Triangle ABC with coordinates A (3, 4), B (7,7), and C (8, 1) is translated 6 units left and 7 units down.
we have that
the rule of the translation is
(x,y) -------> (x-6, y-7)
Applying the rule to the coordinates of triangle ABC
A(3,4) ------> A'(3-6,4-7)
A'(-3,-3)
B(7,7) ------> B'(7-6, 7-7)
B'(1,0)
C(8,1) --------> C'(8-6,1-7)
C'(2,-6)
Make Sense and persevere An office manageris selecting a water delivery service. AcmeH2O charges a $15 fee and $7.50 per 5-gallonjug. Best Water charges a $24 fee and$6.00 per 5-gallon jug. How many 5-gallonjugs will the office have to buy each monthfor the cost of Best Water to be less than thatof Acme H20?
You have that Acme H2O charges 15 fee and7.50 per 5-gallon. Furthermore, Best water charges 24 fee and 6.00 per 5-gallon.
In order to find the amount of five-gallons that the office have to buy, you can write, in an akgebraic form, the previous realtions, just as follow:
24 + 6x < 15 + 7.5x
That is, cost of Best water less than cost of Acme H20. x is the amount of five-gallons
You solve the previous inequality, as follow:
24 + 6x < 15 + 7.5x subtract 6x both sides and subtract 15 both sides
24 - 15 + 6x - 6x < 15 - 15 + 7.5x - 6x simplify
9 < 1.5x divide between 1.5 both sides
9/1.5 < 1.5x/1.5 simplify
6 < x
6 < x is the same as x > 6. Hence, Office would have to buy lower than 6 five-gallons.
Complete the table using the equation y = 7x +4. NO -1 0 1 2
We will have the following:
*x = -1 => y = 7(-1) + 4 = -3
*x = 0 => y = 7(0) + 4 = 4
*x = 1 => y = 7(1) + 4 = 11
*x = 2 => y = 7(2) + 4 = 18
*x = 3 => y = 7(3) + 4 = 25
11. The table shows the distance, y, a car can travel in feet in x seconds. Speed or Car Time, x (seconds) 5 10 Distance, y (feet) 700 1,400 2,100 2,800 3,500 15 20 25 Based on the information in the table, which equation can be used to model the relationship between x and y? A. y = 140x B.y = 5x C. y = x + 140 D. y = x + 5
In this case, we'll have to carry out several steps to find the solution.
Step 01:
y = distance
x = time
equation = ?
Step 02:
y = k x
if y = 700ft , x = 5 seconds
700 = k * 5
700 /5 = k
140 = k
y = 140 x
The answer is:
y = 140 x
Solve the system by substitution. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter the general solution in terms of x, where x is any real number.)x − 0.2y = 2−10x + 2y = 10(x, y) =
Start multiplying the first equation for 10
[tex]\begin{gathered} 10(x-0.2y=2) \\ 10x-2y=20 \end{gathered}[/tex]add the resulting equation with the second equation
[tex]\begin{gathered} 10x-2y+(-10x+2y)=20+10 \\ 0=30\rightarrow false\text{ }0\ne30 \\ \end{gathered}[/tex]Answer:
There is no solution for the system
A woman wants to measure the height of a nearby building. She places a 9ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building shadow is 117ft, and the pole casts a shadow that is 6.5 ft long. How tall is the building? Round to the nearest foot.
ANSWER
[tex]162ft[/tex]EXPLANATION
Let us make a sketch of the problem:
Let the height of the building be H.
The triangles formed by the shadows of the building and the pole are similar triangles.
In similar triangles, the ratios of the corresponding sides of the triangles are equivalent.
This implies that the ratio of the length of the shadow of the pole to the pole's height is equal to the ratio of the length of the shadow of the building to the building's height.
Hence:
[tex]\frac{6.5}{9}=\frac{117}{H}[/tex]Solve for H by cross-multiplying:
[tex]\begin{gathered} H=\frac{117\cdot9}{6.5} \\ H=162ft \end{gathered}[/tex]That is the height of the building.
