Given a right triangle with acute angle of 40° and a hypothenuse length of 35 feet, find the length
of the side opposite the acute angle.

Answer:

the line of g(x) is steeper and has lower y intercept

Step-by-step explanation:

f(x)=1/4x-1

g(x)=1/2x-2

g(x) is steeper because the slope of gx is greater than f(x)

y intercept of gx=-2 and for f(x)=-1

the y intercept of g(x) is lower than the y intercept of f(x)

The steepness of a function is dependent on its slope.

The true statement is: (c) the line of g(x) is steeper and has lower y intercept

The equations are given as:

[tex]\mathbf{f(x)= \frac 14x-1}[/tex]

[tex]\mathbf{g(x)=\frac12x - 2}[/tex]

A linear function is represented as:

[tex]\mathbf{y = mx + b}[/tex]

Where:

For f(x)

[tex]\mathbf{m_1 = \frac{1}4}\\\mathbf{b = -1}[/tex]

For g(x)

[tex]\mathbf{m_1 = \frac{1}2}\\\mathbf{b = -2}[/tex]

By comparison:

This means that: the line of g(x) is steeper and has lower y intercept

Hence, the true option is: (c)

Read more about steep and intercepts at:

https://brainly.com/question/3309622

Answer:

r= 0.87

Step-by-step explanation:

It has the strongest correlation, which means it is closest to the line.

The side lengths 8 cm, 6 cm, and 10 cm that can form a right triangle option (B), (C), and (D) are correct.

It is defined as a triangle in which one angle is 90 degrees and the other two angles are acute angles. In a right-angled triangle, the name of the sides are hypotenuse, perpendicular, and base.

We know that Pythagoras theorem:

[tex]\rm Hypotenuse^2 = Perpendicular^2 + Base^2[/tex]

10² = 8² + 6² = 64+36 = 100

Thus, the side lengths 8 cm, 6 cm, and 10 cm that can form a right triangle option (B), (C), and (D) are correct.

Learn more about the right angle triangle here:

brainly.com/question/3770177

#SPJ2

Answer:

x=3

Step-by-step explanation:

15x=27+6x

subtract 6x

9x=27

divide 9

x=3

X=3

Step-by-step explanation:

15x = 27 + 6x

15x - 6x =27

9x =27

X= 27/9

X= 3

[tex]hope \: this \: helps[/tex]

Answer:

Coordinates of point P is [tex](-14,3)[/tex].

Step-by-step explanation:

Given that mid point of line segment [tex]\overline {PQ}[/tex] is at M(-9, 8.5).

Q is at (-4, 14).

Let coordinate of P be [tex](x,y)[/tex].

Using the ratio, we can say the following:

The coordinates of mid point [tex](X,Y)[/tex] of a line with endpoints [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given as:

[tex]X=\dfrac{(x_1+ x_2)}{2}[/tex]

[tex]Y=\dfrac{(y_1+ y_2)}{2}[/tex]

Using the formula for above given dimensions:

[tex]-9 =\dfrac{x+(-4)}{2}\\\Rightarrow x = -18+4 = -14[/tex]

[tex]8.5=\dfrac{(14+ y)}{2}\\\Rightarrow y = 17-14 =3[/tex]

So, the coordinates of point P are [tex](-14,3)[/tex].

Answer:

Hello there!

~~~~~~~~~~~~~~~~~~~~~~`

Convert the fraction to a decimal by dividing the numerator by the denominator.

[tex]109 / 50 = 2.18[/tex]

Hope this helped you. Brainliest would be nice!

Answer: The next step will be 2x - 1 = 9

Step-by-step explanation:

4x -1 = 2x + 9

-2x       -2x  

2x -1 = 9

    +1  +1

2x= 10

x= 5

Answer:

2x-1=9

Step-by-step explanation:

2x-1=9

4x-2x-1=2x-1

2x-2x+9=9

2x-1=9

Answer:

(A)CPCTC

Step-by-step explanation:

Issa knows that ΔRED ≅ ΔTAN by the SSS theorem.

If two triangles are congruent, their corresponding parts will always be congruent. In fact, their corresponding angles will be equal.

Therefore, Issa concluded that ∠R ≅ ∠T by the fact that Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

The correct option is A.

Similarly, we can also conclude that:

Answer:

V=280

Step-by-step explanation:

V=whl

V=(8)(7)(5)

V=280

Answer:

140 units ^3

Step-by-step explanation:

a p e x

Answer:

Step-by-step explanation:

measure of angles of a circle=360

angle ACB=360-82=278 degrees

Answer:

5n = 1.75

Step-by-step explanation:

The 2 bars are equal thus lower equals upper, that is

5n = 1.75

Answer:

Step-by-step explanation:

A.) 600 x 20 = 12,000

    120 x 27 = 3,240

     12,000 + 3,240 = 15,240

B.) 600 x 13 = 7,800

     120 x 20 = 2,400

     7,800 + 2,400 = 10,200

C.) 600 x 18 = 10,800

    120 x 25 = 3,000

    10,800 + 3,000 = 13,800

D.) 600 x 11 = 6,600

     120 x 18 = 2,160

     6,600 + 2,160 = 8,760

Answer:

The mean salary for the 50 employees of the new company = $87

Step-by-step explanation:

Mean for any n set of number is \

mean = sum of n terms/ n

_________________________________

For company A

The mean salary for the 20 workers in company A is $90 per week,

mean = $90

n = 20

using above formula

90 = sum of salary of 20 workers/20

sum of salary of 20 workers = 90*20 = $1800

__________________________________________________

For company B

The mean salary for the 30 workers in company A is $85 per week,

mean = $85

n = 30

using above formula

85 = sum of salary of 30 workers/30

sum of salary of 30 workers = 85*30  = $2,550

____________________________________________

If two companies merge

Total salary for all the 50 workers for both the company =

sum of salary of 20 workers in company A + sum of salary of 30 workers in company B = $1800 + $2550 = $4350

Mean salary of 50 workers will be

n= 50

mean = Total salary of 50 workers/50

mean salary of 50 workers = 4350/50 = 87

The mean salary for the 50 employees of the new company = $87

Answer:

Height = 3cm

Volume = 50.27cm^3

Step-by-step explanation:

Well to solve for the height with slant height and radius we can use the Pythagorean Theorem,

Which is [tex]a^2 + b^2 = c^2[/tex].

So we have c and a, so we have to fill those in.

(4)^2 + b^2 = (5)^2

16 + b^2 = 25

-16

b^2 = 9

[tex]\sqrt{b} \sqrt{9}[/tex]

b = 3cm

So to find the volume of a cone we use the following formula [tex]\pi r^2 \frac{h}{3}[/tex].

So we have the radius and height so we just fill those in.

(pi)(4)^2(3)/3

(pi)16(1)

pi*16

About 50.27cm^3

Answer:

Primary source

Step-by-step explanation:

This is because it says "your" house, it means that you are the one looking and counting at the number of cars.

If this was not said "your", there is a higher chance that it is a secondary source, but in this case, it is a primary source.

Its Primary source

HOPE IT HELPS

Answer:

Altogether they lost 150 pennies.

Step-by-step explanation:

X = Dante's pennies

Y = Mia's pennies

X + Y = 350                                       1/2 X = 2/3 Y

