What is the slope of the line? – –Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of ? y + 2 =(x + 3) y – 2 = (x – 3) y + 3 = (x + 2) y – 3 = (x – 2)

Answer:

The correct option is 1.

Step-by-step explanation:

Statement                                          Reasons

1.   AB is parallel to DC and         Definition of parallelogram

    AD is parallel to BC

2.   angle 1 = angle 2,                   If two parallel lines are cut by a

    angle 3 = angle 4                    transversal then the alternate

                                                      interior angles are congruent

3.    BD = BD                                   Reflexive Property

4.    [tex]\triangle ADB\cong \triangle CBD[/tex]                 ASA postulate

5.   AB = DC, AD = BC                  (CPCTC)

If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate.

According to alternate interior angles theorem, two parallel lines are cut by a transversal then the alternate interior angles are congruent.

Therefore option 1 is correct.

Answer:

answer is x=2

The solution set for the equation 6x - 2 = 10 using the replacement set {1, 2, 3, 4} is {2}, as 2 is the only number in the set that, when substituted into the equation, satisfies it.

The solution set for the open sentence 6x - 2 = 10 using the given replacement set {1, 2, 3, 4} can be found by solving the equation for x and then checking which numbers in the replacement set satisfy the equation.

Therefore, the solution set is {2}.

Answer:

a=5, b=10, c=11

Step-by-step explanation:

a= shortest side

b= "third" side

c= longest side

Equations:

c=6+a

b=2a

a+b+c=26

so we can see there is a in all of the equations, so we can plug all of them into the equation for the perimeter

a+(2a)+(6+a)=26-->4a=20-->a=5

with a, we can plug that into the equations to get b and c

c=6+a-->6+(5)-->c=11

b=2a-->b=2(5)--> b=10

Answer:

DC = 55

Step-by-step explanation:

Since this is a parallelogram, opposite sides are congruent.  WE need to find the value of y from AD = BC

AD = BC

6y+40 = 9y+10

Subtract 6y from each side

6y-6y+40 = 9y-6y+10

40 = 3y+10

Subtract 10 from each side

40-10 = 3y+10-10

30 = 3y

Divide each side by 3y

30/3 = 3y/3

10 =y

Since opposite sides are congruent

DC = AB

DC = .5y + 50

   = .5 (10) +50

    =5 + 50

   = 55

DC =55

Answer:

The measure of angle 1 is 55.

Step-by-step explanation:

The top angle= 75 because of the vertical angle theorem

The right angle= 50 because of the alternate exterior angle theorem

75+50=125

There are 180 degrees in a triangle so the angle has to equal 55

Answer:

~5 feet.

Step-by-step explanation:

assuming that it is a right triangle. if a=5 and c=7 then b the other leg is equal to the square root of c squared minus a squared. which equals about 4.9

✿ The Quantity best expressed as -3.2 is a Withdrawal of $3.20

Because :

[tex]\heartsuit[/tex]  The Value which is expressed above sea level should be Positive.

[tex]\heartsuit[/tex]  Profit is always a Positive

[tex]\heartsuit[/tex]  Withdrawal's are Negative

✿ The Quantity best expressed as +5.1 is 5.1 feet above sea level

Because :

[tex]\heartsuit[/tex]  The Value which is expressed above sea level should be Positive.

[tex]\heartsuit[/tex]  Debt and Withdrawals are always Negative

Answer:

first part : a withdrawal of 3.20

second part : 5.1 feet above sea level

Step-by-step explanation:

If a, b and c are the lengths of a right triangle and c is the longest side, then:

[tex]a^2+b^2=c^2[/tex]

We have a = 18cm, b = 24cm and c = 30cm. Substitute and check:

[tex]L_s=18^2+24^2=324+576=900\\\\R_s=30^2=900\\\\L_s=R_s[/tex]

The rational number equivalent to -20/4 is -5.

A rational number equivalent to -20/4 is -5. This can be found by dividing the numerator (which is -20) by the denominator (which is 4). The result of this division is -5. Hence, -5 is the rational number equivalent to -20/4.

