3. In the rhombus, what are m∠1, m∠2 and m∠3? The diagram is not drawn to scale.
Answers
Answer: m∠1 = 128°, m∠2 = 26° and m∠3 = 26°.
Step-by-step explanation: We are given to find the measures of ∠1, ∠2 and ∠3 in the figure.
As shown in the attached figure, ABCD is a rhombus, where m∠A = 128°.
We know that, in a rhombus, all the sides are congruent, the opposite angles are congruent and the adjacent angles are supplementary.
So, from rhombus ABCD, we have
[tex]m\angle A=m\angle C~~~~~\textup{[opposite angles]}\\\\\Rightarrow m\angle 1=128^\circ.[/tex]
Also, in ΔBCD, we have
[tex]BC=CD~~\textup{[all the sides are congruent]}\\\\\Rightarrow m\angle 3=m\angle 2~~\textup{[angles opposite to congruent sides care congruent]}.[/tex]
Now, since the sum of three angles of a triangle is 180°, we have from ΔBCD that
[tex]m\angle 1+m\angle 2+m\angle 3=180^\circ\\\\\Rightarrow 128^\circ+m\angle 2+m\angle 2=180^\circ\\\\\Rightarrow 2\times m\angle 2=180^\circ-128^\circ\\\\\Rightarrow 2\times m\angle 2=52^\circ\\\\\Rightarrow m\angle 2=26^\circ.[/tex]
Therefore, m∠3 = 26°.
Thus, m∠1 = 128°, m∠2 = 26° and m∠3 = 26°.
Related Questions
Which net represents this solid figure?
Answers
Answer:
Bottom Left.
Step-by-step explanation:
Did it got 100%! Thanks so much! Your welcome! Have a great week!
I need some help on this triangle similarity proof in Geometry!
Answers
Write a explicit equation for the sequence 6,18,54,162,...
Answers
6,18,54,162,...
we know that
a1=6
a2=18
a3=54
a4=162
a2/a1=18/6--------> 3
a3/a2=54/18-------> 3
a4/a3=162/54------> 3
therefore
a(n+1)=an*3
a1=6
for n=1
a(1+1)=a1*3---------> a2=a1*3--------> a2=6*3------> a2=18
for n=2
a(2+1)=a2*3---------> a3=a2*3--------> a3=18*3------> a3=54
for n=3
a(3+1)=a3*3---------> a4=a3*3--------> a4=54*3------> a4=162
therefore
the equation for the sequence is
a(n+1)=an*3
Math question!!! PLEASE HELP
solve for x in the triangle
a. 1.7
b. 2.6
c. 2.7
d .3.0
Answers
# 11 let f(x) =x^2 and g(x) =x-1. find (f o g)(-3)
#12 let f(x)= 5x+3 and g(x) =x^2-x+1
preform the function operating then find the domain.
g(x)-f(x)
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g(x) = x-1
g(-3) = -3-1 .... plug in x = -3
g(-3) = -4
Plug this into f(x)
Now compute f(-4)
f(x) = x^2
f(-4) = (-4)^2
f(-4) = 16
Answer: 16
=======================================================
Problem 12
f(x) and g(x) are two polynomials. When subtracting any two polynomials, we end up with some other polynomial. This idea is known as set closure. Set closure is where you take two items from one set, apply an operation to them, and the result is another item from the same set. Another example of this is adding two whole numbers. Adding two whole numbers leads to another whole number.
So in short, h(x) = g(x)-f(x) is a polynomial
The domain of any polynomial is the set of all real numbers. We can plug in any x value we want to get some output value for y.
Let's find the result of g(x)-f(x)
g(x) - f(x) = [ g(x) ] - [ f(x) ]
g(x) - f(x) = [ x^2-x+1 ] - [ 5x+3 ]
g(x) - f(x) = x^2-x+1 - 5x-3
g(x) - f(x) = x^2-6x-2
Domain: Set of all real numbers
Find the surface area of the cylinder to the nearest tenth of a square unit with a radius of 3cm and a height of 18.2 cm. use 3.14 for pi.
Answers
The formula used to find the surface area is 2 x pi x r^2 (area of the faces) + pi x d x h (area of the curved surface which is the diameter times the height).
Substitute the values in and it would be 2 x 3.14 x 3 x 3 + 3.14 x 6 x 18.2. The surface area would be approximately 399.4 square cm. This is approximate because pi is rounded.
Final answer:
The surface area of a cylinder with a given radius of 3 cm and height of 18.2 cm is calculated using the formula 2πr(height + r), which results in approximately 400.1 square centimeters.
Explanation:
The question asks to find the surface area of a cylinder with a radius of 3 cm and a height of 18.2 cm, using 3.14 for pi. The formula for the surface area of a cylinder is 2πr(height + r), where r is the radius, and the height is the vertical dimension of the cylinder.
Plugging in the given values:
Radius (r) = 3 cmHeight = 18.2 cmPi (π) = 3.14We get: Surface Area = 2 * 3.14 * 3 * (18.2 + 3) = 2 * 3.14 * 3 * 21.2 = 400.1 cm²
Therefore, the surface area of the cylinder, rounded to the nearest tenth, is 400.1 square cm.
what is the value of x
plz do not guess will mark brainlist do not comment any questions evrey thing you need is up there just post the answer
Answers
sin 30 = x/8
8 (sin 30) = x
4 = x
Which of the following is a perfect square? 18 81 50 32
Answers
Answer:
The correct answer is 81
Step-by-step explanation:
Here are all the perfect squares.
1 2 1 × 1 1
2 2 2 × 2 4
3 2 3 × 3 9
4 2 4 × 4 16
5 2 5 × 5 25
6 2 6 × 6 36
7 2 7 × 7 49
8 2 8 × 8 64
9 2 9 × 9 81 81 Is a perfect square!
10 2 10 × 10 100
11 2 11 × 11 121
12 2 12 × 12 144
Can I have brainliest please?
Which of the following is an example of inductive reasoning?
A)Math seems fun so you conclude that everyone loves math.
B)All of your friends love math so you conclude that everyone loves math.
C)All of your friends love math. Jo loves math, therefore Jo is your friend.
D)You love math. Jo doesn't love math. Jo is not your friend.
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Inductive reasoning takes into consideration all available fact, and puts them together to reach a valid conclusion. The other statement contain an error of logic, but choice A has a logical conclusion based on the premise.
Answer:
The answer is A
ABCD∼EFGH
AD=45 in. , EH=75 in. , and AB=30 in.
What is EF ?
Enter your answer in the box.
EF =
in.
Also Triangle ABC undergoes a series of transformations to result in triangle DEF .
Is triangle DEF congruent to triangle ABC ?
Select Congruent or Not congruent for each description.
Description Congruent Not congruent
Triangle ABC is rotated 90° clockwise, and then reflected over the line y=x to form triangle DEF.
Triangle ABC is reflected over the x-axis, and then dilated by a factor of 12 to form triangle DEF.
Triangle ABC is rotated 180°, and then translated 4 units down and 2 units right to form triangle DEF.
and
A point at (−1, 10) is rotated 90° counterclockwise about the origin.
What are the coordinates of the resulting image?
(−1, −10)
(1, −10)
(−10, −1)
(10, 1)
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In this case, AD corresponds to EH, while AB corresponds to EF.
Therefore; AD/EH = AB/EF
45/75 = 30/ EF
EF = (30×75)/45
= 50 in
2. Triangle DEF is not congruent ABC.
For congruent triangles; if three pairs of sides are equal in length, then the triangles are congruent. Also triangles are congruent if two pairs of angles of the triangle are equal in measurement, and the included sides are equal in length, then the triangles are congruent.
3. Triangle ABC is rotated 90° clockwise, and then reflected over the line y=x to form triangle DEF. This description is Congruent.
Triangle ABC is reflected over the x-axis, and then dilated by a factor of 12 to form triangle DEF. Description not congruent
Triangle ABC is rotated 180° , and then translated 4 units down and 2 units right to form triangle DEF. The description is Congruent
4. A point (-1,10) is rotated 90° counterclockwise about the origin.
The resulting coordinates of the image is (-10,-1)
A rotation through 90 about the origin is anticlockwise (counter clockwise direction)
Factor the expression. x2 – 10xy + 24y2
Answers
1. You have the following expression given in the problem above:
x²-10xy+24y²
2. When you factor the expression x²-10xy+24y², you obtain the following:
(x-4y)(x-6y)
3. To verify the result you can apply the distributive property and the result must be x²-10xy+24y².
Therefore, the answer is: (x-4y)(x-6y)
Answer:
the answer is: (x-4y)(x-6y)
Step-by-step explanation:
Write a trinomial in one variable of degree 5 in standard form.
Answers
A polynomial of one-variable is given by following expression :-
[tex] Ax^n + Bx^{n-1} +Cx^{n-2}+Dx^{n-3}+Ex^{n-4}+..... [/tex]
where A, B, C, D, E are the coefficients of terms in the polynomial and x is variable of the equation.
A is the leading coefficient and it can not be zero i.e. A≠0.
n is the degree of the polynomial.
It says to write a trinomial in one variable of degree 5.
Trinomial means only three terms with non-zero coefficients, and degree 5 means n = 5.
There could be many answers, but an example of "trinomial of degree 5" would be :-
[tex] Ax^5 + Bx^4 + Cx^3 [/tex]
[tex] 3x^5 + 5x^4 + 2x^3 [/tex]
A trinomial in one variable of degree 5 in standard form is [tex]\( ax^5 + bx^3 + cx \),[/tex] where [tex]\( a \), \( b \), and \( c \)[/tex] are non-zero coefficients and [tex]\( a \neq 1 \)[/tex].
A trinomial is a polynomial with three terms. The degree of a polynomial is the highest power of the variable that appears in the polynomial with a non-zero coefficient. Since we are asked to write a trinomial of degree 5, the highest power of the variable x must be 5.
The standard form of a polynomial lists its terms in descending order of their degrees. Therefore, the first term of our trinomial must be [tex]\( ax^5 \),[/tex] where a is a non-zero coefficient, and [tex]\( a \neq 1 \)[/tex] to ensure that the coefficient is explicit.
Since we want a trinomial, we need two more terms. The next term should have a lower degree, and since we're dealing with a degree 5 polynomial, the next possible lower odd degree is 3 (we choose an odd degree to maintain the trinomial structure with distinct powers). This gives us the second term [tex]\( bx^3 \),[/tex] where b is also a non-zero coefficient.
The third and final term of our trinomial must have a degree lower than 3. The next possible lower odd degree is 1, which gives us the term [tex]\( cx \),[/tex] where c is again a non-zero coefficient.
Putting it all together, we have the trinomial [tex]\( ax^5 + bx^3 + cx \)[/tex] as the standard form of a degree 5 polynomial with three terms.
Ron is five years older than twice his cousin Pat’s age. The sum of their ages is less than 35. What is the greatest age that Pat could be? 7,8, or 10? Please more then one response so I know its right,
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(15,-9) is dilated by a scale factor of 3 what is its new location
Answers
(x, y) ---> k (x, y) ---> (kx, ky)
Applying the transformation to the ordered pair we have:
(15, -9) ---> 3 (15, -9) ---> ((3) * (15), (3) * (- 9)) ----> (45, -27)
Answer:
its new location is:
(45, -27)
Suppose the number of dropped footballs for a wide receiver, over the course of a season, are normally distributed with a mean of 16 and a standard deviation of 2.
What is the z-score for a wide receiver who dropped 13 footballs over the course of a season?
A. −3
B. −1.5
C. 1.5
D. 3
Answers
The formula to calculate a z-score is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
where X is the value we're calculating the z-score for, μ is the mean and σ is the standard deviation.
Using our information we have:
[tex]z=\frac{13-16}{2}=\frac{-3}{2}=-1.5[/tex]
The correct answer is option B. -1.5.
To calculate the z-score for a wide receiver who dropped 13 footballs over the course of a season, we use the z-score formula:
z = (X - μ) / σ
where:
X is the value to be standardized (13 footballs in this case)μ is the mean (16 footballs)σ is the standard deviation (2 footballs)Substitute the values into the formula:
z = (13 - 16) / 2
This simplifies to:
z = -3 / 2 = -1.5
Therefore, the z-score for a wide receiver who dropped 13 footballs is B. -1.5.
Which is the equation of a line that is perpendicular to the line represented represented by y = 3/4x - 1/2 ?
Answers
.. y = -4/3x +c . . . . . for some value of c
_____
The slope of the perpendicular line will be the negative reciprocal of the slope of the given line, which is 3/4.
The equation of a line that is perpendicular to the given line is y = -4/3x + c.
What is equation of a line?The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.
For the given situation,
The equation of a line is y = 3/4x - 1/2 ------ (1)
The general form of equation of line in slope intercept form is
[tex]y=mx+c[/tex]
On comparing the equation 1 with general form,
Slope of the line, [tex]m=\frac{3}{4}[/tex]
Then, the slope of the line perpendicular to the given line is [tex]\frac{-1}{m}[/tex]
⇒ [tex]\frac{-1}{m}=\frac{-1}{\frac{3}{4} }[/tex]
⇒ [tex]\frac{-1}{m}=\frac{-4}{3}[/tex]
No points were defined that this 'normal' should pass through, so its intercepts are indeterminate.
Thus the equation of line in slope intercept form is
[tex]y=\frac{-4}{3}x+c[/tex]
Hence we can conclude that the equation of a line that is perpendicular to the given line is y = -4/3x + c.
Learn more about equation of a line here
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Which equation represents the magnitude of an earthquake that is 100 times more intense than a standard earthquake?
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the magnitude of an earthquake s
M=log[I/S]
where
I----------> is the intensity of the earthquake
S---------> is the intensity of a standard earthquake
in this problem
I=100S
then
M=log[100S/S]
this equation represents the magnitude of an earthquake that is 100 times more intense than a standard earthquake
M=log(100)-----------> M=2
The magnitude of this earthquake is 2 on the Richter scale
To represent an earthquake that is 100 times more intense than a standard earthquake, an increase of 2 on the Richter scale is required due to the logarithmic nature of the scale.
Explanation:The magnitude of an earthquake that is 100 times more intense than a standard earthquake would be represented by an increase of 2 on the Richter scale. This scale is logarithmic, meaning that each whole number increase on the Richter scale represents a tenfold increase in amplitude. To be 100 times more intense, we need a tenfold increase for each magnitude, so an increase from, for example, magnitude 3 to 5 would represent an earthquake that is 100 times more intense.
Learn more about Richter scale here:https://brainly.com/question/33354205
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how do you simplify x^2-4x-21 divided by x+3
Answers
Notice how
3 plus -7 = -4
3 times -7 = -21
which helps us factor the trinomial
After you've factored it, we can cancel out a pair of (x+3) terms leaving us with the final answer of x-7
Note: the cancellation happens because (x+3)/(x+3) = 1. Divide anything (except 0) over itself and you'll get 1. A simpler example of this is 5/5 = 1.
An engineer earns $6000 per month. A contractor makes $80 per hour, while a teacher gets basic salary of $3000 and $50 per hour any additional job. Considering a month, which job
is better;when, and why? Justify your answer using graphs,equations, and tables
Answers
Multiplying 8 hours of work by 20 working days in a month, we will get 160 monthly working hours.
Now let's compute:
Engineer: $6000 per mo. / 160 hrs. = $37.5 per hr.
Contractor: $80 per hr. * 160 hrs. = $12,800 per mo.
Teacher: $3000 per mo. / 160 hrs. = $18.75 per hr. + $50 per hr = $68.75 per hr.
Explain why the equation x^2+y^2=1 does not define y as a function of x
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So take x = sqrt (5)
Substituting into the equation we get:
y^2 = (sqrt 5)^2 - 1
y^2 = 5 - 1
y^2 = 4
So what y value, when it is squared, gives us 4? It could be either 2 or -2. So there are two y-values that match one x value and the equation is not a function.
x^2 + y^2 = 4 is actually the equation for a circle with center at the origin and a radius of 2. Try graphing it by hand by choosing x = 0, -2, and 2 to get four points on the circle. Unless they specify that X Does not equal to one, then this isn't a function. Say X DOES = 1 then you'd have 1/(1^2-1) which would give you 1/0 which isn't a function. So like the other have said, it IS a function UNLESS x=1 Hope that helps!
Translate the following and then create real-world problems using these
expressions.
“6 less than a number”
“2 times the quotient of a number and two”
“4 times the difference of a number and 8”
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2. 2(x/2); Robert lost half his money in the stock market last week, and then doubled that amount this week.
3. 4(x - 8); 4 people spent $8 on a movie. How much money (x) did each person have before seeing the movie?
Which graph represents the function?
Answers
Between x = 0 and x = 3 y is increasing so the correct graph is Graph 2.
f(x) can be factored as
.. f(x) = (x -6)(x +1)/((x -3)(x +2))
so will have zeros at x = {-1, 6}, vertical asymptotes at x = {-2, 3}, and sign changes at all of those points.
The Upper Right graph is the only one with the zeros and asymptotes in the right places.
If the sin 60° = square root of three over two, then which statement is true? (6 points)
cos 30° = square root of three over two, because the cosine and sine are complements
cos 30° = 0, because the cosine and sine are complements
cos 120° = square root of three over two, because the cosine and sine are supplements
cos 120° = 0, because the cosine and sine are supplements
Answers
Answer: The answer is (a) cos 30° = square root of three over two, because the cosine and sine are complements
Step-by-step explanation: Given that -
[tex]\sin 60^\circ=\dfrac{\sqrt 3}{2}.[/tex]
we are to select the correct statement from the given four options.
We know that sine and cosine functions are supplement of each other. So, we have
[tex]\sin 60^\circ=\cos(90^\circ-60^\circ)=\cos 30^\circ=\dfrac{\sqrt 3}{2}.[/tex]
Thus, the correct option is (a) cos 30° = square root of three over two, because the cosine and sine are complements.
The area of a soccer field at 7700 yd.². The width of the field is 70 yards. What is the perimeter of the field?
Answers
Factor the expression. 4x(x^2 − 7) + 3(x^2 − 7)
Answers
To factor an expression, you need to analyze it and find a common variable or expression on the expression given. In this expression, you can observe that the expression x^2 – 7 is common to the two terms. You need to factor it out from the both of them.
4x (x^2 – 7) + 3 (x^2 – 7)
(x^2 – 7) (4x + 3)
This is already the complete factor of the expression.
A rectangular Corn Hole area at the recreation center has a width of 5 feet and a length of 10 feet. If a uniform amount is added to each side, the area is increased to 84 square feet. What is the amount added to each
sidhttps://s3.amazonaws.com/algebranation/testyourself_uploads/MAFS7/7.043.pnge?
Answers
A=LxW
A is the area of the rectangle
L is the length of the rectangle.
W is the widht of the rectangle
2. You have that:
-The rectangular Corn Hole area has a width of 5 feet and a length of 10 feet, so:
L1=10 feet
W1=5 feet
- When a uniform amount is added to each side (x), the area is increased to 84 feet². Then, you have a different length (L2) and a different width (W2):
3. The new length is:
L2=L1+x+x
L2=L1+2x
L2=10+2x
4. The new width is:
W2=W1+x+x
W2=W1+2x
W2=5+2x
5. The new area is:
A2=84 feet²
6. Then, you have:
A=LxW
84=(10+2x)(5+2x)
7. When you apply the distributive property, you obtain a quadratic equation:
4x²+30x-34=0
8. You can solve with by applyin the quadratic formula:
x=(-b±√(b^2-4ac))/2a
a=4
b=30
c=-34
9. Then, the answer is:
x=1 feet
Answer:
I can't believe this guy above me has a verified answer and it is wrong.... anyway the true answer to this is 2. I checked it myself when I put 1 as the answer and got this question wrong, and it showed me the correct answer is 2 so don't believe the verified answer.
Step-by-step explanation:
Review Question #7:
The answer to this question is 2ft, not 1ft.
This is because:
So the width of the second rectangle can be represented by 10+2x, and the length of the second rectangle can be represented by 5+2x. Lets make 2x equal y to make things easier though. Because the product of both 10+2x and 5+2x is 84 square feet, we must multiply the two equations together first.
(10+y)(5+y)=84
This then equals:
50+10y+5y+y^2=84
Then add the like terms:
y^2+15y+50=84
Then set the equation to zero by subtracting 84 from both sides:
y^2+15y-34=0
From that, you can use the box method, or any method to get:
(y+17)=0 and (y-2)=0
Which would then simplify to:
y=-17 and y=2
However, we substituted y for 2x, so plug 2x into y:
2x=-17 and 2x=2
Then simplify from here:
x=-17/2 and x=1
The answer cannot be negative, so that means the answer is x=1, however, even though this is true, the answer is that 2ft was added to EACH SIDE, because the question was asking for what amount was added to each side.
use substitution to solve 3x-2y=11 and x+2y=9
Answers
.. 2y = 9 -x
Substitute that into the first equation.
.. 3x -(9 -x) = 11
.. 4x -9 = 11
.. 4x = 20
.. x = 5
Using our expression for 2y above,
.. 2y = 9 - 5
.. y = 4/2 = 2
The solution is (x, y) = (5, 2).
What is the value of the 5 in 3 590 answer in words
Answers
Please help me out!! :)
Answers
We need to find the area of the regular polygon as shown in the image.
Now in a regular hexagon the line joining the center and the vertex of a hexagon have the same length as the length of each side. (Refer the attached image)
[tex]10 \sqrt3cm=10 \times 1.732=17.32 cm[/tex]
A regular hexagon is made up of 6 equilateral triangles inside which means all the sides are of the same length.
Now, we know that the length of a side of an equilateral triangle is [tex]10 \sqrt 3[/tex] cm. So the area of one equilateral triangle is:
[tex]\frac{\sqrt 3}{4} \times (a)^2[/tex]
Where, 'a' is the side length of the equilateral triangle.
Therefore, area [tex]= \frac{\sqrt 3}{4} \times (10 \sqrt3)^2= \frac{\sqrt 3}{4} \times 100 \times 3=75 \sqrt3[/tex] square centimeters.
Now that we have the area of one equilateral triangle and there are 6 of them in a regular hexagon we can find the area of hexagon.
So, the area of given regular polygon is [tex]=6 \times 75 \sqrt 3=450 \sqrt 3 cm^2[/tex].
Given a polynomial f(x), if (x + 7) is a factor, what else must be true?
A) f(0) = 7
B) f(0) = −7
C) f(−7) = 0
D) f(7) = 0
Answers
When (x + 7) is a factor, f(-7) = 0. Thus, option C is correct: f(-7) = 0.
When the polynomial f(x) has (x + 7) as a factor, it implies that when x is replaced by -7, f(x) becomes zero.
This follows from the factor theorem which states that if (x - c) is a factor of a polynomial f(x), then f(c) = 0.
Therefore, to satisfy this condition, f(-7) = 0.
Consequently, option C, stating that f(-7) = 0, must be true when (x + 7) is a factor of f(x).
Thus, the correct answer is C) f(-7) = 0.