Help me solve this intermediate algebra problem

Answer:

x = -22 , y = -26

Step-by-step explanation:

Solve the following system:

{y = x - 4 | (equation 1)

y - 2 x = 18 | (equation 2)

Express the system in standard form:

{-x + y = -4 | (equation 1)

-(2 x) + y = 18 | (equation 2)

Swap equation 1 with equation 2:

{-(2 x) + y = 18 | (equation 1)

-x + y = -4 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{-(2 x) + y = 18 | (equation 1)

0 x+y/2 = -13 | (equation 2)

Multiply equation 2 by 2:

{-(2 x) + y = 18 | (equation 1)

0 x+y = -26 | (equation 2)

Subtract equation 2 from equation 1:

{-(2 x)+0 y = 44 | (equation 1)

0 x+y = -26 | (equation 2)

Divide equation 1 by -2:

{x+0 y = -22 | (equation 1)

0 x+y = -26 | (equation 2)

Collect results:

Answer: {x = -22 , y = -26

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=x-4&\text{subtract}\ x\ \text{from both sides}\\-2x+y=18\end{array}\right\\\\\left\{\begin{array}{ccc}-x+y=-4\\-2x+y=18&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-x+y=-4\\2x-y=-18\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad x=-22\\\\\text{Put the value of}\ x\ \text{to the first equation:}\\\\y=-22-4\\y=-26[/tex]

Answer:

Part a) Camilo is 34 years old and Juan is 28 years old

Part b) The difference between Camilo's age and Juan's age is 6 years

Part c) The sum of the ages of Camilo and Juan not coincide with the age of Andres' grandmother

Step-by-step explanation:

The question in English is

If Camilo is 6 years older than Juan, Juan is 7 years younger than Andrés and Andrés is 35 years old .

Part a)  How old is Camilo and how old is Juan? raises the equation.

Part b) What's the difference between Camilo's age and Juan's age?

Part c) If Andres's grandmother is 65 years old, does the sum of the ages of Camilo and Juan coincide with the age of Andres' grandmother?

Part a)  How old is Camilo and how old is Juan? raises the equation.

Let

x -----> Camilo's age

y -----> Juan's age

z -----> Andres's age

we know that

[tex]x=y+6[/tex] -----> equation A

[tex]y=z-7[/tex] -----> equation B

[tex]z=35[/tex] -----> equation C

Find the value of y

substitute the value of z in the equation B

[tex]y=35-7=28[/tex]

Find the value of x

substitute the value of y in the equation A

[tex]x=28+6=34[/tex]

therefore

Camilo is 34 years old and Juan is 28 years old

Part b) What's the difference between Camilo's age and Juan's age?

Subtract Juan's age from Camilo's age

so

[tex]x-y=34-28=6\ years[/tex]

Part c) If Andres's grandmother is 65 years old, does the sum of the ages of Camilo and Juan coincide with the age of Andres' grandmother?

Adds Camilo's age and Juan's age

[tex]x+y=34+28=62\ years[/tex]

[tex]62\ years\neq 65\ years[/tex]

therefore

The sum of the ages of Camilo and Juan not coincide with the age of Andres' grandmother

Answer:

The speed of Sharma is slower than the speed of Brandi

I.e ∵   4.67 miles per hour  [tex]<[/tex] 5 miles per hour

      ∴  [tex]S_2[/tex] [tex]<[/tex] [tex]S_1[/tex]

Step-by-step explanation:

Given as :

The distance cover by Brandi = [tex]D_1[/tex] = 2 [tex]\frac{1}{2}[/tex] =[tex]\frac{5}{2}[/tex]

The Time taken by Brandi for jogging =  [tex]T_1[/tex] = 30 minutes =[tex]\frac{1}{2}[/tex] hour

Let the speed of Brandi = [tex]S_1[/tex] = [tex]\dfrac{\textrm Distance }{\textrm Time}[/tex]

or,  [tex]S_1[/tex] = [tex]\dfrac{\textrm  [tex]D_1[/tex]  }{\textrm   [tex]T_1[/tex] }[/tex]

Or.  [tex]S_1[/tex] = [tex]\frac{\frac{5}{2}}{\frac{1}{2}}[/tex]

∴   [tex]S_1[/tex] = 5 miles per hour

Again

The distance cover by Sharma = [tex]D_2[/tex] = 3 [tex]\frac{1}{2}[/tex] =[tex]\frac{7}{2}[/tex]

The Time taken by Sharma for jogging =  [tex]T_2[/tex] = [tex]\frac{3}{4}[/tex] hour

Let the speed of Sharma = [tex]S_2[/tex] = [tex]\dfrac{\textrm Distance }{\textrm Time}[/tex]

or,  [tex]S_2[/tex] = [tex]\dfrac{\textrm  [tex]D_2[/tex]  }{\textrm   [tex]T_2[/tex] }[/tex]

Or.  [tex]S_2[/tex] = [tex]\frac{\frac{7}{2}}{\frac{3}{4}}[/tex]

∴   [tex]S_2[/tex] = [tex]\frac{14}{3}[/tex] = 4.67 miles per hour

Now, ∵   4.67 miles per hour  [tex]<[/tex] 5 miles per hour

         ∴  [tex]S_2[/tex] [tex]<[/tex] [tex]S_1[/tex]

So, Sharma jogged at slower late

Hence The speed of Sharma is slower than the speed of Brandi Answer

Keith can withdraw money from his account for 12 weeks.

Step-by-step explanation:

Total savings = $500

Amount to be left in his account = $200

Withdrawal per week = $25

Let,

x be the number of weeks.

According to given statement;

Total savings - Withdrawal per week * no. of weeks = Amount to be left

[tex]500-25x=200\\-25x=200-500\\-25x=-300\\[/tex]

Dividing both sides by -25

[tex]\frac{-25x}{-25}=\frac{-300}{-25}\\x=12[/tex]

Keith can withdraw money from his account for 12 weeks.

Keywords: savings, linear expression

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Final answer:

Keith can withdraw money from his account for food for 12 weeks before reaching his minimum account balance requirement of $200.

Explanation:

To determine how many weeks Keith can withdraw money from his account while maintaining a balance of at least $200, we need to perform a simple subtraction and division operation. First, we calculate the amount he needs to leave in the account:
$500 initial balance - $200 desired end balance = $300 available to spend.
Keith withdraws $25 per week for food. To find out how many weeks his money will last, we divide the total amount he can spend by the weekly withdrawal amount:
$300 \/ $25 per week = 12 weeks.
Therefore, Keith can withdraw money for food for 12 weeks before his account balance reaches his minimum requirement of $200.

Answer:

A and D

Step-by-step explanation:

Statement (A) and statement (D) are the two pairs of congruent angles in the figure.

Congruent figures are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

It is given that:

The angles are shown in the picture.

It is required to name the two pairs of congruent angles in the figure.

From the figures:

According to the right angles congruent theorem, angle DIB and angle CIA

The right angles congruent theorem states that angle BIA and angle CIB are congruent.

Angle DIB and angle CIA according to the right angles congruent theorem

Angle BIA and angle CIB according to the right angles congruent theorem

Thus, statement (A) and statement (D) are the two pairs of congruent angles in the figure.

Learn more about the congruent figures here:

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Answer:

Area = 374.1  sq. in.

Step-by-step explanation:

A trick to solve this would be to know the area of a hexagon formula and plug the known information.

First, of all, if we count the number of sides, we see that we have 6 sides.

6 sided polygon is a HEXAGON, which has area formula of:

[tex]A=\frac{3\sqrt{3} }{2} a^2[/tex]

Where

a is the side length

Given, the side length is 12 inches ( a= 12), we simply substitute into formula and find area of hexagon shown:

[tex]A=\frac{3\sqrt{3} }{2} a^2\\A=\frac{3\sqrt{3} }{2} (12)^2\\A=\frac{3\sqrt{3} }{2}(144)\\A = 374.12[/tex]

Rounded to nearest tenth (1 decimal place)

Area = 374.1  sq. in.

Answer:

(1.25×4+3×2 )/((1/2)^3) = 88

Step-by-step explanation:

The solution to the equation 1.25×4+3×2 divided By (1/2) third power is 53 applying the order of operation PEMDAS.

To solve 1.25×4+3×2 divided By (1/2) third power, we first have to follow the order of operation, that is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), also known as PEMDAS.

Step 1: Solve the expressions in parentheses and the exponent. As there's none, we move to the next step.

Step 2: Solve the multiplication and division.
1.25×4 equals 5, then 3×2 equals 6, and then 1/2, to the third power, equals 0.125.
So our equation now reads 5+6 divided by 0.125.

Step 3: Execute the division operation. 6 divided by 0.125 equals 48.
Our equation now reads 5 + 48.

Step 4: The last step is addition. 5 + 48 equals 53. So, the answer to the equation 1.25×4+3×2 divided By (1/2) third power is 53.

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Answer:

F(f) = 15t + 35 represents the total amount of savings your friend would make in t weeks.

F(d) = 10t + 90 represents the total amount of saving you, darian, would make in t weeks.

When you graph the equations, plugging in different values for t, you can see that the graphs  intersect at (11,200). This means that at 11 weeks, both you and your friend have the same amount of money saved up, $200.  They will not have the same amount of money in 10 weeks.

Answer:

[tex]y=15x+35[/tex]

Step-by-step explanation:

If you begin with $90 and add $10 each week, then we express it as

[tex]y=10x+90[/tex]

Where [tex]x[/tex] refers to weeks and [tex]y[/tex] refers to the total amount of money in you savings account.

On the other hand, your friend begins with $35 and deposits $15 each week, the equation that expresses your friend's savings is

[tex]y=15x+35[/tex]

Therefore, the sytem of linear equation that models this situation is

[tex]y=10x+90[/tex]

[tex]y=15x+35[/tex]

The graph attached shows this system. There you can notice that the solution is (11, 200), which means in 11 weeks both will have the same amount saved.

Therefore, your friend is wrong, because after 10 weeks you won't have the same amount.

Answer:

165

Step-by-step explanation:

First we need to find the area of the field, A = r^2 * pi

The radius is 290 / 2 = 145 feet

A = 145 * 145 * 3.14 = 66018.5 sqr feet

One bag covers 400 sqr feet

Divide the Area by 400 sqr feet to find number of bags needed.

66018.5 / 400 = 165

He will need at least 165 bags to cover the field

Answer:

4 bags

Step-by-step explanation:

We need to find the area of the circular field. To do this, we use the formula

A=piR^2     (pi multiplied by radius squared)

The radius is going to be 290/2 which is 145 which we plug into the equation.

A=pi145^2

The next step is to square 145, getting 21025. But now we need to multiply that by pi (3.14). We get 66018.5 as the answer.

Now we need to figure out how many square feet one bag can cover. To do this, we multiply 400 by 50 (because one pound can cover 400ft and one bag has 50 pounds). We get 20000 as the amount one bag of grass seed can cover. Now we need to divide 66018.5 by 20000. We get 3.300925. But the groundskeeper can't buy a decimal of a bag so we have to round up to 4 bags of grass seed.

Answer:

D

Step-by-step explanation:

The diagram shows the rectangle with vertices at A(3,4), B(3,7), C(4,7) and D(4,4).

