Answer:
h(x) = x³ + 4x² - 49x - 196
Step-by-step explanation:
h(x) = (x² - 49)(x + 4) <== distribute
h(x) = x²(x) - 49(x) + x²(4) - 49(4)
h(x) = x³ - 49x + 4x² - 196 <== rewrite in standard form (descending degrees)
h(x) = x³ + 4x² - 49x - 196
Hope this helps!
Algebra 1 is all about equations and functions. First, you learned about Linear Functions then Quadratic Functions. Next, you learned about Rational Functions (indirect variation), then Exponential and then Radical Functions. Before Algebra 1 comes to a close, it is good to review these functions and compare them side by side.
Complete the table below. The table is created for you in the Word or PDF Worksheet. If you don't have Microsoft Word, download the PDF and create the worksheet in an application of your choice, complete the worksheet and upload it as a PDF.
All images should be original. Graphed them using a digital calculator such as Desmos.
Resources: Desmos User Guide
Export a graph from Desmos by choosing 'Share' and then 'Export', or you can 'Print' them as a PDF. Alternatively, you can take a screenshot of your graph. You can insert the image into this table or give your image files a distinct name and upload them with this worksheet. You can upload them as a PDF, or you can use an image file format - PNG, JPG or GIF files.
Linear Quadratic Rational Exponential Radical
Parent Function:
Notation
----------------------------
Parent Function:
Graph
----------------------------
Translation:
Graph a function which extends
through quadrant 1, 2, and 4.
If it is not possible to graph
through these quadrants,
chose one or two quadrants and explain the choice.
-------------------------------------
Write the function notation
for the above function
-------------------------------------
Domain and Range of
translated function
Reflection: Write a paragraph summarizing what you learned from this activity.
Answer:
Algebra is simple and the answer is infinity due to there being over one million diffrent possoblitlitys, We know that because of albert ienstine so the answer has been solved.
Step-by-step explanation:
Which division problem is represented with this model?
1/5÷3
1/5÷4
1/3÷2
1/4÷3
We can represent this drawing as follows: 1/5÷3
FractionFraction is a representation of a division between two real integers. A fraction, can be named as a ratio between two natural terms, integers, rational and/or reals. They consist of a numerator and a denominator.
Looking at the image, we can see that it is divided into 5 parts. In one of these parts, there is one that is divided into three ''group''.
- We know that the numerator indicates the amount that was divided and the denominator indicates the total amount. Therefore, the answer will be:
5 parts in total. = 1 ÷ 3
1 whole part - divided into three 5
So, the correct answer is 1/5 ÷ 3
1 Which expression is equivalent to
12x - 3x?
A x(123)
(B) 8x
© 3(3x - x)
(D 9
If your options are:
A. x(12-3)
B. 8x
C. 3 (3x-x)
D. 9
Then the following is true.
Answer: (A) x(12-3)
First, we will simplify the given expressions;
A. x(12-3) = 12x - 3x
B. 8x = 8x
C. 3 (3x-x) = 9x - 3x
D. 9 =9
This means the answer to your question is;
A. x(12-3)
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Which of the following pairs of numbers contain like fractions
A. 3/2 and 4 44
B. 3/2 and 2/3
C.6/7, and 1 1/5,
D.5/6 and 10/12
Answer:
D. 5/6 and 10/12
Step-by-step explanation:
PLEASE EXPLAIN I NEED THIS
The amount of bacteria in a culture doubles every minute. The culture starts with
20 bacteria.
a. Write an equation modelling the number of bacteria, y, after x minutes.
Answer:
exponential function, x = time in minutes, y = number of bacteria
Step-by-step explanation:
y = 20 × (2)^x
Please help me do this mathematics question experts
[tex]\textbf{(i)}\\\\~~~~~~~y= e^{3x} \sin 2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx} \left( e^{3x} \sin 2x \right)\\\\\\~~~~~~~~~~~~=e^{3x} \dfrac{d}{dx} \sin 2x + \sin 2x \dfrac{d}{dx} e^{3x}\\\\\\~~~~~~~~~~~~=2e^{3x} \cos 2x + 3e^{3x}\sin 2x \\\\\\[/tex]
[tex]\textbf{(ii)}\\\\~~~~~~~~y = \dfrac{e^{3x}}{\cos 2x}\\\\\\\implies \dfrac{dy}{dx} = \dfrac d{dx} \left(\dfrac{e^{3x}}{\cos 2x} \right)\\\\\\~~~~~~~~~~~=\dfrac{\cos 2x \dfrac{d}{dx}\left(e^{3x} \right) -e^{3x} \dfrac{d}{dx}( \cos 2x) }{\cos^2 (2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x+2e^{3x}\sin2x }{\cos^2(2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x}{ \cos^2(2x)} + \dfrac{2e^{3x} \sin 2x}{\cos^2(2x)}\\\\\\~~~~~~~~~~~=3e^{3x}\sec (2x) + 2e^{3x}\sec (2x) \tan (2x)[/tex]
[tex]\textbf{(iii)}\\\\~~~~~~~~~y=( 3x+2)^3\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx}(3x+2)^3\\\\\\~~~~~~~~~~~=3(3x+2)^2 \dfrac{d}{dx} (3x+2)\\\\\\~~~~~~~~~~~=3(3x+2)^2 \cdot 3\\\\\\~~~~~~~~~~~=9(3x+2)^2[/tex]
[tex]\textbf{(iv)}\\\\~~~~~~~~~x^2 +y^2 = 5xy\\\\\\\implies \dfrac{d}{dx}(x^2 +y^2) = 5\dfrac{d}{dx} (xy)\\\\\\\implies 2x + 2y \dfrac{dy}{dx} = 5\left(x \dfrac{dy}{dx} +y\right)\\ \\\\\implies 2x +2y \dfrac{dy}{dx} = 5x \dfrac{dy}{dx} +5y\\\\\\\implies 2y \dfrac{dy}{dx} - 5x \dfrac{dy}{dx} = 5y-2x\\\\\\\implies (2y-5x) \dfrac{dy}{dx} = 5y-2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{5y-2x}{2y-5x}[/tex]
Suzy drove to a hair appointment at 50mph. Her average speed on the return home was 40mph. The return home took 1/4hr longer because of heavy traffic. How far did she travel to her hair appointment?
Since Suzy return took 1/4 hr longer, how far Suzy travelled to her appointment is 50 mi
To answer the question, we need to know what distance travelled by Suzy is
Distance between Suzy's home and hair appointmentThe distance between Suzy and her appointment is d = vt where
v = Suzy's speed = 50 mph and t = time it takes to teach her appointment.So, d = 50t (1)
Now, since Suzy returns home at a speed of v' = 40 mph and takes her 1/4 hr longer to return home,her return time is , t' = (t + 1/4) h
Since the distance she ruturns home is the same, we also have that
d = v't'
= 40(t + 1/4) (2)
Equating (1) and (2), we have
50t = 40(t + 1/4)
50t = 40t + 10
50t - 40t = 10
10t = 10
t = 10/10
t = 1 hr
How far Suzy travelled to her appointmentSubstituting t = 1 into d = 50t, we have
d = 50(1)
d = 50 m
So, how far Suzy travelled to her appointment is 50 mi
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A password is 4 characters long and must consist of 3 letters and one number. if letters cannot be repeated and the password must end with a number, how many possibilities are there? a. 175,760 b. 158,184 c. 156,000 d. 140,400 please select the best answer from the choices provided a b c d
The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The possibility of selecting the password = 26 * 25 * 24 * 10 = 156000
The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000
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help will mark Brainliest!!
Answer:
1/20
Step-by-step explanation:
1/4 = 0.25
0.25 / 5 = 0.05
0.05 as a fraction = 5/100
simplified
5 / 5 = 1
100 / 5 = 20
1/20
For Halloween, Sue wears a monocle that, its packaging claims, has a circumference of
18.212 centimeters. What is the monocle's radius?
Use 3.14
the measure of the radius is 2.9
City A is 300 km due east of city B. City C is 200 km on a bearing of 123° from city B. How far is it from C to A?
Answer:
500 km
Step-by-step explanation:
300 plus 200 is 500km this is how far it is
The distance between City A & City C is approximately 171.3km
Given that, city A is 300 km due east of city B.
City C is 200 km on a bearing of 123° from city B.
We need to find the distance between the cities A and C,
Here we will use the concept of Cosine rule,
{Refer to the figure attached}
From ∆ABC, to find |AC|,
The cosine rule will be used.
|AC|² = |BC|² + |AB|² - 2(|BC|)(|AB|)cosB
Let |AC| = x
x² = 200² + 300² - 2(200)(300)cos33
x² = 40000 + 90000 - 120000cos33
x² = 130000-100644
x² = 29356
x = √29356
x = 171.3359
x ≈ 171.3km
Therefore, the distance between City A & City C is approximately 171.3km
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Use the axiomatic approach for vectors to prove the distributive law of vectors
Step-by-step explanation:
Find the HCF of 9m 80cm 8m 40cm 4m 20cm
14 boys and 16 girls in class
What is the ratio of girls to the total number of students in class? Write ratio in 3 ways
Answer:
1) 16 : 30
2) 8 : 15
3) [tex]\displaystyle \frac{8}{15}[/tex]
Step-by-step explanation:
Boys = 14
Girls = 16
Total students:
= 14 + 16
= 30
Ratio of Girls to total number of students in class:
= 16 : 30
÷2 ÷2
= 8 : 15
= [tex]\displaystyle \frac{8}{15}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Help urgent need this help please
Answer:
First option is the correct answer
[tex] A(\triangle ABC) =572\: yd^2[/tex]
Step-by-step explanation:
Given scale is: 3 cm = 6 yd [tex] \implies[/tex] 1 cm = 2 ydBased upon the above scale, we find:Base of the triangle (AC) = 13 cm = 26 ydHeight of the triangle (h) = 22 cm = 44 yd[tex] A(\triangle ABC) = \frac{1}{2} * AC*h[/tex][tex] \implies A(\triangle ABC) = \frac{1}{2} (26)(44)[/tex][tex] \implies A(\triangle ABC) =572\: yd^2[/tex]What is the area of the circle?
Answer:
530.93
Step-by-step explanation:
area of a circle = πr²
where r = radius
here we are given the diameter
to convert to radius , we divide by 2
so radius = 26 / 2 = 13
so we have A = πr²
==> plug in r = 13
A = π13²
==> evaluate exponent
A = 169π
==> multiply 169 and π
A = 530.93 ( approximately )
Lila's Tea Shop has caffeinated tea
and decaffeinated tea. During the
lunchtime rush, the tea shop served
100 teas in all, 41% of which were
caffeinated. How many caffeinated
teas did the tea shop serve?
Answer:
28 caffinated teas
Step-by-step explanation:
Solve for x. Enter your answer in interval
notation using grouping symbols.
x² + 2x ≥ 15
Answer:
[tex](x−3)(x+5) .....is.. the.. factorised.. form.. of.. the.. expression[/tex]
Step-by-step explanation:
[tex]x^2 + 2x > =15 \\x^2 + 2x - 15 > = 0 \\(x + 4)(x - 2) < 0 , \\{x + 4 < 0 and .x - 2 > 0} or {x + 4 > 0 ,\\and .x - 2 < 0} , \\{x < -4 and .x > 2} or {x > -4 and. x < 2},\\ Discard .x < -4 and. x > 2 because. it. has. no. solutions,\\ leaving .just x > -4 and .x < 2 , -4 < x < 2[/tex]
1/3 off the regular price of $51
Answer:
34.00
Step-by-step explanation:
because get the discounted price, subtract the discount from the original price. To illustrate this principle, here is an example: to take 1/3 off $36.00, divide 36 by 3 and multiply by 1. This becomes 36/3 x 1 to equal 12, which represents a discount of $12.00
You invest $700 at 6.5% and it’s compounded semi-annually for 3 years. How much will your $700 be worth in 3 years?
Answer:
$10,700.
Step-by-step explanation:
What is the value of x in the triangle?
Answer:
3 = x
Step-by-step explanation:
Well, the two unknown sides share the same size due to the same angle, so now, using the fact we only have the info about one side, we need to do a reverse pythagorean theorem.
[tex]c^{2} = a^{2} + b^{2}[/tex]
Our a and b are the same, so I will change them to "x" and combine them.
[tex]c^{2} = 2(x)^{2}[/tex]
Now we plug in our "c" and square it ("C" in this case is: [tex]3\sqrt{2}[/tex] )
[tex]18 = 2(x)^{2}[/tex]
[tex]9 = x^{2}[/tex]
3 = x
Which ordered pair is a solution of the equation?
4x -1 = 3y + 5
(2,3)
(3,2)
(1,1)
(9,10)
Answer:
(3, 2)
(9, 10)
Step-by-step explanation:
Ordered pairs (3, 2) and (9, 10) is the solution of the equation 4x -1 = 3y + 5
4x -1 = 3y + 5 (given)Lets us check for (3, 2)L.H.S. = 4x - 1 = 4(3) - 1 = 12 - 1 = 11 (plug x = 3)R.H.S. = 3y + 5 = 3(2) + 5 = 6 + 5 = 11 (plug y = 2)-> L.H.S. = R.H.S.-> Ordered pair (3, 2) is a solution of the given equation.Similarly, ordered pair (9, 10) is also a solution of the given equation because L.H.S and R. H.S. are equal to 35 on plugging x = 9 and y = 10.I really need help on this
Answer:
y=4
Step-by-step explanation:
steps
3×9+4y=43
4y=43-27
4y=16
Divide both side by 4
4y/4=16/4
y=4
f(x) = 3x^2 + 5x find f(3)
Answer:
f(3) = 42
Step-by-step explanation:
f(x) = 3x² + 5x
Then
f(3) = 3(3)² + 5(3)
= 3×9 + 5×3
= 27 + 15
= 42
The bottom of a circular swimming pool with a diameter of 40feet is made up of blue tiles . How many square feet is that
Answer:
radius = 40 / 2 = 20ft
Circle area = πr² = π × 20² = 1256.6 sq. ft
What principal will yield N75 interest at 30% for 2 years
Step-by-step explanation:
by using the formula of principal
p= I×100/T×R
Answer:
90
Step-by-step explanation:
PRT/100
75×30×2/100
9000/100
=90
Type the correct answer in each box.
A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is ____? units. The point (-7, __?) lies on this circle.
Answer:
the answer is 5 and (-7,5)
Step-by-step explanation:
The radius is 5, and the points (-7, 5) and (-7, -1) both lie on the circle.
Given that:
The points at which the circle is centered are (-3,2)
Passing points = (1,5)
The radius is calculated using the distance formula:
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]
Substituting the coordinates, we have:
d =[tex]\sqrt{({1 - (-3))^2 + (5 - 2)^2[/tex]
= [tex]\sqrt{(1 + 3)^2 + (5 - 2)^2[/tex]
=[tex]\sqrt{(4^2 + 3^2)[/tex]
= [tex]\sqrt{(16 + 9)[/tex]
= 5
Therefore, the radius of the circle is 5 units.
The equation of a circle with center (h, k) and radius r is given by:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Substituting the values, we have:
[tex][-7 - (-3)]^2 + (y - 2)^2 = 5^2[/tex]
[tex](-7 + 3)^2 + (y - 2)^2 = 25[/tex]
[tex](-4)^2 + (y - 2)^2 = 25[/tex]
[tex]16 + (y - 2)^2 = 25[/tex]
[tex](y - 2)^2 = 9[/tex]
Taking the square root of both sides, we have:
y - 2 = ±3
Solving for y, we have two possible values:
y - 2 = 3
y = 5
y - 2 = -3
y = -1
The points (-7, 5) and (-7, -1) both lie on the circle.
Thus, the radius is 5, and the points (-7, 5) and (-7, -1) both lie on the circle.
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CAN ANYONE PLEASE HELP!’
Answer:
130 cm³
Step-by-step explanation:
Volume of the pyramid = 1/3 × base area × height
Calculating base area;
Area = length × width
= 8 × 7
= 56 cm²
Now, Volume = ⅓ × 56 × 7
= ⅓ × 392
= 130.6 cm³.
y=x-2
y=4
x=3
y=2x+1
CAN SOMEBODY HELP ME WITH THIS? SUPER HARD HOMEWORK
Answer:
//Solve equation [2] for the variable y
[2] y = 4
// Plug this in for variable y in equation [1]
[1] (4) - x = -2
[1] - x = -6
// Plug this in for variable y in equation [4]
[4] (4) - 2x = 1
[4] - 2x = -3
// Solve equation [1] for the variable x
[1] x = 6
// Plug this in for variable x in equation [3]
[3] (6) = 3
[3] 0 = -3 => NO solution
No solution
A biology student wants to determine if using a fertilizer would help promote growth of new babies in spider plants. The student has access to 90 spider plants of three varieties: green, variegated, and curly. They all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. After one year, the shoots will be counted for each plant.
Which of the following describes a random block design for this experiment?
A) The plants are numbered 01–90. Using a line from a random number table, the first 45 two-digit numbers, ignoring repeats and the numbers 91–99 and 00, represent the plants that will receive fertilizer. The remaining 45 plants will not receive fertilizer.
B) The plants are paired together based on similar size and numbered 1 and 2. Within each pair, a 6-sided number cube is rolled. If it lands on 1, 2, or 3, plant 1 receives the fertilizer and plant 2 does not receive fertilizer. If the cube lands on 4, 5, or 6, plant 1 does not receive fertilizer and plant 2 receives fertilizer. This is done for each of the 45 pairs of plants.
C) The plants are grouped based on variety. There are 30 plants of each variety. The plants within each variety are numbered 1–30, and the numbers are put in a random number generator. The first 15 unique numbers represent the plants in each variety that will receive fertilizer and the remaining 15 numbers will represent the plants in each variety that will not receive fertilizer.
D) The plants are grouped based on size. The 30 biggest plants are placed in one group and the 30 smallest plants in another other group. The remaining 30 plants are placed in a third group. For each group, a coin is flipped. If the coin lands on heads then the group will receive the fertilizer. If it lands on tails, then the group will not receive fertilizer. Repeat this procedure for the other two groups.
Answer:
it is b
Step-by-step explanation:
that is the most effective way to measure how well the fertilizer works with all of the plants