Answer:
The lengths of the other sides would be 10, as well.
Step-by-step explanation:
Since we already know two of the three angles, we can subtract to find the other angle. The interior angles of a triangle will always add up to 180°. We have 60° and 60°, giving us 120°. 180 - 120 is equal to 60°, so that's the missing angle. Because all of the angles are the same, this is an equilateral triangle, which means the sides also have to be the same length. If one of the sides is 10, all of the sides are 10.
The triangle with sides 10 , 10 and 10 and all angles at 60° is an equilateral triangle
What is an Equilateral Triangle?An equilateral triangle is a triangle in which all three sides have the same length.
Let the triangle be ΔABC , and
∠A = ∠B = ∠C = 60° and AB = BC = CA
Given data ,
Let the triangle be represented as ΔABC
Let the side length of the triangle be AB = 10
Now , the measure of ∠ABC = 60°
And , the measure of ∠BAC = 60°
So , the total sum of all the angles in a triangle = 180°
And , the measure of ∠ACB = 180° - ( 60° + 60° ) = 60°
Therefore , all the angles of the triangle are 60°
So , it is an equilateral triangle
And , the measure of side lengths of the triangle is 10
Therefore , AB = BC = CA = 10
Hence , it is an equilateral triangle
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6. Find an angle which is equal to its complement.
Answer:
x= 45
Step-by-step explanation:
Complementary angles equal 90 degrees
The angles are equal
x+x = 90
2x= 90
Divide by 2
2x/2 = 90/2
x= 45
Find the square roots of these numbers by division method.
a-6090
Can some one help please
Answer: [tex]\fbox{C} \: \: \: \dfrac{4 \times 10^{4} }{3 \times 10^{4} }[/tex]
Step-by-step explanation:
36,070 = 3.607 · 10⁴ ≈ 4 · 10⁴
29,029 = 2.9029 · 10⁴ ≈ 3 · 10⁴
Let's how manytimes greater the distance to the bottom of Challenger Deep is than the distance to the top of Mount Everest:
[tex]\dfrac{4 \times 10^{4} }{3 \times 10^{4} }[/tex]
Answer:
C
Step-by-step explanation:
First, the question is asking how many times greater the distance to the Challenger Deep is compared to Mount Everest. This means that the Challenger Deep will be on top, with the distance to Mount Everest on the bottom.
Next, we can see that in our answers, we are only given one significant digit. This means that we have to round our original numbers to the nearest significant digit and work from there. For Challenger Deep, 36,070 must be rounded to the nearest ten thousandth as it is in the ten thousands. Therefore, it must be rounded to 40,000 or 30,000. As 36,070 is closer to 40,000 than 30,000 (we can tell this because the second number, 6, is greater than 5, so we round up), we can represent this as 40,000. For Mount Everest, we can round 29,029 to either 20,000 or 30,000. 30,000 is the appropriate choice here because 9, the second number, is greater than 5.
Therefore, our ratio is now 40,000 / 30,000 . Our answers are written in scientific notation, so we must convert our numbers to those values.
Let's start with 40,000 . Our one significant digit is 4, so we can write this as 4 * something. For each number in 10 to the power of x (x is a placeholder value), we add x amount of zeros. For example, for 4 * 10², we add 2 zeros, making it 400. There are 4 zeros here, so to write this in scientific notation, we have 4 * 10^4
Similarly, for 30,000 , we can write this as 3 * 10^4 as there are 4 zeros.
Our ratio is thus 40,000 = 4*10^4 , which is the Challenger Deep value rounded, over 30,000 = 3 * 10^4, which is the Mount Everest value rounded. We can write this as [tex]\frac{4*10^{4}}{3*10^{4}}[/tex], or C
Step by step solution please
Answer: A, C, D
Step-by-step explanation:
To find which logarith simplifies to 2, we first need to know how they work.
We now know that [tex]log_a(a^x)=x[/tex].
This tells us that only A, C, D would work.
[tex]8^2=64\\ \\6^2=36\\\\10^2=100[/tex]
Note: whenever you have a log that doesn;t specify the base, it is always 10, as shown in D.
Determine whether the following polygons are similar.
Answer:
The polygons are NOT similar. The ratio of 12 to 18 equals 2 to 3, and the ratio of 26 to 32 equals 13 to 16. They're not the same, thus not similar.
Answer:
They are not similar, and the instructions says to put "None" otherwise, so...
Step-by-step explanation:
You can find this by dividing 32 by 16 to get something like 1.7777....
and dividing 26 by 12 should give the same ratio if they are similar, but it gives something like 2.1666...
Therefore they are not similar.
Congruent means two or more shapes are the same size and are similar, but for some things to be similar means that they have the same ratio, but not necessarily the same dimensions.
The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure.
Answer:
8/12 or 2/3
Where the first number is on the top and vice versa.
Step-by-step explanation:
what is the HCF of 7 and 13
Please help explanation if possible
Answer:
y = | x-5|
Step-by-step explanation:
y = |x-h| +k where (h,k) is the center of the "v"
The "v" is located at (5,) so h=5 and k = 0
y = | x-5| +0
Find the domain for the rational function f(x)=x+1/x-2
Step-by-step explanation:
here's the answer to your question
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE QUESTION!!
Answer:
(base x height x length)/2 = volume
6x8x8 = 384/2 = 192in^3
hope that answers your question
what is the intrest of rs2160 at the rate of 20% for 4years?in how many years will rs1800earn the same intrest at the rate of 12%
Answer:
considering it was simple interest,
We have the formula:
I = PRT ÷ 100
where,
I = InterestP = principalT = time (in years)R = ratefor the first part of the question,
P = Rs. 2160R = 20T = 4Thus, I = (2160 × 20 × 4)÷ 100
I = Rs. 1728
Now, for the second part,
P = Rs. 1800I = 1728R = 12T = 100×I÷PR
T = 100 × 1728÷(1800 × 12)
T = 8 Years
In Exercises 1-4, determine whether the dilated figure or the original figure is closer to the center of dilation. Use the given location of the center of dilation and scale factor k.
1. Center of dilation inside the figure; k = 3
Center of ditation inside the figure, k = 1/2
3. Center of dilation outside the figure: = 120%
4. Center of dilation outside the figure; k = 0.1
When the Center of dilation is inside the figure
The original figure is closer to the center of dilationThe dilated figure is closer to the the center of dilationWhen the Center of dilation is outside the figure
3. The original figure is closer to the the center of dilation
4. The dilated figure is closer to the center of dilation
The center of dilation is the fixed point from which the distances in a dilation are measured
The scale factor is ratio of the side lengths of an original figure or preimage to the side lengths of the newly formed image
Center of dilation is inside the figure
Where the center of dilation is inside the figure, and the scale factor is larger than 1, k = 3 > 1, we have;The distance of a point on the dilated figure, including the distances from the center of dilation is 3 times the distances of points on the original image from the center of dilation
Therefore, the original figure has a shorter distance to and is therefore closer to the the center of dilation than the dilated figure
2. Where the center of dilation is inside the figure, and the scale factor is a fraction between 0 and 1 k = 1/2, we have;
The distance of a point on the dilated figure, including the distances from the center of dilation is 1/2 times the distances of points on the original image from the center of dilation
Therefore, the dilated figure has a shorter distance to and is therefore closer to the the center of dilation than the original figure
Center of dilation outside the figure
3. Given that the center of dilation is outside the figure and the scale factor is larger than 1, k = 120% = 120/100 = 1.2 > 1, we have;
The distance of the dilated figure from the center of dilation is 120% of the distance of the original figure from the center of dilation, therefore, the original figure is closer to the the center of dilation than the dilated figure
4. Where the center of dilation is outside the figure and the scale factor is a fraction between 0 and 1, k = 0.1 < 1
The distance of the dilated figure from the center of dilation is only 0.1 times the distance of the original figure from the center of dilation, and therefore, the dilated figure is closer to the center of dilation
Learn more about scale factors and center of dilation here;
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Reflect Triangle ABC in BC. What kind of figure will result? How would your answer change if ABC is isosceles? a right triangle with right angle at A? a right isosceles trianglewith right angle at A?
9514 1404 393
Answer:
a kitea kite or rhombus, dependinga kitea squareStep-by-step explanation:
The reflections are illustrated in the attached.
A1, A1' are opposite vertices of the reflected original triangle. They are part of a kite figure.
A2, A2' are opposite vertices of a reflected isosceles triangle, where BA=BC. Figure A2BA2'C is a kite.
A2a, A2a' are opposite vertices of a reflected isosceles triangle with AB=AC. Figure A2aBA2a'C is a rhombus.
A3, A3' are opposite vertices of a right triangle with the right angle at A3. Figure A3BA3'C is a kite figure.
A4, A4' are opposite vertices of a reflected right isosceles triangle with AB=AC and the right angle at A4. Figure A4BA4'C is a square.
Need help!
.......................
Answer:
[tex]24x^{3} \sqrt{5x} -4x^{3} \sqrt{10x}[/tex]
Step-by-step explanation:
[tex]2\sqrt{8x^{3} } (3\sqrt{10x^{4} } -x\sqrt{5x^{2} } )[/tex]
[tex]=2.2x\sqrt{2x} (3x^{2} \sqrt{10} -x^{2} \sqrt{5} )[/tex]
[tex]=4x\sqrt{2x} (3x^{2} \sqrt{10} -x^{2} \sqrt{5} )[/tex]
[tex]=12x^{3} \sqrt{2xx10} -4x^{3} \sqrt{2xx5}[/tex]
[tex]=24x^{3} \sqrt{5x} -4x^{3} \sqrt{10x}[/tex]
OAmalOHopeO
Simplify
1/4(1 - 2/3)* + 1/3
Enter your answer in the box as a fraction in simplest form
Answer:
5/12
frsjnjjuvvffklomjyyrx
What is the average rate of change for this quadratic function for the interval
from x = 3 to X = 5?
Answer:
4
Step-by-step explanation:
average = mean of the data
(3 +5)/2
=8/2
=4
Answer:
8
Step-by-step explanation:
f(x2) -f(x1)
---------------
x2-x1
x2 = -3 and x1 = -5
Does anyone know how to do this? IM2 Honors
help! please!!!!!! look at photo :))
Hey there!
We know that Danielle earns $10 per hour, so muliply that by 3 and get 30.
Because Danielle works an extra half an hour, divide 10 by 2 and get 5.
Danielle earns $35 in 3 hours and a half.
Hope this helps! Please mark me as brainliest!
Have a wonderful day :)
For the triangle shown, what are the values of x and y?
60°
30°
6
Select the correct answer.
O x = 2V3, y = 473
O x= 3V3, y = 6/3
O x = 6/3, y = 12
O x = 6V3, y = 1273
Answer:
x = 6/√3 = 2√3
y = 2×2√3 = 4√3
So, 1st option is correct
What is the radius of a hemisphere with a volume of 885 in^3, to the nearest tenth of
an inch?
Answer:
The desired radius is r = 7.5 inches
Step-by-step explanation:
The formula for the volume of a sphere of radius r is V = (4/3)πr³. A hemisphere is half a full sphere, so the formula for the volume of a hemisphere of radius r is (4/3)(1/2)πr³, or (2/3)πr³.
We know that the volume of the hemisphere is 885 in³:
885 in³ = (2/3)πr³ and need to solve this first for r³ and then for r.
This is equivalent to:
885 in³ = (2π/3)r³.
We can now isolate r³ by multiplying both sides of this equation by (3 / [2π]):
(3 / [2π])(885 in³) = (3 / [2π])(2π/3)r³ = r³
Then r³ = 422.556 in³
Finally, we find the desired hemisphere radius by taking the cube root of both sides of the above equation:
r = ∛(422.556 in³) = 7.5 in (which is to the nearest tenth of an inch)
The desired radius is r = 7.5 inches
In the rhombus, m angle 1 equals 106. What are m angles 2 and 3?
Answer:
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+320I am really confused on the graph anyone mind helping me
gabys piggy bank contains nickles and dimes worth $5.15. If she has 66 coins in all, how many of each does she have
8.18
Step-by-step explanation:
8.18
pow pom wyh oqhw uwhwn 8.18 ge wk
Answer:
37 Dimes, 29 Nickels
Step-by-step explanation:
x= dimes
66-x = nickels
.1 (x) = dimes
.05 (66-x) = nickels
Solve
3.3 + 0.5x = 5.15
Solve again then you come out with
x= 37
66 - 37 = 29
What is the product of three and the opposite is 4?
Product is multiplication.
The opposite of 4 is -4
3 x -4 = -12
Answer: -12
How do I solve this: h + 6/5 = 2
help me please brainliest for the best answer!!
Answer:
The volume of the irregular figure would be 102 [tex]cm^3[/tex].
Step-by-step explanation:
If you wish to make the process of calculating the volume easier, you can picture the irregular figure as two rectangular prisms: the large one on the bottom, and the smaller one appearing to protrude from the prism below it. Using this method, you only need to find the volumes of the two rectangular prisms and add the values together to get the volume for the irregular figure. The formula used to find the volume of a rectangular prism is [tex]l*w*h[/tex], where [tex]l[/tex], [tex]w[/tex], and [tex]h[/tex], represents the length, width, and height of the rectangular prism respectively. Using the formula above, the volume of the larger rectangular prism would be [tex]6*3*5=30*3=90 cm^3[/tex], and the volume of the smaller rectangular prism would be [tex]3*2*2=6*2=12 cm^3[/tex]. So the volume of the entire irregular figure would be [tex]90+12=102 cm^3[/tex].
Answer:
102
Step-by-step explanation:
Large rectangle:
6 × 3 × 5 = 18 × 5 = 90
Small rectangle:
7 - 5 = 2
3 × 2 × 2 = 6 × 2 = 12
90 + 12 = 102
Hope this helped.
The value of -48 - x is positive. What are two possible values of x?
Show your work.
Please help I will give you Brainlyest
Answer:
-49
-50
Step-by-step explanation:
When a negative number subtracts another negative number, the number becomes positive.
For example: -48-(-49)=1
-48-(-49) becomes -48+49=1
.simplify
(2a+5)²-(a+3)(a-3)
Answer:
3a^2 + 20a + 34
Step-by-step explanation:
(2a + 5)^2 = 4a^2 + 20a + 25
(a +3)(a - 3) = a^2 - 9
Put these two partial answers together.
4a^2 + 20a + 25 -(a^2 -9 ) Remove the brackets.
4a^2 + 20a + 25 - a^2 + 9
4a^2 + 20a + 25 - a^2 + 9
3a^2 + 20a + 34
Answer: 3a² + 20a + 34
Concept:
When doing simplifying expressions, following the PEMDAS method would be easier.
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionWhen expanding parentheses, following the FOIL method would be easier.
FirstOuterInner LastSolve:
Given expression
(2a + 5)² - (a + 3) (a - 3)
Simplify exponenets
= (2a + 5) (2a + 5) - (a + 3) (a - 3)
Expand parentheses
= 4a² + 10a + 10a + 25 - (a² - 3a + 3a - 9)
= 4a² + 10a + 10a + 25 - a² + 3a - 3a + 9
Combine like terms
= 4a² - a² + 10a + 10a + 3a - 3a + 25 + 9
= 3a² + 20a + 34
Hope this helps!! :)
Please let me know if you have any questions
Charlene is a salesperson. Let y represent her total pay (in dollars). Let x represent the number of
items she sells. Suppose that x and y are related by the equation y=32x + 1900.
What is Charlene's total pay if she doesn't sell any items?
A. $32
B. $1,900
C. $3,200
D. $19
Which functions have a maximum value greater than the maximum of the function g(x) = -(x + 3)2 - 4?
Answer:
max: -4
Step-by-step explanation:
(x+3)^2 》0 mọi x
<=> -(x+3)^2 《0
<=> -(x+3)^2 -4 《 -4
