8. The triangles below are similar. State the following:
1.The similarity ratio
2.Theorem to justify similarity (ex. SSS, SAS, AAA etc)
3.A similarity statement for the two triangles.
Answers
2. Theorem to justify similarity: SAS.
.. MO = 4/3 JO
.. ∠O = ∠O
.. NO = 4/3 KO
3. Similarity statement: ΔMON ~ ΔJOK by SAS.
Related Questions
for a standard normal distribution whats the probability of getting a positive number
Answers
In a standard normal distribution, the probability of getting a positive number is 0.5.
Explanation:Probability of Getting a Positive Number in a Standard Normal Distribution
In a standard normal distribution, the probability of getting a positive number is 0.5. This is because the standard normal distribution is symmetric around 0, and half of the distribution lies to the right of 0, which corresponds to positive numbers.
Which of the quadratic functions has the narrowest graph? Y = 1/6x^2, y = 2x^2, y = -x^2, y = 1/8x^2
Answers
If the absolute value of a is <1 the graph is wider than when a = 1
If the absolute value of a is >1 the graph is narrow than when a = 1
The only function that fits that description is
y = 2x^2
B <<< answer.
Answer:
[tex]y=2x^2[/tex]
B is correct
Step-by-step explanation:
Given: We are given equation of parabola ans to choose narrowest graph.
[tex]y=ax^2[/tex]
Parabola form narrowest and widest.
Larger value of a most narrowest graph.
Smaller value of a most widest graph.
Now, we will see the coefficient of x²
[tex]y=\dfrac{1}{6}x^2,\ \ \ a=\dfrac{1}{6}[/tex]
[tex]y=2x^2,\ \ \ a=2[/tex]
[tex]y=-x^2,\ \ \ a=-1[/tex]
[tex]y=\dfrac{1}{8}x^2,\ \ \ a=\dfrac{1}{8}[/tex]
Now, we arrange the value of a in descending order.
[tex]2>1>\dfrac{1}{6}>\dfrac{1}{8}[/tex]
2 is largest value of these.
Hence, The narrowest graph is [tex]y=2x^2[/tex]
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or .
Since the area of the circle is the area of the square, the volume of the cylinder equals
the volume of the prism or (2r)(h) or πrh.
the volume of the prism or (4r2)(h) or 2πrh.
the volume of the prism or (2r)(h) or r2h.
the volume of the prism or (4r2)(h) or r2h.
Answers
To find this ratio we need to find areas of the circle and the square.
Circle:
[tex]Area= radius^{2} * \pi \\ A_{1} = r^{2} * \pi [/tex]
Square:
[tex]Area= side^{2} \\ A_{2} = (2r)^{2} \\ A_{2} 4r^{2}= [/tex]
Now we divide these two areas to find ratio:
[tex]ratio= \frac{ A_{1} }{ A_{2} } \\ ratio= \frac{r^{2} * \pi }{4r^{2}} \\ ratio= \frac{ \pi }{4} [/tex]
"Since the area of the circle is the area of the square,"
From the ratio above we can see that areas are not same.
"the volume of the cylinder equals"
Formula for volumes of cylinder and prism follow the formula:
[tex]Volume=base*height[/tex]
For cylinder:
[tex]V=r^{2} * \pi *h[/tex]
For prism:
[tex]V= (2r)^{2} \\ V=4 r^{2} [/tex]
The ratio of the area of the cross sectional circle and area of the cross sectional square is π : 4
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b or [tex]\dfrac{a}{b}[/tex]
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).
Suppose that we've got a = 6, and b= 4, then:
[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
For this case, we're specified that:
Radius of the circle of the cross section of the cylinder = r unitsSide length of the square cross section of the square prism = 2r unitsThen, the area of the circle is:
[tex]\pi r^2 \: \rm unit^2[/tex]
and the area of the square is: [tex]\rm side^2 = (2r)^2= 4r^2 \: \rm unit^2[/tex]
The ratio of the area of the circle to the area of the square is:
[tex]\dfrac{\pi r^2}{4r^2} = \dfrac{\pi}{4} = \pi : 4[/tex]
Thus, the ratio of the area of the cross sectional circle and area of the cross sectional square is π : 4
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how many liters of a 60% acid solution must be mixed with a 75% acid solution to obtain 20L of a 72% solution
Answers
y = amount of the 75% solution
now, how much is 60% of x? well, (60/100) * x, or 0.6x.
and how much is 75% of y? well, (75/100) * y, or 0.75y.
well, the resulting mixture is 72% of acid and then water or other liquids, but we know is that much off 20 liters, how much is that then? well 72% of 20 is (72/100) * 20, or 14.4.
regardless of what "x" and "y" are, we know that the resulting substance has to be 20 liters, thus x + y = 20.
and we also know that the amount of acid in each amount, will add up to the acid in the resulting amount.
since we know that there is 0.6x liters of only acid and 0.75y liters of only acid in each, thus 0.6x + 0.75y = 14.4.
[tex]\bf \begin{array}{lccc} &\stackrel{liters}{amount}&\stackrel{\%~of~acid}{amount}&\stackrel{acid~liters}{quantity}\\ &------&------&------\\ \textit{60\% solution}&x&0.60&0.6x\\ \textit{75\% solution}&y&0.75&0.75y\\ ------&------&------&------\\ mixture&20&0.72&14.4 \end{array} \\\\\\ \begin{cases} x+y=20\implies \boxed{y}=20-x\\ 0.6x+0.75y=14.4\\ -------------\\ 0.6x+0.75\left( \boxed{20-x} \right)=14.4 \end{cases} \\\\\\ 0.6x-0.75x+15=14.4\implies -0.15x=-0.6 \\\\\\ x=\cfrac{-0.6}{-0.15}\implies x=4[/tex]
how many liters of "y"? well, y = 20 - x.
Which fraction is between 0 and 1/2?
A. 2/3
B. 7/10
C. 3/5
D. 3/8
Answers
Your answer is D
Hope this helps
Fraction D. 3/8 is between 0 and 1/2.
Explanation:
1/2 is 0.50, or half.
2/3 is not the correct answer because the denominator is 3, and half of 3 would be 1.5, and 2 is greater than that.
7/10 is not the correct answer because the denominator is 10, and half of 10 is 5. 7 is greater than that.
3/5 is not the correct answer because the denominator is 5, and half of 5 is 2.5. 3 is greater than that.
can someone please help me
Answers
Most folks like to eliminate fractions first. To do that, you can multiply by 12.
9(x -3) < 4(x -4)
Now, eliminate parentheses.
9x -27 < 4x -16
Subtract 4x to put the variable on one side only. Add 27 to put the constant on the other side only.
5x < 11
Divide by the coefficient of x to get x by itself.
x < 11/5
39. You can actually work these without eliminating fractions. Just do the arithmetic in the usual way.
Eliminate parentheses.
(2/5)(3 -2n) ≥ (3/8)(2 -3n)
6/5 -(4/5)n ≥ 3/4 -(9/8)n
Add (9/8)n -6/5
n(9/8 -4/5) ≥ 3/4 -6/5
(13/40)n ≥ -9/20
Multiply by the inverse of the coefficient of n
n ≥ (-9/20)*(40/13)
n ≥ -18/13
A pair of vertical angles has measures
(2z+43)°
and
(−10z+25)°
.
What is the value of z? Vertical angles = each other
(2z+43)°
=
(−10z+25)°
−
3
2
−
11
4
−31
Answers
-2z -2z
43=-12z+25
-25 -25
18=-12z
z=-1.5
So Z=3/2
Answer:
The answer is Z equals negative 3/2
Step-by-step explanation:
The percents of different drinks sold at a snack shop are shown in the circle graph. What percent of the drinks sold were colas?
Answers
Ice tea: 30%
Lemonade: 32%
Colas: ?
The percent of the drinks sold that were colas is 38%.
One whole circle is equivalent to 100%. Since the ice tea takes up 30% of the circle and lemonade takes up 32% of the circle, the remaining portion for colas is no longer 100%. We simply deduct these percentages from 100% to get the percentage of colas which is 38%.
Describe how to find the perimeter of an enlarged figure if you know the scale factor and the dimensions of the original figure.
Answers
Answer:
Perimeter of any figure is given by adding up all the side measurements.
So, when a figure is enlarged by a scale factor then we can multiply all the sides with the scale factor to get the new sides measurements and then we can find the perimeter.
Or simply we can find the perimeter of the original figure and then multiply by the scale factor.
In both the methods, the answer will be the same.
We can take an example:
Lets suppose the original figure to be a rectangle with length 5 cm and width 2 cm. The rectangle is enlarged by a scale factor of 6.
The original perimeter is = [tex]2(5+2)[/tex]
= [tex]2(7)=14[/tex] cm
1st method:
Multiply the length by 6 and width by 6 to get new dimensions.
Length becomes: [tex]5\times6=30[/tex]
Width becomes: [tex]2\times6=12[/tex]
Perimeter becomes: [tex]2(30+12)[/tex]
= [tex]2(42)=84[/tex] cm
2nd method:
Simply multiply 6 with the original perimeter.
[tex]14\times6=84[/tex] cm
We can see that in both methods, the perimeter is same.
Sample Response:
To find the perimeter of an enlarged figure, you can multiply the original figure’s perimeter by the scale factor. You could also multiply each dimension of the original figure by the scale factor to find the dimensions of the enlarged figure, and then add to find the perimeter.
Let v be the vector from initial point P1 to terminal point P2. Write v in terms of i and j. 2) P1 = (0, 0); P2 = (3, -4)
Answers
The vector [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \)[/tex].
Its magnitude is [tex]\( \sqrt{45} \)[/tex] in reduced radical form.
To find vector [tex]\( \mathbf{v} \)[/tex] from point [tex]\( P_1 \)[/tex] to point [tex]\( P_2 \)[/tex], we subtract the coordinates of [tex]\( P_1 \)[/tex] from the coordinates of [tex]\( P_2 \)[/tex]:
[tex]\[\mathbf{v} = \begin{pmatrix} x_2 - x_1 \\ y_2 - y_1 \end{pmatrix}\][/tex]
Given [tex]\( P_1 = (-2, 5) \) and \( P_2 = (4, 2) \), we can calculate \( \mathbf{v} \):[/tex]
[tex]\[\mathbf{v} = \begin{pmatrix} 4 - (-2) \\ 2 - 5 \end{pmatrix} = \begin{pmatrix} 6 \\ -3 \end{pmatrix}\][/tex]
So, [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \)[/tex].
To find the magnitude of [tex]\( \mathbf{v} \)[/tex], we use the formula:
[tex]\[|\mathbf{v}| = \sqrt{v_x^2 + v_y^2}\][/tex]
Where [tex]\( v_x \)[/tex] and [tex]\( v_y \)[/tex] are the components of [tex]\( \mathbf{v} \)[/tex]
For [tex]\( \mathbf{v} = 6\mathbf{i} - 3\mathbf{j} \), \( v_x = 6 \) and \( v_y = -3 \)[/tex]:
[tex]\[|\mathbf{v}| = \sqrt{(6)^2 + (-3)^2} = \sqrt{36 + 9} = \sqrt{45}\[/tex]
Thus, the magnitude of vector [tex]\( \mathbf{v} \) is \( \sqrt{45} \)[/tex] in reduced radical form.
Correct question is:
Let v be the vector from initial point P1 to terminal point P2.
Write v in terms of i and j, and find the magnitude of vector v.
Leave the magnitude in reduced radical form.
P1 = (-2,5) , P2 = (4,2)
A certain mixture of nuts contains cashews, almonds, and macadamia nuts. Each container must include three times as many almonds as cashews and twice as many cashews as macadamia nuts. If there are a total of 24 ounces in each container, how many ounces of cashews must be included?
Answers
C:M = 2:1
A:C:M = 6:2:1
The proportion of cashews is 2/(6+2+1) = 2/9 of the mix. For 24 ounces, that is
.. (2/9)*(24 oz) = 5 1/3 oz . . . . . of cashews
The circumference of a circle is 18.84 kilometers. What is the circle's radius? C=18.84 km Use 3.14 for . kilometers
Answers
The Circle's radius is roughly 3 kilometers.
To find the compass of a circle when given the circumference, we can use the formula
C = 2πr
where C is the circumference, and r is the compass.
Given that the circumference is18.84 kilometers, we can substitute these values into the formula and break for the compass
18.84 = 2 x3.14 x r
Dividing both sides of the equation by 2 x 3.14
18.84 /( 2 x 3.14) = r
Simplifying the right side
r ≈18.84/6.28
r ≈ 3 kilometers.
Thus, the circle's radius is roughly 3 kilometers.
Learn more about Circumference here:
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8,321/100 is equal to which number?
Answers
The answer is 83.21
Hope this helps
Rewrite the equation of the parabola in vertex form. y= x2 + 8x - 21
Answers
Answer:
[tex]y=(x+4)^{2}-37[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
(h,k) is the vertex of the parabola
if a> 0 then the parabola open upward (vertex is a minimum)
if a< 0 then the parabola open downward (vertex is a maximum)
In this problem we have
[tex]y=x^{2}+8x-21[/tex]
Convert to vertex form
Complete the square
[tex]y+21=x^{2}+8x[/tex]
[tex]y+21+16=(x^{2}+8x+16)[/tex]
[tex]y+37=(x^{2}+8x+16)[/tex]
[tex]y+37=(x+4)^{2}[/tex]
[tex]y=(x+4)^{2}-37[/tex] --------> equation in vertex form
The vertex is the point [tex](-4,-37)[/tex]
the parabola open upward (vertex is a minimum)
Answer:
the answer is y=(x+4)^2-37
Step-by-step explanation:
A circle has an area of 75 square centimeters. Which answer is closest to the measure of its radius?
A) 2.75 centimeters
B) 4.9 centimeters
C) 9.8 centimeters
D) 23.9 centimeters
Answers
75 = [tex] \pi r^2 [/tex]
[tex]r [/tex] ≈ 4.89
So, answer is B.
Answer:
4.9
Step-by-step explanation:
Find complete factorization of the expression 32xy-56xyz
Answers
32xy-56xyz
We will use the distributive property for this.
Find a common factor. Biggest one is 8.
Since both numbers have xy, put that next to 8 outside the parenthesis and keep the z with the value for 56xyz.
8xy(4-7z) <== factored expression
I hope this helps!
~kaikers
A science class is tracking the progress of plant growth. The class starts the experiment with a plant five centimeters high. The plant grows two centimeters each day. The model for plant growth "y" is given by: y = 2x + 5. What is the meaning of the y-intercept in this equation? A) the y-intercept is the starting date Eliminate B) the y-intercept is two times larger than five C) the y-intercept is the starting height of the plant D) the y-intercept is the largest height the plant can grow
Answers
In the equation of a straight line, there is a slope (2) and a y intercept (5). The y intercept is where the line crosses the y axis. It is the starting point for the y values. The science class starts the experiment with the plant being 5 centimeters high and since this is the starting point/height, this is also the y intercept.
5÷4×6+e=5what does this equal ?
Answers
So following (parenthesis, exponents, multiplication, devision, addition, subtraction)
e=125/24 or 5 5/24
what is the 4Th rule of probability in statistics?
Answers
Final answer:
The fourth rule of probability in statistics is the sum rule, which states that the probability of the occurrence of one event or the other event, of two mutually exclusive events, is the sum of their individual probabilities.
Explanation:
The fourth rule of probability in statistics is the sum rule. The sum rule is used when considering two mutually exclusive outcomes that can come about by more than one pathway. It states that the probability of the occurrence of one event or the other event, of two mutually exclusive events, is the sum of their individual probabilities.
For example, if we flip a penny (P) and a quarter (Q), the probability of getting one coin coming up heads and one coin coming up tails can be calculated as [(PH) (QT)] + [(QH) × (PT)]
=( [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] ) + ( [tex]\frac{1}{2}[/tex] ×[tex]\frac{1}{2}[/tex] )
[tex]= \frac{1}{2}[/tex]
solve for x 3x−91>−87 OR 21x−17>25
Answers
Answer:
x > 4/3
Step-by-step explanation:
The first inequality can be solved this way ...
3x -91 > -87
3x > 4 . . . . . . . add 91
x > 4/3 . . . . . . divide by 3
__
The second inequality has solution ...
21x -17 > 25
21x > 42 . . . . . . add 17
x > 2 . . . . . . . . . divide by 21
__
The solution set is the union of these overlapping solutions, so will be equal to the first solution:
x > 4/3
Answer:
The solution is [tex]x>\frac{4}{3}[/tex]
Step-by-step explanation:
A compound inequality is an inequality that combines two simple inequalities.
We want to solve for x the following compound inequality
[tex]3x-91>-87 \:{OR} \:{21x-17>25}[/tex]
Solving the first inequality for x, we get:
[tex]3x-91+91>-87+91\\\\3x>4\\\\x>\frac{4}{3}[/tex]
Solving the second inequality for x, we get:
[tex]21x-17+17>25+17\\\\21x>42\\\\x>2[/tex]
So our compound inequality can be expressed as the simple inequality:
[tex]x>\frac{4}{3}[/tex]
The graph of a compound inequality with an "or" represents the union of the graphs of the inequalities. A number is a solution to the compound inequality if the number is a solution to at least one of the inequalities.
Graphically, we get
what is 6 ×2/3 in simplest form
Answers
Brainliest please?
how to solve 5/8h = 1,1/2=5
Answers
Answer:
C
Step-by-step explanation:
Is this your question? I know that sometimes I accidentally put an equal sign instead of a plus.
it takes Joanna 15 minutes to complete 4 puzzles. At that rate, how many puzzles can she complete in 1 hour 45 minutes
Answers
4 puzzles = 15 min
1 puzzle = 15/4 = 3.75 min
x puzzles = 105 min (which is the same as 1 hour 45 minutes)
divide 105 / 3.75 = 28
soooo....
28 puzzles = 105 min
Joanna can complete 28 puzzles in 1 hour 45 minutes.
Hope this helped! :)
1 hour 45 min = 95 min. 95/15 = 7. 7 x 4 = 28
the expression below is scientific notation for what number??
Answers
The answer is option A ".00000236".
Reason:
First write the equation:
2.36*10^-6
The exponent is negative so move to the left:
=.00000236
If you need anymore help feel free to ask me!
Hope this helps!
~Nonportrit
Two circles have the same radius. Complete the description for whether the combined area of the two circles is the same as the area of a circle with twice the radius. The combined area of two circles with the same radius is ___πr2. The area of a circle with twice the radius is ___πr2. The combined area of two circles is as the area of a circle with twice the radius.
Answers
Identify the first step in solving the equation below. 2003-05-04-00-00_files/i0420000.jpg A. Subtract 2w from each side. B. Multiply each side by w. C. Add 2w to each side. D. Divide each side by 2.
Answers
The answer to your problem is A)0.0310 and D)1.01
A significant figure is any number that is not a stand-alone zero which means any zero in the middle of a sequence of numbers or at the end of a sequence of numbers is counted as significant, for example: these zeros are significant (1, 2, 3, and 4 is significant as well) | |0000123004 | | | |these zeros are nonsignificant
find the domain of the function f(x)=24/x^2-20x+96
Answers
Find the inverse of the function. y = 2x2 –4
Answers
x=2y²-4
x+4=2y²
(x+4)/2=y²
√((x+4)/2)=y
Answer:
The inverse function is [tex]y=\sqrt{\frac{x+4}{2}}[/tex]
Step-by-step explanation:
The given function is [tex]y=2x^2-4[/tex].
This function is only invertible on the interval, [tex]x\ge 0[/tex].
To find the inverse on this interval, we interchange [tex]x[/tex] and [tex]y[/tex].
[tex]x=2y^2-4[/tex]
We now make [tex]y[/tex] the subject to get,
[tex]x+4=2y^2[/tex]
[tex]\Rightarrow \frac{x+4}{2}=y^2[/tex]
[tex]\Rightarrow \pm \sqrt{\frac{x+4}{2}}=y[/tex]
But the given interval is [tex]x\geq 0[/tex], This implies that, [tex]y\geq 0[/tex].
[tex]y=\sqrt{\frac{x+4}{2}}[/tex]
A bag contains 15 green, 18 yellow, and 16 orange balls. One ball is randomly selected. To the nearest percent, what is the probability of the event? Drag and drop the correct value into the box. P(yellow)=
Answers
Since the bag contains 15 green, 18 yellow, and 16 orange balls, the total number of balls in the bag are 15+18+16=49.
Therefore, the probability of the event that the drawn ball is yellow is given by:
P(yellow)=[tex] \frac{Number of Yellow Balls}{Total Number of Balls} [/tex]
[tex] \therefore P(Yellow)=\frac{18}{49}\times 100\approx36.73\approx37 [/tex]%
Thus, the the probability of the event, to the nearest percent, that the drawn ball is yellow is 37%.
Use completing the square to solve for x in the equation (x - 12)(x + 4) = 9.
A. x = -1 or 15
B. x = 1 or 7
C. x (plus sign over minus sign) square root of 41.
D. x (plus sign over minus sign) square root of 73.
Please help! This is timed!
Answers
(x - 12) (x + 4) = 9
Expand out terms of the left-hand side:
x^2 - 8 x - 48 = 9
Add 48 to both sides:
x^2 - 8 x = 57
Add 16 to both sides:
x^2 - 8 x + 16 = 73
Write the left hand side as a square:
(x - 4)^2 = 73
Take the square root of both sides:
x - 4 = sqrt(73) or x - 4 = -sqrt(73)
Add 4 to both sides:
x = 4 + sqrt(73) or x - 4 = -sqrt(73)
Add 4 to both sides:
Answer: x = 4 + sqrt(73) or x = 4 - sqrt(73) Thus the Answer is D:
Answer:
It is D.x=4+√73
Step-by-step explanation:
Got it right on edg.2022 :))