Answer:
x=49
Step-by-step explanation: If we have the equation 2x-45=x+4 we would first subtract x from both sides of the equation giving us x-45=4. We then have to isolate x to do this we add 45 to both sides giving us the answer x=49.
Dan plays basketball on his high school team. During
the last game Dan scored 18 points, while for the
season he averages 20 points per game. What percent
of Dan's average did he score during this game?
The percent of Dan's average did he score during this game is 11.11%
What percent of Dan's average did he score during this game?Dan's score in the high school basketball team during last game= 18 points
Dan's score in the high school basketball team during this season = 20 points
Percent of Dan's score during this game = (20 - 18) / 18 × 100
= 2/18 × 100
= 11.11%
In conclusion, Dan scored an average percentage of 11.11% during this game.
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A survey stopped men and women at random to ask them where they purchased
groceries, at a local grocery store or online. Results are shown in the table below, but
some values are missing. Fill in the missing values.
Answer:
1. Women
Store
66-34= 32
Online
13
Total
32+13= 45
2. Men
Total
34+9=43
3. Total
online
13+9=22
total
66+22= 88
let $l$ be the line with equation $\dbinom{10}{3} \dbinom{-2}{1}t$. let $\mathbf{v}$ be a vector from the origin to a point on $l$. find the minimum value of $\|\mathbf{v}\|$.
The minimum value of [tex]$\|\mathbf{v}\|$[/tex] is zero.
The minimum value of [tex]$\|\mathbf{v}\|$[/tex] is zero, as it is the distance between the origin and a point on the line. To solve this problem, the formula [tex]$\|\mathbf{v}\| = \sqrt{x^2 + y^2}$[/tex] can be used, where x and y are the coordinates of the point on the line. Since the equation of the line is [tex]$\dbinom{10}{3} \dbinom{-2}{1}t$[/tex], the coordinates of the point on the line can be found by substituting [tex]$t = 0$: $x = 10 \cdot 0 - 2 \cdot 0 = 0$, and $y = 3 \cdot 0 + 1 \cdot 0 = 0$[/tex] . Substituting these values into the formula for [tex]$\|\mathbf{v}\|$ gives $\|\mathbf{v}\| = \sqrt{0^2 + 0^2} = 0$[/tex]. Therefore, the minimum value of [tex]$\|\mathbf{v}\|$[/tex] is zero.
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eighty-four percent of products come off the line ready to ship to distributors. your quality control department selects 12 products randomly from the line each hour. let x represent the number of these products that are within specifications. looking at the binomial distribution, if x is less than , the outcome would be considered unusual, and the production line should be repaired. group of answer choices fewer than 7 fewer than 6 fewer than 9 fewer than 8
If 84% of products come off the line ready to ship to distributors, then the probability of a product being within specifications is 0.84.
Since we are selecting 12 products randomly from the line each hour, the number of products within specifications (x) follows a binomial distribution with parameters n = 12 and p = 0.84.
Using a binomial cumulative distribution function (CDF), we can calculate the probability that x is less than a certain value. For example, if x is less than 7, the probability of this outcome would be considered unusual and the production line should be repaired.
So, the answer is "fewer than 7".
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Use this table to find all the missing expense values.
Expenses Budget Percent of Budget
Utilities
5%
Labor
15%
Supplies
30%
Rent $2,400 40%
Advertising
10%
TOTAL
100%
The missing expense values are given as follows:
Utilities: $300.Labor: $900.Supplies: $1800.Advertising: $600. Total: $6000.How to obtain the missing expenses?The missing expenses are obtained applying the proportions in the context of this problem.
The rent expense of $2,400 is 40% of the total expenses, hence the total expenses are given as follows:
0.4x = 2400
x = 2400/0.4
x = $6000.
The utilities expenses are 5% of that, hence:
0.05 x 6000 = $300.
The labor expenses are 15% of the total, hence:
0.15 x 6000 = $900.
The supplies expenses are 30% of the total, hence:
0.3 x 6000 = $1800.
The advertising expenses are 10% of the total, hence:
0.1 x 6000 = $600.
