Solve the following problems. Remember that all reasoning must be explained, and all steps of math work must be shown!
Topic: Perpendicular to Chord Property
Answers
Since the diagram shows a right triangle and gives out some measurements of the sides, you can use the Pythagorean Theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to find the length of MP.
Given:
hypotenuse = 7 – because the radius is 7 units and it can be used as the hypotenuse
One side of the triangle = 4 – because the length of PO is 4 units and it can be used as one sides of the triangle
To Solve:
Since we know two values of the triangle, you can use the Pythagorean Theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to find what the other value is. The variables c and b in the formula are already given, and we need to find what a is to find the length of MP. So, plug the given values of c and b into the formula:
[tex]a^{2}+4^{2}=7^{2}[/tex]
Simplify:
[tex]a^{2}+16=49[/tex]
Subtract 16 from both sides of equation:
[tex]a^{2}=33[/tex]
Do the square root of both sides to isolate the variable a:
[tex]\sqrt{a^{2}}=\sqrt{33}[/tex]
Evaluate:
[tex]a=\sqrt{33}[/tex] Which simplifies to [tex]a= 5.744562646....[/tex] and round it to the nearest tenth to finally get [tex]a=5.7[/tex]
Answer: The length of MP is 5.7 units
How to solve Part AIf you look at the diagram in the question, you can see that the length of MN is twice the length of MP. So multiply the length of MP, which is 5.7, by 2:
5.7 · 2 = 11.4
Answer: The length of MN is 11.4 units
___________________________________________________________
Question 2:How to solve Part ALook at the first image below ↓
Description of the first image:
The first image shows a drawn image of the circle with labeled parts and measurements from the infomation given from the question.
The diameter is 26cm, which means that the radius is 13cm because the radius half of the diameter in a circle. The very top line is the surface of the water where it’s filled and it has a length of 20cm. Side b of the triangle is 10cm becuase it’s half the length of the the surface of the water bowl. The hypotenuse (side c) is 13cm because it’s the length of the radius. And side a is what what we need to find because it’s the distance between the surface of the water and the center of the bowl. But after when you find the length of side a, you need to add the length of the radius (which is 13cm) to the length of side a because that’s the rest of the length/depth of the water that’s filled in the bowl. The length of the radius is included with the depth of the water.
Total information given:
⇒ radius = 13cm – because the radius is half of the diameter, and the diameter has a length of 26cm
⇒ length of the surface where the water’s filled = 20cm
⇒ hypotenuse (side c) = 13cm – because it’s the length of the radius
⇒ side b = 10cm – because it’s half the length of the surface where the water’s filled
To Solve
Since there is a right triangle shown in the image, you can use the Pythagorean Theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to find the missing length of side a. Plug the given values of c and b into the formula:
[tex]a^{2}+10^{2}=13^{2}[/tex]
Simplify:
[tex]a^{2}+100=169[/tex]
Subtract 100 from both sides of the equation:
[tex]a^{2}=69[/tex]
Do the square root of both sides to isolate the variable a:
[tex]\sqrt{a^{2}}=\sqrt{69}[/tex]
Evaluate:
[tex]a=\sqrt{69}[/tex] Which simplifies to [tex]a= 8.30662386....[/tex] and round it to the nearest tenth to finally get [tex]a[/tex] ≈ [tex]8.3[/tex]
This means that 8.3 is just the length of side a, which is the length between the surface of where the water’s filled and the center of the circle. But, now you need to add 13 to 8.3 to find the total depth of the water because the length of the radius is included with the depth of the water.
So,
13 + 8.3 = 21.3
Answer: The depth of the water is approximately 21.3 cm
How to solve Part B (is in the image below)Sorry for the very, VERY long explanation and the long solving process, but I really, really hope you understand and that this helps with your question! :)
Related Questions
Make x the subject of the formula
m=x+y/n
HELPPP
Answers
Answer: x=m-y/n
Step-by-step explanation:
The expression with x as the subject is x = mn - y.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
m = (x + y) / n
x as the subject means we have to solve for x.
Now,
m = (x + y) / n
Multiply both sides by n.
mn = x + y
Subtract y on both sides.
mn - y = x
x = mn - y
Thus,
x = mn - y.
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suppose you have an argument that has three premises, all of which are true, and a true conclusion. if so, then the argument must be
Answers
The conclusion might be accurate or inaccurate.
