The value of x in the triangle is 8 and the value of y is [tex]8\sqrt2[/tex]
How to determine the value of x in the triangle
From the question, we have the following parameters that can be used in our computation:
The triangle
Using the Pythagoras theorem, we have:
[tex]x^2 = 10^2 - 8^2[/tex]
This gives
[tex]x^2 = 36[/tex]
take the square root of both sides
x = 8
How to determine the value of y in the triangle
Using the Pythagoras theorem on the second triangle, we have
[tex]y^2 = 8^2 + 8^2[/tex]
This gives
[tex]y^2 = 2(8^2)[/tex]
take the square root of both sides
[tex]y = 8\sqrt2[/tex]
Hence, the value of x is 8 and the value of y is [tex]8\sqrt2[/tex]
Tyler knows that the ratio of male to female horses on the farm is 2 to 3. If there are 12 male horses, how many female horses are there?
20 POINTS
Answer:
18 female horses.
Step-by-step explanation:
By proportion 2 : 3 = 12 : x where x is the number of female horses.
12 / 2 = x / 3
2x = 3*12 = 36
x = 18.
Find the quotient. x + 4/x2 ÷ 2 /x
The simplified form of the expression [tex]\( \frac{x + 4}{x^2} \div \frac{2}{x} \) is \( \frac{x + 4}{2x} \).[/tex]
To simplify the given expression, we'll first deal with the division of fractions by turning it into multiplication with the reciprocal of the divisor.
So, the given expression [tex]\( \frac{x + 4}{x^2} \div \frac{2}{x} \)[/tex] becomes:
[tex]\[ \frac{x + 4}{x^2} \times \frac{x}{2} \][/tex]
Next, let's factor the numerator x+4 and simplify:
[tex]\[ \frac{x + 4}{x^2} \times \frac{x}{2} = \frac{x + 4}{x^2} \times \frac{x}{2} = \frac{(x + 4) \cdot x}{x^2 \cdot 2} \][/tex]
Now, we'll simplify the expression by canceling out common factors:
[tex]\[ = \frac{x(x + 4)}{2x^2} \]\[ = \frac{x(x + 4)}{2x^2} = \frac{x(x + 4)}{2x \cdot x} \][/tex]
[tex]\[ = \frac{x + 4}{2x} \][/tex]
The range of the following relation R {(3,-2), (1, 2), (-1, -4),(-1, 2)} is
A.{-1, 1, 3}
B.{-1, -1, 1, 3} ♡
C.{-4, -2, 2, 2}
D.{-4, -2, 2}
Answer:
D.{-4, -2, 2}
Step-by-step explanation:
all y components
same y value are not repeated
PLEASE HELP ASAP?!!!!!!!
Answer:
76.9 in^2
Step-by-step explanation:
Area of circle
= (3.14) x(10.7)^2
= 3.14 x 114.49
= 359.4986 in^3
Let x = area of the smaller sector
x/77 = 359.4986/360
360x = 359.4986 x 77
360x = 27,681.3922
x = 76.9 (to the nearest tenth)
Find the x coordinate of the point.
Answer:
x= -17
Step-by-step explanation:
When we have 2 points, we can find the slope using
m = (y2-y1)/(x2-x1)
Substituting what we know
1/5 = (0-3)/(x--2)
1/5 = -3/(x+2)
Using cross products
1*(x+2) = 5*(-3)
x+2 = -15
Subtract 2 from each side
x+2-2 = -15-2
x=-17
What is the slope of the line segment?
a 1/4
b -1/4
c 4
d 4
to get the slope of any line, we can simply use two points off of it, for this one, say (3,12) and (4,16)
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{16}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{16-12}{4-3}\implies \cfrac{4}{1}\implies 4[/tex]
A parallelogram whose vertices have coordinates R(1, -1), S(6, 1), T(8, 5), and U(3, 3) has a shorter diagonal of ___ . 5 √(13) √(97)
Answer:
[tex]|SU|=\sqrt{13}[/tex]
Step-by-step explanation:
The given parallelogram has vertices R(1, -1), S(6, 1), T(8, 5), and U(3, 3) .
Recall the distance formula;
We use the distance formula to determine the length of the diagonals.
