According to the Pythagorean theorem we see that there are no distinct right triangles possible with hypotenuse length 10 and a leg of length 5. Thus, option 2 is correct.
It is given to us that -
Hypotenuse length = 10
Leg of length = 5
We have to find out the number of distinct right triangles that have the given hypotenuse length and leg of length.
For a right triangle, the Pythagorean theorem states that -
[tex]a^{2} +b^{2} =h^{2}[/tex] ---- (1)
where, a and b = Legs of the right triangle
and, h = hypotenuse of the right triangle
Substituting the given values of hypotenuse length and one leg of length in equation (1), we have
[tex]a^{2} +b^{2} =h^{2}\\= > 5^{2} +b^{2} =10^{2}\\= > b^{2} = 100-25\\= > b^{2} = 75\\= > b = 8.65[/tex]------ (2)
From equation (2), we see that another leg's length of the right triangle is equal to 8.65 which is not possible it is not a real number.
Therefore, applying the Pythagorean theorem we see that there are no distinct right triangles possible with hypotenuse length 10 and a leg of length 5. Thus, option 2 is correct.
To learn more about Pythagorean theorem visit https://brainly.com/question/14930619
#SPJ1
A book was bought for $40 and later sold at profit of 25%. What was the selling price of the book?
Answer:
The book was 50 dollars
Step-by-step explanation:
0.25% x 40 dollars = $10
10 + 40 (the original amount) = $50
Answer:
$50
Step-by-step explanation:
25% of $40 is $10 dollars. so a book sold with 25% profit is $50
15. A scale model of the Shanghai Tower is 3 inches tall. The actual tower is 2,073 feet tall. What is the scale?
en español porfis
The scale is of 8,292 ft. 1 ft in the scale is equal to 8292 ft of the actual.
Given, a scale model of the Shanghai Tower is 3 inches tall.
The actual tower is 2,073 feet tall.
We have to find the scale.
Now, as 1 ft = 12 inch
1 inch = 1/12 ft
3 inches = 3/12 ft
3 inches = 1/4 ft
So, 1/4 ft of scale = 2,073 ft of actual
1 ft of scale = 8,292 ft of actual
So, 1 ft in the scale is equal to 8,292 ft of the actual.
Hence, 1 ft in the scale is equal to 8,292 ft of the actual.
Learn more about Unitary Method here https://brainly.com/question/28627316
#SPJ9
12x(4+16)-78×3 =
O A) 6
O B) 54
O C) 159
OD) 486
Answer:
The answer for 12x(4+16)-78×3= is 6
Help asap, The graph compares the total cost of buying movie tickets for members and nonmembers of a movie club
A negative correlation is the relationship where an increase in one of the variable say x lead to a decrease in the other variable say y
In the question given, the variables are the number of workers in the x- axis and the hours of complete job in the y axis
Therefore option C is the only option where increase in the number of workers led to decrease in the hours of complete job
Hence the correct answer is option C
The robotics team needs new uniforms. The students plan to sell plush toy lions(The school mascot) for 5$ each. The students find three companies on-line that sell stuffed mascots. Company a sell 18 lions for $51.84. company B sells 12 lions for 34.32. company c charges 42.75 for 15 lions. which company has the best buy
Answer:
Company B would be the best place to get their supply from. First, I multiplied all of the quantities by 5 (33.72*5)(44.48*5)(42.6*5) and got my sums. Then, I subtracted the price to be earned from selling the plush toys by the price of the bundle. Lastly, I compared the amounts earned by using each.
A. $26.28 B. $35.52 C. $32.4
Company B is the best place to buy from.
Draw the figure and its rotation as described. Identify the coordinates of the image. J(−4, 1), K(−2, 1), L(−4,−3) 90° clockwise about vertex L.
The new coordinates of the image after rotation are L′(−4,1), J′(0,−3), and K′ (0,−5).
Step 1:
The first thing we have to do is to graph the figure. We will color it red. The graph is shown below:
Step 2:
We know that the distance between L and J is 4 units upward. If we rotate it 90° clockwise, the direction will become right. Therefore,
J′ is 4 units to the right of L. We can see that the distance between
J and K is 2 units to the right. If we rotate it 90° clockwise, the direction will become downwards. Therefore, K′ is 2 units down of L′.
Then, connect L and K′ to complete the figure. The new coordinates are L′(−4,1), J′(0,−3), and K′ (0,−5). We will graph it and color it blue.
Hence the answer is the new coordinates of the image after rotation are L′(−4,1), J′(0,−3), and K′ (0,−5).
To learn more about coordinates click here https://brainly.com/question/17206319
#SPJ1
Let f= {(5,5),(8,-8),(-8,5)}. Find (a) f(5) and (b) f(-8).
The given function f(x) is
[tex]f(x)=\lbrace(5,5),(8,-8),(-8,5)\rbrace[/tex]We need to find
a) f(5)
It means finding the value of the y-coordinate in the ordered pair that has x-coordinate = 5
Look at the function
At x = 5, y = 5 (1st orderd pair), then
f(5) = 5
b) f(-8)
It means finding the value of the y-coordinate in the ordered pair that has x-coordinate = -8
Look at the function
At x = -8, y = 5, (last ordered pair), then
f(-8) = 5
The limousine that you hired costs $400 plus $45 for each hour of service. If your total cost for the limousine is $670, how many hours did you have the vehicle?
Answer: 6 hours
Step-by-step explanation:
670-400
270
270/45
6 hours
meic had m CDs. He gave 3 CDs to a friend. How many CDs does meic have now?
AS per the concept of algebraic expression, There are m - 3 CDs meic have now.
Algebraic expression:
Algebraic expression refers the idea of expressing numbers using letters or alphabets without specifying their actual values.
Given,
Meic had m CDs. He gave 3 CDs to a friend.
Here we need to find the number of CDs does meic have now.
Here we know that the number of CDs Meic have is M.
Ad he gave 3 of his CDs to his friend.
Which means that 3 number of CDs in the total number is reduced.
So, the total number of CDs is calculated as,
=> number of CDs - 3
Therefore, the number f CDs does Meic had is m - 3.
To know more about Algebraic expression here.
https://brainly.com/question/953809
#SPJ1
how would I graph the line, 3x+4y= -4
Given the equation:
3x + 4y = -4
Let's graph the line that represents the equation above.
To grah the line, rewrite the equation in slope-intercet form:
y = mx + b
Where m is the slope and b is the y-intercept.
Rerite the equation for y:
3x + 4y = -4
Subtract 3x from both sides:
3x - 3x + 4y = -3x - 4
4y = -3x - 4
Divide all terms by 4:
[tex]\begin{gathered} \frac{4y}{4}=-\frac{3x}{4}-\frac{4}{4} \\ \\ y=-\frac{3}{4}x-1 \end{gathered}[/tex]The slope of the line is -3/4, while the y-intercept is at (0, -1).
Now, let's graph the line using 3 points.
• When x = -4:
Substitute -4 for x and solve for y
[tex]\begin{gathered} y=-\frac{3}{4}\ast(-4)-1 \\ \\ y=3-1 \\ \\ y=2 \end{gathered}[/tex]• When x = 0:
Substitute 0 for x and solve for y
[tex]\begin{gathered} y=-\frac{3}{4}\ast(0)-1 \\ \\ y=-1 \end{gathered}[/tex]• When x = 4:
Substitute 4 for x and solve for y
[tex]\begin{gathered} y=-\frac{3}{4}\ast4-1 \\ \\ y=-3-1 \\ \\ y=-4 \end{gathered}[/tex]Therefore, we have the following points:
(-4, 2), (0, -1) and (4, -4)
Plot the three points on the graph, then connect all 3 points using a straight edge.
We have the graph attached below:
The exact Value of the sine, cosine, and tangent about of the angle
Answer:
Below are the exact values of sine, cosine, and tangent of the given angle -11π/12.
[tex]sin(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4}[/tex][tex]cos(-\frac{11\pi}{12})=\frac{-\sqrt{6}-\sqrt{2}}{4}[/tex][tex]tan(-\frac{11\pi}{12})=\frac{sin(-\frac{11\pi}{12})}{cos(-\frac{11\pi}{12})}=2-\sqrt{3}[/tex]Explanation:
We can use the following trigonometric identities to solve the exact value of the given angle.