The polynomial, 3x2 - x +1, can be classified as a 2nd degree trinomial.True or false?
The polynomial given is:
[tex]3x^2\text{ - x + 1}[/tex]A second degree polynomial is one in which the highest degree of powers is of the second degree.
Basically, a polynomial in which the highest power is 2.
By observing the given polynomial, it is a second degree polynomial.
So, the answer is True.
The median for the set of six ordered data values is 28.5.7,12,23,_,41,49What is the missing value
Given data:
• 7,12,23,,X, ,41,49
• Median : 28.5
• X=?
→When we divide the data set into three equal parts , as in (7;12) (23,X) and (41;49)
→ We get that the median is (23+x )/2= 28.5
23+x = (28.5*2 )
x = 57 -23
x =34Check : 34+23 = 57/2 = 28.5 This means that x = 34 is correct.I paid $17.80 for 5 gallons of gas. using the unit rate. how much would you pay to fill all the way up if my car holds 14 gallons of gas ?
Answer: 67
Step-by-step explanation:
Stan stray kids. !!
I think you have to create a tree diagram PLS HELP
Given a coin and spinner
We need to flip the coin once and spin the spinner once
so, the tree diagram will be as following :
So, the all possible outcomes will be :
H1 , H2 , H3 , H4 , H5 , T1 , T2 , T3 , T4 , T5
Find the number of permutations of the letters in the word. APPLICATION
SOLUTION:
We want to find the number of permutations of the letters in the word APPLICATION.
The word has 11 letters of which A,P,I are repeated two times.
Thus, the formula for the possible permutations of a word with repeated letters is;
[tex]=\frac{n!}{n_1!n_2!...n_k!}[/tex]Thus, we have;
[tex]\frac{11!}{2!2!2!}=4989600[/tex]Enter the equation in standard form.y = 4x - 9
The general form of the standard line is:
[tex]Ax+By=C[/tex]So, we need to change the given equation to the standard form
the given equation is;
[tex]y=4x-9[/tex]Making x and y on the left side
So,
[tex]-4x+y=-9[/tex]And can be written as:
[tex]4x-y=9[/tex]The points (2,-2) and (-4, 13) lie on the graph of a linear equation. What isthe linear equation? *
Answer:
[tex]y=-\frac{5}{2}x+3[/tex]Explanation:
Given the two points on the graph to be (2, -2) and (-4, 13), we can use the point-slope form of the equation of a line below to write the required linear equation;
[tex]y-y_1=m(x-x_1)[/tex]where m = slope of the line
x1 and y1 = coordinates of one of the points
Let's go ahead and determine the slope of the line;
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{13-(-2)}{-4-2}=\frac{13+2}{-6}=-\frac{15}{6}=-\frac{5}{2}[/tex]Let's go ahead and substitute the value of the slope into our point-slope equation using x1 = 2 and y1 = -2;
[tex]\begin{gathered} y-(-2)=-\frac{5}{2}(x-2) \\ y+2=-\frac{5}{2}x+5 \\ y=-\frac{5}{2}x+5-2 \\ y=-\frac{5}{2}x+3 \end{gathered}[/tex]10/13 ÷ 2 and 4/7.....