For diagonal R(1,-1) and T(8,5), We have;
[tex]|RT|=\sqrt{(8-1)^2+(5--1)^2}[/tex]
[tex]|RT|=\sqrt{(7)^2+(6)^2}[/tex]
[tex]|RT|=\sqrt{49+36}[/tex]
[tex]|RT|=\sqrt{85}[/tex]
For the diagonal S(6,1) U(3,3)
[tex]|SU|=\sqrt{(6-3)^2+(5-3)^2}[/tex]
[tex]|SU|=\sqrt{(3)^2+(2)^2}[/tex]
[tex]|SU|=\sqrt{9+4}[/tex]
[tex]|SU|=\sqrt{13}[/tex]
Therefore the shorter diagonal is:
[tex]|SU|=\sqrt{13}[/tex]
A fantasy board game makes use of four dice. The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each. If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist? A. 30 B. 240 C. 2,400 D. 3,000
Answer: Option C
2,400
Step-by-step explanation:
When launching the first 6-sided die there are 6 possible outcomes
When launching the 4-sided die there are 4 possible outcomes
When throwing each die of 10 faces there are 10 possible outcomes
So if all the dice are thrown together, the number of possible combinations that can be obtained is:
[tex]S = 6 * 4 * 10 * 10\\S = 24 * 100[/tex]
[tex]S = 2400[/tex] possible results
Finally the answer is the option C.
One angle of an isosceles triangle measures 110°. Which other angles could be in that isosceles triangle
Answer:
180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.
Step-by-step explanation:
Please mark brainliest and have a great day!
If anyone could please help me with this question???I know that you can get three triangles out of the shape.
Answer:
See below.
Step-by-step explanation:
The triangles are similar because the angles marked 125 are equal and the sides either side of these angle are in the same ratio:
1.3 / 2.5 = 2.6 /5.
If we are given the length of AE we would find CF from the equation:
1.3 / 2.5 = CF / AE
CF = (1.3 * AE) / 2.5.
consider the explicit formulas for two sequence
These are the formulas right?.. I hope so, anyways..
- f(n)= 2^(n-1) -1
- g(n)=3n+6
f(7)=2^{7-1}-1 - f(7)=2^{6}-1 - f(7)=64-1 - f(7) = 63
g(10)=3\X 10+6 - g(10)=30+6 - g(10) = 36
= f(7)>g(10)
I hope that it helped..
Answer:
The one above is right.
Step-by-step explanation:
What are the coordinates of the point shown on the
coordinate plane?
x-coordinate =
y-coordinate =
Final answer:
The coordinates of the point are (4, 3), where 4 is the x-coordinate (horizontal direction) and 3 is the y-coordinate (vertical direction).
Explanation:
The coordinates of a point on a Cartesian coordinate system are determined by its horizontal position (x-coordinate) and its vertical position (y-coordinate). Given that the point is on the first coordinate axis (x-axis) and in the (1, 2)th coordinate plane, we understand that the x-coordinate is related to the horizontal direction and the y-coordinate is related to the vertical direction.
In the context of this problem, if the figure on the coordinate plane indicates that the point is 4 units to the right of the origin along the x-axis and 3 units above the origin along the y-axis, then the coordinates of the point are ( extbf{4}, extbf{3}). Here, the convention is that moving to the right of the origin increases the x-coordinate and moving upwards increases the y-coordinate.
Which expression is equivalent to
o ooo
Answer:
a
Step-by-step explanation:
becuase you distribute the numbers
By definition of multiplication of powers of the same base we have to put the same base and add the exponents, then, we can rewrite the expression as:
[tex](2 ^ {\frac {1} {2} + \frac {3} {4}}) ^ 2 =\\(2 ^ {\frac {4 + 6} {8}}) ^ 2 =\\(2 ^ {\frac {10} {8}}) ^ 2 =\\(2 ^ {\frac {5} {4}}) ^ 2 =[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So, we have:
[tex]2 ^ {\frac {10} {4}} =\\2 ^ {\frac {5} {2}} =[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So, the expression is equivalent to:
[tex]2 ^ {\frac {5} {2}} = \sqrt {2 ^ 5}[/tex]
ANswer:
Option B
Lynn is taking a trip in her car. She spent 387.00 on gasoline and snacks. Lynn spent 35.80 on snacks for the entire trip. Gasoline costs 2.54 per gallon.
How many gallons of gasoline did Lynn purchase on her trip?
Answer:
138.27 gallons
Step-by-step explanation:
Total cost = snacks + gallons * cost per gallon
387 = 35.80 + g*2.54
Subtract 35.80 from each side
387-35.80 = 35.80-38.50 + g*2.54
351.20= + g*2.54
Divide by 3.54 on each side
351.20/2.54 = 2.54g/2.54
138.2677165 = g
Rounding to the nearest hundredth
138.27 gallons
Given : Lynn spent 387.00 on gasoline and snacks
Given : Lynn spent 35.80 on snacks for the entire trip
Money spent on gasoline :
Total money spent on gasoline and snacks - Money spent on snacks
[tex]:\implies[/tex] Money spent on gasoline = 387.00 - 35.80
[tex]:\implies[/tex] Money spent on gasoline = 351.20
Given : Gasoline costs 2.54 per gallon
[tex]\implies \mathsf{Number\;of\;gallons\;of\;gasoline = \dfrac{Total\;money\;spent\;on\;gasoline}{Cost\;of\;gasoline\;per\;one\;gallon}}[/tex]
[tex]\implies \mathsf{Number\;of\;gallons\;of\;gasoline = \dfrac{351.20}{2.54}}[/tex]
[tex]\implies \mathsf{Number\;of\;gallons\;of\;gasoline = 138.27}[/tex]
A line contains the point 0,2. If the slope of the line is m=-6 write the equation of the line using slope intercept form
Answer:
y = -6x + 2Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-interept (0, b)
We have the slope m = -6 and the point (0, 2) → b = 2.
Substitute:
y = -6x + 2
Karl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute?
Answer: 720 feet
Step-by-step explanation: 120 x 6= 720
Answer:
720
Step-by-step explanation:
120/10 to find his feet per second which is 12 feet per second
12*60
since there are 60 seconds in a minute
= 720
At a Kentucky Friend Chicken, a survey showed 2/3 of all people preferred skinless chicken over the regular chicken. If 2,400 people responded to the survey, how many people preferred regular chicken?
Answer:
800 people
Step-by-step explanation:
We are given in the question that 2/3 of 2400 people preferred skinless chicken.
We have to find the number of people who prefer skinless chicken
[tex]So,\\= \frac{2}{3} *2400\\=1600[/tex]
1600 people prefer skinless chicken,
So,
The number of people who prefer regular chicken = 2400-1600
= 800 people
Answer: kentucky friend chicken? XD
Step-by-step explanation:
Which equation results from adding the equations in this system? x+6y=9 and -x+2y=-15
Answer:
8y=-6 or 4y=-3
Step-by-step explanation:
We are given two equations
[tex]x+6y=9\\and\\-x+2y=-15[/tex]
In order to add the equations, the left hand side of one equation will be added to the left hand side of second equation. similarly, the right hand side of first equation will be added to the right hand side of the equation so,
[tex]x+6y+(-x+2y)=9+(-15)\\Combining\ alike\ terms\\x+6y-x+2y=9-15\\6y+2y=-6\\8y=-6\\Can\ also\ be\ written \ as\\4y=-3[/tex]
Answer:
The resultant equation is 8y = -6
Step-by-step explanation:
To get the system of equation that will results from adding the statement, we will follow the steps below;
x+6y=9 -------------------------------------------------------------------------------(1)
-x+2y=-15-------------------------------------------------------------------------------(2)
Adding equation (1) and equation(2), we will have;
(1-1)x + (6+2)y =(9-15)
x variable will go away
8y =-6
The resultant equation is 8y = -6
What is the measure of arc QR?
26°
52
104
128°
The answer to this question is option C. 104 °
(Late answer!)
Ariana and William go shrimping. Ariana caught nine less than five times the number of shrimp that William caught. If C represents the number of shrimp William caught, write the expression that gives the number shrimp the Ariana caught
The expression that gives the number of shrimp Ariana caught will be 5C - 9.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Ariana and William go shrimping. Ariana caught nine less than five times the number of shrimp that William caught. If C represents the number of shrimp William caught.
Then the expression is given as,
⇒ 5C - 9
The expression that gives the number of shrimp Ariana caught will be 5C - 9.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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A cone has a height of 2.5 inches and a radius of 5 inches. What is the volume of the cone?
Answer: [tex]65.44\ in^3[/tex]
Step-by-step explanation:
To calculate the volume of a cone you can use this formula:
[tex]V_{(cone)}=\frac{1}{3}\pi r^2h[/tex]
Where "r" is the radius and "h" is the height of the cone.
In this case you know that this cone has a height of 2.5 inches and a radius of 5 inches. Then:
[tex]h=2.5\ in\\r=5\ in[/tex]
Finally, you need to substitute these values into the formula. Then you get that the volume of the cone is:
[tex]V_{(cone)}=\frac{1}{3}\pi (5\ in)^2(2.5\ in)\\\\V_{(cone)}=65.44\ in^3[/tex]
Polygon ABCD is a rectangle. What is its area? Round your answer to the
nearest tenth.
(2, 5)
(-4, 3)
(-3, 0)
(3, 2)
A. 20.0 square units
B. 19.0 square units
C. 25.6 square units
D. 39.7 square units
Answer:
Option A. 20.0 square units
Step-by-step explanation:
Let
[tex]A(2, 5),B(-4, 3),C(-3, 0),D(3, 2)[/tex]
Plot the points
see the attached figure
The area of the rectangle is equal to
[tex]A=AB*AD[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
[tex]A(2, 5),B(-4, 3)[/tex]
substitute in the formula
[tex]AB=\sqrt{(3-5)^{2}+(-4-2)^{2}}[/tex]
[tex]AB=\sqrt{(-2)^{2}+(-6)^{2}}[/tex]
[tex]AB=\sqrt{40}\ units[/tex]
step 2
Find the distance AD
[tex]A(2, 5),D(3, 2)[/tex]
substitute in the formula
[tex]AD=\sqrt{(2-5)^{2}+(3-2)^{2}}[/tex]
[tex]AD=\sqrt{(-3)^{2}+(1)^{2}}[/tex]
[tex]AD=\sqrt{10}\ units[/tex]
step 3
Find the area of rectangle
[tex]A=AB*AD[/tex]
we have
[tex]AB=\sqrt{40}\ units[/tex]
[tex]AD=\sqrt{10}\ units[/tex]
substitute
[tex]A=(\sqrt{40})*(\sqrt{10})[/tex]
[tex]A=20\ units^{2}[/tex]
Solve the equation for X.
(x - 4) - (x + 7) = 8x please help me solve this somebody I don't understand how
Answer:
x = - [tex]\frac{11}{8}[/tex]
Step-by-step explanation:
Given
(x - 4) - (x + 7 ) = 8x
Distribute parenthesis noting second is distributed by - 1
x - 4 - x - 7 = 8x ← simplify left side
- 11 = 8x ( divide both sides by 8 )
x = - [tex]\frac{11}{8}[/tex]
What is 3 In 3 - In 9 expressed as a single natural logarithm?
In 3
In 6
In 18
In 27
Answer:
ln 3
Step-by-step explanation:
Using the rule of logarithms
log [tex]x^{n}[/tex] ⇔ n log x
Given
3 ln 3 - ln 9
= 3 ln 3 - ln 3²
= 3 ln 3 - 2 ln 3
= ln 3
The given logarithmic expression → {3 ln(3) - ln(9)} can be written as ln(3).
What is logarithm?Logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Given is the logarithmic expression as -
3 ln(3) - ln(9)
We can solve the expression as -
3 ln(3) - ln(9)
ln(3³) - ln(9)
ln(27) - ln(9)
ln(27/9)
ln (3)
Therefore, the given logarithmic expression → {3 ln(3) - ln(9)} can be written as ln(3).
To solve more questions on logarithmic, visit the link-
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Solve both questions please ❤️❤️
Answer:
1. y=7.2
2. x=18
Step-by-step explanation:
1. Triangles CMN and CBA are similar triangles (by AAA postulate). Similar triangles have proportional corresponding sides, so
[tex]\dfrac{CM}{CB}=\dfrac{CN}{CA}\\ \\\dfrac{12}{12+y}=\dfrac{10}{10+6}\\ \\12\cdot 16=10\cdot (12+y)\\ \\192=120+10y\\ \\10y=72\\ \\y=7.2[/tex]
2. GK is angle G bisector. Use angle bisector's property:
[tex]\dfrac{GH}{GI}=\dfrac{KH}{KI}\\ \\\dfrac{40}{24}=\dfrac{30}{x}\\ \\40x=24\cdot 30\\ \\4x=24\cdot 3\\ \\x=6\cdot 3=18[/tex]
What is the slope of a line that is perpendicular to the line whose equation is 5y+2x=12?
