What is the equation of the line that passes through (5, -2) and (-3, 4)? 3 x + 4 y - 7 = 0 3 x - 4 y - 7 = 0 -3 x + 4 y - 7 = 0

Answer:

25/33

Step-by-step explanation:

-1 2/3 ÷ ( -2 1/5)

Change from mixed number to improper fraction

- ( 3*1 + 2) /3 ÷  - ( 5*2+1) /5

-5/3 ÷ -11/5

Copy dot flip

-5/3 * -5/11

25/33

Answer:

Option B.

Step-by-step explanation:

If a line passing through two points, then the slope of line is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that f(x) passing through the points (0,-2) and (1,1). So, slope of f(x) is

[tex]m_1=\dfrac{1-(-2)}{1-0}=1+2=3[/tex]

It is given that g(x) passing through the points (-4,0) and (0,2). So, slope of g(x) is

[tex]m_2=\dfrac{2-0}{0-(-4)}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]

Since, [tex]\dfrac{1}{2}<3[/tex], therefore [tex]m_2<m_1[/tex].

The slope of g(x) is less than the slope of f(x).

Therefore, the correct option is B.

Answer:

  Geometric sequences are exponential functions

Step-by-step explanation:

Geometric sequences are exponential functions.

The general term of a geometric sequence is given by the exponential function ...

  a[n] = a[1]·r^(n-1)

where a[1] is the first term and r is the common ratio.

You will notice that the independent variable (n) is in the exponent of this function. Hence it is an exponential function.

Answer:

[tex]-37,-32,-27,-22,-17,-12,-7,-2,3,8,\\13,18,23,28,33,38,43,48,53,58\\63,68,73,78,83,88,93,98,103,108\\113,118,123,128,133,138,143,148,153,158\\163,168,173,178,183,188,193,198,203,208,\\213,218,223,228,233,238,243,248,253,258[/tex]

Step-by-step explanation:

The nth term of an arithmetic sequence is obtained using the formula:

[tex]a_n=a+(n-1)d[/tex]

Given that: [tex]a_5=23$ and a_{20}=98.[/tex]

a_n=a+(n-1)d

[tex]a_5=23=a+(5-1)d \implies a+4d=23\\a_{20}=98=a+(20-1)d \implies a+19d=98\\$We solve simultaneously$:\\a+19d=98\\a+4d=23\\15d=75\\d=5\\Recall:a+4d=23\\a+4(15)=23\\a=23-60\\a=-37[/tex]

Therefore, the first 60 terms of the sequence are:

[tex]-37,-32,-27,-22,-17,-12,-7,-2,3,8,\\13,18,23,28,33,38,43,48,53,58\\63,68,73,78,83,88,93,98,103,108\\113,118,123,128,133,138,143,148,153,158\\163,168,173,178,183,188,193,198,203,208,\\213,218,223,228,233,238,243,248,253,258[/tex]

   First 60 terms of the arithmetic sequence will be 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283, 288, 293, 298.

           difference 'd', sequence will be an arithmetic sequence and the

           explicit formula for the nth term of the sequence will be,

           [tex]A_n=a+(n-1)d[/tex]

           Here, [tex]a=[/tex] First term

                     [tex]n=[/tex] nth term

                     [tex]d=[/tex] common difference

Given in the question,

Two terms [tex]a_5=23, a_{20}=98[/tex]

If 5th term of the sequence is 23,

[tex]23=a+(5-1)d[/tex]

[tex]23=a+4d[/tex]  -------(1)

If 20th term of the sequence is 98,

[tex]98=a+(20-1)d[/tex]

[tex]98=a+19d[/tex] ----------(2)

Subtract equation (1) from equation (2),

98 - 23 = a + 19d - (a + 4d)

75 = 15d

d = 5

Substitute the value of 'd' in equation (1),

23 = a + 4(5)

a = 23 - 20

a = 3

     Therefore, first 60 terms of the arithmetic sequence will be 3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, 73, 78, 83, 88, 93, 98, 103, 108, 113, 118, 123, 128, 133, 138, 143, 148, 153, 158, 163, 168, 173, 178, 183, 188, 193, 198, 203, 208, 213, 218, 223, 228, 233, 238, 243, 248, 253, 258, 263, 268, 273, 278, 283, 288, 293, 298.

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Answer:

A) girls=boys +22 .B)Boys=girls-22

Step-by-step explanation:

Answer:

Because these are in slope-intercept form which is much easier because y=mx+b means that m=the slope, and b=y intercept so all your information is laid out in front of you.

Step-by-step explanation:

Answer:

B (the second choice)

Step-by-step explanation:

to calculate the area of a circle you use the formula A= π r²

the radius of the circle is 5 in, so the only answer that could work is

π(5in)²(30/360).

Hope this helps <3

~sunflowerpug

UwU

Answer:

5%

Step-by-step explanation:

104/99=1.05

Answer: 5%

Step-by-step explanation:

if you do the math of 99+5% you will get 103.95 and if you round that to the tenth you get 104.

Answer:

140  

Step-by-step explanation:

The table is:

               |Sample 1      | Sample 2

catfish     | 3                 | 5

bass         | 9                 | 9

trout         | 8                 | 6

all fish      | 20               | 20

The average number of trouts is (8 + 6)/2 = 7

The average number of the total amount of fish is 20

So, there are 7 trouts within 20 fish. To find the expected number of trouts in a population of 400 fish, we have to solve the next proportion:

7 trouts / 20 fish = x trouts / 400 fish

x = 7*400/20

x = 140 trouts

Answer:

140

hope this helps

Hope it helps <3

(If it does, please give brainliest, only need one more for rank up :) )

Answer:

2. [tex]18\sqrt{5}[/tex]

3. [tex]52.303...[/tex]

4. [tex]11.608...[/tex]

Step-by-step explanation:

2. Using the Pythagorean Theorem, we can see that [tex]a^2+b^2=c^2[/tex]. Therefore, [tex]90^2+90^2=8100+8100=c^2[/tex]. We know that [tex]8100+8100[/tex] is [tex]16200[/tex]. The square root of [tex]16200[/tex]  is [tex]90\sqrt{2}[/tex].

3. Same as before, we use the Pythagorean Theorem. This time, we're calculating [tex]b[/tex] instead of [tex]c[/tex]. This means we have to do [tex]60^2-29.4^2=b^2[/tex], which gives us [tex]3600-864.36[/tex], which equals [tex]2735.64[/tex]. We can put this in decimal form, which would give us [tex]52.303[/tex][tex]...[/tex]

4. This one, we do [tex]15^2-9.5^2[/tex], which would give us [tex]134.75[/tex]. Simplifying this would give us [tex]11.608...[/tex].

Hope this helped! Just remember the Pythagorean Theorem.

A circle is a curve sketched out by a point moving in a plane. The length of AC in the given figure is 5 units. The correct option is

3.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

In a circle, the angle between the radius and tangent is always equal to 90°. Therefore, we can write that in the given figure ΔABC, the triangle is a right angle triangle with ∠B as the right angle.

Now, for the triangle using the Pythagoras theorem we can write,

AC² = AB² + BC²

AC² = 3² + 4²

AC² = 9 + 16

AC = √25

AC = 5

Hence, the length of AC in the given figure is 5 units.

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Answer:

Yes they are equivalent

Step-by-step explanation:

2(-2) = -4, plus 6(2) = 8 and

(-3)(-3) = 9, plus (-1)(1) = 8

Answer:

Yes they are equivalent

Step-by-step explanation:

the other fella right, check his reasons out, hope you guys learn from this question Stay safe everyone who sees this

Step-by-step explanation:

( 2 - 1)(4+2)

= (1)(6)

= 6

Answer:

Step-by-step explanation:

2sin²β-7sinβ-4=0

2sin²β-8sin β+1 sin β-4=0

2 sin β(sin β-4)+1(sin β-4)=0

(sin β-4)(2sin β+1)=0

either sin β-4=0

sin β=4 (rejected,as |sin β|≤1)

or

2 sin β+1=0

sin β=-1/2=-sin (π/6)=sin (π+π/6),sin (2π-π/6)

β=7π/6,11π/6

Answer:

Step-by-step explanation:

a. the inequality is x+y >= 2  (red line) that keeps onlythe two farms in the region.

b. substituting the coordinates of the farms in the inequality and see if they are satisfied:

C(2,2)  2+2 = 4 > 2    checks

F(3,4)   3+4 = 7 > 2    checks.

The other farms will not , for example,

D(1,-2) 1-2 = -1 < 2     does not check.

...

c. y > -4x + 3 is shown in blue.

Farms that satisfy given inequality can raise chickens, i.e. to the right of the blue line, or farms C,E and F.

If necessary, we can again check by the coordinates as in part b.

C(2,2)   -4(2) + 2 = -8+2 = -6   y=2 > -6, so checks.

...

===============================================

Work Shown:

The notation P(B|A) has a vertical line separating the B and A

Given values

----------

P(B|A) = P(B and A)/P(A) ... conditional probability formula

P(B and A) = P(B|A)*P(A) ... solve for P(B and A)

P(B and A) = 0.88*0.46 ... plug in given values

P(B and A) = 0.4048

P(B and A) = 0.405 .... rounding to three decimal places

This is the same as P(A and B).

Answer:

16

Step-by-step explanation:

Putting a + in front of a number indicates that the number is positive. so we are just going to add it up.

10+6=16

10:6=5:3

Hope it helps:)

Answer:

30t

Step-by-step explanation:

2(15)t

30t

Answer: 30t

Step-by-step explanation:

The group earned 15t, or 15$ an hour for t hours.  Then it was doubled(15t * 2=30t)

Answer:

Step-by-step explanation:

a) angle CAD= angle ODA ( in triangle OAD, OA=OD(same radius) angels opp                          to equal sides are equal)

hence angle CAD=42

b)angle b =90(angle subtended by diameter)

hence using angle sum property in triABC,

angle ACB=66-------------eq4

c) in tri OAD,

Angle AOD=180-(42+42)-------(using angle sum prop.)

=> 96-----------------eq1

angleACD=1/2 Angle AOD ( angle subtende by an arc at centre is double the angle subtended...)

hence angle ACD =1/2 x 96(from eq1)

angleACD=48--------------eq3

from eq 3,and eq4,

angle BCD= 48+66

=114 degree...

hope this helped you........pls mark brainliest

a) Measure of angle CAD is, 42°

b) The size of ACB is, 66°

c) The size of angle BCD is, 114°

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

In the diagram O is the center of the circle.

And, AOC is a straight line.

Here, Angle BAO is 24° and Angle ADO is 42°​.

Now,

a) In triangle OAD,

⇒ OA=OD (same radius)

And, Angels opposite to equal sides are equal.

Hence, We get;

⇒ ∠CAD= ∠ODA

⇒ ∠ CAD = 42°

b) We have;

⇒ ∠B =90     (Angle subtended by diameter)

Hence, By using angle sum property in ΔABC,

⇒ ∠ BAC + ∠ACB + ∠B = 180°

⇒ 24 + ∠ACB + 90° = 180°

⇒ ∠ ACB = 66°

c) In ΔOAD,

⇒ ∠AOD = 180 - (42 + 42)   ( By using angle sum property)

              = 96

And, Angle subtended by an arc at center is double the angle subtended.

Hence, We get;

⇒ ∠ACD = 1/2 ∠AOD

               = 1/2 × 96

               = 48°

Hence, We get;

⇒ ∠ BCD = 48° + 66°

               = 114°

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Hey there! :)

Answer:

5a².

Step-by-step explanation:

Solve this expression by finding how many times 9a² goes into [tex]45a^{4}[/tex]. Since we are only dividing from a monomial, long division does not need to be used.

Begin by solving for the coefficient:

45 ÷ 9 = 5.

Solve for the exponent of a:

[tex]a^{4}[/tex] ÷ a² (subtract exponents when dividing) = a². Therefore:

[tex]45a^{4}[/tex] ÷ 9a² = 5a².

Answer:

294 in^2 = A

Step-by-step explanation:

Let h represent the length of the hypotenuse, b the base and h the height.  Because this is a right triangle, the Pythagorean Theorem applies.

(hypotenuse)^2 = (base)^2 + (height)^2

         h^2           =  (h - 7)^2  +  (h - 14)^2

Perimeter of the triangle is 84 inches, equal to (h) + (h - 7) + (h - 14), which in turn simplifies to 84 = h + h - 7 + h - 14, or 84 = 3h - 21, or 3h = 105.  Solving this for h, we get h = 35.

Then the base is (35 - 7), or 28, and the height is (35 - 14), or 21.

The area of the triangle is found using the formula

A = (1/2)(base)(height) = (1/2)(28)(21) = 294 in^2 = A

Answer:

missing info my dude

Step-by-step explanation:

Answer: If three points lie on the same line, there is only one plane that can pass through them.

Step-by-step explanation:

Answer:

x= 116°

y= 127°

Step-by-step explanation:

x... The angle subtended at the centre is twice the angle subtended at the cicumfernce by the same arch

y.... Angle in a cyclic quadrilateral add up to 180°

hence 180-53=127

Answer:

8 oz, $41

Step-by-step explanation:

For 4 oz, Chef Mate sells their's for $22 and Grocery Gourmet sells their's $25. Chef Mate sells his vanilla extract for $4.75/oz and Grocery Gourmet sells their's for $4/oz. At the 8th ounce, Chef Mate and Grocery Gourmet will charge the same amount, $41.

Chef Mate: $22 (price of 4 oz) + ($4.75 × 4) = $41

Gourmet Garden: $25 (price of 4 oz) + ($4 × 4) = $41

Answer: 04) 16​

Step-by-step explanation:

The given expression is : [tex](22+42)\div2^2[/tex]

Since  [tex]22+42=64[/tex]

and

[tex]2^2=2\times2=4[/tex]

So, by using these values the given expression will become

[tex](22+42)\div2^2=64\div 4 =16 \ \ \ [\text{As }16\times4=64][/tex]

Thus, the value of the expression [tex](22+42)\div2^2[/tex] is 16.

Hence, the correct option is "04) 16​."

Answer:

y=-1/5+1

Step-by-step explanation:

Answer:

y = -1/5x + 1

Step-by-step explanation:

In these types of problems you want to guesstimate the slope and draw an imaginary solid line amongst the dots. The slope you'll end up with is -1/5 because the graph is decreasing.

and just to check, i typed this into my graphing calculator and can confirm this as the answer. :)

Answer:

B(6 , -11)

Step-by-step explanation:

(x-2 , y+3)  = (4 , -8)

Compare the x & y co ordinates

x - 2 = 4   ; y + 3 = -8

x = 4 +2  ; y = -8 - 3

x = 6      ; y = -11

B(6 , -11)

i cannot see the question for #33, but for

#34, im sure there are a bit more efficent ways to find surface area, but i just find the area of each square. area of top and bottom=240 square inches (120+120); area of shorter sides=60 square inches (30+30); area of longer sides= 72 square inches (36+36). add all of those together, so the total surface area is 372 square inches. So basically Charlene will need 372 square inches of wrapping paper

#35 the formula for volume is length*width*height. So do 60*45.5*14=38,220 cubic ft.

#36 first find the area of that triangle. (6*14)/2=42. Then find area of square which is 20*14=280. Add those (280+42) and get 322. So the area of the polygon is 322 square mm

Answer as a fraction = 18/25

Answer in decimal form = 0.72

Answer in percent form = 72%

=========================================================

Explanation:

We have A = 6+6+1 = 13 people who rent their home (add the values along the bottom row). There are B = 5+6 = 11 people who drive an SUV (add up the values in the SUV column). There are A+B = 13+11 = 24 people who either rent their home or drive an SUV. Keep in mind that 6 people have been double counted if we just go with A+B without adjustment. These 6 people both rent their home and drive an SUV. To correct for the double-count, we subtract off 6 from A+B to get A+B-6 = 24-6 = 18.

So there are 18 people who rent their home, drive an SUV, or both.

This is out of 4+5+3+6+6+1 = 25 people surveyed total.

The probability of selecting someone who rents their home or drives an SUV is 18/25. In decimal form that is equivalent to 0.72 which converts to 72%

Answer:   x < 3

Step-by-step explanation:

4(x + 3) < 3(x + 5)

4x + 12 < 3x + 15           Distributed

 x + 12 < 15                   Subtracted 3x from both sides

       x  < 3                     Subtracted 12 from both sides

Answer:

4x^2+9x-15<0

Step-by-step explanation:

x.4(x+3)<3(x+5)

(4x)(x+3)<3x+3x5

(4x)(x+3)<3x+15

4xx+4x.3<3x+15

4x^1+1+4x3x<3x+15

4x^2+12x<3x+15

(4x^2+12x)+(-3x-15)<(3x+15)+(-3x-15x)

4x^2+9x-15<3x-3x+15-15

4x^2+9x-15<0