Given the expression;
[tex]\frac{10}{13}\div2\frac{4}{7}[/tex]First we need to convert the mixed fraction 2 4/7 into improper fraction as shown;
[tex]\frac{10}{13}\div\frac{18}{7}[/tex]Change the division sign to multiplication as shown;
[tex]\begin{gathered} =\frac{10}{13}\times\frac{7}{18} \\ =\frac{5}{13}\times\frac{7}{9} \\ =\text{ }\frac{35}{117} \end{gathered}[/tex]Hence the answer to the expression is 35/117
consider the discrete random variable x given in the table below calculate the mean variance and standard deviation of eggs also calculate the expected value of x around solution to three decimal places if necessary
The mean and the expected value are computed as follows:
[tex]\mu=\sum ^{}_{}x_i\cdot P(x_i)[/tex]Substituting with data:
[tex]\begin{gathered} \mu=1\cdot0.07+6\cdot0.07+11\cdot0.08+15\cdot0.09+18\cdot0.69 \\ \mu=0.07+0.42+0.88+1.35+12.42 \\ \mu=15.14 \\ E(x)=15.14 \end{gathered}[/tex]The variance is calculated as follows:
[tex]\sigma^2=(x_i-\mu)^2\cdot P(x_i_{})[/tex]Substituting with data:
[tex]\begin{gathered} \sigma^2=(1-15.14)^2\cdot0.07+(6-15.14)^2\cdot0.07+(11-15.14)^2\cdot0.08+(15-15.14)^2\cdot0.09+(18-15.14)^2\cdot0.69 \\ \sigma^2=(-14.14)^2\cdot0.07+(-9.14)^2\cdot0.07+(-4.14)^2\cdot0.08+(-0.14)^2\cdot0.09+2.86^2\cdot0.69 \\ \sigma^2=199.9396\cdot0.07+83.5396\cdot0.07+17.1396\cdot0.08+0.0196\cdot0.09+8.1796\cdot0.69 \\ \sigma^2=26.860 \end{gathered}[/tex]And the standard deviation is the square root of the variance, that is:
[tex]\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{26.8604} \\ \sigma=5.183 \end{gathered}[/tex]Rewrite the fraction (4/1)
Answer:
4
Explanation:
Given the fraction 4/1, this can be rewritten as 4 because any number divided by 1 can also be written as the number itself, both are equivalent.
I need help with this problem if anyone can help me please do Find the value of the variable
Answer:
u=11
Explanation:
The statement "The quotient of 44 and 4 is u" can be represented mathematically as:
[tex]u=44\div4[/tex]We can then solve the equation for u.
[tex]\begin{gathered} u=\frac{44}{4}=\frac{4\times11}{4} \\ \implies u=11 \end{gathered}[/tex]The value of u is 11.
asymptoteg(x) = -3*2^x+5
what is x? how would i find the value of x?
Given:
Find-:
The value of "x."
Explanation-:
Use a trigonometric is:
[tex]\tan\theta=\frac{Perpendicular}{\text{ Base}}[/tex]In a triangle:
[tex]\begin{gathered} \text{ Angle}=x \\ \\ \text{ Base }=3 \\ \\ \text{ Pespendicular }=4 \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} \tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}} \\ \\ \tan x=\frac{4}{3} \\ \\ x=\tan^{-1}(\frac{4}{3}) \\ \\ x=53.13 \end{gathered}[/tex]So, the angle is 53 degree
On Thursday Tyler‘s math teacher helped him write the expression T equals -2 parentheses 3+ age parentheses to represent the temperature change for that day indicate all the expressions below the equivalent to T equals negative age parentheses 3+ H parentheses
t = - 2 (3 + h )
Step 1: Expand the parenthesis so that -2 multiplies all the terms in the bracket
t = -2 x 3 - 2 x h
t = - 6 - 2h
Comparing the answer to the options provided
Option C is the best option
Could you please help me with questions 36 & 37?
We have to determine if the functions are linear or not.
We can do this by rearranging the equations in this form:
[tex]y=mx+b[/tex]where m and b are constants.
NOTE: There are many ways to prove that a function is linear, but this is the easiest for this question.
36.
[tex]\begin{gathered} x+\frac{1}{y}=7 \\ \frac{1}{y}=-x+7 \end{gathered}[/tex]As this function can not be written in the form y=mx+b, then it is not linear.
37.
[tex]\begin{gathered} \frac{x}{2}=10+\frac{2y}{3} \\ \frac{x}{2}-10=\frac{2y}{3} \\ \frac{2y}{3}=\frac{1}{2}x-10 \\ y=\frac{3}{2}(\frac{1}{2}x-10) \\ y=\frac{3}{4}x-15 \end{gathered}[/tex]This function is now in the form y=mx+b, where m=3/4 and b=-15. Then, this function is a linear function.
Answer:
36. Non-linear.
37. Linear.
Stanley marked two points on the grid below to show the locations of the fiction section, point F, and the travel section, point T, in a bookstore.
