The base of an isosceles triangle is 70 centimeters long. The altitude from the vertex angle to the base is 75 centimeters long. Find, to the nearest whole degree, the measure of the base angles of this triangle.
Answers
We get two similar right angled triangles ADC and BDC. For triangle ADC, AD = 35cm, DC = 75cm. Tangent of angle DAC can be written as:
[tex]tan(DAC)= \frac{CD}{DA} \\ \\ tan(DAC)= \frac{75}{35}= \frac{15}{7} [/tex]
Angle DAC is equal to tangent inverse of 15/7 which equals 65 degrees, rounded of to nearest whole degree.
Angle DBC = DAC = 65 degrees
Thus the base angles for the given isosceles triangle will be 65 degrees each, rounded of to nearest whole degree.
Related Questions
please someone help me!
Answers
.. P = 2(3x/(x +10) +x^2/(x -5))
.. = 2(3x(x -5) +x^2(x +10))/((x +10)(x -5))
.. = 2(x^3 +13x^2 -15x)/(x^2 +5x -50)
[tex]P=\frac{2x^{3}+26x^{2}-30x}{x^{2}+5x-50}[/tex]
A rectangle is 1/2 feet long and 3/4 feet wide. What is the area of the rectangle?
Answers
The area of the rectangle having a length of 1.2 feet and a width of 3/4 feet is 3/8 sq feet.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the area of a rectangle is (length×width).
Given, A rectangle is 1/2 feet long and 3/4 feet wide.
Therefore, The area of this rectangle is,
= (1/2×3/4) sq feet.
= 3/8 sq feet.
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PLEASE HELP ME QUICKLY!!!
BRAINLIEST AVAILABLE TO CORRECT ANSWER
Answers
Choose the correct box of the best buy available.
a .a box of cookies for $1.89
b. two boxes of cookies for $3.69
Answers
A $4,000.00 principal earns 5% interest, compounded annually. After 4 years, what is the balance in the account?
$500,000.00
$4,862.03
$4,600.00
$20,250.00
24.
A $6,000.00 principal earns 8% interest, compounded semiannually. After 35 years, what is the balance in the account?
$22,800.00
$39,600.00
$88,712.07
$93,429.71
25.
A tractor costs $15,450.00 and depreciates in value by 14% per year. How much will the tractor be worth after 3 years? $22,889.85
$15,408.00
$8,451.28
$9,827.07
Answers
6000(1+ .08/2)^35(2)=$93429.71
15450(.86)³=$9827.07
the second one is b
the third is a
What is the interior angle if the outside equals 110?
Answers
algebra 2 unit 2 question. connexus.
Answers
Next, lets convert those decimals into fractions by adding a denominator 1 to each decimal and multiply both its numerator and denominator by a power 10 that lets us get rid of the decimal point:
[tex]( \frac{-2.5}{1} )( \frac{10}{10} )= \frac{-25}{10} =- \frac{5}{2} [/tex]
[tex]( \frac{0.5}{1} )( \frac{10}{10} )= \frac{5}{10} = \frac{1}{2} [/tex]
[tex]( \frac{1.5}{1} )( \frac{10}{10} )= \frac{15}{10} = \frac{3}{2} [/tex]
Since we know that each one of those points is a zero of the function ([tex]x=0[/tex]), we can replace each value into our [tex]x=0[/tex], and work backwards to get our binomials:
[tex]x=- \frac{5}{2} [/tex]
[tex]2x=-5[/tex]
[tex]2x+5=0[/tex]
So, our first binomial is [tex](2x+5)[/tex]
[tex]x= \frac{1}{2} [/tex]
[tex]2x=1[/tex]
[tex]2x-1=0[/tex]
So, our second binomial is [tex](2x-1)[/tex]
[tex]x= \frac{3}{2} [/tex]
[tex]2x=3[/tex]
[tex]2x-3=0[/tex]
So, our next binomial is [tex](2x-3)[/tex]
Now lets put all together to find the equation of our function:
[tex]y=(2x+5)(2x-1)(2x-3)[/tex]
And of course, we can rewrite it in a different order:
[tex]y=(2x-1)(2x-3)(2x+5)[/tex]
We can conclude that the equation that most likely represents the graph of the function is [tex]y=(2x-1)(2x-3)(2x+5)[/tex]
The subject of this question is Mathematics, specifically Algebra 2.
