Solution:
Let the length and the width of the rectangular table be represented as L and W respectively.
Given that the length and the width have a ratio of 8 to 5, this implies that
[tex]\frac{L}{W}=\frac{8}{5}[/tex]If the width of the table is 40 in, the length of the table is evaluated as
[tex]\begin{gathered} \frac{L}{40}=\frac{8}{5} \\ \text{cross multiply} \\ 5\times L=8\times40 \\ \implies5L=320 \\ \text{divide both sides by the coefficient of L, which is 5} \\ \text{thus,} \\ \frac{5L}{5}=\frac{320}{5} \\ \therefore L=64\text{ in.} \end{gathered}[/tex]Hence, the length of the table is 64 in.
Joshua opened a bank account with some money he had saved. During the month, he made deposits of $25 and $40, and he made withdrawals of $15 and
$35. At the end of the month, he had $170 in his account. How much money did he have when he opened the account?
A $285
B $155
C $55
D $15
Initially, Joshua had $155 in his account.
How to find the initial amount?Deposits of $25 and $40
Withdrawals = $15, $35
At the end of the month, he had $170 in his account.
Solution:
Let x be the amount of money he had initially.
Then,
x + 25 + 40 - 15 -35 = 170
x + 65 - 50 = 170
x = 170 + 50 - 65
x = 220 - 65
x = 155
Therefore, initially, he had $155 in his account.
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4. What common characteristics will two parabolas in the family f(×) = a(× - 4)(× - 8) have?
• The Same roots
,• The same axis of symmetry
1) If we compare two parabolas from this family, like:
[tex]\begin{gathered} f(x)=-1(x-4)(x-8) \\ g(x)=2(x-4)(x-8) \end{gathered}[/tex]Note that the difference is in the leading coefficient "a".
2) Both parabolas will have the same roots, the same x-intercepts:
[tex]x_1=4,x_2=8[/tex]In addition to this, we can state that both will share the same axis of symmetry:
[tex]\begin{gathered} f(x)=-1(x-4)(x-8) \\ f(x)=\quad -x^2+12x-32_{} \\ h=\frac{-12}{2(-1)}=6 \end{gathered}[/tex]As well as:
[tex]\begin{gathered} g(x)=2(x-4)(x-8) \\ g(x)=2x^2-24x+64 \\ h=\frac{24}{2(2)}=6 \end{gathered}[/tex]Hence, the answer is:
0. Same roots
,1. Same axis of symmetry
Factories often add filler when making meatballs sold by the bag. One factory obtained 90 kg of beef from overseas. They want to add 1.4 oz of filler for each
pound of beef. How many ounces of filler will the factory need in order to make meatballs out of this shipment of beef?
Use 1 Ib=0.45 kg and do not round any
computations.
One factory that obtained 90 kg of total beef from overseas. The company needs 390 oz of meat filler to make meatballs out of this shipment of beef.
What are meat fillers?In processed meat products, starches are frequently employed as fillers to bind water that would otherwise leak out of the product, increasing its texture and sensory qualities.
As cheap fillers or inferior fiber sources, items including corncobs, feathers, soy, cottonseed hulls, peanut hulls, citrus pulp, screening, weeds, straw, and cereal by-products are frequently used.
One factory that has obtained 135 kg of beef from overseas.
They want to add a total of 1.3oz of filler for each pound of beef.
Given is:
0.45 kg = 1 pound
So, 135 kg = 300 pounds
The company that wants to add a total of 1.3 oz of filler for each pound of beef.
So, for 300 pounds they will need = 390 oz of filler.
Therefore, the company needs 390 oz of filler.
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Fill in the missing parts to these two column proofs:
According to the picture:
For the first statement
[tex]AB\cong CD[/tex]The reason is: Given.
This is because it is given in the information to solve the problem.
The second statement must be:
[tex]BC\cong DA[/tex]And the reason is also: Given.
For the third statement:
[tex]AC\cong AC[/tex]The reason is the Reflexive property.
The fourth statement must be:
[tex]\Delta ABC=\Delta ADC[/tex]The reason is Side Side Side congruence postulate.
The fifth statement must be:
[tex]\measuredangle ABC=\measuredangle CDA[/tex]The reason is congruent triangles definition.
Refer to this diagram for the next five statements. Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.
Given: ∠MRS ≅ ∠MRO
m∠MRO + m∠MRS = m∠SRO
This statement is justified by the angle addition postulate.
I need help with this question but no one is helping me! Can someone please help me
Answer: 36.00%
60% can be written as 0.60 and/or 6/10, which simplifies to 3/5 for easier operations. The probability of 2 students both drink coffee with breakfast can be shown as 0.60 • 0.60 = 0.36. This means there is a 36% chance of both students drinking coffee with breakfast in the morning.
Step-by-step explanation:
An electronic store is having an 18% off sale on everything in the store to the nearest cent which of the following could represent regular prices and sale price of items in the store
during the sale choose all that apply
The following that represent the sales price and the regular prices are:
regular price: $55.43, sales price: $45.45
regular price: $29.99, sales price: $24.59
regular price: $652.30, sales price: $534.89
What are the regular prices and the sales price?Percentage is the fraction of a number out of hundred. The sign that is used to represent percentages is %.
When a discount is given on the price of an item, the price of the item would reduce by the given price or by the percent reduction.
Sales price = regular price x (1 - discount)
Sales price = regular price x (1 - 0.18)
Sales price = regular price x 0.82
Sales price when the initial price is $55.43: $55.43 x 0.82 = $45.45
Sales price when the initial price is $29.99: $29.99 x 0.82 = $24.59
Sales price when the initial price is $215.33: $215.33 x 0.82 = $176.57
Sales price when the initial price is $849.50: $849.50 x 0.82 = $696.59
Sales price when the initial price is $652.30: $652.30 x 0.82 = $534.89
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I will need help with this math problem it has three parts to it
a)The smaller break even quantity is 10
b)The quantity that must be sold to maximize the profit= 14.25
c)The maximum profit = $36.13
STEP - BY - STEP EXPLANATION
What to find?
• The smaller break even quantity is
,• The quantity that must be sold to maximize the profit
,• The maximum profit.
Given:
C(x)= 13x + 370
R(x)=70x - 2x²
a) At the break even quantity, the revenue = cost, that is no profit and no loss.
R(x) = C(x)
So that we have;
70x - 2x² = 13x + 370
Re-arrange.
-2x² + 70x - 13x - 370 =0
-2x² +57x - 370 =0
2x² - 57x + 370 = 0
We can now solve the quadratic equation above.
Using the qudaratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]a=2 b=-57 c=370
Substitute the values into the formula and evaluate.
[tex]x=\frac{-(-57)\pm\sqrt[]{(-57)^2-4(2)(370)}}{2(2)}[/tex][tex]x=\frac{57\pm17}{4}[/tex][tex]Either\text{ x=}\frac{57+17}{4}=\frac{74}{4}=\frac{37}{2}[/tex]Or
[tex]x=\frac{57-17}{4}=\frac{40}{4}=10[/tex]x = 37/2 or x=10
We take the smaller value.
Hence, x=10
Therefore, the smaller break even quantity is 10.
b)To find the quantity that will maximize the profit, find the profit function.
p(x) = R(x) - C(x)
P(x) = 70x - 2x² - (13x +370)
= 70x - 2x² - 13x - 370
P(x) =-2x² + 57x - 370
Equate to zero
-2x² + 57x - 370 = 0
2x² - 57x + 370 =0
The maximum is at x = -b/2a
b= -57 and a=2
Substitute the values
x= - (-57) /2(2)
x= 57 /4
x= 14.25
c) To find the maximum profit, simply substitute x=14.25 into the profit function and simplify.
That is;
P(x) =-2x² + 57x - 370
P(14.25) =-2(14.25)² + 57(14.25) - 370
= -406.125 + 812.25 - 370
= 36.125
≈ 36.13
Hence, the maximum profit is $36.13
solve each formula for the indicated letter. circle the letter next to your answer. write the letter in the box below.
(1) d = rt so, r = d/t
(2) a = F/m so, F = ma
(3) p = w/t so, t = w/p
(4) h = V/B so, B = V/h
(5) A = (abc)/(4r) so, r = (abc)/(4A)
(6) P/Q = R/S so, S = QR/P
(7) a = (v-i)/t so, v = at + i
(8) E/e = (R + r)/r so, e = Er/(R+r)
(9) 1/p + 1/q = 1/f so, f = (pq)/(p+q)
(10) 1/p + 1/q = 1/f so, p = qf/(q-f)
(11) 1/R = 1/r1 + 1/r2 so, R = (r1 r2)/(r1 + r2)
(12) 1/t = (1/a) + (1/b) so, b = (at)/(a - t)
(13) A/B = C/D so, C = AD/B
(14) A = h(a+b)/2 so, b = 2A/h - a
(15) V = Q/r1 - Q/r2 so, Q = Vr1 r2/(r2 - r1)
(16) u = F(P/T - E) so, P = (uT + EFT)/F
The area of a trapezoid is A = 12 (b 1 + b 2)h. Which equation represents the area of a trapezoid when solved for b 1?
If the area of a trapezoid is A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex], then the equation represents the value of [tex]b_{1}[/tex] is [tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]
The trapezoid is a quadrilateral with at least one pair of parallel sides is called trapezoid. There are four vertices and four edges in the trapezoid.
The area of the trapezoid A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex]
Where [tex]b_{1}[/tex] and [tex]b_{2}[/tex] are the length of the parallel sides of the trapezoid
h is the height of the trapezoid
A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex]
Move 1/2 to other side
[tex](b_{1}+ b_{2})h[/tex] = 2A
Move h to other side
[tex](b_{1}+ b_{2})[/tex] = [tex]\frac{2A}{h}[/tex]
Move [tex]b_{2}[/tex] to other side
[tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]
Hence, if the area of a trapezoid is A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex], then the equation represents the value of [tex]b_{1}[/tex] is [tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]
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A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag?
A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag?
The number of red marbles in the bag is 114 .
in the question ,
it is given that ,
total number of marbles in the bag = 120 marbles
let the number of red marbles [tex]=[/tex] r
let the number of black marbles [tex]=[/tex] b
so , According to the question
b + r = 120 ...eqn(1)
also given that for every black marble there is 19 red marbles
which is represented by , r = 19b
Substituting r = 19b in eqn (1) , we get
b + 19b = 120
simplifying further , we get
20b = 120
b = 6
and r = 19(6) = 114
Therefore , The number of red marbles in the bag is 114 .
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Convert 39 yards into miles. Round your answer to the nearest hundredth.
The conversion from yards to miles is given by:
[tex]1\text{ mile }\to1760\text{ yards}[/tex]The conversion factor is:
[tex]\frac{1\text{ mile}}{1760\text{ yards}}[/tex]Now, if we want to know how many miles are 39 yards, we multiply 39 yards by the conversion factor:
[tex]39\text{ yards }\cdot\frac{1\text{ mile}}{1760\text{ yards}}\approx0.02\text{ miles}[/tex]Simplify 2(x+8)+6x Write your answer in factored form
Answer:
8x + 16 is your answer
Step-by-step explanation:
(+2) The
The ratio of
women children = 11:3 and the
ratio of
men children = 5:2
Find the ratio of men:women
The ratio of both men and women 15:22
What is Ratio ?
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Given,
The ratio of men and children = 5:2
The ratio of women and children = 11:3
To find the ratio of men and women we have to divide both the ratio:
men/children/women/children
or,
men/children x children/women
putting the values
=5/2 x 3/11
=15/22
Hence, the ratio of men:women is 15:22
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Simplify using the laws of exponents. Leave your answer an exponential form. The box is to type in the exponent.
