we know that
Rigid motion preserves
1) Length sides
2) Interior angles
In a rigid motion the pre image and the image are congruent
Your business needs to put aside funds to purchase new office equipment in 4 years. You can afford to put aside $250 per month, and you are able to invest in an account offering 3% per year, compounded monthly. How much money will this amount to at the end of this time? $12,732.80 $12,451.67 ООО $27.135.16 $13,014.63
x = 3 %= 3/100 = 0.03/12 = 0.0025
n = 4 years
PMT = 250
FV = future value
[tex]\begin{gathered} FV=PMT\frac{(1+x)^n-1}{x} \\ FV=250\times\frac{(1+0.0025)^{12\times4}-1}{0.0025} \\ FV=\text{ \$}12732.802104 \\ FV=\text{ \$}12732.80 \end{gathered}[/tex]The answer is A.
Please I just need the answer not explantionI’m on a timed homework Question attached below as fileThank you
The ratio between 2 feet and 45 inches will be
[tex]\frac{2\text{ ft}}{45\text{ inches}}[/tex]We can also write 2 ft in inches, and it will be
[tex]2\text{ ft = 24 inches}[/tex]Therefore
[tex]\frac{24\text{ inches}}{45\text{ inches}}=\frac{8}{15}[/tex]The ratio is
[tex]\frac{8}{15}[/tex]A 7.5 % of what amount gives $37.50? ANS. $ _________.
If 7.5% of a certain amount gives $37.50
To obtain the amount
Step 1: let the unknown amount be y
7.5% of y will be:
[tex]\frac{7.5}{100}\times y=\frac{7.5y}{100}=0.075y\text{ }[/tex]Step 2: Equate 0.075y to $37.5 and then solve for y
[tex]\begin{gathered} 0.075y=37.5 \\ \text{divide both sides by 0.075} \\ \frac{0.075y}{0.075}=\frac{37.5}{0.075} \end{gathered}[/tex]Then,
[tex]y=\frac{37.5}{0.075}=500[/tex]Hence, the original amount is $500
Are these lines parallel or not:L1 : (2,-1), (5,-7), and L2: (0,0), (-1,2) A. ParallelB.No
So,
Two lines are parallel when their slopes are the same.
So, let's find the slope of each line, and then compare them.
[tex]\begin{gathered} L_1\colon(x_1,y_1)=(2,-1);\text{ }(x_2,y_2)=(5,-7) \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Replacing the ordered pairs in the equation, we obtain:
[tex]m=\frac{-7-(-1)}{5-2}=\frac{-6}{3}=-2[/tex]Thus the slope of the first line is -2. Let's use the same process to find the slope of the second line:
[tex]L_2\colon(x_1,y_1)=(0,0);\text{ }(x_2,y_2)=(-1,2)[/tex]Given:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\to m=\frac{2-0}{-1-0}=\frac{2}{-1}=-2[/tex]As you can see, the slope of both lines is the same. So, the lines are parallel.
What is the rational expression as a sum of partial fractions?
Rewrite the expression as:
[tex]\frac{-x^2+2x-5}{x^2(x-1)}[/tex]The partial fraction expansion is of the form:
[tex]\frac{-x^2+2x-5}{x^2(x-1)}=\frac{A}{x-1}+\frac{B}{x}+\frac{C}{x^2}[/tex]Multiply both sides by x²(x - 1):
[tex]\begin{gathered} -x^2+2x-5=Ax^2+(x-1)(Bx+C) \\ -x^2+2x-5=-C+(A+B)x^2+(C-B)x \end{gathered}[/tex]Equate the coefficients on both sides:
[tex]\begin{gathered} -5=-C_{\text{ }}(1)_{} \\ 2=C-B_{\text{ }}(2) \\ -1=A+B_{\text{ }}(3) \end{gathered}[/tex]So, from (1):
[tex]C=5[/tex]Replace C into (2):
[tex]\begin{gathered} 2=5-B \\ B=3 \end{gathered}[/tex]Replace B into (3):
[tex]\begin{gathered} -1=A+3 \\ A=-4 \end{gathered}[/tex]Therefore, the answer is:
[tex]\frac{-x^2+2x-5}{x^2(x-1)}=\frac{-4}{x-1}+\frac{3}{x}+\frac{5}{x^2}[/tex]Cómo hallar el valor de variables
Variables are the unknows, on this case we have 2 variables
Y and X
variables are always represented by letters
X is
we write the original equation
