The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.
What do these functions have in common?
Here we have the functions:
[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]
f(x) is quadratic, and g(x) is exponential.
Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards. So first and second options are false.
Also, g(x) never intersects the x-axis, so third option is false.
Finally, the y-intercepts of the given functions are:
[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]
So the y-intercepts are equal, meaning that the correct option is D.
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Answer:
Both f(x) and g(x) have the same y-intercept of (0, 1).
Step-by-step explanation:
I got it right on the test.
Mr. Garcia had some blueberries. He sold 2 3/4 kilograms of the blueberries and packed the rest equally into 9 bags. Each bag contained 1/4 kilogram of blueberries. Find the mass of blueberries that mr. Garcia had at first
Answer:
Mr. Garcia had 5 kilograms of blueberries at first
Step-by-step explanation:
to make this easiest, we can imagine that we're undoing mr. garcia's actions.
So, we can start by 'unpacking' mr garcia's bags
we know that each of the nine bags had 1/4 kilograms, so we can multiply 1/4 by 9 to find the collective mass packed into bags
(remember, multiplication is repeated addition. we could also add 1/4 + 1/4 + 1/4... nine times, but this would take a while)
so,
1/4 x 9 = 9/4
(9 = 9/1 [if that is how you're used to multiplying a fraction])
Then, he also sold 2 3/4 kilograms
so, we can add 2 3/4 + 9/4 to find the total mass of the blueberries at first
2 3/4 + 9/4 = 2 + 12/4
(12/4 = 3)
2 + 3 = 5
So, Mr. Garcia had 5 kilograms of blueberries at first
What does the expression n + 3 represent?
Answer:
Step-by-step explanation:
BASICALLY ANYTHING WITH 3
b solve each problem . use ñ= 3.14 1. what is the volume of a regular cylinder whose base has radius of 5 cm and has height of 4 cm? 2. the diameter of sphere is 10 cm. find the volume. 3. juice is sold in aluminum cans that measure 7 inches in height and 4 inches in diameter. how many cubic inches of juice are contained in a full can? 4. the square pyramid has a volume of 297 cm³. the area of the base is 81 cm². What is the height.? 5. A glass is 10 cm deep and 8 cm wide . How much liquid the glass hold?
#1
Volume
πr²hπ(5)²(4)100π3.14(100)314cm³#2
Radius=10/2=5cm
Volume
4/3πr³4/3π(5)³125(4/3π)500π/3523.3cm³#3
Volume
π(4/2)²(7)2²(7π)28π87.92in³#4
V=1/3a²hV=1/3(81)h27h=297h=11cm#5
radius=8/2=4
Volume
π(4)²(10)160π502.4cm³502.4mLAnswer:
1) 314 cm³
2) 523.33 cm³
3) 87.92 in³
4) 11 cm
5) 502.4 cm³
Step-by-step explanation:
Part 1[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 5 cmh = 4 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 5^2 \cdot 4\\& = 3.14 \cdot 25 \cdot 4\\& = 3.14 \cdot 100\\& = 314 \: \sf cm^3\end{aligned}[/tex]
Part 2[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3\quad\textsf{(where r is the radius)}[/tex]
Given:
d = 10 cm ⇒ r = 5 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =\dfrac{4}{3} \cdot 3.14 \cdot 5^3 \\& =\dfrac{4}{3} \cdot 3.14 \cdot 125 \\& =\dfrac{500}{3} \cdot 3.14 \\& = 523.33\: \sf cm^3\:(2\:dp)\end{aligned}[/tex]
Part 3[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
d = 4 in ⇒ r = 2 inh = 7 inπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 2^2 \cdot 7\\& = 3.14 \cdot 4 \cdot 7\\& = 3.14 \cdot 28\\& = 87.92\: \sf in^3\end{aligned}[/tex]
Part 4[tex]\textsf{Volume of a square pyramid}=\sf \dfrac{1}{3} a^2h \quad\textsf{(where a is the base edge and h is the height)}[/tex][tex]\textsf{Area of base of square pyramid}=\sf a^2 \quad\textsf{(where a is the base edge)}[/tex]
