Answer:
B
Step-by-step explanation:
Let the two numbers be a and b.
The product of the two is 120 and their sum of their squares is 289. In other words:
[tex]\displaystyle ab = 120 \text{ and } a^2 + b^2 = 289[/tex]
And we want to find the sum of the two numbers.
We can use the perfect square trinomial. Recall that:
[tex]a^2 + 2ab + b^2 = (a+b)^2[/tex]
From the first equation, multiply by two:
[tex]2ab = 240[/tex]
Add the two equations together:
[tex](a^2+b^2)+(2ab) = (289)+(240)[/tex]
Simplify and rewrite:
[tex]a^2+2ab+b^2 = 529[/tex]
Factor using the perfect square trinomial pattern:
[tex](a+b)^2 = 529[/tex]
And take the square root of both sides:
[tex]\displaystyle a + b = \pm\sqrt{529} = \pm23[/tex]
Hence, the sum of the two numbers is 23 or -23.
In conclusion, our answer is B.
7/9+6/8+6/3=
I really need the answer
Answer:
[tex]\frac{1}{30}[/tex]
Step-by-step explanation:
Take it in steps. First, find 7/9+6. Then we'll find 8+6/3, and, finally, we'll divide the two answers.
1:
7/9+6 = 7/15
2:
8+6/3 = 14/3
3:
[tex]\frac{\frac{7}{15}}{\frac{14}{3}}[/tex] or [tex]\frac{7/15}{14/3}[/tex]
Then take that in chunks: 7/14 and 15/3.
7/14 = 1/2
15/3 = 5/1
Use those to rewrite it as [tex]\frac{1/5}{2/3}[/tex].
1/5 = .2
2/3 ≈ .6667 so we'll keep writing it as 2/3
[tex]\frac{\frac{.2}{2}}{3}[/tex]
.2/2 = .1, so:
[tex]\frac{.1}{3}[/tex] = [tex]\frac{1}{30}[/tex]
How do Curves A and B compare to each other with respect to f and f ′?
The answer cannot be determined.
f: Curve B, f ′: Curve A
f: Curve A, f ′: Curve B
Neither Curve A nor Curve B are derivatives of each other.
It's likely that curve A is f and curve B is f '.
The points where curve B crosses the horizontal axis correspond to the extrema of curve A at around 0 and 0.45, and the extremum of curve B corresponds to the inflection point of curve A at around 0.2. These observations are consistent with the first and second derivative tests.
If f(x)= 2|x|+3x, then the value of f(-1) is
Answer:
-1
Step-by-step explanation:
f(-1) = 2|-1| + 3(-1)
|-1| = 1
=> f(-1) = 2(1) - 3
=> f(-1) = 2 - 3
=> f(-1) = -1
This year Amanda watched 80 movies. She thought that 56 of them were very good. Of the movies she watched, what percentage did she rate as very good?
I keep getting 30 but it’s not right. Can anyone tell me the steps?
2[10-3(4-2)]+1
Answer:
9
Step-by-step explanation:
[tex]2[10-3(4-2)]+1\\=2(10-3\times2)+1\\=2(10-6)+1\\=2\times4+1\\=9[/tex]
In a charity triathlon, Mark ran half the distance and swam a quarter of the distance. When he took a quick break to get a drink of Gatorade, he was just starting to bike the remaining 24 miles. What was the total distance of the race?
The total distance of the race is D = 96 miles
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let's denote the total distance of the race as "d" miles.
According to the given information, Mark ran half the distance and swam a quarter of the distance. This can be expressed as:
Distance Mark ran = d/2 miles
Distance Mark swam = d/4 miles
After Mark's quick break, he was just starting to bike the remaining 24 miles. Since he has already completed running and swimming, the total distance he has covered at that point is:
And this distance is equal to 24 miles, as given in the problem:
d/2 + d/4 + 24 = d
On simplifying the equation , we get
( 3/4 )d + 24 = d
Subtracting ( 3/4 )d on both sides , we get
( 1/4 )d = 24
Multiply by 4 on both sides , we get
d = 96 miles
Hence , the total distance of the race, denoted by "d", is 96 miles
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I have to calculate the lengths of all the triangles sides using pythagoras theorem
Answer:
√62 = 8
y = 8
√225 = 15
z = 15
Pythagoras theorem
a^2 + b^2 = c^2
in this case...
y^2 + z^2 = x^2
8^2 + 15^2 = √289
8^2 + 15^2 = 17
x= 17
Akilometer is approximately 1094 yards . Toby runs a 6 km race. About how many yards does he run?
Select the correct answer.
Based on these segment lengths, which group of segments cannot form a triangle?
OA 12,7,8
OB. 8, 7, 13
OC. 1,2,3
OD. 80,140, 70
Reset
Next
2021 EdimentumAll rights
Answer:
C
Step-by-step explanation:
If you add up the length of two sides, the sum must be greater than the third side of the triangle.
If you add 1 and 2, it equals 3
But that means it will be equal to the length of the third side, 3
It will be impossible to make a triangle with those lengths of sides no matter how the sides or angles are set.
It's sort of difficult to explain this without any visual
You can look up "triangle inequality" to find out more about this
please help me, if you help then thanks!
Answer:
B. [tex] {a}^{ - 7 - 10} [/tex] (second option)
Step-by-step explanation:
[tex] \frac{ {a}^{ - 7} }{ {a}^{10} } [/tex]
[tex] {a}^{ - 7 - 10} [/tex]
[tex] - 7 - 10 = - (7 + 10) = - 17[/tex]
The inverse of the relation y = 9x – 4 can be obtained graphically by:
The inverse of the function y = 9x -4 is obtained by a reflection in the line at ( y = x ). Hence Option D is correct.
What is the reflection of a line?Each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point but is on the other side of the line. This transformation is known as a reflection over the line.
The inverse relation for y= 9x -4 will be calculated by putting the value of x equal to y or replacing x by y and y by x in the equation.
Hence Option D is correct.
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what is the zero turn for the arithmetic sequence 128,96,64,32
You are falling by [tex]32[/tex],
[tex]128, 128 - 32, 128 - 32\cdot2,\dots[/tex]
In general your sequence is defined as,
[tex]a_n=128-32\cdot n[/tex] where [tex]0\leq n \lt\infty[/tex].
The question is at which [tex]n[/tex] does the value [tex]a_n=0[/tex].
If you divide [tex]128[/tex] with [tex]32[/tex] you get the number of steps needed to stuff [tex]128[/tex] with [tex]32[/tex], [tex]4[/tex].
If you plug in [tex]n=4[/tex], you get [tex]a_4=128-32\cdot4[/tex], since [tex]32\cdot4=128[/tex] you get [tex]a_4=0[/tex].
The zero turn of the arithmetic sequence is thus at [tex]n=4[/tex].
Hope this helps :)
help me do this please!
Answer:
m<ABD = 37°
m<DBC = 58°
Step-by-step explanation:
m<ABD + m<DBC = m<ABC
2x + 23 + 9x — 5 = 95
11x + 18 = 95
-18 -18
--------------------
11x = 77
/11 /11
---------------------
x = 7
Now, plug this into the equation for m<ABD and m<DBC to find their values.
m<ABD = 2x + 23
= 2(7) + 23
= 14 + 23
= 37
m<DBC = 9x — 5
= 9(7) — 5
= 63 – 5
= 58
Now, check to see if our values are right or not.
2x + 23 + 9x — 5 = 95
2(7) + 23 + 9(7) — 5 = 95
14 + 23 + 63 – 5 = 95
100 – 5 = 95
95 = 95 CORRECT
What's the X-Intercepts of (2x-5)(x+1)=9 or (2x-5)(x+1)-9
Answer:
Step-by-step explanation:
Either way works. It comes to the same thing.
(2x-5)(x+1)=9
F: 2x*x = 2x^2
O: 2x*1 = 2x
I: -5 * x = -5x
L: -5*1 = -5
2x^2 + 2x - 5x - 5 = 9 Subtract 9 from both sides
2x^2 - 3x - 14 =0 Divide by 2 (it makes life easier).
Factoring you get
(2x - 7)(x + 2)
2x - 7 = 0
2x = 7
x = 3.5
x + 2 = 0
x = -2
The x intercepts = (3.5,0) and (-2,0)
I've put a graph up for the given equation.
Round 57.5958961796 to the nearest hundredth.
Help please! Find the area of the shape below. (Show work)
9514 1404 393
Answer:
292 yd²
Step-by-step explanation:
We can find the area of the remaining L shape by subtracting the area of the 21×22 rectangle at lower left from the 26×29 overall rectangle.
shape area = (26 yd)(29 yd) -(21 yd)(22 yd) = 754 yd² -462 yd²
shape area = 292 yd²
__
Additional comment
The area of a rectangle is the product of its length and width.
There are many ways the area of this shape can be calculated. The area can be divided into two rectangles, two trapezoids, three rectangles, and other ways.
If you cut up the given shape into smaller pieces, you will generally need to know the widths of the arms of the L. One of those is shown as 7 yd. The other is 26-21 = 5 yd.
Using the method we did, we only needed the dimensions shown on the figure.
The width of a rectangle measures (2p - 9q) centimeters, and its length measures
(7p - 10q) centimeters. Which expression represents the perimeter, in centimeters,
of the rectangle?
Given Data : Length = (7p - 10q) and Breadth = (2p - 9q)
Calculation :
⟹ Perimeter = 2(Length + Breadth)
⟹ Perimeter = 2(7p - 10q + 2p - 9q)
⟹ Perimeter = 2(9p - 19q)
⟹ Perimeter = 18p - 38q centimetres
Answer : 18p - 38q centimetresThe required perimeter of the rectangle is 18p - 38q centimeters.
It is required to find the required perimeter of the rectangle.
What is rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
Given:
width of a rectangle = (2p - 9q) centimeters,
length measures= (7p - 10q) centimeters.
We know that
⟹ Perimeter = 2(Length + Breadth)
By put the value width and length in perimeter we get,
⟹ Perimeter = 2(7p - 10q + 2p - 9q)
⟹ Perimeter = 2(9p - 19q)
⟹ Perimeter = 18p - 38q centimeters
Therefore, the required perimeter of the rectangle is 18p - 38q centimeters.
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What is the measurement??
Answer:
83°
.......................
Answer:
83
Step-by-step explanation:
(25x3) + (10x3) is my question i dont know the answer
Answer:
75+30=105....................
1. If a = -1 , the value of3a + 1 is
Answer:
[tex]f(a) = 3a + 1 \\ Now,\: a = - 1 \\ f( - 1) = 3( - 1) + 1 \\ f( - 1) = - 3 + 1 \\ \boxed{ f( - 1) = - 2}[/tex]
Therefore, -2 is the right answer.Solve if x measure of AOC = 7x-2 measure of AOB = 2x+8 measure of BOC = 3x+14.
Answer:
x=3[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
im assuming this a triangle if so all angles add up to 180 so combine all equations and make it so it equals 180
7x-2+2x+8+3x+14=180
Combine Like Terms: 12x+20=180
12x+20-20=180-20
12x=160
12x/12=160/12
x=13[tex]\frac{1}{3}[/tex]
An x measure of AOC = 7x-2 measure of AOB = 2x+8 measure of BOC = 3x+14 value of x is 28.33.
A three angles, AOC, AOB, and BOC, and you're given their measures in terms of x. The problem is likely asking you to find the value of x. Since these angles are in a circle, they must add up to 360 degrees.
The sum of the measures of the angles around a point is 360 degrees:
Angle AOC + Angle AOB + Angle BOC = 360
Substitute the given expressions for the angle measures:
(7x - 2) + (2x + 8) + (3x + 14) = 360
Combine like terms:
12x + 20 = 360
Now, subtract 20 from both sides:
12x = 340
Finally, divide by 12:
x = 340 / 12
x = 28.33
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Find the midpoint of the segment with the given endpoints.
(-7, -9) and (-2,7)
Answer:
(-9/2,-1)
Step-by-step explanation:
Use the midpoint formula to find the midpoint of the line segment.
if 3x+7 Y-37 and x = 3, then Y = ?
Answer:
y = 4
Step-by-step explanation:
Given
3x + 7y = 37 ← substitute x = 3 into the equation
3(3) + 7y = 37, that is
9 + 7y = 37 ( subtract 9 from both sides )
7y = 28 ( divide both sides by 7 )
y = 4
Step-by-step explanation:
What element in the domain has image 7 in the function f(x) = x²– 2?
a. 3 b) 9 c) -1 d) 4
Answer:
[tex]f(x) = 7 \\ f(x) = {x}^{2} - 2 \\ {x}^{2} - 2 = 7 \\ {x}^{2} = 2 + 7 \\ {x}^{2} = 9 \\ x = \sqrt{9} \\ \boxed{x = 3}[/tex]
Therefore, 3 is the element in the domain which has the image 7 in function f(x)=x²-2
A. 3 is the right answer.A
person that weighs 150 pounds on
Earth will weigh 25 pounds on the Moon.
How much will a 90-pound person weigh
on the Moon?
A. 10 lb
B. 12 lb
C. 15 lb
D. 20 lb
Answer:
Step-by-step explanation:
Ans:15 lb
A 90-pound person will weigh 15lb as we weigh six times less on the moon than the earth. So to find out simply divide 90 by 6.
Simplify show step by step 30 POINTS!
Step-by-step explanation:
hopefully it makes sense and is visible
:)
Helppp
Find the measure of ∠3.
Answer:
90°
Step-by-step explanation:
diagonals of a kite intersect each other at 90°
:)
ANSWER :
third option 90 degrees
Step-by-step explanation:
the opossite adjasent angle is 1 that is 90 so angle 3 is opposite adjacent angle of angle 1
*The opposite adjacent angles will always be same
Find the differential of the function w=x^(4)sin(y^(4)z^3)
Step-by-step explanation:
[tex]w = x^4\sin(y^4z^3)[/tex]
The differential [tex]dw[/tex] is
[tex]dw = 4x^3\sin(y^4z^3)dx [/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(4y^3z^3)dy [/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(3y^4z^2)dz[/tex]
Solve the equation. Check your solution.
Answer:
x = 5
Step-by-step explanation:
x^2/(x + 5) = 25/(x+5) Subtract the right side from both sides.
x^2/(x + 5) - 25/(x + 5) = 0
x^2 - 25
======= = 0
x + 5
(x + 5)(x - 5)
============= = 0
(x + 5)
Cancel x + 5 in the numerator and denominator.
x - 5 = 0
x = + 5
Does it check?
x^2/(x + 5) = 25/(x + 5)
x = 5
5^2/(10) = 25/10
25/10 = 25/10 Yes it checks.
Supplementary angles are pairs of angles whose measures total 180º. Determine the measure of
supplementary to an angle with a measure of 92°
Hi there!
»»————- ★ ————-««
I believe your answer is:
88°
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
As mentioned in the question, supplementary angles add up to 180°.⸻⸻⸻⸻
[tex]\boxed{\text{Setting Up An Equation...}}\\\\a + 92 = 180\\----------\\ a - \text{Unknown angle measure.}\\----------\\\rightarrow a + 92 - 92 = 180 - 92\\\\\rightarrow \boxed{ a = 88}[/tex]
⸻⸻⸻⸻
The unknown angle measurement should be 88°.
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
