The conditions to be added are:
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
The SAS (Side-Angle-Side) triangle congruence theorem states that if two triangles have two sides and the included angle of one triangle is congruent to two sides and the included angle of the other triangle, then the two triangles are congruent.
Therefore, in addition to sharing a common side, the two triangles must have congruent angles between the sides that are not the common side. Specifically, the angle opposite the common side must be congruent in both triangles.
To summarize, for the SAS triangle congruence theorem to apply, the following conditions must be met:
The two triangles share a common side.
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles (the "included" side).
Thus,
The conditions to be added are:
The two triangles have congruent angles between the sides that are not the common side.
The two triangles have congruent lengths for the sides adjacent to the congruent angles.
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What percent of 210 is 70?
Two less than twice a number is the same as four times the number
Final answer:
The algebraic expression representing 'two less than twice a number is the same as four times the number' is solved, resulting in the number being -1.
Explanation:
The student's question involves solving a simple algebraic equation. We are given that two less than twice a number is the same as four times the number. To represent this algebraically, let's let the unknown number be n. The phrase 'twice a number' can be written as 2n. 'Two less than' this expression would be 2n - 2. The statement implies this is equal to four times the number, which is 4n. Therefore, the equation we need to solve is 2n - 2 = 4n. To solve this equation, we need to isolate the variable n on one side of the equals sign.
Subtract 2n from both sides: -2 = 2n.
Divide both sides by 2 to find the value of n: n = -1.
In conclusion, the number that satisfies the condition given is -1.
A ball is thrown from a height of 70 feet with an initial downward velocity of 4/fts. The ball's height h (in feet) after t seconds is given by the following.
h=70-4t-16t^2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. 1.97 is the time taken by the ball to hit the ground.
What is Distance?Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given that a ball is thrown from a height of 70 feet with an initial downward velocity of 4/fts. The ball's height h (in feet) after t seconds is given by the following.
h=70-4t-16t²
Now we can take h=0
h=-16t²+70-4t
-16t²+70-4t
Divide by 2
-8t²-2t+35
Now apply quadratic formula
a=-8, b=-2, c=35
t=-b±√b²-4ac/2a
t=2±√-2²-4(-8)(35)/2(-8)
t=2±√4+1120/-16
we get t= 1.97 and t= -2.22
You get the numbers to be : 1.97 and -2.22
We do not consider negative values. So the correct answer is 1.97
Hence 1.97 is the time taken by the ball to hit the ground.
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A club decides to sell T-Shirts for 15$ as a fund-raiser. It cost $20 plus $9 per T-Shirt to make them. How many T-Shirts need to be made to make a profit of at least $150?
Redo, Answers please?
I need to know the solution
Find the missing length.
What is the circumference of this circle, in millimeters? use 22/7 for pi
r = 49
Answer: circumference = 308mm
Step-by-step explanation: the formula for the circumference of a circle is given by
C=2πr
Given that r=49mm
Pi=22/4
C=2*22/7*49
C=44*7=308mm
In geometry, the circumference of a circle is the distance around it. That is, the circumference would be the length of the circle if it were opened up and straightened out to a line segment. Since a circle is the edge of a disk, circumference is a special case of perimeter.
A given line has the equation 10x + 2y = −2.
What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?
Step 1
Find the slope of the given line
we have
[tex]10x+2y=-2[/tex]
Isolate the variable y
Subtract [tex]10x[/tex] both sides
[tex]2y=-10x-2[/tex]
Divide by [tex]2[/tex] both sides
[tex]y=-5x-1[/tex]
The slope of the given line is
[tex]m=-5[/tex]
Step 2
Find the equation of the line that is parallel to the given line and passes through the point [tex](0, 12)[/tex]
we know that
If two lines are parallel. then their slope are equal
In this problem we have
[tex]m=-5[/tex]
[tex](0, 12)[/tex]
The equation of the line into slope-intercept form is equal to
[tex]y=mx+b[/tex]
substitute the values
[tex]12=-5*0+b[/tex]
[tex]b=12[/tex]
the equation of the line is
[tex]y=-5x+12[/tex]
therefore
the answer is
[tex]y=-5x+12[/tex]
Simplify 5 − (−1).
a. 6
b. −6
c. 4
d. −4
Answer: it is a
Step-by-step explanation: :) :v :B
Mason and Nora decided to swim across the river. Mason began swimming 8 seconds earlier than Nora.
Mason swam at a speed of 5 feet per second.
Nora swam at a speed of 9 feet per second.
For how many seconds had Mason been swimming at the moment when the two swimmers had swam exactly the same distance?
A square garden plot has an area of 75 ft^2. Find the length of each side in simplest radical form. Calculate the length of each side to the nearest tenth of a foot..
Melissa exercises for 20 minutes every day. She decides to increase her daily exercise time by 5 minutes each week. However, according to her doctor’s orders, she can spend no more than 45 minutes a day exercising. For how many weeks can Melissa increase her exercise time this way?
Answer:
at most 5 weeks
Step-by-step explanation:
The circle given by x^2+y^2-4x-10=0 can be written in standard form like this: (x-h)^2+y^2=14. What is the value of h in this equation??
Answer: H=2
Step-by-step explanation:
we just need to complete the square for the x terms
gropu x terms
x^2-4x
take 1/2 of linear coefient and square it
-4/2=-2, (-2)^2=4
x^2-4x+4
factor
(x-2)^2
h=2
The value of h is 2.
Completing the square for the x terms by grouping x terms
x^2-4x
Taking 1/2 of linear coefficient and squaring it.
-4/2=-2, (-2)^2=4
x^2-4x+4
Factorizing the equation.
(x-2)^2
h=2.
What is an equation?An equation is a mathematical statement this is made of two expressions related with the aid of an identical sign. As instance, 3x – 5 = 16 is an equation. To fix this equation, we get the value of the variable x as x = 7.
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A volcano fills the volume between the graphs z=0 and z=1/(x^2+y^2)^10 and outside the cylinder x+y=1. find the volume.
For this case, we use
the cylindrical coordinates:
x² + y² = r²
dV = r dz dr dθ
The limits are:
z = 0 to z = 1/(r²)^10 = 1/r^20
r = 1 to ∞
θ = 0 to 2π
Integrating over the limits:
V = ∫ [0 to 2π] ∫ [1 to ∞] ∫ [0 to 1/r^20] r dz dr dθ
V = ∫ [0 to 2π] ∫ [1 to ∞] rz | [z = 0 to 1/r^20] dr dθ
V = ∫ [0 to 2π] ∫ [1 to ∞] 1/r^19 dr dθ
V = ∫ [0 to 2π] −1/(18r^18) |[1 to ∞] dθ
V = ∫ [0 to 2π] 1/18 dθ
V = θ/18 |[0 to 2π]
V = π/9
The volume of the volcano is an illustration of definite integral
The volume of the volcano is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]
The graphs are given as:
[tex]\mathbf{z = 0}[/tex] and [tex]\mathbf{z = \frac{1}{(x^2 + y^2)^{10}}}[/tex]
The cylinder is:
[tex]\mathbf{x + y =1}[/tex]
For cylindrical coordinates, we have:
[tex]\mathbf{r^2 =x^2 + y^2}[/tex]
So, we have:
[tex]\mathbf{z = \frac{1}{(r^2)^{10}}}[/tex]
[tex]\mathbf{z = \frac{1}{r^{20}}}[/tex]
Where:
[tex]\mathbf{r = 1 \to \infty}[/tex]
[tex]\mathbf{\theta = 0 \to 2\pi}[/tex]
So, the integral is:
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{20}}} \, r\ dr } \, d\theta }[/tex]
Cancel out r
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{19}}} \, dr } \, d\theta }[/tex]
Rewrite as:
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {r^{-19}} \, dr } \, d\theta }[/tex]
Integrate
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}r^{-18}}} |\limits^{\infty}_1 \, d\theta }[/tex]
Expand
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(\infty^{-18} -1^{-18}) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(0 -1) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}( -1) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{\frac{1}{18} }} , d\theta }[/tex]
Integrate
[tex]\mathbf{V = \frac{1}{18}(\theta)|\limits^{2\pi}_0}[/tex]
Expand
[tex]\mathbf{V = \frac{1}{18}(2\pi - 0)}[/tex]
[tex]\mathbf{V = \frac{1}{18}(2\pi )}[/tex]
Cancel out 2
[tex]\mathbf{V = \frac{1}{9}\pi}[/tex]
Hence, the volume is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]
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please help on b (left of c) and c !!!
rewrite each of the following expressions so that your answer has no negative or fractional exponents
Find the area of the circle with the given radius or diameter. Use = 3.14.
r = 6
A =
37.68 sq. units
113.04 sq. units
226.08 sq. units
Answer: 113.04 sq. units
Calculate the upper and lower limit for a 95% confidence interval about this mean. a family needs a new car, but isn't sure they can fit the payment into their budget. a sample of 36 months of grocery bills yields a mean of $94 with a standard deviation of $10. if the upper limit of a 95% confidence level is below $100, the family can afford to buy the car. standard error = (standard deviation)/(square root of sample size) upper limit (dollars and cents) lower limit (dollars and cents)
To find the upper and lower limits of a 95% confidence interval for the given data, calculate the standard error, use the multiplier of 2, and apply the formula Sample mean ± Multiplier * Standard error.
To calculate the upper and lower limit for a 95% confidence interval, we use the formula: Confidence interval = Sample mean ± Multiplier * Standard error. For this case, the sample mean is $94 and the standard deviation is $10. The standard error is calculated as $10 / √36 = $10 / 6 ≈ $1.67.
With a 95% confidence level, the multiplier is approximately 2. Therefore, the upper limit would be $94 + 2($1.67) = $94 + $3.34 ≈ $97.34, and the lower limit would be $94 - $3.34≈ $90.66.
Constantine picks two letters at random from the word constantinople with replacement. what is the probability that both letters picked are consonants?
The lengths of the sides of a triangle are 6, 8, 10. Can the triangle be a right triangle? Yes or no?
Use Gauss-Jordan elimination to solve the following system of equations. 3x + 5y = 7 6x − y = −8 A. x = 2, y = 1 B. x = 5, y = 6 C. x = 3, y = −1 D. x = −1, y = 2
HELP if f(x)=-14x-2, then f^-1(x)=?
Determine the number of possible triangles, abc, that can be formed given c = 85°, a = 10, and c = 13. 0 1 2
Final answer:
Correcting for the apparent typo in the question, assuming 'c' refers to an angle and a side length respectively, there can only be one possible triangle formed given the angle and two sides. This is based on geometric principles where a unique triangle can be determined from an angle opposite and its respective side length.
Explanation:
The question presents a probable typo since it mentions two different values for 'c'. Assuming 'c = 85°' refers to an angle, and 'c = 13' refers to the length of a side opposite this angle, the proper interpretation involves finding possible triangles given an angle and two sides. However, the principles of geometry dictate that with one angle and two sides specified, especially in this non-ambiguous manner where one side length and the angle opposite are known, one can determine a unique triangle, assuming the given information leads to a viable geometric figure.
By using the Law of Sines, one might attempt to find the other angles or sides, but since we only have one angle and one side length, we directly know there's no ambiguity - geometrically speaking, there's only one way to construct such a triangle, thus, only one possible triangle can be formed given the corrected assumptions.
Which value is in the domain of f(x)?
A.) –7
B.) –6
C.) 4
D.) 5
Answer:
C) 4
Step-by-step explanation:
The given function is
[tex]f(x)=\left \{ {{2x+5,\:-6\:<\:x\le0} \atop {-2x+3,\:0\:<x\le4}} \right.[/tex]
The function is defined on two intervals.
The first interval is
[tex]-6\:<\:x\le0[/tex] and the second interval is [tex]\:0\:<x\le4[/tex].
[tex]-7[/tex] does not belong to any of these intervals.
[tex]-6[/tex] does not also belong to any of these intervals.
[tex]4[/tex] belongs to the interval [tex]\:0\:<x\le4[/tex].
Hence 4 is in the domain of f(x).
[tex]5[/tex] does not also belong to any of the intervals.
Therefore the correct answer is C.
The area of one circle is 4 times as large as a smaller circle with a radius of 3 inches. the radius of the larger circle is
A can factory requires 2 sheets of metal to make 36 cans and 10 sheets of metal to make 180 cans. The proportionality constant between the number of cans made and the number of sheets of metal used is
a-36
b-18
c-288
d-5
One student can paint a wall in 10 minutes. another student can paint the same wall in 15 minutes. working together, how long will it take for them to paint the wall?
Answer:
6 days
Step-by-step explanation:
Given that one student can paint a wall in 10 minute and another student in 15 minutes.
Since if number of persons increase, painting time decreases, this is a question of inverse proportion
Hence if they work together they can paint in one day
[tex]\frac{1}{10} +\frac{1}{15}[/tex] part of the work
i.e. work completed in 1 day when they work together
=[tex]\frac{1}{10} +\frac{1}{15} \\=\frac{9+6}{90} \\=\frac{1}{6}[/tex]
Hence in 6 days they can together complete the full work
Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
-3x^5 + 9x^4 + 5x^3 + 3
The perimeter of a square is 96 inches. if the side length is 2x + 4, what is the value of x and the length of each side?
Subtract: (2x2 − 7x + 5) − (−6x2 − 4x − 2)
Answer:
8x^2 - 3x + 7
Step-by-step explanation:
I took the test.