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3 years ago

In ΔHIJ, the measure of ∠J=90°, JI = 48, IH = 73, and HJ = 55. What is the value of the tangent of ∠H to the nearest hundredth

Mathematics

1 answer:

babunello [35]3 years ago

3 0

Answer:

The value of the tangent of ∠H to the nearest hundredth is 41.11⁰

Step-by-step explanation:

Given;

∠J=90°

JI = 48

IH = 73

HJ = 55

If we sketch this triangle, we will observe that ΔHIJ is a right angled triangle, with hypotenuse as "IH", opposite as "JI" and adjacent as "HJ".

To determine the value of the tangent of ∠H, we apply the following formula;

$Tan \ H = \frac{Opposite \ side}{Adjacent \ side} = \frac{JI}{HJ} \\\\Tan \ H =\frac{48}{55} \\\\Tan \ H = 0.8727\\\\H = Tan^{-1} (0.8727)\\\\H = 41.111^o\\\\H = 41.11^o (nearest \ hundredth)$

Therefore, the value of the tangent of ∠H to the nearest hundredth is 41.11⁰

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A college admissions office uses the following linear equation to predict the grade point average of an incoming student: x = 0.

kramer

A college admissions office uses the following equation to predict the grade point average of an incoming student:

z = 0.003x + 0.8y − 4,

where z is the predicted college GPA on a scale of 0 to 4.3, and x is the sum of the student’s SAT Math and SAT Verbal on a scale of 400 to 1600, and y is the student’s high school GPA on a scale of 0 to 4.3. The college admits students whose predicted GPA is at least 2.3.

Will a student with SATs of 1050 and high school GPA of 3.0 be admitted

Answer:

A. No because Z = 1.55 which is less than the required predicted college gpa of 2.3 for admission.

Step-by-step explanation:

Z = 0.003x + 0.8y - 4

X = sat score

Y = high school gpa

Z = predicted college gpa

X =1050

Y = 3.0

Z = .003 *(1050) + 0.8*(3.0) -4

Z = 1.55 which is less than the required predicted college gpa of 2.3 for admission

5 0

2 years ago

What is the multiplicative inverse of 5 in z11, z12, and z13? you can do a trial-and-error search using a calculator or a pc?

grin007 [14]

A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.

1. $Z_{11}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{4};$
$5\cdot 4=20=\overline{9};$
$5\cdot 5=25=\overline{3};$
$5\cdot 6=30=\overline{8};$
$5\cdot 7=35=\overline{2};$
$5\cdot 8=40=\overline{7};$
$5\cdot 9=45=\overline{1};$
$5\cdot 10=50=\overline{6}.$

The multiplicative inverse of 5 in $Z_{11}$ is 9.

2. $Z_{12}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{3};$
$5\cdot 4=20=\overline{8};$
$5\cdot 5=25=\overline{1};$
$5\cdot 6=30=\overline{6};$
$5\cdot 7=35=\overline{11};$
$5\cdot 8=40=\overline{4};$
$5\cdot 9=45=\overline{9};$
$5\cdot 10=50=\overline{2};$
$5\cdot 11=55=\overline{7}.$

The multiplicative inverse of 5 in $Z_{12}$ is 5.

3. $Z_{13}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11},\overline{12}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{2};$
$5\cdot 4=20=\overline{7};$
$5\cdot 5=25=\overline{12};$
$5\cdot 6=30=\overline{4};$
$5\cdot 7=35=\overline{9};$
$5\cdot 8=40=\overline{1};$
$5\cdot 9=45=\overline{6};$
$5\cdot 10=50=\overline{11};$
$5\cdot 11=55=\overline{3};$
$5\cdot 12=60=\overline{8}.$

The multiplicative inverse of 5 in $Z_{13}$ is 8.

8 0

2 years ago

The organizers of a fair projected a 25 percent increase in attendance this year over that of last year, but attendance this yea

ch4aika [34]

Answer:

The correct option is C

Step-by-step explanation:

The organizers of a fair projected a 25 percent increase in attendance this year over that of last year

Let x = the attendance for last year

The projected attendance for this year would be last year's attendance + 25% of last year's attendance. This means

Projected attendance for this year

= x + 25/100 × x

= x + 0.25x = 1.25x

But attendance for this year actually decreased by 20 percent.

This means the actual attendance for this year would be

attendance for last year - 20% of attendance for last year. This means

Actual attendance for this year is

x - 20/100 × x

= x - 0.2x = 0.8x

percentage of the projected attendance that was the actual attendance would be

0.8x / 1.25x × 100 = 0.64 × 100

= 64%

The correct option is C

7 0

2 years ago

Mr. Barrow scored his high school students' essays on a scale of 0 to 10. He recorded data about the scores in the table below.

Fynjy0 [20]

09 08 07 06 10 1

wrryetryytrwertry (It was too short)

7 0

2 years ago

Read 2 more answers

A 2-column table with 10 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1,

Murrr4er [49]

Answer- A,D,E

Step-by-step explanation:

A two column table with 5 rows. The first column, x, has the entries, negative 2, 0, 2, 4. The second column, y, has the entries, 6, 3.5, 1, negative 1.5.

Which equations represent the data in the table? Check all that apply.

y – 6 = y minus 6 equals StartFraction negative 5 Over 4 EndFraction left-parenthesis x plus 2 right-parenthesis.(x + 2)

y – 2 = –y minus 2 equals negative StartFraction 5 Over 4 EndFraction left-parenthesis x minus 1 right-parenthesis.(x – 1)

y + 2 = y plus 2 equals StartFraction negative 5 Over 4 EndFraction left-parenthesis x minus 6 right-parenthesis.(x – 6)

y – 1 = –y minus 1 equals negative StartFraction 5 Over 4 EndFraction left-parenthesis x minus 2 right-parenthesis.(x – 2)

y – 3.5 = –1.25x

Im just rephrasing the question

5 0

2 years ago

Read 2 more answers