Mathematics Questions and Answers

Give some examples of real-life objects that are solids of revolution.

Write an equation of the line (0,2) and (3,3) in slope intercept form

# Find the domain and range of the function graphed below. | Domain: | | | --- | --- | | Range: | |

Which equation is represented by the graph below? $$\begin{array}{l} y = \ln x \\ y = \ln x + 1 \\ y = e^x \\ y = e^x + 1 \end{array}$$

"Fill in the gaps to factorize this expression: 3x+15=3(_+_)"

The table represents the function $f(x)$. What is $f(3)$ ? | $x$ | $f(x)$ | | --- | --- | | -3 | -9 | | -2 | -6 | | -1 | -3 | | 0 | 0 | | 1 | 3 | | 2 | 6 | | 3 | 9 |

7 Which graph represents $y$ as a function of $x$ ?

True or false. To solve the equation 5x=20 you can use the multiplication property of Equality. Explain your reasoning.

Simplify √245

What is cos 60°?

3. Use Laplace transforms to solve the initial value problem $\bar{y}+4 \dot{y}+5 y=f(t), y(0)=0, \dot{y}(0)=0$ , where $f(t)=1-u(t-\pi)$. As the first step, graph the forcing function, $f(t)$. Once you have solved the equation, please write simplified expressions for $y$ when $0 \leq t<\Pi$ and when $t \geq \boldsymbol{\Pi}$ Also, please sketch the graph of the solution or attach a desmos-generated graph. For full credit, please show all steps of the process. Don't hesitate to add your personal commentary.

4. Diego said that the answer to the question "How many groups of $\frac{5}{6}$ are in 1?" is $\frac{5}{5}$ or $1 \frac{1}{5}$. Do you agree with his statement? Explain or show your reasoning.

Directions: Complete each proof. 1. Given: $m \angle 4+m \angle 7=180^{\circ}$ Prove: $c\|d$ | Statements | Reasons | | :-- | :-- | | | | | | | | | | | | | | | | 2. Given: $m \angle 3=m \angle 8$ Prove: $m \angle 3+m \angle 6=180^{\circ}$ | Statements | Reasons | | :-- | :-- | | | | | | | | | | 3. Given: $p \| q: \angle 1 \cong \angle 5$ Prove: $\angle 2 \cong \angle 5$ | Statements | Reasons | | :-- | :-- | | | | | | | | | | | | |

Factorize fully: 5x−15

How do you find the mean and median on a line plot?

"What is the product of (a − 5) and (a + 3)? A. A2 − 15 B. A2 + 2a − 15 C. A2 − 2a − 15 D. A − 5 − 2"

How do I find equation of the line of symmetry? 7 Refer to the following graph of $y=x^{2}-2$ to answer the following questions. (a) What is the value of $y$ when $x=3$ ? Answer: (a) (b) Write down the equation of the line of symmetry. Answer: (b) (c) What is the least value of $y$ ? Answer: (c) (d) Draw the line $y=7$. Answer: (d) On the graph

Which function has the greater maximum value, f(x) or g(x)? $$f(x) = -2x^2 + 8x - 1$$

"Using the Associative Property of Addition, complete the statement: 17+(6+2x)=(17+6)+2x"

Then determine which answer choice matches the graph you drew.

"Which pair of numbers is relatively prime? A. 7 and 21 B. 4 and 15 C. 6 and 9 D. 9 and 27"

13. Select all of the following graphs which are one-to-one functions.

Simplify √98

"Such a path that begins and ends at the same vertex and passes through all other vertices exactly once is called a _________________ circuit. a) Euler b) Hamiltonian c) Closed d) Bipartite"

Explain why 3x2 can be said to be in both standard form and factored form.

"Is 88 a perfect square? A. Yes, because there is a number, 44, that can be multiplied by 2 to give 88. B. No, because the proper factors of 88 are 2, 4, 8, 11, 22, and 44, and none of these factors gives 88 when multiplied by itself. C. Yes, because there is a whole number, 7,744, which is equal to 88 multiplied by itself. D. No, because perfect squares must be odd numbers."

An object is placed 19.0 cm to the left of a converging lens that has a focal length $$f_1 = +10.2$$ cm. How far is the image from the lens? (Give your answer to at least one decimal place.) A screen is placed 41.0 cm to the right of the converging lens. A diverging lens is placed between the converging lens and the screen. When the diverging lens is 11.8 cm to the right of the converging lens the image formed by the lens combination is located at the screen. What is the focal length $$f_2$$ of the diverging lens?

Which equation represents a linear function? $$ y=-3 x^{2}+2 \quad y=-4 x+5 \quad y=x^{3} \quad y=2 x^{2} $$

Find the areas of the trapezoids.

Dee Wallace's salary was $58,900 in 2003 and increased to $64,900 in 2008. What was the annual rate of change in his salary?

"Mark the statements that are true. A. An angle that measures 30° also measures π/3 radians. B. An angle that measures π/6 ​radians also measures 30°. C. An angle that measures π/3 ​radians also measures 60°. D. An angle that measures 180° also measures π/2 ​ radians."

