Write as one logarithm. Simplify.
log5 125 – log5 25

Answer:

A

Step-by-step explanation:

Given

[tex]\frac{4}{5}[/tex] = [tex]\frac{z}{20}[/tex]

Multiply both sides by 20 to clear the fractions

16 = z → A

Answer:

A. z = 16

Step-by-step explanation:

Multiply both sides by 20 isolate the variable z.

[tex]\frac{4}{5} *\frac{z}{20}[/tex]

[tex]\frac{4}{5} *20 = \frac{z}{20} *20[/tex]

[tex]z = \frac{4}{5} *20[/tex]

Multiplying [tex]\frac{4}{5}[/tex] by 20 will give us 16.

[tex]\frac{4}{5} *\frac{20}{1} = \frac{80}{5}[/tex][tex]= 16[/tex]

Therefore, z is equal to 16.

Answer:

The length of each piece is 2.5.

Step-by-step explanation:

10/4=2.5

Answer:

2.5 ft

The drawing will help

Answer:

70 cm^2

Step-by-step explanation:

A=LW=10*7=70

Answer:

D

Step-by-step explanation:

he did not devide56 by 8

Answer:

D

Step-by-step explanation:

Jonas should have divided 56 by 8.

8x=56

8x/8 = 56/8

x = 7

Answer:

c=2

Step-by-step explanation:

7(2c-1)-3=6+6c

14c-7-3=6+6c

14c-10=6+6c

14c-6c-10=6

8c-10=6

8c=6+10

8c=16

c=16/8

c=2

Answer:

Step-by-step explanation:

[tex]7(2c-1)-3=6+6c\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(7)(2c)+(7)(-1)-3=6+6c\\\\14c-7-3=6+6c\qquad\text{combine like terms}\\\\14c+(-7-3)=6+6c\\\\14c-10=6+6c\qquad\text{add 10 to both sides}\\\\14c-10+10=6+10+6c\\\\14c=16+6c\qquad\text{subtract}\ 6c\ \text{from both sides}\\\\14c-6c=16+6c-6c\\\\8c=16\qquad\text{divide both sides by 8}\\\\\dfrac{8c}{8}=\dfrac{16}{8}\\\\c=2[/tex]

Value of ring after four years with appreciation of 4 % each year is 4445.46

Given that  

Tom bought his fiancée Marie a 3800 diamond engagement ring

Marie discovers that the value of the ring appreciates 4% each year  

Need to determine value of ring after four years

Initial value of the ring = 3800

Appreciation of 4% in value means 4% increase

After 1 years , value increases by 4%  which means  

Value after 1 year = Initial value of the ring + 4% of Initial value of the ring

[tex]\begin{array}{l}{=3800+4 \% \text { of } 3800} \\\\ {=3800+\frac{4}{100} \times 3800=3952}\end{array}[/tex]

After 2 years, value increases  by 4% of Value after 1 year which means

Value after 2 years = Value after 1 year + 4% of Value after 1 year

[tex]\begin{array}{l}{=3952+4 \% \text { of } 3952} \\\\ {=3952+\frac{4}{100} \times 3952=4110.08}\end{array}[/tex]

After 3 years, value increases  by 4%  of  Value after 2 years which means  

Value after 3 years = Value after 2 years + 4% of Value after 2 years

[tex]\begin{array}{l}{=4110.08+4 \% \text { of } 410.08} \\\\ {=4110.08+\frac{4}{100} \times 4110.08=4274.4832}\end{array}[/tex]

After 4 years , value increases  by 4%  of  Value after 1 year which means  

Value after 4 years = Value after 3 years + 4% of Value after 3 years

[tex]\begin{array}{l}{=4274.4832+4 \% \text { of } 4274.4832} \\\\ {=4274.4832+\frac{4}{100} \times 4274.4832=4,445.46}\end{array}[/tex]

Value of ring after four years with appreciation of 4 % each year is 4445.46

To calculate the future value of a ring appreciating at 4% each year for 4 years, compound interest formula is used. The ring's value after 4 years is approximately $4,445.46.

