Answer:
The zeros are 1 and 2
Step-by-step explanation:
Given
[tex]y =x^2 - 3x + 2[/tex]
Required
The zeros
[tex]y =x^2 - 3x + 2[/tex]
Expand
[tex]y =x^2 - 2x-x + 2[/tex]
Factorize
[tex]y =x(x - 2)-1(x - 2)[/tex]
Factor out x - 2
[tex]y =(x - 1)(x - 2)[/tex]
Set to 0
[tex](x - 1)(x - 2)=0[/tex]
Solve for x
[tex]x - 1 = 0 \to x =1[/tex]
[tex]x - 2 = 0 \to x =2[/tex]
Hence, the zeros are 1 and 2
Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet. Which integer represents Gemma’s position with respect to sea level?
–32
Answer:
-24 feet
Step-by-step explanation:
Boat is 4 feet above sea level => +4 feet
She descends 28 feet => -28 feet
Position = +4-28 = -24 feet
Therefore,
Gemma is 24 feet below the sea level
Answer:
-24 feet
Step-by-step explanation:
Because she is 4 feet above sea level, she can descend 4 feet to be at sea level. Now she only has to descend 24 feet below sea level, which is -24 feet.
There are 12 squares and 9 circles . What is the simplest ratio of circles to total shapes?
:) sorry i put the wrong answer before bc i thought i knew it but it was the wrong one and i dont know how to delete the answer sorrryyyyyyyyyyyyyyyy
Caleb types 100 words in 5 minsutes . What is the unit rate
Answer:
The unit rate is 20.
Step-by-step explanation:
Divide 100 (words) by 5 (minutes) to get 20 words every minute.
Consider a fishery in which harvesting is taking placeat a constant rateh. The population at the fisherywill be modeled by
dP/dt = kP- h
Required:
Find the general solution to this DE.
Answer:
The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
Step-by-step explanation:
We are given the following differential equation:
[tex]\frac{dP}{dt} = kP - h[/tex]
Solving by separation of variables:
[tex]\frac{dP}{kP-h} = dt[/tex]
Integrating both sides:
[tex]\int \frac{dP}{kP-h} = \int dt[/tex]
On the left side, by substitution, u = kP - h, du = kDp, Dp = du/k. Then
[tex]\frac{1}{k} \ln{kP-h} = t + K[/tex]
In which K is the constant of integration.
[tex]\ln{kP-h} = kt + K[/tex]
[tex]e^{\ln{kP-h}} = e^{kt + K}[/tex]
[tex]kP - h = Ke^{kt}[/tex]
[tex]kP = Ke^{kt} + h[/tex]
[tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
How many vertices does a triangular prism have?
4 5 6 9
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Vertices are the vertex points. there are 4 vertices at the bottom and 2 vertices at the top which makes 6.
Hope this helps
what is the area of a rectangular driveway measuring 20 feet long and 15 feet wide?
Answer:
300 square feet
Step-by-step explanation:
Area is found by multiplying the length and width of a surface
ANSWER ASAPPP PLSSS. ILL MARK BRAINLIEST TOO
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 10(1.02)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points)
Answer:
Step-by-step explanation:
11.04 = 10(1.02)^n
1.104 = 1.02^n
ln 1.104 = ln 1.02^n
ln 1.104 = n ln 1.02
n = ln 1.104/ ln 1.02
n = 4.99630409516
4.99 can be rounded to 5.
So a reasonable domain would be 0 ≤ x < 5
PART B)
f(0) = 10(1.02)^0
f(0) = 10(1)
f(0) = 10
The y-intercept represents the height of the plant when they began the experiment.
f(1) = 10(1.02)^1
f(1) = 10(1.02)
f(1) = 10.2
(1, 10.2)
f(5) = 10(1.02)^5
f(5) = 10(1.1040808)
f(5) = 11.040808
f(1)=10(1.02)^1
f(1)=10.2
Average rate= (fn2-fn1)/(n2-n1)
=11.04-10.2/(5-1)
=0.22
the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.
