Answer: No .
Step-by-step explanation:
If we make two triangles with lengths of 4 centimeters and 2 centimeters and an included angle of 50°, then by SAS congruence postulate both triangle will be congruent.
According to the definition of congruence , if two shapes are congruent then they have equal size and shape.
i.e. they look exactly same.
It means only one triangle is possible with the given measurement .
SAS congruence rule : It says that if two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then we can say that these two triangles are congruent.No, only one triangle can be drawn with side lengths of 4 centimetres, 2 centimetres, and an included angle of 50°.
To determine if more than one triangle can be drawn with given side lengths and an included angle, we can use the Side-Angle-Side (SAS) congruence postulate.
According to this postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Given:
One side length is 4 cm (side a).
Another side length is 2 cm (side b).
The included angle between these two sides is 50° (angle C).
Using the Law of Cosines, we can find the length of the third side (side c) of the triangle. The Law of Cosines states that for any triangle with sides a, b, and c, and the angle opposite side c being the following equation holds: [tex]\[ c^2 = a^2 + b^2 - 2ab \cos(\gamma) \][/tex]
Substituting the given values:
[tex]\[ c^2 = 4^2 + 2^2 - 2 \cdot 4 \cdot 2 \cdot \cos(50^\circ) \][/tex]
[tex]\[ c^2 = 16 + 4 - 16 \cdot \cos(50^\circ) \][/tex]
[tex]\[ c^2 \approx 20 - 16 \cdot 0.6428 \][/tex]
[tex]\[ c^2 \approx 20 - 10.2848 \][/tex]
[tex]\[ c^2 \approx 9.7152 \][/tex]
[tex]\[ c \approx \sqrt{9.7152} \][/tex]
[tex]\[ c \approx 3.118 \text{ cm} \][/tex]
Hence, the answer is no; only one triangle can be drawn with side lengths of 4 centimetres, 2 centimeters, and an included angle of 50°.
Solve the system of linear equations using elimination.
−2x − y = 3
−9x − y = 17
A)
(2, 1)
B)
(2, −1)
C)
(−2, 1)
D)
(−2, −1)
PLEASE HELP I NEED IT BY TODAY
Answer:
C (-2,1)
Step-by-step explanation:
−2x − y = 3 (1)
−9x − y = 17 (2)
(1) y = -2x - 3
(2) y = -9x - 17
-2x - 3 = -9x - 17
7x = -14
x = -2
y = -2(-2) - 3
y = 4 - 3
y = 1
find value of a and b in the triangle. (please help)
The equation 4 + 9 = 4 + 9 is an example of which property of equality? *
Transitive
Symmetric
Substitution
Reflexive
Answer:
Reflexive
Step-by-step explanation:
The reflexive property of equality says that a given real number is always equal to itself.
For example :
[tex]y = y[/tex]
[tex]a = a[/tex]
[tex]b = b[/tex]
[tex]5 = 5[/tex]
are all examples of reflexive properties of equality.
[tex]4 + 9 = 4 + 9[/tex]
can be simplified to
[tex]13 = 13[/tex]
Which is explains why it is the reflexive property.
Which of the following is the solution to | x | +5 <= 1
Answer:
NO SOLUTION
Step-by-step explanation:
Step 1: Subtract 5 from both sides
|x| + 5 - 5 ≤ 1 - 5
|x| ≤ -4
x ≤ NO SOLUTION
Answer: NO SOLUTION
find x when - 1/2 + x = - 21/4
Step-by-step explanation:
-1 / 2 + x = -21 /4
x = -21/4 + 1/2
x = (-21 + 2)/4
x = -19/4
0.45 plus 9x equals 27
Answer:
x = 2.95
Step-by-step explanation:
Step 1: Convert words into an expression
0.45 plus 9x equals 27
0.45 + 9x = 27
Step 2: Solve for x
0.45 + 9x - 0.45 = 27 - 0.45
9x / 9 = 26.55 / 9
x = 2.95
Answer: x = 2.95
what is the half life formula
N = N₀* [tex](\frac{1}{2} )^{\frac{t}{h} }[/tex]
where N is how much you currently have
N₀ is the starting amount
t is the time
and h is the half life of the substance.
The half-life formula for a radioactive isotope is amount remaining = (amount initial) × e^(-t/t1/2), where e is the base of natural logarithms, t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. The formula can be used to calculate how much of a radioactive isotope remains after a certain amount of time.
