Answers
=============================================================
Explanation:
a = 26 and b = 26 are the congruent legs
angle C = 60 degrees is between sides 'a' and b
c = unknown base which is opposite angle C
We'll use the law of cosines to find this missing side.
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 26^2 + 26^2 - 2*26*26*cos(60)
c^2 = 676
c = sqrt(676)
c = 26
It turns out that all three sides are the same length (26), which means this isosceles triangle is really equilateral. Consequently, it means all three interior angles are 60 degrees each.
---------------
Here's another way to see why we have an equilateral triangle.
The vertex angle is 60 degrees. Let x be the measure of each base angle. Those two base angles add to the 60 degrees to get 180
x+x+60 = 180
2x+60 = 180
2x = 180-60
2x = 120
x = 120/2
x = 60
Each base angle is 60 degrees, so all three angles are 60 degrees. This points us to the triangle being equilateral and we can say all three sides are 26 units long.
If we didn't have an equilateral triangle, then we'd have no choice but to use the law of cosines mentioned earlier.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:base \:\:side = 26 \:\: units [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
As the two sides of the triangle are equal, the corresponding angles opposite to the the sides are equal as well.
[tex] \textsf{let each of those angles measure ' x ' } [/tex]
[tex]\qquad \tt \rightarrow \:x + x + 60 = 180[/tex]
[ sum of all interior angles of a triangle ]
[tex]\qquad \tt \rightarrow \:2x + 60 = 180[/tex]
[tex]\qquad \tt \rightarrow \:2x = 180 - 60[/tex]
[tex]\qquad \tt \rightarrow \:2x = 120[/tex]
[tex]\qquad \tt \rightarrow \:x = \cfrac{120}{2} [/tex]
[tex]\qquad \tt \rightarrow \:x = 60 \degree[/tex]
Therefore, all angles of the triangle are equal. that being the case we can conclude that it's an equilateral triangle.
henceforth, all its sides are equal to one another.
[tex]\qquad \tt \rightarrow \:base \: \: side = \: \: 26 \: \: units[/tex]
Related Questions
solve for 2.5w+12 on a graph
Answers
x-intercept -4.8
y-intercept 12
slope 2.5
plot points
x y
-2, 7
-1, 9.5
0, 12
1, 14.5
2 ,17
y-intercept 12
slope 2.5
plot points
X y
-2.7
-1.9.5
0, 12
1.145
2,17
Carl scored a total of 24 points by making 6 two-point baskets and some three-point baskets. Which equation can be used to find the number of three-pointers he scored, and how many three-point shots did Carl score?
A. 3p + 12 = 24
Carl made 12 three-point baskets.
B. 3p + 12 = 24
Carl made 4 three-point baskets.
C. p + 6 = 24
Carl made 18 three-point baskets.
D. p + 6 = 24
Carl made 30 three-point baskets.
Answers
Answer:
A.3p+12=24
Step-by-step explanation:
carl Made 12 three-pint baskets.
Which of the following best describes how the y values are changing over each interval?
X
y
1
4
2
8
3
12
4
16
5
20
They are increasing by 4 each time.
O They are increasing by 6 each time.
O They are being multiplied by 2 each time.
O They are being multiplied by 4 each time
Answers
Answer:
y=ax+b
a=-0.6020457867
b=-2.256697516 <------- There is your value for b, which is the answer to the problem.
You can use these values for a and b to generate an equation in slope-intercept form, which you can then enter under Y= and view the graph.
Step-by-step explanation:
The value of y is multiplied by 2 each time when the value of x increases by 1 and this can be determined by using the arithmetic operations.
What is an mathematical expression?Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.
Given that,
Table -- x y
1 20
2 40
3 80
4 160
5 320
The following steps can be used in order to describe how the y values are changed over each interval:
Step 1 - When value of (x = 1) and the value of (y = 20).
Step 2 - When value of (x = 2) and the value of (y = 40).
