.83/0.0745\\k = 37.98 m^{-1}s^{-1}[/tex]

See more about statistics at brainly.com/question/10951564

Please help me with this question. I will give 10 points and brainliest :) I beg you! I need this right!

Answers

Each day Luna spent 35 euros. Since she spent the same amount of money each day, 35 euros, all you need to do is add 35 euros to the amount of money she had left after the first day. Your answer will be 350 euros.

I hope this helps! :)

gavin bakes 70 cookies in a hour. how many cookies can he bake in 4 hours?

A.350
B.240
C.280
D.210

Answers

280, you simply just multiply 70 and 4.

Final answer:

To find out how many cookies Gavin can bake in 4 hours, we multiply the number of cookies he makes in one hour (70) by 4, resulting in 280 cookies.

Explanation:

If Gavin bakes 70 cookies in one hour, to calculate the number of cookies he can bake in 4 hours, we simply need to multiply the amount he can bake in one hour by 4. The calculation is as follows:

Multiply the number of cookies baked in one hour (70) by the number of hours (4).
70 cookies/hour × 4 hours = 280 cookies.

Therefore, the correct answer is C. 280 cookies.

Divide 180° in a ratio of 4:5:9

Answers

in plain and short, we'll simply divide 180 by (4+5+9), and give 4 pieces of those to the ratio of 4, 5 to the ratio of 5 and 9 to the ratio of 9, thus

[tex]\bf \cfrac{180}{4+5+9}\implies 10\qquad \qquad \qquad \qquad \qquad \stackrel{4\cdot 10}{40}~:~\stackrel{5\cdot 10}{50}~:~\stackrel{9\cdot 10}{90}[/tex]

what is |x−4| , if x>4

Answers

If x is larger than 4, then |x-4| is the same as x-4

We can drop the absolute value bars because the expression x-4 is always positive. For example, if x = 10 (which is larger than 4), then x-4 = 10-4 = 6 is positive. There are no cases in which x-4 is negative if x > 4.

A rectangular park has an area of 2/3 square mile.The length of the park is 2 2/3 the width of the park.What is the width of the park?

Answers

The width is 1/2 mi.

We know that area of a rectangle is length times width:

A = lw

The length is 2 2/3 the width, so
l = 2 2/3w

We will change this to an improper fraction; multiply the denominator by the whole number and add the numerator:
l = 8/3w

Using this for l in the area formula, we have:
A = (8/3w)(w) = 8/3w²
2/3 = 8/3w²

Divide both sides by 8/3:

2/3÷8/3 = 8/3w²÷8/3
2/3×3/8 = w²
2/8 = w²
0.25 = w²

Take the square root of both sides:
√0.25 = √w²
0.5 = w

Use the discriminant to determine how many x-intercepts the graph of the equation has. y = –4x2 + 3x + 2 zero one two three

Answers

To find the x-intercept, substitute in 0 for y and solve for x.

x-intercept: ( 3 + √41 / 8 , 0 ) , ( 3 - √41 / 8 , 0 )

Answer: two

Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem. A cube-shaped bin has an edge length of 34 yard. What is the volume of the container?

Answers

1. A cube is a solid formed by six equal faces, this is that it has equal width, height, and length measurements. You can solve this exercise by applying the formula given in the problem to calculate the volume of the container, which is:

V=s³

s=34 yards

2. When you substitute the value of "s" into the fomula for calculate the volume (V=s³), you obtain:

V=(34 yards)³
V=39304 yards³

3. Then, the volume of the container is:  V=39304 yards³

In Queensland, approximately 32% of household waste is recycled. What are the factors of 32?

Answers

32 = 2*16 = 2*2*8 = 2*2*2*4 = 2*2*2*2*2

32 = 2^5 . . . . . the only prime factor is 2. It has multiplicity 5.

32 = 1*32 = 2*16 = 4*8
Divisors of 32 are 1, 2, 4, 8, 16, 32.

What is the greatest common factor of 7ab and 8b^3

Answers

Answer:

Step-by-step explanation:

The greatest common factor is the largest value two numbers share in common which multiplies to each of the numbers.

7ab has factors 7, a, b

[tex]8b^3[/tex] has factors 2, 4, 8, b, b, b

These share in common b.

pls find 5he area of each rectangle thxs

Answers

(7 cm)*(10 cm) = 70 cm^2

The area is the product of length and width.

length × width
7×10=70

A teacher asks 90 students who drive how many speeding tickets they received in the last year. predict the shape of the distribution and explain. select the correct answer below.
a. the distribution will be left-skewed. most people will have at least one ticket, but there will be a few people with no tickets.
b. the distribution will be left-skewed. most people will have no tickets, but there will be a few people with 1, 2, 3, or more tickets.
c. the distribution will be right-skewed. most people will have no tickets, but there will be a few people with 1, 2, 3, or more tickets.
d. the distribution will be roughly symmetric. the number of people who have fewer tickets than the mean and the number of people who have more tickets than the mean is roughly equal.
e. the distribution will be right-skewed. most people will have at least one ticket, but there will be a few people with no tickets.

Answers

Final answer:

The distribution of speeding tickets received by students is predicted to be right-skewed, with most students having no tickets and a few having multiple, indicative of a mode less than the median, which is less than the mean.

Explanation:

The question concerns the prediction of the shape of the distribution of speeding tickets received by 90 students who drive over the last year. The correct answer is c. the distribution will be right-skewed. Most individuals tend to obey traffic laws to avoid fines and penalties, meaning the majority of people will have no tickets.

However, there will always be a few individuals who, due to various reasons, might accumulate one or more tickets within a year. This creates a long tail to the right in the distribution, as we have a large number of students with 0 or very few tickets and a smaller number with higher counts of tickets. This results in the mode being less than the median, which is less than the mean, a characteristic of a right-skewed distribution.

Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero.

Answers

This question is in reverse (in two ways):

1. The definition of an additive inverse of a number is precisely that which, when added to the number, will give a sum of zero.

The real problem, in certain fields, is usually to show that for all numbers in that field, there exists an additive inverse.

Therefore, if you tell me that you have a number, and its additive inverse, and you plan to add them together, then I can tell you in advance that the sum MUST be zero.

2. In your question, you use the word "difference", which does not work (unless the number is zero - 0 is an integer AND a rational number, and its additive inverse is -0 which is the same as 0 - the difference would be 0 - -0 = 0).

For example, given the number 3, and its additive inverse -3, if you add them, you get zero:
3 + (-3) = 0

However, their "difference" will be 6 (or -6, depending which way you do the difference):

3 - (-3) = 6
-3 - 3 = -6

(because -3 is a number in the integers, then it has an additive inverse, also in the integers, of +3).

---

A rational number is simply a number that can be expressed as the "ratio" of two integers. For example, the number 4/7 is the ratio of "four to seven".

It can be written as an endless decimal expansion
0.571428571428571428....(forever), but that does not change its nature, because it CAN be written as a ratio, it is "rational".

Integers are rational numbers as well (because you can always write 3/1, the ratio of 3 to 1, to express the integer we call "3")

The additive inverse of a rational number, written as a ratio, is found by simply flipping the sign of the numerator (top)

The additive inverse of 4/7 is -4/7

and if you ADD those two numbers together, you get zero (as per the definition of "additive inverse")

(4/7) + (-4/7) = 0/7 = 0

If you need to "prove" it, you begin by the existence of additive inverses in the integers.
ALL integers each have an additive inverse.
For example, the additive inverse of 4 is -4

Next, show that this (in the integers) can be applied to the rationals in this manner:

(4/7) + (-4/7) = ?
common denominator, therefore you can factor out the denominator:

(4 + -4)/7 = ?
Inside the bracket is the sum of an integer with its additive inverse, therefore the sum is zero
(0)/7 = 0/7 = 0

Since this is true for ALL integers, then it must also be true for ALL rational numbers.

Emma was given a system of equations to solve by graphing. Which statement correctly identifies Emma’s error?

Emma’s Graph
mc015-1.jpg
Line 1 should have a y-intercept at (0, 2).
Line 2 should have a y-intercept at (0, 2).
Line 1 should have a slope of 2.
Line 2 should have a slope of –5.

Answers

line one should have a y-intercept at (0,2).

The solution for the system of equations is incorrect because line [1] should have a y-intercept at (0, 2) and not at (0, 1).

What is the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is the system of equations of straight lines -

y = -1/3x + 2

y = 2x - 5

plotted on the graph.

The error Emma made is that while plotting Equation [1] -

y = -1/3x + 2

The line should have passed from point (0, 2) on y - axis and not from (0, 1)

Therefore, the solution for the system of equations is incorrect because

Line [1] should have a y-intercept at (0, 2) and not at (0, 1).

To solve more questions on straight lines, visit the link below-

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[Refer to the image attached for full question]

A shoe box measures 15in. by 7 in. by 4 1/2 in. What is the surface area of the box?

Answers

we know that

4 1/2----> (4*2+1)/2-----> 9/2

[surface area of the box]=2*[area of the base]+[perimeter of the base*height]
[area of the base]=15*7------> 105 in²
perimeter of the base=2*(15+7)-----> 44 in

[surface area of the box]=2*[105]+[44*9/2]----> 210+198---> 408 in²

the answer is
408 in²

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