All the angles are measured in degrees, show that the triangle is isosceles.
Answers
n ==> number of sides
∴ (3 - 2) × 180° = 180°
(4x + 8°) + (5x + 2°) + (6x - 10°) = 180°
Remove the parenthesis
4x + 8° + 5x + 2° + 6x - 10° = 180°
Simplify
15x = 180°
x = 12°
An isosceles triangle has 2 equal angles and sides.
In this case, we check them by the angle.
Substitude x into 4x + 8, 5x + 2 and 6x - 10
1. 4(12°) + 8° = 56°
2. 5(12°) + 2° = 62°
3. 6(12°) - 10° = 62°
Notice 2 and 3 have the same angular value.
∴ ∆ is an isosceles ∆.
The triangle is isosceles.
What is a triangle?A triangle is a polygon that has three vertices on each of its three sides. The angle that is created within the triangle is 180 degrees. It indicates that the sum of a triangle's interior angles is 180 degrees. This is a polygon with the fewest sides. At the end of the day, a triangle is characterized as a three-sided two-layered figure whose inside points are equivalent to 180°.
Given a triangle let the triangle be ΔABC
given angles (4x + 8), (5x + 2) and (6x - 10)
let ∠A = (4x + 8), ∠B = (5x + 2) and ∠C = (6x - 10)
we know that sum of angle of triangle is 180⁰
∠A + ∠B + ∠C = 180
4x + 8 + 5x + 2 + 6x - 10 = 180
15x = 180
x = 180/15 = 12
∠A = 4x + 8 = 4(12) + 8 = 56⁰
∠B = 5x + 2 = 5(12) + 2 = 62⁰
∠C = 6x - 10 = 6(12) - 10 = 62⁰
since ∠B = ∠C
it is the property of an isosceles triangle, An isosceles triangle is a triangle with any two sides that are the same length and angles on opposite sides that are the same size.
Hence the Given triangle is isosceles.
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Related Questions
A small airplane used 5 2/3 gallons of fuel to fly 2 hour trip. How many gallons were used each hour
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Use the graph of f to estimate the local maximum and local minimum. (explain)
Answers
Answer:
The graph has local maximum at (0,0) and minimum at (-2,-4) and (2,-4).
Step-by-step explanation:
Consider the provided graph.
it is not always possible to find maximum or minimum for the whole function, but locally it is.
To find the local maximum and minimum we need to choose an interval first.
Local maximum: f(c) ≥ f(x) for all x in the interval
Local minimum: f(c) ≤ f(x) for all x in the interval
For better understanding refer the figure 1
Now consider the provided graph:
The graph of the function at (-2,-4) and (2,-4) shows the minimum value that is -4.
Because at x = -2 and 2 the value of function f(x)≥f(c) for every x in the domain.
Also the graph of the function has local maximum at (0,0) as at x = 0
The value of function f(x)≤f(c) for every x in the domain.
Hence, the graph has local maximum at (0,0) and minimum at (-2,-4) and (2,-4).
hey i need help solving these and not just the answer i really would like to know how
Answers
1)
Let's put some name of vertex:
A with angle A=45°
B with angle B=90°
C The 3 vertex of the triangle of left.
AC=9 , y=AB=BC
With Pythagore, we can say: y²+y²=9²==>2y²=81===>y=9/√2=9√2/2
The other triangle is BDC: cos(60°)=x/y==>x=y*1/2=9√2/4
2)
Let's give some names:
A with angle A=60°
B with angle B=90
C the 3th vertex of the left triangle.
AB=10, BC=y
tan 60°=y/10=sin(60°)/cos(60°)=(√3/2)/(1/2)=√3==>y=10√3
D is the 3 th vertex of the right triangle.
We use Pythagore: y²+y²=x²
x²=2*(10√3)²===>x=10*√6
the top of a certain mountain in California has an altitude of 14,721 ft above sea level. The bottom Death Valley is 282 ft below sea level. using 0 as sea level, find the difference between these two elevations. what is the difference between these two elevations?
Answers
Which is the next number in this pattern. What is the rule ? 0,1,1.5,1.75
A.2
B.1.875
C.1.85
D.1.8
Answers
Determine the ordered pair that lies on the unit circle corresponding to startfraction 5 pi over 4 endfraction .
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Rewrite and simplify ln(4500) in terms of ln5 and ln6
Answers
Simplified form of the given logarithmic expression ln(4500) will be ln(4500) = 3ln(5) + 2ln(6)
Given logarithmic expression in the question is,
ln(4500)We have to convert this expression in terms of ln(5) and ln(6).
Since, Factored form of 4500 = 5×5×5×6×6
= 5³×6²
Therefore, ln(4500) = ln(5³×6²)
= ln(5³) + ln(6²) [Since, ln(a × b) = ln(a) + ln(b)]
= 3ln(5) + 2ln(6) [Since, ln(a³) = 3ln(a)]
Hence, ln(4500) = 3ln(5) + 2ln(6) will be the answer.
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Luis ate three of the eight pizza slices. he paid $2.70 as his share of the cost. how much did the whole pizza cost?
Answers
Find the distance from point A(−1, 7) to the line y= 3x. Round your answer to the nearest tenth.
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its equation will be y - 7 = -1/3(x + 1)
= y = -1/3x + 20/3
where the lines intersect:-
3x = -1/3x + 20/3
10/3 x = 20/3
x = 2 and y = 3*2 = 6
so we need to find distance between (-1,7) and (2,6)
this is sqrt[((7-6)^2 + (-1-2)^2)] = sqrt 10 = 3.2 to nearest tenth.
I assume that we want to find the minimum distance between the point A(-1, 7) and the line y = 3x.
We will get that the distance is 3.22
So first, let's see how to get the distance between two points (x₁, y₁) and (x₂, y₂). We just use the general formula:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Now we want to find the distance between (-1, 7) and a point on the line y = 3*x, that can be written as (x, 3x)
That distance is:
[tex]d = \sqrt{(-1 - x)^2 + (7 - 3x)^2}[/tex]
Now we want to minimize this, which is equivalent to minimize d^2, then we can define:
D = d^2
and write:
[tex]D = (-1 - x)^2 + (7 - 3x)^2\\\\D = 1 - 2x + x^2 + 49 - 42x + 9x^2\\\\D = 10x^2 - 44x + 50[/tex]
Now we need to minimize this, which is a parabola, so the minimum will be at the vertex of the parabola (we know this because the leading coefficient is positive, thus the parabola opens upwards).
Remember that for a parabola like:
a*x^2 + b*x + c
The vertex is at:
x = -b/2a
Then for our parabola, the vertex will be at:
x = -(-44)/(2*10) = 44/20 = 2.2
Thus the minimum distance is given by:
[tex]d = \sqrt{(-1 - 2.2)^2 + (7 - 3*2.2)^2} = 3.22[/tex]
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Tiana's checking account charges a $7.75 monthly service fee and a $0.16 per-check fee. If Tiana writes 17 checks per month, should she switch to a checking account that charges a $10.50 monthly service fee and no per-check fee? A. No, because her monthly fees are currently greater than $10.50. B. No, because her monthly fees are currently less than $10.50. C. Yes, because her monthly fees are currently less than $10.50. D. Yes, because her monthly fees are currently greater than $10.50.
Answers
the answer to this question is B
Answer:
Option B. is correct.
Step-by-step explanation:
Tiana's checking account charges a $7.75 monthly service fee and $0.16 per check fee.
If Tiana writes 17 checks per month, her total charges =
0.16 × 17 = 2.72 + 7.75 = $10.47
Her total account charges $10.47 for 17 checks.
In the question it is asking that she should switch to a checking account that charges a $10.50 monthly service fee and no per check fee.
Answer : No, because her monthly fees are currently less than $10.50.
A train traveling 50 mph left a station 30 minutes before a second train running at 55 mph. How soon did the second train overtake the firstIf 50x represents the distance the slower train travels, then the faster train travels?
Answers
Train B : 55 mph
After 30 mins train A has travelled 25 miles
Relative speed of trains is 5 mph
Consider train A at rest and train B at 5 mph
t = 25 / 5 h
t = 5 h
Second train overtakes after 5 h
For two trains with speeds given as 50 mph and 55 mph and a 30-minute head start for the first, the second train overtakes the first after 5 hours, based on their relative speed.
Here's how to solve a similar problem based on the given examples:
Let the first train's speed be 50 mph and the second train's speed be 55 mph.
The first train has a 30-minute head start, which at 50 mph means it has traveled 25 miles before the second train departs (since 50 miles/hour * 0.5 hours = 25 miles).
The second train travels 5 mph faster than the first, so the relative speed is 55 mph - 50 mph = 5 mph.
Now calculate the time it takes for the second train to catch up by dividing the head start distance by the relative speed: Time = Distance / Relative Speed, which is Time = 25 miles / 5 mph = 5 hours.
So, the second train will overtake the first train after 5 hours.
You forget the last two digits of your password for a website. What is the probability that you randomly choose the correct digits?
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Which graph models the equation 2x + 3y = 6?
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graph according to y=mx + b
b is y intercept, so the graph crosses the point (0, 6)
m is the slope and slope is rise over run. So go down 2 and right 3 from (0,6) as many times as you need to fill up the graph.
Then go up 2 and left 3 from (0,6) as many times as you need to fill the graph.
Put arrows at each end of your line to show that it's a line.
Answer: i did the test and i got B and i was right so its B
Step-by-step explanation:
What is the greatest common factor of 125,50 and 275
Answers
In the diagram ABC = WRS. What is the perimeter of WRS?
Answers
Perimeter = 12 for both triangles.
Rewrite the rational expression x^3+5x^2+3x-10/x+4 in the form q(x)+r(x)/b(x).
Answers
Hope I helped :)
Answer:
[tex]x^2+x-1-\frac{6}{x+4}[/tex]
Step-by-step explanation:
Rational expression form : [tex]\frac{a(x)}{b(x)}=q(x)+\frac{r(x)}{b(x)}[/tex]
a(x) = dividend
b(x) = divisor
q(x) = quotient
r(x) = remainder
Given expression : [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex]
We know that [tex]Dividend = Divisor \times Quotient+Remainder[/tex]
So, [tex]x^3+5x^2+3x-10 =x+4 \times (x^2+x-1)-6[/tex]
Thus a(x) = dividend = [tex]x^3+5x^2+3x-10 [/tex]
b(x) = divisor= [tex]x+4[/tex]
q(x) = quotient=[tex]x^2+x-1[/tex]
r(x) = remainder=-6
Substitute the value in the rational form.
[tex]\frac{x^3+5x^2+3x-10}{x+4}=x^2+x-1-\frac{6}{x+4}[/tex]
Hence the rational expression [tex]\frac{x^3+5x^2+3x-10}{x+4}[/tex] in the form of [tex]q(x)+\frac{r(x)}{b(x)}[/tex] is [tex]x^2+x-1-\frac{6}{x+4}[/tex]
For a normal distribution, the z value for an x value that is to the right of the mean is always:
Answers
In a normal distribution, the Z value for an X value that is to the right of the mean is always positive. It indicates how many standard deviations X is larger than the mean. Conversely, Z values are negative for X values to the left of the mean because they are smaller than the mean.
Explanation:In a normal distribution, the Z value corresponds to the number of standard deviations a value X is from the mean. Specifically, for an X value that is to the right of the mean, the Z score will always be positive. This is because values to the right of the mean are larger than the mean.
For example, if X = 10 and the mean is 5, and this corresponds to a Z score of 2.5, it means that X is 2.5 standard deviations to the right of the mean. In other words, X is larger than the mean by 2.5 times the standard deviation. The actual Z score, such as 2.5 in this example, indicates how far the score is from the mean, with greater Z scores indicating values further to the right of the mean.
In contrast, X values to the left of the mean have negative Z scores, indicating they are smaller than the mean. Finally, if X equals the mean, then X has a Z score of zero. This basic understanding of Z scores and their relation to the mean in a normal distribution is crucial in many statistical analyses.
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the scatter plot shows how many desks and computers were found in 12 different offices
how many offices had 11 computers
1
2
3
4
Answers
Answer:
It's three. Look at 11 on the Y axis (computers) and count how many dots are at 11. There's a total of three computers based on the dots at 11.
Step-by-step explanation:
A scatter plot is a set of points plotted on horizontal and vertical axes.
It shows the relationship between two sets of data.
The number of offices that have 11 computers is 3.
What is a scattered plot?A scatter plot is a set of points plotted on horizontal and vertical axes.
It shows the relationship between two sets of data.
We have,
Horizontal axes = number of desks
Vertical axes = number of computers
Each dot in the scatter plot indicates offices.
Number of offices = 12 dots = 12
We need to find the number of dots that is with 11 computers.
We see that there are 3 dots with 11 computes so there are 3 offices that have 11 computers.
Thus the number of offices that have 11 computers is 3.
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To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.
At approximately what angle does the wire meet the ground?
Answers
12 feet would be the hypotenuse...
56.4 degrees my friend. That is ur answer.
Answer for 6-9 please asap
Answers
7.True
8. False
9. False
Weight can change, but mass is constant
#7 is true
Sodium and Chlorine make table salt
#8 is true
this one is both true and false, like adding kool-aid to water changes the color, but so does fireworks, which explodes into colors.
#9 is false
it goes Reactants>Products
hope this helps!
1. In ΔPQR, PQ = PR and M is the midpoint of QR . Prove that PM bisects ∠QPR.
ANSWER FORMAT: ΔPQM = Δ (?) because... (reason)
2. In ΔABC, m∠B = m∠C. The angle bisector of ∠B meets
AC
at point H and the angle bisector of ∠C meets
AB
at point K. Prove that BH = CK.
ANSWER FORMAT: ΔBCK = Δ (?) because... (reason)
3. In ∆ABC the median
AM
is extended to ray
AM
and point P on
AM
is taken so that
PM = AM. What is the distance from point P to vertices C and B if AB = c and AC = b?
Answers
How much in Federal taxes does Curtis annually pay?
Answers
he pays 29.59 a week
multiply that by 52 weeks in a year
29.59 * 52 = 1538.68 a year
Answer is A
21: stan bought a monster truck for $2,000 down and payments of $450 a month for five years. what's the total cost of the monster truck?
Answers
2000 + 450(60)
2000 + 27000 = 29,000
He spend $27,000 on the truck.
Hope this helps!
Answer:
The total cost of the monster truck = 29000 $
Step-by-step explanation:
Stan bought a monster truck for $2,000 down and payments of $450 a month for five years.
Initial payment = 2000 $
Monthly payment = 450 $
Number of years paid = 5
Number of months in 5 years = 12 x 5 = 60
Total amount paid = 2000 + 60 x 450 = 29000 $
The total cost of the monster truck = 29000 $
Given: x - 5 > -2.
Choose the solution set.
{x | x R, x > -7}
{x | x R, x > -3}
{x | x R, x > 3}
{x | x R, x > 7
Answers
x-5>-2
x> -5+2
X>3
Answer is: {x | x R, x > 3}
Find the equation of the line that is parallel to the given line and passes through the given point y= -x +5; (2,7)
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Théo Has $5 more than Denise and denise has $11 more than Rudy. Together they have $45. How much money does each have?
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x+(x-5)+(x-5-11)=45
x+x-5+x-16=45
3x-21=45
3x=66
x=22
x-5=17
x-5-11=6
theo has 22 dollars, denise has 17 dollars, rudy has 6 dollars.
Write the equation of the line that passes through (–1, 5) and has a slope of 3 in point-slope form.
Answers
The equation for point-slope form is y-y1 = m (x-x1).
Let's plug in the numbers for the equation: y-5 = 3 (x+1). This is the equation for point-slope form with the given slope and pair.
Hope this helps!
May
The equation of the line that passes through the point (-1,5) and has a slope of 3 in point-slope form is y = 3x + 8.
Explanation:The subject of this question relates to Mathematics, specifically algebra and line equations. The line equation in point-slope form is given by y - y1 = m(x - x1). In this equation, (x1, y1) represents the point that the line passes through and m represents the slope of the line. In our case, we know that the line passes through the point (-1,5) and has a slope of 3.
By substituting these values into the point-slope formula, we get the following:y - 5 = 3(x - (-1)), or, after simplifying, y - 5 = 3x + 3. So, the equation of the line that passes through (-1,5) and has a slope of 3 is y = 3x + 8.
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Help please!!! Q: A manufacturing company finds that 0.0019 of the light bulbs it makes are defective. Write this as a percent.
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(:
The height of a triangle is 7 ft more than its base. if the area of the triangle is 30 ft^ what is the lentgh of the base
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area=0.5(base)(height)
height=base+7
let base=x
area=0.5(x)(7+x)
30=3.5x+0.5x^2
multiply the equation by 2
60=7x+x^2
subtract 60 from both sides
x^2+7x-60=0
(x-5)(x+12)=0
thus x=5 or x=-12 since we are only considering positive answers
x=-12 is rejected
so base=5 and height=5+7=12
Solve for x.
5(x - 3) + 4(x + 3) = 3(x - 1)
x = 0
x = 1/4
x = 1/2
x = 1
Answers
5x−15+(4x+12)=3(x−1)
Simplify by adding terms.
Remove unnecessary parentheses.5x−15+4x+12=3(x−1)
Add 5x and 4x to get 9x.9x−15+12=3(x−1)
Add −15 and 12 to get −3.9x−3=3(x−1)
Simplify the right side.
Apply the distributive property.9x−3=3x+3⋅−1
Multiply 3 by −1 to get −3.9x−3=3x−3
Move all terms containing x to the left side of the equation.
Since 3x contains the variable to solve for, move it to the left side of the equation by subtracting 3x from both sides.9x−3−3x=−3
Subtract 3x from 9x to get 6x.6x−3=−3Move all terms not containing x to the right side of the equation.
Since −3 does not contain the variable to solve for, move it to the right side of the equation by adding 3 to both sides.6x=3−3Subtract 3 from 3 to get 0.6x=0Divide each term by 6 and simplify.x=0
9x - 3 = 3x - 3
9x = 3x
3x = x
3x - x = 0
2x = 0
x = 0