Answer:
[tex]x^3 + 8x^2 + 11x-20[/tex]
Step-by-step explanation:
f(x) = x^2 + 3x − 4
g(x) = x + 5
To find f(x) * g(x) we multiply f(x) with g(x)
[tex]f(x) * g(x) = (x^2 + 3x -4) * (x+5)[/tex]
First multiply each term in f(x) and multiply with x+5
x^2 times x+5 becomes [tex]x^3+5x^2[/tex]
3x times x+5 becomes [tex]3x^2 + 15x[/tex]
-4 times x+ 5 becomes -4x -20
so f(x) * g(x) = [tex]x^3 + 5x^2 +3x^2 + 15x -4x -20[/tex]
Combine like terms
f(x) * g(x) = [tex]x^3 + 8x^2 + 11x-20[/tex]
Answer: [C]: " x³ + 8x² + 11x − 20 " .
______________________________________________________
Step-by-step explanation:
______________________________________________________
Given: " f(x) = x² + 3x − 4 " ; and
" g(x) = x + 5 " ;
Find: " f(x) ⋅ g(x) " :
______________________________________________________
f(x) ⋅ g(x) =
" (x² + 3x − 4) (x + 5) " ;
↔ " (x + 5) (x² + 3x − 4) " ;
______________________________________________________
Note: " (a + b) (c + d + e) = ac + ad + ae + bc + bd + ae " ;
______________________________________________________
→ " (x + 5) (x² + 3x − 4)
= (x * x²) + (x * 3x) + (x*-4) + (5*x²) + (5*3x) + (5*-4) " ;
= (x³) + (3x²) + (-4x) + (5x²) + (15x) + (-20) ;
= x³ + 3x² − 4x + 5x² + 15x − 20 ;
→ Combine the "like terms" :
+ 3x² + 5x² = + 8x² ;
− 4x + 15x = + 11 x ;
______________________________________________________
→ And rewrite:
______________________________________________________
→ " x³ + 8x² + 11x − 20 " ;
______________________________________________________
→ which is: Answer choice: [C]: " x³ + 8x² + 11x − 20 " .
______________________________________________________
Hope this helps!
Best wishes!
______________________________________________________
The percent change of 40;50
Answer:
25%
Step-by-step explanation:
Change = Final - initial
% Change =(Final - Initial)/Initial × 100%
% Change = (50 - 40)/40 × 100%
% Change = 10/40 × 100%
% Change = 25%
Answer:
25%
Step-by-step explanation:
1) Find the difference of the two numbers, do (Largest Number)-(Smallest Number).
2) Use your difference as a fraction. Use the difference over the initial value.
3) Create a proportion
10/40 = x/100
4) Cross multiply, 10*100 = 200, 40*p = 40p
5) Simplify expression 1,000=40p
6) Solve, 1,000/40 = 25
7) Put it as a fraction, 25/100
8) Make it a percent 25%
pleasee answer the question in the picture
Answer:
a (5,2)
Step-by-step explanation:
To get to the smiley face, we move 5 units in the x direction from the origin, then we move 2 units up in the y direction (x,y) so the point is at (5,
PRE CALC PLEASE HELP!!!
Topic: Rational Functions
If f(x)=2x^3-bx^2+cx+12, Were b and c integers, list all possible rational roots of f(x)
Answer: [tex]\bold{\pm \{1, 2, 3, 4, 6, 12, \dfrac{1}{2}, \dfrac{3}{2}\}}[/tex]
Step-by-step explanation:
Q P
f(x) = 2x³ - bx² + cx + 12
Possible rational roots are all of the factors of P divided by all of the factors of Q, including both positive and negative signs.
[tex]\quad \pm \dfrac{\text{factors of P}}{\text{factors of Q}}\\\\=\pm \dfrac{\text{factors of 12}}{\text{factors of 2}}\\\\=\pm \dfrac{1,2,3,4,6,12}{1,2}\\\\=\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \dfrac{1}{2}, \pm \dfrac{3}{2}\\[/tex]
Solve 100 divided by 5 x 4 + 4³
Answer:
144
Step-by-step explanation:
4 x 4 x 4 = 64
100/5 = 20
20 x 4= 80
80 + 64 =144
Answer:
100 /( 5 x 4 + 4³) = 1 4/21
100 / 5 x 4 + 4³ = 144
Step-by-step explanation:
100 /( 5 x 4 + 4³)
PEMDAS tells us to do what is inside the parenthses
We will do the power in side the parentheses first 4^3 = 64
100 /( 5 x 4 + 64)
Now we will multiply
100/(20+64)
Now we add inside the parentheses
100/84
Divide the top and bottom by 4
25/21
Changing from an improper fraction to a mixed number
1 4/21
OR
100 / 5 x 4 + 4³
If the quantity is not in parentheses
We will do the power first 4^3 = 64
100 / 5 x 4 + 64
Then we do the multiplication and division from left to right
20 *4+64
80+64
144
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:think as it as coordinates on a graph. Time=x Amount=y. So if the time is 0 and the amount is 60 you would graph a point on (0,60)
Step-by-step explanation:
What is the eighth term in the arithmetic sequence defined by the explicit formula an=2n+7? Enter your answer in the box.
Answer:
The 8th term is 23
Step-by-step explanation:
If we are given the formula for the sequence
an=2n+7,
then to find the 8th term we substitute n=8 into the formula.
a8 = 2(8) +7
a8 = 16+7
a8 = 23
The 8th term is 23
How do you convert a fraction to a decimal? Say, [tex]\frac{2}{5}[/tex] ?
Answer:
you divide the top number by the bottom number
Step-by-step explanation:
2/5 = 0.4
show that the points p(7,12) and q(-3,-12) and r (14,5) lie on a circle with center c(2,0)
If the points P (7, 12), Q (-3, -12) and R (14, 5) lie on a circle with the center C (0, 2), then the distance OP, OQ and OR are the same.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute:
[tex]OP=\sqrt{(2-7)^2+(0-12)^2}=\sqrt{(-5)^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OP=13}\\\\OQ=\sqrt{(2-(-3))^2+(0-(-12))^2}=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OQ=13}\\\\OR=\sqrt{(2-14)^2+(0-5)^2}=\sqrt{(-12)^2+(-5)^2}=\sqrt{144+25}=\sqrt{169}\\\\\boxed{OR=13}[/tex]
OP = OQ = OR, therefore the points P, Q and R lie on one circle.
Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y-3=-1/5(x+2);(-2,7)
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have the line
[tex]y-3=-\dfrac{1}{5}(x+2)\to m=-\dfrac{1}{5}[/tex]
If m₁ and m₂ are the slopes of the perpendicular lines, then
[tex]m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
Therefore the slope of ouer line is
[tex]m=-\dfrac{1}{-\frac{1}{5}}=5[/tex]
We have the point (-2, 7). Put the coordinates to the equation of a line in the point-slope form:
[tex]y-7=5(x-(-2))[/tex]
[tex]y-7=5(x+2)[/tex] use the distributive property
[tex]y-7=(5)(x)+(5)(2)[/tex]
[tex]y-7=5x+10[/tex] add 7 to both sides
[tex]\boxed{y=5x+17}[/tex]
PLS HELP ASAP
Which equation represents a proportional relationship?
y=32x
y=−2x
y = 4x + 3
y=2(x+1)
The proportional relationship:
y = ax for a > 0.
Therefore your answer is:
y = 32xSneakers normally cost $89.99, but on sale, they are marked down to $56.49. What percent off is the sale price?
Answer:
60%
Step-by-step explanation:
Use the equation a=pw. A= Part P= Percent. W= Whole
A= $56.49
P = x (unknown)
W= $ 89.99
Equation = 56.49=89.99x
You divide 89.99 on both sides to be equal and isolate the variable x. You would divide 56.49 by 89.99 and will get 0.627736415. You would round it to the nearest tenth , 0.6 so the percent is 60%
The percent off is 37.2263 % of the sale price.
What Is Percentage Change?In finance, percentage change is frequently used to denote the percentage-based price change of a stock over time. Depending on whether the change is an increase or a reduction, a simple mathematical formula is employed to quantify this change as a percentage.The most common use of percentage change in finance is to monitor changes in stock and market index prices.Comparing the values of several currencies also involves using change expressed as a percentage.Additionally, balance sheets with comparative financial statements contain percentage change.Depending on whether there is an increase or decrease, there are slight differences in how to calculate percentage change.Calculations :
According to the given conditions, state = 33.5/89.99 Multiply the numerator and denominatorwith the same whole number = 3350/8999
Rewrite a fraction as a decimal = 0.372263Multiply a number for both thenumerator and the denominator = 0.372263 x [tex]\frac{100}{100}[/tex]
Write as a simple fraction = 0.372263 x 100 / 100Calculate the product or coefficient = 37.2263 / 100Rewrite a fraction with the denominatorequal to 100 as a percent = 37.2263 %
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David sells two calculators for ₹1500 each .He earns a profit of 25% on
one and suffers a loss of 25% on the other. Find his total profit or loss on
the whole deal. Also calculate it as a percentage
Answer:
100% profit of 1500
Step-by-step explanation:
One the first calculator David earns 25% profit:
25% + 1500 = 1,875
He gets a 25% on the second calculator:
1500 - 25% = 1,125
In total he receives 1125 + 1875 = 3000
Therefore he has 100% profit
What is the 33rd term of this arithmetic sequence? 7, 17, 27, 37,47
Answer:
327 FOR A FACTTTTT
Step-by-step explanation:
Answer:
the answer would be 327
Step-by-step explanation:
hope this helps :)
If a person draws 2 cards at random from a standard deck of 52 cards, what is the probability that they get 2 aces?
Answer:4/52=1/13
Step-by-step explanation:
The deck has 52 cards and contains 4 aces. When you draw a card, the probability of drawing an ace is 4/52=1/13
Find the x-intercepts (solve for x) for the following AND PLEASE SHOW YOUR WORK! y=−2x^2−9x+5
Answer:
see explanation
Step-by-step explanation:
To find the x- intercepts set y = 0, that is
- 2x² - 9x + 5 = 0
To factorise the quadratic consider the factors of the product of the coefficient of the x² term and the constant term that sum to give the coefficient of the x- term.
product = - 2 × 5 = - 10 and sum = - 9
The factors are - 10 and + 1
Use these factors to split the middle term
- 2x² - 10x + x + 5 = 0 ( factor the first/second and third/fourth terms )
- 2x(x + 5) + 1(x + 5) ( factor out (x + 5) )
(x + 5)(- 2x + 1) = 0
equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
- 2x + 1 = 0 ⇒ x = [tex]\frac{1}{2}[/tex]
x-intercepts are x = - 5 and x = [tex]\frac{1}{2}[/tex]
What is 4:2 the same as
Answer:
4:2 is the same as:
2:1
8:4
or anything that is proportional to 4:2
Step-by-step explanation:
A proportion is anything that corresponds in size or amount to something else.
Answer:
2:1
Step-by-step explanation:
just reduce the ratio b and divivd bith sides by 2
Choose all of the equations that graph as an increasing function.
2
A. y = -- x + 7
3
B. y = -3x - 4
C. y = -5x
D. = 0.05x + 10
Answer:
A. y = -(-x) +7 = x + 7
D. y = 0.05x + 10
Which steps should be used to compare the fractions 2/9 and 5/6
Answer: you need to get a common denominator.. once you have a common denominator, you can compare numerators to see what is larger..
Step-by-step explanation:
to get the common denominator, you would first see what this would be.. in this case 18, as that's the lowest. then, you would multiply each fraction by 2/2 for first and 3/3 for second, which are just funky looking ones. therefore, D is the correct answer.
Answer:It is C
Step-by-step explanation:In the question it says to COMPARE the fraction.
Hope it helps !!!!! PLZ MARK ME BRAINLIEST!!!!!
a used automobile dealership recently reduced the price of a used compact car by 10 % if the price of the car before discount was $33500 find the discount and the new price
Answer: The new price is $3350.
Answer:
$3350; $30 150
Step-by-step explanation:
Original price = $33 500
Discount = 33 500 × 10 %
Discount = 33 500 × 0.10
Discount = $3350
New price = Original price - Discount
New price = 33 500 - 3350
New price = $30 150
Question 1(Multiple Choice Worth 1 points) (02.06 MC) Charles wants to determine which car is the fastest. The actual speed of four cars is shown below: Car A B C D Speed (in km/h) 60.34 60.32 60.33 60.35 If the speedometer can only measure to the nearest tenth of a second, which car will have a different measurement?
Answer:
Car D will have a different measurement because the 60.35 would round up to be 60.31 where all the other would round down and remain at 60.30
Step-by-step explanation:
the sum of two numbers is 53. their difference is 17. Find the numbers.
Answer: the two numbers is 35 and 18
Step-by-step explanation: 35+18=53 35-18=17
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Final answer:
The two numbers are 35 and 18. We found these by solving the simultaneous equations x + y = 53 and x - y = 17, representing their sum and difference.
Explanation:
Finding Two Numbers Given Their Sum and Difference
Let's denote the two unknown numbers as x and y. According to the conditions given:
x + y = 53 (Equation 1: The sum of the two numbers)
x - y = 17 (Equation 2: The difference of the two numbers)
We can solve these two simultaneous equations to find the values of x and y.
Add the two equations:
(x + y) + (x - y) = 53 + 17
2x = 70
x = 35
Substitute x in Equation 1:
35 + y = 53
y = 53 - 35
y = 18
Therefore, the two numbers are 35 and 18.
What is the equation of the line, in standard form, that passes through (4, -3) and is parallel to the line whose equation is 4x + y - 2 = 0?
answers:
4x - y = 13
4x + y = 13
4x + y = -13
Answer:
The equation of this line would be 4x + y = 13
Step-by-step explanation:
In order to find this equation we must first find the slope of the original line. To do this, we solve the original equation for y.
4x + y - 2 = 0
4x + y = 2
y = -4x + 2
The original slope (the coefficient of x) is -4, which means the new slope will also be -4 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line. Just plug in the numbers and solve for the coefficient.
y - y1 = m(x - x1)
y + 3 = -4(x - 4)
y + 3 = -4x + 16
4x + y + 3 = 16
4x + y = 13
Find the area of this trapezoid. Be sure to include the correct unit in your answer.
Answer:
the area of this trapezoid= 81 square inches
Step-by-step explanation:
To find area of trapezoid , we use formula
[tex]Area = \frac{a+b}{2} * h[/tex]
Where a,b are the base of the trapezoid
h is the height of the trapezoid
Here a= 3 in
b = 15 in
h = 9 in
Plug in all the values in the formula
[tex]Area = \frac{a+b}{2} * h[/tex]
[tex]Area = \frac{3+15}{2} * 9[/tex]
[tex]Area = \frac{18}{2} * 9[/tex]
Area = 9 * 9 = 81
the area of this trapezoid= 81 square inches
write an equation of a line that passes through (3,0) and (6,-3) in slope intercept and point slope form
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (3, 0) and (6, -3). Substitute:
[tex]m=\dfrac{-3-0}{6-3}=\dfrac{-3}{3}=-1[/tex]
The point-slope form:
[tex]y-(-3)=-1(x-6)\\\\\boxed{y+3=-(x-6)}[/tex]
or
[tex]y-0=-1(x-3)\\\\\boxed{y=-(x-3)}[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
From the second point-slope form we have slope-intercept form:
[tex]y=-(x-3)\\\\y=-x-(-3)\\\\\boxed{y=-x+3}[/tex]
Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack.
Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.
Let x = the number of packages of pasta and y = the number of jars of pasta sauce.
Identify each point as either a solution to the system or not a solution to the system of inequalities.
(1, 12) Solution or Not a Solution
(2, 10) Solution or Not a Solution
(4, 5) Solution or Not a Solution
(6, 10) Solution or Not a Solution
(12, 8) Solution or Not a Solution
(18, 6) Solution or Not a Solution
Answer:
1,12/ Not a solution
2,10/ solution
4,5/ solution
6,10/ not a solution
12,8/ not a solution
18,6/ not a solution
Step-by-step explanation:
all you have to do is put it into the equation.
for example:
1,12
1x1+12x3= $37
1x1+12x1.5= 19lbs
This is not a solution because he can carry it but doesn't have the money to buy it.
Answer:
(1,12)=no solution
(2,10)=Solution
(4,5)=Solution
(6,10)=no solution
(12,8)=no solution
(18,6)=no solution
Step-by-step explanation:
You have to add the money and pounds each together. For example, the equation you would set up would be, for money: 1(1)=1 and the jars 3(12)=36. Together, it equals 37, which would be over the total amount that Tyler may buy. If you do all of these to show your work, then the answers are the ones shown above.
What decimal is represented by this expanded form?
5×10,000+3×1,000+2×10+8×1+ 6×1/100+4×1/1,000
Answer:
53028.064 I think
Step-by-step explanation:
Use the drop-down menus to identify the values of the parabola
Answer:
What drop down menues??????????????????????
Step-by-step explanation:
Answer:
options?
Step-by-step explanation:
five more then -8 times a number is 29. What is the number? Let the mystery number be represented by n.
Answer:
The mystery number is -3
Step-by-step explanation:
five more then -8 times a number is 29.
-8n +5 = 29
Subtract 5 from both sides
-8n +5-5 = 29-5
-8n = 24
Divide by -8 on each side
-8n/-8 = 24/-8
n= -3
The mystery number is -3
The mystery number in the equation is -3, determined by solving the algebraic equation 5 + (-8 × n) = 29.
The equation given in the problem statement translates to the mathematical expression 5 + (-8 × n) = 29, where n is the mystery number. To find the value of n, we can perform the following steps:
Subtract 5 from both sides to get -8n = 24.
Divide both sides by -8 to isolate n, giving us n = 24 / -8.
Calculate the result to find that n = -3.
Therefore, the mystery number is -3.
Dianna earns $8.50 an hour working as a lifeguard write an equation to find Dianna’s money earned?
y=8.5x
y= money earned
x= hours worked
The equation to find Dianna's money earned as a lifeguard is e = 8.50h.
To find Dianna's money earned, we can write an equation using the formula for calculating earnings:
Earnings=Hourly Rate × Number of Hours Worked
In this case, Dianna's hourly rate is $8.50, and let's denote the number of hours she worked as ℎ.
So, the equation to find Dianna's money earned
E=8.50×h
Where:
E represents the total earnings
8.50 represents Dianna's hourly rate
h represents the number of hours worked
This equation will give us the total amount of money Dianna earned based on the number of hours she worked.
a student phototcopies a drawing without realizing tht the copier is set to enlarge the image by 15%. if the height of the actual drawing is 4.25 inches, approximately how tall is the phototcopied drawing?
If an image is being enlarged by 15% you would take the base number multiply it by the percent in decimal form and add the result to the base number.
4.25*0.15=0.6275
0.6375+4.25=4.8875
Answer: 4.8875
To find out the height of the photocopied drawing, we first calculate 15% of the original height (4.25 inches) and add this to the original height. The photocopied drawing is approximately 4.89 inches tall.
Explanation:The student photocopied a drawing with the copier set to enlarge the image by 15%. If the original drawing is 4.25 inches tall, the enlarged photocopied drawing would be larger by 15% of 4.25 inches.
Firstly, to find 15% of 4.25 inches, you multiply 4.25 by 0.15 (the decimal equivalent of 15%), which equals 0.6375 inches.
Adding this to the original height of the drawing, we get 4.25 inches + 0.6375 inches = 4.8875 inches, which is approximately 4.89 inches when rounded to two decimal places.
So, the photocopied drawing is approximately 4.89 inches tall.
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