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Which, if any, of the following equations are quadratic equations? How do you know?
x2=10
6x2+2=80
4x3-6=25
2(x+4)2=65
(5x-2)=3x4
Answer:
(5x-2)=3x4
Step-by-step explanation:
add that's in the () first
Answer: .
Step-by-step explanation:
what is x-5>-12 solve for x
Answer:
x>-7
Step-by-step explanation:
x-5>-12
x>5-12
x>-7
x > -7.
Step-by-step explanation:1. Write the expression.[tex]x-5 > -12[/tex]
2. Add "5" ob both sides of the equation.[tex]x-5+5 > -12+5\\ \\x > -7[/tex]
3. Verify your answer.If x >-7 is the correct answer, then substituting x by "-7" in the inequation should make the inequation return the same value on both sides of the inequality symbol (>).
Substituting:
[tex](-7)-5 > -12\\ \\-12 > -12[/tex]
That's correct! x > -7 is the correct answer.
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Clothing Online An online clothing company sells custom sweatshirts. The company charges $2.50 for shipping plus $6.50 for each sweatshirt. Write a linear function rule that models the total cost y (in dollars) for any number of sweatshirts x.
Use pencil and paper. Describe how the linear function rule would change if the shipping charge applied to each sweatshirt.
When there is a single shipping charge, the linear function rule is y =_____
The linear function for the cost is:
f(x) = 6.5*x + 2.5
How to write the linear function?A general linear function is something like:
y = a*x + b
Where a is the slope and b is the y-intercept.
Here we know that there is a fixec charge of $2.50 plus $6.50 for each sweatshirt, then if you buy x of these, the cost will be modeled by the linear function below:
f(x) = 6.5*x + 2.5
The slope is the cost of each item and the y-intercept is the fixed cost.
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22 Answer:
The variables x and y vary directly. Use the given values to write
an equation that relates x and y: x = 4, y = -16
23 Answer:
Find the slope of the graph of the equation: y = 2x + 5
24 Answer:
Find the y-intercept of the graph of the equation: y = 2x + 5
25 Answer:
Find the slope of the graph of the equation: y = 5 - 3x
26 Answer:
Find the y-intercept of the graph of the equation: y = 5 - 3x
27 Answer:
Solve the equation algebraically: 4x - 3 = 2
28 Answer:
Solve the equation algebraically: 9 = 10 - x
29 Answer:
Are the graphs of the two equations parallel lines
y = 2x + 1 and 2y = 4x + 5
a. yes
b. no
30 Answer:
Do the graphs of the two equations demonstrate parallel lines?
y = 4x - x and y = -4x + 3
a. yes
b. no
The slope of the graph of the equation: y = 2x + 5
Slope = 2
The y-intercept of the graph of the equation: y = 2x + 5
Y-intercept = 5
The slope of the graph of the equation: y = 5 - 3x
Slope = -3.
The y-intercept of the graph of the equation: y = 5 - 3x
Y-intercept = 5
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
1) y = 2x + 5 Slope = 2 is the slope of the equation's graph.
2.) The equation's graph's y-intercept is written as y = 2x + 5 Y-intercept = 5.
3) y = 5 - 3x Slope = -3 is the slope of the equation's graph.
4) The graph's y-intercept is as follows: y = 5 - 3x Y-intercept = 5.
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Determine the equation of the parabola of this graph.
taking a looksie at the picture above, we can see the parabola has zeros/solutions at x = -2 and x = 1, we can also see that it passes through (0 , 2) as well, so
[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 1 &\implies x -1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a( x +2 )( x -1 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ a ( 0 +2 )( 0 -1 ) = 2\implies -2a=2\implies a=\cfrac{2}{-2}\implies \boxed{a=-1} \\\\[-0.35em] ~\dotfill\\\\ -(x+2)(x-1)=y\implies -(x^2+x-2)=y\implies {\Large \begin{array}{llll} -x^2-x+2=y \end{array}}[/tex]
Check the picture below.
I need help with the 2 questions. What is the mean age of the employees to the nearest year?
