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Questions in mathematics

[Jawaban] Find the exact value of [tex]$\cos (\alpha+\beta)$[/tex], given [tex]$\sin \alpha=\frac{2}{5}$[/tex] for [tex]$\alpha$[/tex] in Quadrant II and [tex]$\cos \beta=\frac{1}{3}$[/tex] for [tex]$\beta$[/tex] in Quadrant IV. A. [tex]$\frac{8 \sqrt{2}-\sqrt{15}}{15}$[/tex] B. [tex]$\frac{8 \sqrt{2}+\sqrt{15}}{15}$[/tex] C. [tex]$\frac{4 \sqrt{2}+\sqrt{21}}{15}$[/tex] D. [tex]$\frac{4 \sqrt{2}-\sqrt{21}}{15}$[/tex]

[Jawaban] Drag each tile to the correct box. Arrange the equations in order from least to greatest based on their solution. Equation A: [tex]$\quad 5(x-6)+3 x=\frac{3}{4}(2 x-8)$[/tex] Equation B: [tex]$\quad 2.7(5.1 x+4.9)=3.2 x+28.9$[/tex] Equation C: [tex]$\quad 5(11 x-18)=3(2 x+7)$[/tex] [tex]$\ \textless \ $[/tex] [tex]$\square$[/tex] [tex]$\ \textless \ $[/tex] [tex]$\square$[/tex]

[Jawaban] 1. How much is 7005 greater than 5849? 2. How much is 3768 less than 5012? 3. The sum of two numbers is 8324. If one of the numbers is 5896, what is the other number? 4. What number must be added to 5679 to get 9123? 5. What number must be subtracted from 6314 to get 4869? 6. The difference between two numbers is 2895. If the larger number is 8560, find the smaller one.

[Jawaban] Which transformation will result in an image that is congruent to its pre-image? A. $(x, y) \rightarrow(-x,-4 y)$ B. $(x, y) \rightarrow(4 x, y-4)$ C. $(x, y) \rightarrow(-4 x, y)$ D. $(x, y) \rightarrow(-x,-y)$

[Jawaban] A tangent to the parabola [tex]$y^2=4 a x$[/tex] makes an angle of [tex]$60^{\circ}$[/tex] with the [tex]$x$[/tex]-axis; find its point to contact.

[Jawaban] A company has determined that its weekly profit is a function of the number of items that it sells. Which could represent the weekly profit in thousands of dollars, [tex]$y$[/tex], when the company sells [tex]$x$[/tex] items? [tex]$y^2=4 x^2-100$[/tex] [tex]$y=-x^2+50 x-300$[/tex] [tex]$x=-y^2+60 y-400$[/tex] [tex]$x^2=-6 y^2+200$[/tex]

[Jawaban] \begin{aligned} 3 y+11 & =4 x \\ 10 x+2 y+1 & =0\end{aligned}

[Jawaban] Which equation represents a circle with the same radius as the circle shown but with a center at (-1, 1)? A. (x – 1)^2 + (y + 1)^2 = 16 B. (x – 1)^2 + (y + 1)^2 = 4 C. (x + 1)^2 + (y –1)^2 = 4 D. (x + 1)^2 + (y – 1)^2 = 16

[Jawaban] $2.35 \cdot \frac{2}{3} = \newline \frac{7}{30} \newline \frac{7}{15} \newline \frac{27}{30}

[Jawaban] A bank features a savings account that has an annual percentage rate of $5.7 \%$ with interest compounded annually. Makayla deposits $\$ 6,500$ into the account. How much money will Makayla have in the account in 1 year? Answer = $\$ \square$ . Round answer to the nearest penny. What is the annual percentage yield (APY) for the savings account? $APY=$ $\square$ \%. Round to the nearest hundredth of a percent.