The question refers to the calculation of the future value of an investment, which is a common problem in mathematics dealing with compound interest. Tom bought an engagement ring for $3,800, and its value appreciates at a rate of 4% each year. To find the value of the ring after 4 years, we use the formula for compound interest:

Future Value = Present Value x (1 + Rate of Interest)Number of Years

Step-By-Step Calculation

After applying the compound interest formula, the value of the ring after 4 years would be approximately $4,445.46.

Answer:

41) 7 packages

42) not sure

43) 11. 8.69/.79

44) 5. 14.50/2.90

45) 13.72. subtract

Answer:

41)7 packages

42)$10.00

43)$8.69

44)5 packages

Step-by-step explanation:

41) 14 packages =$40

÷2                     ÷2

___                  ___

  7                     20

42) 28 kuna :$5.00

      28x2=56 $5.00x2=10.00

43) 1p= $0.79

$8.69/.79=11

11p=$8.69

44) So, 44 is basically the same thing as 43, but different #s. if 1s=2.90, 14.50/2.90=5

Answer:

-5.4c

Step-by-step explanation:

We're combining two "like" terms here.

It may make the problem easier to visualize if we write one of these terms over the other, as follows:

-2.6c

- 2.8c

----------

Adding, we get:

-2.6c

- 2.8c

----------

- 5.4c (answer)

x = 17

m∠JKL = 87°

m∠KJL = 58°

m∠KLJ = 35°

m∠KLM = 145°

Step-by-step explanation:

The exterior angle theorem says that the sum of two interior angles is equal to the exterior angle

In the given triangle, the interior angles are:

m∠K = (7x-32)°

m∠J = (5x-27)°

The interior angle is:

m∠L = (9x-8)°

So writing mathematically

m∠J+m∠K = m∠L

[tex]7x-32+5x-27 = 9x-8\\12x -59 = 9x - 8\\12x-9x = 59-8\\3x = 51[/tex]

Dividing both sides by 3

[tex]\frac{3x}{3} =\frac{51}{3}\\x = 17[/tex]

Now m∠JKL

= [tex]7x-32\\=7(17) - 32\\=119-32\\=87[/tex]

m∠KJL

[tex]= 5x-27\\=5(17)-27\\=85-27\\=58[/tex]

m∠KLJ

[tex]=188-9x\\=188-153\\=35[/tex]

m∠KLM

[tex]=9x-8\\=9(17) -8\\=153-8\\=145[/tex]

Hence,

x = 17

m∠JKL = 87°

m∠KJL = 58°

m∠KLJ = 35°

m∠KLM = 145°

Keywords: Angles, Triangle

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Answer:

-9 2/7 is bigger than -9.3.

Step-by-step explanation:

Imagine these two integers on a number line. On the negative side of the line, these two lie. The way I think of it is that the smaller the value is on the positive side, the bigger it is on the negative side. For example, -1 is bigger than -5. -0.5 is bigger than -1. -13.5 is bigger than -13.7.

The given fraction - 9 2/7 is bigger than the given number - 9.3.

Given the fraction is - 9 2/7

-9 2/7 = - (9 + 2/7)

Now, 2/7 is equal to approximately 0.286.

So, - 9 2/7 = - ( 9 + 2/7 ) = - ( 9 + 0.286) = - 9.286

Thus, 9.286 < 9.3

When negative quantity multiplied then inequality sign changes so,

( -1 ) ( 9.286 ) > ( -1 ) ( 9.3 )

- 9.286 > - 9.3

Therefore the given fraction - 9 2/7 is bigger than the given number - 9.3.

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Answer:

3 ≤ y ≤ 5

Step-by-step explanation:

Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour, then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hour.

Therefore, the speed (y) of Rosalie ranges from 5 mph to 3 mph including the values.  

So, the range of this relation is 3 ≤ y ≤ 5. (Answer)

We can see here that the range of this relation is: D. 3 ≤ y ≤ 5

To determine the range of this relation, let's first calculate the distances Rosalie covers during each phase of her training:

Jogging phase:

Time = 30 minutes = 0.5 hours

Speed = 5 miles per hour

Distance = Speed × Time = 5 × 0.5 = 2.5 miles

Walking phase:

Time = 60 minutes = 1 hour

Speed = 3 miles per hour

Distance = Speed × Time = 3 × 1 = 3 miles

Now, let's consider the range of distances Rosalie covered during her training:

The minimum distance she covered is 2.5 miles (jogging phase), and the maximum distance is 2.5 + 3 = 5.5 miles (jogging + walking phases).

The given options are:

A. 0 ≤ y ≤ 5

B. y ≤ 5

C. y ≥ 0

D. 3 ≤ y ≤ 5

Since the minimum distance covered is 2.5 miles and the maximum distance covered is 5.5 miles, the correct option that represents the range of this relation is:

D. 3 ≤ y ≤ 5

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Answer:

4/25 pounds of candy per person.

Step-by-step explanation:

(4/5)/5=(4/5)(1/5)=4/25

To find the unit rate, you divide the total weight of the candy (4/5 pounds) by the total number of people (5). Therefore, each person received 4/25 pound of candy.

The unit rate is found by dividing the total quantity by the total number of units. In this problem, Deon divided 4/5 pounds of candy among 5 people.

To find the amount of candy per person which is the unit rate, you divide the total weight of the candy (4/5 pounds) by the total number of people (5). So, 4/5 divided by 5 equals 4/25. Thus, each person received 4/25 pound of candy.

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Answer:

Yes she made an error. Explanation is below.

Step-by-step explanation:

Let the sample space for a six sided number cube be S

[tex]n(S) = \{1,2,3,4,5,6\}\\n(S) = 6[/tex]

Let the event of a number getting greater than two be B

[tex]n(B) = \{3,4,5,6\}\\n(B) = 4[/tex]

To find:

the probability of complement of B that is

p(~B) = ?

Solution"

First we need to solve probability for number getting greater than two

[tex]p(B) = \frac{n(B)}{n(S)}[/tex]

Now substituting the values we get

[tex]p(B) = \frac{4}{6}[/tex]

[tex]p(B) = \frac{2}{3}[/tex]

but we need complement of B so

[tex]p(\textrm{complement of B)} = 1 - p(B)\\p(\~B) = 1 - p(B)\\p(\~B) = 1 - \frac{2}{3}\\ =\frac{1}{3} \\[/tex]

P(complement of rolling a number greater than two) = [tex]\frac{1}{3}[/tex]

Answer: 5; PO

6; PM

7; MNO

8; QN

9; OQ

10; PQO

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

because, 190% as a decimal is 1.9. So 1.9 times 20 is 38. Not 380.

Please mark me brainliest

Answer:

The quotient is x -2

Step-by-step explanation:

1. Let's simplify and find out the quotient of the following division:

(x^3+3x^2-4x-12) / (x^2+5x+6)

(x³ + 3x² - 4x - 12)/ (x² + 5x + 6)

(x + 2) (x² + x - 6) / (x + 2) (x + 3) ⇒ Factorizing on the numerator and the denominator

(x² + x - 6) / (x + 3) ⇒ Eliminating (x + 2) on the numerator and the denominator

(x + 3) (x - 2) / (x + 3) ⇒ Factorizing on the numerator

x - 2 ⇒ Eliminating (x + 3) on the numerator and the denominator

The quotient is x -2

Answer:

The answer is x-2 on EDGE

Step-by-step explanation:

When subtracting with a negative number anywhere in the expression you will do something called "Same-Add-Opposite."

This means that you will keep the first number in the expression (in this case that is -2) the same:

-2 - (-3)

Then turn the subtraction sign into an addition sign.

-2 + (-3)

Finally you will take the "opposite" sign of the second number (in this case you will take the opposite of -3). When I say "opposite sign" I mean that if this number is positive it will become negative. If it was negative it will become positive.