Explanation:The subject of this question is Mathematics, specifically Algebra 2.
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In the standard equation for a circle centered at any point, a change in the value of the number that is part of the x-term results in a vertical movement ? True or false?
Answers
Answer:
It is False as Changing value of x coordinate results in horizontal movement not in vertical moment.
Step-by-step explanation:
Standard form of circle is given by,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where, ( h, k ) = Coordinates of circle and r is radius of circle.
here h is part of x- term.
So, if change value of h to p keeping k and r constant. The coordinate of center shifted in horizontal line whose equation is y = k.
Therefor, It is False as Changing value of x coordinate results in horizontal movement not in vertical moment.
1. Write using exponents. (–4)(–4)
Answers
[tex] (-4)(-4) = (-4)^{2}[/tex]
Analyze the key features of the graph of the quadratic function f(x) = -x2 + 2x + 10. A. Does the parabola open up or down?
B. Is the vertex a minimum or a maximum?
C. Identify the axis of symmetry, vertex and the y-intercept of the parabola.
Answers
the parabola open down
the vertex is a maximum
the axis of symmetry is the y axis
the y-intercept of the parabola.is the point (0,10)
SOS
Answer
A: Down
B: Max
C:
AOS: x = 1Vertex: (1, 11)Y-Int: (0, 10)Step-by-step explanation:
A: If the leading coefficient (a) is positive, the graph opens UP. If it is negative, the graph opens DOWN.
B: Anytime the graph goes UP, there's a minimum. Anytime the graph goes DOWN, there's a maximum
C:
AOS: [tex]x = \frac{-b}{2a}, a=-1, b=2, c=10[/tex]
Vertex: [tex](\frac{-b}{2a}, y)[/tex]
Y-INT: let x=0 and solve for y. The coordinate of the y-intercept is (0, y).
Hope this helps!!
What is the next number in the sequence? 55, 34, 21, 13, 8…?
Answers
Each number in the sequence is the (positive) difference of the previous two numbers.
Tiny's Tattoo Parlor sold 389 tattoos this month. 43 of those tattoos were arm tattoos. Based on this data, what is a reasonable estimate of the probability that the next customer does not get an arm tattoo?
Answers
Answer:
346/389
Step-by-step explanation:
correct on khan academy!
The reasonable estimate of the probability that the next customer does not get an arm tattoo is 346/389.
What is Probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Here, Based on the given conditions, formulate
Probability = Favorable outcome / Total outcome
Calculate the sum or difference: (389-43)/389
get the result: 346/389
Thus.the reasonable estimate of the probability that the next customer does not get an arm tattoo is 346/389.
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A study found that 3939% of the assisted reproductive technology (art) cycles resulted in pregnancies. twenty-fourfour percent of the art pregnancies resulted in multiple births. (a) find the probability that a random selected art cycle resulted in a pregnancy and produced a multiple birth. (b) find the probability that a randomly selected art cycle that resulted in a pregnancy did not produce a multiple birth. (c) would it be unusual for a randomly selected art cycle to result in a pregnancy and produce a multiple birth? explain
Answers
P(A and B) = P(A).P(B│A)
Look for P(A) and P(B│A).
P(A) = 39/100 = 0.39
P(B│A) =24/100 = 0.24
The probability that a randomly selected ART cycle resulted in a pregnancy and produced a multiple birth is P(A and B) is:
P(A and B) = P(A). P(B│A)
= 0.39 * 0.24
= 0.0936
(b) Let B ’ - the complement of B. This means that this is the probability that a randomly selected ART cycle that resulted in a pregnancy did not make a multiple birth is P(B’│A).
Determine P(B’│A) using the formula the complement of an event, P(E’) = 1 – P(E), where E is an event and E’ is its complement. Recall that P(B│A) = 0.24.
P(B’│A) = 1 – P(B│A)
= 1 – 0.24
= 0.76
(c) Knowing that P(A and B) = 0.0936. An event that happens with a probability of 0.05 or less is normally considered unusual. Use this information to know whether it would be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth.
0.0936;
0.2964; and
no.
Explanation:
39% of ART cycles result in pregnancy. Of those, 24% result in multiple births. To find the probability that a random ART cycle results in a pregnancy with multiple births, we want to find 24% of 39%; this means we multiply these:
0.24(0.39) = 0.0936.