1. Rotate rectangle ABCD by 180° about the point (3,4) (vertex A). This rotation has the rule:

[tex](x,y)\rightarrow (6-x,8-y)[/tex]

So, the image points have the coordinates A'(3,4), B'(3,1), C'(2,1) and D'(2,4)

2. Dilate by a scale factor of 2 with the center of dilation at origin. This dilation has the rule:

[tex](x,y)\rightarrow (2x,2y)[/tex]

So, the image points have the coordinates A''(6,8), B''(6,2), C''(4,2) and D''(4,8)

3. Reflect it over the y-axis. This reflection has the rule:

[tex](x,y)\rightarrow (-x,y)[/tex]

So, the image points have the coordinates A'''(-6,8), B'''(-6,2), C'''(-4,2) and D'''(-4,8) that are exactly the coordinates of the second rectangle shown.

Thus, correct option is option D.

Answer:

3 large, 13 small

Step-by-step explanation:

large: x

small: y

x + y = 16

16x + 9y = 165

Multiply first equation by 9 and subtract the equations.

9x + 9y = 144

-(16x + 9y = 165)

-7x = -21

x = 3

Now substitute this x value into the first equation

x + y = 16

3 + y = 16

y = 13

Answer: B 7.5

Step-by-step explanation:

Y = Kx

4 = k30

k = 30/4

k = 7.5

or

Y = KX

X Y

Answer:

If a vine tear is occurs after the fruit, cover it with soil and it should produce secondary roots. Number of Fruit on a Vine: A single pumpkin plant normally produces two to five pumpkins. Miniature varieties will produce up to a dozen or so.

Step-by-step explanation:

Answer: i dont see the answer listed. The answer is 29 ²/₃m

Step-by-step explanation:

89m long piece of rubber is cut into 3 pieces. In other words, divided into 3 pieces.

89m ÷ 3 = 29.66666666m

Which concerts to 29²/₃m

Answer:

B(6, - 11 )

Step-by-step explanation:

Since the translation rule is (x - 2, y + 3 )

Then to go back the way do the opposite, that is

(x + 2, y - 3 ), thus

B(4 + 2, - 8 - 3 ) → B(6, - 11 )

Answer:(6, -11)

Step-by-step explanation:

Answer:31%

Step-by-step explanation:look the pic

Answer:

31%

Step-by-step explanation:

Lance and Mary will need approximately $12,995 for a down payment on the property.

To calculate the amount of money needed for a down payment, you need to find 20% of the property cost. In this case, the property cost is $64,975.

Step 1: Convert 20% to a decimal by dividing it by 100: 20/100 = 0.2

Step 2: Multiply the property cost by 0.2: $64,975 * 0.2 = $12,995

Therefore, Lance and Mary will need approximately $12,995 for a down payment on the property.

Answer:

45/16 or 2 13/16, the maximum amount of sundaes that Anton can make with ice cream is 2.

Step-by-step explanation:

1 7/8=15/8

2/3x<=15/8

x<=(15/8)/(2/3)

x<=(15/8)(3/2)=45/16

Answer:

y=5/x

Step-by-step explanation:

Just divide by x on both sides to isolate y

Answer:

=2.5

Step-by-step explanation:

Replace x in the equation with the x value of the given solution:

f(x) = -2 -3 = -5

Since replacing x with 2 , the equation equals -5, then (2,-5) is a solution.

Answer:

yes

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

Answer:

Number of Adult's tickets sold on Saturday = 3,356

Number of Children's tickets sold on Saturday = 2, 928

Total number of tickets sold over these two days is 8,938.

Step-by-step explanation:

Here, the number of tickets sold on FRIDAY:

Adult Ticket sold = 1,678

Children's Tickets sold = 976

So, the total number of tickets sold on Friday  

= Sum of ( Adult + Children's ) tickets  = 1,678  + 976 = 2,654 ....  (1)

The number of tickets sold on SATURDAY:

Adult Ticket sold =   2 times  the number of adult tickets sold on Friday  

                             =  1,678 x 2  = 3,356

Children's Tickets sold = 3 times the number of children's tickets sold on Friday.

