Angle α is in quadrant III, and angle β is in quadrant II. If sin α = –4∕5 and sin β = 1∕2, find cos (α + β).

Answer: (6, -3)

(x^2-4x+4)/16-(y^2+6y+9)/25 = 1

x = 6

y = -3

6^2 = 36

4 * 6 = 24

36 - 24 = 12

12 + 4 = 16

16/16 = 1

-3^2 = 9

6 * -3 = -18

9 - 18 = -9

-9 + 9 = 0

0/25 = 0

1 - 0 = 1

I really hope this helped, at least a little bit.

The coordinates of the center of the hyperbola is  (6,-3).

Hyperbola is a type of "smooth curve, lying in the plane defined by its geometric properties or by the equation for which it is in solution set".

According to the question,

[tex]\frac{(x-2)^2}{4^2}[/tex]  -  [tex]\frac{(y+3)^2}{5^2}[/tex] = 1

Standard form of hyperbola = [tex]\frac{(x-k)^2}{a^2}[/tex]  -  [tex]\frac{(y-h)^2}{b^2}[/tex]  = 1.

The expression 'y' is positive leading coefficient so the hyperbola so the hyperbola is open upward and downward . Comparing with standard equation we get center of hyperbola (2,-3) and 'a' point the hyperbola is 4 and the 'b' point of hyperbola is 5 and mark point 5 unit right as well as left on x-axis and 4 unit up and down on y-axis.

From above discussion we get clearly the coordinate of hyperbola is

(6-3).

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Answer:

No.

Step-by-step explanation:

The point (7,1) contains a x-value of 7 and a y-value of 1.  7 does not equal 1.

Answer:

The equation is true.

Step-by-step explanation:

Answer:

The extended volume of hemisphere to nearest cubic centimeter is V = 134 cm^3

Step-by-step explanation:

- The shaved ice is modeled as a sphere.

- The half of the shaved ice sphere extends above the cup holder.

- The volume of sphere with radius r = diameter d / 2 :

- We are to calculate the volume of the extended part of the sphere with diameter d = 8 cm or radius r = 4 cm.

- The extended volume of hemisphere to nearest cubic centimeter is V = 134 cm^3

                                             Hopes This Helps

Answer:

y=46.445

x=24.04

Step-by-step explanation:

rule for first triangle which is  right isosceles triangle with angles 30-60-90

sin 30 = opp/hypt.

0.5= opp/34

opp=17 which is the height

the part of y in the first triangle = a^2+b^2=c^2

a^2= 17^2 , b^2=y , c^2 =34

y ( first triangle )= √867=29.445

second triangle is right angle triangle 45-90-45

x= 24.04

sin 45= opp/hypt.

1/√2 =17/x

x= 17*√2 = 24.04

solving for other part of y in the right triangle

h= y = 17

the whole base y= 29.445+17 = 46.445

Answer:

y= 3x +11

Step-by-step explanation:

slope-intercept form:

y= mx+c, where m is the gradient and c is the y-intercept.

Given that the slope is 3, m=3

substitute m=3 into the equation:

y= 3x +c

To find the value of c, substitute a coordinate.

When x= -3, y=2,

2= 3(-3) +c

c -9= 2

c= 9 +2 (+9 on both sides)

c= 11 (simplify)

Thus, the equation of the line is y= 3x +11.

Answer:

C. 6

Step-by-step explanation:

Answer:

A. 2

Step-by-step explanation:

slope formula is : [tex]\frac{y2-y1}{x2-x1}[/tex] or the difference in y-coordinates in 2 points divided by the difference in x-coordinates in 2 points.

in this question, they have given you both the difference in x and difference in y.

therefore this question is saying : [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{6}{3}[/tex]

[tex]\frac{6}{3}[/tex]= 2

therefore, the correct slope value is A. 2

Answer:

365cm^2

Step-by-step explanation:

Answer:

365cm ^2

I think

Answer:

50 feet

Step-by-step explanation:

[tex]\mid -20 \mid +\mid 30\mid = \\\\20+30= \\\\50[/tex]

Hope this helps!

Answer:

50

Because you just a

on the -20 is a abouloute number which its going to be a postive number so i add the 20 + 30

Answer:

Step-by-step explanation:

First you have to make it into a fraction, then multiply it by 100 :

Q1.

[tex]0.47 = \frac{47}{100} [/tex]

[tex] \frac{47}{100} \times 100 = 47[/tex]

Q2.

[tex]0.98 = \frac{98}{100} [/tex]

[tex] \frac{98}{100} \times 100 = 98[/tex]

Q3.

[tex]0.25 = \frac{25}{100} [/tex]

[tex] \frac{25}{100} \times 100 = 25[/tex]

Answer:

Step-by-step explanation:

Given the following :

- - - Jhs

Basic level - - - - Boys - - - - Girls - - - - Total

Primary - - - - - - - 49 - - - - - - 51 - - - - - - 100%

Jhs - - - - - - - - - - 56 - - - - - - 44. - - - - - - 100%

With the information above,

Primary Dropout percentage:

BOYS : [49 / (49 +51)] × 100.= 49%

GIRLS : [51 / (49 +51)] × 100.= 51%

Jhs: Dropout percentage

BOYS : [56 / ( 56 + 44) × 100 = 56%

GIRLS : [44 / (44 +56)] × 100.= 44%

Answer:

x>-8

Step-by-step explanation:

-122<-3(-2-8x)-8x

-122<6+24x-8x

-128<16x

x>-8

Answer:

$7.00

Step-by-step explanation:

First you have to order the prices from least to greatest-

$4.00, $5.00, $7.00, $7.00, $8.00, $9.00, $9.00

Median means the number in the middle so you find the middle number which is $7.00 (the 4th number from least to greatest)

Answer:

V = m/d

Step-by-step explanation:

d = m/V, m = mass and V = volume

We want to solve for V

Multiply each side by V

dV = m/V *V

dV = m

Divide each side by d

dV / d = m/d

V = m/d

Answer:

S divided by R = 0

the arc is 5.9 and radius is 3.5329 then the central idea becomes 1.67

Step-by-step explanation:

Answer:

7x=84

divide by 7

12=x

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

We are looking for the value of x. To find this, we must isolate x on one side. To do this, we can divide by 7 on both sides, leaving us with x=12.

