We can construct an unlimited number of triangles when given only two sides and no indication of the angle, such as a = 10m and b = 15m
Consider this:
With 10m and 15m side lengths and an angle value ranging from 0 to 360 degrees, how many distinct triangles are possible?
Make one of the triangles with sides of 10 meters, 15 meters, a 30 degree angle, and a third side that may be adjusted to your preferred length using a protractor. A triangle has been built by you.
By changing the length and angle of the third side, we can produce a completely different triangle that is similar to this one.
Keep in mind that you choose the side lengths and angle. This suggests that you might make a different decision. Using the same angles, you can make an infinite number of different triangles.
As a result, using just one angle and one side length, we can create an unlimited number of triangles.
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the amount Evelyn makes a week she gives x haircuts a $25 each and y perms at $90 each
the expression representing the total amount earned by Evelyn is $ 25 x + $ 90 y .
We are given that
Evelyn makes x haircuts for $ 25 and y perms for $ 90.
We need to write an expression representing the situation
We will use multiplication for the same.
So, Amount earned from the haircuts = x × $ 25 = $ 25 x
Amount earned from perms = y × $ 90 = $ 90 y
Total amount earned = $ 25 x + $ 90 y
Therefore, we get that, the expression representing the total amount earned by Evelyn is $ 25 x + $ 90 y .
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Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks. He must arrive at his friend’s house by 7:00 p.m. What is the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time?
The latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m
How to find the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time?Given that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks and He must arrive at his friend’s house by 7:00 p.m.
The time it takes Lyle to drive to his friend's house is given by t = d/v where
d = distance travelled and v = average speedGiven that Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, we have that
d = 720 km and v = 80 km/hSubstituting the values of the variables into t, we have
t = d/v
= 720 km/80 km/h
= 9 h
So, it takes Lyle 9 hours to drive.
Now, since Lyle takes an hour for Lunch and two 15 minutes breakes, this extra time is t' = 1 h + 2 × 15 min
= 1 h + 30 min
= 1 h + 30 min/60 min × 1h
= 1 h + 0.5 h
= 1.5 h
So, the total time Lyle takes to reach his friend's house is T = t + t'
= 9 h + 1.5 h
= 10.5 h
Since Lyle must reach his friend's place no later than 7:00 pm, 10.5 hrs from 7:00 pm is 8:30 am.
So, Lyle must leave no later than 8:30 a.m
So, the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time is 8:30 a.m
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A stop sign in the shape of a regular octagon is inscribed in a circle. Find following measure.
m NQ
An octagon is known to be a type of polygon that is said to have up to 8 sides the octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane then the measure of arc NPQ is 180°.
What is the inscribed of a circle?An inscribed angle of a circle is an angle whose vertex is a point A on the circle and whose sides are line segments (called chords) from A to two other points on the circle.
An octagon is known to be a type of polygon that is said to have up to 8 sides the octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane. A regular octagon will have all its sides equal in length.
The surface area of a regular octagon encircled by a circle of radius one unit. Divide the octagon into eight congruent triangles. We can find the area of one triangle and multiply it by 8 to get the area of the entire octagon.
The complete question is:
A stop sign in the shape of a regular octagon is inscribed in a circle.
What is the measure of arc NPQ?
A. 45°
B. 90°
C. 135°
D. 180°
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The focus of a parabola is (0, -1). The directrix is the line y = 0. What is the equation of the parabola in vertex form?
In the equation y = (-k)² +h, the value of pls
The vertex of the parabola is the point (
The equation of this parabola in vertex form is y =
).
x²-1
The equation of the parabola in vertex form is
P is -[tex]\frac{1}{2}[/tex]
(0,-[tex]\frac{1}{2}[/tex])
y=[tex]\frac{-1}{2}[/tex][tex]x^{2}[/tex] -[tex]\frac{1}{2}[/tex]
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a variety of seemingly unrelated mathematical descriptions, all of which may be shown to define the same curves.
