A) Write an expression for the given number trickB) Simplify the expression you came up with.
Answers
A) The expression for the given number trick = 8(x + 7)
B) 8x + 56
Explanation:
A) Pick a number:
Let the number = y
Add 7:
it becomes = y + 7
Multiply by 8:
it becomes = 8(x + 7)
The expression for the given number trick = 8(x + 7)
B) We sipmlify the expression by opening the bracket:
8(x + 7) = 8 × x + 8×7
= 8x + 56
Related Questions
How many times can 2/7 be subtracted from 6/7
Answers
Answer:
Exactly three times.
Step-by-step explanation:
(6/7) / (2/7) = (6/7) * (7/2) = 3/1 * 1/1 = 3
I need help with part "C" and "D"
Answers
3x²cos( x³ ) and 3sin²( x ) cos( x ) are the derivatives of the composite functions f(x) = sin(x³) and f(x) = sin³(x) respectively.
What are the derivative of f(x) = sin(x³) and f(x) = sin³(x)?Chain rule simply shows how to find the derivative of a composite function. It states that;
d/dx[f(g(x))] = f'(g(x))g'(x)
Given the data in the question;
f(x) = sin(x³) = ?f(x) = sin³(x) = ?First, we find the derivate of the composite function f(x) = sin(x³) using chain rule.
d/dx[f(g(x))] = f'(g(x))g'(x)
f(x) = sin(x)
g(x) = x³
Apply chain rule, set u as x³
d/du[ sin( u )] d/dx[ x³ ]
cos( u ) d/dx[ x³ ]
cos( x³ ) d/dx[ x³ ]
Now, differentiate using power rule.
d/dx[ xⁿ ] is nxⁿ⁻¹
cos( x³ ) d/dx[ x³ ]
In our case, n = 3
cos( x³ ) ( 3x² )
Reorder the factors
3x²cos( x³ )
Next, we find the derivative of f(x) = sin³(x)
d/dx[f(g(x))] = f'(g(x))g'(x)
f( x ) = x³
g( x ) = sin( x )
Apply chain rule, set u as sin( x )
d/du[ u³ ] d/dx[ sin( x )]
Now, differentiate using power rule.
d/dx[ xⁿ ] is nxⁿ⁻¹
d/du[ u³ ] d/dx[ sin( x )]
3u² d/dx[ sin( x )]
Replace the u with sin( x )
3sin²(x) d/dx[ sin( x )]
Derivative of sin x with respect to x is cos (x)
3sin²( x ) cos( x )
Therefore, the derivatives of the functions are 3x²cos( x³ ) and 3sin²( x ) cos( x ).
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please help me I’m really not understanding this my answer was completely wrong
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From the table, we can see that:
Gross profit for Q 1 = 85 x 1000= 85,000
Gross profit for Q 2= 94 x 1000 = 94, 000
Hence the increase in Gross profit = 94,000 - 85,000 = 9000
Then,
[tex]\begin{gathered} \text{Percentage change = }\frac{9000}{85000}\text{ x 100} \\ =\frac{900000}{85000} \\ =\text{ 10}.58823529 \\ \approx\text{ 10. 6 \% ( to the nearest tenth )} \end{gathered}[/tex]CONCLUSION:
The percent change = 10. 6 % ( to the nearest tenth)
A motorcycle can be purchased for $9000 or leased for a down payment of $400 and $290 per month. Find a function that describes how the cost of the lease depends on time. Assuming that the monthly payments are made, how long can the motorcycle be leased before more than the purchase price has been paid?Question content area bottomPart 1The function that models the situation is p= enter your response here, where p is the amount paid on the lease in dollars and t is the time in months.(Simplify your answer.)
Answers
Let's find the function p that describes that situation, at the initial time we must pay 400, then
400 - 0
After one month we must pay 290, it will sum with the previous 400 that we have paid
400 - 0
690 - 1 month
In the third month, we must add 400, the previous 290 and 290 again, two times.