Explanation:The half-life formula for a radioactive isotope is given by:
amount remaining = (amount initial) × e^(-t/t1/2)
Here, e is the base of natural logarithms (approximately 2.71828182), t is the elapsed time, and t1/2 is the half-life of the isotope. The variables t and t1/2 must have the same units of time. To evaluate the exponential function, you may need to use a calculator or an inverse logarithm function. It is important to note that the length of time t does not need to be an exact multiple of half-lives.
Hi, I need help with my math please
Answer:
Answer:
A-H are all true facts except for C which is false. that you have to show and prove are true and false.
Rate of change Purr Island (5 questions name the letter to the workings answer and matched it) Show constant = 4 cats per year also seen as 40% rate of change. The common factor of 3 is only seen up on year 1 and year 4. as year 0 shows 2 and 4 does not fit into 2. Explain year 2 that 4 does not fit into 10 on year 2 does not as 2p-6p-10p-14p-18p may change 10p over the last 3 years and CF 3 does not fit into that or any individual (adjacent) proceeding years.
Step-by-step explanation:
The rate of change Meow Island : 3 of the 8 questions is asked to say true to all of them (name the letter to the answer the workings after you wrote this and matched it) Shows it triples = and yes they have common factors of 3 show 2, 6, 18, 54, 162 each share a common factor of 3, draw tree diagrams or show common factors of 3 and state you compare them to factors of 2 162>2x81 162> 3x27 54>2x27 54>3x18 18>2x9
18>3x6 6>2x3 6>3x2 2>2 population start number this doesnt have a common factor until it is factored into 6 ro show a common factor for 6. This also proves linear change occurs over the 4 years as population 2-156 is a series of 4 changes and underline the >3x numbers.
What is the greatest common factor of the polynomial’s terms? 18x^2y^3-6xy^2+3x^3y
Answer:3xy
Step-by-step explanation:18x^2y^3= 3,6,x,x,y,y,y
6xy^2=. 3,2,x,y,y
3x^3y=. 3,x,x,x,y
All three have this in common a 3xy
The greatest common factor of the given polynomial's terms 18x^2y^3-6xy^2+3x^3y is 3xy. This is determined by factoring each term, and finding the greatest factor that occurs in all of the lists.
Explanation:In mathematics, the greatest common factor (GCF) of a set of terms in a polynomial, is the largest term that divides each term exactly. To find the greatest common factor for the given polynomial 18x^2y^3-6xy^2+3x^3y, first, we list the factors for each term.
The term 18x^2y^3 factors as 2*3*3*x*x*y*y*y, the term -6xy^2 factors as -2*3*x*y*y, and the term 3x^3y factors as 3*x*x*x*y.
The greatest factor that occurs in all three lists is 3*x*y, so 3xy is the greatest common factor of the polynomial’s terms.
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Write each function in vertex form, and identify its vertex.
14. h(x)=3x^2−24x+53
15. h(x)=x^2 +8x−10
16. g(x)=x^2 −3x+16
17. h(x)=3x^2 −12x−4
Answer:
its C or 16
Step-by-step explanation:
The functions f(x) and g(x) are defined below.
f(x)= 2e^x + 1
g(x)= 1/2e^x + 5/2
Determine where f(x) = g(x) by graphing.
A. x = 0
B. x = 0; x = 3
C. x = 1; x = 3
D. x= 3
Answer:
Answer : A x=0
Step-by-step explanation:
hello :
f(x)= 2e^x + 1 graph red
g(x)= 1/2e^x + 5/2 graph bleue
2e^x + 1
= 1/2e^x + 5/2
by graphic solution one solution x=0
Answer:
d) x=3
Step-by-step explanation:
Help with this question
Answer:
158
Step-by-step explanation:
20 + 60 + 40 = 120 + 38 = 158
I think this is right. (I tired)
Jamie recently started working as
manager at a company. He will be paid
an annual salary of $42,600 and will be
paid monthly. The company requires the
following deductions:
• Social Security (6.2%)
• Medicare (1.4%)
• State Income Tax (3%)
• Federal Income Tax (13%)
• Medical and Dental Insurance ($260 per month)
• Retirement ($280 per month)
How much should his monthly net paycheck be?
a $2587.55
b. $2172.20
$2667 20
$2712.40
d
Answer:
B
Step-by-step explanation:
From annual salary of 42,600, we have to subtract the following percentages:
Social Security:
0.062 * 42,600 = 2641.2
Medicare:
0.014 * 42,600 = 596.4
State Income Tax:
0.03 * 42,600 = 1278
Federal Income Tax:
0.13 * 42,600 = 5538
Total Deductions (from percentages) = 2641.2 + 596.4 + 1278 + 5538 = 10053.6
Now, remaining salary:
42,600 - 10053.6 = 32546.4 (annual)
Divided by 12 to get monthly:
32546.4 / 12 = 2712.2 (monthly)
Now, monthly deductions are:
260 + 280 = 540
Net Salary: 2712.2 - 540 =2172.2
Based on the information given his monthly net paycheck is: b. $2172.20.