-2 + 3

Now you must solve. When adding a positive number with a negative number you will act as if you are subtracting the two numbers, then the answer will take the sign of the largest number (disregarding the signs).

In this case the largest number is 3 (disregarding the signs) and its sign is positive. Your answer will have a negative sign.

-2 + 3

1

-2 - (-3) = 1

Hope this helped!

~Just a girl in love with Shawn Mendes

The question is incomplete, here is the complete question:

The perimeter of a rectangle is twice the sum of its length and its width, the perimeter is 40 meters and the length is 2 meters more than twice its width. What is the length?

The length of the rectangle is 14 meters

Step-by-step explanation:

The formula of the perimeter of a rectangle is P = 2(L + W), where

Assume that the width of the rectangle is x meters

∵ The width of the rectangle = x meters

∵ Its length is 2 meters more  than twice its width

- Multiply x by 2 and then add to the product 2

∴ The length of the rectangle = 2 x + 2 meters

∵ The formula of the perimeter is P = 2(L + W)

- Substitute L by 2 x + 2 and W by x

∴ P = 2(2 x + 2 + x)

- Add like terms in the bracket

∴ P = 2(3 x + 2)

- Simplify the right hand side

∴ P = 6 x + 4

∵ The perimeter of the rectangle = 40 meters

- Equate P by 40

∴ 6 x + 4 = 40

- Subtract 4 from both sides

∴ 6 x = 36

- Divide both sides by 6

∴ x = 6

∴ The width of the rectangle is 6 meters

∵ The length = 2 x + 2

- Substitute x by 6

∴ The length = 2(6) + 2 = 12 + 2 = 14 meters

The length of the rectangle is 14 meters

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Answer:

[tex]y<\frac{1}{4}x+3[/tex]

Step-by-step explanation:

we know that

The solution of the inequality in the graph is the shaded area below the dashed line

The slope of the dashed line is positive

The y-intercept of the dashed line is (0,3)

The dashed line pass through the points (0,3) and (4,4)

The slope of the dashed line is

[tex]m=(4-3)/(4-0)=1/4[/tex]

The equation of the dashed line in slope intercept form is

[tex]y=\frac{1}{4}x+3[/tex]

therefore

The inequality represented by the graph is

[tex]y<\frac{1}{4}x+3[/tex]

Answer: 1.4862

Step-by-step explanation: To find 6% of 24.77, first write 6% as a decimal by moving the decimal point two places to the left to get 0.06.

Next, the word "of" means multiply so we will multiply 0.06 by 24.77.

(0.06) (24.77) = 1.4682

Therefore, 6% of 24,77 is 1.4862.

Number of projects that can be presented is 15.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that

Time alloted for each team = 1/5

Total time for the presentation = 3 hours

Division equation can be written as :

Number of projects = 3 / (1/5), where 3 hours is divided into 1/5 equal parts.

Number of projects = 15

Multiplication equation can be written as :

Number of projects = 3 × 5 = 15

Hence 15 projects can be presented.

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The complete question is as follows:

Teams of students in Mr. Reed’s classroom are presenting Social Studies projects. Each team has 1/5 hour for their presentation.

Suppose Mr Reeds class has 3 hours for presentations. How many projects can be presented show your solution by writing both a division equation and a multiplication equation.

Answer:

Step-by-step explanation:

The expression given here is

                         [tex]x^2+19x+2[/tex]

Now if we differentiate this expression we can find the portions in its graph where it is increasing and decreasing or neither both.

If the differentiated expression is less than zero with the constant infront of highest degree positive then in the values corresponding to that [tex]x[/tex] the graph is decreasing.

If the differentiated expression is greater than zero with the constant infront of highest degree positive then in the values corresponding to that [tex]x[/tex] the graph is increasing.