[tex]7y+3x=9[/tex]now we try to x be alone to solve, then we subtract 7y on both sides
[tex]\begin{gathered} (7y-7y)+3x=9-7y \\ 0+3x=9-7y \\ 3x=9-7y \end{gathered}[/tex]now we divide on both sides by 3 to solve x
[tex]\begin{gathered} \frac{3x}{3}=\frac{9-7y}{3} \\ \\ x=\frac{9-7y}{3} \end{gathered}[/tex]Y is
write original equation
[tex]7y+3x=9[/tex]subtract 3x on both sides to remove 3x on right
[tex]\begin{gathered} 7y+(3x-3x)=9-3x \\ 7y+0=9-3x \\ 7y=9-3x \end{gathered}[/tex]and divide by 7 to solve y
[tex]\begin{gathered} \frac{7y}{7}=\frac{9-3x}{7} \\ \\ x=\frac{9-3x}{7} \end{gathered}[/tex]A large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 96 ft per second. The function h(t)=96t-16t^2 gives the height of the falling debris above the ground, in feet, t seconds after the explosion. use the function to find the height of the debris one second after explosion (After 1 second the height is___)and how many seconds after the explosion with the debris hit the ground (___seconds)
a) 80feet
b) 6 seconds
Explanation:Given the formula that represents the height of the falling debris above the ground expressed as:
[tex]h(t)=96t-16t^2[/tex]In order to get the height of the debris one second after explosion, we will substitute t = 1sec into the formula as shown:
[tex]\begin{gathered} h(1)=96(1)-16(1)^2 \\ h(1)=96-16 \\ h(1)=80ft \end{gathered}[/tex]Hence the height of the debris one second after the explosion is 80feet
The debris hits the ground at the point where the height is 0 feet. Substitute h = 0 into the function as shown:
[tex]\begin{gathered} 0=96t-16t^2 \\ -96t=-16t^2 \\ 16t^2=96t \\ 16t=96 \\ t=\frac{96}{16} \\ t=6secs \end{gathered}[/tex]Therefore the debris hits the ground 6 seconds after the explosion
for the equation -x+y=-7 write it in slope-intercept form and give the slope of the line and give the y intercept.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
- x + y = - 7
Step 02:
equation of the line:
Slope-intercept form of the line
y = mx + b
- x + y = - 7
y = x - 7
slope = m = 1
y-intercept = b = - 7
The answer is:
Slope-intercept form of the line:
y = x - 7
slope = 1
y-intercept = - 7
what type of angle is
Answer:
Obtuse angle
Explanation:
An angle with a measure between 90° and 180° is an obtuse angle. So, if m
Answer: Obtuse Angle
Step-by-step explanation:
An obtuse angle is always larger than 90° but less than 180°
Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have $1,000,000 after 40 years with an APR of 5% compounded quarterly. Round your answer to the nearest cent, if necessary.
Given:
There are given that the initial amount, time period, and rate are:
[tex]\begin{gathered} future\text{ value:1000000} \\ time\text{ period:40 year} \\ rate:\text{ 5\%} \end{gathered}[/tex]Explanation:
To find the present value, we need to use the present value formula:
So,
From the formula of present value:
[tex]PV=FV\frac{1}{(1+\frac{r}{n})^{nt}}[/tex]Then,
Put all the given values into the above formula:
So,
[tex]\begin{gathered} PV=FV\frac{1}{(1+\frac{r}{n})^{nt}} \\ PV=1000000\frac{1}{(1+\frac{0.05}{4})^{4\times40}} \end{gathered}[/tex]Then,
[tex]\begin{gathered} PV=1,000,000\times\frac{1}{(1+\frac{0.05}{4})^{4\times40}} \\ PV=1,000,000\times\frac{1}{(1.0125)^{160}} \\ PV=1,000,000\times\frac{1}{7.298} \\ PV=137023.84 \end{gathered}[/tex]Final answer:
Hence, the amount is $137023.84
select the correct answer. and the figure, angle k measures 45°. what is the measurement of angle c? 38° 45° 90° 98°.
From the figure, we can conclude that the little triangle is an isosceles triangle, the greatest angle is 90 because ∠A = 90 and they are supplementary, therefore, using the triangle sum theorem:
[tex]\begin{gathered} m\angle J=m\angle K \\ m\angle K+m\angle K+90=180 \\ 2m\angle K=180-90 \\ 2m\angle K=90 \\ m\angle K=\frac{90}{2} \\ m\angle K=45 \end{gathered}[/tex]Evaluate t^2 -6 when t= -4
The Solution:
The given expression is
[tex]\begin{gathered} t^2-6 \\ \text{where t=-4} \end{gathered}[/tex]Substituting -4 for t in the expression above, we get
[tex]\begin{gathered} (-4)^2-6 \\ 16-6 \\ 10 \end{gathered}[/tex]Therefore, the correct answer is 10.
Answer:
the answer is 10.
Step-by-step explanation:
Expand (y + 1)(y + 4)
The given expression is:
(y + 1) (y + 4)
To expand the expression, each of the terms in the first bracket multiplies each term in the second bracket
The expression then becomes:
[tex]\begin{gathered} y^2+\text{ 4y + y + 4} \\ y^2\text{ + 5y + 4} \end{gathered}[/tex]Find the trigonometric ratio (NOT the angle) of cos X (write as a fraction in lowest terms.) x=19y=22z=29
Cosidering angle X in the triangle we have the adjacenb leg being 2y= 2 and the hypotenuse of the triangle i sz-= 29.
We know that
[tex]cos=\frac{adjacent}{hyp}[/tex]So:
[tex]cosX=\frac{22}{29}[/tex]Answer: CosX = 22/29
Which of the following is the equation of the line of best fit?A. Y= 50/3xB. Y= 20/3xC. Y=2/3x D. Y=5/3x
The best fit line passes through the point (3,50) and (6,100).
The euation of line passing through point (x_1,y_1) and (x_2,y_2) is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Determine the equation of line passing through point (3,50) and (6,100).
[tex]\begin{gathered} y-50=\frac{100-50}{6-3}(x-3) \\ y-50=\frac{50}{3}(x-3) \\ y=\frac{50}{3}x-\frac{50}{3}\cdot3+50 \\ y=\frac{50}{3}x \end{gathered}[/tex]So equation of best fit line is y = 50/3x.
Option A is correct answer.
Dylan is driving to a concert and needs to pay for parking. There is an automatic fee of $5 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $2 for every hour he had his car in the lot. How much total money would Dylan have to pay for parking if he left his car in the lot for 6 hours? How much would Dylan have to pay if he left his car in the lot for tt hours?Cost of parking for 6 hours: Cost of parking for tt hours:
Here, we have a fixed parking cost and a variable parking lot that is a function of the time spent in the lot. Our approach is to create an algebraic relationship and then slot in our variable vales to solve.
Let c represent the cost of parking.
Let t represent the time car spent in the lot.
We then have:
[tex]c=5+2t[/tex]To calculate the cost of 6 hours in the lot, we have:
[tex]\begin{gathered} c=5+2(6) \\ c=5+12=17 \end{gathered}[/tex]$17 for a 6 hour packing.
Cost for tt hours.
[tex]c=5+2(tt)[/tex]Cost for tt hours = c = 5+2(tt)
Initial Knowledge CheckGoode Manufacturing pays Donald Sanchez a $590 monthly salary plus a 4% commission on merchandise he sells each month. Assume Donald's sales were$27,800 for last month.Calculate the following amounts:1. Amount of Commission:2. Gross Pay:
Solution:
Given:
[tex]\begin{gathered} monthly\text{ salary}=\text{ \$}590 \\ commission\text{ rate}=4\text{ \%} \\ Sales\text{ made}=\text{ \$}27,800 \end{gathered}[/tex]1) Amount of commission is 4% of merchandise sales made.
Hence,
[tex]\frac{4}{100}\times27800=\text{ \$}1112[/tex]Therefore, the amount of commission is $1112.
2) Gross pay is the total amount recevied.
Hence,
[tex]\begin{gathered} Gross\text{ pay}=590+1112 \\ =\text{ \$}1702 \end{gathered}[/tex]Therefore, the gross pay Donald recieved is $1702.
Please help with with wuestion 1 I really need help
Given: Evan illustrates 1/6 of a children's book of paper in 1/3 hours.
Required: To determine how long Evan will take to illustrate an entire page.
Explanation: Let x denotes the length of the complete page. Then according to the question, the time taken to illustrate 1/6th of x is 1/3 hours, i.e.
[tex]x\times\frac{1}{6}=\frac{1}{3}[/tex]We need to determine how long Evan will take to illustrate the complete page. So the time taken to illustrate x is-
[tex]\begin{gathered} x=\frac{1}{3}\times6 \\ =2\text{ hours} \end{gathered}[/tex]Final Answer: It will take Evan 2 hours to illustrate an entire page.
Hello! May I please have some help on this one? I worked it out but my answer is wrong.
SOLUTION
Arranging r books from n books is given as n permutation r
[tex]\begin{gathered} ^nP_r\text{ is the number of ways of arranging r books from n books } \\ \\ n=10 \\ r=4 \\ \\ ^{10}P_4=5040\text{ \lbrack input into calculator \rbrack} \end{gathered}[/tex]There are 15 tables set up for a banquet, of which 3 have purple tablecloths.What is the probability that a randomly selected table will have a purple tablecloth?Write your answer as a fraction or whole number.P(purple)
To determine the probability of an event "A" you have to calculate the quotient of the number of favorable outcomes for A and the number of possible outcomes.
[tex]P(A)=\frac{nº\text{favorable outcomes}}{nº\text{ of possible outcomes}}[/tex]Let the event of interest be A: the table has a purple tablecloth.
The favorable outcomes for this event will be the number of tables that have a purple tablecloth, in this case there are 3 tables with purple tablecloth.
The number of possible outcomes is given by the total number of tables that are set up, which are 15 tables.
You can calculate the probability of A as follows:
[tex]\begin{gathered} P(A)=\frac{nº\text{ tables with purple tablecloth}}{nº\text{ tables}} \\ P(A)=\frac{3}{15}=\frac{1}{5} \end{gathered}[/tex]The probability of selecting a table at random and that it will have purple tablecloth is 1/5
What is the image point of (4, -6) after a translation right 5 units and up 4 units?Submit Answer
When you translate the pre-image point (x,y) right 5 units and up 4 units, we have the image point:
[tex](x,y)\rightarrow(x+5,y+4)[/tex]Therefore, the image point of (4, -6) after a translation right 5 units and up 4 units is:
[tex](4,-6)\rightarrow(4+5,-6+4)=(9,-2)[/tex]The image point is (9, -2)
The volume of the rectangular box shown below is 96. If the base of the box has the dimensions shown, what is the height of the box? 4 3
we get that the height is
[tex]h=\frac{96}{4\cdot3}=8[/tex]so we get that the height is 8
What is the best choice for the common denominator in this problem.
Given:-
[tex]\frac{1}{5}+\frac{2}{6}[/tex]To find the required value.
So to add the given fraction. first we should have same denominator. so we take LCM,
[tex]\text{LCM of 5 and 6 is 30.}[/tex]So we get,
[tex]\frac{1}{5}+\frac{2}{6}=\frac{1\times6}{5\times6}+\frac{2\times5}{6\times5}=\frac{6}{30}+\frac{10}{30}=\frac{16}{30}[/tex]So the correct denominator is 30.
can you please help me with this it's on surface area of prisms/cylinders and word problems
Solution
For this case we can find the lenghts of the slants like this:
[tex]s2=\sqrt[]{4.5^2+3.5^2}=5.70[/tex][tex]undefined[/tex]Suppose that the scores on a statewide standardized test are normally distributed with a mean of 63 and a standard deviation of 2. Estimate the percentage of scores that were(a) between 59 and 67. %(b) above 69. %(c) below 59. %(d) between 57 and 67. %
a) Percentage of scores that were between 59 and 67 = 95.45%
b) Percentage of scores above 69 = 0.135%
c) Percentage of scores below 59 = 2.2755%
d) Percentage of scores between 57 and 67 = 97.59%
Explanations:The mean, μ = 63
Standard deviation, σ = 2
When x = 59
[tex]\begin{gathered} z\text{ = }\frac{x-\mu}{\sigma} \\ z\text{ = }\frac{59-63}{2} \\ z\text{ = }-2 \end{gathered}[/tex]When x = 67
[tex]\begin{gathered} z\text{ = }\frac{x-\mu}{\sigma} \\ z\text{ = }\frac{67-63}{2} \\ \text{z = 2} \end{gathered}[/tex]P(59 < x < 67) = P(-2 < x < 2) = 0.9545
Probability that scores fall between 59 and 67 = 0.9545
Percentage of scores that were between 59 and 67 = 95.45%
b) above 69
P(x > 69)
[tex]\begin{gathered} z\text{ = }\frac{x-\mu}{\sigma} \\ z\text{ = }\frac{69-63}{2} \\ z\text{ = 3} \end{gathered}[/tex]P(x > 69) = P(z > 3) = 0.0013499
Percentage of scores above 69 = 0.135%
c) below 59
P(x < 59)
[tex]\begin{gathered} z\text{ = }\frac{59-63}{2} \\ z\text{ = -2} \end{gathered}[/tex]P(x < 59) = P(z < -2) = 0.02275
Percentage of scores below 59 = 2.2755%
d) between 57 and 67.
when x = 57
[tex]\begin{gathered} z\text{ = }\frac{57-63}{2} \\ z\text{ = -3} \end{gathered}[/tex]P(57 < x < 67) = P(-3 < x < 2) = 0.9759
Percentage of scores between 57 and 67 = 97.59%
Number 50 use the graph to estimate the limits and value of the function or explain why the limits do not exist
In this case, notice that the graph of G(x) approximates to 1 when x goes to 2 from the left, and also the graph approximates to 1 when x goes to 2 from the right, thus, we have the following limits:
[tex]\begin{gathered} \lim _{x\rightarrow2^-}G(x)=1 \\ \lim _{x\rightarrow2^+}G(x)=1 \end{gathered}[/tex]since both limits are equal, we have that the limit of G(x) when x goest to 2 is:
[tex]\lim _{x\rightarrow2}G(x)=1[/tex]sally built a small ramp for her bicycle. the ramp 10 meters long and creates a 15 degrees angles with the ground. how tall is the ramp at the highest point?
A right triangle is formed, where the length of the ramp (10 m) is the hypotenuse, and the height (h) of the ramp is the opposite side to the angle of 15°.
From defintion:
[tex]\sin (angle)=\frac{\text{opposite side}}{hypotenuse}[/tex]Substituting with data:
[tex]\begin{gathered} \sin (15)=\frac{h}{10} \\ \sin (15)\cdot10=h \\ 2.6\text{ m =h} \end{gathered}[/tex]The ramp is 2.6 meters tall
See your levelsELEWhat is the area of this figure?9 ft3 ft7 ft5 ft2 ft16 ftsquare feetSubmit
S = 59 ft²
1) Let's find out the area of that figure by tracing auxiliary lines to decompose that into smaller rectangles:
2) So we can calculate the rectangle to the left
S = w * l Rectangle Area formula
S = 7 x 2
S = 14 ft²
And the larger one:
S= 9 x 5
S = 45 ft²
3) Now let's add them up to find out the area of the polygon:
S= S_1 +S_2
S = 14 +45
S = 59 ft² And that's the answer
Evaluate the expression when b=-4 and c = 2 9c-b
Given that b = -4 and c = 2;
To evaluate 9c - b, we will substitute the given values of b and c into the expression.
Thus, we have:
[tex]\begin{gathered} 9c-b \\ 9(2)-(-4) \\ 18+4 \\ =22 \end{gathered}[/tex]Line segment XY begins at ( - 6,4) and ends at ( - 2,4). The segment is reflected over the x-axis and translated left 3 units to form line segment X ‘ Y ‘. Enter the length , in units , of the lines segment X’ Y’ .
ANSWER
4 units
EXPLANATION
The transformations made to the line segment XY are a reflection and a translation. Both of these transformations do not change the size of the figure, so the length of line segment X'Y' is the same as the length of line segment XY.
The distance between two points (x₁, y₁) and (x₂, y₂) is found with the Pythagorean Theorem,
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^^2}[/tex]In this case, the endpoints of line segment XY are (-6, 4) and (-2, 4), so its length is,
[tex]d=\sqrt{(-6-(-2))^2+(4-4)^2}=\sqrt{(-6+2)^2+0^2}=\sqrt{(-4)^2}=\sqrt{16}=4[/tex]Hence, the length of line segment X'Y' is 4 units.