The conclusion could be true or false if an argument has some true premises and some false premises and is valid. You only know that the premises cannot both be true and the conclusion must be false because the argument is sound. But the incorrect premises already rule out the possibility of possessing this set of truth values (that is, you cannot have all true premises). As a result, the argument's validity is unaffected whether the conclusion is true or untrue. As a result, the conclusion of an argument that contains only false premises may or may not be true.
Can an argument have all true premises and a false conclusion?TRUE. A valid argument cannot, by definition, have a false conclusion and all true premises.
Therefore, a valid argument must have an erroneous premise if it has a false conclusion.
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How can you adjust both numbers and use compensation to find $7.99 + $19.99 mentally?
Answers
The adjustment of both numbers and using compensation to find $7.99 + $19.99 mentally is $27.98
How to calculate the value?It should be noted that compensation is the mental strategy in Mathematics used for addition by adjusting one of rte addends.
It should be noted that $7.99 is almost the same as $8. It should be noted that $19.99 is the same as $20. This is the compensation or the numbers.
Therefore, the addition of the numbers $7.99 + $19.99 will be:
= $7.99 + $19.99
= $27.98
In conclusion, the answer is $27.98.
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Please help fast :(
Answers
Answer:
1/2
1/4
1/4
0/16
2 times
Step-by-step explanation:
THERE ARE 16 SQUARES TOTAL
8 triangles: 8/16 = 1/2
4 stars: 4/16 = 1/4
4 empty spaces: 4/16 = 1/4
0 circles = 0/16
8*1/4 is 2, so 2 times.
diamond problem for -2 and -5
Answers
Step-by-step explanation:
if I understand you correctly, then let's call the missing numbers l, r (for left and right).
and
-2 = l × r
-5 = l + r
l = -r - 5
therefore,
-2 = (-r - 5) × r = -r² - 5r
that gives us the quadratic equation
-r² - 5r + 2 = 0
for the general solutions
x = (-b ± sqrt(b² - 4ac))/(2a)
we have here
a = -1
b = -5
c = 2
and x = r, of course
r = (5 ± sqrt(25 - 4×-1×2))/(2×-1) =
= (5 ± sqrt(25 + 8))/-2 = (5 ± sqrt(33))/-2
r1 = (5 + sqrt(33))/-2 = -5.372281323...
r2 = (5 - sqrt(33))/-2 = 0.372281323...
as l = -r - 5, we see that r1 = l2, and r2 = l1.
but these are the only solutions.
there are no integer number solutions.
a line passes through the points (4, 13) and (2, 5). What is it’s equation in slope intercept form
Answers
Answer:
y = 4 x - 3
Step-by-step explanation:
Find the equation of the line in slope-intercept form with the properties:
point: p_1 = (4, 13)
point: p_2 = (2, 5)
The slope of the line through points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1):
m = (5 - 13)/(2 - 4) = (-8)/(-2) = 4
Substitute the slope m = 4 and point (x_1, y_1) = (4, 13) into the point-slope equation y - y_1 = m (x - x_1):
y - 13 = 4 (x - 4)
Add 13 to both sides:
y = 13 + 4 (x - 4)
Distribute: 4 (x - 4) = 4 x - 16:
Answer: y = 4 x - 3
Solve two thirds times v plus 6 equals one third times v minus 2.
v equals negative eight thirds
v equals eight thirds
v = −24
v = 24
Answers
The value of v using the equation ( 2v/3 ) + 6 = ( v/3 ) - 2 is v = - 24.
Two-thirds of anything is an amount that is two out of three equal parts of it. Similarly, one-third of something is an amount that is one out of three equal parts of it.
Now, we have
Two-thirds times v plus 6 equals one-third times v minus 2.
Hence, when the above statement is expressed as an equation we get:
Two third of v + 6 = one third of v - 2
2/3 × v + 6 = 1/3 × v - 2
( 2v/3 ) + 6 = ( v/3 ) - 2
Adding 2 on both sides of the equation,
( 2v/3 ) + 6 + 2 = ( v/3 ) - 2 + 2
( 2v/3 ) + 8 = ( v/3 )
Subtracting 2v/3 from both sides of the equation,
2v/3 + 8 - 2v/3 = v/3 - 2v/3
8 = ( v - 2v )/3
- v/3 = 8/1
By cross multiplication,
- v × 1 = 8 × 3
- v = 24
Multiplying each side by - 1,
v = - 24
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In a recent year, 17.3% of all registered doctors were female. If there were 41,000 female registered doctors that year, what was the total number of registered doctors?
Round your answer to the nearest whole number. PLEASE HELP DUE IN 30 MINUTES!!!
Answers
The total number of registered doctors are estimated as 236,995.
What is meant by percentage?A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is one hundredth part; thus, 100 percent signifies the entire amount and 200 percent specifies twice this same given amount.
The concept of cumulative percentage (percentile) is widely used in statistics. For example, a student who achieves the 83rd percentile on an investigation has outperformed 83 percent of the students with and who a comparison is made. The likelihood of an event occurring can be expressed as a percentage. (or fraction).Now, as per the given question;
It says, from all the registered doctors 17.3% is female doctors.
Now, let use assume that the total number of registered doctors be 'x'.
Then, 17.3% of this x will give 41,000 female doctors.
So, the equation will form as;
17.3% of x = 41,000
Or, (17.3×x)/100 = 41,000
x = (41,000×100)/17.3
x = 236,994.21
x = 236995 (nearest whole number)
Therefore, the total number of the registered doctors are estimated as 236995.
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Robert is preheating his oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 25° per minute after being turned on. What is the temperature of the oven 10 minutes after being turned on? What is the temperature of the oven t minutes after being turned on?
Answers
The temperature of the oven 10 minutes after being turned on will be 315°.
The temperature of the oven t minutes after being turned on will be 65 + 25t
How to compute the value?The temperature of the oven 10 minutes after being turned on will be:
= 65 + (25 × t)
where t = number of minute
= 65 + (25t)
= 65 + 25(10)
= 65 + 250
= 315°
The temperature of the oven 10 minutes after being turned on will be 315°.
The temperature of the oven t minutes after being turned on will be:
= 65 + (25 × t)
= 65 + 25t
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what is the distance between (-2.63, 7),(1.85,7)
Answers
The distance between the points is 4.48
What is the distance between the points?The coordinates of th points are given as:
(-2.63, 7) and (1.85,7)
The distance between the two points is calculated using
d = √(x2 - x1)^2 + (y2 -y1)^2
So, we have
d = √(-2.63 - 1.85)^2 + (7 - 7)^2
Evaluate
d = 4.48
Hence, the distance between the points is 4.48
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Does 44,555 and 45,555 round to 50,000?
Answers
45,555 does, but the other one doesn't.
A city park measures 7/8 mile wide by 3/4 mile long. What is the area of the park?
Answers
Length = 3/4 mile = 0.75
Width = 7/8 mile = 0.875
0.75 x 0.875 = 0.66 miles²
find the percentage if the denominators are not the factors of 100
Answers
Answer:
external factors that impact negatively on lifestyle choices namely.unsafe road use
#11 i Solve -14>w+3 or 3w > -27 Solution: or
Answers
The values of the inequalities will be:
1. -14>w+3 = w < -17
2. 3w > -27 = w > -9
How to explain the inequality?It should be noted that an inequality simply means the expression that illustrates that the variables aren't equal. This can be used by uinng less than, greater than, etc.
The inequalities will be:
-14>w+3
Collect like terms
-14 - 3 > w
-17 > w
w < -17
3w > -27
Divide both side by 3
3w/ 3 > -27/3
w > -9
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a line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. find the other endpoint (x2, y2) of the line segment in terms of x1, y1, xm, and ym. use the result to find the coordinates of the endpoint (x2, y2) of each line segment with the given endpoint (x1, y1) and endpoint (xm, ym).
Answers
The coordinates are:
For the first line, coordinates are (3, 7).For the second line, the coordinates are (12, 0).What are coordinates?A coordinate system in geometry is a system that uses one or more numbers, or coordinates, to determine the position of points or other geometric elements on a manifold such as Euclidean space.To find the coordinates:
In Analytical Geometry, the midpoint of a line is calculated as the mean of two points, as follows:
[tex]$$x_m=\frac{x_1+x_2}{2}, y_m=\frac{y_1+y_2}{2}$$[/tex]
Each segment has two endpoints and two midpoints, which are as follows:
(1,-9), as well as its midpoint (2,-1)(-2,18), as well as its midpoint (5,9)We must be cautious not to add the wrong coordinates.
