In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
sin x + 1 = 0
Step 02:
0 ≤ x< 2π
sin (x) = - 1
x = arc sin (-1)
x = - π / 2
The answer is:
x = - π / 2 = - 90 degrees
Which statement is true for the inequality 2(x-2)< x +2Select one:The inequality is true for all values of x.The inequality is only true for numbers less than 6.The inequality is never true.The inequality is only true for numbers greater than -6.
We are given the following inequality
[tex]2(x-2)Let us solve the inequality for xExpand the parenthesis on the left side of the inequality
[tex]\begin{gathered} 2(x-2)Combine the like terms together [tex]\begin{gathered} 2x-4So, the solution of the inequality is x < 6The inequality is only true for numbers less than 6
Determine the value of the given expression -3 1/3x1 5/6
Let's begin by listing out the information given to us:
-3 1/3 x 1 5/6 ⇒ -10/3 x 11/6
⇒ -10 x 11 / (3 x 6) = -210/18
⇒ -210/18 = -35/3
⇒ -35/3
Emilio has a coupon for 20% off of his purchase at a store with no sales tax. He finds a backpack that is already on sale for 30% off. The store will apply his coupon to the sale price of the backpack. If the original price of the backpack is $65.00, how much will Emilio pay?
Answer:1 plus 1
Step-by-step explanation:21234
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
Petunia has a vegetable garden and has collected data about the amount of rain received and how high her tomato plant is growing. She displayed the information as graphed below.Based on the trend line, how tall should her tomato plant grow if there is 11 cm of rain? A. 9 cm B. 11 cm C. 10 cm D. 8 cm
To get the solution to the problem, we will need to get the relationship in terms of an equation in the linear form given to be:
[tex]y=mx+b[/tex]where m is the slope, b is the y-intercept, y is the height of tomato, and x is the amount of rain.
The slope can be calculated using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the diagram, we can get two points as sown below:
Therefore, the slope will be:
[tex]\begin{gathered} (x_1y_1)=(0,0) \\ (x_2,y_2)=(6,5) \\ \therefore \\ m=\frac{5-0}{6-0}=\frac{5}{6} \end{gathered}[/tex]The y-intercept is b = 0.
Therefore, the equation becomes:
[tex]y=\frac{5}{6}x[/tex]Therefore, for 11 cm of rain, the
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.
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]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]the amount of money in an account with continuously compounded interest is given by the formula A
SOLUTION
Given the question as contained in the image on the question tab;
[tex]A=Pe^{rt}[/tex][tex]\begin{gathered} A=2P \\ r=7.5\text{ \%} \\ t=? \\ \end{gathered}[/tex][tex]\begin{gathered} 2P=Pe^{0.075t} \\ Divide\text{ both sides by P;} \\ 2=e^{0.075t} \\ ln2=ln(e^{0.075t}) \\ ln2=0.075t \\ t=\frac{ln2}{0.075} \\ t=9.2\text{ years} \end{gathered}[/tex]Final answer:
9.2 years.
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°
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 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
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
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)
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]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.
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]John is ordering 5bags of cat food from Canada. Each bag has a mass of 6 kg. To determine the shipping costs, John needs to know the total weight in pounds. What is the weight of the cat food in pounds?
Given,
The number of cat food bags is 5.
The mass of 1 bag is 6 kg.
Required:
The total weight of the food in pounds.
The weight of bags in kilogram is,
[tex]\begin{gathered} Weight\text{ of bags = number of bags}\times mass\text{ of 1 bag} \\ =5\times6 \\ =30\text{ kg} \end{gathered}[/tex]As known that,
1 kg = 2.2046 pounds.
SO,
The weight of food in pounds is:
[tex]\begin{gathered} 1\text{ kg = 2.2046 pounds} \\ 30\text{ kg = 30}\times2.2046\text{ pounds} \\ =66.1387\text{ pounds} \end{gathered}[/tex]Hence, the weight of the food in pounds is 66.1387 pounds.
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
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]Which equations have exactly one y-value for any given x-value? Select all that apply.A.y = −xB.x = 4C.y = x2D.y = x3
x=4 is a vertical line, therefore there are more than one y-value for x=4.
y=x^2 is a parabola, and we can find one corresponding y-value for 2 x-values.
y= -x and y=x3 are functions in which one x-value has one corresponding y-value.
The answers are: A and D.
What is the inverse of the function f(x) = x + 2?1 / 8x + 2?Oh(x) = 18x - 2Oh(x) = 9x - 18h(x) = 9x + 18Oh(x) = 18x + 2
The inverse of f(x) = x+2 is
[tex]f\text{'(x)}=x-2[/tex]SOLUTION
to get the inverse of a function you need to follow the steps
1. rewrite f(x) as y
2. swap x and y
3. solve for y
[tex]\begin{gathered} f(x)=x+2 \\ y=x+2 \\ x=y+2 \\ y=x-2 \\ f^{\prime}(x)=x-2 \end{gathered}[/tex]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.
Hi, can you help me to solve this exercise please!
For any given graph on a coordinate grid, the coordinates lie on a point denoted as (x, y), that is , where x = ? and y = ?, then you have your point.
The line or the parabola can touch the horizontal axis (x-axis) or the vertical axis (y-axis) depending on the equation.
The intercept(s) is denoted as the value of the graph when it touches either the x-axis or the y-axis.
The y-intercept is the value of the function (graph) when it touches the y-axis. This is derived by looking at the value when x = 0.
From the graph provided here, the parabola touches the y-axis at the point when x = 0, y = -9 (at the bottom)
ANSWER:
The y-intercept is -9
left on together the cold and hot water faucets of a certain bathtub Take 5 minutes to fill the tub if it takes the hot water faucet 15 minutes to fill the tub by itself how long will it take the cold water faucet to fill the tub on his own
So this a filling time question
So we will use the simple mathematical equation
Let hot water takes t1 and cold water takes t2 time respectively
So t1= 15 min
t2= x min (let)
And let together they fill in 5 mins.
[tex]\frac{1}{t1}+\frac{1}{t2}=\frac{1}{t}[/tex]So by using above equation we can calculate this.
[tex]\begin{gathered} \frac{1}{15}+\frac{1}{x}=\frac{1}{5} \\ \frac{1}{x}=\frac{1}{5}-\frac{1}{15} \end{gathered}[/tex]Therefore x comes out to be 15/2 mins. i.e. 7.5 mins
So Cold water takes 7.5 mins to fill.
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
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:
Jane needs to solve for the value of n in the equation 10n=150 which of these steps would best help Jane solve the equation A. Divide both sides of the equation by 10B. Multiply both sides of the equation by 10C. Subtract 10 from both sides of the questionD. Subtract 10 from the left side of the equation to the right side of the equation
The solution is;
Divide both sides of the equation by
Consider the line y=3/4x +3. Find the equation of the line that is parallel to this line and passed through the point (-8, 6)
The slopes of two lines parallel to each other is equal. The equation given is
[tex]\begin{gathered} y=\frac{3}{4}x+3 \\ \text{The slope is the coefficient of x.} \\ \text{That means the slope of the parallel line is }\frac{3}{4} \\ \text{If the other line passes through the point (-8, 6), then} \\ U\sin g\text{ the known values which are x, y and m, the other line becomes} \\ y=mx+b \\ 6=\frac{3}{4}(-8)+b \\ 6=-6+b \\ 6+6=b \\ b=12 \\ \text{Having known the values of m and b, the parallel line is now shown as;} \\ y=\frac{3}{4}x+12 \end{gathered}[/tex]The equation of the parallel line is derived as
y = 3/4x + 12