Considering the given triangle is a right-angled triangle. Therefore, one side of the triangle is [tex]11\sqrt{2}[/tex] and the other side of the triangle is [tex]22\sqrt{2}[/tex]. Since we have to find one of the legs of the triangle, we can assume [tex]22\sqrt{2}[/tex] is the length of the hypotenuse and [tex]11\sqrt{2}[/tex] the length of one of the sides of the right-angled triangle.
Therefore, by Pythagoras' theorem,
[tex]\sqrt{ (22\sqrt{2}) ^{2} - (11\sqrt{2} )^{2} } =[/tex] length of one leg of the triangle = 26.95 units
Therefore, The length of one leg of the triangle is 26.95 units.
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Answer:
b…22
Step-by-step explanation:
what is 2.405 and 1.537 as a fraction to the simplest form
Answer:
2.405 = 481/200 or 2 81/200
1.537 = 1537/1000 or 1 537/1000
Step-by-step explanation:
Hope it helps:)
Answer:
2.405 = 481/200 or 2 81/200
1.537 = 1537/1000 or 1 537/1000
Step-by-step explanation:
what is the x-intercept of the linear equation that is parallel to y=-3x-5 and passes through (2, 6)?
x-intercept of the linear equation that is parallel to y=-3x-5 and passes through (2, 6) is 4
What is the equation of the line?
The slope of the line and a point on the line can be used to create the equation of a line.
The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.
Given equation of line is y = -3x - 5
Passing points (a,b) = (2,6)
As we know equation of the line is y = mx + c where m is the slope of the line and c is the y-intercept
On comparing the given equation of the line with y = mx + c , we have slope of the line is -3
Slope of two parallel lines is equal.
Equation of line having slope and passing point is given by y-b = m (x-a)
Therefore, equation of line having slope -3 and passing point (2,6) is y - 6 = -3(x - 2)
⇒ y - 6 = -3x + 6
⇒ y = -3x + 6 + 6
⇒ y = -3x + 12
Equation of line having slope and x-intercept is given by y = m(x - a) where m is the slope and a is the x- intercept
y = -3x + 12 can be written as y = -3(x-4)
On comparing this equation with y = m(x-a) we have x-intercept is 4
Therefore, x-intercept of the linear equation that is parallel to y=-3x-5 and passes through (2, 6) is 4
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Which is a solution to the equation? (x −2)(x + 5) = 18 Group of answer choices x = −4 x = −2 x = −7 x = −10
Answer:
-7
Step-by-step explanation:
-7-2= -9
-7+5= -2
-9×-2=18
Answer: n = - 13/4
Step-by-step explanation: got it correct :)
2x+4y=6
3x-12-бу
Solve X and Y
Answer:x=12
y=−186
Step-by-step explanation:x=63x+4y=12
Consider the first equation. Subtract 63x from both sides.
x−63x=4y
Combine x and −63x to get −62x.
−62x=4y
Divide both sides by −62.
x=−
62
1
×4y
Multiply −
62
1
times 4y.
x=−
31
2
y
Substitute −
31
2y
for x in the other equation, 63x+4y=12.
63(−
31
2
)y+4y=12
Multiply 63 times −
31
2y
.
−
31
126
y+4y=12
Add −
31
126y
to 4y.
−
31
2
y=12
Divide both sides of the equation by −
31
2
, which is the same as multiplying both sides by the reciprocal of the fraction.
y=−186
Substitute −186 for y in x=−
31
2
y. Because the resulting equation contains only one variable, you can solve for x directly.
x=−
31
2
(−186)
Multiply −
31
2
times −186.
x=12
The system is now solved.
x=12,y=−186
find the greatest common factor of 615 and 570.
Given the numbers:
[tex]615\text{ and 570}[/tex]Let's find their greatest common factor:
Step 1: Let's determine the factors of the numbers.
a.) 570
The factors of 570 are: 1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570
b.) 615
The factors of 615 are: 1, 3, 5, 15, 41, 123, 205, 615
Their common factors are: 1, 3, 5, 15
But the greatest among all factors is 15.
