Combine like terms to create an equivalent expression.
-5.8c+4.2-3.1+1.4c−5.8c+4.2−3.1+1.4c

Answer:

R+T=24

2t+9=R

(2t+9)+t=24

3t+9=24

3t=15

t=5

r+5=24

r=19

Teo is 5 and Richard is 19

Richard is 19 years old and Teo is 5 years old.

To solve this problem, we'll start by assigning variables to Richard's age (R) and Teo's age (T).

From the given information, we can form the following equations:

We can solve this system of equations by substituting the second equation into the first equation, which gives us:

(2T + 9) + T = 24

Combining like terms, we get 3T + 9 = 24. Subtracting 9 from both sides gives 3T = 15. Dividing by 3, we find T = 5.

Substituting this value back into the first equation, we get R + 5 = 24. Subtracting 5 from both sides gives R = 19.

Therefore, Richard is 19 years old and Teo is 5 years old.

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Answer:

Joel will save $145.

Step-by-step explanation:

1125-980=145

Answer:

8

Step-by-step explanation:

5 + 7 = 12

48 / 12 = 4

5 x 4 = 20

7 x 4 = 28

There are 8 girls more than boys

The sales tax rate is 5%.

Step-by-step explanation:

Given,

Amount of sales tax = $49

Price of dining room set = $980

Sales tax rate = [tex]\frac{Amount\ of\ sales\ tax}{Price\ of\ dining\ room\ set}*100[/tex]

Sales taxa rate = [tex]\frac{49}{980}*100[/tex]

[tex]Sales\ tax\ rate=\frac{4900}{980}\\Sales\ tax\ rate=5\%[/tex]

The sales tax rate is 5%.

Keywords: percentage, division

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Answer:

Part 1) [tex]c=\sqrt{146}\ cm[/tex]

Part 2) [tex]c=8\sqrt{2}\ in[/tex]

Part 3) The diagonal of rectangle is [tex]d=3\sqrt{29}\ cm[/tex]

Part 4) The length of the diagonal of computer monitor is [tex]d=15\ in[/tex]

Part 5) The ramp is [tex]10.59\ ft[/tex] long

Part 6) The distance between their houses is [tex]=4\sqrt{2}\ mi[/tex]

Part 7) [tex]234.31\ mi[/tex]

Part 8) 120 feet of wire is required

Step-by-step explanation:

Part 1) we know that

To find the length of the hypotenuse in a right triangle apply the Pythagorean Theorem

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

where

c is the hypotenuse (the greater side)

a and b are the legs

we have

[tex]a=11\ cm\\b=5\ cm[/tex]

substitute

[tex]c^2=11^2+5^2[/tex]

[tex]c^2=146[/tex]

[tex]c=\sqrt{146}\ cm[/tex]

Part 2) we know that

To find the length of the hypotenuse in a right triangle apply the Pythagorean Theorem

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

where

c is the hypotenuse (the greater side)

a and b are the legs

we have

[tex]a=8\ in\\b=8\ in[/tex]

substitute

[tex]c^2=8^2+8^2[/tex]

[tex]c^2=128[/tex]

[tex]c=\sqrt{128}\ in[/tex]

simplify

[tex]c=8\sqrt{2}\ in[/tex]

Part 3) we know that

To find the length of the diagonal in a rectangle apply the Pythagorean Theorem

[tex]d^2=b^2+h^2[/tex]

where

d is the diagonal of rectangle

b and h are the base and the height of rectangle

we have

[tex]b=15\ cm\\hb=6\ cm[/tex]

substitute

[tex]d^2=15^2+6^2[/tex]

[tex]d^2=261[/tex]

[tex]d=\sqrt{261}\ cm[/tex]

simplify

[tex]d=3\sqrt{29}\ cm[/tex]

Part 4) we know that

To find the length of the diagonal of a computer monitor apply the Pythagorean Theorem

[tex]d^2=w^2+h^2[/tex]

where

d is the diagonal of computer monitor

w and h are the wide and the high of computer monitor

we have

[tex]w=12\ in\\h=9\ in[/tex]

substitute

[tex]d^2=12^2+9^2[/tex]

[tex]d^2=225[/tex]

[tex]d=\sqrt{225}\ in[/tex]

simplify

[tex]d=15\ in[/tex]