What is the median age of the employees?
Consider a given function.
find a and b .
The values of a and b, considering the range of the function, are given as follows:
a = -3.b = 4.What is the range of a function?The range of a function is the set that contains all the output values that can be assumed by the function.
Hence, considering the graph, the range of a function is given by the values of y from the graph.
The minimum and maximum value of the function are given as follows:
Minimum of -3.Maximum of 4.Hence the values of a and b are given as follows:
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use cylindrical shells to find the volume of the solid that is generated when the region that is enclosed by the given curves is revolved about the x-axis. y
The volume of the solid that is generated when the region that is enclosed by the given curves V=253/5π
When the volume of a solid is calculated by using the shell method, the result will be a definite integral that represents the sum of the volumes of infinite thick cylinders.
If the axis of rotation is horizontal, the cylinders are horizontal same. The volume of a horizontal cylinder will be 2πrh dy.
The graph defines the area enclosed by a parabola concave upwards, the y-axis, and the line x = 3 in the first quadrant.
There is the volume of the solid is calculated by using the formula:
[tex]V=2\pi \int\limits^d_c {y[g(y)-h(y)]} \, dy[/tex]
y is the radius of the cylinder
h is the height of the cylinder.
Given information is that:
g(y)=3, h(y)=y¹/², c=0, d=9
Now plug the values in the formula:
[tex]V=2\pi \int\limits^9_0 {y(3-y^\frac{1}{2} )} \, dy\\\\\\V=2\pi \int\limits^9_0 (3y-y^\frac{3}{2} )} \, dy[/tex]
Solving the integral:
[tex]V=2\pi (\frac{3}{2} y^2-\frac{2}{5} y^\frac{3}{5})|_0^9[/tex]
Apply the fundamental theorem of calculus:
[tex]V=2\pi [(\frac{3}{2} (9)^2-\frac{2}{5} (9)^\frac{3}{5})-V=2\pi (\frac{3}{2} (0)^2-\frac{2}{5} (0)^\frac{3}{5})]\\\\V=2\pi (\frac{243}{10} -0)\\\\V=2\pi (\frac{243}{10})\\[/tex]
V=243/5π
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A rectangular field is four times as long as it is wide. If the perimeter of the field is 560 yards, what are the field’s dimensions?
Answer:
Width=56 yards
length=224 yards
Step-by-step explanation:
let:
Width=x
length= x*4= 4x
perimeter = 2*x + 2*4x
working
[tex](x \times 2) + (4x \times 2) = 560[/tex]
[tex]2x + 8x = 560[/tex]
[tex]10x = 560[/tex]
[tex] \frac{10x}{10} = \frac{560}{10} [/tex]
[tex]x = 56[/tex]
[tex]4x = 56 \times 4 = 224[/tex]
width =56 yards
length = 224 yards
The table gives the volume of cylinders where the height is a function of the radius of the base. Given radius, r, the height can be modeled with the function h(r), the base area of the of the cylinder with the function B(r), and the volume of the cylinder with the function V(r).
The volume of the cylinder will be 138.2 inches³
How to calculate the volumeFrom the information, the shape has a height 3 in more than 4 times the radius of the cylinder's base.
The volume of a cylinder is equal to V = πr²h
where
r is the radius of the base
h is the height
In the problem, h = 3 + 4r
r = 2 inches
To calculate h, h = 3 + 4 × 2
h = 11 inches
The volume of a cylinder is equal to:
v = πr²h
v = π × 2² × 11
v = 44π inches³
V = 138.2 inches³
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Write a function rule for the volume of the cylinder shown at the right with a height 3 in more than 4 times the radius of the cylinder's base. What is the volume of the cylinder when it has a radius of 2 in?
to study this, you have sleep-deprived subjects (such as parents of newborn babies or night-shift workers) record the number of minutes they sleep each night and take a series of motor performance assessments, with 1 minute being the smallest unit on the scale. suppose the first subject sleeps 250 minutes. determine the real limits of 250.