Answer:
Part A
The domain should be 0 ≤n≤5
Part B
f(n) = 10(1.02)^n
The function is in the form y =a b^x where a is the y intercept
The y intercept is 10. This is the value when n =0 days.
Part C
The average rate of growth over the 4 days is .21 cm per day
Step-by-step explanation:
f(n) = 10(1.02)^n
Part A
Let f(n) = 11.04
11.04 = 10 * 1.02 ^n
Divide each side by 10
11.04/10 = 1.02^n
1.104 = 1.02^n
Taking the log of each side
log 1.104 = log 1.02^n
We know log a^b = b log a
log 1.104 = n log 1.02
log 1.104 / log 1.02 = n
4.99630=n
Rounding n to 5
The domain should be 0 ≤n≤5
Part B
f(n) = 10(1.02)^n
The function is in the form y =a b^x where a is the y intercept
The y intercept is 10. This is the value when n =0 days.
Part C
To find the average rate of change
f(5) - f(1)
-----------
5-1
f(5) = 11.04
f(1) = 10 *1.02 =10.2
11.04 - 10.2
-----------
5-1
.84
-----
4
.21 cm per day
The average rate of growth over the 4 days is .21 cm per day
PLEASEEEEEEEEEE HELPPPPPP PLSEASEEEE IM BEGGING SOMEONE PLEASEEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEE PLEASEEEEE
Answer:
30 degree
Step-by-step explanation:
x + x + 60 + 60 = 180 degree (being sum of interior angles of a triangle )
2x 120 = 180
2x = 180 - 120
x = 60/2
x = 30 degree
Answer:
I'm not quite sure but there is 180 degrees in a triangle and they give us two 60 degrees which add up to 120. So, I'm assuming x = 60 or either 30 degrees if we're solving for both the x's at the top.
I'm really sorry if this is wrong.
In the population of young children eligible to participate in a study of whether or not their calcium intake is adequate, 52% are 5 to 10 years of age and 48% are 11 to 13 years of age. For those who are 5 to 10 years of age, 18% have inadequate calcium intake. For those who are 11 to 13 years of age, 57% have inadequate calcium intake.
Required:
a. Use letters to define the events of interest in this exercise.
b. Convert the percents given to probabilities of the events you have defined.
Answer:
(a) A = 5 to 10 years old
B = 11 to 13 years old
C = adequate calcium intake
I = inadequate calcium intake.
(b) P(A) = 0.52, P(B) = 0.48, P(I|A) = 0.18, P(I|B) = 0.57.
Step-by-step explanation:
Complete question
Please find the attached image
(a) A = 5 to 10 years old
B = 11 to 13 years old
C = adequate calcium intake
I = inadequate calcium intake.
b) P(A) = 0.52, P(B) = 0.48, P(I|A) = 0.18, P(I|B) = 0.57.
5+9+9 divided by 3= ?
The amount of increase from the cost to the selling price is called the?
Answer:
profit
hope it is helpful to you
Step-by-step explanation:
Markup is the percentage amount by which the cost of a product is increased to arrive at the selling price.
The measure of ∠1 =
a. 110
b. 62.5
c. 55
Answer:
option C
Step-by-step explanation:
1. Find the length of X (in the picture) plssss I need help.
Step-by-step explanation:
[tex] \frac{5}{4} = \frac{x}{6} \\ 4x = 30 \\ x = 7.5[/tex]
Eric wants to buy a new hat
which costs $17. He made
$5 by raking leaves and
$8 by washing cars.
How much more money does he need?
Answer:
the answer is 4
Step-by-step explanation:
you subtract 13 from 17 =4
Which of the following best describes the equation below? y = x + 8 OA. function only B. both a relation and a function Oc. neither a relation nor a function OD. relation only?
9514 1404 393
Answer:
B. both a relation and a function
Step-by-step explanation:
Every linear equation with defined slope is both a relation and a function.
__
Only a vertical line of the form x=constant is linear equation that is a relation, but not a function.
The points P and Q have coordinates (-1, 6) and (9, 0) respectively.
The line l is perpendicular to PQ and passes through the mid-point of PQ.
Find an equation for l, giving your answer in the form ax + by + c =0, where a, b and c are integers.
Answer:
[tex]3y - 5x +11=0[/tex]
Step-by-step explanation:
Given
[tex]P(x_1,y_1) = (-1,6)[/tex]
[tex]Q(x_2,y_2) = (9,0)[/tex]
Required
The equation of l
First, calculate the slope (m) of PQ
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{0-6}{9--1}[/tex]
[tex]m = \frac{-6}{10}[/tex]
[tex]m = \frac{-3}{5}[/tex]
Since l is perpendicular to PQ, the slope of l is:
[tex]m_2 = -\frac{1}{m}[/tex]
[tex]m_2= -\frac{1}{-3/5}[/tex]
[tex]m_2 = \frac{5}{3}[/tex]
Next, calculate the midpoint of PQ
[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]
[tex]M = \frac{1}{2}(-1+9,6+0)[/tex]
[tex]M = \frac{1}{2}(8,6)[/tex]
[tex]M = (4,3)[/tex]
The equation of l is:
[tex]y = m(x -x_1) + y_1[/tex]
[tex]y = \frac{5}{3}(x -4) +3[/tex]
Multiply through by 3
[tex]3y = 5(x -4) +9[/tex]
Open bracket
[tex]3y = 5x -20 +9[/tex]
[tex]3y = 5x -11[/tex]
Rewrite as:
[tex]3y - 5x +11=0[/tex]
If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x).
True or false?
Answer:
False
Step-by-step explanation:
Take the point (2, 3) = (x, y)
Rotated 90º clockwise (3, -2) = (y, -x)
Rotated 90º counter clockwise (-3, 2) = (-y, x)
Neither rotation becomes (-3, -2)
As preparation for designing a new line of business wear, a clothing manufacturer asked a large sample of department store customers, "What is your favorite
color of dress shirt?" The ple chart below summarizes their responses.
(a) Which color was chosen by approximately one fourth of
the customers?
Answer:
white
Step-by-step explanation:
if you cut the shape in half both ways it makes white take up a fourth.
What is the value of x in the triangle?
3/2
X
help please<3
Answer:
x = 3
Step-by-step explanation:
Assuming the acute angle are 45degrees
Hypotenuse = 3√2
Opposite = x
According to SOH CAH TOA
Sin 45 = opposite//hypotenuse
Sin 45 = x/3√2
1/√2 = x/3√2
Cross multiply
√2x = 3√2
x = 3
Hence the value of x is 3
Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.
Carpeted Un-Carpeted
15.9 8.1 15 7.2 10.4 6.1
11.2 16 11.2 6.8 11.3 6.8
8.6 10 12.1 6.3
Requried:
State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.
Answer:
The null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:
H[tex]_{0}[/tex]: μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].
H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].
Step-by-step explanation:
In the question, the given assertion is that carpeted rooms have more bacteria than uncarpeted rooms, i.e. μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].
The assertion made in the question can either be the null hypothesis (H[tex]_{0}[/tex]) or the alternate hypothesis (H[tex]_{1}[/tex]). An equality must be present in the null hypothesis. The alternative hypothesis expresses the exact opposite of the null hypothesis if the claim is the null hypothesis.
Therefore, the null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:
H[tex]_{0}[/tex]: μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].
H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].
What is the domain of the square root function graphed below?
Answer:
Set the expression inside the square root greater than or equal to zero. We do this because only nonnegative numbers have a real square root, in other words, we can not take the square root of a negative number and get a real number, which means we have to use numbers that are greater than or equal to zero.
Step 2: Solve the equation found in step 1. Remember that when you are solving equations involving inequalities, if you multiply or divide by a negative number, you must reverse the direction of the inequality symbol.
Step 3: Write the answer using interval notation.
The list price on slacks is $22, and the list price on jumpers is $37. If Petit’s Clothing Store orders 30 pairs of slacks and 40 jumpers at a discount rate of 11%, what is the trade discount on the purchase?
Answer:
The trade discount is
$235.4
Step-by-step explanation:
Given data
Slacks= $22
Jumpers= $37
Number of orders for Slacks= 30
Number of orders for Jumpers= 40
Total cost
22*30=$660
37*40=$1480
=$2140
11% discount can be computed as
=11/100*2140
=$235.4
Find the area of the figure below (Do Not put the units in your answer)
Answer:
54
Step-by-step explanation:
Area of rhombus= (12×9) ÷2
Can anyone help me with this question!
9514 1404 393
Answer:
D. (x² -2x -3) +(-x² +4x +2)
Step-by-step explanation:
The tiles on the first row model (x² -2x -3).
The tiles on the second row model (-x² +4x +2).
If the difference is being modeled, it will show as ...
(x² -2x -3) -(-x² +4x +2) = (x -2x -3) +(x² -4x -2) . . . . . matches none
If the sum is being modeled, it will show as ...
(x² -2x -3) +(-x² +4x +2) . . . . . matches D
_____
Additional comment
As is often the case, you can select the correct answer without even any understanding of the question. You can do that because the correct answer is the only one that is a true statement. All of the other answer choices are incorrectly "simplified."
Learning Task 1: Conduct a survey of the favorite fruit of your classmates and/or friends 10 boys and 10 girls by
sending them messages on messenger or SMS. Use the table to record the data.
Favorite Fruit of My Classmate and Friends
Tally
Fruits
Boys
Girls
1. pineapples
2. ripe mangoes
3. rambutan
4. lansones
5. buko
Answer the following questions:
1. What is the set of data all about?
2. Which fruit is the favorite among the girls Boys
3. What is the least favorite fruit among the girls Boys
4. What is the top choice fruit of both girls and boys
5. What is the least favorite fruit of both boys and girls
Answer:
1 Its all about there favorite fruits
2 the favorite fruits of the girls are buko less than the boys.
3 the least fruit favorite fruits is pineapple among the girls boys.
4 the top choice of the fruit is the lansones both girls and boys.
5 the rambutan is the least favorite both of them
Step-by-step explanation:
Hope its help po pa brainlest
Answer:
girl
-apple
-masanas
boy
-lansones
-rambotan
sorry yan lang alam ko
Complete the function, count_bases(s). It takes as input a DNA sequence as a string, s. It should compute the number of occurrences of each base (i.e., 'A', 'C', 'G', and 'T') in s. It should then return these counts in a dictionary whose keys are the bases.
Answer:
The function is as follows:
def count_bases(DNA_str):
retDNA = {}
for i in DNA_str:
if i in retDNA:
retDNA[i]+=1
else:
retDNA[i] = 1
return retDNA
Step-by-step explanation:
This defines the function
def count_bases(DNA_str):
This initializes a dictionary
retDNA = {}
This iterates through the dictionary
for i in DNA_str:
If an item exists in the dictionary
if i in retDNA:
The count is updated by 1
retDNA[i]+=1
Otherwise
else:
The count is set to 1
retDNA[i] = 1
This returns the DAN
return retDNA
if the volume of a Sphere is 36 pie cm³. then find its radius
I will give brainliest
Answer: r = 3
Step-by-step explanation:
V=(4/3)πr^3 (this is the formula to identify a volume of the sphere. Since we know that V = 36π, add it into the following formula like so:
36π = (4/3)πr^3; from here we can cancel out the π
36 = (4/3)r^3; multiply both sides by 3/4
27 = r^3;
the final answer is r = 3.
given the function f(x) = 2x^2 - 6x +4. calculate the following values
Answer:
x^1 = 1, x^2 =2
Step-by-step explanation:
its hard to explain but there's the answer
which figure shows the radius of circle O?
Answer:
D
Step-by-step explanation:
The radius of a circle refers to a segment connecting the center of the circle to the circumference of the circle. This can be seen in selection D), as a segment connects the center of the circle (O) to the circumference or outer edge of the circle.
Can someone answer with steps and explanation? Thanks.
Answer:[tex]\color{yellow}{}[/tex]
∆ABC
∆DEF
∆ABC
<C
<D
<X
BE>
CF>
AD>
34>
x9×>
A=3.7