To find the probability that it will not result in multiple births, we subtract from 100%; since 24% of the pregnancies are multiple births, 100-24 = 76% will not be multiple births.
Now we find 76% of 39%; we multiply again: 0.76(0.39) = 0.2964.
In statistics, a result is considered unusual if the probability is 0.05 or less. Our probability was 0.0936, which is greater than 0.05; thus it is not unusual.
△JKL∼△QRS , JK is 8 centimeters, QR is 12 centimeters, and RS is 9 centimeters.
What is KL ?
Enter your answer in the box.
Answers
Answer:
The measure of KL is 6 centimeters.
Step-by-step explanation:
It is given that △JKL∼△QRS.
The corresponding sides of two similar triangles are proportional.
[tex]\frac{JK}{QR}=\frac{KL}{RS}[/tex]
[tex]\frac{8}{12}=\frac{KL}{9}[/tex]
[tex]8\times 9=KL\times 12[/tex]
Divide both sides by 12.
[tex]KL=\frac{72}{12}[/tex]
[tex]KL=6[/tex]
Therefore we can say that if △JKL∼△QRS, then the measure of KL is 6 centimeters.
Answer:
6
Step-by-step explanation:
He did too much math lol, a simple way of this is by dividing both sides initially.
12/9 = 1.5
9/1.5 = 6
△ABC∼△LMN , AB is 8 inches, BC is 14 inches, and LM is 12 inches.
What is MN ?
Answers
We setup a proportion using the given information.
AB/LM = BC/MN
8/12 = 14/MN
8(MN) = 12 * 14
8(MN) = 168
MN = 168/8
MN = 21
What are the solutions to the equation?
n^2−8n+16=25
Enter your answers in the boxes.
n1=
n2=
Answers
The equation becomes,
n^2-8n-9 = 0
Factoring the equation now gives you (n-9)(n+1) = 0.
In order to find the solutions to this equation, find values of 'n' that make the equation equal to 0.
In this case, if n is 9 or -1, we get the answer 0.
Proof: (9-9)(n+1) => (0)(n+1) = 0
or (n-9)(-1+1) => (n-9)(0) = 0.
Hope this made sense! If it didn't, please ask questions!
Answer:
help
Step-by-step explanation:
helppppppppppppppppppppppp
Answers
log base 2 of 100 is about 1/4 the value of log base 6 of 20
Explanation:
We will get the value of each of them separately and then compare these values.
log base 2 of 100 = 6.6438
log base 6 of 20 = 1.6719
Comparing these values, we will find that:
log base 2 of 100 is about 1/4 the value of log base 6 of 20
Hope this helps :)
Jenna throws a stone off a pier and into the ocean. The graph models how the height of the stone, above sea level, changes over time.
Select from the drop-down menu to interpret the decreasing interval of the graph.
The stone was falling toward the water from
https://static.k12.com/nextgen_media/assets/8090396-NG_AL1_O_07_012_Quiz_05.png
Answers
This should get you a hundred on the 4.11 quiz. :)
a cylinder has a circumgerence of 12pi cm and a height that is half the radius. what is the total surface
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and surely you know how much that is.
what is the surface area?
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so as you can see, the figure is really just 3 rectangles and 2 triangles.
the rectangles are 5x7, another 5x7, and the one at the bottom is a 6x7.
the triangles have a base of 6, a height of 4.
so, just the area of each, add them up, and that's the area of the figure.
[tex]\bf \stackrel{left~and~right}{(5\cdot 7)}+\stackrel{bottom}{(6\cdot 7)}+\stackrel{front~and~back}{2\left[\frac{1}{2}(4)(6) \right]}[/tex]
One of the factors of 6x3 − 864x is
A. 4
B. X^2
C. X + 12
D. X - 8
Answers
Consider the expression [tex]6x^3-864x.[/tex] This expression consists of two terms: [tex]6x^3[/tex] and [tex]-864x.[/tex]
These two terms have common factors 6 and x, because:
[tex]6x^3=6x\cdot x^2;[/tex][tex]-864x=6x\cdot (-144).[/tex]Then
[tex]6x^3-864x=6x(x^2-144).[/tex]
You know that [tex]144=12^2.[/tex] Use the formula for the difference of squares:
[tex]x^2-144=x^2-12^2=(x-12)(x+12).[/tex]
Therefore,
[tex]6x^3-864=6x(x-12)(x+12).[/tex]
Answer: correct choice is C.
