Find all interior angles of a triangle, using the given the ratios among them. Angles' ratio: 3:4:5

A horizontal force of 100 N is to be applied to a 10 kg slab that is initially stationary on a frictionless floor, to accelerate the slab. A $10 \mathrm{~kg}$ block lies on top of the slab; the coefficient of friction $\mu$ between the block and the slab is not known, and the block might slip. Considering that possibility, what is the possible range of values for the magnitude of the slab's acceleration $a_{\text {slab }}$ ? (Hint: You don't need written calculations; just consider extreme values for $\mu$.)

Consider a U-­tube whose arms are open to the atmo­sphere. Now equal volumes of water and light oil $(\rho=49.3 lbm/ft^3)$ are poured from different arms. A person blows from the oil side of the U-­tube until the contact surface of the two fluids moves to the bottom of the U-­tube, and thus the liquid levels in the two arms are the same. If the fluid height in each arm is 30 in, determine the gage pressure the person exerts on the oil by blowing.

What will the multiplier be when the MPS is $0$, $0.4$, $0.6$, and $1$? What will it be when the MPC is $1$, $0.90$, $0.67$, $0.50$, and $0$? How much of a change in GDP will result if firms increase their level of investment by $8 billion and the MPC is$0.80$? If the MPC instead is$0.67$?

Segment AD is the perimeter of an isosceles trapezoid. Follow the steps to construct the isosceles trapezoid.

Place the compass point on B and mark off the distance of one leg $(\overline{C E})$ on the left most perpendicular, naming the new point I. This forms one leg of the isosceles trapezoid.

In this exercise, solve the given inequality and graph the solution set on a number line. Express the solution set in interval notation.

$$-6 \leq \frac{x}{2}-4<-3$$

Solve and write interval notation for the solution set. Then graph the solution set. $\\$$|7-x| \geq-4$

On January 1 Carol Farmer and Jim Romans formed a partnership, Research Consultants. Each partner invested $50,000 in cash on that date. The partnership agreement stated that the partners would share net income or loss equally. During the year Farmer invested an additional$2,000 and withdrew $7,500 for personal use. Romans invested an additional$1,500 and withdrew $8,500. Net income for the first year was$33,176. In your working papers, prepare a statement of changes in partners’ equity for the year ended December 31.

Calculate each rational inequality and graph the solution set on a real number line. Express each solution set in interval notation.

$$\frac{x}{x+2} \geq 2$$

A right triangle's legs are 7 in and 24 in long. What is the measure of the angle opposite the 24-in. leg?

a. How can you use your graph to show that the circumference and diameter are related proportionally? (Remember that these are measurements and will thus have some degree of error.) b. Approximately what is the multiplier between the diameter and the circumference?

You have a manometer consisting of a tube that is $1.1-\mathrm{cm}$ ID. On one side the manometer leg contains mercury, $10\ \mathrm{cc}$ of an oil $(\text{SG} = 1.67)$, and $3\ \mathrm{cc}$ of air as a bubble in the oil. The other leg just contains mercury. Both legs are open to the atmosphere and are in a static condition. An accident occurs in which $3\ \mathrm{cc}$ of the oil and the air bubble are removed from the one leg. How much do the mercury height levels change?

By using cross products, tell whether the ratios can form a proportion. $\frac{4}{3}, \frac{12}{9}$

Elaine is creating a garden in the shape of a right triangle. The length of one leg can be represented by the expression $x^{2}-16$. Elaine decided that the length of the hypotenuse side of her garden should be the same as the given leg increased by 32. What is the length of the third side of Elaine's garden?