400 - 0
690 - 1 month
980 - 2 months
If we repeat that we will see that we will have 290*3 plus 400, in other words, more 290 per month. We can write an expression to do it, it's
[tex]p=400+290\cdot t[/tex]Where t is the time in months, verify that our expression is coherent with our previous logic, now we have our expression let's go to the next step. The lease will be equal to the purchase price when p = 9000, which means that the person paid 9000 on the lease, if we use it in our equation we can solve it for t
[tex]9000=400+290\cdot t[/tex]Let's solve it for t
[tex]\begin{gathered} 9000=400+290t \\ \\ 290t=9000-400 \\ \\ 290t=8600 \\ \\ t=\frac{8600}{290} \\ \\ t=29.65 \end{gathered}[/tex]Then, if we lease the motorcycle for 30 months, we will pay $9100, more than the purchase price, if we lease it for 29 months, we will pay $8810.
Final answer:
Expression:
[tex]p=400+290t[/tex]How long you can lease it before it costs more than the purchase price:
[tex]t=29[/tex]The table and the graph represent the rate at which two machines arebottling milk in gallons per second.
Answers
Given:
There are given the information about the two machines, one is in table form and another is in the graph.
Explanation:
We need to find the rate of change from both of the machines.
So,
For machine 1:
Choose two-point and find the slope by using the slope formula:
So,
The points are;
[tex](1,0.6),and,(2,1.2)[/tex]From the formula to find the rate of change:
[tex]r=\frac{y_2-y_1}{x_2-x_1}[/tex]Then,
[tex]\begin{gathered} r=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ r=\frac{1.2-0.6}{2-1} \\ r=\frac{0.6}{1} \\ r=0.6 \end{gathered}[/tex]Now,
For machine 2:
We need to choose two points from the graph.
So,
Two points are:
[tex](8,6),and,(16,12)[/tex]Then,
From the formula:
[tex]\begin{gathered} r=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ r=\frac{12-6}{16-8} \\ r=\frac{6}{8} \\ r=0.75 \end{gathered}[/tex]Final answer:
Hence, the machine 2 is faster at botting milk because the value of the rate of machine 2 is greater than the value of rate of machine 1.
Solve for the variable: 1 - p = 7
Answers
Given,
Solve for the variable,
[tex]1-p=7[/tex]Solution:
Take the variable on one side of the equation and the constant on another side of the equation.
[tex]\begin{gathered} -p=7-1 \\ -p=6 \\ p=-6 \end{gathered}[/tex]Thus, the value of p is -6.
If a full air container has a volume of 2.3 m3, and 78.1 % of that air is nitrogen, what is the volume of nitrogen in the container. Quote your answer to an appropriate number of significant figures.
Answers
The amount of nitrogen is 1.80 cubic meters if a full air container has a volume of 2.3 m³, and 78.1 % of that air is nitrogen.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
From the data given:
The total volume of the air container = 2.3 cubic meters
78.1 % is nitrogen.
The amount of nitrogen = 78.1 % of 2.3
= (78.1/100)x2.3
= 1.7963 cubic meters
The number 1.7963 to three Significant Figures is 1.80
The amount of nitrogen = 1.80 cubic meters
Thus, the amount of nitrogen is 1.80 cubic meters if a full air container has a volume of 2.3 m³, and 78.1 % of that air is nitrogen.
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Which statement about the following equation is true?
2x2 – 9x + 2 = –1
The discriminant is less than 0, so there are two real roots.
The discriminant is less than 0, so there are two complex roots.
The discriminant is greater than 0, so there are two real roots.
The discriminant is greater than 0, so there are two complex roots.
Answers
Answer:
The discriminant is greater than 0, so there are two real roots.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.2 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\If $b^2-4ac > 0 \implies$ two real roots\\If $b^2-4ac=0 \implies$ one real root\\If $b^2-4ac < 0 \implies$ no real roots\\\end{minipage}}[/tex]
Given equation:
[tex]2x^2-9x+2=-1[/tex]
Add 1 to both sides of the equation so that the equation equals zero:
[tex]\implies 2x^2-9x+2+1=-1+1[/tex]
[tex]\implies 2x^2-9x+3=0[/tex]
Compare the equation with ax²+bx+c=0:
a = 2b = -9c = 3Substitute the values of a, b and c into the discriminant formula and solve:
[tex]\begin{aligned}\implies b^2-4ac&=(-9)^2-4(2)(3)\\&=81-4(2)(3)\\&=81-8(3)\\&=81-24\\&=57\end{aligned}[/tex]
As 57 > 0, the discriminant is greater than zero, so there are two real roots.
Answer:
B on Edge 23
Step-by-step explanation:
trust me bro
If h(x) = 2x and k(x) =2x -k, what is h(k(x))?