What is the value of 0.36 repeating times 11/2?
Answers
The value of 0.36 repeating times 11/2 is 2.
What is Fraction?A fraction represents a part of a whole.
To find the value of 0.36 repeating (which we can write as 0.36363636...) times 11/2.
Convert the repeating decimal to a fraction.
Let x = 0.36363636...
Then 100x = 36.36363636...
Subtracting x from 100x, we get:
99x = 36
x = 36/99 = 4/11
Now Multiply the fraction by 11/2.
(4/11) x (11/2) = 2
Therefore, the value of 0.36 repeating times 11/2 is 2.
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If a chicken farm sold 3000 dozen eggs last week how many individual eggs were sold
Answers
3000*12= 36,000
That means that a total of 36,000 eggs were sold last week.
Hope This Helps! :)
multiply3000x12
12=number of eggs in a dozen
Please help me, will give thanks, lots of points, friend request, and brainliest. Alongside that, I will help you with any questions in science, english, or history that you may have.
Assume a and b are nonzero rational numbers and c and d are irrational numbers. For each of the following expressions, determine whether the result is irrational, rational, or both. Justify your answers.
Part A: b(a + d)
Part B: left parenthesis b square root of five end square root right parenthesis cubed
Part C: a + (cb)
Answers
They give you too much freedom in your choice though. Like for part A, what if we let b=-1 (rational) c=pi (irrational d=pi (irrational) Then bc+d = -pi + pi = 0 (rational) Maybe they didn't want you to consider 0 because otherwise all of these options can be rational.
Do you understand the difference between a rational and irrational number? Rationals can be written as a fraction containing whole numbers. Irrationals can not. Here are some examples of rational numbers: 3/2 is rational because its a whole number divided by a whole number. 7 is a rational number because it can be written as 7/1. −4 is a rational number, it also can be written in this form −4/1. This next one maybe seem surprising, but, 0 is a rational number. It also can be written as 0/1, but not as 0/0 (Which is not a number).
So in the end
A: virtually any sum or product involving an irrational number will be irrational.
B. (√7)^2 = 7 ... rational
C. all numbers involved are rational, so this result is rational
You have the following "rules."
- the sum of rational and irrational is irrational
- the product of rational and irrational is irrational
A. The first rule applies inside parentheses. The second rule applies then.
B. The result is (rational)*(5^(3/2)). The latter factor is irrational, so the second rule applies.
C. The second rule applies inside parentheses. The first rule applies then.
What are the solutions to the equation? n2−8n+16=25 Enter your answers in the boxes.
n1=
n2=
Answers
(n - 9)(n + 1) = 0
n1= 9
n2= -1
Using the graph below, what is the 10th term of the arithmetic sequence?
A.a10 = 26
B.a10 = 31
C.a10 = 30
D.a10 = 436
Answers
The 10th term of an arithmetic sequence can be found using the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. Without the graph or additional information, we cannot compute the 10th term for the given sequence.
Explanation:The question asks us to determine the 10th term of an arithmetic sequence using a provided graph. Unfortunately, the actual graph is not provided in the question. An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference. To find the 10th term of an arithmetic sequence, we would use the formula:
an = a1 + (n - 1)d
where an is the nth term of the sequence, a1 is the first term, n is the term number, and d is the common difference. However, without the graph or additional information such as the first term or the common difference, we cannot accurately determine the 10th term, and any answer from the provided options would be purely a guess.
To find the 10th term of an arithmetic sequence, we need to use the formula an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. In this case, the common difference is -3. Substituting the values into the formula, the 10th term is -24.
Explanation:To find the 10th term of an arithmetic sequence, we need to identify the common difference and use the formula:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
In this case, the given sequence is 3; 14; 11; 5; 16; 17; 28; 41; 31; 18. By comparing the terms, we can see that the common difference is -3.
Substituting the values into the formula:
a10 = 3 + (10-1)(-3) = 3 - 27 = -24
The 10th term of the arithmetic sequence is -24.
Reggie currently has a square rug in his living room. He is moving soon and has determined that for his new living room, he will need a rug that has a width that is two feet shorter than his current rug and a length that is five feet longer than his current rug. Let x represents the side measure of Reggie's current rug, in feet. Determine the equation that represents the area, y, in square feet, of the rug needed for his new living room.
y = x2 + 3x - 10
y = x2 - 7x + 10
y = x2 - 3x - 10
y = x2 + 7x + 10
Answers
y = x² + 3x - 10
Explanation:
Reggie's current rug has a square shape.
This means that:
length of rug = x ft
width of rug = x ft
For the new rug:
1- the length is 5 ft longer than the current rug. This means that:
new length = x + 5 ft
2- the width is 2 ft shorter than the current rug. This means that:
new width = x - 2 ft
The area of the new rug can be calculated as follows:
area of new rug = new length * new width
area of new rug = (x + 5)(x - 2)
area of new rug = x(x) - 2(x) + 5(x) - 5(2)
area of new rug = x² - 2x + 5x - 10
area of new rug = x² + 3x - 10 ft²
Hope this helps :)
Answer:
C. y = x² + 3x - 10
Step-by-step explanation:
Reggie's current rug has a square shape.
This means that:
length of rug = x ft
width of rug = x ft
For the new rug:
1- the length is 5 ft longer than the current rug. This means that:
new length = x + 5 ft
2- the width is 2 ft shorter than the current rug. This means that:
new width = x - 2 ft
The area of the new rug can be calculated as follows:
area of new rug = new length * new width
area of new rug = (x + 5)(x - 2)
area of new rug = x(x) - 2(x) + 5(x) - 5(2)
area of new rug = x² - 2x + 5x - 10
area of new rug = x² + 3x - 10 ft²
Just took the test <3.Suppose that F(x) = x^3 and G(x) = (4x)^3 − 5. Which statement best compares the graphs of F(x) and G(x)?
A.The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down.
B.The graph of G(x) is the graph of F(x) stretched horizontally and shifted 5 units down.
C.The graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units down.
D.The graph of G(x) is the graph of F(x) compressed horizontally and shifted 5 units down.
Answers
The graph of G(x) is the graph of F(x) stretched horizontally by a factor of 4 and shifted 5 units down.
Explanation:Comparing the functions [tex]F(x) = x^3[/tex] and [tex]G(x) = (4x)^3 - 5[/tex]reveals the relationship between their graphs. G(x) is a horizontal stretch of F(x) by a factor of 4 due to the presence of "4x." Additionally, the constant term "-5" shifts the graph downward by 5 units. Consequently, G(x) can be accurately characterized as a horizontal stretching of F(x) and a vertical shift downward by 5 units, altering the shape and position of the original cubic function F(x).
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Which pair of measurements is equivalent?
8,600 mg, 86 g
2,500 g, 250 kg
3.4 kg, 3,400 g
480 g, 4.8 mg
Answers
8,600 mg = 86,000 mg; So now, the first one is not equivalent.
2,500 g = 250,000 g; Not that one either.
3.4 kg = 3.4 kg; This one is correct. We can check by checking the last pair.
480 g = .0048 g; Nope.
So 3.4 kg, 3400 g would be the correct answer.
Answer:
3.4 kg, 3,400 g
Sue's Sushi placed two orders with its fish supplier. One order was for 15 pounds of salmon and 8 pounds of tuna; the order totaled $259. The other order was for 12 pounds of salmon and 6 pounds of tuna; this order totaled $204. What is the cost for one pound of salmon and one pound of tuna?
Answers
y= tuna cost per pound
$15x + $8y= $259
$12x + $6y= $204
Solve for one variable in one equation and substitute it in the other equation.
15x + 8y= 259
subtract both sides by 8y
15x= 259 - 8y
divide both sides by 15
x=(259-8y)/15
Substitute in second equation
12x + 6y= 204
12((259-8y)/15) + 6y= 204
multiply everything by 15 to eliminate fraction
(15)(12(259-8y)/15) + (15)(6y)= (204)(15)
(12*259) + (12*-8y) + 90y= 3060
multiply inside parentheses
3108 - 96y + 90y= 3060
combine like terms & subtract 3108 from both sides
-6y= -48
divide both sides by -6
y= $8 cost of tuna per pound
Substitute y=8 in either equation
15x + 8y= 259
15x + 8(8)= 259
15x + 64= 259
15x= 195
x= $13 cost of salmon per pound
CHECK:
12x + 6y= 204
12(13) + 6(8)= 204
156 + 48= 204
204= 204
ANSWER: One pound of salmon costs $13 and one pound of tuna costs $8.
Hope this helps! :)