Trent lifts weights 7 days a week. He spends 18 minutes lifting weights on Monday, 29 minutes on Tuesday, 40 minutes on Wednesday, and 51 minutes on Thursday. If this pattern continues, how many minutes will Trent lift weights on Saturday? ​

Answer:

The required points of the given line segment  are ( - 1, - 5 ).

Step-by-step explanation:

Given that the line segment AB whose midpoint M is ( 3, -2 ) and point A is ( 7, - 9), then we have to find point B of the line segment AB -

As we know that-

If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and  ( [tex]x_{2}, y_{2}[/tex] ) then the mid points M are-  

M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex]  , [tex]\frac{ y_{1} + y_{2} }{2}[/tex] )

Here,

Let A ( 7, - 9 ), B ( x, y ) with midpoint M ( 3, - 2 ) -

then by the midpoint formula M are-

( 3, - 2 )  = (  [tex]\frac{7 + x}{2}[/tex] , [tex]\frac{ - 9 + y}{2}[/tex] )

On comparing x coordinate and y coordinate -

We get,

( [tex]\frac{ 7 + x}{2}[/tex] = 3  , [tex]\frac{- 9 + y}{2}[/tex]  = - 2)

( 7 + x = 6, - 9 + y = - 4 )

( x = 6 - 7, y = - 4 + 9 )

( x = - 1, y = -5 )

Hence the required points  A are ( - 1, - 5 ).

We can also verify by putting these points into Midpoint formula.

Answer:

[tex]12x+3y\leq 60[/tex]

Step-by-step explanation:

Let

x ----> the numbers of trophies you can buy

y ----> the numbers of medals  you can buy

we know that

The term "at most" means "less than or equal to"

so

The number of trophies multiplied by $12 plus the number of medals multiplied by $3 must be less than or equal to $60

The inequality that represent this situation is

[tex]12x+3y\leq 60[/tex]

[tex]3x + 12y\leq 60[/tex]

Step-by-step explanation:

Answer:

22 4/5 yards

Step-by-step explanation:

(7 3/5) x 3 = 22 4/5

To convert 7 3/5 feet to yards, you use the conversion 1 yard = 3 feet. After converting the mixed number to an improper fraction, you divide by 3, yielding the answer 2 8/15 yards, which corresponds to option C.

To convert feet to yards, we can use the conversion factor that 1 yard is equal to 3 feet. Since the student needs to find out how many yards are in 7 3/5 feet, we can convert mixed numbers to improper fractions to simplify the calculation.

The mixed number 7 3/5 can be converted to an improper fraction by multiplying the whole number 7 by the denominator 5 and adding the numerator 3, then placing the result over the original denominator: (7 * 5) + 3 = 35 + 3 = 38, so 7 3/5 becomes 38/5.

To convert 38/5 feet to yards, divide by 3 because there are 3 feet in 1 yard:

38/5 feet * 1 yard/3 feet = (38/5)/3 = 38/5 * 1/3

This simplifies to 38/5 * 1/3 = 38/15 yards

Then divide 38 by 15 to get 2 with a remainder of 8, so we have 2 and 8/15 yards.

Therefore, the answer is C. 2 8/15 yards.

Answer:

T1 =2 , Tn = 1 /tn-1 For The Geometricseries 6 + 3 + 3/2 + 3/4 + .

Step-by-step explanation:

Answer:

2, 5, 8, 11, 14

Step-by-step explanation:

Find the first 5 terms by substituting n = 2, 3, 4, 5 into the recursive formula

t₂ = t₁ + 3 = 2 + 3 = 5

t₃ = t₂ + 3 = 5 + 3 = 8

t₄ = t₃ + 3 = 8 + 3 = 11

t₅ = t₄ + 3 = 11 + 3 = 14

The first 5 terms are 2, 5, 8, 11, 14

Answer: 20

Step-by-step explanation: For every 6 adult camels there are 5 baby camels so if you add both together, you get 11 and if you multiply that times 4 you get 44. Now you multiply 4 times the 5 baby camels to go your answer, 20.

There are 20 baby camels at the zoo.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Let x be the number of groups of adult and baby camels, each consisting of 6 adult camels and 5 baby camels. Then we know that:

The total number of adult camels is 6x.

The total number of baby camels is 5x.

The total number of adult and baby camels is 44.

Therefore, we can write the equation:

6x + 5x = 44

Simplifying, we get:

11x = 44

Dividing both sides by 11, we get:

x = 4

So there are 4 groups of adult and baby camels. To find the number of baby camels, we can multiply the number of groups by the number of baby camels in each group:

5x = 5(4) = 20

Therefore, there are 20 baby camels at the zoo.

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To find the value of x for the box of cereal, set the given expression for the surface area equal to 192 and solve for x.

To find the value of x, we need to set the given expression for the surface area of the box equal to 192 and solve for x. So, we have:

2x^2 + 48x + 88 = 192
2x^2 + 48x - 104 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's factor it:

(2x - 4)(x + 26) = 0

Setting each factor equal to zero and solving for x, we get:

2x - 4 = 0, x = 2
x + 26 = 0, x = -26

So, the possible values of x are 2 and -26. However, since the dimensions of a box cannot be negative, the value of x for the box of cereal is 2.

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Answer:

5/3

Step-by-step explanation:

30/18=5/3

Answer:

B)

Step-by-step explanation:

Do the zero property.

x-7=0, x+6=0

x=0+7=7,

x=0-6=-6

Answer:

b 100% true

Step-by-step explanation:

Answer:

Antarctica's highest recorded temperature was 15 degrees.

Step-by-step explanation:

I am going to say that Antarctica highest recorded temperature is x.

I suppose there is a small typing mistake.

It is that the difference between Antarctica highest recorded temperature and this is 49.44.

So we have that x - (-34.44) = 49.44 instead of -34.44 - x = 49.44, which would lead to a highest temperature way lower than the one recorded in this winter.

Sooo

x - (-34.44) = 49.44

x + 34.44 = 49.44

x = 49.44 - 34.44

x = 15

Antarctica's highest recorded temperature was 15 degrees.

Answer:

f = 4 e = -2

Step-by-step explanation:

e - 2f = -10

8e + 4f = 0

Solve by substitution

8e + 4f = 0

8e = -4f

e = -0.5f

Substitute into e - 2f = -10

-0.5f - 2f = -10

-2.5f = -10

2.5f = 10

f = 4

Substitute into 8e + 4f = 0

8e + 16 = 0

8e = -16

e = -2

Answer:

e=-2, f=4. (-2, 4).

Step-by-step explanation:

e-2f=-10

8e+4f=0

-------------

e=-10+2f

e=2f-10

8(2f-10)+4f=0

16f-80+4f=0

20f=0+80

20f=80

f=80/20

f=4

e-2(4)=-10

e-8=-10

e=-10+8

e=-2

What is the solution to the following equation?

х+ (-21) = 8

О А. x= 27

B. х = 29

с.   х = 13

D. х = 17

Option B

The solution to given equation is x = 29

Given that we have to find the solution of given equation

Given equation is x + (- 21 ) = 8

The value of the variable is found by adding, subtracting, multiplying or dividing both sides of the equation to simplify the equation and isolate the variable.

The goal is to have the variable on one side of the equation and numbers on the other.

From given equation,

x + ( -21) = 8

Let us first remove the brackets around -21

We know when we multiply a positive sign number with negative sign number, we get a negative sign number

x + 1( - 21 ) = 8

x - 21 = 8

Move -21 from L.H.S to R.H.S

x = 21 + 8

x = 29

Thus solution to given equation is x = 29 Thus Option B is correct

Answer:

5 1/4 or 5.25

Step-by-step explanation:

Multiplying fractions means that we can multiply the numerator by the numerator and the denominator by the denominator straight across without needing a common denominator.

3*7 = 21

4*1 = 4

We end up with the improper fraction 21/4. We can convert this into a mixed number.

Because 4 goes into 21 a total of 5 times with 1 left over, we end up with the mixed number of 5 1/4, or as a decimal, 5.25

Answer:

t=44°

Step-by-step explanation:

The sum of the interior angles of any pentagon is always 540 degrees.

Let's set up an equation with this information: (all figures are in degrees)

[tex]t+3t+t+32+149+139=540[/tex]

Now we combine all like terms.

[tex]5t+320=540[/tex]

Now begin to isolate t be subtracting 320 from both sides.

[tex]5t=220[/tex]

Finally divide both sides by 5 to isolate t.

t=44°

Answer:

Multiples:

2: 2 4 6 8 10 12 14 16 18 20

3: 3 6 9 12 15 18 21 24 27 30

The LCM is 6 (underlined)

Answer:

Step-by-step explanation:

Letting "a" and "c" represent the costs of adult tickets and child tickets, the problem statement gives us two relations:

  3a +5c = 52

  2a +4c = 38

__

We can solve this system of equations using "elimination" as follows:

Dividing the first equation by 2 we get

  a +2c = 19

Multiplying this by 3 and subtracting the first equation eliminates the "a" variable and tells us the price of a child ticket:

  3(a +2c) -(3a +4c) = 3(19) -(52)

  c = 5 . . . . . . collect terms

  a +2·5 = 19 . . substitute for c in the 3rd equation above

  a = 9 . . . . . . subtract 10

One adult ticket costs $9; one child ticket costs $5.

Answer:

The probability that 5 chosen bagels of which exactly 3 are Asiago cheese = 0.3087 or 30.87%

Step-by-step explanation:

Given:

Total  bagels brought to school = 10

Number of Asiago cheese bagels = 7

To find the probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese.

Solution:

Let probability of choosing an Asiago cheese bagel be the successful event.

Probability of choosing one Asiago cheese bagels = [tex]\frac{7}{10}=0.7[/tex]

Probability of success = 0.7

Probability of failure ( not choosing an Asiago cheese bagel) = 1 - Probability of success = [tex]1-0.7=0.3[/tex]

Using Bernoulli Trials

To calculate the binomial probability of obtaining  exactly [tex]r[/tex] events in [tex]n[/tex] trials the formula used is:

⇒ [tex]nCr.p^r.q^{(n-r)}[/tex]

where [tex]p\rightarrow[/tex] Probability of success

[tex]q\rightarrow[/tex] Probability of failure

Thus,  probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese can be calculated as :

⇒ [tex]5C3(0.7)^3(0.3)^2[/tex]

⇒ [tex]\frac{5!}{(5-3)!3!}(0.343)(0.09)[/tex]

⇒ [tex]\frac{5!}{(2)!3!}(0.343)(0.09)[/tex]

⇒ [tex]10(0.343)(0.09)[/tex]

⇒ [tex]0.3087\ or\ 30.87\%[/tex] (Answer)

Answer:

Step-by-step explanation:

Answer:

[tex]3,462\ bacteria[/tex]

Step-by-step explanation:

In this problem we have a exponential function of the form

[tex]y=a(b^x)[/tex]

where

x is the time in hours

y is the numbers of bacteria

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

we have that

[tex]a=3,000\ bacteria[/tex]

For x=8, y=3,300

substitute in the exponential function

[tex]3,300=3,000(b^8)[/tex]

solve for b

[tex]1.1=(b^8)[/tex]

[tex]b=\sqrt[8]{1.1}[/tex]

[tex]b=1.0120[/tex]

Find the value of r

[tex]r=b-1=1.0120-1=0.0120=1.20\%[/tex]

The equation is equal to

[tex]y=3,000(1.012^x)[/tex]

For x=12 hours

substitute the value of x in the equation

[tex]y=3,000(1.012^{12})[/tex]

[tex]y=3,462\ bacteria[/tex]

Answer:

40x20+4x3+

2347

32

Step-by-step explanation:

Let's simplify step-by-step.

4x3+12+14+40x20−32+

43

32

+90−12

=4x3+12+14+40x20+−32+

43

32

+90+−12

Combine Like Terms:

=4x3+12+14+40x20+−32+

43

32

+90+−12

=(40x20)+(4x3)+(12+14+−32+

43

32

+90+−12)

=40x20+4x3+

2347

32

Answer:

Step-by-step explanation:

=40x^20+4x^3+2347/32

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Answer:

(a) 24 cents.

(b) The slope is: [tex]24[/tex]

Step-by-step explanation:

(a) Notice that the x-axis is labeled as "Weight (ounces)" and the y-axis is labeled as "Cost (cents)".

You can identify that when:

[tex]x=1;y=24[/tex]

[tex]x=2;y=48[/tex]

[tex]x=3;y=72[/tex]

Then, you can determine that the cost of the cheese increases 24 cents for each ounce Dale buys.

(b) The slope can be found with the following formula:

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

If you choose two points on the line, for example the points (0,0) and (2,48), and you substitute the corresponding coordinates into the formula, you get that the slope of the line is:

[tex]m=\frac{0-48}{0-2}\\\\m=24[/tex]

Answer:

y = 20

Step-by-step explanation:

Since AB and AC are congruent then the triangle is isosceles, thus

∠B = ∠C = 25°

To find ∠A subtract the sum of the 2 angles from 180°

∠A = 180° - (25 + 25)° = 180° - 50° = 130°, thus

3y + 70 = 130 ( subtract 70 from both sides )

3y = 60 ( divide both sides by 3 )

y = 20

The right answer is Option C.

Step-by-step explanation:

Given inequality is

6(2x-1)  > 24

Solving the inequality

[tex]6*2x-1*6>24\\12x-6>24[/tex]

Adding 6 on both sides

[tex]12x-6+6>24+6\\12x>30[/tex]

Dividing both sides by 12

[tex]\frac{12x}{12}>\frac{30}{12}\\x>\frac{5}{2}[/tex]

Therefore,

[tex]x>\frac{5}{2}[/tex]

The right answer is Option C.

Keywords: inequality, division

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Answer:

217.6 mg of medicine

Step-by-step explanation:

13.6 kilograms in 30 pounds

13.6*16

Building B offers more square feet per employee

Building B offers 2.2375 square feet more space for 1 employee than building A

Solution:

Building A has 7500 square feet of office space for 320 employee

Let us find the square feet needed for 1 employee

[tex]\text{ square feet needed for 1 employee } = \frac{7500 square feet}{320 employee}[/tex]

[tex]\text{ square feet needed for 1 employee } = \frac{7500}{320} = 23.4375[/tex]

Thus unit rate for building A is 23.4375 square feet per employee

Building B has 9500 square feet of office space for 370 employees

[tex]\text{ square feet needed for 1 employee } = \frac{9500}{370}\\\\\text{ square feet needed for 1 employee } = 25.675[/tex]

Thus unit rate for building B is 25.675 square feet per employee

On comparing the unit rate of both buildings, we can clearly see that Building B offers more square feet per employee

To find out how much more Building B offers more square feet per employee than building A, we can find difference between unit rates of both buildings

[tex]\rightarrow 25.675 - 23.4375 = 2.2375[/tex]

Thus Building B offers 2.2375 square feet more space for 1 employee than Building A

Final answer:

Building B offers 25.68 square feet per employee, which is 2.24 square feet more per employee than Building A, which offers 23.44 square feet per employee.

Explanation:

To determine which building offers more square feet per employee, we calculate the square footage per employee for each building:

Building A: «Building A has 7500 square feet of office space for 320 employees.

Building B: «Building B has 9500 square feet of office space for 370 employees.

Now we calculate the square footage per employee for both buildings:

For Building A: 7500 square feet / 320 employees = 23.44 square feet per employee.

For Building B: 9500 square feet / 370 employees = 25.68 square feet per employee.

Comparing the two, Building B offers more square footage per employee. To find out how much more:

25.68 - 23.44 = 2.24 square feet more per employee in Building B than Building A.

Answer:

The moss will cover [tex]2\frac{11}{24}[/tex] inches of the ruler after 2 days.

Step-by-step explanation:

After one hour, the moss had covered [tex]1\frac{1}{8}[/tex] inches of the ruler.

Again, after two hours, it had covered another [tex]1\frac{1}{3}[/tex] inches of the ruler.

Therefore, after two hours the moss covers altogether ([tex]1\frac{1}{8} + 1\frac{1}{3}[/tex]) inches of the ruler.

Now, ([tex]1\frac{1}{8} + 1\frac{1}{3}[/tex])

= [tex]\frac{9}{8} + \frac{4}{3}[/tex]

= [tex]\frac{9\times 3 + 4 \times 8}{24}[/tex]

= [tex]\frac{59}{24}[/tex]

= [tex]2\frac{11}{24}[/tex] inches

Therefore, the moss will cover [tex]2\frac{11}{24}[/tex] inches of the ruler after 2 days. (Answer)

the answer is 38

16+18+4

Answer:

46

Step-by-step explanation:

The picture are irrelevant and is used to trick you.

Let swirly hair = s

Let curly hair = c

Let flat hair = f

Ok, now we can rewrite the picture in math terms

s = 16

c = 2 + s = 2 + (16) = 18

s = 4 + f → f = s - 4 = (16) - 4 = 12

s + c + f = 16 + 18 + 12 = 46

Step-by-step explanation:

A line that passes through the origin is proportional (y = mx).  But a line that doesn't pass through the origin isn't proportional (y = mx + b).  So all proportional relationships are linear, but not all linear relationships are proportional.

proportional relationship is just a linear relationship where the line passes through the origin (0, 0).

Answer:

First answer at the top.

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

here,

if y=3 then

width is 3+4=7

We know,

Area = l*b

6*7=42 ans

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}[/tex]

[tex]\text{The formula of an area of a rectangle:}\\\\A=l\times w\\\\l-\text{length}\\w-\text{width}\\\\\text{We have:}\\\\l=6,\ w=y+4\\\\\text{Substitute:}\\\\A=6\times(y+4)\\\\\text{use the distributive property}:\ a(b+c)=ab+ac\\\\A=(6)(y)+(6)(4)\\\\A=6y+24[/tex]

[tex]\text{Put}\ y=3\ \text{to the expression}\\\\A=6(3)+24=18+24=42\ in^2[/tex]

[tex]\bold{METHOD\ 2:}[/tex]

[tex]\text{Put}\ y = 3\ \text{to}\ y+4:\ 3+4=7\\\\\text{Put the values of length and width to the formula of an area of a rectangle:}\\\\A=(6)(7)=42\ in^2[/tex]

Answer:we multiply by the reciprocal of a fraction when completing a division problem because it is a rule in mathematics that when you divide two fraction, you change the division sign to multiplication and flip the fraction at the right of the multiplication sign.

Step-by-step explanation:

For example if you have 4÷ 1/2. It basically means how many 1/2 can one get in 4. And the answers is 8.

Therefore multiplying by the reciprocal of a fraction when completing a division problem is a short cut method that has been tested and proven to be correct.