Math test english 10 potx

Use the distance formula or the Pythagorean theorem to find the distance.. Use the Pythagorean theorem to find the length of the hypotenuse... First, find the hypotenuse by using the Pyt

26 Choice f is correct Subtract the numbers in y from the corresponding numbers in x.

27 Choice b is correct log3x = 2 is equivalent to 32= x Therefore, x = 9.

28 Choice h is correct Factor the numerator Use the denominator as a clue Most likely, one of the

fac-tors in the numerator will be the same as the denominator Also, notice that the numerator is the dif-ference of two squares

(x − x3)−(x3+ 3)

The x − 3 in the numerator cancels with the x − 3 in the denominator leaving an answer of x + 3.

29 Choice b is correct Use the distance formula or the Pythagorean theorem to find the distance The

dis-tance formula is d = (x21)− x22+ (y  Substitute the x and y values for points A and C and − y1)2 solve

d = (−2 − −1)−1 − 32+ ()2

d = (−1) (−4)2+2

d = 1 + 16

d = 17

To use the Pythagorean theorem (which is what the distance formula is derived from), draw the

seg-ment on a coordinate plane and create a right triangle where A C is the hypotenuse.

The legs of the right triangle are 1 and 4 Use the Pythagorean theorem to find the length of the hypotenuse

a2+ b2= c2

12+ 42= c2

1 + 16 = c2

17 = c2

17 = c

(−1,3)

(−2,−1) 1

4

5 0

6 6

3 − ( − 2) 4 − 4

5 − ( − 1) 6 − 0

30 Choice f is correct Since the line is parallel to 3y − 9x = 24, they have the same slope Put the equation

into y = mx + b form to easily see the slope:

3y − 9x = 24

3y = 9x + 24

y = 3x + 8

The equation above indicates that the slope is 3 The line you are looking for also has a slope of 3

You are looking for the line y = 3x + 4 You must put the answer choices in y = mx + b form to

com-pare them to this equation Equation f is correct.

f y = 3x + 4

g y = 3x + 5

h y = 2x + 4

i y = 2x + 1

j y = −13x −194

31 Choice d is correct You are looking for an x and a y value The x value must be 9 since one of the

equations is x = 9 To find y, substitute 9 for x in the second equation.

3(9) + y = 4

27 + y = 4

y = −23

The ordered pair is (9, −23) This point is a solution to both equations

32 Choice i is correct.37 is close to 36, which is 6 125 is close to 121, which is 11; (6)(11) = 66

33 Choice d is correct The equation is quadratic, so it can be solved by either setting the equation equal

to zero and factoring or using the quadratic formula In this case, factoring is the easiest option First, set the equation equal to zero:

x2− 6x − 27 = 0

(x − 9)(x + 3) = 0

x − 9 = 0 x + 3 = 0

x = 9 x = −3

The solution set is {−3, 9}

34 g Find the probability of each event and multiply the answers to find the probability of both events

occurring The probability of getting tails is 1and the probability of rolling a 3 is 1; (1)(1) = 1

37 Choice e is correct Think about what you would do if he used 2 bags for each pizza.

12 ÷ 2 = 6 pizzas Follow the same pattern and divide the 12 bags by 34

12 ÷34=

112×43= 438= 16

Mike can make 16 pizzas

38 Choice g is correct Convert the given rate of meters per second to kilometers per hour.

190.709ms ×1100k0mm ×16m0sin×601mhin= 3609,.070900hkm = 36.8hkm

Round the answer to 37 km/h

39 Choice c is correct Originally, Larry had 20 socks in the drawer Since he pulled a red one out already,

there are only 19 left in the drawer and 5 of them are red

P(red) = # to r te a d l = 159

40 Choice i is correct Multiply the 5 and 6 to get 30 Then, multiply the powers of 10 10−4× 108= 104 Since the bases are the same, you can just add the exponents So far you have 30 × 104, but this is not

an answer choice Change your answer to scientific notation by moving the decimal in 30 to 3.0 Since the decimal has been moved one place to the left, you must increase the power of 10 by one Therefore, the answer is 3 × 105

41 b sin = hy o p p o p t o es n it u e se First, find the hypotenuse by using the Pythagorean theorem, or noticing that it is a

3-4-5 triangle (multiplied by 2) Therefore, the missing side is 5 × 2= 10 sin B = 160= 35

42 Choice h is correct Use the formula tan = a o d p j p a oc s e i n te t tan x = 43

43 Choice d is correct There are 3 pairs of sides The two sides that measure 6 × 8 each have an area of 48.

The two sides that measure 6 × 10 each have an area of 60 The two sides that measure 8 × 10 each have an area of 80 Since there are two of each side, multiply the area of each by 2, then add the areas

48 × 2 = 96

60 × 2 = 120 96 + 120 + 160 = 376

80 × 2 = 160

44 Choice j is correct The radius of the large circle is 7 (add the inner radius plus the extra 3 from the

ring) Therefore, the area of the large circle is 49π Subtract the area of the inner circle, which is 16π 49π − 16π = 33π

45 Choice a is correct Take the square root of the area to find the length of one side.100 = 10, so the length of the sides of the square is 10 centimeters When the diagonal is drawn it creates a right trian-gle with legs of 10 cm each and the diagonal is the hypotenuse

Use the Pythagorean theorem to find the diagonal

102+ 102= x2

100 + 100 = x2

200 = x2

200 = x

102 = x

46 Choice i is correct Use the Pythagorean theorem to find the hypotenuse.

a2+ b2= c2

42+ 92= c2

16 + 81 = c2

97 = c2

97 = c

47 Choice c is correct The formula for area of a circle is A = πr2 Change the radius to an improper frac-tion; 312= 72 Use the formula to find the area using the improper fraction A = π(72)2= 449π The area is

449π square inches

48 Choice f is correct Substitute 15 for y in the equation and solve for x.

y = 4x2− 1

15 = 4x2− 1

16 = 4x2

4 = x2

2 = x

10 cm

10 cm

50 Choice f is correct Use the identity tanθ = csionsθθ.

56=

Multiply both sides by 167to isolate the sinθ

167×56= sinθ

157= sinθ

51 Choice d is correct The original formula was V = lwh If each dimension is tripled, the length is 3l, the

width is 3w, and the height is 3h When these values are substituted into the equation, the equation becomes V = (3l)(3w)(3h) or V = 27lwh Thus, the new rectangular solid has a volume 27 times the

original volume

52 Choice j is correct The sum of the measures of the angles in a triangle is 180° In a right triangle, the

right angle is 90°, so another 90° is split between the remaining two angles

7x + 8x = 90

15x = 90

x = 6

The value of x is 6, but the question asks for the measure of the smaller angle, which is 7x Substituting

in 6 for x, yields (7)(6) = 42 The measure of the angle is 42°.

53 Choice c is correct Use the Pythagorean theorem to find the missing leg.

a2+ b2= c2

92+ x2= 102

81 + x2= 100

x2= 19

x = 19

The length of the missing side is 19

54 Choice j is correct Call the width w and the length 2w The perimeter is then

P = w + w + 2w + 2w

72 = 6w

12 = w

The width is 12 Since the length is twice the width, the length is 24

sinθ



55 Choice e is correct Three of the answer choices can be immediately eliminated because the length of the height cannot be negative Answer choices b, c, and d all have negative lengths.

Call the height h and the base h + 5 The area of a triangle is b2h Substitute in h and h + 5 for the base

and height, and set the area equal to 80 since the are of the given triangle is 80;h(h2+ 5)= 80

Solve for h The equation is quadratic, so the quadratic formula will be used;h2+25h = 80

h2+ 5h = 160

h2+ 5h − 160 = h

Use the quadratic formula to solve

The negative value is eliminated from the answer because it does not make sense The answer is

56 Choice i is correct The easiest way to find the length of one side is to draw the square on the

coordi-nate plane and count the spaces There are 7 spaces between (−2, 3) and (5, 3) Therefore, the length of

a side is 7

The distance formula can also be used First, you must decide which points are consecutive vertices of the square Let’s use (−2, 3) and (5, 3) The distance formula is then:

d = (5 − (−2))(3 − 3)2+2

d = 72+ 0

d = 49

7

−5 + 665 

−5 ± 665 

−5 ± 25 + 6 40 

−5 ± (5) 4(1)(− 2 − 160)