                                                                X = 4/3 Y

4/3 Y + Y = 350

7/3 Y = 350

Y = 350 * 3/7

Y = 50 * 3

Y = 150

X + 150 = 350

X = 200

                                                     1/2 * 200 = 2/3 * 150

                                                       100 .      =   100

1/2 * 200 = 100 -> Dante lost 100 pennies

1/3 * 150 = 50 -> Mia lost 50 pennies

Altogether they lost 150 pennies.

Answer: B) 76.86

Step-by-step explanation:

Follow the steps others took to get D, then divide by 12 to get 76.86

Hope it helps <3

the volume of the cylinder is d)168 units

The attached picture was omitted from the question.

Answer:

C = 41.88 feet

a = 33.1°

b = 56.9°

Step-by-step explanation:

From the diagram, we have a right angle triangle.

C = hypotenuse

C = sqrt(35^2 + 23^2)

C = sqrt(1225 + 529)

C = sqrt(1754)

C = 41.88 feet

The connecting Angles:

Angle 'a'

Using tan = opposite / Adjacent

Tan a = 23 / 35

tan a = 0.6571428

a = tan^-1 (0.6571428)

a = 33.1°

Angle 'b' :

Sum of angles in a triangle = 180

a + b + 90 = 180

33.1 + b + 90 = 180

b + 123.1 = 180

b = 180 - 123.1

b = 56.9°

Answer:

Volume of a sphere = 4/3πr³

π = 3.14

r = radius which is 3in

Volume = 4/3 × 3.14 × 3²

= 37.68

= 38 cubic inches to the nearest hundredth

Hope this helps

Answer:

38 cubic inches

Step-by-step explanation:

Answer:

Hey there!

Choice A represents a function, because a function only has one y value for every x value.

Hope this helps :)

Answer:

A

Step-by-step explanation:

In a function, the x value can only go to one y value

B has x=5 going to y = 13 and y = 17

C had x = -3 with y values of 1 and -1

D has x = -4 going to y = 52 and 16

A each input has only one output value

Answer:

2√6

Step-by-step explanation:

x + y = 6

xy = 3

Square the first equation.

x² + 2xy + y² = 36

Subtract 4xy from both sides.

x² − 2xy + y² = 36 − 4xy

Factor.

(x − y)² = 36 − 4xy

Substitute.

(x − y)² = 36 − 4(3)

(x − y)² = 24

Take square root.

x − y = ±√24

x − y = ±2√6

Take absolute value.

|x − y| = 2√6

Answer:

The numbers are 11 and 13

Step-by-step explanation:

Let

the first odd whole number=x

Reciprocal=1/x

Second odd whole number=x+2

Reciprocal=1/x+2

The difference

(1/x) - 1/(x+2)=2/143

(x+2)-x / (x)(x+2)=2/143

x+2-x/x(x+2)=2/143

2/x(x+2)=2/143

2(143)=2(x^2+2x)

286=2x^2+4x

2x^2+4x-286=0

x^2+2x-143=0

Solve the quadratic Equation

x=-b +or- √b^2-4ac/2a

a=1

b=2

c=-143

x= -b +or- √b^2-4ac/2a

=-2 +or- √(2)^2-(4)(1)(-143) / 2(1)

= -2 +or- √4-(-572) / 2

= -2 +or- √4+572/2

= -2 +or- √576/2

= -2 +or- 24/2

x= -2+24/2

= 22/2

=11

Or

x= -2-24/2

= -26/2

= -13

Taking the positive value

x=11

The second odd whole number=x+2

=11+2

=13

Answer:

x =- 3 and y = -7

Step-by-step explanation:

2X-2Y=-8

X=2y + 11

We need to isolate both X and Y in both equations

so

2x-2y=-8

(add 2y to both sides)

2x=-8+ 2y

(divide both sides by 2)

x=-4+y and x=2y+11

because both of these equations are the same we can put them together

4+y=2y+11

(subtract y)

4=y+11

(subtract 11)

-7=y

so y = -7

then to find x you just need to plug in y to one of the equations

x=2(-7) + 11

x= -14 +11

x = -3

Answer:

x = - 19, y = - 15

Step-by-step explanation:

Given the 2 equations

2x - 2y = - 8 → (1)

x = 2y + 11 → (2)

Substitute x = 2y + 11 into (1)

2(2y + 11) - 2y = - 8 ← distribute and simplify left side

4y + 22 - 2y = - 8

2y + 22 = - 8 ( subtract 22 from both sides )

2y = - 30 ( divide both sides by 2 )

y = - 15

Substitute y = - 15 into (2) for corresponding value of x

x = 2(- 15) + 11 = - 30 + 11 = - 19

Solution is x = - 19, y = - 15

Answer:

1463 : 5080

Step-by-step explanation:

There are 1463 cherry-flavored jelly beans.

There are 5080 non cherry-flavored jelly beans.

The ratio of cherry-flavored jelly beans to non-flavored jelly beans is:

1463 : 5080

Answer:

the 95th percentile for the sum of the rounding errors is 21.236

Step-by-step explanation:

Let consider X to be the rounding errors

Then; [tex]X \sim U (a,b)[/tex]

where;

a = -0.5 and b = 0.5

Also;

Since The error on each loss is independently and uniformly distributed

Then;

[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]

where;

n = 2000

Mean [tex]\mu = \dfrac{a+b}{2}[/tex]

[tex]\mu = \dfrac{-0.5+0.5}{2}[/tex]

[tex]\mu =0[/tex]

[tex]\sigma^2 = \dfrac{(b-a)^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{(0.5-(-0.5))^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{(0.5+0.5)^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{(1.0)^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{1}{12}[/tex]

Recall:

[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]

[tex]n\mu = 2000 \times 0 = 0[/tex]

[tex]n \sigma^2 = 2000 \times \dfrac{1}{12} = \dfrac{2000}{12}[/tex]

For 95th percentile or below

[tex]P(\overline X < 95}) = P(\dfrac{\overline X - \mu }{\sqrt{{n \sigma^2}}}< \dfrac{P_{95}- 0 } {\sqrt{\dfrac{2000}{12}}}) =0.95[/tex]

[tex]P(Z< \dfrac{P_{95} } {\sqrt{\dfrac{2000}{12}}}) = 0.95[/tex]

[tex]P(Z< \dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}}) = 0.95[/tex]

[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1- 0.95[/tex]

[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} = 0.05[/tex]

From Normal table; Z >   1.645 = 0.05

[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1.645[/tex]

[tex]{P_{95}\sqrt{12} } = 1.645 \times {\sqrt{{2000}}}[/tex]

[tex]{P_{95} = \dfrac{1.645 \times {\sqrt{{2000}}} }{\sqrt{12} } }[/tex]

[tex]\mathbf{P_{95} = 21.236}[/tex]

the 95th percentile for the sum of the rounding errors is 21.236

Answer: The area is 24 square units.

Step-by-step explanation:

Things you need to use in this exercise:

Area of a circle = pi*r^2

r is the radius, equal to half the diameter.

Ok, in the image we can see 3 half-circles.

one has a diameter of 8 units: with area A (the left one)

other has a diameter of 6 units: with area B (the bottom one)

and the other has a diameter equal to the hypotenuse of the right triangle: with area C (the white semicircle that also includes the right triangle)

Now, you can think the shaded area as:

The sum of the areas of the half circles A and B, minus the area of the half-circle C, plus the area of the right triangle (because the white triangle is also included in the white semicircle)

So the area is:

A + B - C + area triangle

A = pi*(8/2)^2 = 3.14*4^2 = 50.24

B = pi*(6/2)^2 = 3.14*3^2 = 28.26

the area of the triangle is equal to:

T = 6*8/2 = 24

Now, to obtain the area of the white semicircle ( C) we need the hypotenuse of the triangle, so here we can use the Pythagorean's theorem:

H^2 = 8^2 +6^2

H = √(8^2 + 6^2) = 10

Then:

C = pi*(10/2)^2 = 3.14*5^2 = 78.5

Then the shaded area is:

Area = 50.24 + 28.26 + 24 - 78.5 = 24

Answer:

d=16

Step-by-step explanation:

d: distance (10,4),(-6,4)

d=√(x2-x1)^2+(y2-y1)^2

d=√(-6-10)^2+(4-4)^2

d=√16^2

d=16

Answer:

go 4 to right or where is positive then thats it

Step-by-step explanation:

lololololololololololololol

Answer:

First one: true        Second one: true

Step-by-step explanation:

First Question: the lines will be parellel even though the shape grows or gets smaller

Second Question: the angle will stay the same even if it grows into a larger or smaller shape.