Answer:
8√3
Step-by-step explanation:
Let a, b = the positive numbers, and the sum = s,
(1)---- ab = 192
(2)--- a + b = s
Since we want to find the minimum sum, we'll have to substitute one of the variables (either a or b) from (1) to (2), I'll choose b,
From (1), b = 192/a
Substitute b = 192/a into (2),
s = a + 192/a
Now, we are able to use a concept of calculus (maximum & minimum) to solve it, just remember 2 steps in finding the values of x in maxima minima question:
1) find dy/dx
2) Find x from dy/dx = 0
ds/da = 1 - 192/a²
When ds/da = 0,
1 - 192/a² = 0
a² = 192
a = ±√192
a = 8√3 , -8√3
Since a is positive, a = 8√3
Substitute a into (1),
b = 192/(8√3)
b = 8√3
Therefore, the two positive numbers are 8√3... and 8√3
I know that the answer is 27 and that 3 + x = 7 but where do you get 4?
Answer:
27
step by step explanation
if you are calculating for the area of the figure, divide the shape into two figures and you will get two rectangles
for shape 1
length=3 width=5
for shape2
length 7-3=4
width=3
area of shape1. =3×5=15
area of shape2. =4×3=12
area of the shape= 12+15 = 27
can someone help me with this please
perspective
I hope this helps you
:)
id
11. A chessboard has diagonals of length
40 cm. What is the length of each side of the
board, to the nearest tenth of a centimetre?
Explain your reasoning.
Answer:
√800 = 28 cm
Step-by-step explanation:
Your c value is 40cm beacause c=length of the hypotenuse, or in this case the diagonal of the chess board.
You now have 2a2=402.
Start solving it:
2a2=402
2a2=1600
(2a2)/2=1600/2
a2=800
√(a2)=√800
a=√800 cm
You can plug this back in to check your answer, and also be sure that a=b is true.
a2+b2=c2
(√800)2+(√800)2=c2
800+800=c2
1600=c2
√1600=√c²
40=c
The measures of two angles of a triangle are 29° and 61°. Is the triangle acute, right, or obtuse? Use geometric terms in your explanation.
Assuming that Dave’s marginal tax bracket is 25%, but how much did his federal taxes declined this year if he contribute 7000 to his retirement account?
The marginal tax bracket of Dave shows that the amount of the federal tax is $28000.
How to compute the tax?Let the federal tax be represented by x.
From the information, Dave’s marginal tax bracket is 25%, and he contributed 7000.
Based on the information, the amount will be:
25% of x = 7000
0.25 × x = 7000
0.25x = 7000
x = 7000/0.25
x = $28000
In conclusion, the amount is $28000.
Learn more about tax on:
https://brainly.com/question/25783927
Can y’all figure out the answer for me please
The answer is A. True.
Hope this helps
Answer:
True
Step-by-step explanation:
Two triangles are similar { ~ } only when they have same shape. And as these figures have same shape so they are similar. And their corresponding sides are equal too...
An ellipse has focused F1 (-2,4) and F2 (0,7) and the point (4,4) is on the ellipse. Identify the constant sum for the ellipse.
Answer:
please solve this quickly tommorow is my maths exam
Answer:
11
Step-by-step explanation:
which term describes the point where the three medians of a triangle intersect?
Answer: It is the centroid of a triangle or A. Centroid
Step-by-step explanation:The centroid of a triangle is the intersection of the three medians of the triangle (Where each median connecting a vertex with the midpoint of the opposite side)
The incenter of a triangle is the point where the angle bisectors of the all vertices of the triangle intersect.
The orthocenter of the triangle is the point where all three altitudes of the triangle intersect. where An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side.
The circumcenter of the triangle is the point where the perpendicular bisector of the sides of the triangle intersect.
Solve for x
2x3=x2+6x
please help me. Thanks
Answer:
heya! ^^
[tex]2x {}^{3} = x {}^{2} + 6x \\ \\ 2x {}^{3} = x(x + 6) \\ \\ dividing \: both \: sides \: by \: x \\ \\ \frac{2\cancel{x} {}^{3} }{\cancel{x}} = \frac{\cancel{x}(x + 6)}{\cancel{x}} \\ \\ 2x {}^{2} = x + 6 \\ \\ 2x {}^{2} - x - 6 = 0 \\ \\ by \: splitting \: the \: middle \: term \: ( - x) \\ \\ 2x {}^{2} - 4x + 3x - 6 = 0 \\ \\ 2x(x - 2) + 3(x - 2) = 0 \\ \\ 2x + 3 = 0 \: \: \: or \: \: \: (x - 2) = 0 \\ \\ x = \frac{ - 3}{2} \: \: \: \: or \: \: \: \: x = 2[/tex]
hope helpful :D
Which of the following algebraic expression represents 2 less than 3 lots of n? (A) - (B) (C) 3(n - 2) 2 – 3n 3 + n - 2 3n - 2 (D)
Answer:
D
2 less than means 2 to be subtracted3lots of n means 3 to be multiplied with n i.e 3nHence the expression is 3n-2
URGENT I HAVE ALMOST 0 TIME LEFT I NEED LAST MINUTE HELP
A parabola has zeros of 7 and 1 and passes through the point (3,4). Determine the equation of the parabola.
Answer:
The zeros are the points where the parabola intercepts the x-axis.
[tex]\sf x = 7 \implies x - 7 = 0[/tex]
[tex]\sf x = 1 \implies x - 1 = 0[/tex]
[tex]\sf \implies y = a(x - 7)(x - 1)[/tex] where a is some constant
If the parabola passes through point (3, 4) then:
[tex]\sf \implies a(3 - 7)(3 - 1) = 4[/tex]
[tex]\sf \implies a(-4)(2) = 4[/tex]
[tex]\sf \implies -8a = 4[/tex]
[tex]\sf \implies a = -\dfrac12[/tex]
So the equation of the parabola is:
[tex]\sf y = -\dfrac12(x - 7)(x - 1)[/tex]
Or in standard form:
[tex]\sf y = -\dfrac12x^2+4x-\dfrac72[/tex]
Spot the quadratic equation:-
(x-1)(x-7)x(x-7)-1(x-7)x²-7x-x+7x²-8x+7Find a through (3,4)
a(x²-8x+7)=4a(9-24+7)=4a(-8)=4a=-1/2Equation:-
y=-1/2(x-7)(x-1)What net is shown below?
triangular prism
rectangular prism
O square pyramid
triangular pyramid
Answer:
Rectangular Prism
as Opposite sides are equal
Answer:
rectangular prism because it has dimensions of 5 sides and if you fold it, it would turn into a rectangular prismI think of a number, add 5,then square the answer. The result is 100. What could the number be?
x=
x=
Answer:
x = 5
x = -15
Explanation:
Let the number be "x"
===================
(x + 5)² = 100x + 5 = ±√100x + 5 = ±10x + 5 = 10, x + 5 = -10x = 10 - 5, x = -10 -5x = 5, -15Answer:
x= 5 or -15
Step-by-step explanation:
let the number be x
(x+5)^2=100
x^2+10x+25=100
x^2+10x-75=9
look for factors of 75 that when you gives you 10 and when you multiply gives you -75
those factors are 15 and -5
replace 10x with 15x and -5x
x^2+15x-5x-75=0
then group them, and factorize
x(x+15)-5(x+15)=0
x-5=0 or x+15=0
x= 5 or x= -15
The triangle shown below has an area of 16 units^2 squared.
Find the missing length.
x = ______ units
Answer:
8 units
Step-by-step explanation:
Given:
Base = 4 unitsHeight = x unitsArea of triangle = 16 units²Formula:
[tex]\text{Area of triangle:} \ \dfrac{1}{2} \times \text{Base} \times \text{Height}[/tex]
Substitute the base, height and the area of the triangle to determine the measure of the height (x).
[tex]\implies 16 \ \text{units}^{2} = \ \dfrac{1}{2} \times 4\times x[/tex]
Simplify the right hand side of the equation.
[tex]\implies 16 \ \text{units}^{2} = \ 2\times x[/tex]
Divide both sides by 2 to isolate "x".
[tex]\implies \dfrac{16 \ \text{units} }{2} = \dfrac{2\times x}{2}[/tex]
[tex]\implies 8 \ \text{units} = x[/tex]
The measure of the height (x) is 8 units.
Answer: 8
Step-by-step explanation:
Write the equation in slope-intercept form. y=−5(x+6)+2x
Answer:
y = −3x −30
Step-by-step explanation:
Slope-intercept form: y = mx + b
y = mx + b
m = slopeb = y-intercept (when x = 0)y = −5(x + 6) + 2x <== distribute -5
y = −5(x) + −5(6) + 2x
y = −5x −30 + 2x <== combine like terms
y = −3x −30
y = −3x −30
-3 = slope-30 = y-intercept (0, -30)Hope this helps!
Identify the indicated angles as Adjacent, vertical, linear, or complimentary
Classify the following triangle as acute, obtuse, or right.
