微積分
極限、導數、最優化與函數性質。
-
a mound of sand at a rock-crushing plant is growing over time. the equa…
D. 14 hours
-
values from the function $g(x)=2\\sqrt3{x+3}-1$ are shown in the table.…
$x=-3$
-
the graph of $y = f(x)$ and $y = 4$ is shown. what is the value of $x$ …
$x=3$
-
solve: $2\\sqrt3{3x - 1} - 6 = -2$ $x = \\square$
$x = 3$
-
22. using the graph below, write the equation of the line in slope-inte…
$y=4x+2$
-
what is a commodity? a. something that producers are unable to sell to …
D. Something of value that can be bought, sold, or traded.
-
in capitalism, what does competition do for consumers? a. it limits the…
D. It keeps prices fair for consumers.
-
e $(-8 cdot -3) - 5$
19
-
test prep evaluate the expression. $13 - 2 \\times 5 + 7^2$ show hints …
52 (corresponding to the last option: 52)
-
$40 - 4^{2} \\times 2 + 1 = \\square$ options: 7, 8, 9, 4, 5, 6
9
-
evaluate the expression. enter the correct answer in the box. show hint…
277
-
evaluate the expression. enter the correct answer in the box. show hint…
277
-
evaluate the expression. enter the correct answer in the box. show hint…
18
-
find the missing number to make the equation true. $7 + 8 + \\underline…
10
-
13. graph: $y = -x$
A straight line passing through the origin $(0,0)$, $(2,-2)$, and $(-2,2)$, sloping downward from left to right across the coordinate grid.
-
use the graph of the function f to decide whether each quantity exists.…
(a) $4$ (b) $6$ (c) $\text{DNE}$ (d) $4$
-
consider the following function. $f(x)=\\frac{1}{x-8}$ determine whethe…
(a) $-\infty$ (b) $+\infty$ (or $\infty$)
-
consider the following function. $f(x) = 6x - 9$ find the limit. $lim_{…
6
-
find and write the missing number to make the equations true. 6. $4 + 8…
6. $7$ 7. $7$ 8. $3$ 9. $20$ 10. $16$
-
a function $f$ is continuous on the closed interval $-2, 5$, differenti…
D. None of the above
-
set f write the missing number to make equation true. $14 + 6 = \\_\\_\…
8
-
title dear reader, where do you want to go in life? how do you plan to …
1. the lessons about resisting corrupting power from Frodo's journey in Middle-earth 2. *The Burden of Power: Lessons from Mordor* 3. share cautionary lessons about corrupting pow…
-
understanding exponential decay functions which statements are true abo…
The function has a constant multiplicative rate of change The base must be less than 1 and greater than 0. The domain is all real numbers.
-
graph this function. $y = 5(2)^x$ plot two points to graph the function.
Plot the points $(0, 5)$ and $(1, 10)$ on the coordinate grid, then draw a smooth exponential curve passing through these points (and extending upwards as $x$ increases, approachi…
-
subtract. write your answer as a mixed number in simplest form $2\\frac…
$1\frac{1}{9}$
-
graph this function. $y = 5(2)^x$ plot two points to graph the function.
Plot the points $(0, 5)$ and $(1, 10)$ on the coordinate grid, then draw a smooth exponential curve passing through these points (and extending upwards as $x$ increases, approachi…
-
find the missing number in the equation collects on sunday. $12 + 29 + …
1. Missing number for $12 + 29 + 37 + \_\_ = 90$: 12 2. Missing number for $18 - 10 = 9 - \_\_$: 1 3. Missing number for $35 + 30 = 45 + \_\_$: 20
-
analyze the end behavior of the polynomial function. $f(x) = -x^3 + 8x^…
$\boldsymbol{x \to \infty,\ f(x) \to -\infty}$ $\boldsymbol{x \to -\infty,\ f(x) \to \infty}$
-
a pizza box with a lid is made from a 19-inch-by-40-inch piece of cardb…
2.88
-
analyze the graph and select all properties that apply to the polynomia…
Maximum: (-6.29,11.10) and (-1.98,30.01) Positive: (-7,-5) and (-4,-1)
-
what is the next number in this sequence: 2, 6, 10, 14? select one: a. …
1. b. 18 2. d. 10
-
write your answer as an integer or as a positive or negative mixed numb…
### First Section (Integer/Mixed Number): 1. $-18 \div -7 = 2\frac{4}{7}$ 2. $28 \div -4 = -7$ 3. $30 \div 9 = 3\frac{1}{3}$ 4. $-7 \div -6 = 1\frac{1}{6}$ 5. $-80 \div -10 = 8$ 6…
-
2. calculate. (1) $\frac{1}{3}+\frac{1}{6}+\frac{1}{8}$ $=$ (2) $\frac{…
(1) $\frac{5}{8}$ (2) $\frac{3}{5}$ (3) $\frac{23}{42}$ (4) $\frac{13}{24}$ (5) $\frac{25}{48}$ (6) $\frac{1}{2}$
-
the distance between $-1$ and $7$ on a number line equals $|-1 - 7|$ un…
D. 8 units
-
8. graph the function $f(x) = 3 + \\sqrt{x}$.
The graph is a vertical shift up 3 units of the square root parent function, passing through points $(0, 3)$, $(1, 4)$, $(4, 5)$, $(9, 6)$, with a domain of $x \geq 0$ and range o…
-
federalists & anti-federalists name: who would say that? read each stat…
1. F 2. A 3. A 4. A 5. F 6. F 7. A 8. F 9. A 10. A 11. F 12. F 13. A 14. F For "Sound Off": One could disagree with Hamilton: The Constitution's creation by the people does not in…
-
part 2 of 2 think about the process what should you do first to $y=\\fr…
A. Plot a point at the y-intercept. To graph the line fully: 1. The y-intercept is $b=-1$, so plot the point $(0, -1)$. 2. The slope $m=\frac{1}{5}$, meaning from the y-intercept,…
-
use the functions to answer parts a and b.$f(x)=0.75x$$g(x)=0.09375x^{2…
### Part a: $h(6)=3.815$, $h(8)=5.960$, and $h(12)=14.552$ ### Part b: Function h exceeds both function f and function g when $x=13$ (the smallest integer value; for real numbers,…
-
question 21 (1 point)amendment 21: repeals amendment _____.○17○18questi…
1. Question 21: 18 2. Question 22: number 3. Question 23: presidential
-
use the functions to answer parts a and b.$f(x)=0.75x$$g(x)=0.09375x^{2…
### Part a: $h(6)=3.815$, $h(8)=5.960$, and $h(12)=14.552$ ### Part b: Function h exceeds both function f and function g when $x=13$ (the smallest integer value; for real numbers,…
-
explain the difference between the establishment clause and the free ex…
### First Question Answer: - The Establishment Clause forbids government from establishing or endorsing a national religion and limits state-religion entanglement. - The Free Exer…
-
nameperioddatetopic 06 – class 04 – exponential growth and decayself-as…
a. $y = 500000(1.15)^t$ b. About 1,156,530 members The function $y=ab^x$ represents exponential growth when $a>0$ and $b>1$.
-
answer attempt 1 out of 5 the graph above is a . its domain can best be…
half-line (ray) real numbers addition or subtraction (a constant amount) a linear function with a negative slope
-
question evaluate. express your answer in scientific notation. $2.7 \\t…
$6.97 \times 10^{-1}$
-
**#5.) express in simplest radical form: $sqrt{8} \times sqrt{6}$ #6.) …
#5: $4\sqrt{3}$ #6: A) $\frac{4\sqrt{5}}{5}$ #7: b. $(0, 3)$ #8: $5\sqrt{30} - 1$
-
graph the inverse of the provided graph on the accompanying set of axes…
Plot the points $(3, -10)$, $(2, -5)$, $(1, 0)$, $(0, 5)$, $(-1, 10)$ on the axes, then draw a straight line through them to get the inverse graph.
-
determine the domain on which the following function is decreasing.
The function is decreasing on the interval $(5, 14)$ or $5 < x < 14$
-
select the correct answer. what is the range of this function? a. $4 \\…
D. $-\infty < y \leq 4$
-
a function $f$ is continuous on the closed interval $-2, 5$, differenti…
D. None of the above
-
set f write the missing number to make equation true. $14 + 6 = \\_\\_\…
8
-
title dear reader, where do you want to go in life? how do you plan to …
1. the lessons about resisting corrupting power from Frodo's journey in Middle-earth 2. *The Burden of Power: Lessons from Mordor* 3. share cautionary lessons about corrupting pow…
-
understanding exponential decay functions which statements are true abo…
The function has a constant multiplicative rate of change The base must be less than 1 and greater than 0. The domain is all real numbers.
