Answer:
x = 6.73 (corrected to 3 significant figures.)
Step-by-step explanation:
(x-5)^2=3
Square root both sides of the equation.
[tex]\sqrt{(x-5)^2} =\sqrt{3}[/tex]
[tex](x-5) = \sqrt{3}[/tex]
Add 5 to both sides.
[tex]x = \sqrt{3} + 5[/tex]
x = 6.73 (corrected to 3 significant figures.)
Answer:
x=-22 or -13
Step-by-step explanation:
(x-5)^2=3
Or,x^2-10x+25=3
Or,x^2-10x=3-25
Or,x (x-10)=-22
Either
x=-22
Or,
x-10=-22
x=-22+10
x=-12
x=-22,-12
which function has a constant additive rate of change of –1/4? A coordinate plane with a straight line with a negative slope. The line passes through (negative 2, 2) and (2, 1). A coordinate plane with a curved line passing through (negative 1, 2), (0, negative 1), the minimum (2, negative 2), and (4, negative 1). A two column table with five rows. The first column, x, has the entries, 20, 21, 22, 23. The second column, y, has the entries negative 1, negative 1.5, negative 2, negative 2.5. A two column table with five rows. The first column, x, has the entries, negative 12, negative 11, negative 10, negative 9. The second column, y, has the entries, 7, 11, 14, 17.
Answer:
A
Step-by-step explanation:
edge 2020
The function shown in graph (A) has a constant additive rate of change is -1/4 option (A) is correct.
What is the rate of change?It is defined as the change in values of a dependent variable with respect to the independent variables.
As we know,
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the first graph:
The line goes through the points:
(-2, 2) and (2, 1)
y - 1 = (1-2)/(2+2)[x -2]
y - 1 = (-1/4)[x -2]
y = -x/4 + 1/2 + 1
y = -x/4 + 3/2
The constant additive rate of change = -1/4
Thus, the function shown in graph (A) has a constant additive rate of change is -1/4 option (A) is correct.
Learn more about the rate of change here:
brainly.com/question/12786410
#SPJ6
Find x A. 46–√ B. 32 C. 43–√ D. 6–√
Answer:
[tex]\textbf{A. }4\sqrt{6}[/tex]
Step-by-step explanation:
The hypotenuse of the isosceles right triangle is √2 times the length of one leg, so is 6√2.
The hypotenuse of the 30°-60°-90° right triangle is 2/√3 times the length of the longer leg.
[tex]x=\dfrac{2}{\sqrt{3}}\cdot 6\sqrt{2}\\\\=\dfrac{(2\sqrt{3})(6\sqrt{2})}{3}\quad\text{rationalize the denominator}\\\\\boxed{x=4\sqrt{6}}[/tex]
I need help with this please
Hey there! :)
Answer:
0.3.
Step-by-step explanation:
Looking at the row for "Less than 80° F", the column for "Rain" shows a 0.3 probability in the table. Therefore:
The probability of rain on a day less than 80°F is 0.3.
Hour many hours are in 7 days?
Answer: 168 hours
Step-by-step explanation:
There are 24 hours in a day. Thus, simply multiply 7*24 to get 168.
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------------------
Answer: There are 168 hours in 7 days.
Since there 24 hours in a day, Multiply 24 times 7 and you get 168.
Example : 24 x 7 = 168.
Working out simultaneous equations.
Answer:
x = 6/5
y = 8/5
Step-by-step explanation:
3x - y = 2
2x + y = 4
Add the equations, cancelling y.
5x = 6
x = 6/5
Put x as 6/5 in the second equation and solve for y.
2(6/5) + y = 4
12/5 + y = 4
y = 4 - 12/5
y = 8/5
The useful life of an electrical component is exponentially distributed with a mean of 1000 hours a. What is the probability the circuit will last more than 2000 hours?
Answer:
0.865
Step-by-step explanation:
To solve for the probability we would be using the formula:
F(x) = 1 - e^−λx
Therefore, P(x > 2000) = F(x) = 1 - e^−λx
Mean = 1000 hours
λ = 1/mean = 1/1000 hours
x= 2000 hours
F(x) = 1 - e^−(1/1000)2000
F(x) = 1 - e^−2
= 0.8646647168
Therefore, the probability the the circuit will last at least 2000 hours = 0.865
Un agricultor tiene 140 metros de malla para instalar una cerca en su huerta de hortalizas y esa tiene forma de rectangulo a) encuentra una función que modele el área de la huerta que pueda cercar b)¿Para que valor de la longitud del largo, el area es Maxima?
Tenemos que sean x e y los lados de la huerta entonces el perímetro sería:
P = 2*x + 2*y
Sabemos que el perimetro es 140, reemplazando:
140 = 2*x + 2*y
x + y = 70
despejamos y, nos queda:
y = 70 - x
Ahora tenemos que el área sería:
A = x*y
reemplazamos y:
A = x*(70 - x)
A = 70*x - x^2
Esta sería la ecuación que modela el área de la huerta.
Derivamos e igualamos a 0:
0 = 70 - 2*x
x = 70/2
x = 35
ahora calculamos y:
y = 70 - 35
y = 35
El área máxima sería:
A = 35*35
A = 1225 m^2
What is the area of a circle whose diameter is 64
Answer:
A ≈ 3215.36
Step-by-step explanation:
A = πr²
Radius - D/2
Radius - 64/2 → 32
A = 3.14(32)²
A = 3215.36
Hope this helps! :)
Answer:
3215.36 um²
Step-by-step explanation:
d = 2r => r = d/2 = 64/2 = 32 um
A = π·r²
= 3.14·32²
= 3.14·1024
≈ 3215.36 um²
factorize:
(1 - a^2) (1 - b^2) + 4ab
Answer:
(ab+a-b+1)(ab-a+b+1)
Step-by-step explanation:
(1 - a²) (1 - b²) + 4ab= 1 -a²-b² +a²b² +4ab = (a²b² +2ab +1 )- (a²-2ab+b²)= (ab+1)² - (a-b)²= (ab+1 +a-b)(ab+1 -a+b)= (ab+a-b+1)(ab-a+b+1)Plz help also can you plz explain
Answer:
-1, 1
Step-by-step explanation:
what is 1/3 of -3 and 3
ayuda porfavor :b lo nesesito para hoy por fa
Answer:
a) x = 10
Step-by-step explanation:
En este romboide, el angulo A es igual a el angulo C, y el angulo ABC es igual a el angulo CDA.
Entonces, el angulo C es 7x.
En un triangulo, los angulos se suman para ser 180 degrados. En el triangulo BCE, hay un angulo recto.
7x + 2x + 90 = 180
7x + 2x = 90
9x = 90
x = 10
Espero que este te ayude!
The y-intercept of the graph of a line is located at (0, –2). The line also passes through the point (5, 1).
Answer:
y - 1 = (3/5)x
Step-by-step explanation:
First find the slope of this line. As we move from (0, -2) to (5, 1), x (the 'run') increases by 5 and y (the 'rise') increases by 3. Thus, the slope of this line is m = rise / run = 3/5.
Using the point-slope formula for the equation of a straight line:
y - 1 = (3/5)(x - 5), or
y - 1 = (3/5)x This can also be written as 5y - 5 = 3x, or
y = (3/5)x + 1
What is the equation of the following line written in slope-intercept form? Oy=-3/2x-9/2
Oy=-2/3x+9/2
Oy=3/2x-9/2
Answer:
y = -3/2x-9/2
Step-by-step explanation:
We have two points ( -3,0) and (-1,3)
The slope is
m = (y2-y1)/(x2-x1)
= (-3-0)/(-1- -3)
= (-3-0)/(-1+3)
= -3/2
Using slope intercept form
y = mx+b where m is the slope and b is the y intercept
y =-3/2x+b
Using the point (-3,0)
0 = -3/2(-3) +b
0 = 9/2+b
b = -9/2
y = -3/2x-9/2
someone help asap math 10
Answer:
Required angle measures 39°
Step-by-step explanation:
Let's say, x measures the angle between the hypotenuse and the common base of two triangles.
Sin(x) = 5/8
x = 39°
This angle is complementary to the angle other than theta (let's say y) in the required triangle.
90 - x = y and 90 - theta = y
>>> Theta = x
Best Regards!
The altitude at which we boil an egg affects how long it takes for the egg to achieve perfect hardness. It takes 198198198 seconds to boil a perfect egg at the lowest place possible, the edge of the Dead Sea, which has an altitude of -418−418minus, 418 meters. The highest place possible is the summit of Mount Everest which has an altitude of 884888488848 meters. It takes 209209209 seconds to boil a perfect egg there. T(a)T(a)T, left parenthesis, a, right parenthesis models the time (in seconds) it takes to boil a perfect egg at an altitude of aaa meters. Which number type is more appropriate for the domain of TTT?
Answer:
The domain is -418 < a < 8848 where a is an integer.
Step-by-step explanation:
We see from the data given that the domain of T(a) takes both positive and negative integer values ( 8848 meters and -418 meters); T(a) never gets decimal values (and in real life thy won't be of much use because we are not looking for that much accuracy).
So the appropriate number type for the domain of T(a) would be integers. And if you are interested, the domain is -418 < a < 8848.
Which situations would be represented with a positive number? Check all that apply.
The temperature outside is 34°F.
The Dead Sea is 1,349 feet below sea level.
Nicole lost 2 pounds last month.
Sebastian owes his friend $4
A football team gains 11 yards on a play.
Long Island Sound is at sea level.
Answer:
A and e
Step-by-step explanation:
Find the sum of the first 50 terms of the sequence below. Please Help!
Answer:
in 1st sequence put 1 instead of n
i.e
a1=3×1+2
=3+2
=5
Step-by-step explanation:
now do all the 50 terms by placing 1 to 50 instead of n
Solve the inequality -2x < 5, illustrating your solution on a number line.
Is -6 a solution of the inequality?
Answer:
No.
Step-by-step explanation:
Let's first and try to isolate x.
-2x < 5
(Divide by -2)
x > -5/2 ( < changes to > b/c it was divided by a negative)
x > -2.5
Since x is all values greater than -2.5, -6 is not within those bounds.
Thus, -6 is not a solution to the inequality.
Hope that helps!
the sum of the first 6 terms of a geometric series is 15624 and the common ratio is 5. what is the first term of the series?
Answer:
first term a=4
Step-by-step explanation:
Sum of the first 6 terms S6 = 15624
common ratio r= 5
n= 6
first term a=?
Formula: S6= a(r^n-1)/r-1
15624 = a( 5^6-1)/5-1
15624 = a(15625-1)/4
15624= a( 15624)÷4
15624= 15624a÷4
Cross multiply
15624×4 = 15624a
62496 = 15624a
divide both sides by 15624
62496÷15624 = 15624a÷15624
4 = a
a= 4
NEED HELP NOW!!! Need help finding vertex form
Answer:
y = (x-.5)^2 -12.25
Step-by-step explanation:
first, find the vertex
x from (x,y) = -b/2a
ax^2-bx - c
1x^2-1x -12
-1/2(-1) = -1/-2 - 1/2
(1/2,y) then use x value to find y value
y = 1/2^2 - 1/2 - 12
y = .25 -.5 - 12 = -12.25
(.5,-12.25) input values into this formula:
y = a(x-h)^2 + k where h = x-value and k = y-value. use same a value = 1
y = (x-.5)^2 -12.25
BRAINLIEST! will give BRAINLY! can someone please explain, I don't understand how to do this.
Answer:
101.58 in
Step-by-step explanation:
The ramp r is the hypotenuse of a right triangle with the ground and 28 in height being the legs.
The angle of elevation 16° is the angle inside the triangle opposite the 28 in height.
Using the sine ratio in the right triangle, then
sin16° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{28}{r}[/tex] ( multiply both sides by r )
r × sin16° = 28 ( divide both sides by sin16° )
r = [tex]\frac{28}{sin16}[/tex] ≈ 101.58 in
Answer:
The 3rd answer
Step-by-step explanation:
Which relation is a function of x?
Answer: The bottom option, the graph.
Step-by-step explanation:
A relation is something that gets input from a set, called domain (usually the x) and "transforms" them into an output, from a set called the range.
Now, a relation is only a function if, for all the elements x in the domain, each one of them has only one element y in the range associated to it.
For example, in the first set we can see that the value x = 1 appears two times, it is related to different values in the range, then this is not a function.
The second relation is not a function.
the third relation is:
x = 3*y^2 - 7
This is a function, but in this relation x is the output and y the input, so this is a function of y.
In the fourth relation we can see a graph, this is a function (each value in the domain is related to only one in the range), and in the horizontal axis we can see a x, so this is a function of x.
Answer:
D
Step-by-step explanation:
Please help! Rhombus LMNO is shown with its diagonals. The length of LN is 30 centimeters. What is the length of LP? A.) 14 B.) 15 C.) 20 D.) 30
Answer:
B
Step-by-step explanation:
Since the diagonals of a rhombus bisect each other, that means P is the midpoint of LN. Therefore, LP = 1/2 * LN = 1/2 * 30 = 15.
What are the excluded values?
Answer:
y = 0
z = 5
Step-by-step explanation:
Since you cannot have a zero in the denominator (divide by 0 or undefined error), you have to exclude values that can turn the bottom into a zero. If you plug in 0 for y, you would get an error, and if you plugged in z for 5, you would get another error because you would be multiplying 0 in the denominator, so those 2 values must be excluded.
What is the inverse of the function f(x) = one-quarterx – 12?
Hey there! :)
Answer:
y = 4x + 48
Step-by-step explanation:
Original equation:
y = 1/4x -12
Switch 'x' and 'y' to solve for the inverse:
x = 1/4y - 12
Add 12 to both sides:
x + 12 = 1/4y - 12 + 12
x + 12 = 1/4y
Multiply both sides by 4:
4(x+12) = y
4x + 48 = y
The inverse is y = 4x + 48
Answer:
4x + 48
Step-by-step explanation:
f(x) = 1/4x - 12
y = 1/4x - 12
Add 12 to both sides.
y + 12 = 1/4x
Multiply both sides by 4.
4y + 48 = x
Switch variables.
4x + 48 = y
y is directly proportional to x when y=30, x=6 a) work out an equation connecting y and x b) work out the value when x=12
Answer:
a) y = 5x
b) y = 60
Step-by-step explanation:
a) Standard equation of direct proportion:
y = kx
We need to find k. We can use the given values of x and y to find k.
x = 6; y = 30
30 = k * 6
k = 30/6 = 5
Now we use k = 5 in the standard equation to get this problem's direct proportion equation.
y = 5x
b)
x = 12
y = 5x
y = 5 (12)
y = 60
I need help with this question!
Answer:
A = 0 -7 b= 0 -7
3 2d 3 2d
Let's calculate A and B:
A= 0*2d- 3*(-7) = -3*(-7) = 21B= 0.2d- 3*(-7) = -3*(-7) = 21Calculte (AB)^(-1):
(AB)^(-1) = (21*21)^(-1) = (21²)^(-1) = 21^(-2)Calculte B^(-1) and A^(-1):
B^(-1) * A^(-1) = 21^(-1) * 21^(-1)= 21^(-1-1) = 21^(-2)so:
(AB)^(-1) = B^(-1) * A^(-1)
I really need help, someone please help me
Answer:
18.84 meters.
Step-by-step explanation:
The formula for a circle is πr^2.
πr^2 = 28.26
3.14 * r^2 = 28.26
r^2 = 9
r = plus or minus 3.
But since this deals with the area of a circle, there is no way a radius can be negative. So, the radius is 3 meters.
The formula for the circumference is 2πr.
2 * 3.14 * 3 = 6 * 3.14 = 18.84.
So, the circumference of the circle is 18.84 meters.
Hope this helps!
Simplify the expression x5 • x7.
Answer:
x12
Step-by-step explanation:
When multipling numbers that are the same with exponent you can just add the exponents.
so x5*x7=x12
(It would be subtraction if there was division)
Hope this helped you and feel free to ask questions!
Answer:
x^12
Step-by-step explanation:
When multiplying exponents, the rule below is followed.
[tex]x^a * x^b= x^{a+b}[/tex]
Basically, the base remains the same, but the numbers in the exponents are added.
We are given:
[tex]x^5*x^7[/tex]
We leave the base (x)as is, and add the numbers in the exponents (5 and 7).
[tex]x^5*x^7\\[/tex]
[tex]x^{5+7[/tex]
[tex]x^{12}[/tex]
The expression [tex]x^5*x^7\\[/tex] can be simplified as: [tex]x^{12{[/tex]
Can someone help me please