Net paycheckDeduction
Social security=42,600×62%
Social security = 2641.2
Medicare=42,600×1.4%
Medicare = 596.4
State Income Tax= 42,600×3%
State Income tax = 1278
Federal Income Tax=42,600×13%
Federal Income Tax = 5538
Total Deductions = 2641.2 + 596.4 + 1278 + 5538
Total deduction= 10053.6
Net paycheck:
Net paycheck=(42,600 - 10,053.6)/12- (260 + 280)
Net paycheck=32,546.4/12-540
Net paycheck= 2712.2 - 540
Net paycheck=$2172.2
Therefore, his monthly net paycheck is: b. $2172.20.
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14+16+11+2+6+6+15+2+11
And round to the nearest tenth
Answer:
83
Step-by-step explanation:
Add the numbers together
Answer:
80
Step-by-step explanation:
14 + 16 = 30
30 + 11 = 41
41 + 2 = 43
43 + 6 = 49
49 + 6 = 55
55 + 15 = 70
70 + 2 = 72
72 + 11 = 83, which, rounded to the nearest tenth, is 80
What is the solution to the differential equation dydx=5y2 with the initial condition y(0) = 3?
Differential equation is a way to represents the relation between the functions and their variables. The solution to the differential equation given in the question is,
[tex]y=\dfrac{3}{15x-1}[/tex]
Given-
The equation in the question is,
[tex]{dy\times {dx}=5y^2[/tex]
What is differential equation?Differential equation is a way to represents the relation between the functions and their variables.
Rewrite the equation,
[tex]\dfrac{dy}{5y^2} =dx[/tex]
Integration both sides,
[tex]-\dfrac{1}{5y} =x+c[/tex]
Here, c is the integrating constant.
Now the given initial condition is,
[tex]y(0)=3[/tex]
Use this for the integrated function to find the value of the constant,
[tex]-\dfrac{1}{5\times 3} =c[/tex]
[tex]c=-\dfrac{1}{15}[/tex]
Put this value in equation we get,
[tex]-\dfrac{1}{5y} =x-\dfrac{1}{15}[/tex]
[tex]y=\dfrac{3}{15x-1}[/tex]
Hence the solution to the differential equation given in the question is,[tex]y=\dfrac{3}{15x-1}[/tex]
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To solve the differential equation dy/dx = 5y^2 with the initial condition y(0) = 3, use separation of variables and integration. Substitute the initial condition to find the specific solution.
Explanation:To solve the differential equation dy/dx = 5y^2 with the initial condition y(0) = 3, we can use separation of variables.
First, rewrite the equation as dy/y^2 = 5dx. Integrate both sides: ∫1/y^2 dy = ∫5 dx. This simplifies to -1/y = 5x + C.
Next, apply the initial condition y(0) = 3: -1/3 = 0 + C. Therefore, C = -1/3.
Substitute C back into the equation: -1/y = 5x -1/3. Solve for y: y = -1/(5x -1/3).
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A family of two adults and three children went to a water park. Admission to the water park costs $18 per person. Nora used the expression 2 (18) + 3 (18) to model the total cost for the family, and Alex used the expression 5 (18). Which property of operations makes both of their expressions correct?
associative property
commutative property
distributive property
identity property
Answer
Distributive Property.
Step-by-step explanation:
First you solve for the first equation by multiplying 2 by 18 which is 36. Then 3 times 18 which is 54. Then you add them together to get 90.
Next you solve for the second equation by multiplying 5 by 18 which is 90.
Both of these equations are solved by the distributive property because your distributing the number outside of the parenthesis.
Greg's ceiling fan rotates 30 degrees and then stops. How many more times does it need to rotate to make a full rotation?
Answer:
330 degrees
Step-by-step explanation:
a full rotation is 360 degrees and if you subtract 30 from 360 its 330
Final answer:
To complete a full rotation, Greg's ceiling fan, which has already rotated 30 degrees, needs to rotate one more time, as there are 330 degrees left to reach 360 degrees, which is a full rotation.
Explanation:
Greg's ceiling fan rotates 30 degrees and stops. To determine how many more times the fan needs to rotate to complete a full rotation, first, we need to know that one full rotation is equal to 360 degrees. As the fan has already rotated 30 degrees, we subtract this from 360 degrees:
360 degrees - 30 degrees = 330 degrees.
Now, because one full rotation is 360 degrees, we divide the remaining degrees by 360 to find the number of additional rotations needed:
330 degrees / 360 degrees per rotation = 0.9167 rotations.
Since a fan cannot complete a fraction of a rotation in terms of action, Greg's ceiling fan would need to rotate one more time to make it a complete rotation.
Janet has three coins.
One coin has a value
that is 5 times another
coin. The third coin has
a value that is 2 times
another coin. She has
404 altogether. What
coins does she have?
Write an equation to
represent your work and
solve.
Answer:
Janet has coins worth 252.5, 101, and 50.5.
Step-by-step explanation:
Let us call the three coins [tex]a,b[/tex], and [tex]c[/tex].
The first coin [tex]a[/tex] is 5 times another coin (let's say [tex]b[/tex]); therefore,
[tex]a = 5b[/tex],
and the third coin is 2 times the value of another coin (it's coin [tex]b[/tex]):
[tex]c =2b[/tex].
The total worth of all coins is 404; therefore,
[tex]a+b+c =404[/tex]
or
[tex]5b+b+2b =404[/tex]
[tex]8b =404[/tex]
[tex]\boxed{b = 50.5}[/tex]
with the value of [tex]b[/tex] in hand, we find [tex]a[/tex] and [tex]c[/tex]:
[tex]a = 5b = 5(50.5)[/tex]
[tex]\boxed{a = 252.5}[/tex]
and for [tex]c:[/tex]
[tex]c = 2 b = 2 (50.5)[/tex]
[tex]\boxed{c = 101}[/tex]
Thus, Janet has 3 coins worth 252.5, 101, and 50.5.
A wise man once said,
“400 reduced by 3 times
my age is 244." How old is
the wise man?
The wise man's age can be calculated by solving the equation 400 - 3x= 244, leading to the solution that he is 52 years old.
To determine the wise man's age, we need to set up an equation based on the given statement:
Let's call the wise man's age x
The statement says, "400 reduced by 3 times my age is 244." This can be written as:
400 - 3x = 244
To find x, follow these steps
400 - 3x = 244
3x = 400 - 244
3x = 156
x = 156 / 3
x = 52
So, the wise man is 52 years old.
do these measurements represent the side lengths of a right triangle 12ft 20ft and 24ft
A. yes
B. No
Answer:
B. No
Step-by-step explanation:
We can test this theory using Pythagorean's theorem:
a² + b² = c²
12² + 20² = 24²
144 + 400 = 576
544 ≠ 576
So you can conclude that this is not a right triangle.
Write the equation of a line in y =mx+b
form that has a slope of 3/4 and a y-intercept of 0.
Answer:
y = ¾x
Step-by-step explanation:
y = mx + b, where
m = slope and
b = y-intercept
If slope = ¾ and y-intercept =0, the equation is
y = ¾x
X/4 < -1.5 for a million dollars and Brainliest. Send cash app too
Answer:
x < -6
Step-by-step explanation:
X/4 < -1.5
Multiply each side by 4
X/4*4 < -1.5*4
x < -6
∠ABC measures 124° and ∠MNO measures 56°. Therefore, the two angles are
Answer:
Supplementary
Step-by-step explanation:
Since the two angles add up to 180 degrees, they are supplementary
Please Answer both with Solution and Explanation. Will give Brainliest
1. What are the roots of [tex]x^{2}[/tex] - 2x + 2?
2. The number 16 has four fourth roots. In other words, there are four complex numbers that can be entered in the square in the equation below:[tex]\[\square^4=16.\][/tex]Find them. Please
Step-by-step explanation:
1) Given quadratic expression is [tex]x^2-2x+2[/tex]
First equate the given expression to zero then we will find the roots.
Since the given equation is quadratic hence it has two roots.
To find the roots of the given quadratic equation :For the quadratic equation we have that [tex]ax^2+bx+c=0[/tex]
Therefore roots [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] here a and b are coefficients of [tex]x^2andx[/tex] respectively and c is a constant
[tex]x^2-2x+2=0[/tex] here a=1 ,b=-2 and c=2
Now Substitute the values in [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] we get
[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(2)}}{2(1)}[/tex]
[tex]=\frac{2\pm \sqrt{4-8}}{2}[/tex]
[tex]=\frac{2\pm \sqrt{-4}}{2}[/tex]
[tex]=\frac{2\pm \sqrt{4i^2}}{2}[/tex]
[tex]=\frac{2\pm2i}{2}[/tex]
[tex]=2(\frac{1\pm i}{2})[/tex]
[tex]x=1\pm i[/tex]
Therefore [tex]x=1+i[/tex] and [tex]x=1-i[/tex] are the roots of the given quadratic equation.
2) Given that the number 16 has four roots.In other words, there are four complex numbers that can be entered in the square .
Let x be the given number 16
i.e., x=16
From the given we can write [tex]x^4=16[/tex]Since the number has complex number as its rootsTherefore we can write [tex]x^4=(2i)^4[/tex] as below[tex]=2^4i^4[/tex] ( by using the formula [tex](ab)^m=a^mb^m[/tex] )
[tex]=16(1)[/tex] ( by [tex]i^2=-1[/tex] and [tex]i^4=(i^2)^2=(-1)^2=1[/tex] )
[tex]x^4=16=(2i)^4[/tex]
Therefore [tex]x^4=(2i)^4[/tex]
Since powers are same we can equate the bases ( bases are equal )
Therefore x=2i,2i,2i,2i are the roots of the given number 16 and they are complex numbers too
Help plzzzz I don't understand how to do this
Mercury's distance = 5.8 x 10¹⁰
Venus' distance = 1.86 farther or more than Mercury's, namely 1.86(5.8 x 10¹⁰)
Earth's distance = 2.58 farther or more than Mercury's, namely 2.58(5.8 x 10¹⁰)
[tex]\bf \stackrel{\textit{venus' distance}}{1.86(5.8\times 10^{10})}\implies \begin{cases} 1.86(58000000000)\\ 107880000000\\ 1.0788\times 10^{11} \end{cases} \\\\\\ \stackrel{\textit{earth's distance}}{2.58(5.8\times 10^{10})}\implies \begin{cases} 2.58(58000000000)\\ 149640000000\\ 1.4964\times 10^{11} \end{cases}[/tex]
about how many meters farther is Earth's than Venus? well, we can simply get their difference, we know the Earth is farther than Venus, so we can just subtract Venus' distance from Earth's to get the difference, namely 149640000000 - 107880000000.
[tex]\bf \stackrel{earth}{149640000000} - \stackrel{venus}{107880000000}~~ = ~~41760000000\implies \stackrel{\textit{rounded up}}{4.2\times 10^{10}}[/tex]
Select Statistical or Not statistical to classify each question.
Question Statistical Not statistical
Which radio station does each of my friends prefer?
How far can each radio station broadcast its signal?
Which radio station is located on the west side of town?
Answer:1 yes. 2 yes. 3 no.
Step-by-step explanation:
i did it in the oms
Which is the best estimate of the avarge rate of change for the quadratic function on the interval 0 ≤ x ≤ 4
Answer:
A) -1
Step-by-step explanation:
The missing graph is attached.
The possible answers were:
-1
-2
-3
-4
The average rate of change of a function f(x) on a≤x≤b is given by:
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
We want to find the best estimate of the average rate of change for the quadratic function on the interval 0 ≤ x ≤ 4.
From the graph, f(0)=0 and f(4)=-4
[tex] \frac{f(4) - f(0)}{4 - 0} = \frac{ - 4 - 0}{4 - 0} = \frac{ - 4}{4} = - 1[/tex]
Joshua and his friend Maxine want to buy charcoal pencils to add to their growing collection of art
supplies. They go to store A and find out that a 10 pack is worth $16.25. But at store B a 10 pack is worth
$7.65 but of lesser quality. Find out how much one pencil is worth at store A and store B.
what is the third angle of a triangle if two of the angles measure 29 ° and 87 °.
Answer:
64°
180°-29°-87°=64°
The table represents a function.
A 2-column table with 4 rows. The first column is labeled x with entries negative 6, negative 2, 0, 3. The second column is labeled f of x with entries 3, 1, 4, negative 2.
What is f(–2)?
f(–2) = 1
Solution:
The table represents a function.
x f(x)
–6 3
–2 1
0 4
3 –2
To find the value of f(–2):
f(–2) means the value of f(x) for the corresponding x value –2.
In the table, if the x value is –2, then f(x) is 1.
See the value of f(x) which correspond to x = –2.
Hence f(–2) = 1.