Answer:

1) 2.71%

2) $38.32

Step-by-step explanation:

Opening balance = $1220

Balance after 10 days (after expense) = $1690

Balance after 10 days(after payment) = $1340

APR = 33%

1) Periodic interest rate = APR × [tex]\frac{No. of days in a billing cycle}{365}[/tex]

                                  =  33%× 30/365

                                  = 2.71%

2) Interest charged for first 10 days = [tex]\frac{1220*2.71*\frac{10}{30} }{100}[/tex]

                                                              = $11.02

Interst charged for the next 10 days = [tex]\frac{1690*2.71*\frac{10}{30} }{100}[/tex]

                                                            = $15.2

Interest charged for the next 10 days = [tex]\frac{1340*2.71*\frac{10}{30} }{100}[/tex]

                                                           = $12.10

Total interest for 30 days = 11.02+15.2+12.10

                                          = $38.32

Answer:

sqrt(15)/2 = g

h = sqrt(5) /2

Step-by-step explanation:

We know that sin 30 = opposite / hypotenuse

sin 30 = h/ sqrt(5)

Multiply by sqrt(5) on each side

sqrt(5) sin 30 = h

sqrt(5) (1/2) = h

h = sqrt(5) /2

cos 30 = adjacent/ hypotenuse

cos 30 = g / sqrt(5)

Multiply each side by sqrt(5)

sqrt(5) cos (30 ) = g

sqrt(5)  (sqrt(3)/2) = g

sqrt(15)/2 = g

First check the difference between terms:

[tex]\{1-(-3),5-1,9-5,\ldots\}=\{4,4,4,\ldots\}[/tex]

So every term differs by 4. The first term in the sequence is [tex]a_1=-3[/tex]. Recursively, the sequence is given by

[tex]\begin{cases}a_1=-3\\a_n=a_{n-1}+4&\text{for }n>1\end{cases}[/tex]

Then

[tex]a_2=a_1+4[/tex]

[tex]a_3=a_2+4=a_1+4(2)[/tex]

[tex]a_4=a_3+4=a_1+4(3)[/tex]

and so on, with the general rule

[tex]a_n=a_1+4(n-1)\implies a_n=4n-7[/tex]

Then the 250th term of the sequence would be

[tex]a_{250}=4(250)-7=993[/tex]

Answer:

The number of plain bagels are 18 and it is 75% of the total bagels .

The amount of salt in a plain bagel to that in a sesame bagel is 81.5% .

Step-by-step explanation:

Formula

[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]

As given

Jen buys sesame bagels and plain bagels. If the ratio of sesame to plain is 1:3 and Jen bought 2 dozen bagels .

As one dozens contains 12 items .

Thus

Total number of bagels bought by Jen = 2 × 12

                                                                 = 24

Let us assume that the x be the scalar multiple of sesame bagels and plain bagels .

Number of sesame bagels = 1x

Number of plain bagels = 3x

Than the equation becomes

x + 3x = 24

4x = 24

[tex]x = \frac{24}{4}[/tex]

x = 6

Thus

Number of plain bagels = 3 × 6

                                        = 18

Part value = 18

Total value = 24

Putting all the values in the formula

[tex]Percentage = \frac{18\times 100}{24}[/tex]

[tex]Percentage = \frac{1800}{24}[/tex]

Percentage = 75 %

Therefore the number of plain bagels are 18 and it is 75% of the total bagels  .

As given

Suppose each plain bagel has 0.53 gram of salt, and each sesame bagel has 0.65 gram.

Part value = 0.53 grams

Total value = 0.65 grams

Putting all the values in the formula

[tex]Percentage = \frac{0.53\times 100}{0.65}[/tex]

[tex]Percentage = \frac{5300}{65}[/tex]

Percentage = 81.5 %

Therefore the amount of salt in a plain bagel to that in a sesame bagel is 81.5% .

Answer:

The measure of angle CAD is 83 degrees.

Step-by-step explanation:

Given information: ABCD is a parallelogram, AC is a diagonal, [tex]\angle ABC=40^{\circ}[/tex] and  [tex]\angle ACD=57^{\circ}[/tex].

The opposite sides of parallelogram are congruent.

The diagonal AC divides the parallelogram in two congruent triangles.

In triangle ABC and ADC,

[tex]AB\cong CD[/tex]                                     (Opposite sides of parallelogram)

[tex]\angle ABC\cong \angle ADC[/tex]         (Opposite angles of parallelogram)

[tex]BC\cong DA[/tex]                                     (Opposite sides of parallelogram)

By SAS postulate,

[tex]\triangle ABC\cong \triangle CDA[/tex]

Since we know that opposite angles of parallelogram are equal, therefore

[tex]\angle ABC\cong \angle ADC[/tex]

[tex]\angle ADC=40^{\circ}[/tex]

According to the angle sum property the sum of interior angles of a triangle is 180 degrees.

