Problem Set
1. Use the set of ordered pairs below to answer each question.
{(4,20), (8,4),(2,3), (15,3), (6,15),(6,30), (1,5),(6,18),(0,3)}
a. Write the ordered pair(s) whose first and second coordinate have a greatest common factor of 3.
b. Write the ordered pair(s) whose first coordinate is a factor of its second coordinate.
c. Write the ordered pair(s) whose second coordinate is a prime number.

Answer:

If each youth saves $10 daily, their weekly savings would be $1400. So they donated $1400 to the church.

Step-by-step explanation:

Let the daily pay plan for each youth be $y

Daily pay plan for 20 youth = $20y

Weekly pay plan = 7×20y = $140y

Assuming each youth saves $10 daily

Daily savings for 20 youth = 20×$10= $200

Weekly savings for 20 youth = 7×$200= $1400

If they used the early pay plan ($140y) to go swimming, they saved $1400 which they donated to the church.

Answer:

$375 saved or roughly 33%.

Step-by-step explanation:

With daily plan;

(15)4.00 = 60.00  

(25)60.00 = $1,500.00

If the youth group saved up enough for each of them to swim 15 times and 25 students are attending, they originally had $1,500.00 saved for the trip.  

With early pay;

(25)45.00 = $1,125.00

1,500.00 - 1,125.00 = $375 saved or roughly 33%.

Hope this helps! And please, do not copy-paste this answer. Write it in your own words, thanks <33

Answer:

The two numbers are

518

694

Step-by-step explanation:

As per requirements the two equations will be

X+Y=1212

X-Y=518

When we subtract these equations we get

X=1212-518

X=694

Now put the X value and find the Y value in any equation

X+Y= 1212

Y=1212-X

Where X = 694

Y=1212-694

Y=518

X=694 and Y=518

Answer:

answer is 865.

Step-by-step explanation:

865+347 is 1212 an the diff is 518.

and the largest number out of 865 and 347 is 865

Answer:

The simplified fractional equivalent is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

we know that

A terminating decimal is a decimal that ends. So, it's a decimal with a finite number of digits.

we have

[tex]0.25[/tex]

Let

[tex]x=0.25[/tex]

Multiply by 100 both sides

[tex]100x=25[/tex]

Divide by 100 both sides

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

Simplify

Divide by 25 both numerator and denominator

[tex]x=\frac{1}{4}[/tex]

Answer: e) 2(n+1)

Step-by-step explanation:

De las opcionas dadas, e) 2(n+1) es la correcta.

Empecemos por explicar la siguiente regla:

(número par)(número par)=número par

(número par)(número impar)=número par

(número impar)(número impar)=número impar

Ahora bien, en la expresión  2(n+1) el resultado de lo que se encuentra dentro del paréntesis va a ser multiplicado por 2, el cual es un número par, por lo tanto el resultado final va a ser un número par independientemente de si lo que está en el paréntesis es par o impar.

Por ejemplo, si elegimos 1 que es impar:

2(1+1)=2(2)=4

El resultado es par.

Si probamos con las otras opciones, los resultados serán impares:

a) 2n +1

2(1)+1=2+1=3 impar

b) n(n+2)

1(1+2)=1(3)=3 impar

c) n+(n-1)

1+(1-1)=1+0=1 impar

Answer:

9/10 ( or 0.9)

Step-by-step explanation:

quotient of 3/4 and 5/6

= 3/4 ÷ 5/6

= 3/4 x 6/5

= 18/20

= 9/10 ( or 0.9)

Answer:

9/10

Step-by-step explanation:

Answer:

5(4-1)

Step-by-step explanation:

5(4-1)

20-5

5x4= 20

5x1= 5

Answer:

2,1

Step-by-step explanation:

y=-3x+7

y=-3(2)+7

y=-6+7

y=1

so (2,1)

Answer:

(-8 - 4)/(-4 - 0) = -12/-4= 3

y - 4 = 3(x - 0)

y - 4 = 3x - 0

y = 3x + 4

the answer is c

Answer:

The number of apple bought is 3

The number of orange bought is 2  

Step-by-step explanation:

Given as :

The price of each apple = 27 p = 27 × 0.01 pound = 0.27 pound

The price of each orange = 36 p = 36 × 0.01 pound = 0.36 pound

The Total money paid for the fruits = 1.53 pounds

Let The Total number of apple bought = a

And The Total number of orange bought = o

Now, According to question

Total money paid for the fruits = Total number of apple bought × price of each apple + Total number of orange bought × price of each orange