Image not displaying? What does the function labeled "Continue from previous section" do ? Creates "Continuous Section Breaks" so page numbers will be the same across sections

The test statistic of $z=1.13$ is obtained when testing the claim that $p>0.2$. a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the P-value. c. Using a significance level of $\alpha=0.05$, should we reject $\mathrm{H}_{0}$ or should we fail to reject $\mathrm{H}_{0}$ ? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table! a. This is a $\square$ test. b. P-value $=\square$ (Round to three decimal places as needed.) c. Choose the correct conclusion below. A. Fail to reject $\mathrm{H}_{0}$. There is sufficient evidence to support the claim that $p>0.2$. B. Reject $\mathrm{H}_{0}$. There is not sufficient evidence to support the claim that $p>0.2$. C. Fail to reject $\mathrm{H}_{0}$. There is not sufficient evidence to support the claim that $p>0.2$. D. Reject $\mathrm{H}_{0}$. There is sufficient evidence to support the claim that $p>0.2$.

Suppose that $S=\left\{\mathbf{u}_{1}, \mathbf{u}_{2}, \mathbf{u}_{3}, \mathbf{u}_{4}\right\}$ where $$ \mathbf{u}_{1}=\left(\begin{array}{c} 227 \\ -245 \\ 12 \\ 111 \end{array}\right), \mathbf{u}_{2}=\left(\begin{array}{c} 248 \\ 146 \\ -46 \\ -123 \end{array}\right), \mathbf{u}_{3}=\left(\begin{array}{c} 193 \\ 276 \\ 4 \\ 183 \end{array}\right), \mathbf{u}_{4}=\left(\begin{array}{c} 42 \\ -71 \\ 35 \\ 172 \end{array}\right) \text { and } \mathbf{v}=\left(\begin{array}{c} -38505 \\ -9668 \\ 2067 \\ -8262 \end{array}\right) $$ To avoid typing errors, you can copy and past the following sequences to your Maple worksheet to form entries of the vectors or an augmented matrix. ``` 227, -245, 12, 111 248, 146, -46, -123 193, 276, 4, 183 42, -71, 35, 172 -38505, -9668, 2067, -8262 ``` The vector $\mathbf{v}$ is in the span of $S$ written in the form $$ \alpha \mathbf{u}_{1}+\beta \mathbf{u}_{2}+\gamma \mathbf{u}_{3}+\delta \mathbf{u}_{4} $$ Find a possible set of values for $\alpha, \beta, \gamma, \delta$. Enter the values of $\alpha, \beta, \gamma, \delta$ as a sequence in the box below $$ [\alpha, \beta, \gamma, \delta]= $$

# What is the area of the base of the rectangular prism

Find a linear differential operator that annihilates the given function (use D for the differential operator) e^-x + 7xe^x - x^2 e^x

The Alternating Series Test has three conditions, all of which must be met, in order to guarantee that a series is convergent. Those three conditions are: Condition (1): The series is an alternating series (it has the form $\sum_{n=1}^{\infty}(-1)^{n+1} b_{n}$ where $b_{n}>0$ ); Condition (2): The absolute value of each term is less than or equal to that of the preceding term (the statement $b_{n+1} \leq b_{n}$ is true for all $n$ ); and Condition (3): The terms shrink toward zero for large $n$, or $\lim _{n \rightarrow \infty} b_{n}=0$. Can the Alternating Series Test be applied to the series $\sum_{n=1}^{\infty}(-1)^{n+1} \frac{5 n}{4 n-2}$ to show that it converges? Answer this question by picking the most appropriate answer choice from the list below. (3) No. Condition (1) is not satisfied (expanding the general term does not yield an alternating series), so this test (by itself) is inconclusive and a different convergence test must be used. (4) Yes. All three conditions are met, so the given series converges and no additional testing is required. (5) No. Condition (2) is not satisfied (the absolute value of each term is not shrinking relative to its predecessor), so this test (by itself) is inconclusive and a different convergence test must be used. (6) No. Condition (3) is not satisfied (the terms do not shrink toward zero for large $\boldsymbol{\tau}$ ), so this test (by itself) is inconclusive and a different convergence test must be used.

The functions $f$ and $g$ are defined as follows. $$ f(x)=2 x^{3}+6 \quad g(x)=-3 x+2 $$ Find $f(-2)$ and $g(3)$. Simplify your answers as much as possible.

Isosceles triangles may be obtuse or acute but never right A. True B. False

**Triangle Inequality Theorem 1 (Ss → Aa)** – if one side of a triangle is longer than the second, then the angle opposite the longer side is larger than the angle opposite the second side. **Example:** Figure 1 shows a triangle with sides of different measures. List all angles of figure 1 in ascending order. *Figure 1* **Solution:** By the Triangle inequality theorem 1, **MN** is the longest side and **xP**, the angle opposite **MN** is the largest angle. Also, since **MP** is the shortest side then **xp**, the angle opposite **MP** is the smallest angle. Hence, **xNxMxP**. Exercises: Given the figures below, arrange the angles in ascending order. 1. 2. 3.