One definition of a parabola includes a line and some extent (the focus) (the directrix). The directrix isn't the main focus. The locus of points therein plane that is equally spaced apart from the directrix and the focus is known as the parabola. A right circular conical surface and a plane parallel to a different plane that is tangential to the conical surface intersect to form a parabola, which is additionally known as a conic section.
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For each equation, find the center and radius of the circle.
(x-3)²+(y+1)²=36
The equation of the circle (x - 3)^2 + (y + 1)^2 = 36 has a radius of 6 and a center located at (3 , -1).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x - 3)^2 + (y + 1)^2 = 36, is in standard form, then
h = 3
k = -1
r = 6
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1. Round 68.14 to the nearest tenth. 2.round 61.98265 to the nearest thousandth
Answer:
1. 68.1
2. 61.983
Step-by-step explanation:
nearest tenth is one digit after the decimal. nearest thousandth is three digits after the decimal. since 4 is less than 5, the 1 remains the same. in the second problem, the fourth digit is 6 which is greater than 5 so you change the 2 to a 3.
"A trip to the Science Lab"
A street goes by the name, y=x+17. What is a parallel street to that one? (Write answer in slope-intercept form).
The street can be represented in slope intercept form as follows:
y = x + 4
How to find a street that is parallel?Linear equation can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptParallel lines have the same slope.
The street goes by the name y = x + 17.
The slope of the street is 1.
Therefore, the street parallel to that one should have the same slope.
The street can be represented in slope intercept form is as follows:
y = x + 4
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Find the slope of the line.
a. the line containing (6,-2) and (-3,-5)
The slope of the line containing (6,-2) and (-3,-5) is (3/8).
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = -5 , [tex]y_{1}[/tex] = -2 , [tex]x_{2}[/tex] = -3 , and [tex]x_{1}[/tex] = 6 .
On substituting the values of variables in equation1, we will get
m = ( (-5)-(-2) ) / ( (-3)-(6) ) = (-3/(-8)) = (3/8).
As the slope of a line is (3/8), so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (6,-2) and (-3,-5) is (3/8).
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For any correlation, people often assume that change in one quantity causes change in the second quantity. This is not always true. For each situation, do you think that change in the first quantity causes change in the second quantity? What else may have affected the change in the second quantity?
the size of a car's engine and the number of passengers it is designed for
For the given situation, we can clearly say that the change in one quantity will cause a change in the second quantity as well.
With an increase in the size of the car engine the power the engine will ultimately increase as well. This increased power can easily accommodate more people. So we can make relation from this deduction,
Engine size ∝ Number of People
This clearly states that by increasing one quantity we will increase the other quantity as well.
Similarly, now that they have a direct relation if we decrease the size of the engine, its power will decrease as well and hence the number of people will decrease.
A strong positive correlation we can call it.
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What is the inverse function of f(x) = 4 - x/6?
Answer:
f^-1 (x)= -6x+24
Step-by-step explanation:
the inverse function would be negative six (x) plus 24
Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term. 23,27,31,35,39, . . . .
The sequence 23,27,31,35,39, . . . . is arithmetic and the tenth term is: 59
We can determine that the sequence is arithmetic, because two consecutive terms differ by "d".
To solve this exercise we are going to apply the formula of the arithmetic sequence:
aₙ= a + (n-1) * dd = aₙ₊₁ - aₙWhere:
a = first termd = common difference of the sequencen= number of termsInformation about the problem:
Sequence = 23,27,31,35,39, . . . . Tenth term = ?Calculating the "d" term, we have:
d = aₙ₊₁ - aₙ
d = 27 - 23
d = 4
Calculating the tenth term, we get:
aₙ= a + (n-1) * d
a₁₀= 23 + (10-1) * 4
a₁₀= 23 + (9) * 4
a₁₀= 23 + 36
a₁₀= 59
What is an arithmetic sequence?It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.
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How many solutions does each of the following equations have?
10+5(x+2)=5x-20
Answer:
this equation has no solution
Step-by-step explanation:
How many solutions does each of the following equations have?
