Answer:
if need to solve
Step-by-step explanation:
1.1934
if it help let me know this
A = P + PRT/100Make P the subject from the formula.
ANSWER
[tex]P=\frac{100A}{100+RT}[/tex]EXPLANATION
We want to make the subject of the formula in the given equation:
[tex]A=P+\frac{PRT}{100}[/tex]First, factorize the right-hand side of the equation:
[tex]A=P(1+\frac{RT}{100})[/tex]Simplify the bracket:
[tex]A=P(\frac{100+RT}{100})[/tex]Now, divide both sides by the term in the bracket:
[tex]\begin{gathered} \Rightarrow P=A\cdot\frac{100}{100+RT} \\ \Rightarrow P=\frac{100A}{100+RT} \end{gathered}[/tex]That is the answer.
Sonia opened a savings account and then added the same amount to the savings account every week. After 5 weeks, her savings account had a total of $45. After 10 weeks, her savings account had a total of $70. Which equation represents the amount of money (y), in dollars, in Sonia's savings account after x weeks?
First let's find the amount Sonia puts in her account each week.
To do so, let's find the amount increased between weeks 5 and 10:
[tex]70-45=25[/tex]The account increased $25 in 5 weeks, so for each week, we have:
[tex]\frac{25}{5}=5[/tex]So Sonia puts $5 in her account each week. Now, we need to find the initial value in the account. If after 5 weeks the account has $45, we can subtract $45 by 5 times the amount per week:
[tex]45-5\cdot5=45-25=20[/tex]So the initial amount is $20.
Now that we have the initial amount and the amount she puts per week, we have the following equation for the amount of money y after x weeks:
[tex]y=5x+20_{}[/tex]So the correct option is the third one.
Help I need a example for graphing two variable inequalities
Solution:
To graph, a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equals sign. The graph of this equation is a line.
If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ and ≥ ), graph a solid line.
For example,
Consider the linear inequality in two variables below
[tex]y\leq4x-8[/tex]Step 1:
Put x=0 and find y
[tex]\begin{gathered} y=4x-8 \\ y=4(0)-8 \\ y=0-8 \\ y=-8 \\ (0,-8) \end{gathered}[/tex]Step 2:
Put y=0 and find x
[tex]\begin{gathered} y=4x-8 \\ 0=4x-8 \\ 4x=8 \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \\ (2,0) \end{gathered}[/tex]Hence,
We are going to use the coordinates below to graph the inequality using a solid line because
The inequality sign used is greater than or equal to
[tex](0,-8),(2,0)[/tex]Hence,
The graph of the inequality will be
find the value of x for which r parallels s. then find the measures of angles 1 and 2 measure angle 1= 80-2xmeasure angle 2= 93-3xthe value of x for which r parallels s is....measure of angle 1 is.....°measure of angle 2 is.....°
Since the lines r and s are parallel the angles 1 and 2 must be equal
write an equation
[tex]80-2x=93-3x[/tex]solve the equation for x
[tex]\begin{gathered} 80-2x=93-3x \\ -2x+3x=93-80 \\ x=13 \end{gathered}[/tex]the value for x in which r and s are parallel must be 14
measure of angle 1 and 2 must be 54°
Aldo gets paid biweekly. His gross pay for each pay period is $850.He has 16% withheld for taxes and 7% withheld for personal deductionsWhat is the amount of his annual net pay?a. $8,160b. $17,340c. $17,017d. $17,680
First, we compute the 16% of $850 and the 7% of $850:
[tex]\begin{gathered} 850(0.16)=136 \\ 850(0.07)=59.5 \end{gathered}[/tex]Then, after deductions, Aldo gets paid $850-$136-$59.5=$654.5 biweekly. Therefore, since he gets paid biweekly we multiply $654.5 per 26 and get that Aldo earns $17017 per year.
Answer: Option C.
Simplify the expression (3^1/4)^2 to demonstrate the power of a power property. Show any intermittentstepsthat demonstratehow you arrived at the simplified answer.
(3^1/4)²
= (3^1/4) x (3^1/4)
=(3)^1/4 + 1/4
=(3)^1/2
Which can also be expressed as
= √3
²
Find the coordinates of the circumcenter of triangle PQR with vertices P(-2,5) Q(4,1) and R(-2,-3)
The given triangle has vertices at:
[tex]\begin{gathered} P(-2,5) \\ Q(4,1) \\ R(-2,-3) \end{gathered}[/tex]In the coordinate plane, the triangle looks like this:
There are different forms to find the circumcenter, we are going to use the midpoint formula:
[tex]M(x,y)=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]Apply this formula for each vertice and find the midpoint:
[tex]M_{P,Q}=(\frac{-2+4}{2},\frac{5+1}{2})=(1,3)[/tex]For QR:
[tex]M_{Q,R}=(\frac{4+(-2)}{2},\frac{1+(-3)}{2})=(1,-1)[/tex]For PR:
[tex]M_{P,R}=(\frac{-2+(-2)}{2},\frac{5+(-3)}{2})=(-2,1)[/tex]Now, we need to find the slope for any of the line segments, for example, PQ:
We can apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{1-5}{4-(-2)}=\frac{-4}{6}=-\frac{2}{3}[/tex]By using the midpoint and the slope of the perpendicular line, find out the equation of the perpendicular bisector line, The slope of the perpendicular line is given by the formula:
[tex]\begin{gathered} m1\cdot m2=-1 \\ m2=-\frac{1}{m1} \\ m2=-\frac{1}{-\frac{2}{3}}=\frac{3}{2}_{} \end{gathered}[/tex]The slope-intercept form of the equation is y=mx+b. Replace the slope of the perpendicular bisector and the coordinates of the midpoint to find b:
[tex]\begin{gathered} 3=\frac{3}{2}\cdot1+b \\ 3-\frac{3}{2}=b \\ b=\frac{3\cdot2-1\cdot3}{2}=\frac{6-3}{2} \\ b=\frac{3}{2} \end{gathered}[/tex]Thus, the equation of the perpendicular bisector of PQ is:
[tex]y=\frac{3}{2}x+\frac{3}{2}[/tex]If we graph this bisector over the triangle we obtain:
Now, let's find the slope of the line segment QR:
[tex]m=\frac{-3-1}{-2-4}=\frac{-4}{-6}=\frac{2}{3}[/tex]The slope of the perpendicular bisector is:
[tex]m2=-\frac{1}{m1}=-\frac{1}{\frac{2}{3}}=-\frac{3}{2}[/tex]Let's find the slope-intercept equation of this bisector:
[tex]\begin{gathered} -1=-\frac{3}{2}\cdot1+b \\ -1+\frac{3}{2}=b \\ b=\frac{-1\cdot2+1\cdot3}{2}=\frac{-2+3}{2} \\ b=\frac{1}{2} \end{gathered}[/tex]Thus, the equation is:
[tex]y=-\frac{3}{2}x+\frac{1}{2}[/tex]This bisector in the graph looks like this:
Now, to find the circumcenter we have to equal both equations, and solve for x:
[tex]\begin{gathered} \frac{3}{2}x+\frac{3}{2}=-\frac{3}{2}x+\frac{1}{2} \\ \text{Add 3/2x to both sides} \\ \frac{3}{2}x+\frac{3}{2}+\frac{3}{2}x=-\frac{3}{2}x+\frac{1}{2}+\frac{3}{2}x \\ \frac{6}{2}x+\frac{3}{2}=\frac{1}{2} \\ \text{Subtract 3/2 from both sides} \\ \frac{6}{2}x+\frac{3}{2}-\frac{3}{2}=\frac{1}{2}-\frac{3}{2} \\ \frac{6}{2}x=-\frac{2}{2} \\ 3x=-1 \\ x=-\frac{1}{3} \end{gathered}[/tex]Now replace x in one of the equations and solve for y:
[tex]\begin{gathered} y=-\frac{3}{2}\cdot(-\frac{1}{3})+\frac{1}{2} \\ y=\frac{1}{2}+\frac{1}{2} \\ y=1 \end{gathered}[/tex]The coordinates of the circumcenter are: (-1/3,1).