Or, 0.27 a + 0.36 o = 1.53               ......A

Here The Total quantity of fruits bought is not given, so apply hit and trial method to calculate total number of each fruit

Let The a = 1   and  o = 1

So,  0.27 × 1 + 0.36 × 1 = 1.53    

∴   0.63 ≠ 1.53

Again

Put a = 2 , o = 2

So,  0.27 × 2 + 0.36 × 2 = 1.53    

∴   1.26 ≠ 1.53

Again

Put a = 3 , o = 3

So,  0.27 × 3 + 0.36 × 3 = 1.53    

∴   1.89 ≠ 1.53

Now, Let a = 3  , o = 2

So,  0.27 × 3 + 0.36 × 2 = 1.53    

∴   1.53 = 1.53

so, from hit and trial method , we get the number of apple = a = 3

And he number of orange = o = 2

Hence, The number of apple bought is 3

And The number of orange bought is 2 . Answer

Answer: [tex]2z^{2} + 14 z +6[/tex] and [tex]2(z^{2} + 7 z +3)[/tex]

Step-by-step explanation:

We have the following expression:

[tex]z+(z+6)z+(z+6)z+(z+6)[/tex]

Let's solve it:

[tex]z+z^{2}+6z+z^{2}+6z+z+6[/tex]

We have this result:

[tex]2z^{2} + 14 z +6[/tex]

However if we apply coomon factor 2, we will have a simplified result:

[tex]2(z^{2} + 7 z +3)[/tex]

Answer:

76

Step-by-step explanation:

if w=45, you'd get 2(45-7) by replacing the variable (w) with its value (45)

so first you'd distribute 2 to the 45 and the 7

now it'd be:

90-14=76

so the answer would be 76! :)

Answer:

The answer is 76

Step-by-step explanation:

First you swap in the number like so: 2(45-7)

Then you figure out what's is the parentheses first going with PEMDAS like so : 2(38)

Finally you multiply the number getting your final answer which is :76

Answer:

y-6=4(x-4)

Step-by-step explanation:

y-y1=m(x-x1)

y-6=4(x-4)

Answer:

  (x, y) = (-1.8, -1.4)

Step-by-step explanation:

Modern graphing calculators make it trivially simple to solve many problems by graphing. It has become my favorite method.

The graph shows the solution to be (x, y) = (-1.8, -1.4).

___

If you're graphing by hand, it is usually convenient to start with the y-intercepts, then draw the lines with the required slopes. These equations are written in slope-intercept form, making that approach relatively simple.

The first equation has a y-intercept of (0, 4) and a slope of 3. So, another point on the graph will be left 1 and down 3 (as opposed to right 1 and up 3). That point is (-1, 1).

The second equation has a y-intercept of (0, -5) and a slope of -2. So, another point on the graph of that will be left 1 and up 2, to (-1, -3)

Answer:

∠A ≈ 19.47°

Step-by-step explanation:

As you know , the angle that tangent makes with the radius at the point of tangency is 90°.

∴∠OKA = 90°

As  AO = 15 and OK = 5 ,

[tex]sin(A) = \frac{OK}{AO}[/tex]

[tex]sin(A) = \frac{5}{15} [/tex]

[tex]sin(A) = \frac{1}{3} [/tex]

∠A = [tex]sin^{-1} (\frac{1}{3} )[/tex]

∠A ≈ 19.47°

Answer:

[tex]\mathbf{m\angle A = sin^{-1}(\frac{1}{3}) \approx 19.47^{\circ}}[/tex]

Step-by-step explanation:

This question involves some basic knowledge of trigonometric function. The following formula only works for right angled triangles.

[tex]\mathbf{sin(x) = \frac{perpendicular}{hypotenuse}}[/tex]

In ΔAKO,

m∠AKO = 90°

Therefore ΔAKO is a right angled triangle. If we take ∠A into consideration then base will be AK, perpendicular will be OK and hypotenuse will be AO.

AO = 15

OK = 5

[tex]\therefore \mathrm{sin(\angle A) = \frac{OK}{AO} = \frac{5}{15} = \frac{1}{3}}[/tex]

[tex]\mathrm{sin(\angle A)=\frac{1}{3}}[/tex]

[tex]\mathrm{\angle A=sin^{-1}(\frac{1}{3})}[/tex]

To calculate [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] use scientific calculator

value of [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] is approximately equal to 19.47°

Therefore [tex]\mathbf{m\angle A \approx 19.47}[/tex]

(NOTE : When a line passing through center of a circle, is drawn to a tangent at the point of tangency then the angle made between then is 90°

Therefore m∠AKO = 90°)

Answer:

D

Step-by-step explanation:

We require to calculate the volume (V) of the cone and sphere.