10+5(x+2)=5x-20
10+5x+10=5x-20
10 + 10 = -20
20 = -20
this equation has no solution
Answer:
Step-by-step explanation:
10+5(x+2)=5x-20
10+5x+10=5x-20
5x-5x=-20-10-10
x = -40
ABC and D are four towns
B is 25km due east of A
C is 25km due north of A
D is 45km due south of A
work out the bearing of B from C
Answer:
213.7°
Step-by-step explanation:
The bearing of B from D is angle ADB, which is ∠ADB = arctan(30/45)
≈ 33.7°
The bearing of D from B is that angle plus 180°, so is 180° +33.7° = 213.7°
Answer:
225°
Step-by-step explanation:
In mathematics, a bearing is defined as an angle measured clockwise from north.
See attached graph for a clearer guide to the explanations
Angle ABC is a right isosceles triangle with AB = 25 and AC = 25
m∠BAC =90°
So m∠ABC = m∠ACB = 45°
The angle at BC is 45° from the North (90°-45°) measured clockwise is 45° so we say the bearing from C to B is 045° (we use 3 digits for bearing)
The bearing from B to C on the other hand is determined by adding 180° to the bearing in the opposite direction (C to B) so the bearing from C to B is 180° +045° = 225°
(Here I am not sure whether you are supposed to answer the question in mathematical meaning of bearing or just state the direction in which BC lies relative to north. 45° clockwise from the North is in a NE direction so we can say C is NE from B but I am guessing that's not it)
f(x) = 13 - x
h(x) = x² - 6x - 18
Write (fo h) (x) as an expression in terms of a x.
(ƒ○h)(x) =
Directions: Using the digits 1 to 9 at most one time each, fill in the blanks to make the largest quotient.
Using the digits 1 to 9 at most one time each to make the largest quotient is 98 ÷ 12 .
According to the question we have to use digits 1 to 9 at most one time each to make the largest quotient.
Now we know that the number that is being divided is known as the dividend and the number by which we divide is known as the divisor.
Now dividend should be greater than the divisor.
So tot make the largest quotient the dividend and the divisor will be
98 and 12 respectively.
That is, 98 ÷ 12 = 8.2 which is the largest quotient.
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Alice is going to make a cake for her mother's birthday. It will take 24 minutes to make the cake batter, and the cake needs to bake in the oven for 1 hour and 2 minutes. If Alice wants the cake to be out of the oven by 9:59 A.M., what is the latest time she can start making the cake batter?
The latest time Alice can start making the cake batter is 8:33 A.M
How to calculate the latest time ?Alice is making cake for her mother's birthday
It will take 24 minutes to make the cake batter
The cake also needs to be in the oven for 1 hour 2 minutes
The time needed to make the cake is
1 hour 2 minutes + 24 minutes
= 1 hour 26 minutes
The latest time to start making the cake batter is
9:59 - 1:26
= 8:33
Hence the latest time to start making the cake batter is 8:33 A.M
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Marsha pays $20 each month for a car wash membership. Which of the following represents the total amount subtracted from her account after 6 months of having the membership?
|−20| − 6 = $14
|−20| − |6| = $14
−6|20| = −$120
6|−20| = $120
The total amount subtracted from her account after 6 months of having the membership is −6|20| = −$120. option C
Given:
Cost of membership
Cost per month for a car wash membership = $20
Number of months = 6 months
Total amount subtracted from her account = Number of months × Cost per month for a car wash membership
= 6 (-20)
= -120
Therefore, the total amount subtracted from her account after 4 months of having the membership is −6|20| = −$120.
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Wendy rode her bicycle 87 meters in 12 seconds. What is her speed?
a
0.14m/s
b
0.8 m/s
c
7.3 m/s
d
9.5 m/s
Answer:
c) 7.3 m/s
Step-by-step explanation:
We know that 87 is the total and 12 is the time do you take the total divided by the time so 87/12=7.25. 7.25 rounded is 7.3.
