At a MINIMUM, during dry weather conditions, you should have at least 2 seconds of space between you and the vehicle in front of you (3 seconds is better). Do this by using a fixed object such as a bridge, tree, or even a crack or shadow in the roadway.
Calculate the gap between you and the car in front of you by selecting an inanimate object along the lane. If the other car goes past the target, then "1000 one, 1000 two ..." count. You are three seconds behind this car when you get to "one thousand three" before you go through the piece.
------------------------------------
Hope this helps!
Brainliest would be great!
------------------------------------
With all care,
Forbidden
If –3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?
Answer:
Step-by-step explanation:
REcall that f(x) is a polynomial whose one of its roots is -3+i. The fundamental algebra theorem states that any polynomial of degree n has n complex roots. In the real case, it can be also interpreted as any polynomial can be factored in factors of degree at most 2.
Consider that given a polynomial of degree 2 of the form [tex]ax^2+bx+c[/tex] the solutions are given by
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
In this case, the fact that x is real or complex depends on the number [tex]b^2-4ac[/tex] which is called the discriminant. When this number is negative, we have that x is a complex root. Let say that [tex]b^4-4ac<0[/tex] and that [tex]\sqrt[]{b^4-4ac}=di[/tex], so the roots are given by
[tex] x_1 = \frac{-b + di}{2a}, x_2 = x_1 = \frac{-b - di}{2a}[/tex]
this means that, whenever we have a complex root, the other root is the complex conjugate. Recall that the complex conjugate of a complex number of the form a+bi is obtained by changing the sign of the imaginary part, that is a-bi.
So, in our case since -3+i is a root, then -3-i necessarily is another root.
If -3 + i is a root then -3 - i is too.
Therefore, the answer is -3 - i
By which smallast number must the following number be divided so that the quotient is a perfect cube
(A) 8640
Answer:
60
Step-by-step explanation:
8640/60 is 144. 144 is a perfect square. 12*12 is 144
Hey there! I'm happy to help!
------------------------------------------------------------------
INTRO TO PERFECT CUBES
A perfect cube is any number whose cube root is an integer. In English, that means that if you take any number without a fraction (this is called an integer, such as -7, 8, 100, none have fractions) and multiply it by itself three times, you get a perfect cube.
If you cube the number 4, you get 64, which is (4×4×4). 64 is an example of a perfect cube.
You can use the cube root button on your calculator to see if a number is a perfect cube. If you do the cube root of 64, you get 4, telling you that 64 is a perfect cube. The cube root of 10 is 2.154434...... so 10 is not a perfect square because it does not give you an integer (number that does not have a fraction) as the answer.
------------------------------------------------------------------
SOLVING THE PROBLEM
So, we want to find the smallest numbers we can divide 8640 to equal a perfect cube.
I will assume that we will not be dividing by fractions but only whole numbers (positive integers).
We could try dividing by 1, but we see that 8640 is not a perfect cube because it's cube root is 20.519711....
Let's just keep counting up! The first divisor we run into that gives a quotient that it is a perfect cube is the smallest whole number possible that will give us that result.
8640÷2=4320
∛4320≈16.2865....... Not a perfect cube
8640÷3=2880
∛2880≈14.22757..... Not a perfect cube
8640÷4=2160
∛2160≈12.92660..... Not a perfect cube
8640÷5=1728
∛1728=12, a perfect cube!
Since 12 cubed is equal to 1728, this means that 1728 is a perfect square, so 5 is the smallest number we can divide 8640 by to get a perfect square.
The answer is 5.
I hope that this helps! Have a wonderful day! :D
rectangleabcd is graphed in the coordinate plane. the following are the vertices of the rectangle:a(2,−6),b(5,−6),c(5,−2) andd(2,−2) What is the perimeter of rectangle
ABCd?
Answer:
14
Step-by-step explanation:
The rectangle has side lengths of 3 and 4. There are two of each length, so the total length of all the sides is ...
P = 2(l +w) = 2(4 +3) = 2(7)
P = 14 . . . . units
Does this table represent a function? Why or why not?
