Answer:
[tex]\large\boxed{y=2}[/tex]
Step-by-step explanation:
In this question, we're going to solve the equation.
What we would do is plug in the given information in the right variable. In this case, we would plugin -8 to x, since x = -8
We are solving for y, so we would nee to find how much y = ?
Your equation should look like this:
[tex]4(-8)+9y=-14[/tex]
Lets solve:
[tex]4(-8)+9y=-14\\\\\text{Multiply}\, 4(-8)\\\\-32+9y=-14\\\\\text{Add 32 to both sides}\\\\9y=18\\\\\text{Divide}\\\\y=2[/tex]
When you're done solving, you should get y = 2
This means that y = 2
I hope this helped you out.Good luck on your academics.Have a fantastic day!At a competition with 8 runners, 2 medals are awarded for first and second
place.
Each medal is different. How many ways are there to award the medals?
O A. 56
O B. 28
O C. 40,320
O D. 64
Answer: Option 'A' is correct.
Step-by-step explanation :
Since we have given that
Number of medals = 2
Number of runners = 8
We need to find the number of ways to award the medals.
We would use "fundamental theorem of counting" to find the number of ways.
So, number of ways is given by
8 × 7 = 56
Hence, option 'A' is correct.
Answer:
A. 56
Step-by-step explanation:
You take 8 and then find the next number down and multiply them.
8*7= 56
(Also, I just did this on APEX)
An aerial camera is suspended from a blimp and positioned at D. The camera needs to cover 125 meters of ground distance and will be flown at an altitude of 75 meters. If the camera attachment to the blimp is 20 meters in length, how low should the camera hang from the blimp, from G to D?
Answer:
The camera should low by 12 meters
Step-by-step explanation:
* Lets explain how to solve the problem
- From the figure:
# The length of the camera is represented by FE
∴ EF = 20 meters
# The ground distance covered by the camera represented by AC
∴ AC = 125 meters
# The camera will be flown at an altitude represented by DB
∴ DB = 75 meters
# The altitude should the camera hanged below the blimp
represented by GD
∴ Find the length of GD
* Lets solve the problem
- In the two triangles ADC and EDF
∵ EF // AC
∴ m∠A = m∠E ⇒ alternate angles
∴ m∠C = m∠F ⇒ alternate angles
∵ m∠ADC = m∠EDF ⇒ vertical angles
∴ Δ ADC ≈ Δ EDF ⇒ AAA similarity
∴ Their corresponding sides are proportions
∴ AC/EF = AD/ED = CD/FD = constant ratio
∵ AC = 125 and EF = 20
∴ The constant ratio is 125/20 = 25/4
∵ Their Altitudes have the same ratio of their corresponding sides
∵ BD is the altitude of Δ ADC and GD is the altitude of Δ EDF
∴ BD/GD = 25/4
∵ BD = 75
∴ 75/GD = 25/4
- Use cross multiplication to find GD
∴ 25 GD = (75)(4)
∴ 25 GD = 300
- Divide both sides by 25
∴ GD = 12
∴ The camera should low by 12 meters
The camera should low by 12 meters
Suppose that 6.5 million students in a certain country were in 4th grade. This was 8.6% of all students in the country. Find the number of students in the country that year. Round your answer to one decimal place.
Answer:
7560 million
Step-by-step explanation:
here is the answer for your question
Find the distance from the point (8, 4) to the line y =
x+ 2.
Answer:
The distance is [tex]3\sqrt{2}\ units[/tex]
Step-by-step explanation:
step 1
Find the slope of the give line
we have
y=x+2
so
the slope m is equal to
m=1
step 2
Find the slope of the perpendicular line to the given line
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal of each other
so
we have
m=1 -----> slope of the given line
therefore
The slope of the perpendicular line is equal to
m=-1
step 3
With m=-1 and the point (8,4) find the equation of the line
y-y1=m(x-x1)
substitute
y-4=-(x-8)
y=-x+8+4
y=-x+12
step 4
Find the intersection point lines y=x+2 and y=-x+12
y=x+2 -----> equation A
y=-x+12 ----> equation B
Adds equation A and equation B
y+y=2+12
2y=14
y=7
Find the value of x
y=x+2 -----> 7=x+2 -----> x=5
The intersection point is (5,7)
step 5
Find the distance between the point (8,4) and (5,7)
we know that
The distance from the point (8,4) to the line y=x+2 is equal to the distance from the point (8,4) to the point (5,7)
Find the distance AB
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute
[tex]d=\sqrt{(7-4)^{2}+(5-8)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(-3)^{2}}[/tex]
[tex]d=\sqrt{18}[/tex]
[tex]d=3\sqrt{2}\ units[/tex]
see the attached figure to better understand the problem
Is the following relation a function?
x y
1 −2
1 −3
2 1
3 −2
Answer:
It is not a function!