the real limits are; Lower Real Limits = 249.5 and Upper Real Limits = 250.5
Given the data in the question;
1 minute being the smallest unit on the scale
so we say; 1/2 which 0.5 minutes which we will use to calculate pur real limits time;
given that; the first subject sleeps 250 minutes
so
Lower Real Limits will be;
Lower Real Limits will = 250 - 0.5 = 249.5
Also our Upper Real Limits will be;
Upper Real Limits = 250 + 0.5 = 250.5
Therefore; the real limits are;
Lower Real Limits = 249.5
Upper Real Limits = 250.5
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is 5/11 closer to 0,1/2,1
Based on the given task content; 5/11 is closer to 1/2.
How to solve fractions?A fraction is a number which has a numerator and a denominator. A numerator refers to the upper or top value while a denominator refers to the lower or bottom value of a fraction.
5/11
= 0.454545454545454
Approximately,
= 0.5
1/2 = 0.5
Hence, 1/2 is closer to 5/11
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1.5.2For the telephone usage model of Example 1.18, let Bm denote the event that a call is billed for m minutes. To generate a phone bill, observe the duration of the call in integer minutes (rounding up). Charge for M minutes M = 1,2,3,... if the exact duration T is M-1
(a) The probability that a call is classified as long (L) is [tex]$P[L] = 1 - P[B_3] = 1 - \alpha (1-\alpha)^2 = 0.829$.[/tex]
(b) The probability that a call will be billed for nine minutes or less is
[tex]P[B1] + P[B2] + P[B3] + P[B4] + P[B5] + P[B6] + P[B7] + P[B8] + P[B_9] = \alpha + \alpha(1-\alpha) + \alpha(1-\alpha)^2 + \alpha(1-\alpha)^3 + \alpha(1-\alpha)^4 + \alpha(1-\alpha)^5 + \alpha(1-\alpha)^6 + \alpha(1-\alpha)^7 + \alpha(1-\alpha)^8 = 0.958[/tex]
Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is expressed as a number from 0 to 1, with 0 indicating that an event is impossible and 1 indicating that it is certain to occur. Probability is used to calculate the chance of a random event happening or to predict the outcome of a situation. Probability theory is also used to describe the underlying mechanics and dynamics of random phenomena
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Complete question:
For the telephone usage model of Example 1.18, let [tex]$B_m$[/tex] denote the event that a call is billed for $m$ minutes. To generate a phone bill, observe the duration of the call in integer minutes (rounding up). Charge for M minutes [tex]$M=1,2,3, \ldots$[/tex] if the exact duration T is [tex]$M-1 < t \leq M$[/tex]. A more complete probability model shows that for $m=1,2, \ldots$ the probability of each event [tex]$B_m$[/tex] is
[tex]$$P\left[B_m\right]=\alpha(1-\alpha)^{m-1}$$[/tex]
where [tex]$\alpha=1-(0.57)^{1 / 3}=0.171$[/tex]
(a) Classify a call as long, L, if the call lasts more than three minutes. What is [tex]$P [L]$[/tex] ?(b) What is the probability that a call will be billed for nine minutes or less?W=0+4T
640-7t=W
Please help me
Answer:
2560/11
Step-by-step explanation:
�
=
640
11
and
�
=
2560
11
A transportation commission studies driving times between two cities to determine whether the construction of a new highway reduced commute times. Times for 4040 cars driving on the old highway and times for 5050 cars driving on the new highway are obtained. A summary of the data obtained from the study is given below.Highway: Mean commute times; Population standard deviation1 (Old); 5.35; 0.52 (New); 4.95; 0.81)What is the standard error? Type as: #.###2)What is the z-score? Type as: #.###3) What is the p-value? Type as: #.######
Based on the provided information, standard error is 0.138, z-score is 2.898, and p value is 0.0013995.
The standard error of a statistic refers to the standard deviation of its sampling distribution or an estimate of that standard deviation. It indicates how different the population mean is likely to be from a sample mean. Standard error of two samples is given by:
SE = √((S1^2)/n1+(S2^2)/n2)
In the given case s1 = 0.5, n1 = 40, s2 = 0.8, and n2 = 50. Hence,
SE = √(〖0.5〗^2/40+〖0.8〗^2/50)=0.138
Z-score for two samples is given by:
z = ((x1-x2)/SE) where x1 and x2 are sample means
In the given case x1= 5.35 and x2 = 4.95. Hence,
z = ((x1-x2)/SE) = (5.35-4,95)/0.138=2.898
The p -value from the table is when p(x >z) = 0.0013995.
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The table shows the number of students graduating from a university in selected years. Use a calculator to write a cubic model for the number of graduates in a given year since 1990. Then use the model to estimate the number of graduates in 2001.
P(x) ≈ 27.13x3 − 473.44x2 + 2829.33x − 4381.69
The estimated the number of graduates in 2001 is 5,565.
P(x) ≈ −473.44x2 + 2829.33x − 4381.69
The estimated the number of graduates in 2001 is 4,133.
P(x) ≈ 473.44x2 − 2829.33x + 4381.69
The estimated the number of graduates in 2001 is 3,535.
P(x) ≈ −27.13x3 + 473.44x2 − 2829.33x + 4381.69
The estimated the number of graduates in 2001 is 2,504.
The cubic regression equation is y = 27.13x^3 - 473.44x^2 + 2829.33x - 4381.69 and the estimated the number of graduates in 2001 is 5565
How to determine the cubic regression equationFrom the question, we have the following parameters that can be used in our computation:
See attachment
Using a graphing calculator, we have the following summary:
a = -4381.6892b = 2829.3314c = -473.4406d = 27.1349Standard Error of Regression: 81.5267Coefficient of determination R²: 0.9978The model from the above summary is
y = 27.1349x^3 - 473.4406x^2 + 2829.3314x - 4381.6892
Approximate
y = 27.13x^3 - 473.44x^2 + 2829.33x - 4381.69
In the year 2001, we have
x = 11
So, we have
y = 27.13 * 11^3 - 473.44 * 11^2 + 2829.33 * 11 - 4381.69
Evaluate
y = 5565
The estimated the number of graduates in 2001 is 5565
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the united states of of representatives has 35 more members than four times the number of members in the unites states senate. define a variable and write an expression to represent the number of members in the house of representatives. Then find the number of members in the house of representatives, if there 100 members in the senate.
There are 435 members in the House of Representatives.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
Let's call the number of members in the Senate "s".
The expression for the number of members in the House of Representatives is "h".
According to the problem, there are 35 more members in the House than four times the number of members in the Senate, so the expression for the number of members in the House is:
h = 4s + 35
If there are 100 members in the Senate, then we can substitute this value into the expression:
h = 4 × 100 + 35
h = 435
So, there are 435 members in the House of Representatives.
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A+b+c=90 and 12a+10b+6c=870 solve for a,b, and c
Answer:
Step-by-step explanation:
You can solve for a, b, and c by using a system of linear equations.
Starting with the first equation:
a + b + c = 90
You can isolate a by subtracting b and c:
a = 90 - b - c
Next, substitute the expression for a into the second equation:
12(90 - b - c) + 10b + 6c = 870
Expanding the equation:
1080 - 12b - 12c + 10b + 6c = 870
Combining like terms:
1070 - 2b + -6c = 870
Adding 2b and 6c to both sides:
1070 = 870 + 2b + 6c
Subtracting 870 from both sides:
200 = 2b + 6c
Dividing both sides by 2:
100 = b + 3c
Finally, subtracting 3c from both sides:
100 - 3c = b
To find c, substitute the expressions for a and b back into the first equation:
a + b + c = 90
90 - b - c + b + c = 90
90 - c = 90
-c = 0
Therefore, c = 0.
To find b, substitute c = 0 into the expression for b:
100 - 3c = b
100 = b
Therefore, b = 100.
Finally, to find a, substitute b = 100 and c = 0 into the expression for a:
a = 90 - b - c
a = 90 - 100 - 0
a = -10
Note that negative values for a, b, and c are possible, but not necessarily meaningful for this specific problem or context.
The solution is:
a = -10
b = 100
c = 0
Write by which rule you know the triangles are congruent, or write CNBD (Cannot Be Determined). Segments and angles are congruent only if marked congruent. FAD congruent to FED by
The congruency rule that shows us that ΔBLK ≅ ΔACK by; SAS Congruency Postulate
How to determine the Congruency Theorem?The image showing the triangles tell us that;
∠BKL ≅ ∠CKA by opposite angles theorem
Likewise we see that BL is parallel to AC and as such;
∠BLK ≅ ∠ACK by alternate angles theorem
Similarly, we will also see that;
∠LBK ≅ ∠CAK by alternate angles theorem
Finally, we see that BL ≅ CA and as such we can conclude that ΔBLK is congruent to ΔACK by SAS Congruence Postulate
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Find a formula for the piecewise function where the taxable income is the input, and the tax is the output using the table.
PLEASE HELP I AM REALLY STRUGGLING WITH THIS
I have added a photo of the table.
The piecewise function of the tax expressed below
How to determine the piecewise functionFrom the question, we have the following parameters that can be used in our computation:
The table of values
To determine the piecewise function, we make use of the following variables:
x = taxable income
f(x) = tax
Using the above and the table of values as guides, we have the following:
f(x) = 0.1x, 0 ≤ x ≤ 9700
f(x) = 970 + 0.12(x - 970), 9701 ≤ x ≤ 39475
f(x) = 4543 + 0.22(x - 39475), 39476 ≤ x ≤ 84200
f(x) = 14382.5 + 0.24(x - 84200), 84201 ≤ x ≤ 160725
f(x) = 32748.5 + 0.32(x - 160725), 160726 ≤ x ≤ 204100
f(x) = 46628.5 + 0.35(x - 204100), 204101 ≤ x ≤ 510300
f(x) = 153798.5 + 0.37(x - 510300), x > 510300
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(-1,4), slope =-2
Write the point slope form of the equation of the line through the given point with the given slope. Then, rewrite the equation into slope intercept form.
The point slope form of the equation of the line through the given point with the given slope is y - 4 = -2(x + 1).
The equation in slope intercept form is y = -2x + 2.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-1, 4), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = -2(x - (-1))
y - 4 = -2(x + 1)
Next, we would rewrite the equation in slope-intercept form as follows;
y - 4 = -2(x + 1)
y = -2x - 2 + 4
y = -2x + 2
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Which of the following is a solution to this inequality?
y less than two thirds times x plus 2
(0, 3)
(−3, 1)
(3, 5)
(1, 2)
The point that is a solution if the inequality:
y < (2/3)*x + 2
is (1, 2).
Which one is a solution of the inequality?Here we want to find a solution for the inequality below:
y < (2/3)*x + 2
To check if an ordered pair is a solution, then we need to replace the values of the ordered point and check if the inequality is true.
If we try with the first point we will get:
3 < (2/3)*0 + 2
3 < 2
That is false.
The correct option is (1, 2)
2 < (2/3)*1 + 2
2 < 8/3
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Need to write an equation
Danielle is working on practice problems and must translate the verbal expression "4 less than twice a number" in to an algebraic expression. Write the algebraic expression that Danielle should write. Type your expression with no spaces.
The translation of the verbal expression "4 less than twice a number" in to an algebraic expression is 2n - 4.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
Danielle is working on practice problems and must translate the verbal expression "4 less than twice a number" in to an algebraic expression.
Let the number is n.
The phrase can be expressed as,
2n - 4.
Therefore, the expression is 2n - 4.
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the bearing of point B from point A is 237 find the bearing from A to B
The bearing from point point A to point B is given as follows:
57º.
How to obtain the bearing between the two points?From the text in this problem, the bearing from point B to point A is given as follows:
237º.
To obtain the inverse bearing, that is, the bearing from point A to point B, we must subtract the bearing from point B to point A given in this problem by 180º, as follows:
237 - 180 = 57º.
Hence the bearing from point point A to point B is of 57º.
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