In the graph it is:
9.) What type of relationship is indicated by the following set of ordered pairs (linear or quadratic)? Explain/Show
how you know by finding successive differences
X
-2
-1
0
1
2
3
Y=-4x-3
Y
14
-1
-6
-1
14
39
10.) Write the equation for question 9 showing all your work for full credit.
11.) Calculate fl-7) for the equation you wrote in Q10. Pls answer all 3 question will mark Brainliest
Step-by-step explanation:
9)
it is not linear, because while x is increasing with every data point by 1, y is decreasing and increasing again, and the differences from one point to the other vary.
for a linear relationship also y has to change in a constant way, and the difference from one point to the next would be the same for all points.
10)
so, since it is not linear, it is quadratic then (since that was our only given alternative).
y = ax² + bx + c
we know c from point (0, -6). c = -6.
for a and b we need to use 2 data points with their x and y coordinates.
let's start with the first (-2, 14)
14 = a×(-2)² + b×-2 - 6 = 4a - 2b - 6
we can simplify that
7 = 2a - b - 3
and then
10 = 2a - b
the next point is (-1, -1)
-1 = a×(-1)² + b×-1 - 6 = a - b - 6
5 = a - b
so, we have the 2 equations
10 = 2a - b
5 = a - b
from the second we get
a = 5 + b
and that we can use in the first equation
10 = 2×(5 + b) - b = 10 + 2b - b
0 = b
therefore
5 = a - b = a - 0 = a
a = 5
and the equation is
y = 5x² - 6
11)
f(-7) = 5×(-7)² - 6 = 5×49 - 6 = 245 - 6 = 239
Floyd is an aspiring music artist. He has arecord contract that pays him a base rate of$200 a month and an additional $12 for eachalbum that he sells. Last month he earned atotal of $644.Write an equation to determine the numberof albums (a) Floyd sold last month.Find the number of albums Floyd sold lastmonth.albums
Explanation:
Equate the given data to solve for x.
$200 + $12x = $644.
To determine the number of albums sold, Let x be the number of album sold by Floyd last month.
200 + 12x = 644
12x =644-200
12x = 444
x = 444/12
x= 37.
Floyd has sold 37 albums last month.
Answer:
The equation to determine the number of albums Floyd sold last month is 200+12x = 644.
and the number of album Floyd sold last month is 37.
Reece increases the amount of money he pays into his savings account by 4% each year. This year, he paid £3000 into his account. To the nearest penny, how much did Reece pay into his account a) 1 year ago? b) 10 years ago?
The money deposited 1 year ago is $2884.61 and the money deposited 10 years ago is $2142.85.
Given that, Reece increases the amount of money he pays into his savings account by 4% each year.
What is savings account?A savings account is a bank account at a retail bank. Common features include a limited number of withdrawals, a lack of cheque and linked debit card facilities, limited transfer options and the inability to be overdrawn.
We know that, simple interest = (P×R×T)/100
a) P=$x, R=4% and T=1 year
SI=3000-x
⇒ 3000-x = (x×4×1)/100
⇒ 3000-x=0.04x
⇒ 1.04x=3000
⇒ x=3000/1.04
⇒ x=$2884.61
Money deposited 1 year ago is $2884.61.
b) P=$y, R=4% and T=10 year
SI=3000-y
⇒ 3000-y = (y×4×10)/100
⇒ 3000-y = 0.4y
⇒ 1.4y = 3000
⇒ y=3000/1.4
⇒ y=$2142.85
Therefore, the money deposited 1 year ago is $2884.61 and the money deposited 10 years ago is $2142.85.
To learn more about the savings account visit:
https://brainly.com/question/3811440.
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True or False? When the first coordinate is positive, that point is located to theright of the x-axis.TrueFalse
True
Explanations:Note that when you have the position of a point as (x, y), the first coordinate is the x - axis while the second is the y - axis.
Also note that, to the right of the x axis, you have positive numbers while you have negative numbers to the left.
We can then conclude that When the first coordinate is positive, that point is located to the right of the x-axis
Suppose a person who jumps on Earth returns to the ground in 0.4 second. On Phobos, the same jumper will take 6.4 minutes to return to the ground. How many times longer would it be on Phobos than on Earth for the jumper to return to the ground? Explain.
The times longer would it be on Phobos than on Earth for the jumper to return to the ground is 16 times.
How to calculate the value?From the information, it was given that the person who jumps on Earth returns to the ground in 0.4 second and that on Phobos, the same jumper will take 6.4 minutes to return to the ground.
The number of times longer will be calculated by dividing the values that are given. This will be:.= Time on Phobos / Time on Earth
= 6.4 minutes / 0.4 minutes
= 16
This shows the concept of division of numbers.
Learn more about numbers on:
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Please help me with this question! Will give brainliest !!! I need it ASAP
Answer:
The number is not a square number because the exponent is an odd number.
Step-by-step explanation:
Square numbers or perfect squares are any numbers that once put to the square root equals a whole number. Such as 4 is a square number because the square root of 4 is 2 or 2 to the second power. Numbers that are raised to even powers also fall under this rule. For example, 16 is a square number as it is equal to 2 to the fourth power, or 16 to the fourth root is 2. Since 1953125 can also be written by 5 to the ninth power it does not go under this rule due to the power being 9. 9 is an odd number. For it to be a perfect square the exponent would have to be an even number.
Solve this inequality X-1 less than or equal to 9
Solution of an inequality
We can express the solution (s) of inequalities in several forms.
Here we will use two of them: The set-builder notation and the interval notation.
Let's solve the inequality
x - 1 ≤ 9
Adding 1 to both sides of the inequality:
x ≤ 10
The solution in words is "all the real numbers less than or equal to 10"
In set-builder notation:
{x | x <= 10}
In interval notation: (-inf, 10]
Find the slope of the two points: (-3,-2) & (5, -8)
ter Numerical value ONLY. NO Decimals
*
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-3)}}} \implies \cfrac{-8 +2}{5 +3} \implies \cfrac{ -6 }{ 8 } \implies - \cfrac{ 3 }{ 4 }[/tex]
The point S is plotted on the coordinate grid below. Plot the point S', the reflection
of S over the x-axis.
Click on the graph to plot a point. Click a point to delete it.
Answer:
(1, -2)
Step-by-step explanation:
Reflecting a point over the x-axis means [tex](x,y) \longrightarrow (x, -y)[/tex].
Need help Instructions: Find the measure of each angle Calculate the length of each side Round to the nearest tenth
Given,
The length of the perpendicular is 4.
The measure of the hypotenuse is 14.
Required:
The measure of each angle of the triangle.
As it is a right angle triangle,
The measure of angle C is 90 degree.
By using the trigonometric ratios,
[tex]\begin{gathered} cosA=\frac{AC}{AB} \\ cosA=\frac{4}{14} \\ A=cos^{-1}(\frac{4}{14}) \\ A=73.4^{\circ} \end{gathered}[/tex]By using the trigonometric ratios,
[tex]\begin{gathered} sinB=\frac{AC}{AB} \\ sinB=\frac{4}{14} \\ B=sin^{-1}(\frac{4}{14}) \\ B=16.6^{\circ} \end{gathered}[/tex]Hence, the measure of angle A is 73.4 degree, angle B is 16.6 degree and angle C is 90 degree.
A sample has a sample proportion of 0.3. Which sample size will produce the widest 95% confidence interval when estimating the population parameter?A. 36B. 56C. 68D. 46
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
sample proportion = 0.3
widest 95% confidence interval
sample = ?
Step 02:
p = 0.3
1 - α = 0.95 =>> z α/2 = 1.96
We must check each value to find the solution.
A. sample = 36
[tex]\begin{gathered} 0.3-1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{36}}=0.3-0.1499 \\ 0.3+1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{36}}=0.3+0.1499 \end{gathered}[/tex]confidence interval (0.1501 , 0.4499)
difference = 0.2998
B. sample = 56
[tex]\begin{gathered} 0.3-1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{56}}=0.3\text{ - }0.120 \\ 0.3+1.96\cdot\sqrt[]{\frac{0.3\cdot0.7}{56}}=\text{ 0.3 + }0.120 \end{gathered}[/tex]confidence interval (0.18 , 0.42)
difference = 0.24
Analyzing these two values, we can conclude that the widest confidence interval will be for the smallest sample.
The answer is:
Sample = 36
40.0 Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p=s2+95-142, where s is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?
But cannot be negative, hence s= 42. This implies that 42 shirts will be sold to make a profit of exactly $2000.
To earn a profit of more than $2000, then s must be greater than 42
This makes the answer to be s > 42
The correct answer is the second option
5 In nahiangle Bcm. Ireos B = / 13 which function also cauals
Given data:
The given measurement of angle C is 90 degrees.
The given value of cos(B) =5/13.
The sum of all angles of triangle is,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \angle A+\angle B+90^{\circ}=180^{\circ} \\ \angle A+\angle B=90^{\circ} \\ \angle B=90^{\circ}-\angle A \end{gathered}[/tex]Substitute the above value in the given expression.
[tex]\begin{gathered} \cos (90^{\circ}-A)=\frac{5}{13} \\ \sin A=\frac{5}{13} \end{gathered}[/tex]Thus, the correct answer is sin(A), so the third option is correct.
A store manager records a positive number to show when a deposit is made to the store's bank account and a negative number to show withdrawals.
Which equation could represent how the store manager records making 3 withdrawals of $36 each?
O 3 x 36 108
O 3x-36= -108
-3 x 36 108
O-3 x-36= -108
Answer:
03*36 108 the positive number
3. The sum of two consecutive odd integersis 168. What are the integers?
Integers are numbers such as
[tex]N=\text{ }.\ldots\text{-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9}\ldots.[/tex]And odd numbers are
[tex]1\text{ 3 5 7 9 11 13 }\ldots[/tex]A sprinkler rotates back and forth from point A to point B. The water reaches 8 meters from the base of the sprinkler.What is the length of the arc AB, rounded to the nearest tenth of a meter? Use 3.14 for [tex]\pi[/tex]
20.9m
1) Since we want to know the length of that arc, and the angle is written in degrees, let's use a formula to find this out:
[tex]\begin{gathered} l=\frac{\alpha}{360}\cdot2\pi R \\ l=\frac{150}{360}\cdot2(3.14)\cdot8 \\ l=20.93\approx20.9m \end{gathered}[/tex]2) Rounding off to the nearest tenth we have the length of this arc is 20.9, m
The local humane society is restocking on cat food to prepare for kitten season. Very young kittens need kitten formula which costs $4.00 per bottle. Older kittens need wet cat food which costs $1.50 per can. Answer numbers 5 and 6. 15) Write an algebraic expression to describe how much the humane society will spend on kitten supplies based on the number of bottles and the number of cans they buy. 16) How much money (before tax) will the humane society spend if they buy 5 bottles of kitten formula and 12 cans of wet cat food? Show your work.
Lets call B the nuber of bottles they will buy and C the number of cans.
Then, if each bottle cost $4, the cost of all the bottles will be 4B.
If each can cost $1.50, then, the total cost of the cans is 1.5C.
If we add this two costs, we have the expression we need:
[tex]\text{Cost}=4B+1.5C[/tex]If they buy 5 bottles of kitten formula and 12 cans of wet cat food, we have B=5 and C=12, and the cost is:
[tex]\text{Cost}=4B+1.5C=4\cdot5+1.5\cdot12=20+18=38[/tex]They will spend $38.
Find the weight of the steel rivet shown in the figure (steel weighs 0.0173 pounds per cubic centimeter)Round to the nearest tenth as needed.
step 1
the volume of the figure is equal to the volume of the frustums of the cone plus the volume of the cylinder
Find out the volume of the cylinder
we have
r=2.8/2=1.4 cm
h=10.7 cm
[tex]V=\pi\cdot r^2\cdot h[/tex]substitute given values
[tex]\begin{gathered} V=\pi\cdot1.4^2\cdot10.7 \\ V=20.972\pi\text{ cm3} \end{gathered}[/tex]Find out the volume of the frustum
the formula to calculate the volume is
[tex]V=\frac{1}{3}\cdot\pi\cdot h\cdot\lbrack R^2+r^2+R\cdot r\rbrack[/tex]we have
R=5.6/2=2.8 cm
r=2.8/2=1.4 cm
h=1.9 cm
substitute given values
[tex]V=\frac{1}{3}\cdot\pi\cdot1.9\cdot\lbrack2.8^2+1.4^2+2.8\cdot1.4\rbrack[/tex][tex]V=8.689\pi\text{ cm3}[/tex]Adds the volumes
V=20.972pi+8.689pi
V=29.661pi cm3
Multiply by the density
29.661pi*0.0173=1.6 lb
therefore
the answer is 1.6 lbf(x) = -5x -4 and g(x) = x^2 + 3 find (g+f)(x)
f(x) = -5x -4
g(x) = x^2+3
To find (g+f)(x) , simply add both equations:
(g+f)(x)= x^2+3 + (-5x -4 )
(g+f)(x)= x^2+3 -5x -4
Combine like terms
(g+f)(x)= x^2-5x+3-4
(g+f)(x)= x^2-5x-1
A circle and two distinct lines are drawn on a sheet of paper what is the largest possible number of points of intersection of these figures (it is Q29)
Answer:
C 5
Step-by-step explanation:
The two lines can both intersect the circle twice, and can intersect each other once, so 2 + 2 + 1 = 5
I need help on doing this finding the slope of a line
Given:
[tex](x_1,y_1)=(1,6)and(x_2,y_2)=(6,1)[/tex][tex]\text{Slope(m)=}\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{Slope(m)=}\frac{1-6}{6-1}[/tex][tex]\text{Slope(m)}=-\frac{5}{5}[/tex][tex]\text{Slope (m)=-1}[/tex]6. Find the domain and range of V(x) in this context.7. Think of V(x) as a general function without the constraint of modeling the volume of a box. What would be the domain and range of V(x)?8. Use correct notation to describe the end behavior of V(x) as a function without context.
We have , that measure of the side of the square is x
Therefore
l=26-2x
w=20-2x
h=x
Therefore the Volume function is
[tex]V=(26-2x)(20-2x)x[/tex]Then we simplify
[tex]V(x)=4x^3-92x^2+520x[/tex]6.In the context of obtaining a Volume we can't have negative numbers for x and for the function by observing the graph
Domain
[tex]0\le x\le10[/tex]Therefore for the range
[tex]0\: 7.Because we have a polynomial
the domain without the constrain
[tex]-\infty\: the range without the constrain[tex]-\infty\: 8.Since the leading term of the polynomial is 4 x^{3}, the degree is 3, i.e. odd, and the leading coefficient is 4, i.e. positive. This means
[tex]\begin{gathered} x\to-\infty,\text{ }f(x)\to-\infty \\ x\to\infty,f(x)\to\infty \end{gathered}[/tex]Determine the X intercepts of the para bola whose graph is given below write your answer as ordered pairs separated by a comma if necessary
The x-intercepts are (-1, 0) and (4, 0)
Explanation:Given:
A graph of a parabola
To find:
the x-intercepts of the parabola in ordered pairs
The x-intercept is the value of x when y = 0
On a graph, it is the value of x when the line crosses the x-axis
The line crosses the x axis at x = -1 and x = 4
The x intercept in ordered pairs will be in the form (x, y)
when x = -1, y = 0
when x = 4, y = 0
The x-intercepts are (-1, 0) and (4, 0)
