The solution of given system of linear equations are x = 1 and y = -3.
Given system of linear equations are,
[tex]4x+3y=-5 ..........(1)\\\\ -x+3y=-10..............(2)[/tex]
Subtract equation 2 from equation 1.
[tex]4x+3y-(-x+3y)=-5+10\\ \\ 4x+3y+x-3y=5\\ \\ 5x=5\\ \\ x=5/5=1[/tex]
Substituting value of x in equation 1.
[tex]4(1)+3y=-5\\ \\ 3y=-5-4=-9\\ \\ y=-9/3=-3[/tex]
Hence, The solution of given system of linear equations are x = 1 and y = -3.
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Need help finding the area of the shaded region. Round to the nearest tenth. Need help ASAP
Answer: 294.4 m²
Step-by-step explanation:
Separate the shaded region into two parts:
The section containing the central angle of 230° (360° - 130°)The triangle with sides 11.1, 11.1 & 20.12 (use Law of Cosines)[tex]1.\ Area(A)=\pi\ r^2\ \bigg(\dfrac{\theta}{360}\bigg)\\\\\\.\qquad \qquad =\pi(11.1)^2\bigg(\dfrac{230}{360}\bigg)\\\\\\.\qquad \qquad =247.3[/tex]
[tex]2.\ \text{Use Law of cosines to find the length of the third side.}\\\text{ Then use Heron's formula to find the Area of the triangle.}\\\\s=\dfrac{11.1+11.1+20.12}{2}=21.16\\\\\\A=\sqrt{s(s-a)(s-b)(s-c)}\\\\.\ =\sqrt{21.16(21.16-11.1)(21.16-11.1)(21.16-20.12)}\\\\.\ =\sqrt{2227}\\\\.\ =47.1[/tex]
Area of shaded region = Area of (1) + Area of (2)
= 247.3 + 47.1
= 294.4
Answer:
294.36
Step-by-step explanation:
Find the area of the entire circle.
Subtract out the area of a sector with 130 degrees for the central angle.
Add the area of the isosceles triangle with an apex angle of 130 degrees.
Area of The entire circle
Area = pi * r^2
Area = 3.14 * 11.1^2
Area = 386.88 m^2
Area of the sector with 130 degrees for a central angle
Area_130 = (130/360) * pi * r^2
Area_130 = (130/360) * 3.14* 11.1^2
Area_130 = 139.71
Area of the triangle
1/2 central angle = 130/2 = 65
Bisect the apex angle so that each half = 65 degrees.
Sin(65) = opposite / hypotenuse
Sin(65) = Opposite / 11.1
11.1 * sin(65) = opposite
opposite = 10.06
This is 1/2 the base so the base = 2*10.06 = 20.12
The height of the triangle is found by cos(65) = adjacent/hypotenuse
hypotenuse = 11.1
Cos(65) = adjacent / hypotenuse
adjacent = hypotenuse * cos(65)
adjacent = 4.69 This is the height of the triangle.
Area of the triangle = 1/2 * 20.12 * 4.69
Area of the triangle = 47.19 m^2
Area of the Shaded Area
Area of entire circle - area of sector + area of triangle
=386.88 - 139.71 + 47.19
=294.36
Note
The area of the triangle could be done using Area = 1/2 * 11.1^2 * (2*sin(65)*cos(65) = 1/2 * 11.1^2 * sin(130) = 47.2 but you may not know all the math to do the area this way.
How much did each fish weight
When the following quadratic equation is written in standard form, what is the value of c?-3/4 x^2+2=0
When the quadratic equation is written in standard form the value of c is 8
To find the value of c when the quadratic equation -3/4 x² + 2 = 0 is written in standard form (ax² + bx + c = 0), follow these steps:
Move the constant term to the right side:
-3/4 x² = -2
Multiply both sides by -4/3 to get the standard form:
4x² = 8
Identify the coefficient of x² (a) and the constant term (c):
In this case, a = 4 and c = 8.
Therefore, when the equation is written in standard form, c = 8.
What is the vertex of the quadratic function f(x)=(x-6)(x+2)
Answer:
vertex = (2, - 16)
Step-by-step explanation:
given
f(x) = (x - 6)(x + 2) ← equate to zero to find the zeros
(x - 6)(x + 2) = 0
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 2 = 0 ⇒ x = - 2
The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros, hence
[tex]x_{vertex}[/tex] = [tex]\frac{6-2}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
Substitute x = 2 into f(x) for corresponding y- coordinate of vertex
f(2) = (2 - 6)(2 + 2) = - 4 × 4 = - 16
vertex = (2, - 16)
Eight travelers sleeping in a hostel are snoring The hostel has 15 sleeping travelers. How many travelers are not snoring?
Answer:7
Step-by-step explanation:
There are 15 sleeping and only 8 snoring you subtract 8 from 15 which leave you with 7 and that's how many people
By subtracting the number of travelers snoring (8) from the total number of travelers (15), we determine that there are 7 travelers not snoring.
To find out how many travelers in the hostel are not snoring, we will subtract the number of travelers who are snoring from the total number of travelers. The problem states that 8 travelers are snoring, and there are 15 travelers in total. So, we perform the following calculation:
Total travelers - Travelers snoring = Travelers not snoring
15 - 8 = 7
Thus, there are 7 travelers who are not snoring.
Which equation is equivalent of log x^36 =2
What are the other equations to compare it to ?
Answer:
here x =6
which gives equivalent equation
[tex]log_{6} 36 = 2[/tex]
Step-by-step explanation:
[tex]log_{x} 36 = 2[/tex]
36 = [tex]x^{2}[/tex]
solving it we get ,
x =+6 and x =-6
since x is the base of log so it cannot be negative
therefore x =6
therefore this equation can be
[tex]log_{6} 36 = 2[/tex]
Find the quartiles for these data values of 5, 7, 7, 8, 10, 11, 12, 15, 17
The median {Q2} is 10
Q1 is 7+7/2 which is 7
Q3 is 15+12/2 which is 13.5
Final answer:
The quartiles for the data set (5, 7, 7, 8, 10, 11, 12, 15, 17) are found by arranging the data in order and then finding the medians of the lower and upper halves. The first quartile (Q1) is 7, the median (Q2) is 10, and the third quartile (Q3) is 13.5.
Explanation:
To find the quartiles for the data set (5, 7, 7, 8, 10, 11, 12, 15, 17), you first arrange the data in ascending order, which is already done. The median (Q2) is the middle value when the data set is in order, so since there are 9 data points, the median is the fifth value, which is 10.
The first quartile (Q1) is the median of the lower half of the data. For our data set, the lower half is (5, 7, 7, 8), so the median of this set is the average of the middle two values because we have an even number of data points in the lower half. Thus, Q1 is (7 + 7)/2 = 7.
The third quartile (Q3) is the median of the upper half of the data. For our dataset, the upper half is (11, 12, 15, 17). Similarly, since this is an even set, Q3 is the average of the middle two values, (12 + 15)/2 = 13.5.
Therefore, the quartiles for this data set are:
First quartile (Q1): 7Median (Q2): 10Third quartile (Q3): 13.5-8x – 17 = -4(2x – 1) – 21
Answer:
infinite solutions
Step-by-step explanation:
Distribute the left side and simplify
- 8x - 17 = - 8x + 4 - 21
- 8x - 17 = - 8x - 17
Since both sides are equal the equation has infinite solutions
Given: m∠AOC = 120°, m∠BOD = 150°. Find: m∠FOE.
In the finding of m<FOE, I think it would be 70°.
Answer:
∠FOE = 90°
Step-by-step explanation:
In this question given is m∠AOC = 120°, m∠BOD = 150°.
We have to calculate ∠FOE.
Since ∠AOB + ∠COD + ∠BOC = 180° [ Angle at a point on a straight line ]
∠AOB + ∠COD = 180° - ∠BOC ---(1)
It is given ∠AOC = 120° = ∠AOB + ∠BOC -----(2)
and ∠BOD = 150° = ∠BOC + ∠COD ------(3)
By adding equation (2) and (3)
150 + 120 = ∠ BOC + ∠COD + ∠AOB + BOC
270 = 2∠BOC + ∠COD + ∠ AOB
Now from equation (1)
270 = 2∠BOC + (180 - ∠BOC)
270 = 180 + ∠BOC
270 -180 = ∠BOC
∠BOC = 90°
Since ∠ BOC ≅ ∠FOE (opposite angles)
Therefore, ∠FOE = 90° is the answer.
Use only the digits 0 - 9 and the decimal and the negative sign, if needed, to fill in the blank. If f(x) = 2x + 9, then f(-1) =
Answer:
7
Step-by-step explanation:
Replace both instances of x in f(x) = 2x + 9 with -1:
f(-1) = 2(-1) + 9 = 7
Thus, f(-1) = 7
The value of the function f(x) = 2x + 9 at x = - 1 Or f(-1) is 7.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f(x) = 2x + 9.
We know, Substitution in mathematics is when we replace some specific numerical values to variables according to our wants or given in the problem.
Therefore, f(-1) = 2(-1) + 9.
f(-1) = - 2 + 9.
f(-1) = 7.
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#9. Find the area of the triangle. Thanks!
Answer:
C
Step-by-step explanation:
The area (A) of the triangle is calculated using
A = [tex]\frac{1}{2}[/tex] ab sinC
where a, b are the 2 sides and C is the angle between them
here a = 9, b = 15 and C = 70°, hence
A = 0.5 × 9 × 15 × sin70° = 63.4 cm² → C
Answer:
C.[tex]63.4cm^2[/tex]
Step-by-step explanation:
I love trigonometry
the area of a triangle is equal to [tex]\frac{1}{2}*a*b*sinC[/tex]
we have a b and Angle C so just put that in the formula :)
[tex]\frac{1}{2}*9*15*sin70\\[/tex]
[tex]63.4cm^2[/tex]
what is the measure of angle C?
Does it have any ANSWER CHOISES!
Answer:
c = 36.87
Step-by-step explanation:
arcsin(3/5)=36.87
The local weather report states that there is more than a 2/3 chance of rain for Saturday.
What is the likelihood that it will rain on Saturday?
The likelihood is 66.67% or about 67%. Hope this helped!
Answer: B. It is likely to rain on Saturday.
Step-by-step explanation:
name the polynomial based on degree and number of terms. 7x^2+2x+5
2nd degree trinomial
an equation in slope-intercept form for the line that passes through (4,-4) and is parallel to 3+4x=2y-9
Answer:
[tex]\large\boxed{y=-\dfrac{1}{2}x-2}[/tex]
Step-by-step explanation:
[tex]\text{The slope-intercept form:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\======================[/tex]
[tex]\text{If}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\ \text{are\ parallel, then}\ m_2=-\dfrac{1}{m_1}\\===========================[/tex]
[tex]\text{We have the equation of a line:}\ 3+4x=2y-9.\\\text{Convert it to the slope-intercept form:}\\\\2y-9=3+4x\qquad\text{add 9 to both sides}\\\\2y=12+4x\qquad\text{divide both sides by 2}\\\\y=6+2x\\\\y=2x+6\to m_1=2\\\\\text{therefore}\ m_2=-\dfrac{1}{2}\\\\\text{We have the equation:}\ y=-\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the given point (4, -4) to the equation:}\\\\-4=-\dfrac{1}{2}(4)+b\\\\-4=-2+b\qquad\text{add 2 to both sides}\\\\-2=b\to b=-2\\\\\text{Finally we have the equation:}\ y=-\dfrac{1}{2}x-2[/tex]
Solace this pleasehdbfbfbf
A=bh and since the garden is 2 1/2 by 2 and the trench+garden= 3 1/2 by 3 the trench would be 1 by 1. So A=1x1 = 1
Answer:11/2 m sq
Step-by-step explanation:
Area of the garden =L•W
2 1/2•2=
5/2•2= 5 m sq
Area of the garden & trench =L•W
3 1/2•3 =
7/2•3 =
7•3/2=
21/2 m sq
21/2-5 =
21/2-10/2=
21-10/2=
11/2
The area of the trench is 11/2 m sq
42 is 15% of what number here is to help you people on this question
is/of=%/100
280
42 times 100 divided 15 equals 280.
The ratio of the side lengths of a triangle is 10.5 :18 :22.5. The perimeter of the triangle is 408 centimeters. Determine whether the triangle is a right triangle.
Answer:
Step-by-step explanation:
A point located at (0, -6) is the same distance from 0 as the point located at (0, 6). True or False
Answer:
true
Step-by-step explanation:
Will mark BRAINLIEST!!! Need answer ASAP!!!
Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed.
y > 5
y ≥ x
Answer:
The fourth graph with the long dotted line shows the system.
Step-by-step explanation:
By graphing both inequalities and shading, you'll find that the overlap shows the fourth graph. Also, there was no need to ask here, you really could have just used desmos.com, it's a great online graphing tool.
Answer:
4th graph : )
Step-by-step explanation:
Use your expression to find the total cost for ordering 4 tickets online. Show your work.