Order from least to greatest
-1.2, 2.7, -3.1, -0.3
Don’t you order it with the highest negative to the lowest negative then the last should be the positive?
The formula used to convert degrees Celsius to degrees Fahrenheit is F=95C+32F= 59 C+32.Convert 68°F to degrees Celsius. Solve the formula for C, and then use it to convert the temperature.Which is the correct formula and conversion
Answer:
Step-by-step explanation:
F = 9/5 C + 32 is the correct formula.
9/5 C = F - 32
C = 5/9(F - 32)
So, 68 degrees Fahrenheit
= 5/9(68 - 32)
= 5/9 * 36
= 20 degrees C.
Consider the line -9x-6y=8.
What is the slope of a line perpendicular to this line
What is the slope of a line parallel to this line?
Slope of a perpendicular line:
Slope of a parallel line:
Answer:
Slope of a perpendicular line:
[tex]\boldsymbol{\dfrac{1}{9}}[/tex]
Slope of a parallel line:
[tex]\boldsymbol{-9}[/tex]
Step-by-step explanation:
A line perpendicular to a line y = mx + b will have its slope as[tex]-\dfrac{1}{m}[/tex]
Here slope of given line = -9
[tex]\displaystyle \mathrm {reciprocal\; of\;} -9 = -\dfrac{1}{9}[/tex]
[tex]\mathrm {negative\; of \;reciprocal\;}= -\left(-\dfrac{1}{9}\right) = \dfrac{1}{9}\\[/tex]
parallel lines have the same slope so a parallel line will have slope = -9
The right-angled triangle ABC has an angle BAC of 30º. Taking the length of BC to be one unit:
a. work out the length of AC
b. use Pythagoras' theorem to obtain the length of AB
Answer:
a) [tex]\sqrt{3}[/tex]
b) 2
Step-by-step explanation:
a) tan 30 = opposite side / adjacent side 1/[tex]\sqrt{3}[/tex] so AC is [tex]\sqrt{3}[/tex]
b)3
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]1^{2}[/tex] +[tex]\sqrt{3} ^{2}[/tex] = [tex]c^{2}[/tex]
1 + 3 = [tex]c^{2}[/tex]
4 = [tex]c^{2}[/tex]
[tex]\sqrt{4}[/tex] =[tex]\sqrt{c^{2} }[/tex]
2 = c
The length of AC is √3 units and the length of AB is 2 units by Pythagoras' theorem
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The right-angled triangle ABC has an angle BAC of 30º.
The length of BC be one unit
We have to find the length of AC
tan (30)= opposite side/ adjacent side
1/√3 = opposite side/ adjacent side
The adjacent side is √3 which is length of AC
Now let us find the length of AB by using pythagoras theorem
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
AB² = AC² + BC²
AB²=√3² + 1²
AB²= 4
AB = 2 units
Hence, the length of AC is √3 units and the length of AB is 2 units by Pythagoras' theorem
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Help pls I really need if help then thank you you really help
Solve equation by using the Quadratic Formula. Round to the nearest tenth if necessary. x² = x + 12
The quadratic equation of the form ax² + bx + c = 0.
The value of x = 4 and x = -3
No solution
No real-valued solution
What is meant by quadratic equation?The quadratic equation of the form
ax² + bx + c = 0.
The form is called the standard form of the quadratic equation.
Let the given equation be x² = x + 12
By using quadratic equation, ax² + bx + c = 0
ax² + bx + 12 = 0
x² = x + 12
⇒ x² - x - 12 = 0
Let the quadratic equation be
[tex]$x=\frac{\left(-b\right)\pm \sqrt{\left(b)^2-4\cdot \:a\cdot \left(c)}}{2\cdot \:a}[/tex]
a = 1, b = -1 and c = -12
Substitute the values in the above equation, we get
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \left(-12\right)}}{2\cdot \:1}[/tex]
simplifying the above equation, we get
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\pm \:7}{2\cdot \:1}[/tex] and
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\a++ \:7}{2\cdot \:1}[/tex]
[tex]$x_{1,\:2}=\frac{-\left(-1\right)\a+- \:7}{2\cdot \:1}[/tex]
x = 4 and x = -3
Therefore, the value of x = 4 and x = -3
No solution
No real-valued solution
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How would you find the area of this parallelogram? Describe your strategy.
