Answer:
Option B. [tex](x-4)^{2}=44[/tex]
Step-by-step explanation:
we have
[tex]x^{2}-8x-10=18[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}-8x=18+10[/tex]
[tex]x^{2}-8x=28[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]x^{2}-8x+16=28+16[/tex]
[tex]x^{2}-8x+16=44[/tex]
Rewrite as perfect squares
[tex](x-4)^{2}=44[/tex]
Answer:
b
Step-by-step explanation:
Please help me. I need help with this
See the attached picture:
Suppose the number of items you can deliver in a day is a random variable with some unknown distribution with a mean = 35 and a standard deviation of 8. What is the probability a random sample of 36 days would have a mean between 32.6 and 34.6?
Answer:
P = 0.3462
Step-by-step explanation:
See attached photo for work.
We have a sample mean of 35, a sample standard deviation of 8, and a sample size of 36.
You need to see that the probability of the number of items you can deliver in a day is between 32.6 and 34.6.
The answer is 0.3462, so there's about a 34.62% chance that you will deliver an average of 32.6 to 34.6 packages per day.
The probability a random sample of 36 days would have a mean between 32.6 and 34.6 is 0.3462
What is probability?The chance of happening of an event is called probability.Probability is always less then 1 What is mean?Mean is actually the average of all the observations.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean
What is z-score?A z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
How to find the probability of the random sample?According to the problem,
Mean = 35Standard Deviation = 8Sample = 36Here we need to find P(32.6 < x < 34.6)
Firstly we should find the z-score of 32.6 and 34.6[tex]z_{32.6}[/tex] = [tex]\frac{32.6-35}{\frac{8}{\sqrt{36} } }[/tex] = - 1.80
[tex]z_{34.6} = \frac{34.6-35}{\frac{8}{\sqrt{36} } }[/tex] = -0.30
∴ P(32.6 < x < 34.6) = P ( -1.80 < z < -0.30)
= P(z< -0.30) - P(z < -1.80)
= 0.3821 - 0.0359 = 0.3462
∴ The required probability is 0.3462
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Please help me out if possible!!!!
Answer:
∠PST = 45°
Step-by-step explanation:
The diagonals of a square bisect the angles
∠SPQ = 90° ⇒ ∠SPT = 45°
Which describes the number and type of roots of the equation x^4 - 64 = 0
a. 2 real roots, 2 imaginary roots
b. 4 real roots
c. 3 real roots, 1 imaginary root
d. 4 imaginary roots
ANSWER
a. 2 real roots, 2 imaginary roots
EXPLANATION
The given equation is
[tex] {x}^{4} - 64 = 0[/tex]
We rewrite as difference of two squares,
[tex]( {x}^{2} )^{2} - {8}^{2} = 0[/tex]
We factor using difference of two squares to get;
[tex]( {x}^{2} - 8)( {x}^{2} + 8) = 0[/tex]
We now use the zero product property to get:
[tex]{x}^{2} = 8 \: or \: {x}^{2} = - 8[/tex]
Take the square root of both sides to get;
[tex]{x} = \pm \sqrt{8} \: or \: {x}^{2} = \pm \sqrt{ - 8} [/tex]
[tex]{x} = \pm 2\sqrt{2} \: or \: {x} = \pm 2\sqrt{ 2} i[/tex]
[tex]{x} = - 2\sqrt{2} \: or \: {x} = 2\sqrt{ 2}[/tex]
are two real roots.
[tex]{x} = - 2\sqrt{2}i \: or \: {x} = 2\sqrt{ 2} i[/tex]
are two imaginary roots.
The correct answer is A.
The correct answer is a. 2 real roots, 2 imaginary roots.
To determine the number and type of roots for the equation [tex]\(x^4 - 64 = 0\)[/tex]
1. Start with the equation:
[tex]\[ x^4 - 64 = 0 \][/tex]
2. Rewrite the equation as a difference of squares:
[tex]\[ x^4 - 64 = (x^2)^2 - 8^2 = (x^2 - 8)(x^2 + 8) = 0 \][/tex]
3. Set each factor equal to zero:
[tex]\[ x^2 - 8 = 0 \]\[ x^2 + 8 = 0 \][/tex]
4. Solve each equation separately:
For [tex]\(x^2 - 8 = 0\)[/tex]:
[tex]\[ x^2 = 8 \]\[ x = \pm \sqrt{8} = \pm 2\sqrt{2} \][/tex]
These are two real roots.
For [tex]\(x^2 + 8 = 0\)[/tex]:
[tex]\[ x^2 = -8 \]\[ x = \pm \sqrt{-8} = \pm \sqrt{8i^2} = \pm 2\sqrt{2}i \][/tex]
These are two imaginary roots.
Therefore, the equation [tex]\(x^4 - 64 = 0\)[/tex] has:
- 2 real roots: [tex]\(2\sqrt{2}\) and \(-2\sqrt{2}\)[/tex]
- 2 imaginary roots: [tex]\(2\sqrt{2}i\) and \(-2\sqrt{2}i\)[/tex]
The correct answer is:
a. 2 real roots, 2 imaginary roots
The complete question is- Which describes the number and type of roots of the equation [tex]x^4 - 64 = 0[/tex]
a. 2 real roots, 2 imaginary roots
b. 4 real roots
c. 3 real roots, 1 imaginary root
d. 4 imaginary roots
Evaluate the expression(-3.8)+0+y for the given values of y.
y value value of expression
-3.3 -7.1
-2.6
1
4.2
Answer:
y = -3.3 then -7.1
y = -7.1 then -10.9
y = -2.6 then -6.4
y = 1 then -2.8
y = 4.2 then 0.4
Step-by-step explanation:
(-3.8)+0+y can be simplified to -3.8 + y. Evaluate each value for y by substituting it into the expression and solving.
y = -3.3 then -3.8 + -3.3 = -7.1
y = -7.1 then -3.8 + -7.1 = -10.9
y = -2.6 then -3.8 + -2.6 = -6.4
y = 1 then -3.8 + 1 = -2.8
y = 4.2 then -3.8 + 4.2 = 0.4
To evaluate the expression (-3.8) + 0 + y, substitute the given value of y and perform addition.
Explanation:To evaluate the expression (-3.8) + 0 + y, you simply substitute the given value of y into the expression and perform the addition. Let's evaluate the expression for each given value of y:
For y = -3.3:(-3.8) + 0 + (-3.3) = -7.1For y = -2.6:(-3.8) + 0 + (-2.6) = -6.4For y = 1:(-3.8) + 0 + 1 = -2.8For y = 4.2:(-3.8) + 0 + 4.2 = 0.4Thus, the values of the expression for the given values of y are:
For y = -3.3, the value of the expression is -7.1For y = -2.6, the value of the expression is -6.4For y = 1, the value of the expression is -2.8For y = 4.2, the value of the expression is 0.4Learn more about Evaluating Expressions here:https://brainly.com/question/21469837
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Identify the range of the function shown in the graph.
Answer:
A
All real numbers
Step-by-step explanation:
Given in the question a graph
To find the range of graph
The range is the set of possible output values, which are shown on the y-axis.
We can see in the graph that for negative values of x it have positive values, zero and negative values of y.
The graph extends vertically from (-∞,∞), along the y axis. So the range of the function shown in the graph is (-∞,∞).
Hence, it is concluded that range is All real numbers
Find the area of a rectangle with a length of 27 8 inches and a width of 1 2 inch.
3336_____________________________
help idk "There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete
there are 13 small dogs that compete
The length of a rectangle is x and the width is 2x-8. If the area of the rectangle is 234 yd^2, find the value of x.
Answer:
x = 13
Step-by-step explanation:
The area of a rectangle is found by A = l*w. Since the length here is x and the width is 2x - 8, substitute these values and A = 234 to solve for x.
[tex]A = l*w\\234 = x(2x-8)\\234 = 2x^2 - 8x[/tex]
To solve for x, move 234 to the other side by subtraction. Then remove the common factor between all three terms of 2. Factor and solve.
[tex]2x^2 - 8x - 234 = 0 \\2(x^2 - 4x - 117) = 0\\2(x - 13)(x+9) = 0\\[/tex]
Set each factor equal to 0 and solve.
x - 13 = 0 so x = 13
x + 9 = 0 so x = -9
Since x is a side length and length/distance cannot be negative, then x = 13 is the length of the rectangle.
Which of the equations listed below are linear equations? Equation I: C=2*3.14*r Equation II: A = 3.14*r^2 Equation III: V = 4/3*3.14*r^3
Answer:
Equation I: C=2*3.14*r
Step-by-step explanation:
A linear equation is an equation whose highest exponent on the variable is 1.
C=2*3.14*r.................Exponent of 1
A = 3.14*r^2...............Exponent of 2
A = 3.14*r^2...............Exponent of 3
The amount in an account with a beginning balance of 3000 and interest compounded continuously at an annual rate of 5.5% can be modeled by the equation A=3000^5.5t
Answer:
Step-by-step explanation:false
Can someone help me on this question
Answer:
9
Step-by-step explanation:
✯Hello✯
↪ There is a quadratic formula that needs to be used. 4ac and b^2 are a part of this formula
↪ First we need to work out the Values for A and B and C
A = 1
B = 5
C= 4
↪ now we can substitute this into what the equation is asking. (5)^2-4(1)(4)=9
↪ The answer is 9
↪ I hope this helps you :)
❤Gianna❤
i am confusion ̿'̿'\̵͇̿̿\з=( ͠° ͟ʖ ͡°)=ε/̵͇̿̿/'̿̿ ̿ ̿ ̿ ̿ ̿
ANSWER:
~~~~~~~~~
Im pretty sure the answer is "Relation"
~~~~~~~~~
Relation definition:
A relation is a set of numbers that have a relationship through the use of a domain and a range.
~~~~~~~~~
HOPE THIS HELPS!!!
≠GoodLuck
It is a relation because even if they are negative they still can have a relation between them. Hope this is helpful for you!
Mary mixies white paint and blue paint in the ratios 2:3. She makes a total of 20 litres of paint. How much more blue paint does she needs to add to the mixture so the ratios of white paint to the blue paint become 1:7?
Answer:
44 liters
Step-by-step explanation:
It is 44 liters !!!!!
Work parentheses from inside out, and don't forget to multiply/divide together, left to right, and then do the same for add/subtract.
Answer:
This is correct PEMDAS
Step-by-step explanation:
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
SUUUPPERR URGENT! PLEASE HELP 50 POINTS!!!
When the following quadratic equation is written in general form, what is the value of "c"?
-3/4x^2+2=0
-8
-6
-2
Here is your answer
[tex]\bold{-2}[/tex]
REASON :
Given equation -
[tex] \frac{-3}{4}{x}^{2}+2=0 [/tex]
when, written in general form equation is
[tex] \frac{3}{4}{x}^{2}-2=0 [/tex] (on multiplying both sides by -1)
Now this is quadratic equation in general form, where
[tex] a= \frac{3}{4} [/tex] [coefficient of x^2]
b= 0 [coefficient of x]
c= -2 [constant term]
Hence, c= -2
HOPE IT IS USEFUL
Answer:
-2
Step-by-step explanation:
a = 3/4
[coefficient of x^2]
b= 0 [coefficient of x]
c= -2 [constant term]
Can someone help with either question plz
Answer:
A = 204
Step-by-step explanation:
The formula for the area of a parallelogram is
A = bh
Data:
P = 60
h = AX =12
MX = 5
Calculation:
MA² = MX² + h² = 5² + 12² = 25 + 144 = 169
MA = √169 = 13
P = 2MA + 2MH = 2MA + 2(MX + HX) = 26 + 2(5 + HX) = 60
26 + 10 + 2HX = 60
36 + 2HX = 60
2HX = 24
HX = 12
b = MH = MX + HX = 5 + 12 = 17
A = bh =17 × 12 = 204
The area of the parallelogram is 204.
Please help with this problem! :)
Answer:
∠STP = 90°
Step-by-step explanation:
The diagonals of a square are perpendicular bisectors of each other, hence
∠STP = 90°
P=−4b ^2+6b−9
Q=7b ^2−2b−5
P − Q =
Answer is :−11b^2+8b−4
Answer:
see explanation
Step-by-step explanation:
P - Q
= - 4b² + 6b - 9 - ( 7b² - 2b - 5) ← distribute by - 1
= - 4b² + 6b - 9 - 7b² + 2b + 5 ← collect like terms
= - 11b² + 8b - 4
Answer:
[tex]\large\boxed{P-Q=-11b^2+8b-4}[/tex]
Step-by-step explanation:
[tex]P=-4b^2+6b-9\\Q=7b^2-2b-5\\\\P-Q=(-4b^2+6b-9)-(7b^2-2b-5)\\P-Q=-4b^2+6b-9-7b^2-(-2b)-(-5)\\P-Q=-4b^2+6b-9-7b^2+2b+5\qquad\text{combine like terms}\\P-Q=(-4b^2-7b^2)+(6b+2b)+(-9+5)\\P-Q=-11b^2+8b-4[/tex]
. Write an equation of the line that passes through (2, -1) and is parallel to the graph of y = 5x – 2.
Write your final equation in slope-intercept form.
PARALLEL slopes always have the same slope no matter what because they are parallel
3 1/2 times 4 2/3 without simplest form
Answer:
12 2/6
Three times four is 12.
two times one is 2.
two times three is 6.
Answer:
3 1/2 x 4 2/3 = 98/6
*This is without simplest form*
In simplest form:
3 1/2 x 4 2/3 = 16 1/3
Leah loves chicken wings and is comparing the deals at three different restaurants. Buffalo Bills has 888 wings for \$7$7dollar sign, 7. Buffalo Mild Wings has 121212 wings for \$10$10dollar sign, 10. Wingers has 202020 wings for \$17$17dollar sign, 17. Which restaurant offers the lowest price per wing?
Cost of chicken wings at Buffalo Bills = 8 wings for $7
Cost of 1 wing at Buffalo Bills = [tex]\frac{7}{8} =0.875[/tex]
Cost of chicken wings at Buffalo Mild Wings = 12 wings for $10
Cost of 1 wing at Buffalo Mild Wings = [tex]\frac{10}{12}= 0.833[/tex]
Cost of chicken wings at Wingers = 20 wings at $17
Cost of 1 wing at Wingers = [tex]\frac{17}{20}= 0.850[/tex]
Hence, comparing all the three costs per wing, we can see that Buffalo Mild Wings is serving chicken wings at lowest price of $0.833 per wing.
Answer:
It is B
Step-by-step explanation:
D? Marco draws a card and replaces it 10 times from a standard deck of 52 cards. He draws 8 red cards and 2 black cards. What is the experimental probability of drawing a red card?
A) 1/2
B) 1/4
C) 2/3
D) 4/5
Answer:
D) 4/5
Step-by-step explanation:
He drew and replaced cards 10 times.
8 out of the 10 times, he drew a red card.
8/10 = 4/5
Answer: D) 4/5
You are correct.
Final answer:
The experimental probability of drawing a red card, based on the information given, is 4/5, since Marco drew 8 red cards out of 10 total draws.
Explanation:
The student is asking for the experimental probability of drawing a red card based on Marco's actual draws from a standard deck of 52 cards. Experimental probability is calculated by dividing the number of times the event of interest (drawing a red card) occurred by the total number of trials. In this case, Marco drew a red card 8 times out of 10 total draws.
Therefore, the experimental probability is:
Experimental Probability = Number of red cards drawn / Total number of draws = 8/10
When simplified, 8/10 equals 4/5. Therefore, the correct answer is:
Experimental Probability of Drawing a Red Card = 4/5
The owner of a large manufacturing plant pays the base rate of $11.24 per $100 in wages paid for workers’ compensation insurance. The payroll for September is $179,805. What is the month’s premium for the workers’ compensation insurance?
A $20, 210.08
B $23,459.19
C $19,357.21
D $18,650.93
Answer:
Answer is B
Step-by-step explanation:
To find the workers' compensation insurance premium, multiply the payroll for September ($179,805) by the base rate converted to decimal (0.1124), resulting in a premium of $20,210.08 (Option A).
The question involves calculating the premium for workers' compensation insurance based on the total payroll for the month of September. To determine the monthly premium, we need to apply the base rate to the total payroll amount. The base rate is given as $11.24 per $100 in wages paid. We can calculate the premium with the following steps:
Convert the base rate to a decimal by dividing by 100. This will give us 0.1124.
Multiply the total payroll amount ($179,805) by the decimal base rate (0.1124) to get the premium amount.
Let's perform the calculation:
$179,805 * 0.1124 = $20,210.08
Therefore, the correct option is:
A) $20,210.08
Which capacity is most appropriate for a pitcher of lemonade 3 litters or 30 milliliters
Answer:
3 liters.
Step-by-step explanation:
If you go to the store and you buy a 2 liter of soda making a pitcher of lemonade with one more liter won't hurt.
A milliliter is not a lot. It won't even quench your own thirst. So 3 liters is the best option.
what is the inverse of the function below f(x)=3^x
Answer:
[tex]f^{-1}(x)=\frac{ln(x)}{ln(3)}[/tex]
Step-by-step explanation:
Given: [tex]f(x)=3^x[/tex]
To find the inverse, let's first replace the [tex]f(x)[/tex] with [tex]y[/tex].
[tex]y=3^x[/tex]
Switch the [tex]x[/tex] and [tex]y[/tex].
[tex]x=3^y[/tex]
Solve for [tex]y[/tex].
[tex]y=\frac{ln(x)}{ln(3)}[/tex]
Write it in inverse notation.
[tex]f^{-1}(x)=\frac{ln(x)}{ln(3)}[/tex]
Answer: A) f^-1(x) = log₃x
a person reaching out to the edge of a building edge of a building ledge 85 feet off the ground flicks a twig up and off the ledge with an initial upward velocity of 11 feet per second. what is the maximum height of the twig? when will the twig hit the ground?
Final answer:
The maximum height of the twig is approximately 0.570 meters. The twig will hit the ground approximately 0.683 seconds after being flicked up.
Explanation:
To find the maximum height of the twig, we can use the kinematic equation for vertical motion. The equation is given by:
h = v0y2 / (2g)
Where:
h is the maximum height
v0y is the initial vertical velocity
g is the acceleration due to gravity (approximately 9.8 m/s2)
Plugging in the values, we have:
h = (11 ft/s)2 / (2 * 9.8 m/s2)
Converting the initial velocity from feet per second to meters per second:
11 ft/s * 0.3048 m/ft = 3.35 m/s
Substituting the values into the equation:
h = (3.35) / (2 * 9.8)
Simplifying the equation:
h = 0.570 m
Therefore, the maximum height of the twig is approximately 0.570 meters.
To find when the twig will hit the ground, we can use the equation for time in vertical motion:
t = 2 * v0y / g
Plugging in the values, we have:
t = 2 * 3.35 m/s / 9.8 m/s2
Simplifying the equation:
t = 0.683 s
Therefore, the twig will hit the ground approximately 0.683 seconds after being flicked up.
Javier and Kyle work installing windows and can earn extra money by installing doors. Last week, Javier earned $56 more than Kyle because of door installations. The expression below represents Javier's pay for the week: 14w + 56 What does the constant term of the expression represent?
Answer:
The money Javier earned installing doors.
Step-by-step explanation:
The problem statement gives insufficient information to answer the question with certainty.
The $56 extra earnings from door installation seems to match the 56 added as a term in Javier's pay, so we assume they are related. There is nothing else in the problem statement suggesting that to be the case.
_____
Comment on this problem
The problem fails to teach anything about math or critical thinking. Rather, it requires a student to jump to conclusions without any basis in reasoning. If the rest of the curriculum materials are like this, they should be rejected.
[tex]f(x) - \frac{x^{2}-4 }{x^{4} +x^{3} -4x^{2}-4 }[/tex]
What is the:
Domain:
V.A:
RootsL
Y-Int:
H.A:
Holes:
O.A:
Also, graph it.
a) The given function is
[tex]f(x)=\frac{x^2-4}{x^4+x^3-4x^2-4}[/tex]
The domain refers to all values of x for which the function is defined.
The function is defined for
[tex]x^4+x^3-4x^2-4\ne0[/tex]
This implies that;
[tex]x\ne -2.69,x\ne 1.83[/tex]
b) The vertical asymptotes are x-values that makes the function undefined.
To find the vertical asymptote, equate the denominator to zero and solve for x.
[tex]x^4+x^3-4x^2-4=0[/tex]
This implies that;
[tex]x= -2.69,x=1.83[/tex]
c) The roots are the x-intercepts of the graph.
To find the roots, we equate the function to zero and solve for x.
[tex]\frac{x^2-4}{x^4+x^3-4x^2-4}=0[/tex]
[tex]\Rightarrow x^2-4=0[/tex]
[tex]x^2=4[/tex]
[tex]x=\pm \sqrt{4}[/tex]
[tex]x=\pm2[/tex]
The roots are [tex]x=-2,x=2[/tex]
d) The y-intercept is where the graph touches the y-axis.
To find the y-inter, we substitute;
[tex]x=0[/tex] into the function
[tex]f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}[/tex]
[tex]f(0)=\frac{-4}{-4}=1[/tex]
e) to find the horizontal asypmtote, we take limit to infinity
[tex]lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0[/tex]
The horizontal asymtote is [tex]y=0[/tex]
f) The greatest common divisor of both the numerator and the denominator is 1.
There is no common factor of the numerator and the denominator which is at least a linear factor.
Therefore the function has no holes.
g) The given function is a proper rational function.
There is no oblique asymptote.
See attachment for graph.
A chemist needs 30mL of a 12% acid solution for an experiment. The lab has available a 10% solution and a 25% solution. How many milliliters of the 10% solution and how many milliliters of the 25% solution should the chemist mix to make the 12% solution?
parts of 10% soln, x
parts of 25% soln, y
total soln, x+y =30
{x(0.1) + y(0.25)}/(x + y) = 0.12...eqn 1
x + y = 30...eqn 2
from eqn 2...=》 x = 30-y
subst for x in eqn 1...
=》 {(30-y)(0.1) + y(0.25)}/ 30-y+y = 0.12
=》 (3-.1y+.25y)/30 =0.12
=》 3+.15y = 3.6
=》 .15y = .6
=》 y =4
using x = 30 - y = 26
ans
26ml of 10% soln
4ml of 25% soln
Using a system of equations to represent the scenario, 26mL of 10% solution and 4mL of 25% solution would be required.
Let ;
Amount of 10% solution = a Amount of 25% solution = ba + b = 30 - - - - (1)0.1a + 0.25b = (0.12 × 30)0.1a + 0.25b = 3.6 - - - (2)From (1)
a = 30 - b - - - (3)Substitute (3) into (2)
0.1(30 - b) + 0.25b = 3.6
3 - 0.1b + 0.25b = 3.6
0.15b = 0.6
b = 0.6/0.15
b = 4
From (3) :
a = 30 - 4
a = 26
Hence, 26mL of 10% solution and 4mL of 25% solution would be required.
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