Step-by-step explanation:
It is not a function!
A function can't have two y-values assigned to the same x-value. In this case, you can se that for x=1 we have two y-values, which are y= -2 and y= -3.
We can have have two x-values assigned to the same y-value, that's why it's okay that for x=1 and x=3 we have the same y-value y=-2
Simplify (x - 3)(x^2+ 7x - 8). (1 point)
x^3 + 7x^2 -8x -3x^2 -21x +24
x^3 + 4x^2 -29x +24
For this case we must simplify the following expression:
[tex](x-3) (x ^ 2 + 7x-8)[/tex]
We must apply distributive property:
[tex]x * x ^ 2 + x * 7x-8 * x-3 * x ^ 2-3 * 7x + 3 * 8 =\\x ^ 3 + 7x ^ 2-8x-3x ^ 2-21x + 24 =[/tex]
Adding similar terms we have:
[tex]x ^ 3 + 4x ^ 2-29x + 24[/tex]
Answer:
The simplified expression is:
[tex]x ^ 3 + 4x ^ 2-29x + 24[/tex]
a cereal box has a length of 8 inches, a width of 1 3/4 inches, and a height of 12 1/8. What is the surface area of the box?
Answer:
270 7/16 in^2.
Step-by-step explanation:
The surface area equals the sum of the areas of 3 pairs of congruent rectangles.
These are 2 * 8 * 1 3/4 + 2 * 8 * 12 1/2 + 2 * 1 3/4 * 12 / 1/8
= 16 * 7/4 + 16 * 25/2 + 2 * 7/4 * 97/8
= 28 + 200 + 42 7/16
= 270 7/16 in^2.
in triangle ABC, angle A = 45, c= 17, and angle B = 25. Find a to the nearest tenth.
Answer:
The answer would be 12.8
Step-by-step explanation:
I looked it up and found the answer on another website
it is 12.8
By using the sine rule we got the value of a is 8 units.
Given that, in triangle ABC, angle A = 45, c= 17, and angle B = 25.
We need to find the measure of side a.
What is the sine rule?The sine rule formula is sinA/a=sinB/b=sinC/c.
Now, sin45°/a=sin25°/b=sin110°/17
⇒sin45°/a=0.9397/17
⇒0.7071/a=0.0854
⇒a=8.27≈8
Therefore, the value of a is 8 units.
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Determine the type of correlation that exists in the given data set. Age (years) 23 45 39 74 63 52 59 28 35 11 26 49 IQ 76 82 113 111 109 115 101 127 92 123 128 99 A. According to this data, there is a positive correlation between age and IQ. B. According to this data, there is a negative correlation between age and IQ. C. According to this data, there is no correlation between age and IQ. D. There is not enough information in this data to determine what type of correlation exists between age and IQ.
Answer:
B -0.104
Step-by-step explanation:
Step 1: Write the formula for correlation
r = total xy
√Total x² x Total y²
Step 2: Make a table to calculate all values
Table is attached in the picture below
Step 3 : Solve
Mean of X = Total X/ Total number of X
= 507/12
= 106.33
Mean of Y = Total Y/ Total number of Y
= 1276/ 12
= 42.25
r = total xy
√Total x² x Total y²
r = -352.05/ √3656.25 x 3122.66698
r = -0.104
-0.104 is negative
This negative correlation means there is an inverse correlation between variables.
Answer:
B. According to this data, there is a negative correlation between age and IQ.
Step-by-step explanation:
Correlation shows the strength of relation between two variables. The formula used to calculate correlation is:
[tex]Correlation(r) = \frac{Cov(x, y)}{\sigma_{x}\sigma_{y}}= \frac{E(x-\mu_{x})(y-\mu_{y})}{\sigma_{x}\sigma_{y}}[/tex]
where, Cov(x,y) = Covariance of x and y
[tex]\sigma_{x} [/tex] = standard deviation of x
[tex]\sigma_{y} [/tex] = standard deviation of y
[tex]\mu_{x} [/tex] = mean of x
[tex]\mu_{y} [/tex] = mean of y
and, E denotes the Expectation.
The value of the correlation lies between -1 to +1.
If the value of correlation lies between -1 to 0 then it is known as a negative correlation.
and, If the value of correlation lies between 0 to 1 then it is known as a positive correlation.
Using the above formula of correlation we get Correlation (r) = -0.1225.
Thus, there is negative correlation between age and IQ.
We can also use a correlation calculator for getting the value of correlation.
Hence, option (B) is correct.
what transformation of the parent function, f(x) = x^2, is the function f(x) = -(x + 2) ^2
Answer:
f(x) reflects across the x-axis and translate left 2 ⇒ 2nd answer
Step-by-step explanation:
* Lets talk about the transformation
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new
function g(x) = f(-x)
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Lets solve the problem
∵ f(x) = x²
∵ The parent function is f(x) = - (x + 2)²
- There is a negative out the bracket means we change f(x) to -f(x)
∴ f(x) is reflected across the x-axis
- The x is changed to x + 2, that means we translate the f(x) to the
left two units
∵ x in f(x) is changed to (x + 2)
∴ f(x) is translated 2 units to the left
∴ f(x) reflects across the x-axis and translate left 2
The function f(x) = -(x + 2) ^2 is a reflection over the x-axis and a horizontal shift to the left by 2 units.
Explanation:The given function, f(x) = -(x + 2) ^2, is a transformation of the parent function, f(x) = x^2. The negative sign in front of the function reflects it over the x-axis, making it an upside-down parabola. The addition of 2 inside the parentheses shifts the graph 2 units to the left. Therefore, the transformation is a reflection over the x-axis and a horizontal shift to the left by 2 units.
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what is 19,761 divisible by
The number 19,761 is divisible by the following numbers: 1, 3, 7, 21, 941, 2,823, 6,587, and 19,761.
When 19,761 is divided by any of these numbers, we obtain a whole number without any remainder.
In other words, the factors of 19,761 include 1, 3, 7, 21, 941, 2,823, 6,587, and 19,761.
19,761 ÷ 1 = 19,761
19,761 ÷ 3 = 6,587
19,761 ÷ 7 = 2,823
19,761 ÷ 21 = 941
19,761 ÷ 941 = 21
19,761 ÷ 2,823 = 7
19,761 ÷ 6,587 = 3
19,761 ÷ 19,761 = 1
Thus, we describe a number as divisible by another number or factor when the quotient shows a whole number and there is no remainder.
If I bought 21 pound of beef to make a burger for 9 person party how many people could I invite to dinner if i have 7 pounds? ( Assume people at both parties eat the same amount)
Answer:
3 people
Step-by-step explanation:
We can write a proportion, putting lbs of beef over people
21 lbs 7 lbs
----------- = ------------
9 people x people
Using cross products
21x = 7*9
21x = 63
Divide each side by 21
21x/21 = 63/21
x =3
You can have 3 people
For the equation cross multiplication is key. i do recommend you take in the fact it takes 2.3333etc. to make each persons portion
but none the less the quation should look like 7x9=63 then 63/21 which gives you 3.
you could also do 12/9=2.3, then 7/2.3= 3.04 for a more accurate answer
During the geometry unit, Mrs. Hamade asked her class to make kites in the shape of trapezoids. 8 /9 of the class made trapezoid kites. Only 1 /4 of the trapezoid kites could actually fly. What fraction of the classes' kites flew
_____ of the kites flew
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
THe most common mistake would be to think 1/4th of the kites flew, BUT 1/4th of the trapezoidal kites flew.
Hence, 1/4th of 8/9th of the TOTAL KITES FLEW, that is:
[tex]\frac{1}{4}*\frac{8}{9}=\frac{2}{9}[/tex]
hence, 2/9th of the kites flew
Español
Brian needs to memorize words on a vocabulary list for Spanish class.
He has memorized 24 of the words, which is three-fourths of the list.
How many words are on the list?
Answer:
There are 32 words total on the list.
Step-by-step explanation:
24*4=96;
96÷3=32;
There are 32 words total on the list.
Answer:
gfrwkmsvfbs
Step-by-step explanation:
dfffve
Which of the following is the measure of ZAXY if ray x bisects ZAXB,
which measures 110°?
