Mathematics Questions and Answers

What is sin60∘?

"What is 10,080 minutes in days? (Remember, there are 60 minutes in an hour and 24 hours in a day.) A. 14 days B. 420 days C. 168 days D. 7 days"

"How would one convert 6 lb to ounces (16 oz = 1 lb)? A. 6 lb B. 16 oz C. 6 lb × 16 oz D. 6 lb × (16oz/11b)"

What is your batting average if you get 14 hits in 50 at-bats?

Factor the polynomial expression x2 +5.

If you are asked to calculate a percentage, such as 75% of 45, what would you do?

What does "to the third power" mean?

"What is 37 divided by 19 in simplest form? A. 2 B. 2.05263157895 C. 1.94736842105 D. 1.95"

"When adding or subtracting fractions with different denominators, each fraction's denominator must be converted to an equal value. Which of the following terms describes that equal value? A. Multiple B. Reciprocal C. Greatest Common Factor D. Lowest Common Denominator"

"4 feet (ft.) and 11 inches (in.) equals: a) 4.11 ft. b) 4 ft. 11 in. c) 5 ft. d) 3.7 ft."

"Write 10,000×10 in exponent form. A. 10^2 B. 10^3 C. 10^4 D. 10^5"

Given that a vector is the directed line segment from P(0,0) to Q(3,2), what is the magnitude of that vector?

What is 4x2 −x2?

"Part A A car weighs about 4,000 pounds. How can you convert 4,000 pounds to tons? Enter ""Divide,"" ""Multiply,"" or a number in each box. Words can be used once or not at all. 4,000by?to convert to tons. Part B Which comparison is true? A. 4,000 pounds < 2 tons B. 4,000 pounds > 2 tons C. 4,000 pounds < 1 ton D. 4,000 pounds = 2 tons"

"Convert 13/15 to a decimal and a percent. a) 0.8667, 86.67% b) 0.8667, 8.67% c) 1.15, 115% d) 1.15, 11.5%"

Becca received 138 points out of the 150 possible points on her math test. What percent did she get correct?

"What could 180÷15 mean in this situation? Describe two different possible meanings of this expression. Find the quotient. Explain what it means in each case."

# Solving for Angle Measures What is the value of $\frac{1}{2}(4 k+5)^{\circ}$

What is the factored form of x^2−x−2?

My fraction is equivalent to 8/6 and has a numerator that is 4 more than its denominator. What is the fraction?

"Write 3.8 as a mixed number and as an improper fraction. Provide your answers in simplest form."

How could you find all the factor pairs of 30 using a set of 30 pennies?

"True or False? Every square is a rectangle. Every rhombus is a quadrilateral. Every rhombus with four right angles is a square. Every quadrilateral is a rectangle."

Convert the temperature 25 degrees Fahrenheit to degrees Celsius. Use the formula C= 5/9 (F−32) where "F" represents degrees Fahrenheit and "C" represents degrees Celsius. Round to the nearest tenth.

What is the answer to ∛216?

Determine the value of tan(π/2) with solutions.

What is 36 cm in inches?

What is the conversion of 195 lbs to kg?

What is the conversion of 46 kg to lbs?

How do you write 90% as a decimal?

What is 49 kg in stone and pounds?

# PAIR OF LINEAR EQUATIONS IN TWO VARIABLES ## WISE UP Simultaneous Linear Equations in Two variables : A pair of linear equations in two variables is to form a system of simultaneous linear equations. Examples: i) $2 x-3 y=1$ ii) $x+y=5$ $$ x+\frac{1}{2} y=3 \quad x-y=1 $$ Note : The general form of a pair of linear equations in two variables $x$ and $y$ is $$ \begin{aligned} & a_{1} x+b_{1} y+c_{1}=0 \text { and } \\ & a_{2} x+b_{2} y+c_{2}=0, \text { where } a_{1}, b_{1}, c_{1}, a_{2}, b_{2}, c_{2} \text { are real numbers and } a_{1}^{2}+b_{1}^{2} \neq 0 \text { and } a_{2}^{2}+b_{2}^{2} \neq 1 \end{aligned} $$ Solution : A pair of values of the variables $x$ and $y$ satisfying each one of the equations in a give system of two simultaneous linear equations in $x$ and $y$ is called a solution. Example: For the pair of linear equations $$ \begin{aligned} & 3 x-2 y=4 \text { and } 2 x+y=5 \\ & x=2, y=1 \text { is a solution. } \end{aligned} $$ ## GRAPH OF SIMULTANEOUS LINEAR EQUATIONS We have studied in our previous class that the graph of a linear equation is a straight line. So, th graph of a system of simultaneous linear equations is a pair of straight lines. Thus, the graph of a system of simultaneous linear equations represents either a pair of intersecting lines or a pair of parallel lines or a pair of coincident lines ## Graphical method : Consistent system : A system of simultaneous linear equations is said to be consistent if it has atlea one solution. Note : i) If the system has only one solution then it is called independent. ii) If the system has infinitely many solutions then it is called dependent. - Inconsistent system : A system of simultaneous linear equations is said to be inconsistent if it has solution.

# X Class - CBSE Nature of system of linear equations : Let $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ is a system of | S.No. | Compare <br> ratios | Alachvale <br> Interpretation | Graphical <br> Representation | Nature of the <br> System | | :-- | :-- | :-- | :-- | :-- | | 1. | $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$ | Exactly one <br> solution (unique) | Intersecting lines | Consistent | | 2. | $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{2}}{c_{2}}$ | Infinitely many <br> solutions | Coincident lines | Consistent and dependent | | 3. | $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{2}}{c_{2}}$ | No solution | Parallel lines | Inconsistent | Note: The solution of a consistent system of linear equations is the coordinates of intersecting point of the two lines represented by them. ## EXERCISE 3.1 1. On comparing the ratios, $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$, find out whether the lines representing the given pairs of linear equations intersect a point, are parallel or coincident. Sol. i) $5 x-4 y+8=0$ $7 x+6 y-9=0$ Comparing the given equations with standard forms of equations $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ we have $$ a_{1}=5, b_{1}=-4, c_{1}=8 ; a_{2}=7, b_{2}=6, c_{2}=-9 $$ Now $\frac{a_{1}}{a_{2}}=\frac{5}{7}, \frac{b_{1}}{b_{2}}=\frac{-4}{6}$ $$ \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} $$ Thus the lines representing the pair of linear equation are intersecting. ii) $9 x+3 y+12=0,18 x+6 y+24=0$ We have $a_{1}=9, b_{1}=3, c_{1}=12 ; a_{2}=18, b_{2}=6, c_{2}=24$ Now $\frac{a_{1}}{a_{2}}=\frac{9}{18}=\frac{1}{2}, \frac{b_{1}}{b_{2}}=\frac{3}{6}=\frac{1}{2}$ and $\frac{c_{1}}{c_{2}}=\frac{12}{24}=\frac{1}{2}$

How many cups are 350 grams?

1 fluid ounce (fl oz) is equal to how many tablespoons (tbsp)?

A person is 5.5 feet tall. What is their height in inches?

What is 1000 hours in days?

Convert 0.625 to a fraction in simplest form.

# How much would $\$ 500$ invested at 5\% interest compounded continuously be worth after 8 years? Round your answer to the nearest cent. $$ A(t)=P e^{r t} $$ where: - $P=500$ - $r=0.05$ - $t=8$ Calculate $A(t)$.

What is the conversion of 57 kg to pounds?