[tex]\begin{gathered} sin(x+y)=sin\text{ }x\text{ }cos\text{ }y+cos\text{ }x\text{ }sin\text{ }y \\ cos(x+y)=cos\text{ }x\text{ }cos\text{ }y-sin\text{ }x\text{ }sin\text{ }y \end{gathered}[/tex]For sine function, we have:
[tex]\begin{gathered} sin(-\frac{11\pi}{12})=sin(\frac{\pi}{4}-\frac{7\pi}{6}) \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=sin\text{ }\frac{\pi}{4}cos(-\frac{7\pi}{6})+cos\text{ }\frac{\pi}{4}sin(-\frac{7\pi}{6}) \end{gathered}[/tex]Simplify.
[tex]\begin{gathered} sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{\sqrt{2}}{2}(-\frac{\sqrt{3}}{2})+\frac{\sqrt{2}}{2}(\frac{1}{2}) \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}}{4}+\frac{\sqrt{2}}{4} \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}+\sqrt{2}}{4} \\ sin(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4} \end{gathered}[/tex]For cosine function, we have:
[tex]\begin{gathered} cos(-\frac{11\pi}{12})=cos(\frac{\pi}{4}-\frac{7\pi}{6}) \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=cos\frac{\pi}{4}cos(-\frac{7\pi}{6})-sin\frac{\pi}{4}sin(-\frac{7\pi}{6}) \end{gathered}[/tex]Simplify.
[tex]\begin{gathered} cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{\sqrt{2}}{2}(-\frac{\sqrt{3}}{2})-(\frac{\sqrt{2}}{2})(\frac{1}{2}) \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}}{4}-\frac{\sqrt{2}}{4} \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}-\sqrt{2}}{4} \\ cos(-\frac{11\pi}{12})=\frac{-\sqrt{6}-\sqrt{2}}{4} \end{gathered}[/tex]Lastly, for tangent function, it is the ratio between sine and cosine function.
[tex]tan(-\frac{11\pi}{12})=\frac{sin(-\frac{11\pi}{12})}{cos(-\frac{11\pi}{12})}[/tex]Applying the division rule, we get the reciprocal of the denominator and multiply it to the numerator. The equation becomes:
[tex]tan(-\frac{11\pi}{12})=sin(-\frac{11\pi}{12})\times\frac{1}{cos(-\frac{11\pi}{12})}[/tex]Now, let's replace the sine and cosine value that we have calculated above.
[tex]tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4}\times\frac{4}{-\sqrt{6}-\sqrt{2}}[/tex]Since 4 is a common factor on both numerator and denominator, we can cancel it out. The equation then becomes,
[tex]tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}-\sqrt{2}}[/tex]To further simplify the function, let's remove the radicals in the denominator by rationalization.
[tex]\begin{gathered} tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}-\sqrt{2}}\times\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}+\sqrt{2}} \\ tan(-\frac{11\pi}{12})=\frac{6-\sqrt{12}-\sqrt{12}+2}{6-\sqrt{12}+\sqrt{12}-2} \end{gathered}[/tex][tex]\begin{gathered} tan(-\frac{11\pi}{12})=\frac{8-2\sqrt{12}}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-2\sqrt{4\times3}}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-(2\times2\sqrt{3})}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-4\sqrt{3}}{4} \\ Factor\text{ }4\text{ }in\text{ }the\text{ }numerator. \\ tan(-\frac{11\pi}{12})=\frac{4(2-\sqrt{3})}{4} \\ Cancel\text{ }4. \\ tan(-\frac{11\pi}{12})=2-\sqrt{3} \end{gathered}[/tex]how do you find the distance between the point shown?
We can find the distance between the points shown by adding the distance between each point and the y-axis which is the fourth option.
We are given the points:-
A (-8, -4) and,
B (2, -4)
We have to find the distance between the points AB.
We know that,
Distance between points AB = Distance between A and y -axis + Distance between y -axis and B
Hence, according to the cartesian plane given, we can write,
We can find the distance between the points shown by adding the distance between each point and the y-axis which is the fourth option.
To learn more about distance, here:-
https://brainly.com/question/15172156
#SPJ1
1. The function h(x) has the shape of a parabola has a focus of (-7,-4) and directrixat y = -1Determine the equation of h(x) in standard form by correctly choosing the symbols andnumbers from the math bank.Help ASAP
Let P (x, y) be any point on the parabola whose focus is (-7,-4,) and the directrix y+1 = 0.
As we already know that the distance of a point P from focus = distance of a point P from directrix
[tex]\sqrt[=]{(y+1)^2}\text{ =}\sqrt[+]{(x+7)^2+(x+4)^2}[/tex][tex](y+1)^2=(x+7)^2+(x+4)^2[/tex][tex]y^2+1+2y=x^2+7x+49+x^2+16+4x[/tex][tex]y^2+2y=2x^2+11x+64[/tex][tex]y(y+2)=2x^2+11x+64[/tex][tex]y=\frac{2x^2+11x+64}{y+2}[/tex]a. Identify the form the quadratic is written in andstate the feature of the parabola that could befound.i. y = (x + 2)² - 5Answer:ii. y =- x² + 7x-12Answer:y = (x –9)(x +4)Answer:
i)
The vertex form of a quadratic equation of a parabola opening upwards or downwards is,
[tex]y=a(x-h)^2+k\ldots\ldots(1)[/tex]Here, (h,k) is the coordinates of the vertex of the parabola. If a is positive, the parabola is facing up and if a is negative, the parabola is facing down.
The given equation of parabola is,
[tex]y=(x+2)^2-5\ldots\ldots(2)[/tex]So, the given equation is in the vertex form of the quadratic equation.
Comparing equations (1) and (2), we get
a=1, h=-2, k=-5.
Since a is positive, the parabola opens upwards. The coordinates of the vertex of the parabola is (-2,-5).
The price of a new car is $19995.00. The sales tax rate in Florida is 6.5%. What is the amount of tax on the car?
Answer:
the amount of tax on the car is $1299
Justin is taking an anti-flammatory drug and he must receive 6 milligrams for each 17 kg of weight. Justin weighs 244 pounds
Justin is taking an anti-flammatory drug and he must receive 6 milligrams for each 17 kg of weight.
Justin's weight is 244 pounds i.e., 110.677 Kg.
Theerfore, the amount of anti flammatory drug he needs is
[tex]\frac{6}{17}\times110.677\approx39.063[/tex]Therefore, Justing needs 39.063 miiligrams of anti flammatory drug.
Answer quick! Due today!Please help with explanation each graph shown is a translation of the graph of f(x)=x^2 write the function in vertex form
For a graph with f(x)=x^2, the vertex of the parabola is at the origin.
In the given graph, the parabola is shifted 3 units to the left and 1 unit down.
The general vertex form of a parabola is,
[tex]f(x)=a(x-h)^2+k[/tex]Here, h is the horizontal shift and k is the vertical shift.
Since the graph is only translated and not shrinked or expanded , a=1.
Since the graph is shifted horizonatlly to the left, h is negative.
So, h=-3.
Since the graph is shifted vertically down, k is negative.
So, k=-1.
So, the equation for the given graph becomes,
[tex]\begin{gathered} f(x)=(x-(-3)^2-1 \\ f(x)=(x+3)^2-1_{} \end{gathered}[/tex]Therefore, the function in vertex form is,
[tex]f(x)=(x+3)^2-1[/tex]help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Use the table to find the product of the two polynomials. Write your answers in descending orde.
Given:
Given the polynomial
[tex](4x^2-4x)(x^2-4)[/tex]Required: The product of the polynomials
Explanation:
Fill the table by taking the product of the values written in the left and up of each column.
The product of the polynomials is the sum of each entry in the column. Thus,
[tex](4x^2-4x)(x^2-4)=4x^4-4x^3-16x^2+16x[/tex]Final Answer:
[tex](4x^2-4x)(x^2-4)=4x^4-4x^3-16x^2+16x[/tex]Whats the anwser? need it asap
Answer:
B, yes because if you fold it in half then you have symmetry
Step-by-step explanation:
The quality of being made up of exactly similar parts facing each other or around an axis.
Problem iD: PRABERUZ On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled 1 in miles, d, to the number of hours flying, t, is t=d. How long will it take the airplane to travel 800 miles? 500 Do not include units (hours) in your answer. copted for free from openupresources.org
We have a relation between the distance traveled in miles (d) and the number of hours flying (t) that is t=(1/500)*d.
Then, when d=800, we have:
[tex]\begin{gathered} t=\frac{1}{500}\cdot d \\ t=\frac{1}{500}\cdot800=\frac{800}{500}=1.6 \end{gathered}[/tex]The time is 1.6 hours.
Answer: 1.6
Solve this equation by factorising:
y² + 3y - 10 = 0
Answer:
y = 2
Step-by-step explanation:
Simplify
[tex]( \sqrt{3}) \: ( {}^{5} \sqrt{3} )[/tex]
a :
[tex]3 \frac{1}{10} [/tex]
B:
[tex]3 \frac{3}{5} [/tex]
C:
[tex]3 \frac{9}{10} [/tex]
D:
[tex]3 \frac{7}{10} [/tex]
Employee at an antique store are hired at a wedge of $15 per hours, and they got a $9.75 raise each year. naomi make $20.25 per hours working at the store. how long has she worked there
Number of years she worked at the store is 0.5385 years ( 0.6 years approx. ).
What is rate of change ?A rate of change is a measurement of the ratio of one quantity to another. Rate of Change: 1608042=802=401; Change in Y = Change in X; Change in Distance; Change in Time. It develops either at a 40 or 401 rpm rate. This shows that an automobile is traveling at a 40 mph speed.
CalculationRate of early age of employee = $15 per hour
raise price per year = $9.75
Naomi wage per hour = $20.25
then gain extra wage = 20.25 - 15
= $5.25
number of years she worked = 5.25 / 9.75
= 0.5385 years ( 0.6 years approx)
learn more about rate of change here :
brainly.com/question/12786410
#SPJ4
7) X to the third equals 216
Explanation
[tex]x^3=216[/tex]
Step 1
we can use the fact that
[tex]\sqrt[m]{a}=a^{\frac{1}{m}}[/tex]to isolate x, or in other words we can take the cubic root in both sides
so
[tex]undefined[/tex]x
3. Sharon is using a calculator to find out
how many hours she has spent on a
certain job. She divides, and her display
reads:
4.666666666
Assuming her calculations are correct,
how many hours did she spend on the
job?
A. 4 1/6
B. 4 2/3
C. 4 6/7
D. 46
Answer:
4 6/7
Step-by-step explanation:
(Not really sure you should go with whatever answer you're sure of)
or 4 1/6
Answer:
B. 4 2/3
it's right, I took this last year.
What is the slope of the line that passes through the points (12, -13) and (-18, 11)? Round your answer to the nearest tenth.
The slope of the line is 0.8.
What is slope of the line?
The slope of a line is also called its gradient or rate of change. The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run. The slope formula uses two points, (x1, y1) and (x2, y2), to calculate the change in y over the change in x.
slope of the line = (y2-y1)/x2-x1
Here, the points are (12,-13) and (-18,11)
x1=12,y1=-13, x2=-18, y2=11
m (slope of line) = 11+13/(-18-12)
=24/-30
=-4/5
=0.8
To know more about slope of line, visit;
https://brainly.com/question/5600317
#SPJ1
Which equation best describes the graph of the line that has 1 slope and passes through point (3,-9)? 3
J
9x-18,
M
B
- Part A What is the value of x? (1 point)
Ox=3
Ox=18
Ox=30
Ox=9
3x
Part B Find JM in the previous item. (1 point)
OJM=3
OJM=9
OJM=54
OJM=63
K
Answer:
[tex]x=3, JM=9[/tex]
Step-by-step explanation:
The triangles are congruent by SAS. Using CPCTC,
[tex]9x-18=3x \\ \\ -18=-6x \\ \\ x=3 \\ \\ \\ \\ JM=9(3)-18=9[/tex]
Write an equation of a line in a slope intercept form that has a slope of 3/7 and y intercept of -23
If the slope is 3/7 and the y-intercept is -23, let's replace them in the formula.
y = mx + b
m is the slope and b is the y-intercept.
Then:
[tex]\begin{gathered} y=\frac{3}{7}x+\text{ \lparen}-23) \\ y=\frac{3}{7}x\text{ - }23 \end{gathered}[/tex]