Therefore, their greatest common factor (GCF) is 15.
Find the number for n that makes this equation
true:
205
n(8-3)+7(9 + 1) = 7(9 + 1) + 2(1 + 4)
a) 5 b) 70
c) 2
d) 20
What number is in
PLEASE HELP!!!
1: Add the linear expression
(-2×-5-3×)+(2×-2) what is the sum?
2: Subtract the linear expressions.
(3/4×-1)-(1/3×+4) what's the difference?
3: Add the 2 expression
-6.5b+11 and 3.3b-2
4:Subtract the linear expressions.
(-3.6×+9.4)-(1.9×+3.6) whats the difference?
5: Subtract 5×-2 from -3×+4.
A. -8×+2
B.2×+2
C.8×-6
D.-8×-6
The solution of each expression is
(1) (-2×-5-3)+(2×-2) = - 10
(2) (3/4 x-1)-(1/3 x +4) = -13/12 x -5
(3) -6.5b+11 + 3.3 b - 2 = - 3.2b + 9
(4) (-3.6x+9.4)-(1.9x +3.6) = -5.5 x + 5.8
What are the basic equations?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. An equation is an algebraic statement that demonstrates two mathematical expressions are equivalent in algebra, and this is how it is most usually used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." When two expressions are joined by an equal sign, a mathematical statement is called an equation. An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable.
(1) The sum of the given expressions is given as
(-2×-5-3)+(2×-2)
= -2x - 8 + 2x - 2
= -8 - 2
= - 10
(2) (3/4 x-1)-(1/3 x +4)
(-3/4) x- (1/3) x - 1 - 4
= -13/12 x -5
(3) -6.5b+11 + 3.3 b - 2
= (-6.5+ 3.3) +11 -2
= - 3.2b + 9
(4) (-3.6x+9.4)-(1.9x +3.6)
= (-3.6x-1.9x)+9.4 - 3.6
= -5.5 x + 5.8
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Robert needs to cut four shelves from a board that is meters long. The second shelf is centimeters longer than twice the length of the first shelf. The third shelf is centimeters shorter than the first shelf. The remaining shelf is centimeters longer than the first shelf. If robert must use the entire meter board for the shelves, what is the length of the second shelf, in centimeters?.
The length of the second shelf is 114 centimetres.
Consider the four shelves as A, B, C and D. According to the question, the length of the four shelves is 2.5 cm.
A + B + C + D = 250 cm ( 1 m = 100 cm ⇒ 2.5 * 100 = 250 ) → 1
The length of the second shelf is 18 cm longer than twice the length of the first shelf.
B = 2A + 18 → i
The length of the third shelf is 12 cm shorter than the first shelf.
C = A - 12 → ii
The length of the fourth shelf is 4 cm longer than the first shelf.
D = A + 4 → iii
Substitute i,ii and iii in 1 ⇒ A + B + C + D = 250
A + 2A + 18 + A - 12 + A + 4 = 250
5A + 22 - 12 = 250
5A + 10 = 250
5A = 250 - 10
5A = 240
A = 240/5
A = 48
Substitute A = 48 in i, ii, iii and then we get,
B = 11, C = 36 and D = 52
Therefore, the length of the second shelf B is 114 cm.
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The complete question is
Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 centimetres longer than twice the length of the first shelf. The third shelf is 12 centimetres shorter than the first shelf. The remaining shelf is 4 centimetres longer than the first shelf. If Robert must use the entire 2.5 meter board for the shelves, what is the length of the second shelf, in centimetres?
What is the quotient of two and two fifths ÷ five sixths?
sixty over thirty
seventy two over twenty five
fifteen over twenty-five
twenty two fifths
B ] seventy two over twenty five is the quotient of two and two fifths ÷ five sixths.
Quotient refers to the number produced by division of two numbers.
According to question,
two and two fifths = 22/5 = 5*2+2/5 = 12/5five sixths = 5/6Division of two numbers,
⇒ 12/5 / 5/6
⇒ 12/5 * 6/5
⇒ 72/25
Hence, 72/25 i.e., seventy two over twenty five is the quotient of two and two fifths ÷ five sixths.