  [tex]\frac{d}{dx}(x^2+19x+2)[/tex]

⇒[tex]2x+19[/tex]

For [tex]2x+19>0[/tex] ⇔[tex]x>\frac{-19}{2}[/tex]

For [tex]2x+19<0[/tex] ⇔[tex]x<\frac{-19}{2}[/tex]

Now for us the horizontal span is asked from 0 to 10 for the expression which is from [tex]x=0[/tex] to [tex]x=10[/tex] ,in which portion the value of the expression is strictly increasing so the vlaue increases from [tex]0+0+2=2[/tex] to [tex]10^2+190+2=292[/tex].

5/16 cups___1 muffin

5/4 cups___X=4 muffins

(5/4) / (5/16) = 4

Answer:

X=5

y=2

Step-by-step explanation:

x+4y=13

5+4(2)=13

x-y=3

5-2=3

X=5

Y=2

X+4Y=13

X+Y=13/4=3

X(5)+4Y(*2)=13

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

Explanation:

Graph each inequality given on the same xy coordinate system. You should get what you see in the attached image below. The red shaded region represents all points that make every inequality mentioned to be a true statement. Points A, B, C are vertex points of the boundary region.

A = (2,6)

B = (5,3)

C = (2,3)

For each point A,B,C, plug in the (x,y) coordinates into the C(x,y) function given

------

For point A, (x,y) = (2,6) so x = 2 and y = 6

C(x,y) = (1/2)*x - y

C(2, 6) = (1/2)*2 - 6

C(2, 6) = -5 we'll use this value later

-----

Repeat for point B = (5,3)

C(x,y) = (1/2)*x - y

C(5,3) = (1/2)*5 - 3

C(5,3) = -0.5 we'll use this value later

----

Repeat for point C = (2,3)

C(x,y) = (1/2)*x - y

C(2,3) = (1/2)*2 - 3

C(2,3) = -2 we'll use this value later

-----

In the previous three sections above, we got the following outputs: -5, -0.5, -2

We see that -5 is the smallest and -0.5 is the largest

Therefore, -5 is the min and -0.5 is the max

Answer:

[tex]p=\frac{4\sqrt{10}}{5}[/tex]  

Step-by-step explanation:

step 1

Find the radius of the circle

Remember that AB is a tangent to the circle at point B

so

AB is perpendicular to OA

The radius of the circle is equal to the segment OA

In the right triangle OAB

[tex]sin(30\°)=\frac{OA}{OB}[/tex]

[tex]OA=(OB)sin(30\°)[/tex]

substitute the values

[tex]OA=(16)0.5=8\ units[/tex]

step 2

Find the value of p

In the right triangle OPQ

see the attached figure to better understand the problem

Applying the Pythagoras Theorem

[tex]OP^2=OQ^2+PQ^2[/tex]

substitute the values

Remember that OP is the radius

[tex]8^2=p^2+(3p)^2[/tex]

[tex]64=p^2+9p^2[/tex]

[tex]64=10p^2[/tex]

[tex]p^2=\frac{64}{10}[/tex]

[tex]p=\frac{8}{\sqrt{10}}[/tex]

simplify

[tex]p=\frac{4\sqrt{10}}{5}[/tex]  

Answer:

one million, one hundred fourteen thousand, forty

Step-by-step explanation:

Answer:

7. The numbers 14/81 are relatively prime

8. b=3

9. 0.00001

19. 11

Step-by-step explanation:

7. Relatively prime numbers have no common factors. We only have to factor each number and compare

14=2*7

35=5*7

38=2*19

81=9*9

91=7*13

The first two numbers have 7 in common

The second have 2 in common

The third set have no common factors

The fourth set have 7 in common

The numbers 14/81 are relatively prime

8. [tex]b^{-3}=\frac{1}{27} => b^3=27 => b=\sqrt[3]{27} =3[/tex]

9. [tex]10^{-5}=\frac{1}{100000}=0.00001[/tex]

10. 100,000,000,000=10*10*...10 as many times as zeroes there are, so

[tex]100,000,000,000=10^{11}[/tex]