A. 5/2
B. −2/5
C. −5/2
D. 2/5
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 5y + 2x = 12 into this form
Subtract 2x from both sides
5y = - 2x + 12 ( divide all terms by 5 )
y = - [tex]\frac{2}{5}[/tex] + [tex]\frac{12}{5}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{2}{5}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{5} }[/tex] = [tex]\frac{5}{2}[/tex] → A
PLEASE HELP ME WITH THIS STUPID QUESTION!!!! WHAT DO I HAVE TO PUT IN THE BOX!! 30pts. Will mark brainliest!!!
2
-10 and 10 are 10 units from 0 on the number line
Solve the following proportion for v. V/13=11/13
Round your answer to the nearest tenth.
Answer:
V = 11
Step-by-step explanation:
All you have to do here is to multiply both sides of this equation by 13. This will eliminate the fractions. You'll be left with V = 11.
To solve the proportion V/13 = 11/13, we can equate V to 11 since identical denominators imply equal numerators. No further calculations or rounding needed as V is a whole number.
Explanation:To solve the proportion V/13 = 11/13 for V, we can see that both sides of the equation are divided by the same number, 13. Since the denominators are equal, we can deduce that the numerators must also be equal for the proportion to be true.
Therefore, the value of V must be equal to 11, as V/13 matches 11/13. There is no need for further calculations or rounding since 11 is already a whole number.
Learn more about Proportion here:https://brainly.com/question/14752332
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The radius of a circular park is 120 m to the nearest meter what is the circumference of the park?
Answer:
D. 754 m
Step-by-step explanation:
When calculating the circumference of the circle it ends up as 753.98 but rounded it's 754.
Answer: It’s 754!
Explanation: I also got this one on a test lol
Find the sample Standard deviation and the population standard deviation of the data set? 17,37,56,16,12,16,19,45,14,37,21,26,43,46,42
Answer:
The sample standard deviation is 14.458
The population standard deviation is 13.967
Step-by-step explanation:
* Lets revise the population standard deviation (σ)
1. Work out the Mean (μ) (average of the numbers)
2. Then for each number subtract the Mean and square
the result (xi - μ)²
3. Then work out the mean of those squared differences
[∑(xi - μ)²/N]
4. Take the square root of that (√[∑(xi - μ)²/N]) and to find σ
* Lets revise the sample standard deviation (s)
1. Work out the Mean (x) (average of the numbers)
2. Then for each number subtract the Mean and square
the result (xi - x)²
3. Then work out the mean of those squared differences [∑(xi - x)²/N - 1]
4. Take the square root of that (√[∑(xi - x)²/N - 1]) and to find s
* Now lets solve the problem
- The data are 15 numbers
17 , 37 , 56 , 16 , 12 , 16 , 19 , 45 , 14 , 37 , 21 , 26 , 43 , 46 , 42
∵ x = μ = sum/number
∴ x = μ = (17+37+56+16+12+16+19+45+14+37+21+26+43+46+42)÷15=29.8
- Subtract the mean from each number and square the result
∵ (17 - 29.8)² = 163.84
∵ (37 - 29.8)² = 51.84
∵ (56 - 29.8)² = 686.44
∵ (16 - 29.8)² = 190.44
∵ (12 - 29.8)² = 316.84
∵ (16 - 29.8)² = 190.44
∵ (19 - 29.8)² = 116.64
∵ (45 - 29.8)² = 231.04
∵ (14 - 29.8)² = 249.64
∵ (37 - 29.8)² = 51.84
∵ (21 - 29.8)² = 77.44
∵ (26 - 29.8)² = 14.44
∵ (43 - 29.8)² = 174.24
∵ (46 - 29.8)² = 262.44
∵ (42 - 29.8)² = 148.84
∴ ∑(xi - μ)² = ∑(xi - x)² = 2926.36
∵ N = 15
∴ The sample standard deviation = √[∑(xi - x)²/(N - 1)]
∴ s = √[2926.36/(15 - 1)] = 14.458
∴ The population standard deviation = √[∑(xi - μ)²/N]
∴ σ = √[2926.36/15] = 13.967
Answer:
B
Step-by-step explanation: