We have to find which of the following could represent the lengths of the sides of a right triangle.
To be a right triangle, the lengths a, b and c have to satisfy the Pithagorean theorem:
[tex]a^2+b^2=c^2[/tex]Of course, c has to be the largest of the sides.
We can write for the first option:
[tex]\begin{gathered} 3^2+4^2=5^2 \\ 9+16=25 \\ 25=25 \end{gathered}[/tex]As the expression is satisfied, we can conclude that the triangles with sides 3, 4 and 5 is a right triangle.
Option B (5,12,12) can not be a right triangle, as it has 2 largest sides. It can only have one, that is the hypothenuse. NOTE: it can have two equal smallest sides, but no two largest.
Option C is 15, 30 and 45. We test the equation:
[tex]undefined[/tex]Using long division divide y cubed + 0y squared minus 1 by y +4
Given the expression:
[tex]\frac{y^3+0y^2-1}{y+4}[/tex]Step 1:
Divide the leading term of the dividend by the leading term of the divisor. Multiply the result by the divisor and subtract the final result from the dividend as follows:
[tex]\begin{gathered} \frac{y^3}{y}=y^2 \\ \\ \\ y^2(y+4)=y^3+4y^2 \\ \\ \\ (y^3-1)-(y^3+4y^2)=-4y^2-1 \end{gathered}[/tex]Step 2: Divide the leading term of the obtained remainder by the leading term of the divisor, multiply it by the divisor, and subtract the remainder from the obtained result:
[tex]\begin{gathered} \frac{-4y^2}{y}=-4y \\ \\ \\ -4y(y+4)=-4y^2-16y \\ \\ \\ (-4y^2-1)-(-4y^2-16y)=16y-1 \end{gathered}[/tex]Step 3: Divide the leading term of the obtained remainder by the leading term of the divisor, multiply it by the divisor, and subtract the remainder from the obtained result:
[tex]\begin{gathered} \frac{16y}{y}=16 \\ \\ \\ 16(y+4)=16y+64 \\ \\ \\ (16y-1)-(16y+64)=-65 \end{gathered}[/tex]Since the degree of the remainder is less than the degree of the divisor, we would stop.
Therefore, the answer is:
[tex]\frac{y^3-1}{y+4}=y^2-4y+16+\frac{-65}{y+4}[/tex]Find the height of the cone. Round to the nearest hundredth, if necessary. Show your work.
The height of the cone is 6.16 inches
Explanation:Given:
diameter of the cone = 4 inches
Angle BAC = 72°
To find:
the height of the cone
To determine the height of the cone, we will use the right-angled triangle formed in the cone:
Diameter = 2(radius)
radius = diameter/2
radius = 4/2
radius = 2 inches
Height = BC
To get the height, we will apply the tan ratio (TOA):
[tex]tan\text{ 72\degree = }\frac{opposite}{adjacent}[/tex][tex]\begin{gathered} tan\text{ 72\degree = }\frac{BC}{2} \\ BC\text{ = 2\lparen tan 72\degree \rparen} \\ BC\text{ = 2\lparen3.0777\rparen} \end{gathered}[/tex][tex]\begin{gathered} BC\text{ = 6.1554} \\ \\ The\text{ height of the cone is 6.16 in} \end{gathered}[/tex]Given the card is a club, what is the probability a card drawn at random will be a(n)…12.8?13.10 or ace?
A standard deck has 52 cards, there are four suits in the deck, "clubs", "diamonds", "hearts", and "spades". There are 13 ranks in each suit.
You know that the card drawn at random is a club. This means that there are 13 possible outcomes: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, and K.
→ You have to determine the probability of drawing an "8" given that the card is a club. There is only one 8 of clubs between the 13 cards of the suite, the probability is equal to the number of successes divided by the total number of outcomes:
[tex]P(8|Club)=\frac{1}{13}[/tex]→ You have to determine the probability of drawing a 10 or an ace, given that the card is a club. Once again, since you know that the card's suit is a club, you have to calculate the probability considering the 13 ranks that conform to the suit.
