solve the following equation and verify your answer.
[tex] \\ [/tex]
[tex] \huge \purple{ \frac{3x - 1}{5} - \frac{x}{7} = 3}[/tex]

Answers

Answer 1

Answer:

x = 7

Step-by-step explanation:

[tex]\frac{3x-1}{5}[/tex] - [tex]\frac{x}{7}[/tex] = 3

Multiply through by 35 ( the LCM of 5 and 7 ) to clear the fractions

7(3x - 1) - 5x = 105 ← distribute parenthesis and simplify left side

21x - 7 - 5x = 105

16x - 7 = 105 ( add 7 to both sides )

16x = 112 ( divide both sides by 16 )

x = 7

To verify the answer substitute x = 7 into the left side of the equation and if equal to the right side then it is the solution

[tex]\frac{3(7)-1}{5}[/tex] - [tex]\frac{7}{7}[/tex]

= [tex]\frac{21-1}{5}[/tex] - 1

= [tex]\frac{20}{5}[/tex] - 1

= 4 - 1

= 3 = right side

Then x = 7 is the solution to the equation


Related Questions

Oceanside Bike Rental Shop charges a 13 dollars fixed fee plus 7 dollars an hour for
renting a bike. Keith paid 69 dollars to rent a bike. How many hours did he pay to have
the bike checked out? Let h = number of hours bike was checked out

Answers

Answer:

8 hours

Step-by-step explanation:

69-13=56

56/7=8

13+7h=69

Find the volume of the figure below.

Answers

Answer:

0.6

Step-by-step explanation:

10ft of object and 6ft of ground side

Choose the graph that matches the following system of equations:

x + y = 4
2x + 3y = 18

Picture of coordinate plane with line y equals negative x plus 4 and line y = equals negative 2 thirds x plus 6. They intersect at negative 6, 10.
Picture of coordinate plane with line y equals x minus 4 and line y equals negative 2 thirds x plus 6. They intersect at 6, 2.
Picture of coordinate plane with line y equals x minus 4 and line y equals negative 2 thirds x minus 6. They intersect at negative 1.2, negative 5.2.
Picture of coordinate plane with line y equals x plus 4 and line y equals negative 2x plus 6. They intersect at 0.67, 4.67.

Answers

Answer:

Line x-intersect: -6

y-intersect: 10

Step-by-step explanation:

X + y = 4

x = 4-y

2(4-y) + 3y = 18 (substitution)

8-2y+3y = 18

y = 18-8

y = 10

x + 10 = 4

x = -6

What is the factored form of n3+512 (pleas help fast)

A- (n-8)(n^2+8n+64)
B- (n+4)(n^2-4n+128)
C- (n-4)(n^2+4n+128)
D- (n+8)(n^2-8n+64)

Answers

Answer:

Since both terms are perfect cubes, factor using the sum of cubes formula,

a³+b³=(a+b)(a²-ab+b²) where

a=n and b=8

(n+8)(n²-8n+64)

Answer

(n+8)(-8n+64)

hi

have a good day

thank me later

Carryonlearing

Answer:

Step-by-step explanation:

The only one that has a chance of being correct is D. That's because the first term is correct and you have to assume that the second one is as well.

cubrt(512) = 8

The first term is (n + 8)

The second term is (n^2 - 8*n + 8^2) = n^2 - 8n + 64

All the other answers have the wrong first term

A: it should be n + 8 not n - 8

B and C are both wrong because the cube root of 512 is 8 not 4.

Explanation of approximation, decimal place, significant figure

Answers

Answer:

im not an expert in math but i'll do my best:

1. an approximation is something that is almost, but not exactly something. for example, 5.02 is approximately 5. it's not EXACTLY 5, but it's around 5.

2. decimal place refers to the position of numbers after the decimal point. let's take the decimal number 7.89 for example. there are 2 numbers after the decimal point, which is 8 and 9. hence we say that 7.89 has 2 decimal places.

3. significant figure is kind of hard to explain, so i'll jump into the example straight away.

5.874 to 3 significant figures is 5.87. what i did was count 3 digits: starting from 5 to 7. to round to 3 significant figures, i look at the 4th digit, which is 4 in this case. if it's smaller than 5, i ignore everything past the digit 7, and leave the final answer as 5.87.

if the 4th digit is greater than or equal to 5, i add 1 to the 3rd digit THEN leave out all the numbers after the 3rd digit. (if this were the case, the answer would be 5.88)

lets take a trickier example, 0.064591

in this case i cannot start counting 3 digits starting from 0. i have to count starting from the number 6. the concept in this case is that the 1st significant figure cannot be a 0. in this case the answer to 3 significant figures would be 0.0646.

however, 0 can be a significant figure if it's after another number. for instance 0.90672

the 0 after the 9 would count as a significant figure because it's not the 1st significant figure in the number. however the 0 before the 9 would NOT count as one because 0 cannot be the 1st significant figure. the answer to 3 significant figures would be 0.907.

sorry this was so lengthy, i just hope this answers your question on what these are and how they work. good luck!

Write the converse of the following statement. Then determine its validity.

a. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
b. If a parallelogram is a rectangle, then the diagonals are congruent. TRUE.
c. If a parallelogram is a rectangle, then the diagonals are congruent. FALSE.
d. If the diagonals of a parallelogram are not congruent, then the parallelogram is not a rectangle. FALSE.
d. If a parallelogram is not a rectangle, then the diagonals are not congruent. TRUE.

Answers

The converse and the validity of the statement is:

If a parallelogram is a rectangle, then the diagonals are congruent. TRUE.

The statement is given as:

If the diagonals of a parallelogram are congruent, then is the parallelogram is a rectangle

Considering the following statement

If a then b

Its converse is:

If b then a

So, the converse of the given statement is:

If a parallelogram is a rectangle, then the diagonals are congruent.

The diagonals of a rectangle are true.

Hence, the validity is true.

So, the true statement is (b)

Read more about converse statements at:

https://brainly.com/question/4421013

what cubed is equal to 1000?

Answers

Answer:

10

Step-by-step explanation:

what is the range of a parabola that opens down with a vertex at (1,-3)

Answers

Answer:

-3 to -infinity

Step-by-step explanation:

Hii I would love if anyone would be able to give me the answer to this <3

Answers

Answer:

×=40

Step-by-step explanation:

The total value of all the angles on any line is 180

so x+(4x-20)=180

40+(4×40-20)=180

Answer:

40°

Step-by-step explanation:

The sum of angles x and (4x - 20) is 180°

x + (4x - 20) = 180

5x = 200

x = 40°

d= sqrt ( 2 )^ 2 +( 12 )^ 2

Answers

Answer:

d = 146

Step-by-step explanation:

Answer:

d=146

Step-by-step explanation:

the sqrt of 2(2) is 4 which can be simplified to 2 and the 12 raised to the second power is 144 so 2+144 is 146

help please anybody hmm​

Answers

Answer:

94.6-18.8=75.8

75.8 is the answer

Step-by-step explanation:

Hope this helps

May i get braineist pls?

Find the area of each figure

Answers

Answer:

flu

Step-by-step explanation:

ugh

identify all possible answer for the statement below.

Answers

Answer:

it simple there nothing there Step-by-step explanation:



y=x−4
y=4x+2

Find x and y

Answers

Answer:

x = -2

y = -6

Step-by-step explanation:

x - 4 = 4x + 2

-4 = 3x + 2

-6 = 3x

x = -2

y = -2 - 4;  y = -6

3. The sum of the second term and the ninth term of an arithmetic sequence is -5. The sum of the third and fourth terms of the same sequence is 7. Find the first term of the sequence.

Answers

Answer:

First term of the sequence is [tex]11[/tex]

Step-by-step explanation:

Let [tex]a[/tex] be the first term and [tex]d[/tex] be the common difference

We have

The sum of the second term and the ninth term of an arithmetic sequence is [tex]-5[/tex]

[tex]a+(2-1)d+a+(9-1)d=-5\\\\2a+9d=-5---eqn1[/tex]

The sum of the third and fourth terms of the same sequence is [tex]7[/tex]

[tex]a+(3-1)d+a+(4-1)d=7\\\\2a+5d=7---eqn2[/tex]

eqn 1 - eq2

[tex]4d=-12\\\\d=-3[/tex]

Substituting in eqn 1

[tex]2a+9\times -3=-5\\\\2a=22\\\\a=11[/tex]

First term of the sequence is [tex]11[/tex]

Help ME!

Question 1: Evaluate the expression:
2+5⋅8

Question 8: 10÷(3−1⋅2)

Option answers for Question 8: 4, 10, 10/4, and 2.5

Answers

Answer:

Q1: 42

Q8: 10

Step-by-step explanation:

PEMDAS

Can someone help me with this please? ​

Answers

Die haben sich schon in der Schule gesehen und 5 bis drei z die Frau A bist du noch mal in der Nähe

An 18-foot ladder is leaning against a wall. The bottom of the ladder is 4.5 feet from the base of the wall.


How high up the wall does the ladder reach? Round your answer to the nearest tenth, if necessary.

A

13.5 feet

B

18.6 feet

o

С

22.5 feet

D

17.4 feet

Answers

Answer:

d

Step-by-step explanation:

use Pythagoras theorem

that is a²+b²=c²

so 4.5²+b²= 18²

rearrange to b²=18²-4.5²

so you get b=

[tex] \sqrt{303.75} [/tex]

that is equal to 17.42842506

y^2 - 19 = 0 find the sum and product

Answers

Answer: Sum of the roots:  √19 - √19 = 0

Product of roots:  (√19)(-√19) = -19

Step-by-step explanation:

y2 - 19 = 0

add 19 to both sides

y2 = 19

take square root of both sides

y = ±√19

So y = √19 or y = -√19

I need help with these three questions I have the question and math problems all in the screenshots please help :)

Answers

Answer:

Screenshot 1 = Option B (5x-1)²

Screenshot 2 = (x+9)(x+9)

Screenshot 3 = Option 3 100x²-20x+1

Step-by-step explanation:

Screenshot 1 -

(5x-1)² = (5x-1)(5x-1)

5x · 5x = 25x²

5x · -1 = -5x

5x · -1 = -5x

(-1) · (-1) = 1

25x²- 5x- 5x + 1 = 25x² - 10x + 1

Screenshot 2 -

(x+9)(x+9)

x · x = x²

x · 9 = 9x

x · 9 = 9x

9 · 9 = 81

x² + 9x + 9x + 81 = x² + 18x + 81

Screenshot 3 -

100x²-20x+1

(10x-1)(10x-1)

10x · 10x = 100x²

10x · (-1) = -10x

10x · (-1) = -10x

(-1) · (-1) = 1

100x² - 10x - 10x + 1 = 100x² - 20x +1

What is an equation of the line that passes through the points (4, -1) and (-8, -7)?

Answers

Answer:

y=-1/2x - 3

I think this is it, its been a while though.

Make x the subject of the formula: y=x^{2} + 5

Answers

First, multiply both sides by (x - 5), so you end up with:

(x-5)y = x + 2

Which can be expanded to give you:

xy - 5y = x + 2

Now add 5y to both sides to obtain:

xy = x + 2 + 5y

Now subtract x from both sides:

xy - x = 2 + 5y

Factorise x out:

x(y - 1) = 2 + 5y

Divide both sides by (y - 1):

x = 2 + 5y/y - 1

There you go, x is now the subject.

All the numbers round to 7 except


6.61

7.89

6.58

7.37

Answers

7.89 rounds off to 8
7.89 because it’s closer to 8.00, not 7.00

7/8 in lowest terms ?

Answers

Answer:

7/8 simplified to lowest terms is 7/8.

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 7 and 8 is 1

Divide both the numerator and denominator by the GCD

7 ÷ 1

8 ÷ 1

Reduced fraction:  

7

8

Therefore, 7/8 simplified to lowest terms is 7/8.

3q+3.97=7.57 please help im stuck on ixl

Answers

Answer:

1.2

Step-by-step explanation:

3q+3.97=7.57

3q=7.57-3.97

3q=3.6

q=3.6/3

q=1.2

round 0.006772 to 1 significant figure

Answers

Answer:

0.007

Step-by-step explanation:

0's before other numbers are non-significant. Then you just round your number.

Hope that helps

30x - 12y
i need help

Answers

Step-by-step explanation:

if you factor it will be 6(5x-2y)

if you graph the slope will be 5/2

“write each number as a percent”
6 and 1/2 ( mix number)
Help please

Answers

Answer:

650%

Step-by-step explanation:

Since percent means "out of one hundred", we can use that to find out the answer6 would be 600 percent, and 0.5 would be 50 percentTherefore, the answer would be 650%

Classify the following triangle

(Chose multiple)

-Equilateral
-Isosceles
-Scalene
-Acute
-Equiangular
-Obtuse
-Right

Answers

Answer:

Scalene

Acute

Obtuse

Step-by-step explanation:

≠ Equailateral because all the sides in the given triangle are not equal nor are the three angles 60°

≠ Isosceles because the triangle doesn't have two equal sides nor two equal angles

= Scalene as all the sides are of different lengths and so are all the angles with different degrees.

