Answer:
26
Step-by-step explanation:
If the sides of a triangle are a, b, and c, the triangle inequality theorem tells us, about the sides possible to make up this NON-right triangle:
a + b > c
b + c > a and
a + c > b
Since we have 2 sides, we will call the third unknown side x. Let a = 12 and b = 14:
12 + 14 > x
14 + x > 12 and
12 + x > 14.
The first inequality, solved for x, is that x < 26.
The second inequality, solved for x, is that x > -2. We all know that the 2 things in math that will never EVER be negative are distance/length measures and time; therefore, we can safely disregard -2 as a side length of this, or ANY, triangle.
The third inequality, solved for x, is that x > 2.
We now have the solutions for the side length possibilities:
2 < x < 26
From this inequality statement, we see that the longest the side could possibly be and still make a triangle with the other 2 side lengths given, is 26
Answer:
C. 7 inches
Step-by-step explanation:
The Obtuse Triangle Inequality Theorem: c^2 > a^2 + b^2.
14^2 > 12^2 + b^2.
196 > 144 + b^2.
so b < 52. and the square root of 52 is 7.
Thank you and have a great day!
Determine the principal value of the function: Arc sin(square root of 3/2)
Answer:
π/3
Step-by-step explanation:
We have to find the principal value of [tex]\text{arc sin}(\frac{\sqrt{3}}{2} )[/tex]
arc sin means sin inverse. The sin inverse is a one to one function with its range between [tex]-\frac{\pi}{2} \textrm{ to } \frac{\pi}{2}[/tex]
The principal value of the arc sin will lie within the above given range.
value of sin (60) or sin([tex]\frac{\pi}{3}[/tex]) is [tex]\frac{\sqrt{3}}{2}[/tex].
[tex]\frac{\pi}{3}[/tex] lies between [tex]-\frac{\pi}{2}\textrm{ and } \frac{\pi}{2}[/tex]
So, from here we can say that the Principal Value of Arc sin(square root of 3/2) is π/3
The principal value of the function Arc sin(√3/2) is,
⇒ π / 3
We have to given that,
⇒ Arc sin (√ 3/ 2)
Since, Value of arc sin lies between - π/2 and π/2.
Hence, The principal value of the function Arc sin(√3/2) is,
⇒ Arc sin(√3/2)
⇒ Arc sin(sin π/3)
⇒ π / 3
Therefore, The principal value of the function Arc sin(√3/2) is,
⇒ π / 3
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Which expression is the radical form of m^2.5?
The expression [tex]\rm m^{2.5}[/tex] in radical form is [tex]\rm \sqrt[2.5]{m}[/tex] .
What is a Radical form ?
If n is a positive integer greater than 1 and n is a real number, then
[tex]\rm \sqrt[n]{a}[/tex] = aⁿ
Here the index is represented by n, the radicand is represented by a , and the sign is called the radical.
Left side of the equation is called the radical form
Right side of the equation is called exponent form.
The given exponent form is
[tex]\rm m^{2.5}[/tex]
In radical form this will be written as
[tex]\rm \sqrt[2.5]{m}[/tex]
Therefore the expression [tex]\rm m^{2.5}[/tex] in radical form is [tex]\rm \sqrt[2.5]{m}[/tex] .
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17. Find the value of (+328.62) – (+98.6).
A. –427.22
B. 230.02
C. 427.22
D. –230.02
For this case we must find the value of the following expression:
[tex](+328.62) - (+ 98.6) =[/tex]
We apply distributive property to the term within the parenthesis taking into account tha:
[tex]- * + = -[/tex]
Rewriting we have:
[tex]+ 328.62-98.6 =[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]+328.62-98.6 = 230.02[/tex]
Answer:
230.02
Option B
At 350 degrees Fahrenheit, an oven can cook approximately 3 pounds of turkey per hour. At 450 degrees Fahrenheit, it can cook approximately 4.5 pounds per hour. How many more ounces of turkey can the oven cook at 450 degrees than at 350 degrees in 10 minutes? (1 pound = 16 ounces)
A) 4
B) 6
C) 8
D) 12
Answer:
D
Step-by-step explanation:
In which direction does the parabola open?
Answer:
up
Step-by-step explanation:
A graphing calculator, spreadsheet, or web site can help you with this one, or you can simply plot some points on a graph.
___
Only the highest-degree terms matter for answering this question. Leaving the others out, the form is ...
y = x^2
This tells you that y gets more positive for larger and larger values of x, regardless of their sign. Thus the graph of it is U-shaped, opening upward.
Please help me !! D is also an option but I couldn't get it in the picture
Answer: A) (-1, 0) to (1, 2)
Step-by-step explanation:
Complex numbers are written in the form of ai + b ; where "a" represents the x-coordinate and "b" represents the y-coordinate --> (a, b)
-i → -1i + 0 → (-1, 0)
2 + i → 1i + 2 → (1, 2)
Which graph connects those two coordinates? OPTION A
Charlie entered an elevator and ride up 10 floors and then down 2 floors before realizing he had not pressed the button for Floor 1. He then pressed the button for Floor 1 and rode down 14 floors and exited the elevator on Floor 1. On which floor did he begin?
Answer:
Floor 7
Step-by-step explanation:
He entered the elevator on floor x.
Then he rode up 10 floors. Now he is on floor x + 10.
Then he rode down 2 floors. Now he is on floor x + 10 - 2 = x + 8.
Then he pressed the Floor 1 button and rode down 14 floors to Floor 1. Now he is on floor x + 8 - 14 = x - 6 which is the same as Floor 1.
Floor x - 6 is the same as Floor 1, so we get the equation:
x - 6 = 1
Add 6 to both sides:
x = 7
Since we let x be the floor number he entered the elevator in, he entered the elevator on Floor 7.
Answer:
He began on floor 7
Step-by-step explanation:
This is a question where you have to use the question from the end and work your way backwards if that makes sense.
He had to go down 14 floors to get to floor 1. So 14 + 1 = 15. He was on the 15th floor.
Next he went down 2 floors. Since this is reverse, add two floors to the answer. 15 + 2 = 17. He was on the 17th floor.
And finally, he goes up 10 floors. Doing this in reverse, take away 10 floors to the answer. 17 - 10 = 7
He started on the 7th floor.Now to make sure it is correct, start from 7 and follow the original order of the question.
7 + 10 = 17
17 - 2 = 15
15 - 14 = 1
Which products result in a perfect square trinomial? Check all that apply. (–x + 9)(–x – 9) (xy + x)(xy + x) (2x – 3)(–3 + 2x) (16 – x2)(x2 – 16) (4y2 + 25)(25 + 4y2)
Answer:
(xy + x)and (xy + x)
(2x - 3) and (-3 + 2x)
(4y² + 25) and (25 + 4y²)
Step-by-step explanation:
* Lets explain the meaning of the perfect square trinomial
- If a binomial multiply by itself, then the answer will be a perfect
square trinomial
- Example: if the binomial (ax + b) multiply by itself, then
(ax ± b)(ax ± b) = (ax)(ax) ± (ax)(b) ± (b)(ax) + (b)(b)
(ax + b)(ax + b) = (ax)² ± 2(axb) + (b)²
∵ (ax + b)(ax + b) = (ax + b)²
∴ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
* From the example above the perfect square trinomial has 3 terms
# 1st term is the square the first term in the binomial
# 2nd term is twice the product of the two terms of the binomial
# 3rd term is the square of the second term of the binomial
* Lets solve the problem
- The product of (-x + 9)and (-x - 9)
∵ -x + 9 ≠ -x - 9
∴ The product of (-x + 9) and (-x - 9) is not a perfect square trinomial
- The product of (xy + x)and (xy + x)
∵ xy + x = xy + x
∴ (xy + x)(xy + x) = (xy + x)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (xy + x) and (xy + x) is a perfect square trinomial
- The product of (2x - 3) and (-3 + 2x)
∵ (-3 + 2x) can be written as (2x - 3)
∴ 2x - 3 = -3 + 2x
∴ (2x - 3)(-3 + 2x) = (2x - 3)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (2x - 3)(-3 + 2x) is a perfect square trinomial
- The product of (16 - x²) and (x² - 16)
∵ 16 - x² can be written as -x² + 16
- If we take -1 common factor from -x² + 16
∴ -x² + 16 = -(x² - 16)
∴ (-x² + 16)(x² - 16) = -(x² - 16)(x² - 16) = -(x² - 16)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∵ -(x² - 16)² = -(x^4 - 32x² + 256) = -x^4 + 32x² - 256
∵ x^4 - 32x² + 256 is perfect square trinomial
∵ -x^4 + 32x² - 256 is not a perfect square trinomial
∴ The product of (16 - x²) and (x² - 16) is not a perfect square trinomial
- The product of (4y² + 25) and (25 + 4y²)
∵ 25 + 4y² can be written as 4y² + 25
∴ 4y² + 25 = 25 + 4y²
∴ (4y² + 25)(25 + 4y²) = (4y² + 25)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (4y² + 25) and (25 + 4y²) is a perfect square trinomial
Which list shows the numbers in order from least to greatest? A. 53.783 B. 53.65 C. 53.09 D. 53.163 A) A, B, D, C B) C, D, B, A C) D, C, B, A D) B, C, A, D
Answer:
B) C,D,B,A
Step-by-step explanation:
The airplane was 32,000 feet above sea level. It landed in a valley 100 feet below sea level. Write an integer to express the change in the altitude
Answer:
- 32,100 ft
Step-by-step explanation:
Initial Altitude = 32,000 ft above sea level = +32,000 feet
Final Altitude = 100 ft below sea level = -100 ft
Altitude change,
= final altitude - initial altitude
= - 100 - (32,000)
= - 32,100 ft
Need help with this math question
Answer:
120
Step-by-step explanation:
If those 2 polygons are similar, then their corresponding angles are the same. The thing that makes them similar as opposed to congruent is that their side lengths exist in proportion to one another instead of being the same.
Answer:
[tex]w = 120\°[/tex]
Step-by-step explanation:
In this case we know that
ABCD and FECG are similar polygons.
This means that their sides are proportional and their corresponding angles are equal.
So if the lines FG and AD are parallel and of proportional length then by definition the angle w is equal to 120 °
Thus
[tex]w = 120\°[/tex]
Can someone please help me on the last two empty boxes :( ??!!
Answer:
trinomial binomialStep-by-step explanation:
mono-, bi-, tri- are prefixes meaning 1, 2, and 3, respectively. A 3-term polynomial is a trinomial; a 2-term polynomial is a binomial.
A chemist wants to mix a 66% alcohol solution with eight liters of 54% alcohol solution to produce a solution that is 65% alcohol. How many liters of the 66% alcohol solution should be used ?
Answer:
We have 8 liters of 54% alcohol.
We will add "x" liters of 66% alcohol to make "8 +x" liters of 65% alcohol.
54 * 8 + 66 x = 65 (8 + x)
432 + 66x = 520 + 65x
x = 88 liters
Step-by-step explanation:
Which is a quadratic function?
f(x) = 2x + x + 3
f(x) = 0x2 – 4x + 7
f(x) = 5x2 – 4x + 5
f(x) = 3x3 + 2x + 2
Answer:
C
Step-by-step explanation:
B isn't right. The 0 makes x^2 go away leaving a linear equation.
A is a linear function.
D is a cubic, so the answer is
C which has an x^2 function
The sum of the digits of a two-digit number is 13. The units digit is one more than twice the tens digit. Find the number.
Answer:49
Step-by-step explanation: 9+4=13 4x2=8 8+1=9
9 is the units digit
4 is the tens digit
Graph the function.
y = –2x^2 + 6x – 2
Answer:
Step-by-step explanation:
easch cube inside the rectangle prism has a edge length of 3/4 inch what is the volume of the rectangle prism
Volume = (edge)^3
Volume = (3/4)^3
Volume = (27/64) inches^3
Done.
Eliminate the parameter.
x = t - 3, y equals two divided by quantity t plus five
Answer:
y = 2/(x +8)
Step-by-step explanation:
Solve the first equation for t and substitute that expression into the second equation.
x = t -3
x + 3 = t
Then for y, we have
y = 2/(t +5)
y = 2/((x +3) +5) . . . . substitute for t
y = 2/(x +8) . . . . . . . . simplify
Help with this question, please!
Answer:
see below
Step-by-step explanation:
Apart from the pictures being drawn with the axis at a funny angle relative to the edges of the solid, it should be pretty clear from the pictures that the figure has both plane and axis symmetry.
Every point on one side of the axis has a matching point on the other side at the same distance. Every point on one side of the plane of symmetry has a matching point on the other side at the same distance.
A can can be rented for $50 per day with unlimited mileage, or for $40 per day plus 25 cents per mile . For what daily mileages will be unlimited mileage plan save you money ?
Find the arc length intercepted by a central angle of radians in a circle whose radius is 18.4 inches. 13.8π 15.2π 24.5π
Final answer:
The arc length intercepted by a central angle of π radians in a circle of radius 18.4 inches is calculated as arc length = θ × radius, resulting in 18.4π inches.
Explanation:
To find the arc length intercepted by a central angle of θ radians in a circle with radius r, we use the formula:
arc length (s) = θ × r
Given that the central angle θ is π radians and the radius r is 18.4 inches, we can compute the arc length as follows:
arc length (s) = π × 18.4 inches
By multiplying, we get:
arc length (s) = 18.4π inches
Therefore, the arc length intercepted by a central angle of π radians in a circle with a radius of 18.4 inches is 18.4π inches.
A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth.
Check the picture below.
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{27.6}\\ b=\stackrel{opposite}{h}\\ \end{cases} \\\\\\ \sqrt{30^2-27.6^2}=h\implies \sqrt{138.24}=h\implies 11.76\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the triangle}}{\cfrac{1}{2}bh\implies \cfrac{1}{2}(27.6)(11.76)}\implies 162.288\implies \stackrel{\textit{rounded up}}{162.3}[/tex]
To find the area of the right triangle with a given hypotenuse and adjacent leg, use the Pythagorean theorem to calculate the other leg. Then, use the base and height (the two legs) in the area formula for a right triangle. The area of the triangle is approximately 148.7 cm².
To find the area of a right triangle, you need two perpendicular sides, known as the legs of the triangle. Since we are given the hypotenuse (30 cm) and one adjacent leg (27.6 cm) which is one of the legs, we need to find the other leg. Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In mathematical terms, this is expressed as a² + b² = c². Therefore, the length of the other leg (b) can be found using the equation b² = c² - a², where c is the hypotenuse and a is the given adjacent leg.
Substituting the given values, we have b² = 30² - 27.6². Calculating this gives b ≈ 10.8 cm.
Now, the area of the triangle can be calculated using the formula for the area of a right triangle, which is (1/2) × base × height. In this case, the base and height are the two legs of the triangle. Substituting the lengths of the legs we have, Area ≈ (1/2) × 27.6 cm × 10.8 cm. The result is approximately 148.7 cm², which is the area of the triangle rounded to the nearest tenth.
Tomas used 3 1/3 cups of flour and now has 1 2/3cups left. Which equation can he use to find f, the number of cups of flour he had to begin with?
f+3 1/3=1 2/3
f-3 1/3=1 2/3
3 1/3f=1 2/3
f/3 1/3=1 2/3
For this case we have that the variable "f" represents the number of cups of flour that Tomas had initially.
If of that amount Luis used [tex]3 \frac {1} {3}[/tex] of cups of flour, then we have the following expression:
[tex]f-3 \frac {1} {3}[/tex]
If Luis has[tex]1 \frac {2} {3}[/tex] cups of flour left, then we have the following equation:
[tex]f-3 \frac {1} {3} = 1 \frac {2} {3}[/tex]
Finally, the equation that represents the given situation is:
[tex]f-3 \frac {1} {3} = 1 \frac {2} {3}[/tex]
Answer:
Option B
At the start of the first down, the football was 30 yards from the Tigers' end zone. During three downs, the ball moved 9
yards farther from their end zone, then 14 yards closer to it, and then 2 yards closer to it. How many yards from their end
zone was the ball at the end of the third down?
Answer:
23
Step-by-step explanation:
30 + 9 = 39.
39 - 14 = 25.
25 - 2
= 23
Answer:
23
Step-by-step explanation:
A textbook store sold a combined total 440 of physics and sociology textbooks in a week. The number of sociology textbooks sold was 54 less than the number of physics textbooks sold. How many textbooks of each type were sold?
First subtract the difference of the two by the total:
440 - 54 = 386
Now divide that by 2:
386 / 2 = 193
193 is the number of Sociology books sold.
Now add 54 to 193 for the total Physics books:
193 + 54 = 247 Physics books were sold.
A national study found that a car's value decreases by 15 percent annually. If the car was purchased for $66,000, how much will the car be worth in 10 years? A. $12,993.71 B. $11,768.35 C. $18,429.50 D. $13,792.14
Answer:
A. $12,993.71
Step-by-step explanation:
Each year, the car's value is multiplied by 1-0.15 = 0.85. After 10 years, the car's value will be ...
$66,000×0.85^10 ≈ $12,993.71
If fis a function and x is an element in its domain, which statement is true about the graph of f?
OA.
The graph of f is the graph of the equation f = x.
OB.
The graph of fis the graph of the equation x = f(y).
OC.
The graph of fis the graph of the equation y = x.
D.
The graph of f is the graph of the equation y = f(x).
Reset
Next
The right choice here is
"The graph of f is the graph of the equation y = f(x)."
Horizontal and vertical axes of the Cartesian plane are conventionally labeled and referred to as "x" and "y", respectively. When we talk about the graph of f(x) in that context, we usually mean the graph of y = f(x). However, this convention may not be followed in all cases. There may be no "y" label on the graph at all, or the horizontal axis may be labeled something other than "x".
The coordinates of vertex S are (_,_)
The area of rectangle PQRS is_____square units.
Answer:
vertex s is -2,-2
Step-by-step explanation:
and with the rectangle is q to p is 4cm coz one box is 1 cm and r to q is 3cm so you multiply them and the answer is 12cm
It costs 31.95d + 0.10m dollars to rent a car for d days and drive it m miles. How much does it cost to rent a car for 5 days if the car is driven a total of 600 miles ?
Answer:
$219.75
Step-by-step explanation:
Just plug in the values
x = final cost
31.95(5) + 0.10(600) = x
159.75 + 60 = x
219.75 = x
Can someone help me?
Thanks-Aparri
Answer:
10y
Step-by-step explanation:
9y + y = 10y
Answer:
[tex]10y[/tex]
Step-by-step explanation:
[tex]9y + y = y(9 + 1) = y(1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) = y \times 10 = 10y[/tex]