Answers
If h(x) = 2x and k(x) =2x -k, then h(k(x)) would be:
h(k(x))= 2*(2x-k)
h(k(x))= 4x - 2k Using distributive property
Final answer is: h(k(x))= 4x - 2k
What is the area of a rectangle with side lengths of 6/8 meter and 4/10 meter? In fraction in simplest form
Answers
SOLUTION
We want to find the area of the rectangle with the given side lengths as indicated in the question.
The area of a rectangle is given as
[tex]\text{Area = leghth }\times\text{ width}[/tex]So, this means to get the area, we will multiply the side lengths, we have
[tex]\begin{gathered} \text{Area = leghth }\times\text{ width} \\ \text{Area = }\frac{6}{8}\times\frac{4}{10} \end{gathered}[/tex]Solving the fraction, we have
[tex]\begin{gathered} \text{Area = }\frac{6}{8}\times\frac{4}{10} \\ 4\text{ divide itself is 1, }8\text{ divide 4 is 2, we have } \\ \text{Area = }\frac{6}{2}\times\frac{1}{10} \\ \text{now, 2 divide itself is 1, 6 divide 2 is 3, we have } \\ \text{Area = }\frac{3}{1}\times\frac{1}{10} \\ \text{Area = }\frac{3}{10} \end{gathered}[/tex]Hence the area in fraction in the simplest form is
[tex]\frac{3}{10}\text{ meter}[/tex]please answer this question
Answers
It's important to know that similar figures have equal angles, for example, if two triangles are similar, then their corresponding angles are congruent.
Having said that, D is true because all rectangles have equal angles.
A parabola has a directrix of y=1 and a focus of (1,12). Which statement is true?A)The parabola opens upward.B)The parabola opens downward.C)The parabola opens to the left.D)The parabola opens to the right.
Answers
1) Since the directrix is y=1 and the focus (1,12) We can write that, using the distance formula:
[tex]\begin{gathered} \sqrt[]{(y-1)^2}=\sqrt[]{(x-1)^2+(y-12)^2} \\ (y-1)^2=(x-1)^2+(y-12)^2 \\ y^2-2y+1=x^2-2x+1+y^2-24y+144 \\ -2y+1=x^2-2x+1-24y+144 \\ -2y+24y=x^2-2x+145 \\ -22y=x^2-2x+145 \\ y=\frac{x^2-2x+145}{22} \\ \\ y=\frac{x^2-2x+145}{22} \end{gathered}[/tex]2) Then we can state that the correct option is A the parabola opens upward.
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.2 minus twice a number.
Answers
Given the statement:
2 minus twice a number.
Let's represent the sentence as an algebraic expression where the number is the letter x.
To represent the statement as an algebraic expression, we have:
A number is the letter x ==> x
• 2 minus twice the number ==> 2 - 2x.
Therefore, the algebraic expression that represents the sentence is:
2 - 2x
ANSWER:
2 - 2x
which number set(s) does -10 belong toirrational numberswhole numbersrational numbersintegersreal numberscounting or natural numbersNo number set describes this number.
Answers
Given:
The number is -10.
To describe the number:
Explanation:
Since 10 is a whole number and it has a minus sign.
So, -10 is an integer number.
Since it is an integer number.
So, it must be a rational number as well as the real number.
Therefore, -10 is a number that belongs to the sets
Integer numbers
Rational numbers
Real numbers
Final answer:
• Integer numbers
,• Rational numbers
,• Real numbers
Patsy’s pizza sells one 20-inch cheese pizza or two 12-inch cheese pizzas for 11.99. Determine which size gives more pizza (A= 3.14r^2)
Answers
Since 20-inch pizza, means it is a circle with a diameter of 20 inches
Since the diameter is twice the radius, then
The raduis = 20/2 = 10 inches
Then the area of it is
[tex]\begin{gathered} A_1=\pi(r)^2 \\ A_1=3.14(10)^2 \\ A_1=3.14(100) \\ A_1=314 \end{gathered}[/tex]The area of the first pizza is 314 square inches
Since the diameter of the other area is 12 inches, then
The radius = 12/2 = 6 inches
Then the area of it is
[tex]\begin{gathered} A_2=3.14(6)^2 \\ A_2=3.14(36) \\ A_2=113.04 \end{gathered}[/tex]Then the area of the second pizza is 113.04 x 2 = 226.08 square inches
Since the area of the first offer is greater than the area of the second offer, then
The first size gives more pizza
Type in the value ol 29 С A 21 20 B sin A= COSA = tanA= sinC = cosC =
Answers
Given,
The measure of side AC is 29.