-
graph this function. $y = 8(0.5)^x$ plot two points to graph the functi…
Plot the points $(0, 8)$ and $(1, 4)$ (or other valid pairs like $(2, 2)$) on the grid, then draw a smooth decreasing curve through them that approaches the x-axis as $x$ increase…
-
find the missing number in the equation collects on sunday. $12 + 29 + …
1. Missing number for $12 + 29 + 37 + \_\_ = 90$: 12 2. Missing number for $18 - 10 = 9 - \_\_$: 1 3. Missing number for $35 + 30 = 45 + \_\_$: 20
-
analyze the end behavior of the polynomial function. $f(x) = -x^3 + 8x^…
$\boldsymbol{x \to \infty,\ f(x) \to -\infty}$ $\boldsymbol{x \to -\infty,\ f(x) \to \infty}$
-
a pizza box with a lid is made from a 19-inch-by-40-inch piece of cardb…
2.88
-
analyze the graph and select all properties that apply to the polynomia…
Maximum: (-6.29,11.10) and (-1.98,30.01) Positive: (-7,-5) and (-4,-1)
-
what is the next number in this sequence: 2, 6, 10, 14? select one: a. …
1. b. 18 2. d. 10
-
write your answer as an integer or as a positive or negative mixed numb…
### First Section (Integer/Mixed Number): 1. $-18 \div -7 = 2\frac{4}{7}$ 2. $28 \div -4 = -7$ 3. $30 \div 9 = 3\frac{1}{3}$ 4. $-7 \div -6 = 1\frac{1}{6}$ 5. $-80 \div -10 = 8$ 6…
-
2. calculate. (1) $\frac{1}{3}+\frac{1}{6}+\frac{1}{8}$ $=$ (2) $\frac{…
(1) $\frac{5}{8}$ (2) $\frac{3}{5}$ (3) $\frac{23}{42}$ (4) $\frac{13}{24}$ (5) $\frac{25}{48}$ (6) $\frac{1}{2}$
-
the distance between $-1$ and $7$ on a number line equals $|-1 - 7|$ un…
D. 8 units
-
hobbes and the need for government power the only way to erect such a c…
be completely powerful.
-
federalists & anti-federalists name: who would say that? read each stat…
1. F 2. A 3. A 4. A 5. F 6. F 7. A 8. F 9. A 10. A 11. F 12. F 13. A 14. F For "Sound Off": One could disagree with Hamilton: The Constitution's creation by the people does not in…
-
part 2 of 2 think about the process what should you do first to $y=\\fr…
A. Plot a point at the y-intercept. To graph the line fully: 1. The y-intercept is $b=-1$, so plot the point $(0, -1)$. 2. The slope $m=\frac{1}{5}$, meaning from the y-intercept,…
-
question 21 (1 point)amendment 21: repeals amendment _____.○17○18questi…
1. Question 21: 18 2. Question 22: number 3. Question 23: presidential
-
use the functions to answer parts a and b. $f(x)=0.75x$ $g(x)=0.09375x^…
## Part a: $f(6)=4.5$, $f(8)=6$, $f(12)=9$ $g(6)=3.375$, $g(8)=6$, $g(12)=13.5$ $h(6)\approx3.815$, $h(8)\approx5.961$, $h(12)\approx14.552$ ## Part b: When $x=11$ (the smallest i…
-
explain the difference between the establishment clause and the free ex…
### First Question Answer: - The Establishment Clause forbids government from establishing or endorsing a national religion and limits state-religion entanglement. - The Free Exer…
-
nameperioddatetopic 06 – class 04 – exponential growth and decayself-as…
a. $y = 500000(1.15)^t$ b. About 1,156,530 members The function $y=ab^x$ represents exponential growth when $a>0$ and $b>1$.
-
answer attempt 1 out of 5 the graph above is a . its domain can best be…
half-line (ray) real numbers addition or subtraction (a constant amount) a linear function with a negative slope
-
question evaluate. express your answer in scientific notation. $2.7 \\t…
$6.97 \times 10^{-1}$
-
**#5.) express in simplest radical form: $sqrt{8} \times sqrt{6}$ #6.) …
#5: $4\sqrt{3}$ #6: A) $\frac{4\sqrt{5}}{5}$ #7: b. $(0, 3)$ #8: $5\sqrt{30} - 1$
-
find and write the missing numbers to make the equations true. 11. $13 …
11. 15 12. 3 13. 12 14. 40 15. 63; Number story: Lila has 28 stickers, and her friend gives her 35 more. How many stickers does Lila have in total? The matching equation is $28 + …
-
in this section, youll solve word problems by applying regrouping to ad…
B. Mya regrouped 1 instead of 10 into the tens place and regrouped 10 instead of 100 into the hundreds place.
-
8. a polynomial function has single roots at $x=-4$ and $x=6$, and a tr…
$P(x) = \frac{2}{3}(x+4)(x-6)(x-1)^3$ (Expanded form optional: $P(x)=\frac{2}{3}x^5 - \frac{8}{3}x^4 - \frac{34}{3}x^3 + \frac{116}{3}x^2 - 20x - 48$)
-
which sentence contains a verb used in the imperative mood?○ linda aske…
D. Think about the consequences of choosing that research topic.
-
question 14 (3 points) what did the espionage and sedition acts limit d…
d. Freedom of Speech
-
graph the function $f(x) = -3\\log_{2}(-x - 4) - 8$ on the axes below. …
Asymptote: Vertical, $x=-4$ Points to plot: $(-5, -8)$ and $(-6, -11)$
-
question solve for the exact value of $x$. $4\\ln(4x - 3) + 8 = 16$ ans…
$x = \frac{e^2 + 3}{4}$
-
simplifying radicals review name: aliyah washington simplify each radic…
1. $7$ 2. $8\sqrt{3}$ 3. $72$ 4. $35\sqrt{7}$
-
question 4. determine the simplified expression equivalent to $5\\sqrt{…
The simplified expression is $60\sqrt{2}$, so the top box is filled with 60 and the bottom box under the radical is filled with 2.
-
the function $f(x)$ is defined below. what is the end behavior of $f(x)…
as $x \to -\infty, y \to -\infty$ and as $x \to \infty, y \to \infty$
-
$\\ln(z) = 8.812$ $z = $
$z \approx 6703.93$ (or exactly $e^{8.812}$)
-
$7.1663 = 5\\ln(y)$ $1.4333 = \\ln(y)$ $y = \\square$
$y \approx 4.19$
-
name: _______________ properties of logarithms: matching directions: ma…
1. E. $4\log x - \log y$ 2. B. $\log5 + \log x + \log y$ 3. Q. $\log3 + 3\log2$ 4. O. $\log6 + \log11$ 5. F. $4\log2 - \log5$ 6. G. $\log x + \log y + 2\log z$ 7. A. $5(\log6 - \l…
-
$e^{w} = 960,464.9826$ $w = $
$13.775$ (rounded to three decimal places; exact calculated value is approximately $13.77500001$)
-
select the correct answers from each dropdown.consider this polynomial,…
Braulio $\boldsymbol{did\ not}$ found the value of $a$ because he $\boldsymbol{used\ the\ wrong\ root\ (1\ instead\ of\ -1)}$ Zahra $\boldsymbol{did}$ found the value of $a$ becau…
-
$\\ln(w)=8.2219$ $w=$
$3740.0$ (or approximately $3740$; more precisely, $e^{8.2219}\approx3740$)
-
question video examples the graph of $y = f(x)$ is shown below. accordi…
-7
-
values that make an inequality true (mquestionvideo exampleswhich inequ…
B. $-m + 3.5 \leq 8$
-
select the correct answer.this table represents values of a cubic polyn…
B. The function is increasing on the interval [-2, 1].
-
topic: graphing systems of linear equations progress match each system …
- $y=2x+3$ and $x+y=-3$ → consistent - $3y=9x-6$ and $3y-6x=4$ → consistent - $y=-\frac{1}{2}x+2$ and $x+2y=4$ → dependent (Note: The "inconsistent" and "independent" labels have …
-
select the correct answer. which equation could possibly represent the …
A. $f(x) = (x - 4)(x + 2)(x + 4)$
-
select the correct ordered pairs in the table consider the function bel…
$(-4, -12)$, $(1, -2)$, $(2, -18)$
-
consider function f:$f(x) = x^3 + 2x^2 - 5x - 6$select the locations of…
1. Zeros locations: $(-3, 0)$, $(-1, 0)$, $(2, 0)$ 2. End behavior: - As $x$ approaches positive infinity, $f(x)$ approaches positive infinity - As $x$ approaches negative infinit…
-
evaluate $f(2)$ from the graph.
1
-
does the function $f(x)=0.7e^{0.64x}$ represent continuous growth, cont…
The function represents continuous growth because $r > 0$.
-
an oil tank is being drained for cleaning. after $t$ minutes there are …
a. $V(25)$ represents the volume of oil left in the tank after 25 minutes, which is 0 litres (the tank is fully drained). b. $\frac{3500-21875}{15}=-1225$ litres per minute c. $-7…
-
question 4 of 5 select all the correct locations on the graph. consider…
The common zeros are $x=-3$, $x=-1$, and $x=1$ (the points $(-3,0)$, $(-1,0)$, and $(1,0)$ on the graph of $g$)
-
select the correct answer. what is the set of x-intercepts of this grap…
(-3, 0), (-1, 0), (3, 0)
-
which statement is true about the point (2,0)○ it is a relative minimum…
It is a relative minimum and an x-intercept.