[tex]\angle CAD+\angle ACD+\angle ADC=180^{\circ}[/tex]

[tex]\angle CAD+57^{\circ}+40^{\circ}=180^{\circ}[/tex]

[tex]\angle CAD=83^{\circ}[/tex]

Therefore the measure of angle CAD is 83 degrees.

Answer:

A Experimental Probability

Step-by-step explanation:

The 59 percent is based on the data from the actual data.  The theoretical probability is 50 percent for male and 50% and female.

Answer:

A. $100

B. 29%

Step-by-step explanation:

A. To find total price of the items Sammy bought we will add the price of shoes and jacket after discount.

Let us find price of shoes after 25% discount.

[tex]\text{Price of shoes after discount}=40-(\frac{25}{100}*40)[/tex]

[tex]\text{Price of shoes after discount}=40-(\frac{1}{4}*40)[/tex]

[tex]\text{Price of shoes after discount}=40-10=30[/tex]

Therefore, price of shoes after discount is $30.

Now let us find price of jacket after 30% discount.

[tex]\text{Price of jacket after discount}=100-(\frac{30}{100}*100)[/tex]

[tex]\text{Price of jacket after discount}=100-30[/tex]

[tex]\text{Price of jacket after discount}=70[/tex]

Therefore, price of jacket after discount is $70.

Now let us add both prices to find the total price of the items.

[tex]\text{Total price of items}=30+70[/tex]

[tex]\text{Total price of items}=100[/tex]

Therefore, the total price of the items bought by Sammy is $100.

B. To find the percent discount which Sammy got on his total purchases, we will use percent change formula.

[tex]\text{Percent change}=\frac{\text{Difference}}{\text{Original value}}\times 100[/tex]  

Total price without discount= 100+40=140

[tex]\text{Discount percent}=\frac{140-100}{140}\times 100[/tex]

[tex]\text{Discount percent}=\frac{40}{140}\times 100[/tex]

[tex]\text{Discount percent}=0.2857142857142857\times 100[/tex]

[tex]\text{Discount percent}=28.57142857142857\approx 29[/tex]

Therefore, Sammy got approximately 29% discount on his total purchases.

Answer:

Sammy bought a car and got a discount of 2/5 off the original price of $30,000. How much did Sammy pay for the car after the discount?  

Step-by-step explanation:

Answer:

142.2 meters.  

Step-by-step explanation:

We have been given that a box measures 70 cm X 36 cm X 12 cm is to be covered by a canvas.      

Let us find total surface area of box using surface area formula of cuboid.

[tex]\text{Total surface area of cuboid}=2(lb+bh+hl)[/tex], where,

[tex]l[/tex] = Length of cuboid,

[tex]b[/tex] = Breadth of cuboid,

[tex]w[/tex] = Width of cuboid.

[tex]\text{Total surface area of box}=2(70\cdot36+36\cdot 12+12\cdot 70)[/tex]

[tex]\text{Total surface area of box}=2(2520+432+840)[/tex]

[tex]\text{Total surface area of box}=2(3792)[/tex]

[tex]\text{Total surface area of box}=7584[/tex]

Therefore, the total surface area of box will be 7584 square cm.  

To find the length of canvas that will cover 150 boxes, we will divide total surface area of 150 such boxes by width of canvass as total surface area of canvas will also be the same.

[tex]\text{Width of canvas* Length of canvass}=\text{Total surface area of 150 boxes}[/tex]

[tex]80\text{ cm}\times\text{ Length of canvass}=150\times 7584\text{cm}^2[/tex]

[tex]\text{ Length of canvass}=\frac{150\times 7584\text{ cm}^2}{80\text{ cm}}[/tex]

[tex]\text{ Length of canvass}=\frac{1137600\text{ cm}^2}{80\text{ cm}}[/tex]

[tex]\text{ Length of canvass}=14220\text{ cm}[/tex]

Let us convert the length of canvas into meters by dividing 14220 by 100 as 1 meter equals to 100 cm.

[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}[/tex]

[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100\frac{cm}{m}}[/tex]

[tex]\text{ Length of canvass}=\frac{14220\text{ cm}}{100}\times\frac{m}{cm}[/tex]

[tex]\text{ Length of canvass}=142.20\text{ m}[/tex]

Therefore, 142.2 meters of canvas of width 80 cm required to cover 150 such boxes.