O A. 50°
O B. 55°
O C. 45°
O D. 110
Answer:
55
Step-by-step explanation:
bisect means to cut in half so it is half of 110 so it is 55
Answer:
I believe the answer is 55°.
Step-by-step explanation:
Sense line Y is cut between angle AXB, you would need to find the half of 110°.
So, 110 ÷ 2 = 55.
Therefore, 55° is the correct answer.
Find the measure of angle C of a triangle ABC if measure of angle a = 24 degrees and measure of angle b = 130 degrees
The measure of angle C in triangle ABC, given that the measure of angle a is 24 degrees and angle b is 130 degrees, is 26 degrees.
Explanation:To find the measure of angle C in triangle ABC, we use the fact that the sum of the angles in a triangle is 180 degrees. Given the measure of angle a is 24 degrees and angle b is 130 degrees, we can add these two measures and subtract from 180 degrees to find the measure of angle C.
First, add the measures of angle a and b: 24 + 130 = 154 degrees. Next, subtract this sum from 180 degrees: 180 - 154 = 26 degrees.
Therefore, the measure of angle C in triangle ABC is 26 degrees.
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what is the solution to √3x+54 + 6 = 10
Answer:
x = -(38/3)
Step-by-step explanation:
Well first you have to isolate the square root on the left hand side.
Then eliminate the radical on the left hand side.
Last step
Solve the linear equation :
Rearranged equation
3x + 38 = 0
Subtract 38 from both sides
3x = -38
Divide both sides by 3
A possible solution is :
x = -(38/3)
For this case we must solve the following equation:
[tex]\sqrt {3x + 54} + 6 = 10[/tex]
Subtracting 6 from both sides of the equation:
[tex]\sqrt {3x + 54} = 10-6\\\sqrt {3x + 54} = 4[/tex]
We square both sides of the equation squared:
[tex]3x + 54 = 4 ^ 2\\3x + 54 = 16[/tex]
We subtract 54 from both sides of the equation:
[tex]3x = 16-54[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]3x = -38[/tex]
We divide between 3 on both sides:
[tex]x = \frac {-38} {3}\\x = - \frac {38} {3}[/tex]
Answer:
[tex]x = - \frac {38} {3}[/tex]
Which property is 7x +(4x + 1) = (7x + 4x) + 1t
Answer:
associative property
Step-by-step explanation:
This illustrates the associative property. It doesn't matter in which order you combine the terms here.
This is an example of associative property which states,
[tex]a+(b+c)=(a+b)+c[/tex]
Hope this helps.
r3t40
2 pounds of salt in 9 gallons of water. At this rate, how many pounds of salt are needed for 18 gallons of water?
Answer:
4
Step-by-step explanation:
Pounds of salt : gallons of water
(2 : 9) x 2
4 : 18
- 4 pounds
the binomial expansion of (x^2+y)^2 is?
Answer:
x^4+2x^2y+y^2
Step-by-step explanation:
first we expand the brackets
(x^2+y)(x^2+y)
the it will become
x^4+x^2y+yx^2+y^2
then finally the answer will become
,x^4+2x^2y+y^2
Answer:
x⁴+2x²y+y²
Step-by-step explanation:
Given the equation( x²+y)², to expand, we will open the bracket by multiplyimg the function x²+y by itself to have;
(x²+y)² = (x²+y)(x²+y)
(x²+y)² = x⁴+x²y+x²y+y²
(x²+y)² = x⁴+2x²y+y²
Therefore the expansion form of (x²+y)² is x⁴+2x²y+y²
Solve x − 7y = 8 for x
Answer:
x = 8 + 7y
Step-by-step explanation:
Given
x - 7y = 8 ( isolate x by adding 7y to both sides )
x = 8 + 7y
Linear equation is the equation in which the highest power of the unknown variable is one.The value of the variable x for the given expression is,
[tex]x=7y+8[/tex]
Given-The given linear equation is,
[tex]x-7y=8[/tex]
Linear equationLinear equation is the equation in which the highest power of the unknown variable is one. The linear equation are used to find out the value of unknown variable.
In the above linear equation the coefficient of the variable x is one and the coefficient of the variable y is negative seven.
The number eight is the constant which is equal to the given expression of variables.
To solve the equation for x refers to get the value of the variable x. As there is only one linear equation and the unknown variables are two. Thus the value of variable x can be obtained in the form of the variable y.
Let solve the given equation,
[tex]x-7y=8[/tex]
Add [tex]7y[/tex] both sides of the equation. thus,
[tex]x=8+7y[/tex]
[tex]x=7y+8[/tex]
Thus the value of the variable x for the given expression is,
[tex]x=7y+8[/tex]
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please help‼️
the height of a triangle is 12 yd less than its bass, x. the area of the triangle is 14 cm^2. which equation can be used to find x?
What are the coordinates of the vertex of the parabola described by the equation below? y=2(x+5)^2+3 APEX
Answer:
The vertex is the point (-5,3)
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
a is a coefficient
(h,k) is the vertex
If a > 0 the parabola open upward and the vertex is a minimum
If a < 0 the parabola open downward and the vertex is a maximum
In this problem we have
[tex]y=2(x+5)^{2}+3[/tex]
a=2
so
the parabola open upward and the vertex is a minimum
h=-5, k=3
therefore
The vertex is the point (-5,3)
For what value of x should you evaluate the polynomial P(x)= 2x^3-x^2-5x-2 to determine if 2x-3 is a factor of p(x)??
Choose one of the Answers: -3/2, 3/2, 2/3, -2/3.
Please help
Answer:
[tex]\dfrac{3}{2}[/tex]
Step-by-step explanation:
If 2x - 3 is a factor of P(x), then 3/2 is a zero of P(x).
[tex]\begin{array}{rcl}2x - 3 & = & 0\\2x & = & 3\\\\x & = & \mathbf{\dfrac{3}{2}}\end{array}\\\\\mathbf{P(\frac{3}{2})} \text{ will equal zero if $(2x-3)$ is a factor of $P(x)$}[/tex]
Joseph has started completing the square on the equation 3x2 - 7x + 12 = 0. He has worked to the point where he has the expression x2 - x = -4. Use complete sentences describe Joseph’s steps up to this point and whether or not his work is accurate.
Answer:
x = 7/6 + (i sqrt(95))/6 or x = 7/6 - (i sqrt(95))/6 thus NO, x^2 - (7 x)/3 = -4 would be correct.
Step-by-step explanation:
Solve for x:
3 x^2 - 7 x + 12 = 0
Hint: | Write the quadratic equation in standard form.
Divide both sides by 3:
x^2 - (7 x)/3 + 4 = 0
Hint: | Solve the quadratic equation by completing the square.
Subtract 4 from both sides:
x^2 - (7 x)/3 = -4
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 49/36 to both sides:
x^2 - (7 x)/3 + 49/36 = -95/36
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x - 7/6)^2 = -95/36
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x - 7/6 = (i sqrt(95))/6 or x - 7/6 = -(i sqrt(95))/6
Hint: | Look at the first equation: Solve for x.
Add 7/6 to both sides:
x = 7/6 + (i sqrt(95))/6 or x - 7/6 = -(i sqrt(95))/6
Hint: | Look at the second equation: Solve for x.
Add 7/6 to both sides:
Answer: x = 7/6 + (i sqrt(95))/6 or x = 7/6 - (i sqrt(95))/6
Answer:
Joseph's work wasn't accurate
Step-by-step explanation:
Take a look at the image to understand the procedures
Find the diagonal of a square whose sides are of the given measure. Given = 6sqrt2
Answer:
=12 units
Step-by-step explanation:
When a square is cut along one diagonal, it forms a right angled triangle whose legs are the sides of the square and the hypotenuse is the diagonal of the square.
Therefore, the Pythagoras theorem is used to find the hypotenuse.
a² + b² = c²
(6√2)²+(6√2)²=c²
72+72=c²
c²=144
c=√144
=12
The diagonals of the square measure 12 units each.
Is 24/40=4/7 a true proportion? Justify your answer
A proportion
[tex]a\div b = c\div d[/tex]
is nothing but a comparison between two fractions: we can rewrite it as
[tex]\dfrac{a}{b}=\dfrac{c}{d}[/tex]
So, we can multiply both sides by the two denominators b and d to get
[tex]\dfrac{a}{b}=\dfrac{c}{d} \iff ad = bc[/tex]
In other words, a proportion is true if the product of the inner terms is the same as the product of the outer terms.
In your case, we have the check is the following:
[tex]24 \div 40 = 4\div 7 \iff 24\cdot 7 = 40\cdot 7 \iff 168 = 280[/tex]
which is clearly false. So, 24:40 = 4:7 is not a true proportion. In fact, if we convert fractions into numbers, we have
[tex]\dfrac{24}{40} = 0.6,\quad \dfrac{4}{7} = 0.\overline{571428}[/tex]
which makes even more clear that the proportion doesn't hold.
The radius of the circle is 4 cm and the measure of the central angle is 90°.
The area of the sector with a central angle measuring 90° and radius of length 4 cm is π cm2.
The triangle in the sector is .
The area of the triangle is cm2.
The area of the segment of the circle is
(4π − ) cm2.
Answer:
i) 4π
ii) An isosceles triangle
iii) 8 cm^2[/tex]
iv) [tex](4\pi - 8)cm^2[/tex]
Step-by-step explanation:
The radius of the circle is 4 cm and the measure of the central angle is 90°.
We know that the area of sector of a circle = [tex]\frac{central angle}{360} *\pi *r^2[/tex]
Given: r = 4 and central angle = 90
Now plug in these values in the above formula, we get
Area of the sector = [tex]\frac{90}{360} *\pi *4^2\\= \frac{1}{4} *\pi *16\\= 4\pi[/tex]
i) 4π
ii) In the triangle, the two sides are equal in measure, because the two sides represents the radius of the circle. The radius are the same in measure in a circle.
Therefore, the triangle is the second is an isosceles triangle.
iii) Area of a right triangle = [tex]\frac{1}{2} *base*height[/tex]
Here base = 4 and height = 4, plug in these values in the triangle formula, we get
The area of the triangle = [tex]\frac{1}{2} *4*4\\= 2*4\\= 8 cm^2[/tex]
iv) The area of the segment of the circle is (4π - area of the triangle).
= [tex](4\pi - 8)cm^2[/tex]
The area of a sector is calculated using:
[tex]A = \frac{\theta}{360} \times \pi r^2[/tex]
So, we have:
[tex]A = \frac{90}{360} \times \pi \times 4^2[/tex]
[tex]A = \frac{1}{4} \times \pi \times 4^2[/tex]
[tex]A = 4\pi[/tex]
Hence, the area of the sector is [tex]4\pi[/tex]
(b) The triangleOne of the angles in the triangle is 90 degrees.
So, the triangle is a right-angled triangle
The area of the triangle is then calculated as:
[tex]A = \frac 12 bh[/tex]
This gives
[tex]A = \frac 12 \times 4 \times 4[/tex]
[tex]A = 8[/tex]
Hence, the area of the triangle is 8, and the triangle is a right triangle
(c) The area of the segment of the circleThis is the difference between the areas of the circle and the triangle.
So, we have:
[tex]A = 4\pi - 8[/tex]
Hence, the area of the segment is [tex] 4\pi - 8[/tex]
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Find the value of x in the picture
Answer: [tex]x=128\°[/tex]
Step-by-step explanation:
It is important to remember the following:
[tex]Angle\ formed\ by\ two\ chords=\frac{1}{2}(Sum\ of\ intercepted\ arcs)[/tex]
In this case you can observe in the figure that "x" is an Angle formed by two chords, therefore, you can find its value applying the formula.
Therefore, the value of "x" is this:
[tex]x=\frac{1}{2}(202\°+54\°)\\\\x=\frac{1}{2}(256\°)\\\\x=128\°[/tex]
help me with the work
Answer:
Option B k > 0
Step-by-step explanation:
we know that
Observing the graph
The slope of the line is positive
The y-intercept is negative
we have
[tex]3y-2x=k(5x-4)+6\\ \\3y=5kx-4k+6+2x\\ \\3y=[5k+2]x+(6-4k)\\ \\y=\frac{1}{3}[5k+2]x+(2-\frac{4}{3}k)[/tex]
The slope of the line is equal to
[tex]m=\frac{1}{3}[5k+2][/tex]
Remember that the slope must be positive
so
[tex]5k+2> 0\\ \\k > -\frac{2}{5}[/tex]
The value of k is greater than -2/5
Analyze the y-intercept
[tex](2-\frac{4}{3}k) < 0\\ \\ 2 < \frac{4}{3}k\\ \\1.5 < k\\ \\k > 1.5[/tex]
1.5 is greater than zero
so
the solution for k is the interval ------> (1.5,∞)
therefore
must be true
k > 0