A. Obtuse
B. Acute
C. Right
D. None of these
Answer: this is a acute triangle
Step-by-step explanation: acute triangle angles are all less than 90°
The circumference of the circle is 24 cm and the radius is √x+2. Find x and its radius. Use = 3.14 . Round your answer to two decimals.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
Circumference of a circle :
[tex]\qquad \tt \dashrightarrow \:2 \pi r[/tex]
And we have been given that Circumference = 24 cm
So, let's equate them and find radius (r) :
[tex]\qquad \tt \dashrightarrow \:2 \pi r = 24[/tex]
[tex]\qquad \tt \dashrightarrow \:r = \dfrac{ 24}{2 \pi}[/tex]
[tex]\qquad \tt \dashrightarrow \:r = \dfrac{ 12}{3.14}[/tex]
[tex]\qquad \tt \dashrightarrow \:r = 3.82 \: \: cm[/tex]
So, we got the radius here. now let's equate it with expression in terms of x to find value of x
[tex]\qquad \tt \dashrightarrow \: \sqrt{x + 2} = 3.82[/tex]
[tex]\qquad \tt \dashrightarrow \:{x + 2} = (3.82) {}^{2} [/tex]
[tex]\qquad \tt \dashrightarrow \:{x } \approx 14.59 - 2[/tex]
[tex]\qquad \tt \dashrightarrow \:{x } \approx 12.59 \: \: cm[/tex]
x = 12.61
===========
[tex]\bold{C = 2\pi r}[/tex] [ C = 24, π = 3.14, r = √x+2 ]
2(3.14)(√x+2) = 24(6.28)(√x+2) = 24√x+2 = 24/6.28x+2 = (24/6.28)²x = (24/6.28)² - 2x = 12.60505497x ≈ 12.61 ( rounded to nearest two decimal places )(b) An Investment is estimated to grow at the rate al 15% per annum. If the worth of the Investment now is ¢850,000 i. What will its worth be in the 6th year? What is the percentage increase in its worth after 6th year? In what year will the investment worth ¢3.23million ?
Answer:
~9.6 years it will be worth 3.23 mil.
Step-by-step explanation:
This problem requires use of the growth formula.
PART 1:
Equation:
[tex]3,230,000 = 850,000 * (1.15)^6[/tex]
By solving this you get:
A valuation of $1,966,101.65078125 after 6 years
PART 2:
Equation:
[tex]3,230,000 = 850,000*(1+.15)^x[/tex]
By solving this (which im too lazy to show the steps for) you get:
x = years
x = ~9.6 years / 9.55196417 years
Write the phrase “the sum of 3 times a number and 5” as a mathematical expression.
Answer:
[tex](3*x)+5[/tex]
Step-by-step explanation:
Let the variable x equal "a number"
The phrase times means we multiply the variable x by the constant 3.
The phrase sum of means we add the constant 5 to the term (3 * x).
[tex](3*x)+5[/tex]
Answer: 3x + 5 that's the answer i had to type this cause the answer was to short to post lol
Multiply.
8×3/5
Enter your answer as a mixed number in simplest form by filling in the boxes.
$$
Answer:8x3/5=4.8
Step-by-step explanation:
Answer:
in simple form its 4.8
for a improper fraction its 43/5
I will comment for the mixed number but if this is correct can u mark me brainliest
what is 22 percent of 198
Answer:
43.56
Step-by-step explanation:
22 percent of 198 can be found by converting 22 percent into decimal form which is
22% = 0.22
because a 100% = 1
Then we can multiply 0.22 by 198
0.22*198 = 43.56
So the answer is 43.56
Hope this helps! :)
Write an equation of the line that passes through (-1,3) and is parallel to the line y=2x+2 .
Answer:
y = 2x + 5
Step-by-step explanation:
REMEMBER:
The new line will be parallel to the line represented by y =2x +2⇒ The equation y = 2x + 2 is written in slope- intercept form (i.e. y=mx + b) where m represents the slope. So the slope of this line is 2. A line parallel to y = 2x + 2 will have the same slope. This means the slope of the new line will also be 2.
To determine the equation of the new line, we can use the given point to find the y intercept of the new line:
⇒ y = 2x + b
Use x = -1 and y =3 to find b (or the y intercept ) of the new line:
⇒ 3 = 2 * (-1) + b
⇒ 3= -2 + b
⇒ b=5
Therefore, the equation of the line passing thru (-1,3) with the same slope as that of y = 2x + 2 will be:
⇒ y = 2x + 5
Answer:
y = 2x + 5
Step-by-step explanation:
Given line equation 2x - y + 2 = 0
Equation of line parallel to this line will be of form
=> 2x - y + k = 0 ( where 'k' is a constant )
Now this line passes through (-1,3)
=> 2(-1) - (3) + k = 0
=> -2 - 3 + k = 0
=> k - 5 = 0
=> k = 5
Therefore the required line equation is 2x - y + 5 = 0 or y = 2x + 5
Hope you've understood the solution.
One number is 4 more than another number. If the greater number is x, what is the other number?
first number: x
second number: x -4
A farm grew 19.8 tons of wheat in 2013. The farm's wheat output increased by 9.8% from 2013 to 2014 and by 5.1 % from 2014 to 2015. Which expression represents a strategy for estimating the total output of wheat, in tons, in 2015?
Answer:
19.8 X 0.098 = 1.9404
increased 1.9404 from 2013 to 2014
19.8 + 1.9404= 21.7404
increasses another 5.1% for 2014 to 2015
21.7404 X 0.051 = 1.1087757
1.1087757 + 21.7404 = 22.8491757
Total output of wheat for 2015 is 1.11
Total output of wheat 22.85 rounded off
Step-by-step explanation:
What is the slope of a line perpendicular to the line whose equation is
5x – 2y = -10. Fully simplify your answer.
Answer:
-2/5
Step-by-step explanation:
5x - 2y = -10
-2y = -5x - 10
y = 5/2x + 5
m = 5/2
Perpendicular lines have slopes that are negative reciprocals of one another. For example, 5 would become -1/5 and 1/3 would become -3.
If m = 5/2
Perpendicular line m = -2/5
Hope this helps!
Answer:
The slope of the line perpendicular to this line is -2/5.
Step-by-step explanation:
5x - 2y = -10
Let's simplify this equation to be in slope-intercept form: y = mx + b.
Start by adding 2y to both sides of the equation.
5x = -10 + 2yNext, add 10 to both sides of the equation.
5x + 10 = 2yDivide both sides of the equation by 2.
(5x + 10)/2 = y (5/2)x + 5 = yThe slope of this line is the coefficient of x; in this case, it is 5/2.
If we want to find the slope of the line perpendicular to this line, we take the opposite (change the sign) reciprocal (flip the fraction).
The slope 5/2 becomes -2/5.
Therefore, the slope of a line perpendicular to the line whose equation is 5x - 2y = -10 is -2/5.
A line has a slope of 2 and a y-intercept of -3/4 which of the following is an equation of the line
Answer:
y = 2x - 0.75
Step-by-step explanation:
Slope-intercept form is:
⇒ y = mx + b
m being the slope and b being the y-intercept.
The given slope and y-intercept:
⇒ Slope ⇒ 2
⇒ Y-intercept ⇒ -3/4
Plug in:
⇒ y = 2x - 0.75 (3/4)
solutions answer equations
Answer:
x² - 6x = 7
x² - 6x + 9 = 7 + 9
(x - 3)² = 16
x - 3 = ± 4
x - 3 = 4 and x - 3 = -4
x: {-1, 7}
Largest value of x = 7
Smallest value of x: -1
I hope this helps!
50 POINTS! Please help me! I give Brainliest!
1. Given the following coordinates, complete the listed transformations in sequence, which means you do one after the other.
X(2, 4)
Y(5,-3)
Z(-7, 1)
a) Rotate the points 90 degrees clockwise
b) Dilation by a scaling factor of 2
c) Reflect across the x-axis
d) Translation 2 Up and 5 to the Left
4 PARTS TO THIS QUESTION! ANSWER ALL PLEASE!
#1
Clockwise 90° rotation rule (x,y)—»(y,-x)
X'=(4,-2)Y'=(-3,-5)Z'=(1,7)#2
Dilation of scale factor 2
X''=(4×2,-2×2)=(8,-4)Y''=2(-3,-5)=(-6,-10)Z''=2(1,7)=(2,14)#3
reflection across x axis rule (x,y)—»(x,-y)
X'''=(8,4)Y'''=(-6,10)Z"'=(2,-14)#4
Rule for given translation (x-5,y+2)
X""=(8-5,4+2)=(3,6)Y""=(-6-5,10+2)=(-11,12)Z""=(2-5,-14+2)=(-3,-12)Answer:
Given points:
X = (2, 4)Y = (5, -3)Z = (-7, 1)Part (a)
Rotate 90° clockwise (about the origin): (x, y) → (y, -x)
X' = (4, -2)Y' = (-3, -5)Z' = (1, 7)Part (b)
Dilation by a scale factor → multiply the points by the scale factor
scale factor = 2
X'' = (8, -4)Y'' = (-6, -10)Z'' = (2, 14)Part (c)
Reflect across the x-axis: (x, y) → (x, -y)
X''' = (8, 4)Y''' = (-6, 10)Z''' = (2, -14)Part (d)
Translate 2 up and 5 to the left: (x, y) → (x - 5, y + 2)
X'''' = (3, 6)Y'''' = (-11, 12)Z'''' = (-3, -12)2root 3 + root 3 is equal to?
Answer:
i believe the answer is C
Step-by-step explanation:
Answer:
(C) 3√3
Step-by-step explanation:
Think of √3 as x.
Then 2x + x = 3x, so
2√3 + √3 = 3√3