Step 3 - When value of (x = 3) and the value of (y = 80).
Step 4 - When value of (x = 4) and the value of (y = 160).
Step 5 - From the above steps, it can be concluded that the value of y is multiplied by 2 each time when the value of x increases by 1.
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Find the tables with unit rates greater than the unit rate in the graph then arrange these tables in order from least to greatest unit rate
Answers
Table 3,4,5,6,7 has a greater value of the unit rate than the unit rate of the graph.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The unit rate of the graph is;
[tex]r_g = \frac{26-0}{14-0} \\\\ r_g = \frac{13}{7} \\\\ r_g = 1.857[/tex]
The unit rate for the given tables;
[tex]\rm r_1 = \frac{26-13}{14-7}\\\\ r_1 = \frac{13}{7} \\\\ r_1 = 1.857[/tex]
[tex]\rm r_2 = \frac{26-13}{14-7} \\\\ r_2 = \frac{9}{5} \\\\ r_2 = 1.8 < 1.818[/tex]
[tex]r_3 = \frac{34-17}{18-9} \\\\r_3 = \frac{17}{9} \\\\ r_3 = 1.889 > 1.818[/tex]
[tex]\rm r_4 = \frac{42-21}{22-11} \\\\ r_4 = \frac{21}{11} \\\\ r_4 = 1.909 > 1.818[/tex]
[tex]\rm r_5 = \frac{38-19}{20-10} \\\\ r_5 = \frac{19}{10}\\\\ r_ 5 = 1.9 > 1.818[/tex]
[tex]\rm r_6 = \frac{50-25}{26-13} \\\\ r_6 = \frac{25}{13} \\\\ r_6 = 1.923 > 1.818[/tex]
[tex]r_ 7 = \frac{46-23}{24-12} \\\\ r_7 = \frac{23}{12} \\\\r_7 = 1.917 > 1.818[/tex]
Hence, table 3,4,5,6,7 has a greater value of the unit rate than the unit rate of the graph.
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Which of the following is most likely the next step in the series?
Answers
Answer:
I think the answer is B
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answers
the y-intercept is (0,6)
Which of the following is the missing justification?
picture is provided
Answers
Subtraction property of equality
====================================================
Explanation:
Let's say we started with the equation a = b
Subtract c from both sides to get a-c = b-c
This is the subtraction property of equality
-----------------
Example:
x+5 = 12
x+5-5 = 12-5 ... using the subtraction property of equality
x+0 = 7
x = 7
------------------
For this current problem, we're subtracting 3 from both sides in the second step.
A very closely related property is the addition property of equality where we add the same thing to both sides.
Technically we could add -3 to both sides to get the same task done in the second step. But the subtraction property is more direct and straight-forward in my opinion.
What is the slope of a line that is perpendicular to the line y = -1/2x+5
-2
-1/2
1/2
2
Answers
Step-by-step explanation:
please mark me as brainlest
Answer:
slope = 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x + 5 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2
Which values of x will make the expression
0-3
0-2
0
02
3
6x²-54
5x²-20
equal to 0? Select two options.
Answers
Answer:
3 and -3
Step-by-step explanation:
Which ordered pair would form a proportional relationship with the point graphed below?
On a coordinate plane, a line goes through points (0, 0), (10, 40) and (negative 10, negative 40).
(40, 10)
(–5, –10)
(5, 20)
(–10, –20)
Answers
Answer:
(5, 20)
Step-by-step explanation:
Answer? Having trouble understanding this question
Answers
Answer:
[tex]\frac{k+5}{k-2}[/tex]
Step-by-step explanation:
[tex]\frac{1-\frac{25}{k^2} }{1-\frac{7}{k}+\frac{10}{k^2} }[/tex]
multiply numerator and denominator by k² to eliminate fractions
= [tex]\frac{k^2-25}{k^2-7k+10}[/tex] ← factor numerator and denominator
------------------------------
k² - 25 ← is a difference of squares
= (k - 5)(k + 5)
k² - 7k + 10
= (k - 5)(k - 2)
------------------------------
= [tex]\frac{(k-5)(k+5)}{(k-5)(k-2)}[/tex] ← cancel (x - 5) on numerator / denominator
= [tex]\frac{k+5}{k-2}[/tex]
It was reported that uninsured drivers caused 1 in 20 accidents. About 682,494 car crashes were reported. About how many of these drivers were uninsured?
Answers
30 POINTS PLEASE HURRY
Jonathan and Kevin each rewrote and evaluated the expression (SEE PICTURE BELOW) They arrived at different answers.
Answers
Answer:
B. took test
Step-by-step explanation:
Answer:
B. Jonathan is correct. Kevin made an error at step 3.
Step-by-step explanation:
8
the probability that a biased coin lands on heads is 0.47
13
the probability that a biased dice lands on an even number is
20
samira flips the coin and rolls the dice.
find the probability that the coin lands on tails and the dice
lands on an even number.
Answers
The probability that the coin lands on tails and the dice lands on an even number is 0.3455
How to determine the probability?Let A represents a biased coin lands on heads and B represents a biased dice lands on an even number
So, we have:
P(A) = 0.47
P(B) = 13/20
The required probability is:
P(A' and B) = P(A) * P(B)
This gives
P('A and B) = (1 - 0.47) * 13/20
Evaluate
P('A and B) = 0.3455
Hence, the probability that the coin lands on tails and the dice lands on an even number is 0.3455
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Determine if the lines through each set of ordered pairs are parallel, perpendicular, or neither. Explain your answer. Ordered pairs: (8, 3) (-2, 5) and (-2, -5) (-1, -10)
Answers
The lines through each set of ordered pairs are neither parallel nor perpendicular.
How to determine the relationship?The ordered pairs are given as:
(8, 3) (-2, 5) and (-2, -5) (-1, -10)
Start by calculating the slope (m) using:
m = (y2 - y1)/(x2 - x1)
For the first pair, we have:
m = (5 - 3)/(-2 - 8)
m = -1/5
For the second pair, we have:
m = (-10 + 5)/(-1 + 2)
m = -5
Both slopes are not equal, so they are not parallel
Also, both slopes are not opposite reciprocals, so they are not perpendicular.
Hence, the lines through each set of ordered pairs are neither parallel nor perpendicular.
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can anybody help meee
Answers
Answer:
a.) f(2) = 3
b.) if f(x) = 2
x=3
Step-by-step explanation:
Here you must notice that on the graph where x is 2, y or f(x) is at 3. This means that the answer where in the function of x, where the input 2, the output or y/f(x) is 3
And if the output is 2, the input is 3 as proven above.
PLEASE HELP ASAP
If "x" varies directly with "y," and
x = -19 when y = 14, what is
"x" when y = 2?
Enter the number that belongs in the green box.
Reduce to simplest form.
X = -
Notice that the negative sign has already been entered.
Answers
The value of x when y = 2 is -19/7
How to solve for x?A direct variation from x to y is represented as:
x = ky
Where k represents the variation constant.
x = -19 when y = 14.
So, we have:
-19 = 14k
Make k the subject
k = -19/14
Substitute k = -19/14 in x = ky
x = -19y/14
When y = 2, we have:
x = -19 * 2/14
Evaluate
x = -19/7
Hence, the value of x when y = 2 is -19/7
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Which of these four sets of side lengths will form a right trangle?
Set 1
4 cm 5 cm 6 cm
Set 3
10 mm 20 mm 30 mm
O Set 1
O Set 2
O Set 3
O Set 4
Set 2
8 in, 12 in 20 in
Set 4
12 R 16 R 20 R
Answers
answer:
set 4
Step-by-step explanation:
because when you divide the numbers 12,16 and 20 by 2 you'll get 6,8 and 10 which is a Pythagoras family....and it will form a right angle triangle
The graph below have the same shape.what is the equation of the blue graph?
Answers
Answer:
g(x) = (x - 5)²
Step-by-step explanation:
This is an example of the transformation of functions.
In this example, we see the graph f(x) has been moved 5 in the positive direction on the x-axis.
Due to the fact that we are working with the x-axis, our transformation will be placed inside the bracket, and it will do the opposite of what we expect.
This means that our transformation will be set out in this format:
[tex]g(x) = f(x-5)[/tex]
We know that:
[tex]f(x) = x^2[/tex]
Therefore,
[tex]g(x) = f(x-5) = (x-5)^2[/tex]
So, [tex]g(x) = (x-5)^2[/tex].
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Using the properties of integer exponents, match each expression with its equivalent expression.
Answers
From the power rules, the matching of each expression with its equivalent expression is:
[tex]5^{-3}=\frac{1}{125}[/tex]
[tex]-5^{-3}=-\frac{1}{125}[/tex]
[tex](-5^{-3})^{-1}=-125[/tex]
[tex](-5^{-3})^{0}=1[/tex]
Power RulesThere are different power rules, see some them:
1. Negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent. See the examples:
[tex]4^{-3}=\frac{1}{4^3} =\frac{1}{64} \\ \\ {\frac{4}{6} }^{-2}=( {\frac{6}{4} })^{2}=\frac{36}{16}[/tex]
2. Power. For this rule, you should repeat the base and multiply the exponents. See the example, [tex](2^{2})^3=2^6=64[/tex].
3. Zero Exponent. When you have an exponent equals to zero, the result must be 1. See the example, [tex]2^0=1[/tex].
From this for your question, you have:
[tex]5^{-3}=\frac{1}{5^3}=\frac{1}{125}[/tex][tex]-5^{-3}=-\frac{1}{5^3}=-\frac{1}{125}[/tex][tex](-5^{-3})^{-1}=(-5)^{3}=-125[/tex][tex](-5^{-3})^{0}=(-5)^{0}=1[/tex]Read more about power rules here:
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how do I do this, i am doing this and i need full points
Answers
Answer:
D is correct ...
nind d d find her r d d d f FBI f
What is the value of x and y?
Answers
Answer:
[tex]\fbox {x = 6 and y = 12}[/tex]
Step-by-step explanation:
Taking the tan and cos values to find x and y :
tan 60° = √3 = 6√3/x⇒ x = 6cos 30° = √3/2 = 6√3/y⇒ y = 12Answer:
x = 6 and y = 12
Step-by-step explanation:
30-60-90 Triangle Theorem
A special right-angled triangle where:
Angles are in the ratio 1 : 2 : 3Sides are in the ratio 1 : √3 : 2Therefore, the formula for the sides is b : b√3 : 2b where:
b = shortest side opposite the 30° angleb√3 = side opposite the 60° angle2b = longest side (hypotenuse) is opposite the right angleThe given triangle is a 30-60-90 triangle, therefore the ratio of its sides is b : b√3 : 2b
We have been given the measure of the side opposite the 60° angle.
⇒ b√3 = 6√3
So b = 6
Therefore, substituting the found value of b into the formula, the sides are in the ratio: 6 : 6√3 : 12
⇒ x = 6 (shortest side)
⇒ y = 12 (longest sides)
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What is the length of BC? (Giving 50 points)
Answers
Answer: Hope this helps you I guess.
2
Answer:
2 is the length of BC
Step-by-step explanation:
If we will look at this line, we can determine that unit interval is 1, so we subtract B from C, which is 2, and that's the answer
16-2t=3/2t+9 solve for t
Answers
answer: t=2
steps:
16-2t = 3/2t+9
7 = 3/2t + 2t
2 is 4/2
7 = 3/2t + 4/2t
7 = 7/2t
7/2t = 7
(2/7)7/2t=7(2/7)
t=7(2/7)
t=2
Select the correct answer.
Identify the end behavior and the zeros of function h.
h(1) = -1³ - 91² +41 +96
Based on these key features, which statement is true about the graph representing function h?
A.
The graph is negative on the intervals (- infinity, -8) and (-4, 3).
B. The graph is positive on the intervals (-8, -4) and (3, infinity).
OC. The graph is negative on the intervals (-3, 4) and (8, ∞).
D. The graph is positive on the intervals (-infinity ,-8) and (-4, 3).
Answers
Based on the key features, the end behavior and the zeros of function h [h(x) = -x³ - 9x² +4x +96], the statement that is true of the above graph is: "The graph is positive on the intervals (-8, -4) and (3, infinity) (Option B)"
A function's "end behavior" refers to how the function's graph behaves at its "ends" on the x-axis.
In other words, if we look at the right end of the x-axis (as x approaches + ∞) and the left end of the x-axis (as x approaches - ∞ ), the end behavior of a function represents the trend of the graph.
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What value of n makes the equation true?
-1/5n+7=2
n=
Answers
[tex] \frac{ - n}{5} + 7 = 2 \\ \\ \frac{ - n + 35}{5} = 2 \\ \\ - n + 35 = 10 \\ \\ - n = 10 - 35 \\ \\ - n = - 25[/tex]
cancel (-) sign both sides ,
[tex]n = 25.[/tex]
what i the solution to this equation
6 (x - 5) = 4x + 20
Answers
6 (x - 5) = 4x + 20
6x - 30 = 4x + 20
6x - 4x = 20 + 30
2x = 50
[tex]x = \frac{50}{2} [/tex]
x = 25
Answer: The value of x = 25 ✅
Step-by-step explanation:
Hii! Do you need to know the solution to the equation [tex]\boldsymbol{6(x-5)=4x+20}[/tex]? No problem! (:
Solving EquationsIn any equation, there's a variable that we need to solve for. Here the variable is "x".
So now let's solve for x...
[tex]\twoheadrightarrow\sf 6(x-5)=4x+20[/tex]
[tex]\bullet[/tex] "distribute" 6
[tex]\twoheadrightarrow\sf 6x-30=4x+20[/tex]
[tex]\bullet[/tex] subtract "4x" from both sides
[tex]\twoheadrightarrow\sf 2x-30=20[/tex]
[tex]\bullet[/tex] add "30" to both sides
[tex]\twoheadrightarrow\sf 2x=50[/tex]
[tex]\bullet[/tex] divide both sides by "2"
[tex]\twoheadrightarrow\sf x=25\;\;\;[/tex] ✅
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Hope that this helped! Best wishes.
[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.[/tex]
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[tex]\bigstar\underbrace[/tex]
Which is the best estimate to the nearest one percent of startfraction 7 over 15 endfraction?
Answers
The best estimate to the nearest one percent of the fraction; 7/15 is; 47%.
What is the best estimate of the fraction to the nearest percent?From the task content, it follows that the fraction given whose estimate is to be determined is; 7/15.
The fraction expressed as a percentage is;
(7/15) × 100 %
= 46.667%.
Hence, when rounded to the nearest one percent; = 47%.
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how to say i like chees burgers without saying that like how to say im not gonna date you while i still will im just dum what is 1+1
Answers
Answer:
2
I believe that the answer my friend
Given that h={A,E,I,O,U},which is the number of possible subsets of set h
Answers
There are 32 subsets of the set h.
We have given that h={A,E,I,O,U},
We should count the elements of the set, then put that number as the exponent of 2.
What is the subset?A set A is a subset of another set B if all elements of set A are elements of set B. In other words, set A is contained inside set B.
Remember that 2 should always be the base in finding the number of subsets: 2^5=32
Therefore there are 32 subsets of the set h.
Here set h is denoted by small h but the set is always denoted by capital letters.
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