[tex]x^2+2x+1=x^2+x+x+1=x(x+1)+1(x+1)=(x+1)(x+1)\\----------------------\\2x+2=2(x+1)\\----------------------\\\\\dfrac{2x+2}{x^2+2x+1}=\dfrac{2(x+1)}{(x+1)(x+1)}\\\\\text{Canceled}\ (x+1)\\\\=\boxed{\dfrac{2}{x+1}}[/tex]

Answer:

1/5, 1/6, 1/7, 1/8

Step-by-step explanation:

The formula for the sequence is (n+3)!/ (n+4)!

The first terms uses n=1

a1 = (1+3)!/ (1+4)! = 4!/5! = (4*3*2*1)/(5*4*3*2*1) = 1/5

The first terms uses n=2

a2 = (2+3)!/ (2+4)! = 5!/6! = (5*4*3*2*1)/(6*5*4*3*2*1) = 1/6

The first terms uses n=3

a3 = (3+3)!/ (3+4)! = 6!/7! = (6*5*4*3*2*1)/(7*6*5*4*3*2*1) = 1/7

The first terms uses n=4

a4 = (4+3)!/ (4+4)! = 7!/8! = (7*6*5*4*3*2*1)/(8*7*6*5*4*3*2*1) = 1/8

Answer:

D. 1/5,1/6,1/7,1/8

Answer:

Commutative property of algebra.

Step-by-step explanation:

We have been given two expressions:

2x+6=10

And 6+2x=10

This is the commutative property  of algebra

which is:  a+b=c  implies b+a=c

Here, a=2x ,b=6 and c=10

On Comparing the two equations with general form of commutative property we get the required result.

Answer:

24 balloons

Step-by-step explanation:

1 hour= 60 min

60 min/ 5 min= 12 min

12 min* 2 balloons= 24 balloons per hour

Answer:

The correct answer is A

Sorry if this is late but hope it helps however finds it

Answer:

q + 10 - r

Step-by-step explanation:

add q and 10 = q + 10

then subtract r from the result = q + 10 - r

Answer:

(q + 10) - r

Step-by-step explanation:

The given verbal expression is " add q and 10, then subtract  r from the results."

Add q and 10 = q + 10

subtract r from the result = (q + 10) - r

So, the final expression is (q + 10) - r

Answer:

4

Step-by-step explanation:

The equation is

x^2 - (2x + 8) = 0   where x is the number to be found.

removing the parentheses by distributing the negative:-

x^2 - 2x - 8 = 0

(x - 4)(x +2) = 0

x =  4, -2.

The value of x  must be 4 because it is positive.

Answer:

Yes he will not have any left over

Step-by-step explanation:

because 64 / 6 = 10.666666..

Answer:

21:38

Step-by-step explanation:

The answer you get is 42:76, but if you simplify it, it's 21:38 by dividing the ratio by 2.

Answer:

78 books

Step-by-step explanation:

Use proportion: If 52 is 2/3 of the books then  number of books shipped = 52 * the inverse of 2/3  which is 52 * 3/2:-

 52 * 3/2

= 156/2

= 78 books

Answer:

Proportion states that the two fractions or ratios are equal.

As per the given statement: A leaky faucet is losing water and is filling a 8-gallon bucket every 25 hours.

Let x represents the number of gallons of water that faucet leak in 13 hours.

then by definition of proportion;

[tex]\frac{8}{25} =\frac{x}{13}[/tex]

By cross multiply we get;

[tex]13 \times 8 = 25x[/tex]

Simplify:

[tex]104 = 25x[/tex]

Divide both sides by 25 we get;

[tex]x = \frac{104}{25}[/tex]

Simplify:

x = 4.16

Therefore, 4.16 number of gallons of water will the faucet leak in 13 hours

Answer:

27 muffins.

Step-by-step explanation:

We have been given that a baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold.

To find the number of muffins sold by noon let us find 45% of 60.

[tex]\text{The number of muffins sold by noon}=\frac{45}{100}\times 60[/tex]

[tex]\text{The number of muffins sold by noon}=0.45\times 60[/tex]

[tex]\text{The number of muffins sold by noon}=27[/tex]

Therefore, 27 muffins were sold by noon.

Answer:

The answer is D)

Step-by-step explanation: