Answer:
3840
Step-by-step explanation:
Given expression:
4(x+5)(x+1)(x+3)(x - 3)
To:
Evaluate the expression ; for x = 5.
Solution:
4(x+5)(x+1)(x+3)(x - 3)Evaluate x = 5 :
4(5+5)(5+1)(5+3)(5 - 3)Simplify using PEMDAS rule:
P : Parentheses
E : Exponents
M : Multiplication
D : Division
A : Addition
S : Subtraction
(4)(10)(5+1)(5+3)(5−3)40(5+1)(5+3)(5−3)(40)(6)(5+3)(5−3)(240(5+3)(5−3)(240)(8)(5−3)1920(5−3)(1920)(2)3840Hence, after evaluating the given expression for x = 5 , the answer'll be 3840.
Hi student, let me help you out! :)
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We are asked to evaluate
[tex]\large\pmb{4(x+5)(x+1)(x+3)(x-3)}[/tex] for x=5.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Use PEMDAS. With the help of this acronym, we will not make any mistakes in the Order of Operations!Here's what PEMDAS stands for:
P=Parentheses
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
So, let's start computing...
///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\///\\//\\\///\\\///\\\///\\\\///\\\\///\\\///\\\///\
Evaluating the expression
First, substitute 5 for x:
[tex]\star~\large\pmb{4(5+5)(5+1)(5+3)(5-3)}[/tex]
Now, use the Order of Operations.
The first operation here is:
[tex]\dag[/tex] P=Parentheses
So we need to perform the operations inside the parentheses first:
[tex]\star~\large\pmb{4(10)(6)(8)(2)}[/tex]
The next operation is multiplication, since we don't have any exponents here:
[tex]\star~\large\pmb{40\times6\times8\times2}[/tex]
Multiply!
[tex]\star~\Large\pmb{3840}~~\square\!\!\!\!\!\checkmark[/tex]
That's the value of the expression 4(x+5)(x+1)(x+3)(x-3) for x=5.
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
Please help! Will mark big brain!
Answer:
The height of the ladder is 6.9 meter
Explanation:
Given:
angle: 60°opposite: 6 meterhypotenuse: height of ladderAs opposite and hypotenuse given, use sine rule:
[tex]\rightarrow \sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\rightarrow \sf sin(60) = \dfrac{6}{h}[/tex]
[tex]\rightarrow \sf h = \dfrac{6}{sin(60)} = 4\sqrt{3} = 6.928 \ meters \quad \approx \ 6.9 \ meters \ \ (one \ decimal \ place)[/tex]
Solve the system 2x + 2y = -6 and 3x - 2y = 11 by using graph paper or graphing technology. What is the solution to the system?
Answer:
the solution is (1,-4)
Step-by-step explanation:
Which is the x-value of the solution of the system of equations? y=3x^2+15 y=5x^2-17
A. x=±1 B. x=±2
C. x=±4 D. x=±16
Answer:
C. x = ±4
Explanation:
Given two equation's:
y = 3x² + 15y = 5x² - 17Solve them simultaneously:
y = y
3x² + 15 = 5x² - 17
5x² - 3x² = 15 + 17
2x² = 32
x² = 16
x = ±√16
x = ±4
Ms. Rudolph randomly selects one student from a group of students. 14 students are wearing a black shirt, 6 students are wearing a red shirt, and 9 students are wearing a blue shirt.
Show your work to determine the PROBABILITY that the selected student is wearing a BLACK shirt?
You may write your answer as a FRACTION or DECIMAL.
Answer:
14
29 as a fraction
Step-by-step explanation:
Based on the given conditions, formulate:
14=19+14+6）
2 Calculate
14
9+14+6
Calculate
14
23+6
Calculate the sum or difference
14
29
X
Calculate the sum or difference
14
29
Alternative forms
~ 0.482759, ~ 48.275862%,
4.827586 × 10
Hope it help :)
Express Books advertised a college dictionary for $27.65 and a dictionary
software package for $29.80. The state tax is 5.5 percent and the city tax
is 1.5 percent. What is the total purchase price?
O $55.67
O $61.47
O $58.99
O $60.60
A
The total purchase price of the dictionary and the software package is $61.47.
What is the total purchase price?The total purchase price is the sum of the dictionary, software package and taxes.
Total cost of the dictionary and the software package = $27.65 + $29.80 = $57.45
Total cost after the taxes = ( 1 + 0.055 + 0.015) x $57.45 = $61.47
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Hello, can someone help with this problem?
The graph shows the probability distribution of a random variable.
What is the value of P(4≤X≤8)?
0.40
0.45
0.50
0.55
Answer:
P(5 ≤ X ≤ 8) = a rectangle with a width of 3 and height of .15 = 3(.15) = .45
P( 4 ≤ X ≤ 5) = a triangle with a base of 1 and a height of (0.15 -0.05) = .10
So....this area = (1/2)(1)(.10) = .05
And another rectangle with a width of 1 and height of .05 = (1) (.05) = .05
So
Adding these areas
P( 4 ≤ X ≤ 8 ) = .45 + .05 + .05 = .55
Step-by-step explanation:
Hoped this helped!
1. suppose you purchased a new car for
$30,000 in 2015. if the value of the car
decreased by 8% each year, during what year
will the car be worth $10,000
A timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−12)2+81
. Which of the following statements is true?
The airplane reaches its minimum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
The airplane reaches its minimum height of 81 feet in 12 seconds.
The airplane reaches its maximum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
Behavior of curvesIf y = [tex]x^{2}[/tex], it means that the second derivate is 2 which is positive, then there is a minimum turning point.
If y = - [tex]x^{2}[/tex], it means that the second derivative will be -2 which is negative, then there is a maximum turning point.
Analysis:
h(t) = -[tex](t - 12)^{2}[/tex] + 81
By expanding,
h(t) = -([tex]t^{2}[/tex] - 24t + 144) +81
h(t) = -[tex]t^{2}[/tex] + 24t - 144 + 81
h(t) = -[tex]t^{2}[/tex] + 24t - 63
at turning point d/dt(h(t)) = 0
d/dt (h(t)) = -2t +24
-2t +24 = 0
if we differentiate again, second derivative is -2 which is negative, so it is a maximum point.
2t = 24
t = 12 seconds
h(t) at t = 12
h(t) = [tex]-(12)^{2}[/tex] + 24(12) - 63 = 81 feet
In conclusion, the maximum height of the airplane after 12 seconds is 81 feet.
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Megan is one of the cheerleaders in her school. To prepare for the forthcoming Cheer Dance Competition, her coach is teaching them how to control their pom-poms when throwing them up into the air. One exercise is to toss the pom-poms twice as high as the previous toss from the top of their heads. If Megan is able to throw her pom-poms 2 feet above her head during her first toss, how high above her head should her fourth toss be? (problem solving)
Answer:
16 feet
Step-by-step explanation:
her first try is 2 and you multiply by 2 every time so her first would be 2 which we would multiply to get 4 which we would multiply again to get 8 which we would multiply AGAIN to get the final answer of 16
HELPP PLEASE 50 POINTS
Tucker bought some envelopes plain envelope cost twenty-five cents each decorative envelopes cost $0.45 each. he bought at least one plain envelope and at least one decorative envelope he spent exactly the same amount on Plain envelopes as on decorative envelopes.
before taxes added what was the least total amount he could have spent?
A. 1.40$
B. 2.30$
C. 3.10$
D4.50$
Answer:
D.
Step-by-step explanation:
0.45*5=2.25
0.25*9=2.25
2.25*2=4.50
Hope this helps!
If not, I am sorry.
Which equation illustrates the matrix associative property of addition
Answer:
c
cuz it is
first of all 4,3 + 0,0 = 4,3
2,1+0,0 = 2,1
and which is the answer
The door prizes at a dance are gift certificates from local merchants. there are four $10 certificates, five $20 certificates, and three $50 certificates. the prize envelopes are mixed together in a bag and are drawn at random.
The probability that none of the prizes is a $10 gift certificate is; 7/99
The expected number of $20 gift certificates drawn is 2.083
How to find the Probability?This is a question of picking objects from a mixture without replacement. The modelling distribution is the hypergeometric distribution, given by the formula:
P(a) = C(A,a) * C(B,b)/C(A+B,a+b)
Where;
a = number of good objects picked
b = number of bad objects picked.
A = number of good objects in the given batch.
B = number of bad objects in the given batch.
a + b = total number of objects picked without replacement.
A + B = total number of objects in the batch.
A) In this question;
A = 4 ($10, good)
B = 3 + 5 = 8 ($20, $50, "bad")
a = 0, b = 5
a + b = 5
Thus;
P(a = 0) = C(4, 0) × C(8, 5)/C(12, 5)
P(a = 0) = 1 × 56/792
P(a = 0) = 7/99
B) $20 is the "good" prize.
Thus;
A = 5
B = 3 + 4 = 7
a + b = 5 (total number of prizes drawn)
Thus;
E[$20] = (5/(5 + 3 + 4)*5)
E[$20] = (5/12)*5
E[$20] = 25/12
E[$20] = 2.083
Complete Question is;
The door prizes at a dance are four $10 gift certificates, five $20 gift certificates, and three $50 gift certificates. The prize envelopes are mixed together in a bag, and five prizes are drawn at random.
What is the probability that none of the prizes is a $10 gift certificate?
What is the expected number of $20 gift certificates drawn?
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which problem is molded by the equation 4x-5=45?
Answer: B.
Step-by-step explanation:
See attached. We examine the equation and decide which situation, or problem, models it correctly.
anyone know the answer
Answer:
56
Step-by-step explanation:because 12345
Which expression equivalent to 9q^ 2 - 2 3 (3q-7)+5q^ 2 ? a 9q ^ 2 - 5/3 * q - 3 b 9q ^ 2 - 2q - 3 14q ^ 2 - 2q + 14/3 d 14q ^ 2 - 5/3 * q - 14/3 d
The equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3
How to determine the equivalent expression?The expression is given as:
9q^ 2 - 2/3(3q - 7) + 5q^2
Open the bracket
9q^ 2 - 2q - 14/3 + 5q^2
Evaluate the like terms
14q^ 2 - 2q - 14/3
Hence, the equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3
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E im so confused-
( Please explain your answer! )
Answer:
B. 180° about the origin
Step-by-step explanation:
You are given a figure and its image, and asked to determine the angle of rotation. All of the answer choices indicate the center of rotation is the origin.
__
You have two clues that the rotation is 180° about the origin:
The original figure is in the 2nd quadrant, and the image is in the 4th quadrant, directly opposite the origin.Line ST is directed to the northeast; line S'T' is directed to the southwest, in exactly the opposite direction.__
To find the angle of rotation, you can look at the angle formed by a point, the center of rotation, and the image of the original point. Here, the angle UOU' is a straight angle, so the angle of rotation about O is 180°--the measure of that angle. (It can be convenient to use points close to the center of rotation, but any corresponding points on preimage and image will do.)
thank you for this :)
1.Isabel exercises no less than 45 minutes per day.
Use t to represent Isabel's amount of exercise (in minutes per day).
2. The vehicle's fuel is at least 45 miles per gallon.
Use f to represent the vehicle's fuel efficiency (in miles per gallon).
[1] t ≥ 45
Since Isabel exercises more ("no less") than 45 minutes a day, we will use greater than or equal to.
-> because being equal is not less, hence still "no less"
[2] f ≥ 45
Because the vehicle's fuel is "at least" that means it can also be equal too, hence the user of greater than or equal to.
helppppppppppppppppppppppppp
Answer:
reason 1.) This is the original expression
reason 2.) you subtract 4 from both sides
reason 3.) you divide both sides by 2 to get x=5
The roots of the quadratic equation x²+bx+c = 0 are a and ß a) Evaluate i) a² + ß², ii) (a − ß)² b) Find the quadratic equation whose roots are (a² +ß²) and (a - 3)²
If ɑ and β are the roots of x² + bx + c = 0, then we can write
x² + bx + c = (x - ɑ) (x - β)
Expanding the right side gives
x² + bx + c = x² - (ɑ + β) x + ɑβ
so that ɑ + β = -b and ɑβ = c.
Recall that for all real numbers m and n,
(m + n)² = m² + 2mn + n²
a) It follows that
(i) ɑ² + β² = (ɑ + β)² - 2ɑβ = (-b)² + c = b² + c
(ii) (ɑ - β)² = ɑ² - 2ɑβ + β² = b² + c - 2c = b² - c
b) I assume you mean to find the quadratic whose roots are ɑ² + β² and (ɑ - β)² (and not (ɑ - 3)²). The simplest quadratic of this form is
(x - (ɑ² + β²)) (x - (ɑ - β)²)
Using the results from part (a), this becomes
(x - (b² + c)) (x - (b² - c))
and expanding, we get
x² - (b² + c + b² - c) x + (b² + c) (b² - c)
= x² - 2b² x + b⁴ - c²
i need help please thanks
Just give me the new coordinates
Answer: number 1 and number 2 and 4 and 5
Step-by-step explanation:
A rectangular solid is dilated by a factor of 0.5
How many times larger is the volume of the resulting cube than the volume of the original cube
Enter your answer as a decimal and do NOT round
Answer:
0.125 times larger
Step-by-step explanation:
given the scale factor of 2 solids is k , then the volume factor = k³
here k = 0.5 , so
volume factor = (0.5)³ = 0.125
Please help :) I don’t understand this
Answer:
Step-by-step explanation:
Part A
Neighborhood A :
2, 2, 2, 4, 4, 5, 5, 5, 5
mean = [tex]\frac{2+2+2+4+4+5+5+5+5}{9}[/tex] = [tex]\frac{34}{9}[/tex] ≈ 3.8
median = 4
mode = 5
range = 3
[tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 5 - 2 = 3
===================
Part B.
Neighborhood B :
1, 1, 2, 2, 3, 4, 5, 5, 12
mean = ( 1 + 1 + 2 + 2 + 3 + 4 + 5 + 5 + 12 ) ÷ 9 = [tex]\frac{35}{9}[/tex] ≈ 3.9
median = 3
mode = 1, 2, 5
range = 11
[tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 5 - 1.5 = 3.5
Outlier = 12
A crate is lifting a boat suspended by wire ropes AB and AD. The point C is vertically below A, and BC measures 5.
a) The gradient of AB is 0.8. How high is AC
The boat suspended by wire ropes AB and AD, AC is 4 units high.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The gradient of AB is 0.8, hence:
AC / BC = 0.8
Since BC = 5, therefore:
AC / 5 = 0.8
AC = 4
The boat suspended by wire ropes AB and AD, AC is 4 units high.
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IF G=(x)=x^2 find the value of g(2).g(3)
Answer: 36
Step-by-step explanation:
[tex]g(2)=2^{2}=4\\g(3)=3^{2}=9\\g(2) \cdot g(3)=4 \cdot 9=\boxed{36}[/tex]
The population of center city is modeled by exponential function
The range of the exponential function will be y ≥ 250,0003. Then the correct option is B.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The Population Of Center City Is Modeled By Exponential Function F, Where X Is The Number Of Years After The Year 2015.
The graph is given below.
We know that the exponential function is given as
y = abˣ
For x = 0, y will be 250,000
250,000 = a
For x = 40, y will be 400,000
400,000 = 250,000b⁴⁰
b = 1.0118
Then we have
y = 250,000 (1.0118)ˣ
Then the range of the exponential function will be y ≥ 250,0003.
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Please please help me 30 points if you can I need the answer I know how to do it I just suck with the fractions
Answer:
1
Step-by-step explanation:
[tex]\text{Given that,}~ (x_1,y_1) = (-2,4)~ \text{and}~ \text{slope,}~ m = -\dfrac 32\\ \\\text{Equation of line,}~\\\\~~~~~~~y -y_1 = m(x-x_1)\\\\\implies y -4 =-\dfrac 32(x+2)\\\\\implies y-4 =-\dfrac 32x - 3\\\\\implies y = -\dfrac 32x -3 +4\\\\\implies y = -\dfrac 32x +1[/tex]
The current equation of the perpendicular line;
⇒ is the slope-intercept form: [tex]y= mx + b[/tex]
m: is the coefficient in front of the x, which is also the slope's valueb: y-intercept of the functionNow for the point-slope form, we need a point on the line and the slope of the line:
⇒ we have
slope = -3/2point: (-2,4)Since this is the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex]
⇒ where the (x₁,y₁) is the point on the line and m is the slope
[tex]= > Equation: (y-4)=-\frac{3}{2}(x+2)[/tex]
To convert the equation to slope-intercept form:
⇒ must isolate 'y' to one side and everything to the other side
[tex]y= -\frac{3}{2}(x+2)+4\\ y=-\frac{3}{2} x-3+4\\y=-\frac{3}{2}x+1[/tex]
Answer: [tex]y = -\frac{3}{2}x+1[/tex]
Hope that helps!
Which is the range of the function f(x) = (9)×?
O all real numbers
O all real numbers less than 0
O all real numbers greater than 0
O all real numbers less than or equal to 0
Using it's concept, it is found that the range of the function [tex]f(x) = 9^x[/tex] is given by:
all real numbers greater than 0.
What is the range of a function?It is the set that contains all possible output values for the function.
In this problem, the function is:
[tex]f(x) = 9^x[/tex]
For exponential functions without vertical shifts, as is the case in this problem, the range is given by:
all real numbers greater than 0.
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Un fabricante de peceras debe indicar el volumen de cada una de ellas. ¿cuál es el volumen de una pecera de forma cilíndrica con un diámetro de 50 cm. Y una altura de 30 cm. ?
El volumen es una cantidad escalar tridimensional. El volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm es 58,904.863 cm³.
¿Qué es el volumen?
Un volumen es un número escalar que expresa la cantidad de espacio tridimensional encerrado por una superficie cerrada.
El volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm será,
Volumen del cilindro = (π/4)×diámetro ²×altura
= (π/4)×(50cm)²×30cm
= 58,904.863cm³
Por lo tanto, el volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm es 58,904.863 cm³.
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a school spent 150$ on advertising for a breakfast fundraiser each plate of food was sold for 8.00$ but cost the school 2.00$ to prepare after all expenses were paid the school raised 2,400$ at the fundraiser . which equation can be used to find x the number of plates that were sold?
Answer:
375 plates were sold
Step-by-step explanation:
$2400 (profit) - $150 (advertising) = $6 (profit per plate $8 cost - $2 expense) times x
2400 - 150 = 6x
Simplify the left side: 2400 - 150 = 2250
2250 = 6x
Divide both sides by 6
2250/6 = 375