The horizontal sides that are each 7 units long with angled sides that
rise 6 vertical units over 2 horizontal units.
The area of the parallelogram is 42 units².
What is the Area of a Parallelogram?The area of a parallelogram can be calculated by finding the product of its base with the altitude. The base and altitude of a parallelogram are always perpendicular to each other.
i.e., The area of a parallelogram = base × height.
To find the perimeter of a parallelogram, add the lengths of the sides. Opposite sides of a parallelogram are equivalent.
Given:
base= 7 units
height = 6 units.
Now, area of a parallelogram,
= 7 × 6
= 42 units²
Hence, area of the parallelogram is 42 units².
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p²m ÷ 4; use m = 4, and p = 7
Answer:
[tex] \sf{49}[/tex]
Step-by-step explanation:
Given that,
m => 4
p => 7
Let us solve the given expression by using the given values.
[tex] \sf \: {p}^{2} m \div 4 \: \: \: \: \: \\ \sf{(7)}^{2} \times 4 \div 4 \\ \sf 49 \times 4 \div 4 \\ \sf196 \div 4 \: \: \: \: \: \: \\ \sf49 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Solve plsssssssssss I’m kinda desperate rn
here is it friend...hope it is clear enough
Answer:
5/6x + 5/12 + 20/6
Simplfied
5/6x + 3 3/4
Step-by-step explanation:
5/6 ( x+ 1/2 + 4)
Distribute
Multiply the term outside the parentheses to each term inside the parentheses
5/6 ( x) + 5/6 *(1/2) +5/6 *( 4)
5/6x + 5/12 + 20/6
We need to get a common denominator for the constant terms
5/6x + 5/12 + 20/6
5/6x + 5/12 + 40/12
Add
5/6x + 45/12
45/12 is an improper fraction so we can make it a mixed number
12 goes into 45 3 times with 9 left over
3 9/12 which simplified to
3 3 /4
The simplified expression is
5/6x + 3 3/4
what does x equal
4x+5x+=6+11
4x+5x+=6+11
9x=17
x=17/9
☞ user58580~ ♥
Answer:
x= 17/9
Step-by-step explanation:
4x+5x=6+11
Combine like terms
9x=17
x=17/9
Given the m∠5=82° use the image below to find the measures of the other angles.
The value of the other angles
∠1 = 180 - 82°
∠2 = ∠1 = 98°
∠3 = ∠ = 98°
∠4 = ∠5 = 82°
According to the given data,
m∠5=82° given
∠5 = ∠7 = ∠4 = ∠8 = ∠6 = ∠12
∠1 = ∠10 = ∠2 = ∠11 = ∠3 = ∠ 12 = 180° - ∠5
we get, measures of other angles
∠1 = 180 - 82°
∠2 = ∠1 = 98°
∠3 = ∠ = 98 °
∠4 = ∠5 = 82°
A transversal is a line that intersects two coplanar lines at two different points. In the figure,
line t is a transversal. The table summarizes the names of angle pairs formed by a transversal.
Corresponding angles lie on the same side of the transversal and on the same
sides of the intersected lines. ∠1 and ∠5
Same-side interior angles lie on the same side of the transversal and between
the intersected lines. ∠3 and ∠6
Alternate interior angles are nonadjacent angles that lie on opposite sides of
the transversal between the intersected lines. ∠3 and ∠5
Alternate exterior angles lie on opposite sides of the transversal and outside
the intersected lines. ∠1 and ∠7
Same-Side Interior Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles have the same measure.
Corresponding Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of corresponding angles have the same measure.
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Help pleaseeeeeeeeee
Answer: 4.7 gallons
Step-by-step explanation:
The range is the difference in the highest number and the smallest number, so 2.8 - -1.9 = 4.7
