The normal price is $25, we need to find the 40% of $25.
40% = 0.4
So if we multiply $25 by 0.4
If f(x) = -x² - 2x, what is f(-2)?
Answer: 0
Step-by-step explanation:
f(-2)= -(-2)^2-2(-2)
= -4+4=0
My dog got hurt and needed surgery,so I had to use my credit card to pay the vet bill. His surgery costed me $5,323.21. If my monthly interest rate is 1.42%, how much is my finance charge for the first billing cycle?
Answer:
$75.59.
Explanation:
• Cost of the surgery = $5,323.21
,• Monthly interest rate = 1.42%
A finance charge is a fee charged for the use of a credit card. A billing cycle is usually between 28 to 31 days, i.e. a month.
To find the finance charge, multiply the interest rate by the cost of surgery.
[tex]\begin{gathered} \text{Fnance Charge}=1.42\%\text{ of \$}5,323.21 \\ =\frac{1.42}{100}\times5,323.21 \\ =\$75.59 \end{gathered}[/tex]The finance charge for the first billing cycle is $75.59.
Can you help me figure out how to find the original radican ??? I have no clue how to do so
So we have:
[tex]-3a^5b^2\sqrt[3]{a^2c}[/tex]And we want to knowthe original before simplification, that is, before evaluating the interior part of the root.
So, we need to figure a way to put the part outside of the root back in.
Taking the cubic root of a number is the same as dividing its exponent by 3, because:
[tex]\sqrt[3]{a^n}=a^{\frac{n}{3}}[/tex]So, thinking in the other direction, we need to multiply the exponents by 3 before taking it back to the inside of the cubic root:
[tex]a^k=a^{\frac{3k}{3}}=\sqrt[3]{a^{3k}}[/tex]So, the b part have a 2 in the exponent, so we can multiply it by 3 to get 6:
[tex]\begin{gathered} b^2=b^{\frac{3\cdot2}{3}}=\sqrt[3]{b^{3\cdot2}}=\sqrt[3]{b^6} \\ -3a^5b^2\sqrt[3]{a^2c}=-3a^5\sqrt[3]{b^6}\sqrt[3]{a^2b^{3\cdot2}c}=-3a^5\sqrt[3]{a^2b^6c} \end{gathered}[/tex]The a part have a 5 in the exponent, so we will get 15:
[tex]\begin{gathered} a^5=a^{\frac{3\cdot5}{3}}=\sqrt[3]{a^{3\cdot5}}=\sqrt[3]{a^{15}} \\ -3a^5\sqrt[3]{a^2b^6c}=-3\sqrt[3]{a^{15}}\sqrt[3]{a^2^{}b^6c}=-3\sqrt[3]{a^2a^{15}b^6c} \end{gathered}[/tex]Now, since we have a² and a¹⁵, we can add their exponents:
[tex]\begin{gathered} a^2a^{15}=a^{17} \\ -3\sqrt[3]{a^2a^{15}b^6c}=-3^{}\sqrt[3]{a^{17}b^6c} \end{gathered}[/tex]Now, the -3 have an exponent of 1, so:
[tex]\begin{gathered} -3=(-3)^1=(-3)^{\frac{3\cdot1}{3}}=\sqrt[3]{(-3)^{3\cdot1}}=\sqrt[3]{(-3)^3}=\sqrt[3]{-27} \\ -3^{}\sqrt[3]{a^{17}b^6c}=\sqrt[3]{-27}^{}\sqrt[3]{a^{17}b^6c}=^{}\sqrt[3]{-27a^{17}b^6c} \end{gathered}[/tex]Thus, we have, in the end:
[tex]^{}\sqrt[3]{-27a^{17}b^6c}=-3a^5b^2^{}\sqrt[3]{a^2^{}c}[/tex]Solve for 3x/2 -4 = 16what does x equal??
The given equation is expressed as
3x/2 - 4 = 16
The first step is to multiply both sides of the equation by 2. It becomes
3x/2 * 2 - 4 * 2 = 16 * 2
3x - 8 = 32
3x = 32 + 8
3x = 40
x = 40/3
x = 13.33
One equation from a system of two linear equations is graphed on the coordinate grid. 51 46 5 4 3 2 1 6 x -1 -21 The second equation in the system of linear equations has a slope of 3 and passes through the point (2,-5). What is the solution to the system of equations? th
First, we need to find the equation for the two equations.