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2=1/2(7x-4) i don’t know how to use the fractions, please help.
Answer:
x= 1.14 to 2d.p.
Step-by-step explanation:
1/2 = 0.5
0.5 * 7x = 3.5x
0.5 * -4 = -2
2=3.5x-2 Solve +2
4=3.5x /3.5
x= 1.14 to 2d.p.
What is the value of x in: [tex] log_{2}(x) - 3 = 1[/tex]a) 2²b) 2³c) 2⁴d) 2¹
Add 3 to both sides:
[tex]\begin{gathered} \log _2(x)-3+3=1+3 \\ \log _2(x)=4 \\ 2^{\log _2(x)}=2^4 \\ x=2^4 \end{gathered}[/tex]At cliffs of insanity point, the great sasquatch canyon is 7117 feet deep. from that point, a fire is seen at a location known to be 10 miles away from the base of the sheer canyon wall. what angle of depression is made by the line of sight from the canyon edge to the fire? express your answer using degree measure rounded to one decimal place.
Angle of depression is 7.7 ° made by the line of sight from the canyon edge to the fire .
What is angle of depression ?The angle of depression is the angle created by the object and the horizontal line as seen from the horizontal line. The distance between two objects is often calculated when the angles and spacing of an object from the ground are known.
Calculationlet f be the the fire
b is the base of the sheer canyon wall
o be the cliffs of insanity point that is canyon edge
so OB = 7117 Feet
bf = 10 miles = 10 * 5280 = 52800 feet
angle of depression is < xof which is equal to < ofb
let the angle of depression is [tex]\theta[/tex]
now from triangle obf ; it is a right angle triangle , where of = hypotenuse
bf = base , ob = height < ofb = [tex]\theta[/tex]
so , tan [tex]\theta[/tex] = ob/bf = 7117/52800
[tex]\theta[/tex] = [tex]tan^{-1}[/tex] ( 7117/52800) = 7.68 ° = 7.7 °
so angle of depression is 7.7 °
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Complete the point-slope equation of the line through (−2,6) (1, 1)
Use exact numbers.
y−6= [ ]
y-6 = -5/3 (x+2) is the point - slope equation of the line through (-2 , 6 ) ( 1 , 1 ) using exact numbers.
What is point - slope equation ?For linear equations, the typical form is y-y1=m(x-x1). It highlights the line's slope and a line point (that is not the y-intercept).
The two approaches for determining the equation of a line given a point and its slope are as follows:
(a). Input the slope and the (x, y) point values into the equation y = mx + b, then solve for b using the substitution technique
b) Point-slope form: (x 1, y 1), where (y 1, x 1) is the point and (m, the slope) is the specified slope.
CalculationFirst you need to find the slope, (y2-y1)/(x2-x1). This is (1-6)/(1-(-2)) or -5/3
Now that you know the slope you can use that for the point-slope equation
The point-slope equation is y-y1 = m(x-x1). If we start with y-6, the x value is -2 (from our point (-2,6)
y-6 = -5/3 (x-(-2))
or, y-6 = -5/3 (x+2)
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Mauricio fue en bicicleta de su casa a la de su abuela. Si salió a las 10:00 am y llego a las 2:00 p.m., ¿cuánto tiempo duró el trayecto?
Si pasamos el formato de horas a 24 horas, tenemos lo siguitente:
[tex]\begin{gathered} 10\colon00am=10\colon00hrs \\ 2\colon00pm=14\colon00\text{hrs} \end{gathered}[/tex]claramente podemos ver la diferencia:
[tex]14\text{hrs-}10\text{hrs}=4\text{hrs}[/tex]por lo tanto, el trayecto duro 4 horas
Week 10 Quiz Version A The Zero Product Property is used to find the zeros (or ti the graph will cross the O X-axis © y-axis O z-axis o origin
The roots of a equation are the points where the graph intersects the x-axis. The answer is the first option.
3 (2) ^2 divide [3 x 2] - 5__________________ 8 divide 4 x 2
Solution
Using BODMAS to solve the fraction
[tex]\begin{gathered} \frac{3(2)^2\div[3\times2]-5}{8\div4\times2} \\ \frac{3(4)\div6-5}{2\times2} \end{gathered}[/tex][tex]\begin{gathered} \frac{12\div6-5}{4} \\ \frac{2-5}{4} \\ =-\frac{3}{4} \end{gathered}[/tex]Therefore the answer = -3/4
report a stolen credit card to EFTA or PCI standards?
The correct matching of EFTA and PCI standards are:
A) EFTA
Report a debit card as stolen.Put a stop payment on automatic withdrawals.(B) PCI
Protect credit card information.Uphold a secure network.What is Electronic Fund Transfer Act (EFTA)?The purpose of the Electronic Fund Transfer Act (EFTA), a law passed by Congress, is to safeguard consumer financial transactions made using electronic tools like debit cards and automated teller machines (ATMs).The purpose of the Payment Card Industry Data Security Standard (PCI DSS) is to guarantee that financial institutions, such as banks, have a robust and secure network architecture to safeguard clients' personal information.So, match the following as follows:
(A) EFTA
Report a debit card as stolen.Put a stop payment on automatic withdrawals.(B) PCI
Protect credit card information.Uphold a secure network.Therefore, the correct matching of EFTA and PCI standards are:
A) EFTA
Report a debit card as stolen.Put a stop payment on automatic withdrawals.(B) PCI
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Complete question:
Match the correct EFTA and PCI Standards.
report a stolen debit card
protect credit card data
place a stop payment on
recurring payments
maintain a secure network
12. Given that a line has slope = 5 and passes through the point (2,3), what's its equation
Given slope m=5 and the point as (2, 3)
[tex]\begin{gathered} y-y_1=m(x-x_{1)} \\ \text{Where x}_1=2 \\ y_1=3 \\ y-3=5(x-2) \\ y=5x-10+3 \\ y=5x-7 \end{gathered}[/tex]The equation of the line is y = 5x - 7
how do i solve this for standard equation and foci?
For this problem, we are given the graph of an ellipse, and we need to determine its expression in the standard form.
The standard equation of an ellipse is given below:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Where (h,k) is the center of the ellipse, a is the horizontal radius and b is the vertical radius.
The center of the ellipse on our problem is (-2,2), the vertical radius is 2 and the horizontal radius is 3. We have:
[tex]\begin{gathered} \frac{(x+2)^2}{3^2}+\frac{(y-2)^2}{2^2}=1 \\ \frac{(x+2)^2}{9}+\frac{(y-2)^2}{4}=1 \end{gathered}[/tex]In order to calculate the Foci, we need to first find the eccentricity of the ellipse, which is given by the following formula:
[tex]\begin{gathered} e=\sqrt{a^2-b^2} \\ e=\sqrt{3^2-2^2} \\ e=\sqrt{9-4}=\sqrt{5} \end{gathered}[/tex]The coordinates of the foci are given by:
[tex]\begin{gathered} F(h+e,k)=(-2-\sqrt{5},2) \\ F^{\prime}(h-e,k)=(-2+\sqrt{5},2) \end{gathered}[/tex]The coordinates for the foci are: (-2-sqrt(5), 2) and (-2+sqrt(5), 2).
please help
my homework is due tom
I finished the rest
a) The coordinates of the point B is (6, 6) and the coordinates of the point D is (4,0).
b) The completed rectangle ABCD is shown in the following graph. And the point of C (8,4) is also marked on it.
Coordinates:
Coordinates refers a pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes.
Given,
Here we have the graph attached to the given question with the coordinates A, B and D.
Now, we have to find the following:
a) Coordinates of B and D
b) Draw a complete rectangle on the graph and mark the coordinates C on it.
a) While we looking at the graph, we have identified that,
The point of B is derived by when the point 6 in x axis and y in y axis intersect. Therefore, the coordinate of B is (6,6).
Similar way, the coordinate of D is obtained as (4,0).
b) First, we have to identify the point of C, that can be obtained, we know that the shape of ABCD is rectangle, based on this the coordinate lies at the point of (8,4).
Therefore, the completed graph is attached below.
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the major parts of a salary range consist of all of the following, except: a. minimum b. midpoint c. median d. maximum
The major parts of a salary range typically include the minimum, midpoint, and maximum salary for a position. The median salary is often used as a point of reference within a salary range, but is not considered one of the major parts.
The median salary is the salary at which half of the workers in an occupation earn less and half earn more.The midpoint is the average of the minimum and maximum salaries. It is used to calculate the median salary. The median salary is the salary that is in the middle of the minimum and maximum salaries. It is used to calculate the mean salary. The mean salary is the average of all the salaries.
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Stevens new cell phone plan charges a flat monthly fee of $22.5. The plan allows an unlimited number of text messages, but each minute (m) used for the phone calls cost $0.12.
Write an equation that represents the monthly cost(c) of Steven's phone bill based on how many minutes talked?
The required system of equations to express Stevens monthly fee is
22.5 + 0.12 m = c
Given : A flat monthly fee which is charged for Stevens = $22.5
The cost of each phone call = $ 0.12
Let the cost of each monthly call be represented by the letter m
And the total monthly fee be represented by the letter c
thus according to the question the equation can be expressed as :
22.5 + 0.12 m = c
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Choose the line perpendicular to the following equation through the given point
Answer:
y=-1/2x+1
Step-by-step explanation:
perpendicular is when the gradient of the existing equation is reciprocated (swapped sides and flipped)
new gradient- -1/2
so our new equation is y=-1/2x+c
we have the co-ordinates for x and y so substitute into new equation
1=(-1/2 x 0) + c
so c=1
Hence our equation is : y=-1/2x+1
دیا
A new restaurant just opened up in your
neighborhood. One soda costs $2.75, and five
sodas cost $13.75. Is the cost a proportional or
non-proportional relationship?
proportional
not enough information
non-proportional
The cost for the soda is proportional.
How to calculate the value?For there to be a proportional relationship, there must be a constant.
In this case, one soda costs $2.75.
Also, five sodas cost $13.75. The cost per soda will be:
= $13.75 / 5
= $2.75
Since the values of $2.75 are the same, it has a proportional relationship.
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UBTRACT THE INTEGERS AN PE YOUR ANSWER IN THE BC -34 - 55
-34-55
Since both numbers are negative, we simply have to add the numbers and the result will be negative.
-89
can you pls help wit
DEF is an acute angke because the measure we can notice is less than a right angle
then the value is less than 90°
then right option should be D and E
C isnt because we can notice the angle is
Mia has set up a lemonade stand outside her house and sells small cups and large
cups of lemonade. Each small cup holds 12 ounces of lemonade and each large cup
hold 22 ounces of lemonade. Mia sold 80 cups of lemonade totaling 1460 ounces.
Determine the number of small cups sold and the number of large cups sold.
Answer:
small cups: 30large cups: 50Step-by-step explanation:
You want the number of small (12 oz) cups and large (22 oz) cups sold if 80 total cups and 1460 ounces were sold.
SetupWe can let x represent the number of large cups sold. Then 80-x is the number of small cups sold, and the total ounces of lemonade sold are ...
12(80 -x) +22x = 1460
SolutionSimplifying the equation gives ...
960 +10x = 1460
10x = 500
x = 50
Then the number of small cups sold is ...
80 -x = 80 -50 = 30
30 small cups and 50 large cups were sold.
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Help with problem and pick if it is odd or even
Since
[tex]f(x)=-x^4+x^3+2x+x+1[/tex]even degree function, it will have an even number of real zeros, and, since it has a degree of 4, there will be 4, 2 or 0 real zeroes
A rectangular prism has a volume of 384 cubic inches. Find the height of the prism.h= ____ in
Rectangular prism volume: base length x base width x height
By looking at the image we can see that the height of the prism is 13cm.
To obtain the result in inches, divide by 2.54
13/2.54 = 5.12 inn inche
5÷1/12 write your answer in the simplest form.
Answer:60
Step-by-step explanation:
Answer:
60
Step-by-step explanation: