Two triangle is called SAS to each other when they have two similar side lengths along with identical angles between these two sides. SSS is called when both triangles have three similar side lengths.
What is congruence theorem?Two triangles satisfy congruence theorem when they have equal corresponding side lengths and equal corresponding angles.
What are the criteria for satisfying congruence theorem?Triangles needed to satisfy at least one of 4 criteria. If two triangles have two similar side lengths having equal angles between these two sides. if two triangles have two equal angles along with one similar corresponding side length. If two triangles have identical 3 side lengths or two triangles which are right-angled having equal hypotenuse and an equal corresponding side.
hence, SAS and SSS are the indicator of congruent triangle.
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Consider these dilations. 1. Large triangle right-arrow smaller triangle. 2. Small square right-arrow large square. 3. Line segment right-arrow identical line segment. Which best describes the scale factor for each dilation? Dilation 1 has a scale factor . Dilation 2 has a scale factor . Dilation 3 has a scale factor .
Answer:
Dilation 1 has a scale factor
✔ between 0 and 1
.
Dilation 2 has a scale factor
✔ greater than 1
.
Dilation 3 has a scale factor
✔ equal to 1
.
Step-by-step explanation:
i got it right on edge
Answer: 1.(between 0 and 1) 2.(greater than 1) 3.(equal to 1)
Step-by-step explanation: i hope this helps!
What is the area of the triangle?
16
8
10
units2
Answer:
64 units2
Step-by-step explanation:
16 x 8 / 2 =
128 / 2 =
64
Hope that helps!
What value of x makes this equation true?
need done fast please, offering 25 points!
Answer:-32.5
Step-by-step explanation: move x to the other side and solve
find the product
(-7t+4)^2
Answer:
(-7t+4)(-7t+4)=49t^2-56t+16
Step-by-step explanation:
49t^2 − 56t + 16
Or
\(49t^{2} - 56t + 16\)~Hope you have a good day, Loves!
Also if I'm right can you let me know please?
Also Also if I am right can I please have Brainliest??
what is the correct leaf unit if the 1st observation in a dataset was 0.014, assume values rounded to 3rd decimal?
Answer:
4
Step-by-step explanation:
You want to know the leaf unit corresponding to data value 0.014 when values are rounded to thousandths.
Leaf unitThe leaf unit for data values in a stem-and-leaf plot is the least-significant digit of the data value, when all data values are expressed to the same precision.
The least significant digit of 0.014 is 4. The leaf unit is 4.
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Graphing & Solving Inequalities
Answer:
x ≥ 1
Step-by-step explanation:
3 + 4x ≥ 7
3 - 3 + 4x ≥ 7 - 3
4x ≥ 4
4x / 4 ≥ 4 / 4
x ≥ 1
A quartic polynomial P(x) has rational coefficients. If 2 − i and-√5 are roots of P(x) = 0, what are the other 2 roots?
Answer:
2 + i and + √5
Step-by-step explanation:
Since P(x) is a quartic equation, it has 4 roots.
Since 2 - i and -√5 are two of its roots, then its conjugate pairs of 2 + i and + √5 are its other two roots.
So, its other two roots are 2 + i and + √5
Rewrite, using the distributive
property.
16b-8b = ([?]-8)b = [?]b
Answer:
8b
Step-by-step explanation:
You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:
\(\displaystyle{16b-8b=\left(16-8\right)b}\)
Then evaluate and simplify:
\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)
PLEASE HELP ME THIS IS MOST OF MY GRADE. I PUT 100 POINTS. SERIOUS ANSWERS ONLY. I WILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
hehe good luck loser T^T
Answer:
1. Cheese burger, French fries (regular), Ice cream (regular), any of the beverages.
2. Fried Chicken, Macaroni soup, Mango pie, any of the beverages.
3. Cheese burger, French fries (regular), Ice cream (regular), any of the beverages, because, there are going to be 40 guests and that are a lot of people to feed so I would rather spend more money than on some random people who come to my 2 year old son.
4. PhP 222.2 repeated
Step-by-step explanation:
Which sentence represents the following inequality?
9(x+3) < 6x – 12
A. Nine times the sum of a number and three is less
than six times the same number decreased by
twelve.
B. The product of nine and a number increased by
three is less than the product of six and the same
number decreased by twelve.
C. Nine multiplied by the sum of a number and
three is greater than the product of six and the
Answer:
A is correctStep-by-step explanation:
Given
9(x+3) < 6x – 12Answer choices:
A. Nine times the sum of a number and three is less than six times the same number decreased by twelve.
9(x + 3) < 6x - 12CorrectB. The product of nine and a number increased by three is less than the product of six and the same number decreased by twelve.
9x + 3 < 6x - 12 WrongC. Nine multiplied by the sum of a number and three is greater than the product of six and the ...
9(x + 3) > 6x ...The last choice is incomplete but is wrong anyway by saying "greater"Combine like terms to create an equivalent expression. Enter any coefficients as simplified proper or improper fractions or integers.
-2/3a + 5/6a - 1/6
Answer:1/6a-1/6
Step-by-step explanation:
i did it on khan academy
HELP ASAP PLEASE
What translation is made from f(x) = x to f(x) = (x + 3).
translation 3 units to the left
translation 3 units up
translation 3 units down
translation 3 units to the right
Answer:
3 to the left
Step-by-step explanation:
if it is the brackets it affects X and it usually is the opposite so if shown plus then it means to the left/ means minus
Answer:
translation 3 units up
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Then
f(x) = x + 3
represents a translation of 3 units up
Let f x = 2x + 6 and g x = 4x - 3
Answer:
\(g=\frac{9}{2}, \\x=-6\)
Step-by-step explanation:
1/5 de los animales en el zoológico son monos 5/7 de los monos son machos
¿Qué fracción de los animales en el zoológico son monos machos?
1/7 of the animals in the zoo are male monkeys.
What fraction of the animals in the zoo are male monkeys? Explain with workings.
To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.
Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:
= 1/5
= 5/25.
And 5/7 of the monkeys are male which is written as 5/7.
To get fraction of male monkeys, we will multiply these two fractions:
= (5/25) * (5/7)
= 25/175
= 1/7.
Full question:
1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?
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write each equation in vertex form. then identify the vertex, axis of symmetry and direction of opening. y=x^2+8x+\:18 , y=-\:x^2\:\:12x\:-\:36 and y=2x^2\:+\:12x\:+\:13
The equation in vertex form is y = 2(x+3)² + 1. The vertex is (-3,1), the axis of symmetry is x = -3, and the direction of opening is upwards.
The vertex form of the equation is y = a(x-h)^2 + k, where (h, k) is the vertex. The axis of symmetry is x = h, and the direction of opening is determined by the value of a.
Using this formula, let us write each equation in vertex form and then identify the vertex, axis of symmetry, and direction of opening.
1. y = x² + 8x + 18
To write this equation in vertex form, we need to complete the square. y = x² + 8x + 18 is equivalent to y = (x+4)² - 2. Therefore, the equation in vertex form is y = (x+4)² - 2.
The vertex is (-4,-2), the axis of symmetry is x = -4, and the direction of opening is upwards.2
. y = -x² - 12x - 36To write this equation in vertex form, we need to complete the square. y = -x² - 12x - 36 is equivalent to y = -(x+6)² - 12. Therefore, the equation in vertex form is y = -(x+6)² - 12.
The vertex is (-6,-12), the axis of symmetry is x = -6, and the direction of opening is downwards.3. y = 2x² + 12x + 13To write this equation in vertex form, we need to complete the square. y = 2x² + 12x + 13 is equivalent to y = 2(x+3)² + 1.
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How do you calculate the x-intercept of a line written in Standard Form?
1. Solve for the unknown in each triangle. Round each answer to the nearest tenth.
The values of the missing sides are;
a. x = 35. 6 degrees
b. x = 15
c. x = 22. 7 ft
d. x = 31. 7 degrees
How to determine the valuesTo determine the values, we have;
a. Using the tangent identity;
tan x = 5/7
Divide the values
tan x = 0. 7143
x = 35. 6 degrees
b. Using the Pythagorean theorem
x² = 9² + 12²
find the square
x² = 225
x = 15
c. Using the sine identity
sin 29= 11/x
cross multiply the values
x = 11/0. 4848
x = 22. 7 ft
d. sin x = 3.1/5.9
sin x = 0. 5254
x = 31. 7 degrees
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A hockey player gets 2 goals for every 13 shots. At this rate, how many goals will he make if he
takes 39 shots?
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
2×3=6
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The probability Bob guesses the winner of a certain baseball game is 4/5. The probability Joe independently guesses the winner of another game is 1/3. What is the probability that exactly one of them selects the winner? (Fraction answer)
SANA ALL SMART HAHAHAHHAAHHAHAAHA
Melissa obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 16%. Her loan is for $15,400 for 93 days. Assume each day is 365 of a year. Answer each part below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find the interest that will be owed after 93 days. XS ? (b) Assurning Melissa doesn't make any payments, find the amount owed after 93 days
To calculate the interest owed after 93 days, we use the formula for simple interest: Interest = Principal x Rate x Time. Substituting the given values, the interest amounts to $624.49.
This is the total interest that Melissa will owe to the bank after 93 days.Melissa took out a loan of $15,400 from a bank for home renovations. The bank charges a simple interest rate of 16% per year If Melissa doesn't make any payments towards the loan, the total amount owed after 93 days is obtained by adding the principal and the interest together.
Therefore, the total amount owed would be $16,024.49. This means that if Melissa does not make any payments during the 93-day period, her loan balance will increase to approximately $16,024.49, including both the original principal amount and the accrued interest.
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H(d) models the basketball's height (in meters) at a horizontal distance of dd meters from Kaori. What does the statement H(R)=4H(R)=4 mean
The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.
It is given that Kaori is taking a free-throw. H(d) models the basketball's height (in meters) at a horizontal distance of d meters from Kaori.
The given statement is H(R) = 4H.
Here we have H(R) instead of H(d) and it shows the height of basketball. So it clear that the height of basketball's is 4H because H(R)=4H at d = R
Since d represents the horizontal distance from Kaori, therefore the horizontal distance from Kaori is R.
Thus, Answer: The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.
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x^2+y^2+34y=-64
use the equation to find the completed square and perfect for the x and y values
The completed square and perfect square form of the equation \(x^2 + y^2 + 34y = -64\) is \(x^2 + (y + 17)^2 = 225.\) the equation represents a circle centered at (0, -17) with a radius of 15
To complete the square and write the equation in perfect square form, let's rearrange the given equation:
\(x^2 + y^2 + 34y = -64\)
First, we focus on completing the square for the y terms. To do this, we need to add and subtract a value that allows us to create a perfect square trinomial. The coefficient of y is 34, so we add \((34/2)^2 = 17^2 = 289\) to both sides of the equation:
\(x^2 + y^2 + 34y + 289 = -64 + 289\)
Simplifying the right side:
\(x^2 + y^2 + 34y + 289 = 225\)
Now, we can rewrite the left side of the equation as a perfect square:
\(x^2 + (y + 17)^2 = 225\)
The equation is now in completed square and perfect square form. The x term remains unchanged, while the y term is now written as \((y + 17)^2\).
The completed square and perfect square form of the equation \(x^2 + y^2 + 34y = -64\)is \(x^2 + (y + 17)^2 = 225.\)
In the completed square form, the equation represents a circle centered at (0, -17) with a radius of 15. This is because the equation of a circle centered at (h, k) with a radius r is given by \((x - h)^2 + (y - k)^2 = r^2.\)Comparing this with the completed square form of the given equation, we can identify the center of the circle as (0, -17) and the radius as 15. The equation\(x^2 + (y + 17)^2 = 225\) represents a circle with its center at the origin and a radius of 15.
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The cost of 8 pencils plus tax of $0.10 is $2.15. Write an equation that models the
situation?
Answer:
The answer should be 8x+0.10=2.15
2xy' y = 6x, x > 0, y(4) = 22
The value of y when x=4 is 24. However, the given value of y is 22, so the answer is incorrect
The given equation is written in slope-intercept form as y=6x. This is a linear equation where 'y' is a function of 'x', and the slope is 6.
To calculate the value of y when x=4, first substitute the value of x in the given equation.
y = 6x
= 6 x 4
= 24
Therefore, the value of y when x=4 is 24. However, the given value of y is 22, so the answer is incorrect.
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If you invest $200 at an interest rate of 10%, how much money will you have after three years?
See picture to answer!
Using the law of cosines, it is found that the length of side AB is of AB = 13.
What is the law of cosines?The law of cosines states that we can find the angle C of a triangle as follows:
\(c^2 = a^2 + b^2 - 2ab\cos{C}\)
in which:
c is the length of the side opposite to angle C.a and b are the lengths of the other sides.For this problem, the parameters are:
C = 120, a = 8, b = 7.
Hence:
\(c^2 = a^2 + b^2 - 2ab\cos{C}\)
\(c^2 = 8^2 + 7^2 - 2(8)(7)\cos{120^\circ}\)
\(c^2 = 169\)
\(c = \sqrt{169}\)
c = 13.
Hence AB = 13.
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Tony has a rectangular piece of cardboard that will have congruent squares removed from its corners with a length of 3 inches. The length of the piece of cardboard is four times larger than its width. Tony also know that the volume of the box he is able to create from this piece of cardboard is 336 cubic inches. What are the dimension of this box?
The dimensions of the box are given as follows:
Length of 3 inches.Width of 0.75 inches.Height of 149.3 inches.How to obtain the volume of the rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:
Volume = length x width x height.
The parameters for this problem are given as follows:
Length of 3 inches.Width of 1/4 x 3 = 0.75 inches.Volume of 336 cubic inches.Hence the height of the cardboard is given as follows:
3 x 0.75 x h = 336
h = 336/(3 x 0.75)
h = 149.3 inches.
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A rectangular pane of glass measuring 12 inches by 18 inches is
siirrounded by a wooden frame that is 2 inches wide. What is the distance
around the window, including the frame? *
our answer
The area of the window frame will be 136 square inches.
What is the area of the rectangle?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
Given that a rectangular pane of glass measuring 12 inches by 18 inches is surrounded by a wooden frame that is 2 inches wide.
The area of the rectangular window will be calculated as below:-
Area of window = Area of outer layer - Area of the inner layer
Area of window = 22 x 16 - 18 x 12
Area of window = 352 - 216
Area of window = 136 square inches
Therefore, the area of the window frame will be 136 square inches.
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b. a new ground-approach radar system approved by the federal aviation administration is being considered as a means of reducing congestion. under this system, planes can be processed at a constant rate of 15 per hour (i.e., the variance is zero). what would be the expected number of airplanes circling the airport, waiting in queue for clearance to land, if this system were to be used?
The expected number of airplanes circling the airport, waiting in queue for clearance to land, if this new radar system were to be used is zero.
The new radar system is being considered as a means of reducing congestion, which implies that there is currently an issue with congestion at the airport. One way to reduce congestion is to process planes at a faster rate, which is exactly what the new radar system aims to do.
The statement "planes can be processed at a constant rate of 15 per hour (i.e., the variance is zero)" indicates that the system is able to process planes at a consistent rate of 15 per hour, with no variation in this rate. This means that there should be no planes waiting in queue for clearance to land, as they can all be processed at the constant rate of 15 per hour. Therefore, the expected number of airplanes circling the airport and waiting in queue for clearance to land is zero.
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Time (hours) 2 4 6 8
Distance (miles) 8 16 24 32
Is the linear relationship also proportional? Explain.
Yes, the constant of proportionality is 4.
Yes, there is no constant of proportionality.
No, the constant of proportionality is 4.
No, there is no constant of proportionality.
The linear relationship between time and distance can be considered proportional. The constant of proportionality in this case is 4.
In a proportional relationship, the ratio between the two quantities remains constant. Here, as time increases by 2 hours, the distance also increases by 8 miles. Let's calculate the ratio of distance to time for each pair of values:
For the first pair (2 hours, 8 miles):
Ratio = distance / time = 8 miles / 2 hours = 4 miles/hour
For the second pair (4 hours, 16 miles):
Ratio = distance / time = 16 miles / 4 hours = 4 miles/hour
For the third pair (6 hours, 24 miles):
Ratio = distance / time = 24 miles / 6 hours = 4 miles/hour
For the fourth pair (8 hours, 32 miles):
Ratio = distance / time = 32 miles / 8 hours = 4 miles/hour
As we can see, the ratio of distance to time remains constant at 4 miles per hour for all the pairs. This indicates a proportional relationship between time and distance.
Therefore, the linear relationship is also proportional, and the constant of proportionality is 4.
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