$10.0000000000000000000
10.00
In the number 4,444.444, how does the 4 in the tenths place compare to the 4 in the place to its right?
the 4 in the tens place is 10 times the 4 in the ones place
The 4 in the tenth place is the product of 10 and the 4 to its right
How to interpret the place value?The number is given as:
Number = 4,444,444
The 4 in the tenth place is:
40
The 4 to its right is:
4
Divide both numbers
40/4 = 10
Hence, the 4 in the tenth place is the product of 10 and the 4 to its right
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What is the mean absolute definition of the data set? {12,4,30,16,18} ??
Answer:
the answer is 16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
add the the numbers and divide the sum by how many numbers are given
how many triangles can be made if two sides are 4 inches and the angle between them is 90
Answer:
it's either two or three. Sorry for the short answer.
Step-by-step explanation:
Is this equation even or odd? Please answer asap
Answer:
The equation represents an even function
Step-by-step explanation:
For the function above, the value of f(x) is fixed at 3 for positive or negative values of x.
For the absolute value function below, the value of f(x) will always be positive due to the absolute symbol.
In general, a function f(x) is said to be even if;
f(-x) = f(x) such that the function is symmetrical with respect to the y-axis.
I don’t know these property’s!
1) 3rd down.
2) 2nd down.
3) 1st down.
4) 6th down.
{x^{2} +1/x^{2} }=66 find x-1/x
Answer:
Step-by-step explanation:
The solution is attached herewith.
Answer:
x = ± 8
Step-by-step explanation:
Note that
(x - [tex]\frac{1}{x}[/tex])² = x² - 2 + [tex]\frac{1}{x^2}[/tex] = 66 - 2 = 64
Take the square root of both sides
x - [tex]\frac{1}{x}[/tex] = ± [tex]\sqrt{64}[/tex] = ± 8
plz help 13 points 2 questions 7th grade
Answer:
11 is -1 `0 is c
Step-by-step explanation:
11 you subtract 1 from each 10 look for points on griid
A cylinder has a radius of 10 cm and a height of 9 cm. A cone has a radius of 10 cm and a height of 9 cm. Show that the volume of a cylinder is three times the volume of the cone. someone help me out
Step-by-step explanation:
We start with the formulas for the volumes of a cylinder and a cone.
Cylinder:
[tex] V_{cylinder} = \pi r^2 h [/tex]
Cone:
[tex] V_{cone} = \dfrac{1}{3} \pi r^2 h [/tex]
Now we calculate the two volumes.
Cylinder:
[tex] V_{cylinder} = \pi r^2 h [/tex]
[tex] V_{cylinder} = \pi \times (10~cm)^2 \times 9~cm [/tex]
[tex] V_{cylinder} = \pi \times 100~cm^2 \times 9~cm [/tex]
[tex] V_{cylinder} = 900 \pi~cm^3 [/tex]
Cone:
[tex] V_{cone} = \dfrac{1}{3} \pi \times (10~cm)^2 \times 9~cm [/tex]
[tex] V_{cone} = \dfrac{1}{3} \pi \times 100~cm^2 \times 9~cm [/tex]
[tex] V_{cone} = 300 \pi~cm^3 [/tex]
The volume of the cylinder is 900pi cm^3, and the volume of the cone is 300pi cm^3.
Now we divide the volume of the cylinder by the volume of the cone.
[tex] \dfrac{900 \pi~cm^3}{300 \pi~cm^3} = 3 [/tex]
Dividing the volume of the cylinder by the volume of the cone gives us 3, showing that the volume of the cylinder is 3 times the volume of the cone.
The volume of a cylinder is three times the volume of a cone.
Explanation:To show that the volume of a cylinder is three times the volume of a cone, we need to compare their formulas. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height.
Let's calculate the volume of the cylinder first. Given that the radius (r) is 10 cm and the height (h) is 9 cm, we can substitute these values into the formula: V = π(10 cm)²(9 cm) = 900π cm³.
Now let's calculate the volume of the cone. Again, substituting the values for r and h, we have V = (1/3)π(10 cm)²(9 cm) = 300π cm³.
Comparing the volumes, we have 900π cm³ for the cylinder and 300π cm³ for the cone. Dividing the volume of the cylinder by the volume of the cone, we get (900π cm³) / (300π cm³) = 3. This shows that the volume of the cylinder is three times the volume of the cone
Which model represents 140%
Answer: The answer is H