Answer:
The third table.
Explanation:
In a proportional relationship, the and y values are in a constant ratio.
hello I'm stuck on this question and need help thank you
Explanation
[tex]\begin{gathered} -2x+3y\ge9 \\ x\ge-5 \\ y<6 \end{gathered}[/tex]Step 1
graph the inequality (1)
a) isolate y
[tex]\begin{gathered} -2x+3y\geqslant9 \\ add\text{ 2x in both sides} \\ -2x+3y+2x\geqslant9+2x \\ 3y\ge9+2x \\ divide\text{ both sides by 3} \\ \frac{3y}{3}\geqslant\frac{9}{3}+\frac{2x}{3} \\ y\ge\frac{2}{3}x+3 \end{gathered}[/tex]b) now, change the symbol to make an equality and find 2 points from the line
[tex]\begin{gathered} y=\frac{2}{3}x+3 \\ i)\text{ for x=0} \\ y=\frac{2}{3}(0)+3 \\ \text{sp P1\lparen0,3\rparen} \\ \text{ii\rparen for x=3} \\ y=\frac{2}{3}(3)+3=5 \\ so\text{ P2\lparen3,5\rparen} \end{gathered}[/tex]now, draw a solid line that passes troguth those point
(0,3) and (3,5)
[tex]y\geqslant\frac{2}{3}x+3\Rightarrow y=\frac{2}{3}x+3\text{\lparen solid line\rparen}[/tex]as we need the values greater or equatl thatn the function, we need to shade the area over the line
Step 2
graph the inequality (2)
[tex]x\ge-5[/tex]this inequality represents the numbers greater or equal than -5 ( for x), so to graph the inequality:
a) draw an vertical line at x=-5, and due to we are looking for the values greater or equal than -5 we need to use a solid line and shade the area to the rigth of the line
Step 3
finally, the inequality 3
[tex]y<6[/tex]this inequality represents all the y values smaller than 6, so we need to draw a horizontal line at y=6 and shade the area below the line
Step 4
finally, the solution is the intersection of the areas
I hope this helps you
The ratio of the volume of two spheres is 8:27. What is the ratio of their radii?
We have that the volume of the spheres have a ratio of 8:27.
[tex]undefined[/tex]This means that the relation between linear measures, like the radii, will be the cubic root of that ratio
The sum of a number and -4 is greater than 15. Find the number
x > 19
Explanation:
Let the number = x
The sum of a number and -4 = x + (-4)
The sum of a number and -4 is greater than 15:
x + (-4) > 15
Multiplication of opposite signs gives negative number:
x - 4 > 15
Collect like terms:
x > 15 + 4
x > 19
If each quadrilateral below is a square, find the missing measure
ANSWER
[tex]x=11[/tex]EXPLANATION
The figure given is a square.
Each angle in a square is 90 degrees and the diagonals bisect each angle.
This means that :
[tex]\begin{gathered} 6x-21=45 \\ \text{Collect like terms:} \\ 6x=45+21 \\ 6x=66 \\ \text{Divide through by 6:} \\ x=\frac{66}{6} \\ x=11 \end{gathered}[/tex]That is the value of x.
the equation 5x+7=4x+8+x-1 is true for all real numbers substitute a few real numbers for x to see that this is so and then try solving the equation
The equation 5x+7 = 4x+8+x-1 is true for all real numbers.
Solution for the equation is 5x + 7 = 5x + 7.
Given,
The equation; 5x+7 = 4x+8+x-1
We have to find the solution for this equation.
Here,
5x + 7 = 4x + 8 + x - 1 = 5x + 7
The equation is true for all real numbers;
Lets check;
x = 65 x 6+7 = 4 x 6 + 8 + 6 - 1
30 + 7 = 24 + 13
37 = 37
x = 155 x 15 + 7 = 4 x 15 + 8 + 15 - 1
75 + 7 = 60 + 22
82 = 82
That is,
The equation 5x + 7 = 4x + 8 + x - 1 is true for all real numbers.
The solution for the equation is 5x + 7 = 5x + 7.
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11. Suppose that y varies inversely with x. Write a function that models the inverse function.x = 1 when y = 12- 12xOy-y = 12x
We need to remember that when two variables are in an inverse relationship, we have that, for example:
[tex]y=\frac{1}{x}[/tex]In this case, we have an inverse relationship, and we have that when x = 1, y = 12.
Therefore, we have that the correct relationship is:
[tex]y=\frac{12}{x}[/tex]In this relationship, if we have that x = 1, then, we have that y = 12:
[tex]x=1\Rightarrow y=\frac{12}{1}\Rightarrow y=12[/tex]Therefore, the correct option is the second option: y = 12/x.
Last year, Bob had $10,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 8% simple interest per year. After one year, he received a total of $820 in interest. How much did he invest in each account?
Given:
The total amount is P = $10,000.
The rate of interest is r(1) = 10% 0.10.
The other rate of interest is r(2) = 8%=0.08.
The number of years for both accounts is n = 1 year.
The total interest earned is A = $820.
The objective is to find the amount invested in each account.
Explanation:
Consider the amount invested for r(1) as P(1), and the interest earned as A(1).
The equation for the amount obtained for r(1) can be calculated as,
[tex]\begin{gathered} A_1=P_1\times n\times r_1 \\ A_1=P_1\times1\times0.1 \\ A_1=0.1P_1\text{ . . . . .(1)} \end{gathered}[/tex]Consider the amount invested for r(2) as P(2), and the interest earned as A(2).
The equation for the amount obtained for r(2) can be calculated as,
[tex]\begin{gathered} A_2=P_2\times n\times r_2 \\ A_2=P_2\times1\times0.08 \\ A_2=0.08P_2\text{ . . . . . (2)} \end{gathered}[/tex]Since, it is given that the total interest earned is A=$820. Then, it can be represented as,
[tex]A=A_1+A_2\text{ . . . . . (3)}[/tex]On plugging the obtained values in equation (3),
[tex]820=0.1P_1+0.08P_2\text{ . . . . .(4)}[/tex]Also, it is given that the total amount is P = $10,000. Then, it can be represented as,
[tex]\begin{gathered} P=P_1+P_2 \\ 10000=P_1+P_2 \\ P_1=10000-P_2\text{ . }\ldots\ldots.\text{. .(3)} \end{gathered}[/tex]Substitute the equation (3) in equation (4).
[tex]undefined[/tex]Suppose that y varies inversely with x, and y = 5/4 when x = 16.(a) Write an inverse variation equation that relates x and y.Equation: (b) Find y when x = 4.y =
In general, an inverse variation relation has the form shown below
[tex]\begin{gathered} y=\frac{k}{x} \\ k\to\text{ constant} \end{gathered}[/tex]It is given that x=16, then y=5/4; thus,
[tex]\begin{gathered} \frac{5}{4}=\frac{k}{16} \\ \Rightarrow k=\frac{5}{4}\cdot16 \\ \Rightarrow k=20 \end{gathered}[/tex]Therefore, the equation is y=20/x
[tex]\Rightarrow y=\frac{20}{x}[/tex]2) Set x=4 in the equation above; then
[tex]\begin{gathered} x=4 \\ \Rightarrow y=\frac{20}{4}=5 \\ \Rightarrow y=5 \end{gathered}[/tex]When x=4, y=5.
a= 8 in, b= ? C= 14 in.using pythagorean theorem
by Pythagorean theorem'
[tex]8^2+b^2=14^2[/tex][tex]\begin{gathered} 64+b^2=196 \\ b^2=196-64 \end{gathered}[/tex][tex]\begin{gathered} b^2=132 \\ b=\sqrt[]{132} \\ b=11.48 \end{gathered}[/tex]b = 11.48
Find the solution of this system of linearequations. Separate the x- and y- values with acomma. Enclose them in a pair of parantheses. System of equations4x + 8y = 838x + 7y = 76- 8x - 16y = -1668x + 7y = 76
Given,
System of equation is,
[tex]\begin{gathered} 4x+8y=83\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i) \\ 8x+7y=76\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(ii) \end{gathered}[/tex]Taking the equation (i) as,
[tex]\begin{gathered} 4x+8y=83 \\ 4x=83-8y \\ x=\frac{83-8y}{4} \end{gathered}[/tex]Substituting the value of x in equation (ii) then,
[tex]\begin{gathered} 8x+7y=76 \\ 8(\frac{83-8y}{4})+7y=76 \\ 664-64y+28y=304 \\ 36y=360 \\ y=10 \end{gathered}[/tex]Substituting the value of y in above equation then,
[tex]\begin{gathered} x=\frac{83-8\times10}{4} \\ x=\frac{3}{4} \end{gathered}[/tex]Hence, the value of x is 3/4 and y is 10. (3/4, 10)
System of equation is,
[tex]\begin{gathered} -8x-16y=-166\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i) \\ 8x+7y=76\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(ii) \end{gathered}[/tex]Taking the equation (i) as,
[tex]\begin{gathered} -8x-16y=-166 \\ 8x+16y=166 \\ 4x+8y=83 \\ 4x=83-8y \\ x=\frac{83-8y}{4} \end{gathered}[/tex]Substituting the value of x in equation (ii) then,
[tex]\begin{gathered} 8x+7y=76 \\ 8(\frac{83-8y}{4})+7y=76 \\ 664-64y+28y=304 \\ 36y=360 \\ y=10 \end{gathered}[/tex]Substituting the value of y in above equation then,
[tex]\begin{gathered} x=\frac{83-8\times10}{4} \\ x=\frac{3}{4} \end{gathered}[/tex]Hence, the value of x is 3/4 and y is 10. (3/4, 10)
Given the figure below, determine the angle that is a same side interior angle with respect to1. To answer this question, click on the appropriate angle.
Same side interior angles are angles on the same side of the transversal line, inside the two lines intersected.
<5 is an interior angle, on the same side as <3.
On The left side of the bisector line.
In the figure below, m2 = 49. Find mx 1.
By definition, a Right angle is an angle that measures 90 degrees.
Complementary angles are those angles that add up to 90 degrees.
For this case, you can identify that the angle 1 and the angle 2 are Complementary angles, because when you add them, you get 90 degrees (a Right angle).
Knowing the above, you can set up the following equation:
[tex]m\angle1+m\angle2=90\degree[/tex]Since you know that:
[tex]m\angle2=49\degree[/tex]You can substitute this value into the equation and the solve for the angle 1 in order to find its measure. You get that this is:
[tex]\begin{gathered} m\angle1+49\degree=90\degree \\ m\angle1=90\degree-49\degree \\ m\angle1=41\degree \end{gathered}[/tex]The answer is:
[tex]m\angle1=41\degree[/tex]Write the equation of the function in the graph.. Please show all of your work so i can understand
The vertex form of a parabola is:
[tex]y=a(x-h)^2+k[/tex]where (h, k) is the vertex of the parabola and a is some constant.
From the graph, the vertex is located at (1, 4), that is, h = 1 and k = 4.
Substituting with these values and the point (0, 3), we get:
[tex]\begin{gathered} 3=a(0-1)^2+4 \\ 3-4=a(-1)^2 \\ -1=a\cdot1 \\ -\frac{1}{1}=a \\ -1=a \end{gathered}[/tex]Then, the equation of the function is:
[tex]\begin{gathered} y=-1(x-1)^2+4 \\ y=-(x-1)^2+4 \end{gathered}[/tex]change this standard form equation into slope intercept form. 4x-5y= -17
The slope-intercept form is
[tex]y=mx+b[/tex]We have
[tex]4x-5y=-17[/tex]so we need to isolate the y
[tex]-5y=-4x-17[/tex][tex]y=\frac{-4}{-5}+\frac{-17}{-5}[/tex]We simplify
[tex]y=\frac{4}{5}x+\frac{17}{5}[/tex]ANSWER
The equation in slope-intercept form is
[tex]y=\frac{4}{5}x+\frac{17}{5}[/tex]
which graph show the solution set for -1.1×+6.4>-1.3
Problem
-1.1x + 6.4 > - 1.3
Concept
Solve for x by collecting like terms.
Use this information to answer the following two questions. Mathew finds the deepest part of the pond to be 185 meters. Mathew wants to find the length of a pond. He picks three points and records the measurements, as shown in the diagram. Which measurement describes the depth of the pond? Hide All Z between 13 and 14 meters 36 m 14 m between 14 and 15 meters between 92 and 93 meters Х ag between 93 and 94 meters
it's letter A. Between 13 and 14 meters
Because one side measure 14, and the height (depth) could not be
higher than 14 meters .
The length of the pond can be calculated using the Pythagorean theorem
length^2 = 36^2 + 14^2
length^2 = 1296 + 196
length^2 = 1492
length = 38.6 m
Pls help ASAP!!! Ill give you 5.0
The equivalent equation of 6x + 9 = 12 is 2x + 3 = 4.
Another equivalent equation of 6x + 9 = 12 is 3x + 4.5 = 6
What are equivalent equations?Equivalent equations are algebraic equations that have identical solutions or roots. In other words, equivalent equations are equations that have the same answer or solution.
Therefore, the equivalent equation of 6x + 9 = 12 can be calculated as follows:
6x + 9 = 12
Divide through by 3
6x / 3 + 9 / 3 = 12 / 3
2x + 3 = 4
Therefore, the equivalent equation of 6x + 9 = 12 is 2x + 3 = 4
Another equation that is equivalent to 6x + 9 = 12 is 3x + 4.5 = 6
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what operation helps calculate unit rates and unit prices
Division operation is operation helps calculate unit rates and unit prices.
Division operation -
A rate with 1 as the denominator is referred to as a unit rate. If you have a rate, such as a price per a certain number of items, and the quantity in the denominator is not 1, you can determine the unit rate or price per unit by performing the division operation: numerator divided by denominator.What method do you employ to determine the unit rate?
Simple division of the numerator and denominator yields the unit rate. The outcome tells us how many of the units in the numerator to anticipate for each unit in the denominator.
What in mathematics are rate and unit rate?
A ratio called a rate compares two amounts of DIFFERENT types of UNITS. When expressed as a fraction, a unit rate has a denominator of 1. Divide the rate's numerator and denominator by the denominator to represent the rate as a unit rate.Learn more about Division operation
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Which phrase represents the algebraic expression for n-4.A) The quotient of a number and 4. B) 4 less than a number. C) 4 minus a number. D) 4 more than a number.
B) 4 less than a number.
(6 x 10^-2)(1.5 x 10^-3 + 2.5 x 10^-3)1.5 x 10^3
Given the expression:
[tex]\left(6*10^{-2}\right)\left(1.5*10^{-3}+2.5*10^{-3}\right)1.5*10^3[/tex]Let's simplify the expression.
To simplify the expression, we have:T
[tex]\begin{gathered} (6*10^{-2})(1.5*10^{-3}+2.5*10^{-3})1.5*10^3 \\ \\ =(6*10^{-2})(4.0*10^{-3})1.5*10^3 \\ \\ =(6*4.0*10^{-2-3})1.5*10^3 \\ \\ =(24.0*10^{-5})1.5*10^3 \end{gathered}[/tex]Solving further:
Apply the multiplication rule for exponents.
[tex]\begin{gathered} 24.0*1.5*10^{-5+3} \\ \\ =36*10^{-2} \\ \\ =0.36 \end{gathered}[/tex]ANSWER:
[tex]0.36[/tex]Nora needs to order some new supplies for the restaurant where she works. Therestaurant needs at least 478 forks. There are currently 286 forks. If each set on salecontains 12 forks, write and solve an inequality which can be used to determine s, thenumber of sets of forks Nora could buy for the restaurant to have enough forks.<
Nora needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 478 forks. There are currently 286 forks. If each set on sale
contains 12 forks, write and solve an inequality which can be used to determine s, the
number of sets of forks Nora could buy for the restaurant to have enough forks.
Let
s -----> the number of sets of forks Nora could buy for the restaurant to have enough forks
so
the inequality that represent this situation is
[tex]286+12s\ge478[/tex]solve for s
[tex]\begin{gathered} 12s\ge478-286 \\ 12s\ge192 \\ s\ge16 \end{gathered}[/tex]the minimum number of sets is 16write in exponential form5x5x5
5 x 5 x 5 = 5^3
[tex]\begin{gathered} \\ 5x5x5=5^{3\text{ }}\text{ = 125} \end{gathered}[/tex][tex]=16^{5\text{ }}\text{ = 16 x 16 x 16 x 16 x 16 = 1,048,576}[/tex]Suppose that 27 percent of American households still have a traditional phone landline. In a sample of thirteen households, find the probability that: (a)No families have a phone landline. (Round your answer to 4 decimal places.) (b)At least one family has a phone landline. (Round your answer to 4 decimal places.) (c)At least eight families have a phone landline.
Answer:
(a) P = 0.0167
(b) P = 0.9833
(c) P = 0.0093
Explanation:
To answer these questions, we will use the binomial distribution because we have n identical events (13 households) with a probability p of success (27% still have a traditional phone landline). So, the probability that x families has a traditional phone landline can be calculated as
[tex]\begin{gathered} P(x)=nCx\cdot p^x\cdot(1-p)^x \\ \\ \text{ Where nCx = }\frac{n!}{x!(n-x)!} \end{gathered}[/tex]Replacing n = 13 and p = 27% = 0.27, we get:
[tex]P(x)=13Cx\cdot0.27^x\cdot(1-0.27)^x[/tex]Part (a)
Then, the probability that no families have a phone landline can be calculated by replacing x = 0, so
[tex]P(0)=13C0\cdot0.27^0\cdot(1-0.27)^{13-0}=0.0167[/tex]Part (b)
The probability that at least one family has a phone landline can be calculated as
[tex]\begin{gathered} P(x\ge1)=1-P(0) \\ P(x\ge1)=1-0.167 \\ P(x\ge1)=0.9833 \end{gathered}[/tex]Part (c)
The probability that at least eight families have a phone landline can be calculated as
[tex]P(x\ge8)=P(8)+P(9)+P(10)+P(11)+P(12)+P(13)[/tex]So, each probability is equal to
[tex]\begin{gathered} P(8)=13C8\cdot0.27^8\cdot(1-0.27)^{13-8}=0.0075 \\ P(9)=13C9\cdot0.27^9\cdot(1-0.27)^{13-9}=0.0015 \\ P(10)=13C10\cdot0.27^{10}\cdot(1-0.27)^{13-10}=0.0002 \\ P(11)=13C11\cdot0.27^{11}\cdot(1-0.27)^{13-11}=0.00002 \\ P(12)=13C12\cdot0.27^{12}\cdot(1-0.27)^{13-12}=0.000001 \\ P(13)=13C13\cdot0.27^{13}\cdot(1-0.27)^{13-13}=0.00000004 \end{gathered}[/tex]Then, the probability is equal to
P(x≥8) = 0.0093
Therefore, the answers are
(a) P = 0.0167
(b) P = 0.9833
(c) P = 0.0093
Give a number in scientific notation that isbetween the two numbers on a number line.71 X 103 and 71,000,000
For this problem we have the following two numbers
[tex]71x10^3[/tex][tex]71000000[/tex]Let's convert the two numbers with scientific notation
[tex]71x10^3=71000=7.1x10^4[/tex][tex]71000000=7.1x10^7[/tex]Now we just need to find a number between the two given we know that:
[tex]7.1x10^4<7.1x10^7[/tex]The final answer for this case would be any number between these two numbers and it could be:
[tex]7.1x10^6[/tex]also it could be:
[tex]9.5x10^5[/tex]Or any number between the two given
Answer:
The answer is B,D, And F
Step-by-step explanation:
7.1 × 103 = 7,100
7.1 × 105 = 710,000
Because 7,100 < 710,000 < 71,000,000 then 7.1 × 105 falls between 7.1 × 103 and 71,000,000
What is the equation of the line that is parallel to the graph of y = 2x - 5 and passes through the point (8, 10)?
We know that the equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]To find it we need the slope m and a point that the line passes thorugh. In this case we have the point (8,10) but we don't know the slope. What we know is that the line we are looking for is parallel to the line
[tex]y=2x-5[/tex]We also know that for two lines to be parallel they have the same slope. Then, if we fin the slope of the line y=2x-5, we have the slope of the line we are looking for. To find the slope of the line y=2x-5 we note that it is written in the slope-intercept form
[tex]y=mx+b[/tex]From this we know that the slope is multiplying the x variable when it is written in that form. Hence m=2.
Then the line we are looking for has an slope of 2 and passes through the point (8,10). Pluggin the values in the equation of a line we have.
[tex]y-10=2(x-8)[/tex]Writting it in the slope intercept form we have
[tex]\begin{gathered} y-10=2(x-8) \\ y-10=2x-16 \\ y=2x-16+10 \\ y=2x-6 \end{gathered}[/tex]Then the line parallel to y=2x-5 and passes through the point (8,10) is
[tex]y=2x-6[/tex]A card is drawn from a deck of 52 cards. What is the probability that it is a numbered card (2-10) or a heart?
we know that
Total cards=52
Total numbered card (2-10)=36
Total heart=13
numbered card and heart=9
therefore
The probability is equal to
P=(36+13-9)/52
P=40/52
P=20/26=10/13
The answer is 10/13Perform the indicated operation of multiplication or division on the rational expression and simplify
The division of two fractions is the same as multiplying the first by the inverted second fraction:
Then, in this case:
[tex]\frac{24y^2}{5x^2}\div\frac{6y^3}{25x^2}=\frac{24y^2}{5x^2}\times\frac{25x^2}{6y^3}[/tex]Step 2: multiplication of two fractionsWe multiply two fractions by multiplying the numerators and the denominators:
[tex]\frac{24y^2}{5x^2}\times\frac{25x^2}{6y^3}=\frac{24y^2\times25x^2}{5x^2\times6y^3}[/tex]Step 3: simplifying the numbers of the fractionWe know that
[tex]\frac{25}{5}=5\text{ and }\frac{24}{6}=4[/tex]Then, we can use this in our fraction:
[tex]\begin{gathered} \frac{24y^2\times25x^2}{5x^2\times6y^3}=5\cdot4\frac{y^2x^2}{x^2y^3} \\ \downarrow\text{ since 5}\cdot4=20 \\ 5\cdot4\frac{y^2x^2}{x^2y^3}=20\frac{y^2x^2}{x^2y^3} \end{gathered}[/tex]Step 4: exponents of the resultWe know that if we have a division of same base expressions (same letters), the exponent is just a substraction:
[tex]\begin{gathered} \frac{y^2}{y^3}=y^{2-3}=y^{-1} \\ \frac{x^2}{x^2}=x^{2-2}=x^0=1 \end{gathered}[/tex]Then,
[tex]20\frac{y^2x^2}{x^2y^3}=20y^{-1}\cdot1=20y^{-1}[/tex]Since negative exponents correspond to a division, then we can express the answer in two different ways:
[tex]20y^{-1}=\frac{20}{y}[/tex]Answer:[tex]20y^{-1}=\frac{20}{y}[/tex]A coordinate grid is shown from negative 6 to 6 on both axes at increments of 1. Figure ABCD has A at ordered pair negative 4, 4, B at negative 2, 2, C at negative 2, negative 1, D at negative 4, 1. Figure A prime B prime C prime D prime has A prime at ordered pair 4, 0, B prime at 2, negative 2, C prime at 2, negative 5, D prime at 4, negative 3.
Part B: Are the two figures congruent? Explain your answer.
The two figures ABCD and A'B'C'D' are congruent .
In the question ,
it is given that the coordinates of the figure ABCD are
A(-4,4) , B(-2,2) , C(-2,-1) , D(-4,1) .
Two transformation have been applied on the figure ABCD ,
First transformation is reflection on the y axis .
On reflecting the points A(-4,4) , B(-2,2) , C(-2,-1) , D(-4,1) on the y axis we get the coordinates of the reflected image as
(4,4) , (2,2) , (2,-1) , (4,1) .
Second transformation is that after the reflection the points are translated 4 units down .
On translating the points (4,4) , (2,2) , (2,-1) , (4,1) , 4 units down ,
we get ,
A'(4,0) , B'(2,-2) , C'(2,-5) , D'(4,-3).
So , only two transformation is applied on the figure ABCD ,
Therefore , The two figures ABCD and A'B'C'D' are congruent .
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Consider the function f(x) =cotx. Which of the following are true? 2 answers
Graphing the function f(x) = cot(x) we have the following
We can observe that the function cot(x) has an asymptote at x = 0, and that it has a period of π.
Four more than three times a number, is less than 30. Which of the following is not a solution?61278
Solution
- To solve the question, we simply need to interpret the question line by line.
- Let the number be x.
- "Four more than three times a number" can be written as:
[tex]\begin{gathered} \text{ Three times a number is: }3x \\ \text{ For more than three times a number becomes: }4+3x \end{gathered}[/tex]- "Four more than three times a number is less than 30" can be written as:
[tex]4+3x<30[/tex]- Now, we can proceed to solve the inequality and find the appropriate range of x. This is done below:
[tex]\begin{gathered} 4+3x<30 \\ \text{ Subtract 4 from both sides} \\ 3x<30-4 \\ 3x<26 \\ \text{ Divide both sides by 3} \\ \frac{3x}{3}<\frac{26}{3} \\ \\ \therefore x<8\frac{2}{3} \end{gathered}[/tex]- This means that all correct solutions to the inequality lie below 8.666...
- This further implies that any number greater than this is not part of the solutions of the inequality.
- 12 is greater than 8.666
Final Answer
The answer is 12