The volume of a cone is calculated as

V = [tex]\frac{1}{3}[/tex]πr²h ( r is the radius and h the height )

Here diameter = 5, hence r = 5 ÷ 2 = 2.5, thus

V = [tex]\frac{1}{3}[/tex]π × 2.5² × 8 ≈ 52.36 cm³

The volume of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex]πr³ ( r is the radius )

Here diameter = 5, hence r = 5 ÷ 2 = 2.5, thus

V= [tex]\frac{4}{3}[/tex]π × 2.5³ ≈ 65.45 cm³

Since volume of the sphere is greater than the volume of the cone

Thus when the ice cream melts it will overflow → D

Answer:

y=-2x

Step-by-step explanation:

Answer:

y+2x=8

Step-by-step explanation:

when you put this in slope intercept form it will equal y=-2x+8 . Parallel lines need to have the same slope

Answer:

The y-intercept of the line is 34.

Step-by-step explanation:

There are few points on the z-y plane through which a straight line passes.

The points are (-56,66), (-42,58) and (-28,50).

Now, take the first two points to get the equation of the straight line.

The equation is [tex]\frac{y - 58}{58 - 66} = \frac{z - (-42)}{-42 - (- 56)}[/tex]

⇒ [tex]\frac{y - 58}{- 8} = \frac{z + 42}{14}[/tex]

⇒ 14(y - 58) = - 8(z + 42)

⇒ [tex]y - 58 = - \frac{8}{14}z - 24[/tex]

⇒ [tex]y =  - \frac{8}{14}z + 34[/tex]

This equation is in slope-intercept form.

Hence, the y-intercept of the line is 34. (Answer)

Answer:

x= 65 degrees

Step-by-step explanation:

If the triangles vertices are marked CDE (d as the right angle and c as the leftmost vertex) then:

Alternate interior angles

⇒m∠ACE=85 degrees

m∠ACD=25 and  m∠ACD+m∠DCE=m∠ACE=85 degrees

⇒ 25 + m∠DCE= 85 ⇒ m∠DCE=60 degrees

Since the sum of the angles in a triangle is 180 degrees

⇒ 60 + 90 + m∠DEC = 180 ⇒ m∠DEC= 30 degrees

Finally, since ∠BEC is supplementary to the given 85 degree angle

⇒ 30 + 85 + x = 180 ⇒ x=65

Answer:

[tex]\huge\boxed{x = 65 \ \text{degrees}}[/tex]

Step-by-step explanation:

We can use angle relationships to find the measure of [tex]x[/tex] here.

Let's assume that the triangle has the points ABC, where m∠a is the leftmost angle, m∠b is the right angle, and m∠c is the rightmost angle (I've labeled it in the attached picture).

We have to realize here that a and b are parallel lines. This means that the angles on one side will be equivalent to the other as long as the triangle in the center is symmetrical along both.

It's not. However, we can make it symmetrical by realizing that the 85° angle is the exact same as Line A AC. These are alternate interior angles, meaning their angle measurements will be the same. So Line A A C is also 85°.

Line A A C covers the area even in the triangle. Since we know the total measure and the measure outside the triangle, we can find the measure of m∠a.

[tex]25 + a = 85\\\\a = 85-25\\\\a = 60[/tex]

Now we know that m∠a is 60°. We also know that m∠b is a 90° angle. All triangle angles add up to 180°. Since we know two out of the three, let's find the measure of m∠c by adding up what we know and subtracting from 180.

[tex]60+90+c=180\\\\150+c=180\\\\c=180-150\\\\c=30[/tex]

Now that we know m∠c, we can note that the 85° angle, m∠a, and x are supplementary. This means their angle lengths add up to 180°. Since we know two out of the three, we can do a process similar to finding the missing triangle angle.

[tex]85+30+x=180\\\\115+x=180\\\\x=180-115\\\\x = 65[/tex]

Therefore, x is 65°.

Hope this helped!

Step-by-step explanation:

3×+3(x+y) is equal to 6x+3y

Answer:

B

Step-by-step explanation:

Quotient means divide. I just used a calculator to divide it.

Answer:

(3x − 4) (x + 2)

Step-by-step explanation:

3x² + 2x − 8

Factor using AC method.

3 × -8 = -24

Factors of -24 that add up to 2 are -4 and 6

Divide by 3 and reduce: -4/3 and 6/3 = 2/1

(3x − 4) (x + 2)

Answer:

The numbers of weeks for which both Ava and Addison have same amount of money saved is 100 weeks .