Use the next property:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex][tex]\frac{x^8}{x^2}=x^{8-2}=x^6[/tex]Then, the given expression simplified is equal to x^6The average amount of time spent grocery shopping is 45 minutes with a standard deviation of 12 minutes. Using the Empirical Rule, what percent should spend less than 33 minutes?
You have:
mean = 45
standard deviation = 12
Use the following formula:
PLEASE HELP!!!
Explain how the cosine of an angle in the second quadrant differs from the cosine of its reference angle in the unit circle.
Answer:
the second quadrant is negative but the reference angle is exactly the same but positive
Step-by-step explanation:
looking at 150 on the unit circle in the second quadrant you will see the cosine is negative square root 3 divided by 2 but the reference angle is 30 degrees and when we look at the cosine of that which is the x value of what we see it is positive square root of 3 divided by 2
HELP PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the line perpendicular to y = - (2 / 3) · x and the point (4, - 8) is y = (3 / 2) · x - 14.
How to determine the equation of a perpendicular line
Mathematically speaking, lines are represented by equations of the form y = m · x + b, where m and b are the slope and the intercept of the line. Additionally, two lines are perpendicular to each if the product of their slopes is equal to - 1.
First, we determine the slope of the perpendicular line:
m' = - 1 / m
m' = - 1 / (- 2 / 3)
m' = 3 / 2
Second, the intercept of the perpendicular line is:
b = y - m · x
b = - 8 - (3 / 2) · 4
b = - 8 - 6
b = - 14
Then, the equation of the perpendicular line is y = (3 / 2) · x - 14.
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Select the correct answer from each drop-down menu.
A triangle FGH, right angle at H is shown. Base GH has length labeled 3 units. Height FH has length labeled 4 units, and hypotenuse FG has length 5 units.
Use the figure to complete the following statements.
sin(F) =
cos(F) =
sin(G) =
cos(G) =
The value of given expressions will be sin(F) = 3/5, cos(F) = 4/5, sin(G) = 4/5 and cos(G) = 3/5.
A triangle may be defined as a closed figure having three sides and three angle, the sum of which is equal to 180°. A right-angled triangle is the one which has one angle as 90°. We consider a right-angled triangle FGH which is right-angled at H. The sine of any angle is given by the division of Perpendicular to its Hypotenuse. The cosine of any angle is given by the division of Base to its Hypotenuse. Now, we need to find
sin(F) = Perpendicular/Hypotenuse, for angle at F perpendicular will be GH and Hypotenuse will be FG. So, sin(F) = 3/5
cos(F) = Base/Hypotenuse, for angle at F Base will be FH and Hypotenuse will be FG. So, cos(F) = 4/5
sin(G) = Perpendicular/Hypotenuse, for angle at G perpendicular will be FH and Hypotenuse will be FG. So, sin(F) = 4/5
cos(G) = Base/Hypotenuse, for angle at G Base will be GH and Hypotenuse will be FG. So, cos(F) = 3/5
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HELP PLSSS
(Attached to image)
The inequality is lies between the 5.26 < 5.71
The correct option is (a)
Given,
From the figure,
To see the number line and determine the which of the expression is true.
What is Inequality?
Inequality is defined as an equation that does not contain an equal sign.
Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The number line goes from 5.0 to 6.0 with 9 labeled marks in between.
Each mark increases by point one
There are five labeled points.
A point labeled 5.04 is between 5.0 and 5.1.
A point labeled 5.26 is between 5.2 and 5.3.
A point labeled 5.4 is at the mark labeled 5.4
A point labeled 5.520 is between 5.5 and 5.6.
A point labeled 5.71 is between 5.7 and 5.8.
Then the ascending order of the number line will be :
5.04 < 5.26 < 5.4 < 5.52 < 5.71
Hence, The correct option is (a)i.e., 5.26 < 5.71
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answers pleaseeee
im struggling
Answer:
y=3/4x-2
Step-by-step explanation:
slope=3/4x
y-intercept=-2
Thursday
Each 4th grade class at Garza Elementary collected plastic water bottles to recycle.
Each number on the stem and leaf plot represents how many bottles each class
brought in. Record each answer in the blank box next to each question.
Help fill the table please.
1. how many fourth grade classes brought in between 90 and 100 bottles
2. How many classes brought in more than 100 water bottles
3. how many classes brought in less than 99 water bottles
4. How many fourth grade glasses are represented on the stem and leaf plot
The number of students that collected between 90 and 100 bottles is 3.
The number of students that collected more than 100 bottles are 7.
The number of students that collected less than 90 students are 2
The total number of classes represented is 10.
Here is the completed frequency table
Number of bottles collected Classes
90 - 100 3
101 - 110 6
111 - 120 1
What is a stem and leaf plot?A stem-and-leaf plot is a table that splits a number into a stem and leaf. The stem is the first number in the digit while the leaf is the last number. For example the stem in 45 is 4 and the leaf is 5.
An advantage of the stem-and-leaf plot is that it provides an easy way to present and interpret a dataset. A disadvantage of the stem-and-leaf plot is that it cannot be used for a large dataset.
Bottles collected that are between 90 and 100 are 94, 98, 99
Bottles that are greater than 100 are 105, 107, 107, 113, 114, 119, 120
Bottles that are less than 99 are 94, 98
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
-0.07
Step-by-step explanation:
Find the average
what is 42/100 of x over 35%
The value of x in the expression 42/100 of x over 35% is 0.147.
What is an expression?It should be noted that an expression is simply used to show the relationship between the variables or number given.
Therefore, the information will be expressed as:
42/100 × x/35%
= 42/100 × x/0.35
Cross multiply
100 × x = 0.35 × 42
100x = 14.7
Divide.
x = 14.7 / 100
x = 0.147
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Last year, 49% of business owners gave a holiday gift to their employees. A survey of business owners conducted this year indicates that 40% planned to provide a holiday gift to their employees. Suppose the survey results are based on a sample of 85 business owners.
b. Suppose the business owners in the sample do as they plan. Conduct a hypothesis test that can be used to determine whether the proportion of business owners providing holiday gifts had decreased from last year.
State the hypotheses.
Compute the test statistic and p-value.
c. Using a 0.01 level of significance, would you conclude that the proportion of business owners providing gifts decreased?
Using the z-distribution, it is found that:
b)
The hypotheses are: null [tex]H_0: p \geq 0.49[/tex], alternative [tex]H_1: p > 0.49[/tex]The test statistic is of z = -1.69.The p-value is of 0.0455.c) There is not enough evidence to conclude that the proportion of business owners providing gifts decreased using a 0.01 significance level.
What are the hypotheses tested?At the null hypotheses, it is tested if there is no evidence that the proportion decreased from 49%, that is:
[tex]H_0: p \geq 0.49[/tex]
At the alternative hypotheses, it is tested if there is evidence that the proportion decreased from 49%, that is:
[tex]H_1: p > 0.49[/tex]
What is the value of the test statistic?The test statistic is given according to the following rule:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which the parameters are described as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.Considering that 40% of the sample of 85 planned to provide a gift, and the proportion tested is of 49%, the values of the parameters are given as follows:
[tex]\overline{p} = 0.4, p = 0.49, n = 85[/tex]
Hence the test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.4 - 0.49}{\sqrt{\frac{0.4(0.6)}{85}}}[/tex]
z = -1.69.
What is the p-value of the test and what is the conclusion?Considering a left-tailed test, as we are testing if the proportion is less than a value, with z = -1.69, using a z-distribution calculator, the p-value is of 0.0455.
Since the p-value of the test is greater than 0.01, there is not enough evidence to conclude that the proportion of business owners providing gifts decreased using a 0.01 significance level.
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Factories 6ax2-3ay-8bx2+4by
=[2[tex]x^{2}[/tex]-y][3a-4b] This is the factorized form of 6a[tex]x^{2}[/tex]-3ay - 8 b[tex]x^{2}[/tex] + 4by
What is factorization ?To factorize a number, use the factorization formula. Factorization is the process of dividing a whole into components that, when multiplied together, equal the original number. The factorization approach simplifies any algebraic or quadratic equation by using the basic factorization formula, which represents the equations as the product of factors rather than expanding the brackets. Any equation may have an integer, a variable, or the algebraic expression itself as a factor.
6a[tex]x^{2}[/tex]-3ay - 8 b[tex]x^{2}[/tex] + 4by
Rearrange the expression
6a[tex]x^{2}[/tex] -8bx² -3ay +4by
2[tex]x^{2}[/tex][3a-4b] - y[3a-4b]
=[2[tex]x^{2}[/tex]-y][3a-4b]
This is the factorized form of 6a[tex]x^{2}[/tex]-3ay - 8 b[tex]x^{2}[/tex] + 4by
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A radioactive substance decays according to A=A0e−0.0028t, where A0 is the initial amount and t is the time in years. If A0=710 grams, find the time for the radioactive substance to decay to 366 grams. Round your answer to two decimal places, if necessary.
Solution
- The function given is:
[tex]A=A_0e^{-0.0028t}[/tex]- We have been given:
[tex]\begin{gathered} A_0=710g \\ A=366g \end{gathered}[/tex]- We are required to find the time for the radioactive substance to decay. That means we need to find the value of t in the equation.
- Thus, we have that:
[tex]\begin{gathered} 366=710e^{-0.0028t} \\ \text{ Divide both sides by 710} \\ \frac{366}{710}=e^{-0.0028t} \\ \\ \text{ Take the natural log of both sides} \\ \ln(\frac{366}{710})=\ln(e^{-0.0028t}) \\ \\ \ln(\frac{366}{710})=-0.0028t \\ \\ \text{ Divide both sides by -0.0028} \\ \\ \therefore t=\frac{1}{-0.0028}\ln(\frac{366}{710}) \\ \\ t=236.6541...\approx236.65\text{ years} \end{gathered}[/tex]Final Answer
The answer is 236.65 years
One-third of a number is at least four less than the number. Which inequality represents the number?
When one-third of a number is at least four less than the number, the inequality to represent the information is C. n ≥ 6.
What is an inequality?It should be noted that an inequality is simply used to illustrate the expressions that aren't equal.
Let the number be n.
This will be illustrated as:
1/3n ≥ n - 4
Collect like terms
1/3n - n ≥ -4
-2/3n ≥ -4
Multiply through by -3/2
n ≥ -4 × -3/2
n ≥ 6
The value is n ≥ 6.
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1. 3x-4=232. 9-4x=173.6(x-7)=364. 2(x-5)-8= 34Solve equations
1. 3x - 4 = 23
add 4 to both sides
3x - 4 + 4 = 23 + 4
3x = 27
Divide both sides by 3
3x/3 = 27/3
x = 9
2. 9 -4x = 17
subtract 9 from both sides
9 -9 -4x = 17 - 9
-4x = 8
Divide both sides by -4
-4x/-4 = 8/-4
x = -2
3. 6(x-7) = 36
Divide both sides by 6
x -7 = 6
add 7 to both sides
x - 7 + 7 = 6 + 7
x = 13
4. 2(x-5) -8 = 34
Expand
2x -10 -8 = 32
2x - 18 = 32
2x = 32 + 18
2x = 50
Divide both sides by 2
x =25
Question: how do I figure out if a number is rational or irrational
A number is said to be rational if it can be written or transformed into the p/q form, where p and q are integers and q is a non-zero number; if it cannot be written in this form, it is said to be irrational.
Any number that can be written or stated in the p/q form, where p and q are integers and q is a non-zero number, is said to be rational.
A number that is irrational, on the other hand, cannot be stated in p/q form, and its decimal expansion is non-repeating and non-terminating.
Example: √2, √7, √11
Hence we get the required answer.
Learn more about Irrational numbers here:
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