Answer:
A Yes, because every x value corresponds to exactly one y value
Step-by-step explanation:
A function has a one to one correspondence, or every x goes to only one y value
Since each x goes to only 1 y value this is a function
Answer: It is a function
Step-by-step explanation:
One way to tell if it is a function or not, is to look at the X and Y. While 2 different X values can get the same Y value, one X value should not have 2 different Y values. In the table you can see, there are no repeating X values that have different Y values.
EXAMPLES:
(14, 15)
(13,15)
If these two showed up in a table, it could still be a function
(14, 15)
(14, 16)
If these pairs showed up in a table, than it would not be considered a function
Please answer this in two minutes
Answer:
15
Step-by-step explanation:
Use the Pythagorean Thereom:
[tex]r^{2}[/tex] = [tex]9^{2}[/tex]+[tex]12^{2}[/tex]
[tex]r^{2}[/tex] = 81+144
[tex]r^{2}[/tex] = 225
[tex]r[/tex]= 15
Please mark me as Brainliest!
Kara mixes different colors of paint to create new colors. The table shows the amount of paint Kara mixes per batch.
Select all the batches that will create the same colors as the first batch.
A. Batch 2
B. Batch 3
C. Batch 4
D. Batch 5
E. Batch 6
Answer:
D. Batch 5.
Step-by-step explanation:
The batch should have the same proportion of blue to white to yellow.
In Batch 1, there are two parts of blue, 1.5 parts of white, and 1 part of yellow.
In Batch 5, there are four parts of blue, 3 parts of white, and 2 parts of yellow.
4 / 2 = 2
3 / 2 = 1.5
2 / 2 = 1
Since the proportions are equal to those found in Batch 1, D. Batch 5 will create the same colors as the first batch.
Hope this helps!
what is the distance formula
Answer:
14.42 units
Step-by-step explanation:
Assuming that this is a right triangle (i.e ∠ACB = 90°), we can use the Pythagorean formula to solve this:
AB² = AC² + BC²
AB² = 12² + 8²
AB = √(12² + 8²)
AB = 14.42 units
The 2 equations only pls
Payday context:
It’s the end of the month which means it is time to pay your coffee shop employees. Make sure each employee gets paid the correct amount
(write an equation for each situation and solve) identify variables when applicable
Answer:
she works 50 hours for that week
Step-by-step explanation:
She is paid $18 per hour and received a bonus of $125 per bonus for the first week . she claims her compensation for the first week should be $1025 . The number of hour she worked base on her claim can be calculated below.
Let
the number of hours she worked = a. Therefore,
18a + 125 = 1025
18a = 1025 - 125
18a = 900
divide both sides by 18
a = 900/18
a = 50
she works 50 hours for that week
Find the value.
6x+3 when x=-1/2
PLEASE HELP!!!
Answer:
0
Step-by-step explanation:
6(-0.5) + 3 = -3 + 3 = 0
Answer:
0
Step-by-step explanation:
x= - 1/2 [given]
Now,
> 6x + 3
>6 × - 1/2 + 3
> -6/2 +3
> -3/1 + 3
> -3 + 3
> 0
The library has 6 new books it would like to display near the checkout desk. The librarian plans the six books between a set of bookends. How many different ways can the books be placed between the bookends if order is important?
Answer:
The answer is 6 factorial or 6!
6! = 6 * 5 * 4 * 3 * 2 * 1
which equals 720
Step-by-step explanation:
Answer:
720
Step-by-step explanation:
What is the apothem of a equilateral triangle with radius 9cm
Answer:
4.5 cm
Step-by-step explanation:
apothem=R/2=9/2=4.5 cm
The functions f(x) and g(x) are graphed.
On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Which represents where f(x) = g(x)?
f(2) = g(2) and f(0) = g(0)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Answer:
[tex]f(0)=g(0)[/tex] and [tex]f(2) = g(2)[/tex]
Step-by-step explanation:
According to the question, the curved red line represents [tex]g(x)[/tex] and the straight blue line represents [tex]f(x)[/tex].
The important thing here is that the equality of functions [tex]f(x)=g(x)[/tex] is represented as a common function between their curves. So, we just need to find such a common point for both.
[tex]f(x)[/tex] has points (0, 4) and (2, 0).
[tex]g(x)[/tex] has points (0,4) and (2,0).
Notice that both functions have the same y-value for x=0 and x=2, that means
[tex]f(0)=g(0)[/tex] and [tex]f(2) = g(2)[/tex].
Therefore, the right answer is the first choice.
The correct answer is option A which is f(2) = g(2) and f(0) = g(0)
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
According to the question, the curved red line represents g(x) while the straight blue line represents f(x).
The important thing here is that the equality of functions f(x) = g(x) is represented as a common function between their curves. So, we just need to find a common point for both.
f(x) has points (0, 4) and (2, 0).
g(x) has points (0,4) and (2,0).
Notice that both functions have the same y-value for x=0 and x=2, which means
f(2) = g(2) and f(0) = g(0)
Therefore correct answer is option A which is f(2) = g(2) and f(0) = g(0)
To know more about function follow
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If f(x) = 3x + 2, what is f(5)?
Answer:
17
Step-by-step explanation:
f(5) = (5*3)+2
f(5) = 17
A pennant is shaped like a right triangle with a hypotenuse of 10feet. The length of one side of the pennant is two feet longer than the length of the other side. Find the length of the two sides of the pennant.
Answer:
6 ft and 8 ft
Step-by-step explanation:
let x be the length of one leg then (x + 2) is the other leg.
Using Pythagoras' identity in the right triangle, that is
x² + (x + 2)² = 10² ← expand left side and simplify
x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )
2x² + 4x - 96 = 0 ( divide all terms by 2 )
x² + 2x - 48 = 0 ← in standard form
(x + 8)(x - 6) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 8 = 0 ⇒ x = - 8
x - 6 = 0 ⇒ x = 6
But x > 0 ⇒ x = 6
Thus the 2 sides are 6 ft and x + 2 = 6 + 2 = 8 ft
What is the equation of the line that passes through the point (-6, 6) and has a
slope of
1/3?
Answer:
Using point-slope form we get:
y - 6 = 1/3(x + 6)
y - 6 = 1/3x + 2
y = 1/3x + 8
please helllppppp ....thx if u do
In ∆ABC, AC = 15 centimeters, m B = 68°, and m C = 24°. What is BC to two decimal places?
B
C
=
16.17
(
2
d
p
)
c
m
Explanation:
In triangle ABC, side
A
C
=
15
, Angles are
∠
B
=
68
0
;
∠
C
=
24
0
and
∠
A
=
180
−
(
68
+
24
)
=
88
0
We know by sine law
A
C
sin
B
=
B
C
sin
A
or
15
sin
68
=
B
C
sin
88
or
B
C
=
15
⋅
sin
88
sin
68
=
16.17
(
2
d
p
)
c
m
Step-by-step explanation:
Answer:
16.17 cmStep-by-step explanation:
m∠B = 68°, m∠C = 24°, AC = 15 cm
m∠A = 180° - 68° - 24 = 88°
by sine law:
[tex]\dfrac{BC}{\sin(A)}=\dfrac{AC}{\sin(B)}\\\\\\BC=\dfrac{15}{\sin\left(6\big8^o\right)}\cdot \sin\left(8\big8^o\right)\\\\\\BC\approx\dfrac{15}{0.9272}\cdot 0.9994=16.168032....\\\\\\BC\approx16.17[/tex]
Can somebody plz help me 15-[7+(-6)+1]^3
Answer:
7.
Step-by-step explanation:
15 - [7 + (-6)+ 1]^3
Using PEMDAS:
= 15 - [ 7-6+1]^3
Next work out what is in the parentheses:
= 15 - 2*3
Now the exponential:
= 15 - 8
= 7.
Step-by-step explanation:
Hi,
I hope you are searching this, right.
=15[7+(-6)+1]^3
=15[7-6+1]^3
=15[2]^3
=15-8
=7...is answer.
Hope it helps..
Construct a 99% confidthence interval for the population mean .Assume the population has a normal distribution. A group of 19 randomly selected employees has a mean age of 22.4 years with a standard deviation of 3.8 years. Round to the nearest tenth.
A) Determine the critical value ta/2 with n-the 1 degrees of freedom
B) Determine the lower and upper bound of the confidence interval
C) Interpret the confidence interval.
Confidence interval for mean, when population standard deviation is unknown:
[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean
n= sample size
s= sample standard deviation
[tex]t_{\alpha/2}[/tex] = Critical t-value for n-1 degrees of freedom
We assume the population has a normal distribution.
Given, n= 19 , s= 3.8 , [tex]\overline{x}=22.4[/tex]
[tex]\alpha=1-0.99=0.01[/tex]
A) Critical t value for [tex]\alpha/2=0.005[/tex] and degree of 18 freedom
[tex]t_{\alpha/2}[/tex] = 2.8784
B) Required confidence interval:
[tex]22.4\pm ( 2.8744)\dfrac{3.8}{\sqrt{19}}\\\\=22.4\pm2.5058\\\\=(22.4-2.5058,\ 22.4+2.5058)=(19.8942,\ 24.9058)\approx(19.9,\ 24.9)[/tex]
Lower bound = 19.9 years
Uppen bound = 24.9 years
C) Interpretation: We are 99% confident that the true population mean of lies in (19.9, 24.9) .
100 points timed Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles? 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side 5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side
Answer: A
Step-by-step explanation:
The answer is A. It accurately describes the equation shown. Negative values are represented by negative tiles and positive values are represented by positive tiles.
Hope it helps <3
Which graph corresponds to the equation: y=−2x−6 A. graph that contains the points (0,-3) and (6,0) B. graph that contains the points (3,0) and (5,4) C. graph that contains the points (-3,0) and (-5,4) D. graph that contains the points (-6,0) and (2,-4)
Answer: C. graph that contains the points (-3,0) and (-5,4).
Step-by-step explanation:
Given equation of line: [tex]y=-2x-6[/tex]
Now, Let's check each option
A. Put (x,y)=(0,-3), i.e. x=0 and y=-3 in given equation
[tex]-3=-2(0)-6\\\\\Rightarrow\ -3=-6[/tex]
which is not true.
So, option A. is not correct.
B. Put (x,y) = (3,0), i.e. x=3 and y=0
[tex]0=-2(3)-6\\\\\Rightarrow\ 0=-6-6\\\\\Rightarrow\ 0=-12[/tex]
which is not true.
So option B. is not correct.
C. Put (x,y) = (-3,0), i.e. x=-3 and y=0
[tex]0=-2(-3)-6\\\\\Rightarrow\ 0=0[/tex] , which is true.
Put (x,y) = (-5,4) ,
[tex]4=-2(-5)-6\\\\\Rightarrow\ 4=10-6\\\\\Rightarrow\ 4=4[/tex], which is true.
So both points in option C satisfy the given equation.
That means, option C is correct.
D. Put (x,y) = (-6,0)
[tex]0=-2(-6)-6\Rightarrow\ 0=6[/tex] , which is not true.
So option D. is not correct.
find the value of x in the triangle shown below
Answer:
x=70
Step-by-step explanation:
the angles opposite 3.5 equal 55 degrees
180-55-55=70
Answer:
70°
Step-by-step explanation:
since the both size are equal which is 3.5,it is equal length, so the other angle should be 55 also. Just use the triangle =180° ，180-55-55=70°
Please can someone help me
Answer:
706.86 cm
Step-by-step explanation:
=4pi(r^2)
=12.56(r^2)
=12.56(7.5^2)
=12.56(56.25)
=706.86
Write 4x2 + 16x - 9 in vertex form. Write 5x2 - 10x + 4 in vertex form.
Hi king,
Write [tex]4x^{2} + 16x - 9[/tex] in vertex form:
f(x)=[tex]4x^{2} + 16x - 9[/tex]
f(x)=[tex]4(x+2)^{2} -25[/tex]
Write [tex]5x^{2} - 10x + 4[/tex] in vertex form:
g(x)=[tex]5x^{2} - 10x + 4[/tex]
g(x)=[tex]5(x-1)^{2} -1[/tex]
Have a great day.
what is the value of x if e^3+6+8
Answer:
A
Step-by-step explanation:
John is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 5 miles per hour and returns along the same route at an average speed of 7 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?
(A) 5.5
(B) 5.8
(C) 6.0
(D) 6.3
(E) 6.5
Answer:
Average speed
= 5 5/6 mph , or
= 5.83 mph (to 2 decimals)
Step-by-step explanation:
Average speed is total distance divided by the total time it takes to cover the given distance.
Since uphill = 5 mph, and downhill = 7 mph, we know the average speed is between 5 and 7 mph.
Let
x = distance uphill, and also distance downhill.
Total distance = 2x miles
Total time = x/5 + x/7 hours = 12x/35 hours
Average speed
= total distance/total time
= 2x / (12x/35) mph
= 70x / 12x
= 5 5/6 mph
= 5.83 mph (to 2 decimals)
Grace starts with 100 milligrams of a radioactive substance. The amount of the substance decreases by 14 each week for a number of weeks, w. She writes the expression 100(14)w to find the amount of radioactive substance remaining after w weeks. Ryan starts with 1 milligram of a radioactive substance. The amount of the substance decreases by 40% each week for a number of weeks, w. He writes the expression (1 – 0.4)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Grace’s and Ryan’s expressions mean.
Answer:
100= Initial Amount
1/4= decay factor for each week
w= number of weeks
1/4w= decay factor after w weeks
1 - 0.4= decay factor for each week
w= number of weeks
0.4= percent decrease
Step-by-step explanation:
right here press the picture
Answer:
1133.54 in.^2
Step-by-step explanation:
The answer is the area of the circle which is in white inside the square. We are not looking for the shaded area.
A = (pi)r^2
r = d/2 = 38 in./2 = 19 in.
A = (3.14)(19 in.)^2
A = (3.14)(19 in.)(19 in.)
A = 1133.54 in.^2
Answer:
1133.54 [tex] {in}^{2} [/tex]Step-by-step explanation:
Given,
Diameter ( d ) = 38
Radius ( r ) = 38/2 = 19
π = 3.14
Now, let's find the area :
[tex]\pi \: {r}^{2} [/tex]
Plug the values
[tex]3.14 \times {(19)}^{2} [/tex]
Evaluate the power
[tex]3.14 \times 361[/tex]
Calculate the product
[tex]1133.54 \: {in}^{2} [/tex]
Hope this helps..
Best regards!!
simplify 3(8-4)^2+7*9
━━━━━━━☆☆━━━━━━━
▹ Answer
111
▹ Step-by-Step Explanation
[tex]3(8 - 4)^{2} + 7 * 9\\\\3 * 4^{2} + 7 * 9\\\\3 * 16 + 63\\\\48 + 63\\\\= 111[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
In a survey men in a certain country (ages 20-29), the mean height was 62.8 inches with a standard deviation of 2.8 inches, what height represents the 99th percentile?
Answer:
the height that represents the 99th percentile is 69.324 inches
Step-by-step explanation:
Given that :
the mean height = 62.8 inches
standard deviation = 2.8 inches
For 99th percentile;
Let X be the random variable;
SO, P(Z≤ z) = 0.99
From the standard normal z tables
P(Z )= 2.33
The standard z score formula is :
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]2.33 = \dfrac{X- 62.8}{2.8}[/tex]
2.33 × 2.8 = X - 62.8
6.524 = X - 62.8
6.524 +62.8 = X
69.324 = X
X = 69.324
Therefore; the height that represents the 99th percentile is 69.324 inches