=  976  x 3 = 2, 928

So, the total number of tickets sold on Saturday  

= Sum of ( Adult + Children's ) tickets  = 3,356 + 2,928 = 6, 284 ....  (2)

Now, the total number of tickets booked in these two days :

Sum of tickets booked on (Friday + Saturday)

= 2,654 +  6, 284  =   8,938

Hence, total number of tickets sold over these two days is 8,938.

Answer:

The system of equations are

x + y = 2600   …….equation (1)

and, 6x + 5y = 13700  ……equation (2)

Explanation:

Let x = amount of sales of phone;

y = amount of sales of computer

For phone, 6% of sales is 6% of x, or 6% * x = 0.06x.

Similarly for computer,

5% of y = 0.05y

Given the total sales; x + y = 2600

And commission; 0.06x + 0.05y = 137; or 6x + 5y = 13700

Therefore the system of equations are

x + y = 2600   …….equation (1)

6 x + 5 y = 13700  ……equation (2)

Answer:

(4-1)•n=n•(4-1)

Step-by-step explanation:

It should equal each other so no matter what n equals it will equal each other :3

Step-by-step explanation:

Commutative property: a · b = b · a

(4 - 1) · n = n · (4 - 1)

Answer:

Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).

Step-by-step explanation:

Misha's group was asked to write an expression equivalent to  

7y²z + 3yz² - 3

When Mr. Chen checked their answers, he found only one to be correct.

And she was Helena.

Helena gave the answer as (7y²z + 6yz²- 5 - 3yz² + 2) which is equivalent to (7y²z + 3yz² - 3).  

Because, (7y²z + 6yz²- 5 - 3yz² + 2)

= 7y²z + (6yz² - 3yz²) - (5 - 2)  

= 7y²z + 3yz² - 3 (Answer)

Answer:

(22, 7)

Step-by-step explanation:

Let x and y be the unknown two numbers.

x+y=29

x-y=15

----------

2x=44

x=44/2

x=22

----------

22+y=29

y=29-22=7

x=22, y=7.

Answer:

126 ounces of cereal

Step-by-step explanation:

42*3=126

Answer:

7 lb and 14 oz

Step-by-step explanation:

42 oz × 3 = 126 oz

126 oz = 7 lb and 14 oz

Answer:

n = - 3

Step-by-step explanation:

We have to solve the equation [tex]2^{n} = \frac{1}{8}[/tex] for n.

Now, as the variable is in power, we will take a log on both sides.

So, [tex]2^{n} = \frac{1}{8}[/tex]

⇒ [tex]\log 2^{n} = \log \frac{1}{8}[/tex]

⇒ n log 2 = log 1 - log 8 {Since we know the property of logarithm [tex]\log a^{b} = b \log a[/tex] and [tex]\log \frac{a}{b} = \log a - \log b[/tex]}

⇒ n log 2 = -  log 2³ { Since, log 1 = 0}

⇒ n log 2 = - 3 log 2

⇒ n = - 3 (Answer)

Answer:

The current density of the solution in [tex]m^2[/tex] is [tex]11100A/m^2[/tex]

Step-by-step explanation:

One square decimeter is equal to 0.01 square meter, Thus the current density in square meters is

[tex]\frac{111A}{dm^2} =\frac{111A}{0.01m^2} =\frac{111}{0.01}*\frac{A}{m^2}=\boxed{11100A/m^2}[/tex]

11100 Amperes per square meter.

Answer:

The numbers are messed up, don't copy and paste from khan.

The answer is 100

Step-by-step explanation:

I took the test

Answer:

9:59

Step-by-step explanation:

all you have to do is add the hours to the hours and the minutes to the minutes but if you get a number over 60 in the minutes section then you need to subtract 60 from that side until get a number under 60 then you add however many times you did that to the hours

Answer:

Step-by-step explanation:

9 minutes past 4 = 04:09

Then in 5hours:50minutes, add it to 04:09, then we obtain 09:59