The events "drawing the 10 of clubs" and "drawing the ace of clubs" are mutually exclusive, which means that the probability of the union between both events is equal to the sum of their individual probabilities:
[tex]P((10|Club)\cup(Ace|Club))=P(10|Club)+P(Ace|Club)[/tex]There is only one 10 within the 13 ranks of the suit, the probability can be expressed as follows:
[tex]P(10|Club)=\frac{1}{13}[/tex]You can calculate the probability of drawing the Ace of Clubs using the same logic:
[tex]P(Ace|Club)=\frac{1}{13}[/tex]Now you can calculate the union between both events:
[tex]\begin{gathered} P((10|Club)\cup(Ace|Club))=P(10|Club)+P(Ace|Club) \\ P((10|Club)\cup(Ace|Club))=\frac{1}{13}+\frac{1}{13} \\ P((10|Club)\cup(Ace|Club))=\frac{2}{13} \end{gathered}[/tex]Find the area under the graph of f(x) = e-2ln(x) on the interval [1, 2]. (2 points)0.51.52.3331.75
Explanation:
To solve the question, we will need to re-express the given function as follow:
[tex]f(x)=e^{-2\ln (x)}[/tex]Will become
[tex]f(x)=e^{-2\ln (x)}=e^{\ln x^{-2}}[/tex]Thus
[tex]f(x)=e^{\ln x^{-2}}=x^{-2}[/tex]This simply means that we will find the area under the curve:
[tex]f(x)=x^{-2}\text{ within the interval \lbrack{}1,2\rbrack}[/tex]Thus
The area will be
[tex]\int ^2_1f(x)dx=\int ^2_1x^{-2}dx[/tex]This will then be
[tex]\lbrack\frac{x^{-2+1}}{-2+1}\rbrack^2_1=\lbrack\frac{x^{-1}}{-1}\rbrack^2_1[/tex]This will be simplified to give
[tex]-\lbrack\frac{1}{x}\rbrack^2_1=-\lbrack(\frac{1}{2})-(\frac{1}{1})\rbrack=-1\lbrack-\frac{1}{2}\rbrack=\frac{1}{2}[/tex]Therefore, the area under the curve will be
[tex]\frac{1}{2}=0.5[/tex]Thus, the answer is 0.5
can someone help with algebra 2?
The given function is
[tex]f(x)=\begin{cases}\frac{1}{3}x+1\colon x<-2 \\ x-3\colon-1\leq x<2 \\ 3\colon x\ge2\end{cases}[/tex]A piecewise function is a function that behaves differently on each interval. In this case, we have three intervals with three different behaviors, so let's graph each of them.
First part. 1/3x + 1.We have to find coordinated points for the values x = -4 and x = -3. To do so, we have to evaluate the expression for each value.
[tex]\begin{gathered} \frac{1}{3}\cdot(-4)+1=-\frac{4}{3}+1=\frac{-4+3}{3}=-\frac{1}{3} \\ \frac{1}{3}\cdot(-3)+1=-1+1=0 \end{gathered}[/tex]So we have two points for the first expression: (-4, -1/3) and (-3, 0).
Second part. x - 3.Let's evaluate the expression for x = -1 and x = 0.
[tex]\begin{gathered} -1-3=-4 \\ 0-3=-3 \end{gathered}[/tex]The points are (-1, -4) and (0, -3).
For the third part, we don't have to evaluate any expression because the function, in that interval, is a horizontal line.
Now, we just have to graph all the points on the same coordinated plane, as the image below shows.
Can I please get some help on this Graph y=1
the given expression is,
y = 1
the given expression is the equation of the line,
that is passing through y = 1 and parallel to x- axis,
so, the graph will be,
The first bar is what percent as long as the second bar?
To find the how much the first bar represents from the second bar, we need to calculate the ratio between them.
[tex]\frac{2}{5}[/tex]To convert this ratio to a percentage, we just need to convert the denominator to 100, and the numerator will be the percentual value. We can convert by multiplying both the numerator and denominator by 20.
[tex]\frac{2}{5}\times\frac{20}{20}=\frac{2\times20}{5\times20}=\frac{40}{100}=40\%[/tex]The first bar is 40% as long as the second bar.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
The perimeter of a square is (4x - 44). What is the length of each side?
The perimeter of square is given as,
[tex](4x-44)[/tex]Let length of side is denoted as S.
The formula for the perimeter of square is,
[tex]P=4\times S[/tex]To calculate the side of square , substitute the value of perimeter in the above formula.
[tex](4x-44)=4\times S\text{.}[/tex]Solving the equation we get,
[tex]4(x-11)=4\times S\text{.}[/tex][tex](x-11)=S.[/tex]The length of the square obtained is ,
[tex]S=(x-11).[/tex]Taylor wants four different pairs of sneakers, but can only afford to buy three of thepairs? How many sets of three pairs of sneakers can she possibly choose?