EXPLANATION
We need to calculate the distance between the points (x₁,y₁)=(-8,-3) and (x₂,y₂)=(-3,8) applying the distance equation as shown as follows:
distance=
[tex]\text{Distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting terms:
[tex]\text{Distance = }\sqrt[]{(-3-(-8))^2+(8-(-3))^2}[/tex]Adding numbers:
[tex]\text{Distance}=\sqrt[]{(5)^2+(11)^2}=\sqrt[]{(25+121)}=\sqrt[]{146}[/tex]The shortest distance is sqrt(146)
The probably of selecting a blue pin is 18/25. The chance of selecting a blue pin is _________A.) likely B.) unlikelyC.) impossible
We have the following:
The probability is as follows
[tex]p=\frac{18}{25}=0.72[/tex]That is, we can say that the probability of selecting selecting a blue pin occurs 72% of the time or 18 times out of 25 attempts, therefore we can conclude that it is likely to happen.
The answer is A) likely
Jasper want to venture into the food stall. She plans to create a fund by making deposits of 2,000 in a bank that gives 4% interest compounded quarterly, how much money will be in the fund after 4 years?*228,892.31*101,891.58*228,805.31*103,891.58
We have to calculate the future value of making monthly deposits of $2000 in a bank that gives 4% interest compounded quarterly.
As the frequencies between the deposits and the compounding are different, we have to calculate a equivalent rate that compounds at the same frequency as the deposits (monthly) that keeps the same effective interest rate.
We have a nominal annual rate of 4% that compounds quarterly (m = 3). We can calculate the equivalent nominal annual rate as:
[tex]i=q\cdot\lbrack(1+\frac{r}{m})^{\frac{m}{q}}-1\rbrack[/tex]where m = 3 is the current compounding subperiod, q = 12 is the new compounding subperiod and r = 0.04 is the current annual rate.
We replace the values and calculate:
[tex]\begin{gathered} i=12\cdot\lbrack(1+\frac{0.04}{3})^{\frac{3}{12}}-1\rbrack \\ i\approx12\cdot(1.0133^{\frac{1}{4}}-1) \\ i\approx12\cdot(1.003316795-1) \\ i\approx12\cdot0.003316795 \\ i\approx0.0398 \end{gathered}[/tex]We can now use the interest rate i = 0.0398 compounded monthly as the equivalent rate.
We can calculate the future value of the annuity as:
[tex]FV=\frac{PMT}{\frac{i}{q}}\lbrack(1+\frac{i}{q})^{n\cdot q}-1\rbrack[/tex]Where PMT = 2000, i = 0.0398, q = 12 and n = 4.
We can replace with the values and calculate:
[tex]\begin{gathered} FV=\frac{2000}{\frac{0.0398}{12}}\cdot\lbrack(1+\frac{0.0398}{12})^{4\cdot12}-1\rbrack \\ FV\approx603015.075\cdot\lbrack(1+0.003317)^{48}-1\rbrack \\ FV\approx603015.075\cdot\lbrack1.1722636-1\rbrack \\ FV\approx603015.075\cdot0.1722636 \\ FV\approx103877.55 \end{gathered}[/tex]We get a future value of the annuity of $103,877.55.
We have some differences corresponding to the roundings made in the calculation, but this value correspond to the option $103,891.58.
Answer: $103,891.58
Give the following numberin Base 10.1215 = [ ? ]10
To convert a number in base five to base ten, we shall use the expanded notation with the place value of each of the base five numbers.
The procedure is shown below;
[tex]\begin{gathered} 121_5 \\ \text{Assign place values starting from the right to the left} \\ \text{That is 0, 1 and 2.} \\ We\text{ now have}; \\ (1\times5^2)+(2\times5^1)+(1\times5^0) \end{gathered}[/tex]We can now simplify this as follows;
[tex]\begin{gathered} (1\times25)+(2\times5)+(1\times1) \\ =25+10+1 \\ =36 \end{gathered}[/tex]ANSWER:
[tex]121_5=36_{10}[/tex]From the diagram below, if side AB is 48 cm., side DE would be ______.
The triangle ABC is similar to the triangle DCE.
Hence, we need to find a proportion to find side DE:
If side AB = 48, it will represent the double value of the side DE.
Hence, DE = 48/2 = 24
The correct answer is option b.
Write the first six terms of each arithmetic sequence:a,=200d=20
Recall that the nth term of an arithmetic sequence is as follows:
[tex]\begin{gathered} a_n=a_1+d(n-1), \\ where\text{ }a_1\text{ is the first element and d is the common difference between terms.} \end{gathered}[/tex]We know that:
[tex]\begin{gathered} a_1=200, \\ d=20. \end{gathered}[/tex]Therefore:
1) The second term of the given arithmetic sequence is:
[tex]a_2=200+20(2-1),[/tex]simplifying the above result we get:
[tex]a_2=200+20(1)=220.[/tex]2) The third term of the given arithmetic sequence is:
[tex]a_3=200+20(3-1)=200+20(2)=240.[/tex]3) The fourth therm is:
[tex]a_4=200+20(4-1)=200+20(3)=260.[/tex]4) The fifth term is:
[tex]a_5=200+20(5-1)=200+20(4)=280.[/tex]5) The sixth term is:
[tex]a_6=200+20(6-1)=200+20(5)=300.[/tex]Answer: The first six terms of the given sequence are:
[tex]200,\text{ }220,\text{ }240,\text{ }260,\text{ }280,\text{ }300.[/tex]If the area of a trapezoid is 46 sq. cm. and its height is 4 cm. Find the shorter base if itslonger base is 15 cm.
We are given the following information about a trapezoid.
Area = 46 sq cm
Height = 4 cm
Longer base = 15 cm
We are asked to find the shorter base of the trapezoid.
Recall that the area of a trapezoid is given by
[tex]A=\frac{a+b}{2}\cdot h[/tex]Let us substitute the given values and solve for the shorter side of the trapezoid.
[tex]\begin{gathered} 46=(\frac{a+15}{2})\cdot4 \\ 2\cdot46=(a+15)\cdot4 \\ 92=(a+15)\cdot4 \\ \frac{92}{4}=a+15 \\ 23=a+15 \\ a=23-15 \\ a=8\; cm \end{gathered}[/tex]Therefore, the shorter base of the trapezoid is 8 cm
The function [tex]f(t) = 1600(0.93) ^{10t} [/tex]represents the change in a quantity over t decades. What does the constant 0.93 reveal about the rate of change of the quantity?
Given the function;
[tex]f(t)=1600\cdot(0.93)^{10t}[/tex]The function shows exponential decay with a rate of 0.93
So, the quantity will decrease each year with the rate of 0.93
Which of the following could be the end behavior of f(x) = -x6 + 3x4 + 8x3 – 4x2 – 6? f(x) → ∞ as x → ±∞f(x) → -∞ as x → ±∞f(x) → -∞ as x → -∞ and f(x) → ∞ as x → ∞f(x) → ∞ as x → -∞ and f(x) → -∞ as x → ∞
The given function f is given by:
[tex]f(x)=-x^6+3x^4+8x^3-4x^2-6[/tex]Therefore, as:
[tex]x\to\infty,f(x)\to-\infty[/tex]and
[tex]\begin{gathered} \text{ as } \\ x\to-\infty,f(x)\to-\infty \end{gathered}[/tex]Therefore, the correct answer is:
f(x) → -∞ as x → ±∞
If everyone had the same body proportion your weight in pounds would vary directly with the cube root of your height in feet according to Wikipedia the most recent statics available in 2009 indicated that the average height and weight for an adult male in the United States is 5 feet 9.4 inches in 191 pounds
Given
Height
5 ft 9.4 inches
Weight
191 pounds
Procedure
Let's calculate the equation to define the weight of a person. The structure of the equation would be as follows:
[tex]w=kh^3[/tex]Replacing the values to calculate k
[tex]\begin{gathered} 191=k(5.7833)^3 \\ k=\frac{191}{5.78^3} \\ k=0.98 \end{gathered}[/tex]The equation would be
[tex]w=0.98h^3[/tex]