Answer:
x= -5 + 5[tex]\sqrt{97}[/tex], x= -5 - 5[tex]\sqrt{97}[/tex]
Step-by-step explanation:
Since this quadratic is set to zero, we can use the quadratic formula to solve this.
x^2 + 10x - 2400 = 0
Quadractic formula = x= -b +- [tex]\sqrt{b^2 - 4ac}[/tex] /2a
For this equation:
a= 1, b=10, c=-2400
Plug these numbers into the equation and solve.
x= -10 +- [tex]\sqrt{10^2 - 4(1)(-2400}[/tex])/2(1)
x= -10 +- [tex]\sqrt{100 + 9,600}[/tex]/2
x= -10 +- [tex]\sqrt{9,700}[/tex]/2
x= -10 +- [tex]\sqrt{2^2 * 5^2 * 97}[/tex]/2
x= -10 +- 5 * 2[tex]\sqrt{97}[/tex]/2
x= -10 +- 10[tex]\sqrt{97}[/tex] / 2
Divide by 2.
x= -5 +- 5[tex]\sqrt{97}[/tex]
Answer:
x= -5 + 5[tex]\sqrt{97}[/tex] or x= -5 - 5[tex]\sqrt{97}[/tex]
What is the value of this expression?
Answer:
-3
Step-by-step explanation:
Step 1: Solve (-2+(-1))^2/3 3
1. -2+(-1) = -3
2. (-3)^2 = 9
3. 9/3 = 3
Step 2: Solve (-4)^2-17 -1
1. 3/-1
Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!
Hey is there any chance anyone could help me with this question ASAP?? Tysm :)
Answer:
6
Step-by-step explanation:
A = π. r²
36π = π. r²
eliminate π, we get:
36=r²
r=√36
r = 6
Answer:
r = 6
Step-by-step explanation:
The area (A) of a circle is calculated as
A = πr² ( r is the radius )
Given A = 36π , then
πr² = 36π ( divide both sides by π )
r² = 36 ( take the square root of both sides )
r = [tex]\sqrt{36}[/tex] = 6
Inventor A had 630 inventions, 600% more than the number of inventions inventor B had. How many inventions did B have?
Answer:
105 inventions
Step-by-step explanation:
Find how many inventions Inventor B had by dividing 630 by 6:
630/6
= 105
So, Inventor B had 105 inventions
Devaughn is 7 years older than Sydney. The sum of their ages is 95. What is Sydney's age?
Answer:
44
Step-by-step explanation:
Let's say that Devaughn's age is D, and Sydney's age is S.
We know that D is 7 greater than S, so D = 7 + S.
We know that the sum of their ages, or D + S, is equal to 95, so D+S = 95
We have
D = 7 + S
D + S = 95
What we can do is plug D= 7 + S into the second equation to get
D + S = 95
= (7+ S) + S
= 7 + 2 * S
7+2 * S - 95
subtract 7 from both sides to isolate the coefficient and the variable
2 * S = 88
divide both sides by 2 to isolate the variable
S = 44
Sydney is therefore 44 years old
can someone please help me solve this? thank you!:)
First, we need to set up our two equations. For the picture of this scenario, there is one length (L) and two widths (W) because the beach removes one of the lengths. We will have a perimeter equation and an area equation.
P = L + 2W
A = L * W
Now that we have our equations, we need to plug in what we know, which is the 40m of rope.
40 = L + 2W
A = L * W
Then, we need to solve for one of the variables in the perimeter equation. I will solve for L.
L = 40 - 2W
Now, we can substitute the value for L into L in the area equation and get a quadratic equation.
A = W(40 - 2W)
A = -2W^2 - 40W
The maximum area will occur where the derivative equals 0, or at the absolute value of the x-value of the vertex of the parabola.
V = -b/2a
V = 40/2(2) = 40/4 = 10
Derivative:
-4w - 40 = 0
-4w = 40
w = |-10| = 10
To find the other dimension, use the perimeter equation.
40 = L + 2(10)
40 = L + 20
L = 20m
Therefore, the dimensions of the area are 10m by 20m.
Hope this helps!
Answer:
Width: 10 m
Length: 20 m
Step-by-step explanation:
Hi there!
Let w be equal to the width of the enclosure.
Let l be equal to the length of the enclosure.
1) Construct equations
[tex]A=lw[/tex] ⇒ A represents the area of the enclosure.
[tex]40=2w+l[/tex] ⇒ This represents the perimeter of the enclosure. Normally, P=2w+2l, but because one side isn't going to use any rope (sandy beach), we remove one side from this equation.
2) Isolate one of the variables in the second equation
[tex]40=2w+l[/tex]
Let's isolate l. Subtract 2w from both sides.
[tex]40-2w=2w+l-2w\\40-2w=l[/tex]
3) Plug the second equation into the first
[tex]A=lw\\A=(40-2w)w\\A=40w-2w^2\\A=-2w^2+40w[/tex]
Great! Now that we have a quadratic equation, we can do the following:
Solve for its zeros/w-intercepts.Take the average of the zeros to find the w-variable of the vertex. (The area (A) in relation to the width of the swimming area (w) is what we've established in this equation, and the area (A) is greatest at the vertex. Finding the value of w of the vertex will tell us what the width needs to be for the area to be at a maximum.)Plug this w value into one of the equations to solve for l4) Solve for w
[tex]A=-2w^2+40w[/tex]
Factor out -2w
[tex]A=-2w(w-20)[/tex]
For A to equal 0, w=0 or w=20.
The average of 0 and 20 is 10, so the width that will max the area is 10 m.
5) Solve for l
[tex]40=2w+l[/tex]
Plug in 10 as w
[tex]40=2(10)+l\\40=20+l\\l=20[/tex]
Therefore, the length of 20 m will max the area.
I hope this helps!
the cost of a popular toy is $19.99 , Due to a limited supply , the store manager marks the price of the toy up by 15%. what is the new price ? HURRY PLEASE .
$22.99
Step-by-step explanation:
19.99 increased by 15% ≈ 22.99
Absolute change (actual difference):
22.99 - 19.99 ≈ 3
The difference is $3
The value of -9 is __ than the value of -12 because -9 is to the __of -12 on the number line.
Less
Or
Greater
Answer:
Step-by-step explanation:
-9 is greater than the value of -12 because -9 is to the right of -12 on the number line.
Please help me with this
Answer:
The surface area of the pyramid is 16.65 m^2.
Step-by-step explanation:
Please help I don’t understand
Answer:
8/15
Step-by-step explanation:
The ratio of perpendicular to base is tan B .
Here ,
=> tan B = 8 ft/ 15ft
=> tan B = 8/15
The volume of air inside a rubber ball with radius r can be found using the function V(r)= 4/3pier^3 what does V(5/7) represent?
Answer:
Step-by-step explanation:
I can tell you what it represents, but not what it means. Or maybe the units.
V(5/7) means that wherever you see an r on the right hand side, you put in 5/7 where the R is.
V = 4/3 * pi * r^3
V(5/7) = 4/3 * 3.14 * (5/7)^3
V(5/7) = 4/3 * 3.14 * 125 / 343
V(5/7) = 4/3 * 3.14 * 0.3644
V(5/7) = 1.526 cubic units (of whatever the units of 5/7 were to begin with)
Solve the inequality.
–13.4 ≥ 6.7 + 4.3 + w
–24.4 ≥ w
24.4 ≥ w
23.4 ≥ w
–23.4 ≥ w
Answer:
-24.4 ≥ w
Step-by-step explanation:
-13.4 ≥ 6.7 + 4.3 + w
-13.4 - 6.7 - 4.3 ≥ w
-24.4 ≥ w
What is the value of x in the equation 0.7x – 1.4 = –3.5?
1. -7
2. -3
3. 7
4. 3
Answer:
the answer is -3
Step-by-step explanation:
0.7x - 1.4 = -3.5
add 1.4 to both sides of the equation
you're left with 0.7x = -2.1
then divide both sides by 0.7
you're left with your answer of -3
Which inequality describes the graph?
Answer:
1 describe the inequality graph
The incubation time for Rhode Island Red chicks is normally distributed with mean of 22 days and standard deviation of approximately 3 days. Of 1000 eggs are being incubated, how many chicks do we expect will hatch in 19 to 28 days
Answer:
We should expect 818 chicks to hatch in 19 to 28 days
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean of 22 days and standard deviation of approximately 3 days.
This means that [tex]\mu = 22, \sigma = 3[/tex]
Proportion between 19 and 28 days:
p-value of Z when X = 28 subtracted by the p-value of Z when X = 19.
X = 28
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 22}{3}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.977.
X = 19
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 22}{3}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.159.
0.977 - 0.159 = 0.818
Out of 1000:
0.818*1000 = 818
We should expect 818 chicks to hatch in 19 to 28 days
Which inequality matches the graph?
X, Y graph. X range is negative 10 to 10, and y range is negative 10 to 10. Dotted line on graph has positive slope and runs through negative 3, negative 8 and 1, negative 2 and 9, 10. Above line is shaded.
−2x + 3y > 7
2x + 3y < 7
−3x + 2y > 7
3x − 2y < 7
Given:
The dotted boundary line passes through the points (-3,-8), (1,-2) and (9,10).
Above line is shaded.
To find:
The inequality for the given graph.
Solution:
Consider any two points on the line. Let the two points are (1,-2) and (9,10). So, the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-2)=\dfrac{10-(-2)}{9-1}(x-1)[/tex]
[tex]y+2=\dfrac{10+2}{8}(x-1)[/tex]
[tex]y+2=\dfrac{12}{8}(x-1)[/tex]
[tex]y+2=\dfrac{3}{2}(x-1)[/tex]
Multiply both sides by 2.
[tex]2(y+2)=3(x-1)[/tex]
[tex]2y+4=3x-3[/tex]
[tex]2y-3x=-3-4[/tex]
[tex]-3x+2y=-7[/tex]
Above line is shaded and the boundary line is a dotted line. So, the sign of inequality must be >.
[tex]-3x+2y>-7[/tex]
This inequality is not in the equations. So, multiply both sides by -1 and change the inequality sign.
[tex](-3x+2y)(-1)<-7(-1)[/tex]
[tex]3x-2y<7[/tex]
Therefore, the correct option is D.
Determine the measure of ZA.
45.6°
57.7°
55.2°
32.3°
Step-by-step explanation:
Cos A = 40^2 + 25^2- 34^2 ÷ (2×40×25)
= 200+625-1156 ÷ (2000)
= 1069 ÷2000
Cos A = 0.5345
A= cos inverse 0.5345
A = 57.7
Answer:
57.7
Step-by-step explanation:
took the test
The polygons are similar, but not necessarily drawn to scale. Find the value of x. PLEASE HELPPPP
Answer:
x = 27.5.
Step-by-step explanation:
There are given numbers on each side. If the figures are similar, then they have a set ratio for each value.
So, 55:8 and x:4. If you want to, you can flip it, so that it is 8:55 and 4:x.
With that in mind, it is easy to see what the ratio is. Because 4 is half of 8, x is half of 55. 55 divided by 2 is 27.5.
Therefore, x = 27.5.
Find the value of x and y from the equation
Answer:
x = 5 and y = 3
Step-by-step explanation:
5x - 3y = 16
3x - y = 12 multiply second equation by (-3)
(-3)*(3x-y) = 12*(-3) (remember we need to multiply both sides of the equation)
-9x + 3y = -36 now subtract this from the first equation
5x - 3y -9x + 3y = 16 - 36 (-3y will eliminate +3y)
-4x = -20 and 4x = 20 divide both sides by 4
x = 5 if 3x - y = 12 then 3*5 - y = 12
15 - y = 12
-y = -3 and y = 3
The table shows information about water used in a household.
The value for April is missing.
The mean monthly water used for the six months is 18 m
Work out the value for April.
Answer:
is there is no value of April
Step-by-step explanation:
so the value of the month April is zero
Find two positive numbers so that twice their sum equals their product and one number is 10 times the other number. Enter the smaller number first.
Answer:
Step-by-step explanation:
We'll call the 2 numbers x and y. Starting with the last part of that first sentence "one number is 10 times the other number" can be written, in algebraic form:
y = 10x
Now on to the first statement about the numbers: "twice their sum" is 2(x + y) and "equals their product" is = xy. Putting that all together:
2(x + y) = xy and we know that y = 10x so
2(x + 10x) = x(10x) and
[tex]2(11x)=10x^2[/tex] and
[tex]10x^2-22x=0[/tex] and
x(10x - 22) = 0 so
x = 0 or 10x - 22 = 0 which makes
x equal to [tex]\frac{22}{10}=2.2[/tex]
So x = 2.2 and y = 22.
If a = 5, b = 4, and c = 7, find the value for 3(b + a) = c.
10
15
34
20
Answer:
20
Step-by-step explanation:
3 (b + a) = c
3 (4 + 5) = 7
12 + 15 = 7
27 = 7
27 - 7
20
[tex]\huge\boxed{ \sf{Answer}} [/tex]
Given,
[tex]a = 5 \\ b = 4 \\ c = 7[/tex]
And the equation we need to solve is,
[tex]3(b + a) = c[/tex]
To find the answer, you need to substitute the values of a, b & c in the equation.
[tex]3(b + a) = c \\ 3b + 3a = c \\ ( 3 \times 4) +( 3 \times 5) = 7 \\ 12 + 15 = 7 \\ 12 + 15 - 7 = 0 \\ = 27 - 7 \\ = 20[/tex]
↦ The answer is 20.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Find the quotient: 63/-9
Answer:
-7
Step-by-step explanation:
63/9 but there is an odd number of negative numbers so negative answer
Help pls I’ll mark you brainliest
Answer:
Step-by-step explanation:
If the 2 lines are parallel
then x = 70 cos ( alternate interior angle)
but if not sorry man I just in grade 9 its my best effort
Really sorry. <3
:(
find the slope between the points (-10,8) and (-7,5)
Answer:
-1
Step-by-step explanation:
Slope = (y2 - y1) / (x2 - x1)
Slope = (8 - 5) / (-10 - -7)
Slope = 3 / (-3)
Slope = -1
Tell whether each probability of the event happening is likely or unlikely to happen. Write L if it is likely to happen and U if unlikely to happen on the space before each number.
__ 1. 2:3
__ 2. 4:15
__ 3. 3/10
__ 4. 13/21
__ 5. 6/16
__ 6. 8:11
__ 7. 9:20
__ 8. 11:25
__ 9. 5/16
__ 10. 7/12
__ 11. 6:13
__ 12. 4:9
__ 13. 2:5
__ 14. 19/45
__ 15. 12/25
Please make it quick
Answer:
1.likely. 11.likely
2. likely. 12.likely
3. likely. 13.likely
4. unlikely 14. unlikely
5. likely. 15. likely
6. likely
7. likely
8. likely
9. likely
10. likely
Step-by-step explanation:
im correct if I'm rwong
find the missing side. round to the nearest tenth.
24) HELP ITS DUE IN THE MORNING
A) 14.2
C) 13.8
B) 9.2
D) 15.7
25.
A)37.6
B)30.8
C)45.1
D)5.5
Answer:
24) x = 9.2
25) x = 30.8
Step-by-step explanation:
Given
See attachment for triangles
Solving (24)
To solve for x, we make use of cosine formula
i.e.
cos(40) = adjacent ÷ hypotenuse
So, we have:
cos(40) = x ÷ 12
Multiply both sides by 12
12 cos(40) = x
12 * 0.7660 = x
x = 9.2
Solving (25)
To solve for x, we make use of sine formula
i.e.
sin(25) = opposite ÷ hypotenuse
So, we have:
sin(25) = 13 ÷ x
Multiply both sides by
x sin(25) = 13
Divide by sin(25)
x = 13 ÷ sin(25)
Using a calculator
x = 30.8
Find the measure of the indicated side
Answer: X = 8
Step-by-step explanation:
What should you substitute for y in the bottom equation to solve the system by the substitution method?
A. y=3x+15
B. y =-x-5
C. y=x+5
D. y=-3-15
Max can travel 100 miles in 2 hours. At this rate, how many hours will it take him to travel 650 miles?
Ted can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. When they work together, the situation can be modeled by the equation, where t is the number of hours it would take to clear the field together.
How long will it take Ted and Jacob to clear the field together?
Answer:
[tex]\frac{6}{5}[/tex] of an hour = 1 1/5 hour = 72 minutes
Step-by-step explanation:
[tex]\frac{1}{3} h + \frac{1}{2}h = 1\\\\\frac{2}{6} h + \frac{3}{6}h = 1\\\\\\\frac{5 }{6} h =1\\\\h=\frac{6}{5}[/tex]
it would take Ted and Jacob 1.2 hours, or 1 hour and 12 minutes, to clear the field together.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's start by using the formula for the combined work of two people:
1/t = 1/3 + 1/2
Here, t represents the number of hours it would take to clear the field together.
To solve for t, we can first find a common denominator for the fractions on the right-hand side of the equation:
1/t = (2/6) + (3/6)
1/t = 5/6
To isolate t on one side of the equation, we can take the reciprocal of both sides:
t/1 = 6/5
t = 1.2
Therefore, it would take Ted and Jacob 1.2 hours, or 1 hour and 12 minutes, to clear the field together.
To learn more on Equation:
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