In the first line A:
[tex]$$\begin{aligned}&2=\frac{1+x_2}{2} \\&4=1+x_2 \\&4-1=-1+1+x_2 \\&x_2=3 \\&-1=\frac{y_2-9}{2} \\&-2=y_2-9 \\&+2-2=y_2-9+2 \\&y_2=-7\end{aligned}$$[/tex]
So (3,7) is the other endpoint where the segment begins (1,-9).
The endpoint of the second line b at (-2,18) and its midpoint (5,9).
[tex]$$\begin{aligned}&5=\frac{-2+x_2}{2} \\&10=-2+x_2 \\&+2+10=+2-2+x_2 \\&x_2=12 \\&9=\frac{18+y_2}{2} \\&18=18+y_2 \\&-18+18=-18+18+y_2 \\&y_2=0\end{aligned}$$[/tex]
So, (12,0) is the opposite endpoint.
Therefore, the coordinates are:
For the first line, coordinates are (3, 7).For the second line, the coordinates are (12, 0).Know more about coordinates here:
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The correct question is given below:
A line segment has (x1, y1) as one endpoint and (xm, ym) as its midpoint. Find the other endpoint (x2, y2) of the line segment in terms of x1, y1, xm, and ym. Use the result to find the coordinates of the endpoint of a line segment when the coordinates of the other endpoint and midpoint are, respectively, (1, −9), (2, −1) and (−2, 18), (5, 9).
If f(x)=-2x+3then f(3)-f(4)
Answers
9x10^4 + 9x10^2 ??
add
Answers
Answer:
90900
Step-by-step explanation:
Answer:
9.09 x 10*4.
Step-by-step explanation:
9x10^4 + 9x10^2
= 90000 + 900
= 90900
= 9.09 x 10*4.
A restaurant had 9 days to sell 56 gallons of ice cream before it expired. How much should they sell each day?
5 gallons
5 gallons
6 6/4 gallons
6 6/4 gallons
6 1/2 gallons
6 1/2 gallons
6 2/9 gallons
Answers
Answer:
6 2/9
Step-by-step explanation:
56 divided by 9 is 6.22 and 2/9 is .22
56/9 = 6.22222222222222222…..
And,6.2222….. is equal to 6 2/9
Write an equation in slope intercept form for the line that is parallel to y= 2/5x-2 and passes through the point (-20,-7). Show your work (PLEASE ANSWER ASAP)
Answers
Answer:
y = 2/5x + 1
Step-by-step explanation:
If two lines are parallel, their slopes are equal
so the slope would be 2/5
if y = -7, x = -20, m = 2/5
slope-intercept form:
y = mx + b
-7 = 2/5(-20) + b
-7 = -8 + b
b = 1
then y = 2/5x + 1
Can someone help me please?
Answers
Answer:
112
Step-by-step explanation:
Both angles are vertical angles
so x + 84 = 4x
3x = 84
x = 84/3 = 28
x + 84 = 28 + 84
Consider the arithmetic sequence (87, 83, 79,75...)
A. Find common difference, d
B. Find explicit formula
Answers
Answer:
see explanation
Step-by-step explanation:
A
the common difference d of the arithmetic sequence is
d = a₂ - a₁ = 79 - 83 = - 4
B
the explicit formula of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 83 and d = - 4 , then
[tex]a_{n}[/tex] = 83 - 4(n - 1) = 83 - 4n + 4 = 87 - 4n
Find the value of j. Show all steps to the solution and give reason to your calculations
Answers
Answer:
j=50°
Step-by-step explanation:
10x-20=5x-3+4x-2( ext angle of ∆)
10x-5x-4x=-3-2+20
x= 15
substitute the value if x
10(15)-20+ j=180 ( sum of angles in straight line)
130+j=180
j=180-130
j=50°
Correct to 2 decimal places, the volume of a solid cube is 3.37 m³. Calculate the upper bound for the surface area of the cube.
Answers
the upper bound for the surface area of the cube. is 14 m².
Volume of cube = 3.37 m³
We know the formula is:
V = a³ (where a is the side of the cube)
a³ = 3.37 m³
Cube rooting both the sides, we get that:
a = ∛3.37 m
Surface area will be:
A = 6 a²
A = 6 (∛3.37 m)²
A =6 (2.25 m²)
A = 13.5 m²
A ≈ 14 m²
Therefore, we get that, the upper bound for the surface area of the cube. is 14 m².
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one diagonal of a rhombus has endpoints (-10, 1) and (2, 9). what are the endpoints of the other diagonal?
Answers
The endpoints of the other diagonal are (-2, 2) and (-6, 8).
Distance formula, Algebraic expression that gives the distances between pairs of points in terms of their coordinates (see coordinate system). In two- and three-dimensional Euclidean space, the distance formulas for points in rectangular coordinates are based on the Pythagorean theorem.
Given we have a rhombus with endpoints (-10, 1) and (2, 9)
So as we already know, a rhombus is a parallelogram whose sides are equal, so the distance from say (-10, 1) to either endpoint of the other diagonal must be the same.
Distance between 2 points [tex]$\mathrm{d}=\sqrt{[-2-(-10)]^2+[2-1]^2} \Longrightarrow d=\sqrt{(-2+10)^2+(2-1)^2}$$\mathbf{d}=\sqrt{\mathbf{6 4 + 1}} \Longrightarrow d=\sqrt{65}$[/tex]
While solving with other coordinate we get [tex]$\mathbf{d}=\sqrt{(-6+10)^2+(8-1)^2}[/tex]
[tex]$\mathrm{d}=\sqrt{16+49}\\\Longrightarrow d=\sqrt{65}$[/tex]
So therefore the endpoints of the other diagonal are (-2, 2) and (-6, 8) .
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15. Write an equation and solve the equation to find the value of x so that the triangles have the same perimeter.
Triangle 1: 5,x-4,x-5
Triangle 2: 10,16,x-10
Answers
The equation is 5 + x - 4 + x - 5 = 10 + 16 + x - 10 and on solving the value of x is 20
The perimeter of a triangle is calculated by the summation of all the sides of a triangle
It is given that both the triangles have the same perimeter, so summation of all the sides of one triangle is equal to summation of all the sides of another triangle
Therefore the equation can be 5 + x - 4 + x - 5 = 10 + 16 + x - 10
Further solving the equation to calculate the unknown variable x
5 + x - 4 + x - 5 = 10 + 16 + x - 10
2x - 4 = x + 16
2x - x = 16 + 4
x = 20
The ēquation is 5 + x - 4 + x - 5 = 10 + 16 + x - 10 and on solving the value of x is 2
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The slope for a wheelchair ramp for a home has to be 1/2.
If the vertical distance from the ground to the door bottom is 3 ft, find the distance the ramp has to extend from the home in order to comply with the needed slope.
Answers
In order to comply with the required slope, the ramp must extend 36 ft from the house.
What do we mean by Distance?Distance is a mathematical or qualitative measure of the distance between two objects or points. Distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage (e.g. "two counties over").So, to find the distance:
The formula of slope:
m = change in vertical height/change in horizontal heightVertical distance is now given as 3 ft.
To conform to the given slope, this means that:
1/12 = 3/xCross multiply:
x = 3 × 12x = 36 ftTherefore, in order to comply with the required slope, the ramp must extend 36 ft from the house.
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help please
0.1 - 4.37
Answers
Answer:
-4.27
Hope this helps.
Step-by-step explanation:
Because the negative number ( - 4.37 ) is bigger than 0.1, the answer is going to end up negative. You can swap sides on the equation to become - 4.37 + 0.1, in which case is 4.36 - 0.1 but you have to remember to add the negative sign afterward.
The length of a cell phone is 1.41.4 inches and the width is 4.44.4 inches. The company making the cell phone wants to make a new version whose length will be 1.961.96 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answers
Answer:
61.96 inches.
Step-by-step explanation:
A waiter earned $69.81 on a shift, and then bought himself a discounted meal for
$4.75. How much did he have left over, to the nearest dollar?
He had about $
Answers
Answer:$65
Step-by-step explanation:69.81-4.75=65.06
65.06->65
9. If AB= 25, AN= 2x-6, and NB = x + 7, find x, AN and NB.
2+
N
Answers
The value of x is equal to 8 and the values of AN and NB are 10 and 15 respectively.
The three points A, N and B are collinear, and N is between A and B. Collinear points are defined as set of those points which lie on the same line when plotted.
If A, N and B are collinear then,
AB = AN + NB
According to question, AB = 25, AN = 2x-6 and NB = x+7 thus,
25 = 2x-6 + x+7
25 = 3x + 1
24 = 3x
=> x = 24/3
=> x = 8
Now, AN = 2x-6 = 16-6 = 10
NB = x+7 = 8+7 = 15
Thus, the values of x, AN and NB are 8, 10 and 15 respectively.
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