Step-by-step explanation:

Given as :

The amount of money having with Ava at starting = $100

The money that Ava is saving each week = $5

The amount of money having with Addison at starting = $200

The money that Addison is saving each week = $4

Now, Let The numbers of weeks for which both Ava and Addison have same amount of money saved = n weeks

Now, According to question

The amount of money having with Ava at starting + (The money that Ava is saving each week × numbers of weeks) = The amount of money having with Addison at starting + (The money that Addison is saving each week × numbers of weeks)

Or, $100 + $5 × n = $200 + $4 × n

Or, $5 × n - $4 × n = $200 - $100

Or, n = 100

So,  The numbers of weeks for which both Ava and Addison have same amount of money saved = n = 100 weeks

Hence,The numbers of weeks for which both Ava and Addison have same amount of money saved is 100 weeks . Answer

Answer:

18.3 ( when EPS is 45 cents), otherwise there is none of these

Step-by-step explanation:

PE = Current Price / EPS

current Price = $ 8.22 = 822 cents

EPS = .45 cents (?) ... is it 45 cents ?

if it is 45 cents : PE = 822 / 45 = 18.26 ≈ 18.3

The required PE ratio of the Zolt's is given as 18.3. Option A is correct.

Given that,
Zolt Inc. (zolt) stock is selling for $8.22 per share with an EPS of .45 cents per share.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

PE = Current Price: EPS
PE = Current Price / EPS

Current Price = $ 8.22 = 822 cents

EPS = 0.45 cents = 45 cents

it is 45 cents per PE
So Ratio = 822 / 45 = 18.3

Thus, the required PE ratio of the Zolt's is given as 18.3. Option A is correct.

Learn more about ratios here:

brainly.com/question/13419413

#SPJ5

Answer:

14:26, 21:39, 28:52, 35:65, 42:78, 41:91

Step-by-step explanation:

All of the above are equivalent ratios. These are only a few. More can be found by just simply multiplying 7 by any amount, and 13 by any amount.

Ratios that are equivalent to 7:13 from the given options are 21:39, 28:52, and 14:26. Option A, C, D is correct.

To find equivalent ratios, we need to multiply or divide both terms of the ratio by the same non-zero number. Let's go through the options provided:

Therefore, the equivalent ratios are 21:39, 28:52, and 14:26.

Hence, A. C. D is the correct option.

The complete question is:

Which are equivalent ratios to 7:13?

A) 21:39

B) 72:128

C) 28:52

D) 14:26

E) 36:48

Answer:

4/-3

Step-by-step explanation:

To find the slope

y2 - y1 / x2 - x1 =

12 - -4          16

---------- =     ----

1 - 13           -12

Simplify by dividing both parts by 4

4/-3 is your slope :)

Answer:

Step-by-step explanation:

I've answered this question already.

Answer:

B. 70

Step-by-step explanation:

[tex]7 \div 12 = \frac{7}{12} \\ 120 \times \frac{7}{12} = 70[/tex]

Answer:

B

Step-by-step explanation:

Given that for every 12 seeds, 7 grew into plants

Then for 120 seeds, that is 120 ÷ 12 = 10 times as many seeds, thus

number growing into plants = 10 × 7 = 70 → B

Answer:

[tex]x \approx -0.208[/tex]

Step-by-step explanation:

By applying logarithms to each side of the equation and some algebraic handling:

[tex]x+2 = \log_{4} 12[/tex]

[tex]x + 2 = \frac{\log_{10} 12}{\log_{10} 4}[/tex]

[tex]x = \frac{\log_{10}12}{\log_{10}4} - 2[/tex]

[tex]x \approx -0.208[/tex]

Final answer:

To solve the equation

for x, you can use the change of base formula log base b of y equals log y over log b. By following the steps, you should find the solution to be x ≈ -0.086.

Explanation:

To solve the equation

for x, we can use the change of base formula log base b of y equals log y over log b. Let's solve it step by step:

Therefore, the solution to the equation

is approximately x = -0.086.

Answer:

The blue portion of the flag is actually 2/6 or 1/3 of the flag

Step-by-step explanation:

If you look at the size of the blue portion of the line it takes up twice the space as the white part. Imagine a small line drawn through the middle of the blue rectangle, now you can see that the flag is split up into 6 parts, rather then 5! Since we now have 2/6 of the flag being taken up by blue, that can be reduced down to 1/3 of the flag covered in blue.