The equation graphed has a y-intercept of 3 and a slope of
[tex]m=\frac{-6}{3}=-3[/tex]therefore, the equation of the line is
[tex]\boxed{y=-\frac{1}{2}x+3.}[/tex]For the second equation, we know what it has a slope of 3; therefore it can be written as
[tex]y=3x+b[/tex]Now, we also know that this equation passes through the point y = -5, x = 2; therefore,
[tex]-5=3(2)+b[/tex]which gives
[tex]-5=6+b[/tex][tex]b=-11[/tex]Hence, the equation of the line is
[tex]\boxed{y=3x-11}[/tex]Now we have the equations
[tex]\begin{gathered} y=-\frac{1}{2}x+3 \\ y=3x-11 \end{gathered}[/tex]equating them gives
[tex]-\frac{1}{2}x+3=3x-11[/tex]adding 11 to both sides gives
[tex]-\frac{1}{2}x+14=3x[/tex]adding 1/2 x to both sides gives
[tex]14=\frac{7}{2}x[/tex]Finally, dividing both sides by 7/2 gives
[tex]\boxed{x=4\text{.}}[/tex]The corresponding value of y is found by substituting the above value into one of the equations
[tex]y=-\frac{1}{2}(4)+3[/tex][tex]y=1[/tex]Hence, the solution to the system is
[tex](4,1)_{}[/tex]There are two buildings beside a park.
The first building is 165 3/4 ft tall, and
the second building is 114 1/4 ft tall.
By rounding to the nearest whole number,
estimate the difference between the
heights of the buildings.
The difference of the height of the buildings is 51.5 for the first building is 165 3/4 feet tall, and the second building is 114 1/4 feet tall.
Given that,
There are two building side of a park.
The first building is 165 3/4 feet tall, and the second building is 114 1/4 feet tall.
We have to find the difference of the height of the buildings.
We have to subtract the first building is 165 3/4 feet tall, and the second building is 114 1/4 feet tall.
165 3/4- 114 1/4
660+3/4- 456+1/4
663/4-457/4
165.75-114.25
51.5
Therefore, The difference of the height of the buildings is 51.5 for the first building is 165 3/4 feet tall, and the second building is 114 1/4 feet tall.
To learn more about height visit: https://brainly.com/question/10726356
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Factor the polynomial completely.X^2+x+1
1) Examining the expression below, we can group the first and the second term:
[tex]\begin{gathered} x^2+x+1 \\ x(x+1)+1 \\ \end{gathered}[/tex]Note that there is no way beyond this point. So we could not factor beyond this point.
Solve the inequality algebraically. Express your answer using set notation or interval notation. l x-8l greater than or equal to 4. Rewrite the inequality without the absolute values.
To rewrite the inequality:
[tex]\lvert{x-8}\rvert\ge4[/tex]we need to remember that:
[tex]\lvert{x}\rvert\ge a\text{ is equivalent to }x\ge a\text{ or }x\leq-a[/tex]Then in this case we have:
[tex]\begin{gathered} \lvert{x-8}\rvert\ge4 \\ \text{ Is equivalent to:} \\ x-8\ge4\text{ or }x-8\leq-4 \end{gathered}[/tex]Therefore, we can rewrite the inequality as:
[tex]x-8\leq-4\text{ or }x-8\ge4[/tex]Once we have it written in this form we can solve it:
[tex]\begin{gathered} x-8\leq-4\text{ or }x-8\ge4 \\ x\leq-4+8\text{ or }x\ge4+8 \\ x\leq4\text{ or }x\ge12 \end{gathered}[/tex]Therefore, the solution set of the inequality is:
[tex](-\infty,4\rbrack\cup\lbrack12,\infty)[/tex]Write a coordinate proof of the following theorem:"If a quadrilateral is a kite, then its diagonals are perpendicular."(image attached)thank you ! :)
Given the following coordinate points from the kite
[tex]\begin{gathered} W=(a,4b) \\ X=(2a,b) \\ Y=(a,0) \\ Z=(0,b) \end{gathered}[/tex]For the diagonals to be perpendicular the product of the distance WY and XZ must be zero that is;
[tex]\vec{WY}\cdot\vec{XZ}=0[/tex]Determine the coordinate point WY
[tex]\begin{gathered} \vec{WY}=[(a-a,4b-0)] \\ \vec{WY}=(0,4b) \end{gathered}[/tex]Determine the coordinate point XZ
[tex]\begin{gathered} \vec{XZ}=[(2a-0),(b-b)] \\ \vec{XZ}=(2a,0) \end{gathered}[/tex]Take the dot product of the coordinates
[tex]\begin{gathered} \vec{WY}\cdot\vec{XZ}=(0,4b)\cdot(2a,0) \\ \vec{WY}\cdot\vec{XZ}=[(0)(2a)+(4b)(0))] \\ \vec{WY}\cdot\vec{XZ}=(0,0)=\vec{0} \end{gathered}[/tex]Since the dot product of the coordinates is a zero vector, hence its diagonals are perpendicular.
Write the equation of the circle:center at (5, - 2) , passes through (4, 0)
the equation of the circle is
(x-h)^2 + (y-k)^2 = r^2
if we replace the terms
(4-5)^2 + (0-(-2))^2 = r^2
Now, we can fin the radius if we solve the previous equation
( - 1 )^2 + ( 2 )^2 =r^2
1 + 4 = r^2
5 = r^2
r = SQRT(5)
Now, since we already know r, we can replace it in the circle equation to obtain the result
so, (x-h)^2 + (y-k)^2 = r^2
iquals to, (x-5)^2 + (y+2)^2 = 5
I NEED HELP QUICKLY ITS DUE 8PM AND I HAVE OTHER HOMEWORK TO DO.
Answer:
$5625
Explanation:
The equation for your earning y = 150x - x² is the equation of a parabola, so the maximum point of the parabola has a coordinate x equal to -b/2a
Where b is the number beside the x and a is the number beside the x²
In this case, a is -1 and b is 150, so the x-coordinate of the maximum is:
[tex]x=\frac{-b}{2a}=\frac{-150}{2(-1)}=\frac{-150}{-2}=75[/tex]With the value of x, we can calculate the value of y, so:
y = 150x - x²
y = 150(75) - (75)²
y = 11250 - 5625
y = 5625
Therefore, the maximum amount that you can earn is $5625.
the point M 6,-4 is reflected over the y-axis. what are the cordnates of the resulting point, M?
A reflection over the Y-axis is given by:
[tex](x,y)\rightarrow(-x,y)[/tex]Substitute for (x,y)=(6,-4):
[tex](6,-4)\rightarrow(-6,-4)[/tex]Therefore, the new coordinates of the point after a reflection over the Y-axis, are:
[tex](-6,-4)[/tex]Find the perimeter of the shaded region of this composite figure .You can use 3.14 for pi.llAlso round the answer to the nearest hundreth.
ANSWER
18.58 m
EXPLANATION
We need to find the perimeter of the shaded region of the figure.
The figure is made up of a rectangle with the cut out of a semi-circle, so, to find the perimeter, we will subtract the perimeter of the semi-circle (without the diameter) from that of the rectangle.
The perimeter of the rectangle is:
P = 2(L + B)
where L = length = 8 m
B = breadth = 6 m
So, the perimeter of the rectangle is:
P = 2(8 + 6) = 2 * 14
P = 28 m
The perimeter (circumference) of the semi-circle (without the diameter) is:
C = π * R
where R = radius of the semicircle
The diameter is 6 m, so the radius is:
R = D / 2 = 6 / 2 = 3 m
So, the circumference of the semicircle is:
C = 3.14 * 3
C = 9.42 m
So, the perimeter of the composite figure is:
P = 28 - 9.42
P = 18.58 m
That is the answer.
what is the quotient of the complex numbers below 3 + 2i / 1 - 5i
Take the conjugate of the denominator, use it to multiply the numerator and the denominator
That is;
[tex]undefined[/tex]Answer:
Step-by-step explanation:
A rocket is launched by Team Flash from the ground on Earth-73. The rocket passes a sensor at a height of5760 feet after 8 seconds and lands back on Earth-73 after 53 seconds.Write an equation for the height of the rocket, h, in feet as a function of the number of seconds, t, since therocket was launched.Round to 3 decimal places as needed.After how many seconds will the rocket reach its maximum height?Round to 3 decimal places as needed.What is the maximum height in feet that the rocket reaches?Round to 3 decimal places as needed.
We know two points of the trajectory of the rocket:
1) A height of 5760 ft at time t=8 seconds after launch.
2) A height of 0 ft (landing) at time t=53 seconds after launch.
We also know that the initial position was a height of 0 ft at t=0 seconds.
So we have 3 points to write the equation, that will be a quadratic equation for this kind of trayectory.
As we know we have roots at t=0 and t=53, we can start writing it as:
[tex]h(t)=a(t-0)(t-53)=at(t-53)[/tex]We have one point left, (t,h) = (8, 5760), to find the parameter "a". We can replace t and y in the equation and solve as:
[tex]\begin{gathered} h(t)=at(t-53) \\ 5760=a\cdot8\cdot(8-53) \\ 5760=a\cdot8\cdot(-45) \\ 5760=a\cdot(-360) \\ a=\frac{5760}{-360} \\ a=-16 \end{gathered}[/tex]Then we can write the equation as:
[tex]h=-16t(t-53)=-16t^2+848t[/tex]We can graph it as:
In this kind of trajectories, the maximum height is reached halfway between the launch and the landing.
For any function, we can find the maximum of minimums deriving the function and equal it to 0. We will do it for this function:
[tex]\begin{gathered} \frac{dh}{dt}=-16(2t)+848=0 \\ -32t+848=0 \\ 32t=848 \\ t=\frac{848}{32} \\ t=26.5 \end{gathered}[/tex]The maximum height is reached at time t=26.5 seconds.
Now we can calculate the height at t=26.5 seconds, the maximum height, as:
[tex]\begin{gathered} h(26.5)=-16(26.5)^2+848(26.5) \\ h(26.5)=-16\cdot702.25+22472 \\ h(26.5)=-11236+22472 \\ h(26.5)=11236 \end{gathered}[/tex]Answer:
a) The equation is h(t) = -16t²+848t
b) The maximum height is reached at time t=26.5 seconds.
c) The maximum height is 11236 ft.
HELP. i am so confused. the question is in the picture
1) If we consider that y=f(2x) is a transformed version of y=f(x) then we can set a t-table and plug for the given point (16,8) the x-coordinate x=16
[tex]\begin{gathered} (16,8)-\longrightarrow f(x)-->y=\frac{1}{2}x \\ \end{gathered}[/tex]Since the new function, f(2x) requires us to divide the input by 2 to compensate
how do I multeply Fractions
Multiplying simultaneously numerator by numerator and denominator by denominator.
You can multiply fractions, multiplying simultaneously numerator by numerator and denominator by denominator.
2) Notice that whenever possible, we must simplify it to the lowest possible fraction.
Can u please help me with This am trying to study but can’t get it
Given:
Following Matrices are given.
[tex]A=\begin{bmatrix}{2} & {1} \\ {3} & {4}\end{bmatrix},B=[\text{ }5\text{ 4 \rbrack, C=}\begin{bmatrix}{4} & {1} & {6} \\ {} & {} & {} \\ {5} & {2} & {7}\end{bmatrix}[/tex]Find:
we have to find which Matrix multiplication can be defined.
Explanation:
For Matrix multiplication, the number of columns of first Matrix should be equal to the number of rows of the second Matrix.
Therefore, the following Matrix multiplication can be defined
BC,Because number of columns of B is 2 and number of rows of C is 2.
AC,Because number of columns of A is 2 and number of rows of C is 2.
BA,Because number of columns of B is 2 and number of rows of A is 2.
Therefore, the multiplications BC,AC,BA can be defined.
Solve 431 ÷ 3 on paper. You'll see that there is a remainder.
What digit in the ones place would give us no remainder?
Answer:
2 in the ones place.
Step-by-step explanation:
431/3 won't work because 4+3+1=NOT multiple of 3.
The closest number in the ones place that will make it an integer is 2, because 4+3+2=multiple of 3
Answer:
2, 5, or 8.
Step-by-step explanation:
There is actually a trick to this one.
---
If the digits in a number add up to a multiple of 3, then the whole number is divisible by 3.
For example:
843
Add the digits:
8+4+3=15
You could add the digits again:
1+5=6
Six is a multiple of 3, so 843 is a multiple of 3.
---
Now your number was 431.
4+3+1=8
8 is not divisible by 3, so 431 is not divisible by 3.
432, 435, and 438 would work in this situation.
PLEASE MARK AS BRANLIEST!!3. Which expression is equivalent to 3(x-2) + Zx?A. -XB. 3xC. 5X-2D. 5X-6marios The cost of
Given an expression below :
[tex]3(x-2)+2x[/tex]The expression can be solved by :
Step 1: Opening the bracket
[tex]\begin{gathered} 3(x-2)+2x \\ 3x-6+2x \end{gathered}[/tex]Step 2: Collect like terms
[tex]\begin{gathered} 3x-6+2x \\ 3x+2x-6 \\ 5x-6 \end{gathered}[/tex]Therefore the correct answer for the expression is 5x - 6
Hence the correct value is Option D
Solve the equation 42+7c - 5 = 0 using the quadratic formula
The equation is:
[tex]4c^2+7c-5=0[/tex]so we can use the cuadratic equation so:
[tex]\begin{gathered} c=\frac{-b\pm\sqrt[]{b^2-4(a)(c^{\prime})}}{2(a)} \\ \text{where} \\ a=4 \\ b=7 \\ c^{\prime}=-5 \end{gathered}[/tex]So if we replace in the equation we will have:
[tex]c=\frac{-7\pm\sqrt[]{7^2-4(4)(-5)}}{2(4)}[/tex]So we simplify to solve the problem so:
[tex]c=\frac{-7\pm\sqrt[]{129}}{8}[/tex]jenelle and hadiya went to lunch,the bill,before sales before sales tax and tip,was 37.50.a sales tax of 8% was added.they added an 18% tip on the amount after the tax was added.a)what was the amount,in dollars,of the sales tax.b)what was the total amount they paid,including tax and tip.
$37.50
tax = 8%
tip = 18%
a) 37.5 ------------------ 100%
x ------------------- 8%
x = (8 x 37.5) / 100
x = 3
Tax = $3
b) Money of lunch plus tax = $40.5
40.5 -------------------- 100
x --------------------- 18
x = (18 x 40.5) / 100
x = 7.29
Total amount paid = 7.29 + 40.5
= $ 47.79
Lakshmi bought 7 books for a total of 56 rupees how much would see pay for just three books? 56 rupees Indian money
To find how much would be paid for 3 books, follow the steps below.
Step 01: Find the price of one book.
Let's say the price of one book is x.
Then, the price of 7 books is 7 times x, which is 56 rupes.
[tex]7x=56[/tex]To find x, let's divide both sides by 7:
[tex]\begin{gathered} \frac{7x}{7}=\frac{56}{7} \\ 1x=8 \\ x=8 \end{gathered}[/tex]So, the price of one book is 8.
Step 02: Find the price of 3 books.
If the price of one book is 8, the price of 3 books (P) will be 3 times 8:
[tex]\begin{gathered} P=3\cdot8 \\ P=24 \end{gathered}[/tex]Answer: It would be paid 24 rupees for 3 books.
Evan is going to the 50th state fair this weekend. It costs $10 to enterand each ride is $2. How much will it cost Evan to go to the fair and ride 5rides? **Don't forget the initial cost.**( hint: determine the equation first y =X + and then plug in 5 for x) *
From the question, we are given the following;
Cost of entering the state fair = $10
Amount of each ride = $2
For us to determine the amount it will cost Evan to go to the fair and ride 5 rides, the equation y = $10 + 2x will be used where;
x is the total ride taken = 5 rides
y is the amount it cost evan to enter the state fair and ride 5 rides
Substitute x = 5 into the equation and get y;
y = $10 + 2x
y = $10 + $2(5)
y = $10 + $10
y = $20
Hence it will cost Evans $20 to go to the fair and ride 5 rides
There is a population of 405,000 bacteria in a colony. If the number of bacteria doubles every 44 hours, what will the population be 176 hours from now?
Since the population doubles every 44 hours, it can be modeled using an exponential equation as follows:
[tex]P(t)=405,000\times2^{\frac{t}{44}}[/tex]Where t is the time since the population was 405,000 measured in hours.
Replace t=176 to find the population after 176 hours:
[tex]\begin{gathered} P(176)=405,000\times2^{\frac{176}{44}} \\ =405,000\times2^4 \\ =405,000\times16 \\ =6,480,000 \end{gathered}[/tex]Therefore, the population after 176 hours will be 6,480,000
Find the cost for each pound of jelly beans and each pound of almonds
Let 'x' represent the cost for each pound of jelly beans.
Let 'y' represent the cost for each pound of almonds.
For the first statement, the mathematical expression is
[tex]\begin{gathered} 9x+7y=37\ldots\ldots1 \\ \end{gathered}[/tex]For the second statement, the mathematical expression is,
[tex]3x+5y=17\ldots\ldots2[/tex]Combining the two equations
[tex]\begin{gathered} 9x+7y=37\ldots\ldots\text{.}.1 \\ 3x+5y=17\ldots\ldots2 \end{gathered}[/tex]Applying the elimination method to resolve the systems of equation
Multiply the second equation by 3, in order to eliminate x
[tex]\begin{gathered} 9x+7y=37\ldots\ldots\ldots1 \\ 3x+5y=17\ldots\ldots\ldots2\times3 \end{gathered}[/tex][tex]\begin{gathered} 9x+7y=37\ldots\ldots\text{.}.1 \\ 9x+15y=51\ldots\ldots2 \end{gathered}[/tex]Subtract equation 1 from 2
[tex]\begin{gathered} 9x-9x+15y-7y=51-37 \\ 8y=14 \\ \frac{8y}{8}=\frac{14}{8} \\ y=\frac{7}{4}=1.75 \\ \therefore y=1.75 \end{gathered}[/tex]Substitute y = 1.75 into equation 1 in order to solve for x
[tex]\begin{gathered} 9x+7y=37 \\ 9x+7(1.75)=37 \\ 9x+12.25=37 \\ 9x=37-12.25 \\ 9x=24.75 \\ \frac{9x}{9}=\frac{24.75}{9} \\ x=2.75 \end{gathered}[/tex]Hence, the cost for each pound of jelly beans = x = $2.75.
the cost for each pound of almonds = y = $1.75.
Three points are shown on the coordinate plane.What is the distance from point A to point B?
Answer:
The distance from point A to point B is;
[tex]5\text{ units}[/tex]Explanation:
Given the points A and B with coordinates as shown on the graph;
[tex]\begin{gathered} A(0,5) \\ B(3,1) \end{gathered}[/tex]Recall that the distance between two points can be calculated using the formula;
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]substituting the coordinates of point A and B. we have;
[tex]\begin{gathered} d=\sqrt[]{(3-0)^2+(1-5)^2} \\ d=\sqrt[]{3^2+4^2} \\ d=\sqrt[]{9+16} \\ d=\sqrt[]{25} \\ d=5 \end{gathered}[/tex]Therefore, the distance from point A to point B is;
[tex]5\text{ units}[/tex]Mr.Ortiz has to successfully interview 90% of his assigned households. He was assigned 500 households. He has interviewed 430 households so far. Has he met his goal?
90 % of 500 is found by
0.9 * 500 = 450
430 < 450
so he has not met his goal
Suppose f(x) = x². Find the graph off(x+3).???
If f(x)=x^2
Then f(x+3)=(x+3)^2
[tex](x+3)^2=x^2+6x+9[/tex]Use geogebra to graph the function or calculate the vertex using the equation
x=-b/2a
From the equation we have that
b=6
a=1
x=-6/(2*1)
x=-3
The vertex is on x=-3
Calculate f(-3)=9-18+9=0
The vertex is (-3,0)
y axis cut off point f(0)=0+0+9=9
As "a" is a positive value, parabola open upwards, now you can draw the parabola
This is a sketch, let's use geogebra
Last year, Emma went bowling several times and earned an average score of 130 points. This
year, after taking a class at school, she improved her score to an average of 234 points. What
is the percent of increase in Emma's average score?
Answer:
80%
Step-by-step explanation:
234-130
=104
(n×p)×100=answer
(130×p)÷100= 10
(130 × p) ÷ 100=104
(130 × p) ÷ 100) × 100 = 104 × 100
130p = 10400
130p ÷ 130 = 10400 ÷ 130
p = 80%