The 4 types of triangle with respect to angle measurement :
Acute Triangle
Obtuse Triangle
Right triangle
Equivalent triangle
What are the four types of triangles by angle measurement ?A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
A triangle having three acute angles is known as an acute triangle. A triangle having one obtuse angle and two acute angles is known as an obtuse triangle. No Euclidean triangle may contain more than one obtuse angle because in Euclidean geometry, a triangle's angles must add up to 180°.
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or more than 90°. Only 180° is equivalent to the internal angles of an acute triangle.
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There are four different triangles for measuring angles:
sharp triangle
Sharp triangle
correct triangle
comparable triangle
What are the four different kinds of triangles according to angle?If all three sides of a triangle are the same length, the triangle is equilateral. Equiangular triangles are equilateral triangles in well-known Euclidean geometry. His three internal angles, which are all 60 degrees, are therefore consistent with one another.
An acute triangle is a triangle having three acute angles. Obtuse triangles are those with one obtuse angle and two acute angles. Euclidean geometry mandates that the total of all the angles of a triangle be 180°, hence a triangle cannot have more than one obtuse angle.
A right triangle, also known as a right triangle, right triangle, right triangle, right triangle, right triangle, or formerly right triangle, is a triangle with one or two right sides. The basis of trigonometry is the relationship between the sides of a right triangle and different angles.
An obtuse or obtuse triangle is a triangle with one of its angles obtuse or greater than 90°. An acute triangle has only 180° interior angles.
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On the way to visit her grandmother, Sally drove at an average speed of 85 mph. On the way home (taking the same route) she only averaged 65 mph. If the total round trip took 18 hours, how many hours did it take Sally to drive to her grandmother's? Write your answer as a decimal.
Answer:
7.8 hours
Step-by-step explanation:
We will use the formula:
distance =rate×time
We don't know the distance but it is the same distance going and returning. Two rate×time calculations will both equal that distance from Sally's to Grandma's. See image.
What is the range of the function f(x) = |x – 3| + 4?
R: {f(x) ∈ ℝ | f(x) ≥ 4}
R: {f(x) ∈ ℝ | f(x) ≤ 4}
R: {f(x) ∈ ℝ | f(x) > 7}
R: {f(x) ∈ ℝ | f(x) < 7}
Answer: R: {f(x) ∈ ℝ | f(x) ≥ 4}
Step-by-step explanation:
[tex]|x-3| \geq 0[/tex] for all real x, so the range is [tex]f(x) \geq 4[/tex].
the height of a can of coke is in 11 cm and the radius is 6 cm calculate the total surface area of the can in cm^3 assuming that the
can is a closed cylinde
Answer:
The total surface area of the the cylinder is 640.56cm², surface are is always give in cm² not in cm³ b/c cm³ indicates the volume of the cylinder not the surface area.
Step-by-step explanation:
Hello!
. SA=2πr(r+h) ,or 2πr²+h(2πr)
SA=2(3.14)(6cm)(6cm+11cm)SA=6.28(6cm)(17cm)SA=37.68cm(17cm)SA=640.56cm²Answer:
204π cm^2
which is 640.88 cm^2 to the nearest hundredth.
Step-by-step explanation:
Surface area = 2 * area of the base + area of the curved side.
= 2*π *r^2 + 2*π*r*h
= 2π(6)^2 + 2π(6)(11)
= 72π + 132π
= 204π cm^2.
A couple purchased a home and signed a mortgage contract for $900,000 to be paid with half-yearly payments over a 25-year period. the interest rate applicable is j2 = 5.5% p.a. applicable for the rst ve years, with the condition that the interest rate will be increased by 12% every 5 years for the remaining term of the loan.
A mortgage payment is typically made up of four components: principal, interest, taxes, and insurance. The Principal portion is the amount that pays down your outstanding loan amount. Interest is the cost of borrowing money. The amount of interest you pay is determined by your interest rate and your loan balance.
The term “loan” can be used to describe any financial transaction where one party receives a lump sum and agrees to pay the money back. A mortgage is a type of loan that's used to finance a property. A mortgage is a type of loan, but not all loans are mortgages. Mortgages are “secured” loans.
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What is the slope of a line that is parallel to the line y = 3/4x+2?
Answer: 3/4
Step-by-step explanation:
Parallel lines have the same slope.
The population mean is symbolized as ________________, whereas the sample mean is symbolized as __________________. Group of answer choices n; N N; n
The population mean is symbolized as μ. The sample mean is symbolized M.
What is a Population?
A population in statistics, is a the total number of people of a group that shares similar characteristics that are of interest to a researcher. Example of population a researcher can understudy include:
Sixth grade students taking mathApple watch usersPeople who patronize a shopping mall, etc.What is a Sample?A sample is a subset of a population, which is drawn using any sampling technique. An example of a sample is 100 randomly selected persons who patronize a shopping mall.
What is the Population Mean?The population mean can be defined as the average data value of a particular group characteristics that is measured by the researcher. The symbol for population mean is: μ.
What is the Sample Mean?
The sample mean can be defined as the average data value of the sub-group of an entire population that having characteristics that are of interest to a researcher. The symbol for sample mean is: M.
In summary, the population mean is symbolized as μ. The sample mean is symbolized M.
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Find the mean for the given set of data.
-4, -3,-1,-1, 0, 1
-1 1/3
-1
-3/4
Answer:Find the mean for the given set of data.
-4, -3,-1,-1, 0, 1
-1 1/3
-1
-3/4
Answer is -1 1/3
Step-by-step explanation:
The volume of the oceans on Earth is approximately 1,386 million km^3. As the Earth's temperature rises, the ice in the polar icecaps melts into the oceans, increasing the volume of the oceans. If 1 cm^3 of ice melts, it turns into approximately 0.92 cm^3 water.
1) There are approximately 3,800 cm^3 in a gallon. If 1.9 m^3 of ice melts, how many gallons of water does this produce? (Round your answer to the nearest gallon.)
2) Scientists estimated that the addition of 1,000 km^3 of water would increase sea levels by 364 cm. Greenland's ice sheet is especially vulnerable to melting. Recent reports indicate a melting average of 195 km^3 of ice per year from Greenland, resulting in additional yearly 179.4 km^3 of water. If melting continues at this rate, how many centimeters would the sea increase after 6 years? (Round your answer to the nearest centimeter.)
Answer:
460 gallons392 cmStep-by-step explanation:
The necessary units conversion can be accomplished by multiplying by appropriate conversion factors. Quantity can be found by multiplying rate by time.
1)The number of gallons of water produced by melting 1.9 m³ of ice is ...
[tex]1.9\text{ m$^3$ (ice)}\times\left(\dfrac{100\text{ cm}}{1\text{ m}}\right)^3\times\dfrac{0.92\text{ cm$^3$ (water)}}{1\text{ cm$^3$ (ice)}}\times\dfrac{1\text{ gal}}{3800\text{ cm$^3$}}\\\\=\dfrac{1.9\times10^6\times0.92}{3800}\text{ gal}=\boxed{460\text{ gal}}[/tex]
2)Multiplying the melting rate by time and converting to height, we have ...
[tex]\dfrac{179.4\text{ km$^3$}}{1\text{ yr}}\times\dfrac{364\text{ cm}}{1000\text{ km$^3$}}\times6\text{ yr}\approx\boxed{392\text{ cm}}[/tex]
__
Additional comment
The area of the world's oceans is about 361e6 km², so addition of 1000 km³ of water might be expected to increase the water level by (1000/361)e-6 ≈ 2.77e-6 km = 0.277 cm. Something seems a little off in this problem statement.
find the equation of the line y=mx+b form with the slope 3 that passes through the point (5,19)
The equation of the line that has a slope of 3 and that passes through the point (5,19) is y = 3x + 4
Equation of a straight lineFrom the question, we are to determine the equation of the line that has a slope of 3 and that passes through the point (5,19)
Using the point-slope form of an equation of a line
y - y₁ = m(x - x₁)
Where m is the slope
and (x₁, y₁) is a point on the line
From the given information
m = 3
x₁ = 5
y₁ = 19
Putting the parameters into the equation, we get
y - 19 = 3(x - 5)
y - 19 = 3x - 15
y = 3x -15 + 19
y = 3x +4
Hence, the equation of the line that has a slope of 3 and that passes through the point (5,19) is y = 3x + 4
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1) A school has an enrollment of 1500 students. The student population is expected to increase at a rate of 2.6% each year for the next 5 years.
a) A What is the growth factor as a decimal?
b) Estimate the number of students enrolled 10 years from now. Round to the nearest student.
Show your work!!
The growth factor as a decimal is 1.026 and the number of students enrolled 10 years from now is 1939
How to determine the growth factor?The given parameters are
Initial value of enrollment, a = 1500
Rate, r = 2.6%
The growth factor is then calculated as:
Growth factor = 1 + Rate
This gives
Growth factor = 1 + 2.6%
Evaluate the sum
Growth factor = 1.026
Hence, the growth factor as a decimal is 1.026
The number of students enrolled 10 years from nowAs a general rule, the number of students enrolled t years from now is
Students = Initial value * Growth factor^Number of years
This is represented as
Students = 1500(1.026)^t
10 years from now means t = 10
So, we have
Students = 1500(1.026)^10
Evaluate
Students = 1939
Hence, the number of students enrolled 10 years from now is 1939
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Decrease 100kg by 30%
Answer:
70
Step-by-step explanation:
the 30/100 of 100 is 30
So 100-30=70
Answer:
70kg
Step-by-step explanation:
30% of 100kg is
--> 100 x 30/100 which is 30kg.
If you want to decrease 100kg by 30%, you can take away 30kg from 100kg.
--> 100 - 30 = 70
So 70kg is the remainder.
What are the center and radius of the circle given by x^2 + y^2 - 16x + 8y + 4 = 0?
The center of the circle = (8, -4)
The radius of the circle = [tex]\sqrt{76}[/tex]
Finding the center and radius of a circle from the equationThe given equation of the circle is:
[tex]x^2+y^2-16x+8y+4=0[/tex]
The equation can be expressed and simplified as:
[tex]x^2-16x+y^2+8y=-4\\\\x^2-16y+8^2+y^2+8y+4^2=-4+8^2+4^2\\\\(x-8)^2+(y+4)^2=-4+64+16\\\\(x-8)^2+(y+4)^2=76[/tex]
The general equation of a circle is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
Comparing the two equations:
The center, (a, b) = (8, -4)
The radius, r = [tex]\sqrt{76}[/tex]
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Please help me with this
Answer:A or C
Step-by-step explanation: i guessed plus 19 hours ago
Seventy percent of kids who visit a doctor have a fever and 21% of kids have fever and sore throats .
What is the probability that a kid who goes to the doctor has a sore throat given that he has a fever?
The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 30%
How to determine the probability?The given parameters are:
P(Fever) = 70%
P(Fever and sore throat) = 21%
The probability that a kid who goes to the doctor has a sore throat given that he has a fever is calculated as:
P = P(Fever and sore throat)/P(Fever)
So, we have:
P = 21%/70%
Evaluate
P = 30%
Hence, the probability is 30%
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Consider the function f(x) = x² + 10x + 25 for x ≥ -5.
What is the value of f-¹(x) when x = 4?
Answer:
-3
Step-by-step explanation:
please help me solve this
Explanation:
The proof can be had by making use of the AAS congruence postulate (twice) and CPCTC.
We start by showing ΔPQY≅ΔPRX, then by showing ΔXQN≅ΔYRN. The proof is then a result of CPCTC.
Proof1. PQ≅PR, ∠Q≅∠R . . . . given
2. ∠P≅∠P . . . . reflexive property of congruence
3. ΔPQY≅ΔPRX . . . . AAS congruence postulate
4. PX≅PY . . . . CPCTC
5. PX+XQ=PQ, PY+YR=PR . . . . segment sum theorem
6. PX+XQ = PY +YR . . . . substitution property
7. PX +XQ = PX +YR . . . . substitution property
8. XQ = YR . . . . subtraction property of equality
9. ∠XNQ≅∠YNR . . . . vertical angles are congruent
10. ΔXNQ≅ΔYNR . . . . AAS congruence postulate
11. XN ≅ YN . . . . CPCTC
__
Additional comment
You probably did steps 1-3 in part (a) of the problem.
Solve each equation
Note:now you need to perform inverse operations to solve for the variables. For example in (2/3x -6) try adding 6 to both sides first then multiply the reciprocal of 2/3 (meaning the flipped version)
The factorise form of the two expression are as follows:
2 (x - 3) (x - 9)-3(x + 5)(x + 7) How to solve an expression?b. (x - 3)(2 / 3 x - 6) = 0
Therefore, let's open the brackets
2 / 3 x² - 6x -2x + 18 = 0
2 / 3 x² - 8x + 18 = 0
multiply through by 3
2x² - 24x + 54 = 0
Hence,
2 (x - 3) (x - 9)
c.
(-3x - 15)(x + 7) = 0
Therefore,
-3x² - 21x - 15x - 105 = 0
-3x² - 36x - 105 = 0
-3(x + 5)(x + 7)
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Janice bought 30 items each priced at 30 cents, 2 dollars, or 3 dollars. If her total purchase price was $\$$30.00, how many 30-cent items did she purchase
she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
According to the statement
Janice bought total items = 30
Price of items are 30 cents, 2 dollars, or 3 dollars.
Total purchase price of Janice = 30$
If we let she bought 10 items at price of 3$, Then it is not possible
So, Number of items which are bought by her at price of $3 is less than 10. Similarly Number of items which are bought by her at price of $2 is less than 10.
we know that 1 CENT = 0.01 $
We also know that 10 30-cents will worth 3 dollars, so the number of cents which are bought by her at price of $0.01 is greater than 10.
Now, Let she bought 20 items at price of 0.01$
Then 20*0.3 = 6$
It means 30$-6$ = 24$
24$ are left to purchase the things which are at price of 2$ and 3$.
If we let she purchase 4 items at cost $3 then
Then 4*$3 = 12$
It means 24$-12$ = 12$
Now, with remaining money she bought 6 items at cost $2.
So, she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
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she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
According to the statement
Janice bought total items = 30
Price of items are 30 cents, 2 dollars, or 3 dollars.
Total purchase price of Janice = 30$
If we let she bought 10 items at price of 3$, Then it is not possible
So, Number of items which are bought by her at price of $3 is less than 10. Similarly Number of items which are bought by her at price of $2 is less than 10.
we know that 1 CENT = 0.01 $
We also know that 10 30-cents will worth 3 dollars, so the number of cents which are bought by her at price of $0.01 is greater than 10.
Now, Let she bought 20 items at price of 0.01$
Then 20*0.3 = 6$
It means 30$-6$ = 24$
24$ are left to purchase the things which are at price of 2$ and 3$.
If we let she purchase 4 items at cost $3 then
Then 4*$3 = 12$
It means 24$-12$ = 12$
Now, with remaining money she bought 6 items at cost $2.
So, she bought 20 items at price of 0.01$, 6 items at cost $2, 4 items at cost $3.
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
The value of the constant of variation include 8, 3.2, and 1.25
How to find the constant?From the information given, when x = -0.5, y = -4.0. The constant will be:
y = kx
-4 = -0.5k
k = -4.0/-0.5
k. = 8
When x = 2.5, y = 8
y = kx
8 = 2.5k
k = 8/2.5
k = 3.2
When x = 4, y = 5
y = kx
5 = 4k
k = 5/4
k = 1.25
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Solution
We can start with the pythagorean theorem:
(leg 1)² + (leg 2)² = (hypotenuse)²
Substitute the values we know.
15² + x² = 32²
Solve for x.
X =
Answer:
28.26658805 (I included every digit in case your teacher needs you to round)
Step-by-step explanation:
In order to find x, we need to isolate x by subtracting 15^2 and taking the square root of both sides.
Thus, we have:
[tex]15^2+x^2=32^2\\x^2=32^2-15^2\\\sqrt{x^2} =\sqrt{(32^2-15^2)} \\\sqrt{x^2}=\sqrt{799} \\x=28.26658805[/tex]
Meena’s father’s present age is six times Meena’s age. Five years from now she will be one-third of her father’s present age. What are their present ages?
Answer:
Meena age = 5 yrs Meenas father = 30
Step-by-step explanation:
let,
meena's age = x
meena's father's age = 6x
Five years from now
meena's age will be 1/3(6x)
meena's father's age will be 6x+5
A/Q
x+5+6x+5=2x+6x+5
=x+6x-2x-6x=5-5-5
= -x =-5
= x =5
meena's age = 5
meena's father's age = 6x
= 6×5
= 30
Find the 8th term of the geometric sequence 5, -15, 45
Answer:
a₈ = - 10935
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 5 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-15}{5}[/tex] = - 3 , then
a₈ = 5 × [tex](-3)^{7}[/tex] = 5 × - 2187 = - 10935
Find the midpoint of a and b when a has coordinates (2,3) and b has coordinates (8,9)
The midpoint of co-ordinate is (5, 6)
Add both "x" coordinates, and divide by 2.
Add both "y" coordinates, and divide by 2.
Given that;
Coordinates of A = (2,3)
Coordinates of B = (8,9)
Find:
Midpoint of co-ordinate
Computation:
Midpoint of co-ordinate = [(x1 + x2) / 2], [(y1 + y2) / 2]
Midpoint of co-ordinate = [(2 + 8) / 2], [(3 + 9) / 2]
Midpoint of co-ordinate = [10 / 2], [12 / 2]
Midpoint of co-ordinate = (5, 6)
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Solve the equation. Simplify your answer.
2 (3-x) = 16 (x+1)
I need help cancelling units
Answer:
60:1
Step-by-step explanation:
60:1 = 366:x
60x = 366
x = 6.1
366 minutes is equivalent to 6.1 hours.
Convert 366 minutes to hours.
Knowing that in 60 minutes = 1 hour.[tex]\boldsymbol{\sf{Therefore \ \to \ 366 \not{m}*\dfrac{1 \ hr}{60\not{m}}=6.1 \ hr }}[/tex]
We conclude that a time of 366 minutes is equal to 6.1 hours
There are 60 minutes in 1 hour. To convert from minutes to hours, divide the number of minutes by 60. For example, 120 minutes equals 2 hours because 120/60=2.
(6x - 4)(3 - 2x)/4x - 6
[tex] \frac{(6x - 4)(3 - 2x)}{(4x - 6)} = \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} [/tex]
[tex] \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} = \frac{(3x - 2)(3 - 2x)}{(2x - 3)} [/tex]
[tex] \frac{(3x - 2)(3 - 2x)}{(2x - 3)} = \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} [/tex]
[tex] \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} = - (3x - 2)[/tex]
[tex] - (3x - 2) = 2 - 3x[/tex]
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
the following 3 equations are equivalent :
• x + 1 = 4
• 2 + x = 5
• -5 + x = -2
Step-by-step explanation:
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
-5 + x = - 2
Let’s take this equation :
x + 1 = 4
=======
By Adding 1 to both sides of the equation we get :
x + 1 + 1 = 4 + 1
⇔ x + 2 = 5
⇔ 2 + x = 5
Then the equations x + 1 = 4 and 2 + x = 5 are equivalent.
…………………………………………………………………
On the other hand ,if we subtract 6 from both sides
of the equation x + 1 = 4 we get :
x + 1 - 6 = 4 - 6
⇔ x - 5 = -2
⇔ -5 + x = -2
Then the equations x + 1 = 4 and -5 + x = -2 are equivalent.
Answer:
A. 2 + x = 5
B. x + 1 = 4
E. -5 + x = -2
Step-by-step explanation:
right on edg, hope it helps ya'll.
If the parabola of equation y=k−x2 is tangent to the line of the equation y=x then what is the value of k ?
The value of k is 1/4.
According to the statement
we have given
The equation of parabola is y=k−x2
And tangent to the line of equation is y = x
and we have to find the value of K.
So, let y=k−x2 -(1)
and let y = x -(2)
(2) is the tangent to the (1) then
therefore they cut at
y=k−x2 -(1)
y = x -(2)
so, put (2) in the (1) then
x = k- (x)^2
(x)^2 + x = k
The above written equation has one real number then for this D =0
so, (x)^2 + x - k = 0
-1 -1*4*k = 0
-1 - 4k = 0
-4k = 1
The value of k is -1/4.
So, The value of k is 1/4.
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BRAINLIEST TO CORRECT ANSWER
There is a pair of parallel sides in the following shape.
what is the area
The area of the given figure is 38 square units
Area of a trapezoidThe area of the given trapezoid is expressed as:
A = 0.5(a+b)h
where
a and b are the sides
h is the height
Substitute
A = 0.5(9+10) * 4
A = 19 * 2
A = 38 square units
Hence the area of the given figure is 38 square units
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The plane is tiled by congruent squares of side length $a$ and congruent pentagons of side lengths $a$ and $\frac{a\sqrt{2}}{2}$, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58
The percentage of this plane that's enclosed by the pentagons is closest to: D. 56.
How to determine the percentage?Since the side of the small square is a, then the area of the tile is
given by:
Area of tiles = 9a²
Note: With an area of 9a², 4a² is covered by squares while 5a² by pentagons.
This ultimately implies that, 5/9 of the tiles are covered by pentagons and this can be expressed as a percentage as follows:
Percent = 5/9 × 100
Percent = 0.555 × 100
Percent = 55.5 ≈ 56%.
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Complete Question:
The plane is tiled by congruent squares of side length a and congruent pentagons of side lengths a and a²/a, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58