We have a set of four pairs of sneakers {A; B; C; D} and want to know how many sub-sets of three pairs of sneakers can be made with this.
To calculate that, we just need to have in mind that, for the first pair which Taylor will choose, there are four possibilities. After Taylor chooses the first pair, will be three possibilities for the second pair. And, for the third pair, we will have only the las two possibilities.
So, to gete the total number of sets of three pairs of sneakers that can be made, we just multiply the three correspondent possibilities for each choose: 4*3*2 = 24
which of the following number is rationalA
A rational number is any number that can be expressed as a ratio of two integers, in the form p/q.
We can say that root(16) is a rational number:
[tex]\sqrt[]{16}=4=\frac{4}{1}[/tex]2 4/7 divided by 2 3/5
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed.
Answer:
1 17/28
Step-by-step explanation:
2 4/7=18/17
2 3/5=8/5
18/17÷8/5=90/56=45/28=1 17/28
A 17-1b bag of Zollipops is $120.00. Connecticut 3 sales tax is 6.35% and Missouri's is 4.225%. How much more sales tax does a customer in Connecticut pay for the bag than one in Missouri?
step 1
Find out how much is the sales tax in Connecticut
we have
6.35%=6.35/100=0.0635
Multiply by $120.00
120.00*(0.0635)=$7.62
step 2
Find out how much is the sales tax in Missouri
we have
4.225%=4.225/100=0.04225
Multiply by $120.00
120.00*(0.04225)=$5.07
step 3
Find the difference
so
7.62-5.07=$2.55
therefore
the answer is $2.55What is the equation of a circle with center (2,-3) and radius 3?O -A. (x - 2)2 +(y +37- 3B. (x + 2)2 + (y - 3y - 9O C. (x - 2)2 +(y +3j? = 9x 2 2D. (x - 2) - (+31° - 9
The Equation of a Circle
Given a circle of radius r and centered at the point (h, k), the equation of the circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Please, note the value of the coordinates of the center appear with its signs changed.
We have to find the equation of this circle by substituting the values of r = 3 and (h, k) = (2, -3). Substituting:
[tex]\begin{gathered} (x-2)^2+(y+3)^2=3^2 \\ \text{Operating:} \\ (x-2)^2+(y+3)^2=9 \end{gathered}[/tex]Choice C.
23.35 in.43 in.36 in.A.1505 in.2B.142 in.2C. 71 in.2D. 1260 in.2
TIP
This parallelogram
The area of a parallelogram =BH
The area of a parallelogram
[tex]\begin{gathered} =35\text{ in }\times36in \\ =1,260in^2 \end{gathered}[/tex]The final answer is the last option
option D
Below, the function f(x) =3x-2 f(x)=3x-2 and the function f(x)= 3x+1f(x)=3x+1 are graphed. Compare and contrast the lines. What is similar about the equations and graphs? What is different?
You have the lines associated to the following functions:
f(x) = 3x - 2
f(x) = 3x + 1
The general equation of a line is given by:
y = mx + b
where m is the slope and b the y-intercept.
By comparing the given functions with the general form, you can notice that the slope of the lines are equal (m = 3) and the y-intercept are different, b=-2 and
b = 1.
Due to the slopes are the same you have two parallel lines.
6.Find the volume of the cone in terms of PiA cone with a radius of 10 in and a height of 12 in.a 800pi in ³b 2007pi in ³c 4007pi in^3d 600 in ³
Explanation
We are told to find the volume of a cone with a radius of 10 inches and a height of 12 inches
To do so, we will use the formula
[tex]Volume=\frac{1}{3}\times\pi\times r^2\times h[/tex][tex]\begin{gathered} where \\ radius=r=10inches \\ height=h=12inches \end{gathered}[/tex]Thus, the volume will be
[tex]Volume=\frac{1}{3}\times\pi\times10^2\times12=\frac{100\times12}{3}\times\pi=400\pi\text{ in}^3[/tex](1a) Clare drew a dashed line as shown in the diagram. She said the thattwo resulting shapes have the same area. Do you agree? *
The area of a rectangle is given by the formula:
[tex]A=b\times h[/tex]Where b is the length of the base and h is the height of the rectangle.
The area of a triangle is given by the formula:
[tex]A=\frac{b\times h}{2}[/tex]Where b is the length of the base of the triangle and h is its height.
The resulting shape on the right is a rectangle, whose base is 2 and its height is 4, then the area of this part of the shape is:
[tex]\begin{gathered} A=b\times h \\ A=2\times4=8 \end{gathered}[/tex]The area of the triangle resulting on the left side is:
[tex]\begin{gathered} A=\frac{b\times h}{2} \\ A=\frac{4\times4}{2}=\frac{16}{2}=8 \end{gathered}[/tex]Since the area of both shapes is 8, Clare is right.
The graph below represents compound interest over time with an initial investment of $600 at in interest rate of 6% compounded annually. Which of these statements describes the situation?-it will take less than 10 years to double the initial investment-it will take less than 20 years to triple the initial investment-it will take more than 15 years to double the investment-it will take more than 30 years to triple the initial investment
ANSWER
It will take less than 20 years to triple the investment.
EXPLANATION
We want to identify the statement that best describes the situation represented by the graph of the compound interest over time.
To do this, let us find at what point the compound amount doubles and triples.
Since the initial investment is $600, it implies that double this investment is $1200, and triple this investment is $1800.
Hence, we have to identify what happens at these points on the graph.
Notice that when y approaches $1200 on the vertical axis, x is greater than 10 and less than 15. It occurs at about x = 12 years.
Also, notice that when y approaches $1800 on the vertical axis, x is less than 20 years (also less than 30 years). It occurs at about x = 19 years.
Hence, the only correct statement that describes the situation is that it will take less than 20 years to triple the investment.
The correct answer is the second option.
I need some help with this I don’t understand how I would do it can I have some help
from the graph shown in the question,
we could deduce that:
x = -3,
which means x + 3 = y,
we can also deduce that x = 4,
which means that, x - 4 = y
so, the eqaution of the graph could be
y = (x - 2) (x + 3) (x - 4)
since the graph is a cubic graph
therefore the correct option is B
Calculate the volume of the composite solid . 2 cm 3 cm 2 cm 4 cm 3 cm 4 cm 8 cm
Notice that the solid consists of an 8x4x4cm rectangular prism minus a 3x4x2cm rectangular prism (the gap shown in the image).
Therefore, the volume of the solid is
[tex]V_{solid}=(8*4*4)-(3*4*2)=128-24=104[/tex]The answer is 104cm^3How would you write the equation for the following sentence: 3 hot dogs and 4 sodas cost $20. * Do not put spaces or dollar signs in your answer. Your answer
3h + 4s = 20
1) Let's write an equation for that, calling hot dogs by h and sodas by s.
3h + 4s = 20
Note that in this equation we are relating prices, of hot dogs and sodas and the total cost of them. Similar reasoning is used to set a linear system of equations.
what is the maximum number of turns in the graph of this functuion f(x) x^4-x^3+3x+1
As given by the question
There are given that the function
[tex]f(x)=x^4-x^3+3x+1[/tex]Now,
By the defination, a polynomial of n degree, has a maximum turning points of:
[tex]n-1[/tex]Therefore, if you have the polynomial given in the problem, which is a polynomial of degree 4, that means (n=4).
The maximum number of turns can be obtained as following:
[tex]\begin{gathered} n-1=4-1 \\ =3 \end{gathered}[/tex]Hence, the maximum number of turns in the graph is 3.
If $7025 is invested at a rate of 10% compounded continuously, what will be the balance after 12 years? Round your answer to two decimal places.
p = $7025
r = 10% = 10/100 = 0.1
t = 12
[tex]A=pe^{rt}[/tex]Therefore,
[tex]\begin{gathered} A=7025\times e^{0.1\times12} \\ A=7025\times e^{1.2} \\ A=7025\times3.32011692274 \\ A=23323.8213822 \\ A=\text{ \$}23323.82 \end{gathered}[/tex]Balance after 12 years = $23,323.82
Let f(x) = -2x^2– 7 and g(x) = 4x – 7.(fog)(x) =(gof)(x) =(fog)(1) =
Part 1.
The compositon fog is given by
[tex](f\circ g)(x)=-2(4x-7)^2-7[/tex]which gives
[tex]\begin{gathered} (f\circ g)(x)=-2(16x^2-56x+49)^{}-7 \\ (f\circ g)(x)=-32x^2+112x-98^{}-7 \\ (f\circ g)(x)=-32x^2+112x-105 \end{gathered}[/tex]Then, the answer is:
[tex](f\circ g)(x)=-32x^2+112x-105[/tex]Part 2.
The composition gof is given by
[tex](g\circ f)(x)=4(-2x^2-7)-7[/tex]Then, the answer is:
[tex](g\circ f)(x)=-8x^2-35[/tex]Part 3.
In this case, we need to substitute x=1 into the answer of Part 1, that is,
[tex]\begin{gathered} (f\circ g)(1)=-32(1)^2+112(1)-105 \\ (f\circ g)(1)=-32^{}+112-105 \end{gathered}[/tex]Therefore, the answer is:
[tex](f\circ g)(1)=-25[/tex]Make use of structure. For rectangle ABCD, two vertices are A(-2, 3) and B(4, 6). Find the slopes of BC, CD, and DA. Explain your answer.
We are given a rectangle ABCD
A(-2, 3)
B(4, 6)
We are asked to find the slopes of sides BC, CD, and DA.
Let me first draw a rectangle to better understand the problem
Recall that the slope is given by
[tex]m=\frac{y_2−y_1}{ x_2−x_1}[/tex][tex]\text{where}(x_1,y_1)=(-2,3)\text{and}(x_2,y_2)=(4,6)[/tex]So the slope of side AB is
[tex]m_{AB}=\frac{6-3}{4-(-2)}=\frac{3}{4+2}=\frac{3}{6}=\frac{1}{2}=0.5[/tex]The sides BC and DA are perpenducluar to the side AB.
So their slopes will be
[tex]m_{BC}=m_{DA}=\frac{1}{-m_{AB}}[/tex]Substituting the value of slope of AB
[tex]m_{BC}=m_{DA}=\frac{1}{-0.5}=-2[/tex]The side CD is parallel to the side AB.
Parallel sides have equal slopes so
[tex]m_{CD}=m_{AB}=\frac{1}{2}[/tex]Therefore, the slopes of the rectangle ABCD are
[tex]\begin{gathered} m_{AB}=m_{CD}=\frac{1}{2} \\ m_{BC}=m_{DA}=-2 \end{gathered}[/tex]2. Noelle always leaves a tip of between 10% and 15% for the stylist when she gets her hair done. This can be represented by thesystem of inequalities shown below, where y is the amount of tip and x is the cost of the hair service. Which of the following isa true statement?y > 0.12y < 0.15%O When the cost of the hair service, x, is $75 the amount of tip, y, must be between $11.25 and $15.O When the cost of the hair service, x, is $50 the amount of tip, y, must be between $5 and $7.50.When the tip, y, is $15, the cost of the hair service, x, must be between $50 and $75.aWhen the tip, y, is $10, the cost of the hair service, x, must be between $100 and $150.
Substituting with x = 75 into the inequalities, we get:
y > 0.1*75
y > 7.5
y < 0.15*75
y < 11.25
Substituting with x = 50 into the inequalities, we get:
Name two planes that intersect in VR in the figure to the right.
Answer:
(C)plane VWS and plane RQU.
Explanation:
Consider Rectangle RQUV and RVWS.
They share a common edge which is VR.
Therefore, the planes that intersect in VR are plane VWS and plane RQU.
The correct choice is C.
Each month a shopkeeper spends 5X + 14 dollars on rent and electricity . If he spends 3X -7 dollars on rent how much does he spend on electricity? use pencil and paper for each values of X is the amount the shopkeeper spends on electricity less than 100? explain how you found the values 
The values of x is x<39.5.
Given that the shopkeeper spends on rent and electricity is = 5x+14
Spending of shopkeeper on rent = 3x-7
So shopkeeper spends on electricity = (5x+14) - (3x-7) = 2x+21
Given that amount the shopkeeper spends on electricity less than 100.
So suitable inequality,
2x+21 < 100
2x < 100-21
2x < 79
x < 39.5
All the values of x<39.5.
To know more about Inequality refer to:
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solve the following for x 13 over8 = x over 9
ANSWER:
[tex]x=14\frac{5}{8}=14.625[/tex]STEP-BY-STEP EXPLANATION:
We have the following proportion:
[tex]\frac{13}{8}=\frac{x}{9}[/tex]We solve for x:
[tex]\begin{gathered} \frac{x}{9}=\frac{13}{8} \\ \\ x=\frac{13*9}{8} \\ \\ x=\frac{117}{8}=14\frac{5}{8}=14.625 \end{gathered}[/tex]