Answer:
40
Step-by-step explanation:
x + (4x-20) = 180
5x - 20 = 180
5x = 200
x = 40
Answer:
the answer is 40
Step-by-step explanation:
the value of x and 4x -20 will be 180 degrees because it is a line and so you set the sum of those to 180 and solve for x
Which point lies on a circle with a radius of 5 units and center at P(6, 1)?
Answer:
(1,1);(11,1);(6,6);(6-4)
Step-by-step explanation:
The easiest way to do is add or subtract 5 to the x or y value.
Given: See the diagram.
Prove: DC = DB
Statement
Reason
1. given
2. AG = GC given
3. is the perpendicular
bisector of . deduced from steps 1 and 2
4. DA = DC
5. given
6. AH = HB given
7. is the perpendicular
bisector of . definition of perpendicular bisector
8. DA = DB deduced from steps 6 and 7
9. DC = DB Transitive Property of Equality
What is the reason for the fourth and eighth steps in the proof?
Answer:
Option D.
Step-by-step explanation:
Given: See the diagram.
Prove: DC = DB
Perpendicular bisector theorem : If a point lies on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints.
Proof:
Statement 1: [tex]\overleftrightarrow{DG}\perp \overline{AC}[/tex]
Reason: Given.
Statement 2: AG=GC
Reason: Given
Statement 3: [tex]\overleftrightarrow{DG}[/tex] is perpendicular bisector of [tex]\overline{AC}[/tex].
Reason: Deduced from steps 1 and 2
Statement 4: DA=DC
Reason: Perpendicular bisector theorem
Statement 5: [tex]\overleftrightarrow{DH}\perp \overline{AB}[/tex]
Reason: Given
Statement 6:AH=HB
Reason:Given
Statement 7: [tex]\overleftrightarrow{DH}[/tex] is perpendicular bisector of [tex]\overline{AB}[/tex].
Reason: By definition of perpendicular bisector.
Statement 8: DA=DB
Reason : Perpendicular bisector theorem
Statement 9: DC=DB
Reason: Transitive property of equality.
Hence proved.
Therefore, the correct option is D.
Which of the following could be the ratio of the length of the longer leg of a 30-60-90 to the length of its hypotenuse? CHECK ALL THAT APPLY.
A. √3 : 2
B. 3 : 2√3
C. 1 : √3
D. 3√3 : 6
E. √3 : √3
F. √2 : √3
-Apex Learning, Geometry
In a 30-60-90 triangle, the longer leg is sqrt(3) times the hypotenuse. Therefore, the correct ratios provided are A. sqrt(3) : 2 and D. 3sqrt(3) : 6, with the latter simplifying to the correct ratio when reduced.
Explanation:The ratio of the length of the longer leg to the hypotenuse in a 30-60-90 triangle is determined by the properties of this special right triangle. In such a triangle, the sides are in a fixed ratio: the shorter leg is 1 times the length of the hypotenuse, the longer leg is sqrt(3) times the length of the hypotenuse, and the hypotenuse itself is 2 times the length of the shorter leg.
Using this knowledge, we can evaluate the options given:
A. sqrt(3) : 2 - This ratio correctly represents the longer leg to hypotenuse ratio in a 30-60-90 triangle.D. 3sqrt(3) : 6 - Simplifying this ratio gives us sqrt(3) : 2, which is also a correct representation of the longer leg to hypotenuse ratio.Options B, C, E, and F do not represent the correct ratio of the longer leg to the hypotenuse of a 30-60-90 triangle. Therefore, options A and D are correct.
HELP please:)) Geometry question
Answer:
21.99 units
164.93 units²
Step-by-step explanation:
given radius r = 15 units
angle of sector = 84°
Length of sector = [tex]\frac{84}{360}[/tex] x 2 x π x r
= [tex]\frac{84}{360}[/tex] x 2 x 3.14 x 15
= 21.99 units
Area of sector = [tex]\frac{84}{360}[/tex] x π x r²
= [tex]\frac{84}{360}[/tex] x 3.14 x 15²
= 164.93 units²
A parallelogram has an area of 144 square centimeters. If the base measures 24 centimeters, what is the height?
Answer:
The height is 6.
Step-by-step explanation:
To find the answer, identify the dimensions you have and what you to find. We have the area (144) and base (24) and we need to find the height. To find the height, you must divide area by the base (it's really simple).
Ex.
[tex]144 / 24 = ?\\144 / 24 = 6[/tex]
The quotient you found is the height. Therefore, the answer is 6.
Final answer:
To find the height of a parallelogram with an area of 144 cm² and a base of 24 cm, divide the area by the base to obtain the height of 6 cm.
Explanation:
Mathematics:
To find the height of a parallelogram, you can use the formula Area = base * height. In this case, the area is given as 144 cm² and the base is 24 cm. Substituting these values into the formula, we get 144 = 24 * height. To find the height, divide both sides of the equation by 24: height = 144/24 = 6 cm. Therefore, the height of the parallelogram is 6 centimeters.
15 The heights, in inches, of 12 students are listed below.
61, 67, 72, 62, 65, 59, 60, 79, 60, 61, 64, 63
Which statement best describes the spread of these
data?
(1) The set of data is evenly spread.
(2) The median of the data is 59.5.
(3) The set of data is skewed because 59 is the only
value below 60.
(4) 79 is an outlier, which would affect the standard
deviation of these data.
The statement that best describes the spread of these data is 79 is an outlier, which would affect the standard deviation of these data
What is an outlier?
An outlier is a piece of data that is an abnormal distance from other points.
In other words, an outlier is any value that is numerically distant from most of the other data points in a set of data.
The outlier in the set of data is 79 because it is quite distance from the other numerical value
Generally, outliers significantly affects the standard deviation of data.
Therefore, 79 is an outlier, which would affect the standard
deviation of these data
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The point (x, square root of 3/2) is on the unit circle, what is x?
Answer:
[tex]x=\frac{1}{2}[/tex]
Step-by-step explanation:
When we have a point (a,b) on the unit circle, we can say that
[tex]a^2+b^2=1[/tex]
This is a property of the unit circle.
From the point given [tex](x,\frac{\sqrt{3} }{2})[/tex] , now we can write the equation shown below and solve for x:
[tex]x^2+(\frac{\sqrt{3} }{2})^2=1\\x^2+\frac{3}{4}=1\\x^2=1-\frac{3}{4}\\x^2=\frac{1}{4}\\x=\frac{\sqrt{1}}{\sqrt{4} } \\x=\frac{1}{2}[/tex]
So, x = 1/2
Answer: x = 1/2
Step-by-step explanation:
We have that the point (x, (√3)/2)) is on the unit circle.
we can define a circle of radius R centered in the (0,0) as:
x^2 + y^2 = R^2
This means that:
x^2 + (√(3)/2)^2 = 1
x^2 + 3/4 = 1
x^2 = 1 - 3/4 = 1/4
x = √(1/4) = 1/2
So we have that x is equal to 1/2
Nine times the quantity one-fourh plus a number is six less than the number divided by three
Solve for x: three over four x + five over eight = 4x
Answer:
Step-by-step explanation:
Assuming the problem is: 3/4 x +5/8=4x
Or .75 x+5/8=4x
Subtract .75 on both sides: 5/8=3.25x
Then divide both sides by 3.25: (5/8)/3.25=x
So x=5/26
A park ranger is shining a spotlight to try to count wildlife at night. She
starts with a beam that has an angle of 45°. She then increases the angle
of the beam to 60°.
Which statement most accurately describes the relationship between
segments of the triangles formed by the beam?
Answer:
The statement most accurately describes the relationship between
segments of the triangles formed by the beam is AC < DF
Step-by-step explanation:
* Lets study the figure to answer the problem
- There are two triangles ABC and DEF
- AB = BC
- DE = EF
- AB = DE
∴ AB = BC = DE = EF
- m∠ABC = 45°
- m∠DEF = 60°
∵ The measure of angle ABC is smaller than the measure of
angle DEF
∴ The opposite side to the angle ABC is shorter than the opposite
side of angle DEF
∵ AC is the opposite side to angle ABC
∵ DF is the opposite side to angle DEF
∴ AC is shorter than DF
∴ DF > AC
∴ AC < DF
* The statement most accurately describes the relationship between
segments of the triangles formed by the beam is AC < DF
The odometer in Mr. Jackson’s car shows he has travel 62,222 miles what is the least number of additional miles that Mr. Jackson much travel before the odometer again shows four of the five digits the same as each other
Answer:
444 (gets to 62,666)
Step-by-step explanation:
The closest you can think of first is 63,333. However, as long as there doesn't have to be the four numbers in a row, the "6" in the number can be one of the four same numbers.
This means that you need to get 3 other sixes in the number. There are many ways to do this, but the one requiring the least amount of driving is changing the last three digits (222). If you add 444 to the number, the amount of miles driven is 62,666, there being 4 sixes in the number. This is the least amount of driving needed before the odometer shows four of the five digits the same as each other.
444 is the least number that shows four out of the five digits same.
What is odometer?An odometer is an instrument for measuring the distance travelled by a wheeled vehicle.
Given that,
Total distance covered by Mr. Jackson = 62,222 miles,
The four digits of number 62,222 are same and are 2,
Again, odometer will show four out of 5 digit same, when there will be at least four times 6,
So add 444 in the 62,222
The number = 62,222 + 444 = 62,666
So the least number that can be added to make 4 digit same is 444.
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PLEASE HELP!
Which equation best represents the line?
Remember that the slope intercept formula is:
y = mx + b
m is the slope ([tex]\frac{rise}{run}[/tex])
b is the y-intercept
In this case the slope is...
[tex]\frac{1}{2}[/tex]
The y-intercept is...
(0, 3)
so...
y = [tex]\frac{1}{2}[/tex]x + 3
Hope this helped!
~Just a girl in love with Shawn Mendes
A teacher has assigned numbers 1-8 to eight students in a classroom. The numbers of all the students are put in a basket. The teacher selects a number and replaces it in the basket. Then the teacher selects a second number. Find P(student 1, then student 8).
Answer:
There is a 1/64 possibility.
Step-by-step explanation:
Since the probability of selecting student 1's number is 1/8 and then replacing it leaves us with still 8 numbers to choose from, so student 8's probability of being selected is also 1/8. Multiplying these two gives P=1/64, since (1/8)^2 = 1/64.
Hope this helps!
Answer:
1/64 possibility
Explanation:
Multiply the numbers by the number of students(8x8) to get 64. That means there is 1 in 64 chances. 1/64
have a great day
An annoyed teacher asked her student to do the following: (1) Start with the number 12. Go to step (2). (2) Take the negative of the number reached at the end of the previous step. Go to step (3). (3) Add 1 to the number reached at the end of the previous step. Go to step (4). (4) Go back to step (2) unless you have already gone through step (3) a hundred times; if you have gone through step (3) a hundred times already, tell the teacher the last number you reached. To the teacher's surprise, the student gave her the correct final answer within a minute. What was it?
Answer:
Step-by-step explanation:
// 12
// -12
//-11
//88
Dwight is a construction worker who will be employed for 8 months this year on a contract job, and he needs to calculate his projected yearly earnings in order to fill out a loan application. His contract states that he will make $35 an hour and that will work 45 hours per week for the duration of the contract.
Part 1: how much will dwight make pero week
Final answer:
Dwight will make $1,575 per week by multiplying his hourly wage of $35 by the 45 hours he works each week.
Explanation:
To calculate how much Dwight will make per week, we need to multiply his hourly wage by the number of hours he works per week. According to the question, Dwight earns $35 per hour and works 45 hours per week.
The calculation is as follows: Hourly wage x Hours per week = Weekly earnings
$35/hour x 45 hours/week = $1,575/week
Therefore, Dwight will make $1,575 per week from his construction job.
ab and bc form a right angle at point B. if a= (-3,-1) and B= (4,4) what is the equation of BC?
Answer:
Option C [tex]-7x-5y=-48[/tex]
Step-by-step explanation:
step 1
Find the slope of AB
we have
A(-3,-1) and B(4,4)
The slope m is equal to
[tex]m=(4+1)/(4+3)[/tex]
[tex]m=5/7[/tex]
step 2
Find the slope of BC
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
so
[tex]m1*m2=-1[/tex]
we have
[tex]m1=5/7[/tex]
substitute
[tex]5/7*m2=-1[/tex]
[tex]m2=-7/5[/tex]
step 3
Find the equation of the line into slope point form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-7/5[/tex]
[tex]B(4,4)[/tex]
substitute
[tex]y-4=-(7/5)(x-4)[/tex]
Multiply by 5 both sides
[tex]5y-20=-7x+28[/tex]
[tex]7x+5y=28+20[/tex]
[tex]7x+5y=48[/tex]
Multiply by -1 both sides
[tex]-7x-5y=-48[/tex]
Please Need Help Very Badly!!!
Answer: use a ruler and measure each side multiply by 30 then multiply all of them by each other
hope this helps and if I'm wrong hope you for give me here is some memes
Answer:
50 degrees
Step-by-step explanation:
since angle bac is bisected, bae and eac are equal measurement. therefore:
x+30 = 3x-10
now isolate the variable
x-3x=-10-30
-2x=-40
2x=40
x=20
mEAC =3x-10
=3(20)-10
60-10
=50
this can be proven because BAE is the same measurement as EAC (because of the bisector): x +30
20+30
=50
What is the standard form of the equation of a line for which the length of the normal segment to the origin is 8 and the normal makes an angle of 120degrees with the positive x axis
The standard form of the equation for the specified line, we use the normal form equation, substitute the given values for the angle and the length of the normal segment, and simplify to obtain the equation as [tex]x - \(\sqrt{3}\) y = -16.[/tex]
Explanation:To solve this, we'll use the concept of the normal form of the line equation, which is [tex]x cos(\(\theta\)) + y sin(\(\theta\)) = p, where \(\theta\)[/tex] is the angle the normal makes with the positive direction of the x-axis, and p is the length of the perpendicular from the origin to the line.
Given[tex]\(\theta = 120^\circ\) and \(p = 8\)[/tex], we substitute these values into the normal form to get [tex]x cos(120^\circ) + y sin(120^\circ) = 8.[/tex] Simplifying further using the values of [tex]cos(120^\circ) = -1/2 and sin(120^\circ) = \(\sqrt{3}/2\)[/tex], we obtain the standard form of the equation of the line as [tex]-1/2 x + \(\sqrt{3}/2\) y = 8[/tex], or multiplying through by -2 for a cleaner form: [tex]x - \(\sqrt{3}\) y = -16.[/tex]
the length of a rectangle is 11 yd less than three times the width and the area of the rectangle is 42 yd
The length of the given rectangle is 3 yd and the width is 3.66 yd.
What is a rectangle?A rectangle is a type of parallelogram having equal diagonals.
All the interior angles of a rectangle are equal to the right angle.
The diagonals of a rectangle do not bisect each other.
Given that,
The area of rectangle is 42 square yd.
Suppose the width of the rectangle is x yd.
Then its length is given by 3x - 11 yd.
As per the problem, the following equation can be formed,
x(3x - 11) = 42
Solve the above equation for x as,
x(3x - 11) = 42
=> 3x² - 11x = 42
=> 3x² - 11x - 42 = 0
=> x = -1, 4.66
Since, the width cannot be negative. The value of x is taken as 4.66.
Thus, the length is is given by 3 × 4.66 - 11 = 3.
Hence, the length and width of the rectangle are 3yd and 4.66yd respectively.
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Determine whether the parabola y = -x2 + 15x + 8 opens up, down, left, or right.
What are the coordinates of the roots of the equation x^2+ 4x + 3 = 0 ?
The coordinates of the roots of the given quadratic equation x^2 + 4x + 3 = 0 are -1 and -3.
Explanation:The given equation is a quadratic equation in the form of ax² + bx + c = 0, where a = 1, b = 4, and c = 3. To find the coordinates of the roots, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the given values, we get:
x = (-4 ± √(4² - 4(1)(3))) / (2(1))
Simplifying further, we have:
x = (-4 ± √(16 - 12)) / 2
x = (-4 ± √4) / 2
x = (-4 ± 2) / 2
Therefore, the two roots of the equation are:
x₁ = (-4 + 2) / 2 = -1
x₂ = (-4 - 2) / 2 = -3
Solve the system of equations 4x+3y+6z=3, 5x+5y+6z=5 and 6x+3y+6z=3
The answer is:
The solutions to the system of equations are:
[tex]x=0\\y=1\\z=0[/tex]
Why?To solve the system of equations by the easiest way, we need to use the reduction method. The reduction method consist of reducing the variables applying different math operations in order to be able to isolate the variables.
So, we are given the system:
[tex]4x+3y+6z=3\\5x+5y+6z=5\\6x+3y+6z=3[/tex]
Let's work with the first and the third equation:
[tex]4x+3y+6z=3\\6x+3y+6z=3[/tex]
Then, multiplying the first equation by -1, we have:
[tex]-4x-3y-6z=-3\\6x+3y+6z=3[/tex]
[tex]-4x+6x-3y+3y-6z+6z=-3+3[/tex]
[tex]2x=0[/tex]
[tex]x=0[/tex]
Now, working with the first and the second equation, we have:
[tex]4x+3y+6z=3\\5x+5y+6z=5[/tex]
Then, multiplying the first equation by -1, we have:
[tex]-4x-3y-6z=-3\\5x+5y+6z=5[/tex]
[tex]5x-4x+5y-3y-6z+6z=-3+5[/tex]
[tex]x+2y=2[/tex]
Then, substituting "x" into the equation, we have:
[tex]0+2y=2[/tex]
[tex]y=\frac{2}{2}=1[/tex]
Finally, working with the first equation and substituting "x" and "y", we have:
[tex]4x+3y+6z=3[/tex]
[tex]4*0+3*1+6z=3[/tex]
[tex]0+3+6z=3[/tex]
[tex]6z=3-3=0[/tex]
[tex]6z=0[/tex]
[tex]z=\frac{0}{6}=0[/tex]
Hence, we have that the solutions to the system of equations are:
[tex]x=0\\y=1\\z=0[/tex]
Have a nice day!
Answer:
[tex]x=0\\y=1\\z=0[/tex]
Step-by-step explanation:
Multiply the first equation by -1:
[tex](-1)(4x+3y+6z)=3(-1)\\\\-4x-3y-6z=-3[/tex]
Add the new equation and the third equation an solve for "x":
[tex]\left \{ {{-4x-3y-6z=-3\ \atop {6x+3y+6z=3} \right.\\...........................\\2x=0\\x=0[/tex]
Substitute the value of "x" into the first equation and solve for "y":
[tex]4(0)+3y+6z=3\\\\3y=3-6z\\\\y=\frac{3-6z}{3}\\\\y=1-2z[/tex]
Substitute the value of "x" and [tex]y=1-2z[/tex] into the second equation and solve for "z":
[tex]5(0)+5(1-2z)+6z=5\\\\5-10z+6z=5\\\\-4z=0\\\\z=0[/tex]
Knowing the values of "x" and "z", you can substitute them into any original equation and solve for "y". Then:
[tex]4(0)+3y+6(0)=3\\\\3y=3\\\\y=\frac{3}{3}\\\\y=1[/tex]
What is 127 as a percent?
Hello!
The answer is 127,000%
If f(x) = 2x + 3 and g(x) = x2 + 1,find f(g(3)).
[tex]\bf \begin{cases} f(x)=2x+3\\ g(x)=x^2+1 \end{cases}\qquad \qquad g(3)=(3)^2+1\implies g(3)=\boxed{10} \\\\\\ f(~~g(3)~~)\implies f\left( ~~\boxed{10}~~ \right)=2(10)+3\implies \stackrel{f(g(3))}{f(10)}=23[/tex]
The slope of a line is 58, and the line passes through the point (−8,−4).
What is the slope-intercept form of the equation for this line?
The slope-intercept form of the equation for this line is y = 58x + 460.
Given:
Slope (m) = 58
Point [tex](x_1, y_1)[/tex] = (-8, -4)
Using the point-slope form of the equation, which is
[tex](y - y_1) = m(x - x_1)[/tex]
Substitute the values into the equation:
(y - (-4)) = 58(x - (-8))
(y + 4) = 58(x + 8)
To convert this equation into slope-intercept form
y + 4 = 58x + 464
y = 58x + 464 - 4
y = 58x + 460
Therefore, the slope-intercept form is y = 58x + 460.
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What is the answer to 14+5(x-8)=-36
Hello There!
14 + 5x - 40 = -36
5x - 26 = -36
5x = -10
x = -2
Answer:
Step-by-step explanation:
14+4(x-8)=-36
19(x-8)=-36
x-8= -36-19
-8x=-55
6.875
The measure of angle A is 4 degrees greater than the measure of angle B. The two angles are complementary.Find the measure of each angle. Please help answer this, Thank you!!
Answer:
A = 47° and B = 43°
Step-by-step explanation:
Express angle A in terms of angle B, that is
A = B + 4
Complementary angles sum to 90°, hence
A + B = 90, that is
B + 4 + B = 90
2B + 4 = 90 ( subtract 4 from both sides )
2B = 86 ( divide both sides by 2 )
B = 43
Hence
∠B = 43° and ∠A = B + 4 = 43 + 4 = 47°
Answer:
A= 47°
B= 43°
Explanation:
A complementary angle is a 90° angle.
If A+B= 90 and B+4= A, we can rewrite it as...
B+4+B= 90
→ 2B+4= 90
→ 2B= 86
→ B= 43
Then we go back to the equation A+B= 90 and plug in B as 43...
A+43= 90
→ A= 47
in the equation y= -2x what are the possible values of y?
Please help: tangent 48 degrees = 9/x
Answer:
[tex]x=8.1[/tex]
Step-by-step explanation:
we have that
[tex]tan(48\°)=\frac{9}{x}[/tex]
Solve for x
[tex]x=\frac{9}{tan(48\°)}[/tex]
[tex]x=8.1[/tex]
a simple random sample of 85 is drawn from a normally distributed population, and the mean is found to be 146, with a standard deviation of 34. Which of the following values is outside of the 99% confidence interval for the population mean?
Step-by-step explanation:
hihi, so given a statistic, a sample standard deviation, and the sample size, we can create a 99% confidence interval for this distribution. Given the equations for confidence interval and Margin of Error, all we have to calculate initially is t* (invT(.995, 85-1)) and Standard error (34/sqrt(85)). Once we have these numbers, it's as easy as plugging in and doing some simple calculations to reaching our upper and lower fences of our interval. (136.28, 155.72). Any value below the lower fence or any value above the upper fence is not in our interval
The 99% confidence interval for the given random sample is between 136.5 and 155.5. The critical value for a 99% of confidence interval is 2.58.
How to calculate the percentage of the confidence interval?The formula for the confidence interval is
C.I = μ ± Margin error
Where Margin error = critical value × Standard error and μ - mean
Standard error = δ/[tex]\sqrt{n}[/tex]
δ - standard deviation and n is the sample space.
The critical value (z) is obtained from the percentage confidence interval table.
Calculation:Given that,
Sample space n = 85
Mean μ = 146 and δ = 34
Calculating the standard error:
S.E = δ/[tex]\sqrt{n}[/tex]
= 34/√85
= 3.68
The critical value for the 99% of the confidence interval is 2.58
Calculating the Margin error:
Margin error = 2.58 × 3.68
= 9.49
= 9.5
Then the 99% of the confidence interval is calculated as follows:
C.I = μ - Margin error (lower interval)
= 146 - 9.5
= 136.5
C.I = μ + Margin error (upper interval)
= 146 + 9.5
= 155.5
Thus, the 99% confidence interval is 136.5 - 155.5.
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