When three numbers are added two at a time, the sums are 29, 46, 53. What is the sum of all three numbers?

Answers

Answer 1

Answer:

[tex]Sum = 64[/tex]

Step-by-step explanation:

Let the three numbers be a, b and c; such that:

[tex]a + b = 29[/tex] ---- (1)

[tex]b + c = 46[/tex] --- (2)

[tex]a + c = 53[/tex] --- (3)

Subtract equation 2 from 3

[tex]a - b + c - c = 53 - 46[/tex]

[tex]a - b = 7[/tex] --- (4)

Add this equation to the (1)

[tex]a + a + b - b = 29 + 7[/tex]

[tex]2a= 36[/tex]

Solve for a

[tex]a = 36/2[/tex]

[tex]a = 18[/tex]

Substitute 18 for a in (1)

[tex]a + b = 29[/tex]

[tex]18 + b = 29[/tex]

Solve for b

[tex]b = 29 - 18[/tex]

[tex]b = 11[/tex]

Substitute 11 for b in (2)

[tex]b + c = 46[/tex]

[tex]11 + c = 46[/tex]

Solve for c

[tex]c = 46 - 11[/tex]

[tex]c = 35[/tex]

[tex]Sum = a + b +c[/tex]

[tex]Sum = 18 + 11 + 35[/tex]

[tex]Sum = 64[/tex]


Related Questions

Write an equation in slope-intercept form for the line with slope 2/5 and y-intercept -6 .

Answers

Answer:

[tex] y = \frac{2}{3}x - 6 [/tex]

Step-by-step explanation:

Recall that the the equation of a line in slope-intercept form is given as [tex] y = mx + b [/tex].

m = the slope of the line

b = the y-intercept. This is the point at which the line intercepts the y-axis.

We are given:

slope (m) = ⅖

y-intercept (b) = -6

All you need to do to get an equation of the line is to simply substitute m = ⅔ and b = -6 into [tex] y = mx + b [/tex].

[tex] y = \frac{2}{3}x + (-6) [/tex]

[tex] y = \frac{2}{3}x - 6 [/tex]

The equation for the line is .[tex] y = \frac{2}{3}x - 6 [/tex]

4(3x + 1)
What is the answer to 4(3x + 1)

Answers

12x + 4

Divide 12 by 4

X=3

Answer:

Answer is 12x+4. Hope that helped.

Suppose there is a 1.7 drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 45.1 what will be the temperature when the plane reaches an altitude of 4000

Answers

Answer: 38.3

Step-by-step explanation:

1.7 × 4 = 6.8

45.1 - 6.8 = 38.3

Which of the following represents this function written in intercept form
y= - x2 – x+ 6

A. v= - (x − 2)(x+3)
B. v= (-x+3)(x-4)
c. v= - (x + 2)(x+6)
D. v= - (1+2)(1-6)

Answers

Answer:

v=2(x - 1)(x-6)=2(x²-6x-x+6)=12x²-12x-2x+12

v = 12x²-14x+12  standard form

Step-by-step explanation:

In the past, patrons at a cinema spent an average of $ 2.50 for popcorn with standard deviation of $ 0.90. The amount of these expenditures is normally distributed . Following an intensive public campaign about the negative health effects of eating popcorn by a local medical school, the mean expenditures for a sample of 18 patrons is found to be $ 2.10. At 0.01 level of significance, does this recent experience suggest decline in spending

Answers

Answer:

There's no evidence to show that the recent experience suggests a decline in spending.

Step-by-step explanation:

We are given;

Population mean; μ = $2.5

Population Standard deviation; σ = $0.9

Sample mean; x¯ = $2.1

Sample size; n = 18

Significance level; α = 0.01

Let's define the hypothesis;

Null hypothesis; H0: μ ≥ $2.5

Alternative hypothesis; Ha: μ < $2.5

z-score formula is;

z = (x¯ - μ)/(σ/√n)

z = (2.1 - 2.5)/(0.9/√18)

z = -0.4/0.2121

z = -1.886

Using the p-value from z-score calculator attached and using z = -1.886; α = 0.01; one tail; we have;

P-value = 0.2965

This is more than the significance level. Thus, we will fail to reject the null hypothesis and conclude that there is no evidence to show that the recent experience suggests a decline in spending.

there are 5,280 feet in 1 mile if Riley ran 26,400 feet how many miles did she run ​

Answers

the correct answer is Riley ran 5 miles .

Help I’ll mark you as the brainliest
No answer choice
parallel to y = 5x – 7 but contains (-1,-3)

Answers

Answer:

-3 = -12

Step-by-step explanation:

Have a great day

I hope that is the answer you are looking for :)

Find x.... Figure is not drawn to scale.

Answers

Answer:

33.

Step-by-step explanation:

I assume that the 2 triangles are similar.

x/77 = 24/56

56x = 77*24

x = (77*24(/56

x = 33.

Anyone know how to do this? I’m stuck

Answers

I’ll make it easier, so for number 2 on number 6 7/8 times 8 and 6 and you have 48, then add the top number which would be 55. Then for the second number, 4 1/3 do the same thing! 4*3= 12+1= 13 then add 13+55 and your answer is 68! Then put it in fraction form! 17/25, then all you do is simplify it! If it can’t be simplified (17/25 can not be simplified), it stays the same. Hope that helps! :)

Which is true 0.45>0.5
0.45<0.5

4.05=0.45

4.05 <0.45

Answers

Answer:

4.05 is greater than 0.45

△BCD≅△GEF . If BC=10 , CD=3x+8 and EF=4x+6 , then what is the measure of CD ?

Answers

Given :-

ΔBCD ≅ ΔGEF

Then :-

∠B <=> ∠G ( ∠B = ∠G )

∠C <=> ∠E ( ∠C = ∠E )

∠D <=> ∠F ( ∠ D = ∠F )

BC <=> GE ( BC = GE )

CD <=> EF ( CD = EF )

BD <=> GF ( BD = GF )

Using this let us find CD .

CD = EF

Which means :-

[tex] 3x + 8 = 4x + 6[/tex]

[tex]8 = 4x + 6 - 3x[/tex]

[tex]8 = 1x + 6[/tex]

[tex]1x + 6= 8[/tex]

[tex]1x = 8 - 6[/tex]

[tex]1x = 2[/tex]

[tex]x = 2[/tex]

Then :-

EF =

[tex]EF = 4x + 6 \\ = 4 \times 2 + 6 \\ = 8 + 6 \\ = 14[/tex]

CD =

[tex]CD = 3x + 8 \\ = 3 \times 2 + 8 \\ = 6 + 8 \\ = 14[/tex]

Therefore , CD = 14 .

△BCD≅△GEF

The measure of CD is 14

Given :

Two triangles are congruent

△BCD≅△GEF

When triangles are congruent then the sides are equal

[tex]BC=GE\\CD=EF\\DB=FG\\[/tex]

Given that CD=3x+8 and EF=4x+6

[tex]CD=EF\\3x+8=4x+6\\3x+8-3x=4x-3x+6\\8=x+6\\8-6=x+6-6\\x=2[/tex]

The value of x=2

Now we find measure of CD

[tex]CD=3x+8\\CD=3(2)+8\\CD=14[/tex]

The measure of CD is 14

Learn more :  brainly.com/question/18373823

question 10 I mark as brainliest ​

Answers

Answer:

134 is the answer

Answer: 134

Step-by-step explanation:

54+ (48+72) x 2/3

54+120x2/3=134

Write and equation of a line perpendicular to y=-5x+8 and passes through (10,4)

Answers

im not sure just yet

Solve the following equation
4(3-2x)=15

Answers

Answer:x= -3/8

Step-by-step explanation:

Answer:

-3/8

Step-by-step explanation:

4(3-2x)=15

-3/8

5d+1/2=d-4 section 2.04

Answers

Answer:  d = -9/8

Steps: 5d + ½ = d - 4

Subtract ½ from both sides: 5d + ½ - ½  = d - 4 - ½

Simplify: 5d = d - 9/2

Subtract d from both sides: 5d - d = d - 9/2 - d

Simplify: 4d = -9/2 ÷ 4

Simplify: d = -9/8

PLz mark brainliest:)

whats the answer of 3/4 + 1/4 =

Answers

Answer:

1

Step-by-step explanation:

3/4 + 1/4 since they both have a 4 as the denominator you only have to add the top since they made it easy. and since that would be 4/4 your answer would be 1 whole.

Is this a function or not a function? (Picture)

Answers

Answer:

Not a Function

Step-by-step explanation:

Maria found the least common multiple of 6 and 15. Her work is shown below.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,...
Multiples of 15:15, 30, 45, 60, ...
The least common multiple is 60.
What is Maria's error?

Answers

Answer:

answer                B

Step-by-step explanation:

just got it right on the test.

Answer:

the answer is B, Maria listed factors of each number instead of multiples.

Step-by-step explanation:

In 2 /3 ÷ 4 /5 the is 2/ 3 .

Answers

Answer:

5/9

Step-by-step explanation:

2/3 • 5/2 • 2/3

1/3 • 2/5 • 2/3

multiply 1/3 for 5/2

5

-----------

3 • 2

multiply 3 for 2

5/6 • 2/3

anular el factor común 2

5/3 • 1/3

multiply 5/3 for 1/3

5

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

3 • 3

multiply 3 for 3

5/9

the result

5/9

form decimal

0.5

PLEASE HELP ASAP
IT AN EMERGENCY



Answers

Answer: E) Not enough information

We're given two pairs of congruent sides, and a pair of congruent angles. The angles are not between the two congruent sides. So we don't have enough information to know if the triangles are congruent or not. SSA is not a valid congruence theorem. This is because there are some cases where two triangles are possible leading to ambiguity.

If the marked angles were between the tickmarked sides, then we could use SAS.

Big ideas math segments lesson 1.2
12, 14,16,18

Answers

We do not know your Mathbook, please give us the questions.

The provided arithmetic sequence adds up to 60.

What is an arithmetic sequence?

The difference between every two successive terms in an arithmetic series is always the same. The number "a" is the first term, and "d" is the common difference between the sequence. The nth term of an arithmetic sequence is given by. aₙ = a + (n – 1)d

Given an arithmetic sequence 12, 14,16,18

The general formula for the Sum of arithmetic sequence:

Sn = n/2 [2a+(n−1)d]

where: n = the number of terms to be added.

a = the first term in the sequence.

d = the constant value between terms.

In our case,

a = 12

n = 4

and d = 14 - 12 = 2

thus

Sum = 4/2(2*12 + (4- 1 )2)

Sum = 2( 24 + 6)

Sum = 60

therefore, the Sum of the given Arithmetic sequence is 60.

Learn more about arithmetic sequence here:

https://brainly.com/question/15412619

#SPJ2

The width of a rectangle is 1.8 meters. The perimeter is 6.6 meters. What is the length? Provide your answer below:

Answers

Answer:

perimeter =2(l+w)

6.6=2(l + 1.8)

6.6= 2L + 3.6

L=3/2 =1.5

ans =1.5

What are the similarities and differences between translations, reflections, and rotations? Describe a real-world transformation? Give examples of two different transformations.

Answers

Answer:

There are four main types of transformations: translation, rotation, reflection and dilation.Translation moves the object without rotating it or changing its size. Reflection flips the object about a line of reflection. Rotation rotates a figure about a fixed point. Dilation changes the size of a figure without changing its essential shape.When you reflect a point across the x-axis, the x-coordinate remains the same,but the y-coordinate is transformed into its opposite. a negative angle of rotation turns the figure in a clockwise direction.Transformation can be done in a number of ways, including reflection, rotation, and translation. ~When you reflect a point across the x-axis, the x-coordinate remains the same,but the y-coordinate is transformed into its opposite. a negative angle of rotation turns the figure in a clockwise direction.

Step-by-step explanation:

Transformation simply means changing the size and location of shapes, lines and points in the coordinate geometry

The similarities

Translations, reflections, and rotations are all rigid transformations

This means that, they do not change the side lengths and angle measure of the shape they transform.

The differences

Translation: can only change the position of shapes without rotating or flipping the shape.

Rotation: This means that a shape is to be turned around a center at a particular degree

Reflection: This simply means that, a shape is mirrored over a line

Real-world transformation

A scenario is when the blades of a fan rotates when the fan is powered on

Examples

Reflection

MirrorLeaves of a book

Rotation

Fan rotationWheels of vehicle

Translation

Movement Changing positions

Read more about transformations at:

https://brainly.com/question/13801312

Consider a conical tank, where the height of the tank is 12 meters, and and the diameter of the tank at the top is 8 meters. Water is leaking out of the bottom of a conical tank at an constant rate of 20,000 LaTeX: \text{cm}^3 / \text{min}cm 3 / min. Water is also being pumped in to the tank at a constant unknown rate (call it LaTeX: kk). The water level is currently 8 meters high, and the water level is rising at a rate of 2 LaTeX: \text{cm} / \text{min}cm / min. Find the rate LaTeX: kk at which water is being pumped in to the tank.

Answers

Answer:

The answer is below

Step-by-step explanation:

The height of tank = 12 m = 1200 cm, the diameter of the tank = 8 meters, hence the radius of the tank = 8/2 = 4 m = 400 cm

Let h represent the water level = 8 m = 800 cm. The radius (r) of the water level at a height of 8 m is:

r/h = radius of tank/ height of tank

r/h = 400/1200

r = h/3

[tex]\frac{change\ in\ volume}{change\ in \ time}=water\ in-water\ out\\ \\\frac{dV}{dt=} water\ in-water\ out\\\\V=\frac{1}{3}\pi r^2h\\ \\r=\frac{1}{3}h \\\\V=\frac{1}{3}\pi (\frac{1}{3}h )^2h\\\\V=\frac{1}{9} \pi h^3\\\\\frac{dV}{dt} =\frac{1}{3} \pi h^2\frac{dh}{dt}\\\\\frac{dh}{dt}=2\ cm/min,h=8\ m=800\ cm\\\\[/tex]

[tex]\frac{dV}{dt} =\frac{1}{3} \pi (800)^2(2)=426666.7\ cm^3/min\\\\\frac{dV}{dt=} water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-20000\ cm/min\\ \\water\ in=426666.7\ cm^3/min+20000\ cm/min\\\\water\ in=446666.7 \ cm^3/min[/tex]

2. Arsenic is a compound that occurs naturally in very low concentrations. Arsenic blood concentrations in healthy individuals are Normally distributed, with a mean of 3.2 mg/dl and a standard deviation of 1.5 mg/dl. A researcher believes that one area of the United States has naturally elevated arsenic levels in the ground and water supplies. An SRS of 25 individuals in this area found a sample mean arsenic level of 3.75 mg/dl. What are the null and alternative hypotheses for this study?

Answers

Answer:

The null hypothesis                 [tex]H_o : \mu = 3.2 \ mg/dl[/tex]

The alternative hypothesis      [tex]H_a : \mu > 3.2 \ mg/dl[/tex]

Step-by-step explanation:

From the question we are told that

  The mean is  [tex]\mu = 3.2 \ mg/dl[/tex]

   The standard deviation is [tex]\sigma = 1.5 mg/dl[/tex]

   The sample size is  n = 25

    The sample mean is  [tex]\= x = 3.75 \ mg /dl[/tex]

Generally

   The null hypothesis is : That the mean of the  Arsenic blood concentrations in healthy individuals is [tex]\mu = 3.2 \ mg/dl[/tex]

i.e

The null hypothesis  [tex]H_o : \mu = 3.2 \ mg/dl[/tex]

    The alternative hypothesis is : That the mean of the  Arsenic blood concentrations in healthy individuals is greater than  [tex]\mu = 3.2 \ mg/dl[/tex]

The alternative hypothesis      [tex]H_a : \mu > 3.2 \ mg/dl[/tex]


Adam has two kinds of fruit punch left over from a party. He mixes 5 liters of fruit punch A with 10 liters of fruit punch B to create fruit
punch C. Fruit punch A contains 25% orange juice and the resulting fruit punch C contains 35% orange juice.
What percent orange juice does fruit punch B contain?
OA. 20%
OB. 50%
OC. 40%
OD 25%

Answers

Answer:

A. 20%

Step-by-step explanation:

fruit punch A is half of fruit punch B so times 35 by 2 and then subtract 50. 50 came from 25 times 2.

what is the branch of mathematics that uses variables and operations?

Answers

Answer:

Algebra

Step-by-step explanation:

Answer:

algebra, you can check on google as well

1. The perimeter of a rectangular field is 180 feet. Let x be the length of the field (in feet) and let y be the width (in feet). Write an equation to model the perimeter of the rectangular field. 

Also this question so there's 2 questions


2. Tyrone is designing a rectangular sandbox. He wants the sandbox to be 15 feet long and have a perimeter of 46 feet. How wide does Tyrone’s sandbox need to be? ​

Answers

Answer:

1. 2(x + y) = 180

2. His sandbox needs to be 8 ft wide.

A train travelled a distance of 1350 kilometers in 15 hours find it,s average speed answer pleaseeeeeeeee fast ,thanks​

Answers

Answer:

90

Step-by-step explanation:

1350 divided by 15

A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of LaTeX: 50cm^3/hr. At what rate is it's diameter decreasing

Answers

Complete question is;

A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of 50 cm/hr. At what rate is its diameter decreasing?

Answer:

Diameter is decreasing at the rate of 5/(2πr) cm/hr

Step-by-step explanation:

We are told the stone is wearing away at a rate of 50 cm/hr. This means the volume is decreasing. Thus;

dV/dt = -50 cm/hr

Now, a grindstone is in the shape of a cylinder. Thus, volume of grindstone is;

V = πr²h

dV/dr = 2πrh

Now,to find the rate at which the diameter is decreasing, we'll write;

dr/dt = (dV/dt)/(dV/dr)

dr/dt = -50/(2πrh)

We are given;

Diameter = 200 cm

Radius; r = 200/2 = 100 cm

Thickness; h = 10 cm

Thus;

dr/dt = -50/(2π × r × 10)

dr/dt = -5/(2πr) cm/hr

The rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex] and this can be determined by using the given data.

Given :

A 10 cm thick grindstone is initially 200 cm in diameter and it is wearing away at a rate of 50 [tex]\rm cm^3/hr[/tex].

The following steps can be used in order to determine the rate at which grindstone diameter decreases:

Step 1 - According to the given data, the rate at which grindstone volume decreases is:

[tex]\dfrac{dV}{dt} = 50\;{\rm cm^3/hr}[/tex]        --- (1)

Step 2 -  The formula of the volume of the cylinder (grindstone) is given below:

[tex]V = \pi r^2 h[/tex]

Step 3 - Differentiate the above expression with respect to 'r'.

[tex]\dfrac{dV}{dr} = 2\pi r h[/tex]          --- (2)

Step 4 - So, using the expression (1) and (2) the rate at which grindstone diameter decreases is:

[tex]\dfrac{dr}{dt}=\dfrac{\frac{dV}{dt}}{\frac{dV}{dr}}[/tex]

[tex]\dfrac{dr}{dt}=\dfrac{-50}{2\pi r \times 10}\\[/tex]

[tex]\dfrac{dr}{dt} = -\dfrac{5}{2\pi r }\; {\rm cm/hr}[/tex]

So, the rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex].

For more information, refer to the link given below:

https://brainly.com/question/12748872

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