Answer:

height ≈ 11.9 units

Step-by-step explanation:

Construct a perpendicular bisector from the vertex to the base, thus splitting the triangle into 2 right triangles.

Using the sine ratio in one of these right triangles, then

sin48° = [tex]\frac{opposite}{hypotenuse}[/tex] ( the opposite is the height h )

sin48° = [tex]\frac{h}{16}[/tex] ( multiply both sides by 16 )

16 × sin48° = h , thus

h ≈ 11.9 ( to the nearest tenth )

The business requires $124,200 to pay its employees each week.

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

A small company employs 98 workers. Every employee works 8 hours a day, 5 days a week. Eleven employees are paid $45 per hour, while the remaining employees are paid $30 per hour. 

As per the given question, the required solution would be as:

No. of employees at $30hr: 98 -11 = 87

⇒ 8 hours × 5 days = 40 hour a week

⇒ 40 hour × $30 × 87 =104,400

⇒ 40 hour × $45 × 11 = 19,800

⇒ 104,400 + 19,800 = 124,200

Thus, the business requires $124,200 to pay its employees each week.

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Answer:

i believe it is A because 6/2=3, 4/2=2, which gives the ratio 3/2.

Step-by-step explanation:

The ratio of the number of brooms to the number of mops is 3:2.

In mathematics, a ratio is a phrase used to compare two or more numbers. It is used to express how large or tiny an amount is in comparison to another. A ratio compares two quantities by dividing them. The dividend is referred to as the "antecedent," while the divisor is referred to as the "consequent."

We have,

Number of brooms= 6

Number of mops= 4

So, the ratio of the number of brooms to the number of mops

= 6/4

=3/2

Thus, the required ratio is 3:2.

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Answer:

Step-by-step explanation:

is the given line  3x - 4y = -17?

then,

- 4y = -3x -17

y=(3/4)x+17/4

it is parallel, so slope of our line is 3/4 or 0.75

y=0.75x+b

next, lets plug in the given point to get the y-int

2=0.75*(-3)+b

2=-2.25+b

b-2.25=2

b=4.25

the equation is y=0.75x+4.25

does this clear anything, or am I off topic? please tell me I will help you

The equation of line is [tex]y=\frac{3}{4}x+\frac{17}{4}[/tex]

The given equation of line is,

                            [tex]3x-4y=-17\\\\4y=3x+17\\\\y=\frac{3}{4} x+\frac{17}{4}[/tex]

Compare above equation with [tex]y=mx+c[/tex]

Slope of given line [tex]m=\frac{3}{4}[/tex]

Since, the slope of all parallel lines are same.

So that, slope of required line is also [tex]\frac{3}{4}[/tex]

The equation of line is, [tex]y=\frac{3}{4}x+c\\[/tex]

Substitute point [tex](-3,2)[/tex] in above equation.

                   [tex]2=\frac{3}{4}(-3)+c\\\\\\c=2+\frac{9}{4} =\frac{17}{4}[/tex]

Substitute  value of c in equation of line.

       [tex]y=\frac{3}{4}x+\frac{17}{4} \\\\\\[/tex]

Thus, the equation of line is [tex]y=\frac{3}{4}x+\frac{17}{4}[/tex]

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Answer:

A. M less than or equal to 17

Step-by-step explanation:

Answer:

they would need 15 cases for 410 bag of chips

Step-by-step explanation:

410/7= about 15

Answer:

Step-by-step explanation:

S,wow,w,

Answer:

HI

Step-by-step explanation:

A) (5x-3)(x+1)

B) [tex]\frac{-2 \pm \sqrt{4+60}}{10} = \frac35 \text{or} -1[/tex]

C) it gets up really high

D) Plug values in of x to get y and plot!

Answer:

Klm=(k+1)m -(m+1)k

Klm=km+m -mk-k

Klm=m-k

Step-by-step explanation:

21. supplementary angles (add up to 180°)

22. vertical angles (congruent)

23. vertical angles (congruent)

24. supplementary angles (add up to 180°)

25. supplementary angles (add up to 180°)

26. supplementary angles (add up to 180°)

27. supplementary angles (add up to 180°)

28. supplementary angles (add up to 180°)

29.

(complementary angles)

[tex]4x+3+x-8=90\\5x-5=90\\5x=95\\x=19\\[/tex]

30.

(supplementary angles)

[tex]9x-4+4x-11=180[/tex]  

[tex]13x-15=180\\13x=195\\x=15[/tex]

31.

(vertical angles)

[tex]x-15=60\\x=75[/tex]

32.

(supplementary angles)

[tex]63+11x+2+5x-13=180\\52+16x=180\\16x= 128\\x= 8[/tex]

33.

(complementary angles)

[tex]x+28+6x-15=90\\7x+13=90\\7x=77\\x=11[/tex]

Hope this helps!

Answer:

Answer is 67%

Step-by-step explanation:

If you want to get the number four from 4 rolls the chances would be

1st roll = 1/6 (16.667%)

2nd roll = 2/6 (33.333%)

3rd roll = 3/6 (50.000%)

4th roll = 4/6 (66.667%)

So the answer is 67%