= Actue because QPO and PQO are less than 90°, thus they are acute angles

≠ Equiangular because none of the given angles are of the same degree.

= Obtuse as POQ is greater than 90°

≠ Right because the given triangle does not have a right angle

Find the slope of the line (-3,-2),(1,-2)

Answers

Answer:

0

Step-by-step explanation:

The y-axis is the same so the slope has to be zero, since the line is not going vetrically anytime on the graph

Other Questions
The main physical boundary between Chile and Argentina is ______________.a.el Desierto de Atacamac.the Andes mountain rangeb.el Ro de la Platad.el Ocano Atlntico 5+(3-4)-6/3 please help find the quadratic equation of -9+3p2=-12 differences between stamen and pistil what was johann dobereiner contribution to the periodic table in the late 1800s, china experienced an internal crisis when emperor guang xu launched massive reforms throughout the nation. why were these reforms opposed, thus creating an internal crisis in china? When earth and the moon are separated by a distance of. The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:(image)Which statement best describes a flaw in the student's proof? Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent. Triangles ABD and CDB are congruent by the SAS postulate instead of the SSS postulate. Triangles ABD and BCD are congruent by the AAS postulate instead of the SSS postulate. Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent. Most earthquakes occur in areas close to where tectonic plates meet. There are earthquakes in San Francisco.What can be concluded from this information? A. San Francisco is far away from an area where tectonic plates meet. B. San Francisco is close to an area where tectonic plates meet. C. San Francisco is close to Luzon, an island in the Philippines. D. San Francisco is likely to experience a volcanic eruption in the near future. Describe what you think wolf Kahn by a work of art becomes too descriptive... it dies on youand do you agree or disagree Read the questions. Choose the correct answers. Please help. Due Today Help with 14 15 16!! ( i will give branly toi the best and the fastest so please help :D extra points as wellWhat did some farmers and merchants do after the war? Added taxes to their goods Charged higher prices for their goods Started business schools for men and women Went into business together 1. PART A: Which of the following best describes a central idea ofPresident Reagan's speech?O A In contrast to the communist states in the East, the West hasthrived because it values economic and personal freedom.OB West Berlin is facing economic collapse as it continues to betrapped and limited by the Berlin Wall; this barrier must thereforebe destroyed.OC The people of Berlin loved American presidents, particularly afterthe United States provided relief in the form of the Marshall Plan.OD Due to the tense relationship between the Soviet Union and theUnited States, it is up to the people of Germany to overthrow theirtotalitarian oppressors. (4 3)(3 + 6) (2 )simplifyshow all work What can be used as evidence and reasoning in a CER on the theory of continental drift Learning outcome: You will be able to describe what you and others do on vacation with common irregular verbs. You will also be able to describe plans for a future vacation or trip with the verb phrase ir + a + infinitive .Key words and concepts: Irregular verbs in the present tense; The future: ir + a + infinitive ; Irregular verbs in the present tense; Expressions of future timeComplete each sentence by choosing the more logical verb and writing it in the present tense. The subject of each sentence is yo.1. Todos los aos (yo: conducir / hacer)______un crucero al Caribe con mi familia.2. A veces (yo: dar / poner) ________ un paseo en velero.3. Maana (yo: decir / salir) ________ para el aeropuerto a las seis de la maana.4. No (yo: ver / saber)_______ la hora de irme de vacaciones!5. El prximo mes (yo: ir / tener)________ a hacer un viaje a Mxico.6. Yo (traer / saber)_______ que (that) va a ser un viaje magnfico. expand and simplify 2(8x + 4y - 10)[tex]2(8x + \\4y - 10)[/tex] Write a system of equations to describe the situation below, solve using any method, and fillin the blanksMrs. McMillan, the PE, teacher, is pairing off students to race against each other. Heather canrun 4 meters per second, and Erin can run 5 meters per second, Mrs. McMillan decides to give Heather a head start of 23 meters since she runs more slowly. Once the students startrunning, Erin will quickly catch up to Heather. How far will Erin have to run? How long willthat take?Please help.