The measure of side AB is 20.
The measure of side BC is 21.
The angle ABC is right angle.
The expression of sin in trigonometric ratio is,
[tex]\begin{gathered} \sin \text{ A=}\frac{\text{side opposite to angle A}}{\text{Hypotenuse}} \\ \sin \text{ A=}\frac{21}{29} \\ \sin \text{ C=}\frac{\text{side opposite to angle C}}{\text{Hypotenuse}} \\ \sin \text{ C=}\frac{20}{29} \end{gathered}[/tex]The expression of cos in trigonometric ratio is,
[tex]\begin{gathered} \cos \text{ A=}\frac{\text{side adjacent to angle A}}{\text{Hypotenuse}} \\ \cos \text{ A=}\frac{20}{29} \\ \cos \text{ C=}\frac{\text{side adjacent to angle C}}{\text{Hypotenuse}} \\ \cos \text{ C=}\frac{21}{29} \end{gathered}[/tex]The expression of tan in trigonometric ratio is,
[tex]\begin{gathered} \tan \text{ A=}\frac{\text{side opposite to angle A}}{\text{side adjacent to angle A}} \\ \tan \text{ A=}\frac{21}{20} \\ \tan \text{ C=}\frac{\text{side opposite to angle C}}{\text{side adjacent to angle C}} \\ \tan \text{ C=}\frac{20}{21} \end{gathered}[/tex]Hence, the value of sin A is 21/29, cos A is 20/29 , tan A is 21/20 and the value of
Perform the indicated operation. 22 6/11 x 1 1/2
Answers
Multiplying the two fractions gives us the result 372/11
Here, we are given an expression- 22 6/11 x 1 1/2
To multiply these fractions, we first need to first convert the mixed fraction into an improper fraction. This can be done as follows-
22 6/11 = (22 * 11 + 6)/ 11
= (242 + 6)/ 11
= 248/ 11
similarly we have,
1 1/2 = (1*2 + 1)/2
= (2 + 1)/2
= 3/2
Thus, the given expression becomes-
248/ 11 x 3/ 2
= (248 * 3)/ (11 * 2)
= 744/ 22
= 372/ 11
We cannot simplify this fraction further.
Thus, multiplying the two fractions gives us the result 372/11
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Find the coordinate point for that would make ABCD a rhombus. Answer Choices: (3,5), (5,1), (1,1), (3,4)
Answers
A rhomus has te following shape:
therefore, the top part is missing, if we analyze, it should be 5 on the y axis and 3 on the x axis.
Answer: (3,5)
I need help with my algebra
Answers
N 1
we have the ordered pairs
(1,1) and (4,2)
m=(2-1)/(4-1)
m=1/3
the slope is 1/3FINANCE Yetunde is purchasing a refrigerator, which costs $950. The store has a finance option: pay 10% now, and pay the remaining balance
in one year, with a 5% annual simple interest rate applied to the remaining balance.
How much will she pay up front if she uses the finance option? $
How much interest will she pay at the end of one year? $
What is the total cost of the refrigerator after using the one-year finance option? $
What is the total cost of the refrigerator if she pays the balance and interest at 6 months? $
S
Answers
1. The amount that Yetunde will pay upfront if she uses the finance option is $95.
2. The interest she will pay at the end of one year is $42.75.
3. The total refrigerator cost after using the one-year finance option is $992.75.
4. The total cost of the refrigerator if she pays the balance and interest at 6 months is $971.375.
What is a finance charge?A finance charge is the interest cost added to the amount borrowed or used for credit purchases.
Cost of the refrigerator = $950
Finance Option: Initial deposit = 10% = $95 ($950 x 10%)
Balance to be financed = $855 ($950 - $95)
Simple Interest rate = 5%
Simple interest amount = $42.75 ($855 x 5%)
The total cost with finance option is $992.75 ($950 + $42.75)
Simple interest amount at 6 months = $21.375 ($42.75/2)
The total cost at 6 months = $971.375 ($950 + $21.375)
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Find all the missing elements.Round to the nearest tenth.aba = 5b = 2A C = 6BСA = [?]° B =[ 1°C = [ 1°Inter
Answers
Explanation:
Taking into account the law of cosines, we can write the following equation:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Then, replacing the values for a, b, and c, we get:
[tex]\begin{gathered} 5^2=2^2+6^2-2(2)(6)\cos A \\ 25=4+36-24\cos A \\ 25=40-24\cos A \end{gathered}[/tex]Solving for cos A, we get:
[tex]\begin{gathered} 25-40=40-24\cos A-40 \\ -15=-24\cos A \\ \frac{-15}{-24}=\frac{-24\cos A}{-24} \\ 0.625=\cos A \end{gathered}[/tex]Therefore, the value of angle A is:
[tex]\begin{gathered} \cos ^{-1}(0.625)=A \\ 51.3=A \end{gathered}[/tex]Now, we can use the law of sines, we can write the following equation:
[tex]\frac{\sin B}{b}=\frac{\sin A}{a}[/tex]So, replacing the values and solving for B, we get:
[tex]\begin{gathered} \frac{\sin B}{2}=\frac{\sin 51.3}{5} \\ \sin B=\frac{\sin 51.3}{5}\times2 \\ \sin B=0.3121 \\ B=\sin ^{-1}(0.3121) \\ B=18.2 \end{gathered}[/tex]In the same way, Angle C is equal to:
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \frac{\sin C}{6}=\frac{\sin 51.3}{5} \\ \sin C=\frac{\sin51.3}{5}\times6 \\ \sin C=0.9365 \\ C=\sin ^{-1}(0.9365) \\ C=69.5 \end{gathered}[/tex]So, the answers are:
A = 51.3°
B = 18.2°
C = 69.5°
Use the following figure and information to complete the proof. Given: m∠4=m∠2m∠5=m∠3m∠DBE=180∘ Prove: m∠1+m∠2+m∠3=180∘ Parallel lines m & n. Triangle A B C with A & C on n & B on m. A is to the left of C with angle 2 at A & angle 3 is at C. B is above A & C with angles 4 3 & 5 at C from left to right.© 2019 StrongMind. Created using GeoGebra. Match each numbered statement in the proof to its correct reason.
Answers
Explanation:
The given information is
m∠4 = m∠2
m∠5 = m∠3
m∠DBE = 180
The angle addition postulate says that the angle that the sum of the angles 4, 1, and 5 is equal to the angle DBE, so we can write the following equation
m∠4 + m∠1 + m∠5 = m∠DBE
But, we know that m∠DBE = 180, so by transitivity, we get:
m∠4 + m∠1 + m∠5 = 180
Then, we also know that m∠4 = m∠2 and m∠5 = m∠3, so we can substitute the angles to get
m∠2 + m∠1 + m∠3 = 180
Therefore, we can change the order by the commutative property to get
m∠1 + m∠2 + m∠3 = 180
Answer:
So, the answer is
The accompanying table shows the median household income (in dollars) for 25 randomly selected regions. Complete parts (a) through (g) below.B!: Click the icon to view the table of data.(a) Construct a frequency distribution. Use a first class having a lower class limit of 35,000 and a class width of 5000.IncomeFrequency
Answers
Step 1:
Draw a table with class intervals to construct the frequency distribution table.
Step 2:
Choose a lower class and a class interval.
Lower class limit = 35,000
Class interval = 5000
Step 3:
Get the smallest and largest values from the table
Smallest value = 39712
Largest value = 67729
Step 4:
Draw the table using the class interval.
a) Frequency distribution table
Brad stands 30 feet from a tree. He estimates the angle of elevation from a point onthe ground 30 feet from the tree to the top of the tree to be 60° as shown below.60°30 feetWhich of the following is closest to the height of the tree?
Answers
To determine the height of tree using trigonometric ratio,
The average American student is in class 330 minutes/day. How many seconds/day is this?
Answers
The given time duration is
330 minutes/day
So converting it into seconds, we know that 60 seconds is 1 minute, therefore,
[tex]330\frac{\text{ minutes}}{\text{day}}=330\times\frac{60\sec onds}{day}=19800\text{ seconds/day}[/tex]Thus the answer is 19800 seconds/day.
Match each equation with its solution set.2(5 – 4x) = 8x + 2a. no solution8(x + 5) = 8x + 40b. all real numbers2(5 – 4x) = 2 – 8xc. 1/28(x + 5) = 8x + 5d. 2
Answers
To match the equation with its solution set we need to solve each of them. Let's do that
First equation:
[tex]\begin{gathered} 2(5-4x)=8x+2 \\ 10-8x=8x+2 \\ 8x+8x=10-2 \\ 16x=8 \\ x=\frac{8}{16} \\ x=\frac{1}{2} \end{gathered}[/tex]Second equation:
[tex]\begin{gathered} 8(x+5)=8x+40 \\ 8x+40=8x+40 \end{gathered}[/tex]Since both sides of the equation are exactly the same expression we conclude that this equation is satisfied by all real numbers.
Third equation:
[tex]\begin{gathered} 2(5-4x)=2-8x \\ 10-8x=2-8x \\ 8x-8x=2-10 \\ 0=-8 \end{gathered}[/tex]Since the last line is a contradiction we conclude that this equation has no solutions.
Fourth equation:
[tex]\begin{gathered} 8(x+5)=8x+5 \\ 8x+40=8x+5 \\ 8x-8x=5-40 \\ 0=-35 \end{gathered}[/tex]Once again we have a contradiction in the last line, then this equation has no solutions.
Then the correct match is:
First equation with c.
Second equation with b.
Third equation with a.
Fourth equation with a.
1.Emily needs to make party hats in the shape of a cone. Shewants the hat to have a radius of 6 inches and a height of15 inches. What is the volume of the party hat?a) 565.2b) 94.2c) 2260.8d) 188.4
Answers
Emily needs to make party hats in the shape of a cone. She
wants the hat to have a radius of 6 inches and a height of
15 inches. What is the volume of the party hat?
a) 565.2
b) 94.2
c) 2260.8
d) 188.4
the volume of a cone is equal to
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]we have
pi=3.14
r=6 in
h=15 in
substitute
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot6^2\cdot15 \\ V=565.2\text{ in3} \end{gathered}[/tex]answer is option A
Heather is six years younger than her husband Ryan. Thesum of their ages is 52. How old is Ryan23293146
Answers
Let's begin by listing out the information given to us:
Ryan (r) = r
Heather (h) = r - 6
[tex]\begin{gathered} r+h=52 \\ h=r-6 \\ r+r-6=52 \\ 2r-6=52 \\ 2r=52+6 \\ 2r=58 \\ r=\frac{58}{2}=29 \\ r=29 \\ \\ \therefore Ryan^{\prime}s\text{ age is 29 years old} \end{gathered}[/tex]Therefore, Ryan is 29 years old
Answer:74
Step-by-step explanation:
Josephine can correct her students’ test papers in 7 hours, but if her teacher’s assistant helps, it would take them 5 hours. How long, in hours and minutes, would it take the assistant to do it alone. Write in mixed units
Answers
Answer: it will take the assistant to do it alone 17 1/2 hours
Explanation:
Let x represent the number of hours it will take the assistant to do it alone. This means that the unit work rate per hour is 1/x
If Josephine can correct her students’ test papers in 7 hours, it means that the unit work rate per hour is 1/7
If both of them can do the job in 5 hours, it means that their combined unit rate is 1/5
Since the rates are independent, it means that
1/x + 1/7 = 1/5
The lowest common multiple of the denominators is 35x. Multiplying through by 35x, we have
35 + 5x = 7x
7x - 5x = 35
2x = 35
x = 35/2 = 17/2
it will take the assistant to do it alone 17 1/2 hours
Which statement about this equatiin is true? 3+x=2-3x
1. The equation has no solution
2. The equation has one solution
3. The equation has infinitely many solutions
Answers
The equation has only one solution.
What is solution of equation?Equation solutions are numerical numbers that meet the requirements of the equation. When our answers are used to replace the variables in the equations, true assertions are obtained.
A mathematical equation proves the equality of two expressions. There is a mathematical formula: 4 + 4 = 8. A mathematical formula that has one or more variables is called an algebraic equation. Therefore, (2x + 5 = 35) is a linear equation with one variable. Its graph is a straight line, and its first-degree variable is (x).
Given
3+x = 2-3x
3-2 = -3x - x
1 = -4x
x = -1/4
Hence, x has only one value.
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