Given:
Volume = 297 cm³Area of base = 81 cm²[tex]\implies 81=a^2[/tex]
[tex]\implies a=\sqrt{81}[/tex]
[tex]\implies a=9\: \sf cm[/tex]
Substitute the given values into the formula and solve for h:
[tex]\begin{aligned}\implies \textsf{297} & =\dfrac{1}{3} \cdot 9^2 \cdot h\\\\297 & =\dfrac{81}{3} h\\\\891 & =81 h\\\\h & = 11 \: \sf cm\end{aligned}[/tex]
Part 5[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
d = 8 cm ⇒ r = 4 cmh = 10 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 4^2 \cdot 10\\& = 3.14 \cdot 16 \cdot 10\\& = 3.14 \cdot 160\\& = 502.4\: \sf cm^3\end{aligned}[/tex]
hello fellow indians Question: Lawrence poured 27.328 L of water into a right rectangular prism- shaped tank. The base of the tank is 40 cm by 28 cm. When he finished pouring the water, the tank was ⅔ full. ( 1L=1,000 cm 3).
Answer: andres is 5 years old pls banned him he called e a mean word like the N word
Step-by-step explanation:
Part 3 - Discussion/Explanation Question
In what ways can vertical, horizontal, and oblique asymptotes be identified? Use a mathematical example to
explain the ways.
Step-by-step explanation:
Vertical asymptote can be Identites if there is a factor only in the denominator. This means that the function will be infinitely discounted at that point.
For example,
[tex] \frac{1}{x - 5} [/tex]
Set the expression in the denominator equal to 0, because you can't divide by 0.
[tex]x - 5 = 0[/tex]
[tex]x = 5[/tex]
So the vertical asymptote is x=5.
Disclaimer if you see something like this
[tex] \frac{(x - 5)(x + 3)}{(x - 5)} [/tex]
x=5 won't be a vertical asymptote, it will be a hole because it in the numerator and denominator.
Horizontal:
If we have a function like this
[tex] \frac{1}{x} [/tex]
We can determine what happens to the y values as x gets bigger, as x gets bigger, we will get smaller answers for y values. The y values will get closer to 0 but never reach it.
Remember a constant can be represent by
[tex]a \times {x}^{0} [/tex]
For example,
[tex]1 = 1 \times {x}^{0} [/tex]
[tex]2 = 2 \times {x}^{0} [/tex]
And so on,
and
[tex]x = {x}^{1} [/tex]
So our equation is basically
[tex] \frac{1 \times {x}^{0} }{ {x}^{1} } [/tex]
Look at the degrees, since the numerator has a smaller degree than the denominator, the denominator will grow larger than the numerator as x gets larger, so since the larger number is the denominator, our y values will approach 0.
So anytime, the degree of the numerator < denominator, the horizontal asymptote is x=0.
Consider the function
[tex] \frac{3 {x}^{2} }{ {x}^{2} + 1} [/tex]
As x get larger, the only thing that will matter will be the leading coefficient of the leading degree term. So as x approach infinity and negative infinity, the horizontal asymptote will the numerator of the leading coefficient/ the leading coefficient of the denominator
So in this case,
[tex]x = \frac{3}{1} [/tex]
Finally, if the numerator has a greater degree than denominator, the value of horizontal asymptote will be larger and larger such there would be no horizontal asymptote instead of a oblique asymptote.
which axis shows the dependent varible
The axis on a graph that shows the dependent variable is the: vertical or y-axis.
What is the Dependent Variable?The dependent variable is the variable that is affected by an independent variable. That is, a change in the independent variable, causes the dependent variable to change.
On a graph, the dependent variable (outcome) is usually plotted on the y-axis (vertical axis).
Thus, the axis that shows the dependent variable is the vertical or y-axis.
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For each of the number lines, write an absolute value equation in the form |x - c |=d,
where c and d are some numbers, to satisfy the given solution set.
The absolute value equation that satisfy the solution set of -4 and -8 is |2 - x| = -6
How to determine the absolute value equation?The solution sets on the number line are given as:
x = {-8, -4}
Calculate the average of the solutions
Mean = (-8 - 4)/2
Mean = -6
Calculate the difference of the solutions divided by 2
Difference = (-4 + 8)/2
Difference = 2
The absolute value equation is the represented as:
|Difference - x | = Mean
Substitute known values
|2 - x| = -6
Hence, the absolute value equation is |2 - x| = -6
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Answer:
|b+6|=2
Step-by-step explanation:
Directions: In this last section, you will answer one problem. Be sure to read the
problem carefully and to answer the question completely. Show your work and circle
your answer. Use any method to solve this problem.
74. A restaurant has a total of 60 tables. Some of the tables can seat 4 people and some
seat 2 people. All of the seats are occupied when there are 160 people seated. How man
tables for 4 are there?
Answer:
40 tables
Step-by-step explanation:
I think lol I'm just guessing. Hope you get it right. If I'm right just remember me as legend or the chosen one.
please I need the answer
Answer:
The answer is c
Step-by-step explanation:
one add the numbers 108 & 96=204
then add the numbers from c which is 30+30=60 43+43=86 29+29=58
then add 60+86+58 which will be 204 so c is the answer your welcome
come
Lamar is considering two loans
Which loan will have the lowest total payback?
Answer:
Loan A will have the lowest total paycheck because the total of the principal than the same total for loan B
Which of the following produces an image that is not congruent to the pre-image?
A. translation
B. dilation
C. rotation
D. reflection
Answer:
Dilation
Step-by-step explanation:
it’s a dilation because the dilation changes how big the image is or what it looks like after the original image.
Question 6 of 10
Estimate the sum of the decimals below by rounding to the nearest whole
number. Enter your answer in the space provided.
6.833
3.594
+1.369
————
Answer here
Step-by-step explanation:
7
4
1
----
12
reality
6.833
3.594
1.369
----------
11.796
help pleseeeeeeeeeeeeeeeeeeeeeeee
Complete the information as requested:
1.- Indicated dose: 300 mg of Ceftriaxone ampoules IV every 6 hours for 10 days.
Available: 1.2 g of Ceftriaxone vial. Reconstitute with 5ml of Sterile Water
a) Dose volume … Calculations
b) Number of doses per day to comply with the indication.
c) Number of ampoules needed for the entire treatment
2.- The patient has indicated:
Indicated quantity: 250 mg Tobramycin ampoule every 12 hours
Available Tobramycin 100 mg /ml vial
a) Dose volume for administration according to indication.
b) Number of ampoules needed for one day of treatment.
c) Amount of Tobramycin received per day - mg
3.- A doctor indicates 0.5 g PO c6h x 5 days
The drug available is 125 mg / 5 mL
a) What is the amount of drug administered per dose? in ml
b) how many total doses for the 5 days are required
c) how many 100 ml bottles do I need to deliver
How do you find the length of an unknown leg in a right triange
By using the pythagoras theorum you can find an unknown leg of right angled triangle.
Hypotenuse side is in the front of the 90 degree angle and other two sides can be taken as base and perpendicular, so formula goes as :-
(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2
H^2 = B^2 + P^2
Step-by-step explanation:
Hope it helps you!!What’s the answer to the picture I took?
Answer:
y = - x
Step-by-step explanation:
From the given table:-
( x_1,x_2): (5,-5)
( y_1,y_2): (6,-6)
1) Let's find the slope (m):-
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{ - 6( - 5)}{6 - 5} = \frac{ - 6 + 5}{1} = \frac{ - 1}{1} = - 1[/tex]
2) Substitute x_1= 5, y_1=-5 and m=-1 into y-y_1=m(x-x_1)
[tex]y - ( - 5) = - 1(x - 5)[/tex]
[tex]y + 5 = - x + 5[/tex]
[tex]y = - x + 5 - 5[/tex]
[tex]y = - x[/tex]
when a number x is added to it's square, the total is 12. find two possible values of x
Answer:
x=3 or x=−4Step-by-step explanation:
when a number x is added to it's square, the total is 12. find two possible values of x
x+x^2=12
x^2+x=12
x^2+x−12=12−12
x^2+x−12=0
(x−3)(x+4)=0
x−3=0 or x+4=0
x=3 or x=−4
x=3 or x=−4
(Image: Start Fraction x over 4 End Fraction) + 2 = –2
If the linear equation with one variable is x / 4 + 2 = –2. Then the value of x will be negative 16.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
x / 4 + 2 = –2
Solving for x, we have
x / 4 + 2 = –2
x / 4 = – 2 – 2
x / 4 = – 4
x = – 4 × 4
x = – 16
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can you please help me with this two questions
Answer:
2) d. 60°
3) a. AB
Step-by-step explanation:
Question 2
ΔABC and ΔCDA are congruent because:
they are both right trianglesthey share one side (AC)their hypotenuse are parallel (marked by the arrows)This means the corresponding side lengths and angles are equal.
Therefore,
∠CDA = ∠ABC
⇒ x = 60°
Question 3
The hypotenuse is the longest side of a right triangle - the side opposite the right angle (the right angle is shown as a small square).
Therefore, the hypotenuse of ΔABC is the line AB.
Write the place value of the 1 in 742.513
Hi Student!
Looking at the problem statement, we are asked to find the place value of the 1 in the number 742.513. Let's go from right to left and name each of the place values. 7 is in the hundreds place, 4 is in the tens place, 2 is in the ones place, 5 is in the tenths place, 1 is in the hundredths place, 3 is in the thousandths place.
Therefore, our final answer for which place value the number 1 in 742.513 is, we come to the conclusion of the hundredths place.
If kinaata goes for swimming lessons every 5 days while Wayo goes every 6 days. if both kinaata and Wayo had swimming lessons together at the pool today, after how many days will both meet again at the pool for lessons?
Step-by-step explanation:
we need the least or smallest common multiple for both numbers, 5 and 6.
this is very simple for the small numbers here, but in general we look at the prime factors of both numbers :
6 has the prime factors 2 and 3.
5 has only 5.
so, the LCM is 2×3×5 = 30.
they will meet again after 30 days.
FYI -
the LCM is for larger numbers a and b not automatically a×b. if both numbers share prime factors, the LCM can be smaller than a×b, as the LCM is using every overlapping prime factor only once.
question attached please help
Answer:
h(0.1) = 4.97
Step-by-step explanation:
See attached working :)
Remember that h(0.1) is the same as saying find what the equation is equal to when x = 0.1
URGRENNTTT PLSS HELPP 50 POINTSS!!!!! Students were asked to simplify the expression cotangent theta plus tangent theta over cotangent theta. Two students' work is given.
Student A
Step 1: cotangent theta over cotangent theta plus tangent theta over cotangent theta
Step 2: 1 plus tangent theta over the quantity 1 over tangent theta end quantity
Step 3: 1 + tan2 θ
Step 4: sec2 θ Student B
Step 1: the quantity 1 over tangent theta end quantity plus tangent theta over the quantity cotangent theta
Step 2: the quantity 1 plus tangent squared theta end quantity over tangent theta all over cotangent theta
Step 3: secant squared theta over tangent squared theta
Step 4: csc2 θ
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
The student that simplified the expression incorrectly is student 2
How to determine the incorrect result?The steps are given as:
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)}[/tex]
Student 1:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]1 + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 3: 1 + tan²(Ф)Step 4: sec²(Ф)Student 2:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]\frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]Step 3: sec²(Ф)/tan²(Ф)Step 4: csc²(Ф)As a general trigonometry rule;
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)} = \sec^2(\theta)[/tex]
This means that student 1 is correct, while student 2 is not
The first error in student 2's workings is in step 2, where we have:
[tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)} = \frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]
The above expression is not justified and cannot be proved by any trigonometry rule
Since the step 2 is incorrect, the other steps cannot be used.
Hence, the student that simplified the expression incorrectly is student 2
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Circle O has a radius of 5 centimeters and central angleAOB with a measure of 60°.
The arc length can be found using the formula, ∅ × r, which is: (5π)/3.
What is the Arc Length?Arc length = ∅ × r, where ∅ is the central angle in radians, and r is the radius of the circle.
Given the following:
∅ = 60° = 60° × π/180 (in radians)r = 5 cmLength of the arc = 60° × π/180 × 5 = (60 × π × 5)/180
Length of the arc = (300π)/180 = (5π)/3
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Polygon G H I J K has 5 sides.
Which statements are true about the regular polygon? Select three options.
The sum of the measures of the interior angles is 900°.
Each interior angle measures 108°.
All of the angles are congruent.
The polygon is a regular hexagon.
The sum of the measures of the interior angles is 180(5 – 2)°.
Answer:
Each interior angle measures 108°.All of the angles are congruent.The sum of the measures of the interior angles is 180(5 – 2)°.Step-by-step explanation:
(1) The sum of the interior angles of a polygon is [tex]180(n-2)[/tex] degrees, where n is the number of sides. In this case, n=5, so the sum is 180(5-2)=540 degrees, meaning the first statement is false.
(2) Since the angles add to 540 degrees, dividing this amongst the five equal angles, we get that each angle measures 108 degrees, so this statement is true.
(3) By definition, all angles of a regular polygon are congruent.
(4) A hexagon has 6 sides, but this polygon has only 5 sides, so this statement is false.
(5) This is true. (See statement (1)).
Answer:
Options B, C, E
Step-by-step explanation:
alex has a box of 250 nails. he uses 80 nails. then he loses 35 nails. how many nails does alex have left? what is the hidden question
im really not sure with my answer, please tell which is the correct choice.
Answer:
the orange one
Step-by-step explanation:
(10 + 10) : (5-3) =
20 : 2 =
10
What is the volume of the following solid figure?
Answer: 450
Step-by-step explanation:
The volume is (1/2)(5)(12)(15)=450.
A spinner is spun `40` times for a game.
This graph shows the fraction of games that are wins.
Based on the graph, what is the probability of a spin winning this game?
(i) In decimals: 0.65
(ii) In percentage: 65%
The graph shows that after the spinner is spun after 40 times. The Fraction of wins is 0.65 out of 1. Look at the very end of the graph to look at the conclusion for probability. Similar cases when, after the spinner is spun after 20 times, the probability is 0.65.
Answer:
0.65 or 65%
Step-by-step explanation:
Is this right if not please tell me explanation
Answer:
No, right answer is = 1017.36
Answer:
1017.36
Step-by-step explanation:
All your work is correct, but the final answer is not. In the problem it says to use 3.14 as pi, but when you multiplied you did:
[tex]\pi * 6^{2}*9 = 1017.88[/tex]
instead of
[tex]3.14*6^{2}*9 = 1017.36[/tex]
like you had written above. So the final is actually supposed to be 1017.36
A number is divided in the ratio 5:9. If the first part is 35, find the number.
A number is divided in the ratio of 5:9. If the first part is 35, the number will be 7.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
A number is divided in the ratio of 5:9. If the first part is 35, then we need to find the number.
By unitary method
5x = 35
x = 7
Then the other number will be
9x = 9(7)
= 63
Thus, A number is divided in the ratio of 5:9. If the first part is 35, the number will be 7.
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