Part 5) we know that

To find out the length of the ramp apply the Pythagorean Theorem

[tex]L^2=x^2+y^2[/tex]

where

L is the length of the ramp

x  is the horizontal distance of the ramp

y  is the vertical distance of the ramp

we have

[tex]x=10\ ft\\y=3.5\ ft[/tex]

substitute

[tex]L^2=10^2+3.5y^2[/tex]

[tex]L^2=112.25[/tex]

[tex]L=10.59\ ft[/tex]

Part 6) we know that

To find the distance between their houses apply the Pythagorean Theorem

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

where

c is the hypotenuse (distance between their houses)

a and b are the legs

we have

[tex]a=4\ mi\\b=4\ mi[/tex]

substitute

[tex]c^2=4^2+4^2[/tex]

[tex]c^2=32[/tex]

[tex]c=4\sqrt{2}\ mi[/tex]

Part 7) we know that

The speed is equal to divide the distance by the time

[tex]speed=distance/time[/tex]

so

the distance is equal to multiply the speed by the time

[tex]distance=speed*time[/tex]

First train

speed=60 mph

time=3 hours

distance=60(3)=180 miles

Second train

speed=50 mph

time=3 hours

distance=50(3)=150 miles

To find out how far apart are the trains at the end of 3 hours apply the Pythagorean Theorem

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

where

c is the hypotenuse (distance between the trains)

a and b are the legs

we have

[tex]a=180\ mi\\b=150\ mi[/tex]

substitute

[tex]c^2=180^2+150^2[/tex]

[tex]c^2=54,900[/tex]

[tex]c=234.31\ mi[/tex]

Part 8)  we know that

For one tree is needed three wire

To find out the length of one wire apply the Pythagorean Theorem

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

where

c is the hypotenuse (length of one wire)

a and b are the distance above the ground and the distance from the base

we have

[tex]a=3\ ft\\b=4\ ft[/tex]

substitute

[tex]c^2=3^2+4^2[/tex]

[tex]c^2=25[/tex]

[tex]c=5\ ft[/tex]

so

For one tree is required ----> (5)3=15 ft

therefore

For 8 trees is required

Multiply by 8

15(8)=120 ft

Answer:

[tex]\displaystyle 4 > x[/tex]

Step-by-step explanation:

3 - 2x > −5

- 3 - 3

_________

[tex]\displaystyle \frac{-2x}{-2} > \frac{-8}{-2} \\ \\ x < 4[/tex]

Whenever you divide\multiply by a negative, you reverse the inequality symbol.

** The above answer is written in reverse, which is the exact same result.

I am joyous to assist you anytime.

Answer:

x=4, y=13. (4, 13).

Step-by-step explanation:

3x+2y=38

-6x+4y=28

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

simplify -6x+4y=28 into -3x+2y=14

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

3x+2y=38

-3x+2y=14

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

4y=52

y=52/4=13

3x+2(13)=38

3x+26=38

3x=38-26

3x=12

x=12/3=4

x=4, y=13.

Answer:

Step-by-step explanation:

[tex]5+3w+3-w\qquad\text{combine like terms}\\\\=(3w-w)+(5+3)\\\\=2w+8[/tex]

Equation:

(2.80 ÷ 7) + .75 (to find the original cost of the cookies)

2.80 ÷ 7 (to find the new cost of the cookies)

Answer:

$1.15 is the original cost of the cookies.

$0.40 is the new cost of the cookies.

Equation:

2.80 ÷ 7 (new cost of the cookies)

(2.80 ÷ 7) + .75 (original cost of the cookies)

Answer:

$1.15 is the original cost of the cookies.

$0.40 is the new cost of the cookies.

Answer:

342 miles/6 hours = 57 mph

Answer: Kremena needs to deposit $1,101 today to earn a total of $1,250 in 3 years at 4.5% simple interest rate

Step-by-step explanation:

Interest = Principal (P) × Rate (R) × Time (T)

Amount = Principal (P) + Interest

Amount = P + PRT

Amount = P (1 + RT)

1250 = P (1 + (0.045 × 3))

1250 = P (1 + 0.135)

1250 = P (1.135)

Principal = 1250 ÷ 1.135

Principal = approx. 1101

Final answer:

Kremena needs to deposit approximately $1,101 today at a simple interest rate of 4.5% to have $1,250 in 3 years.

Explanation:

To find out how much Kremena needs to deposit today to have her account worth $1,250 in 3 years at a simple interest rate of 4.5%, we use the simple interest formula:

I = P * r * t, where:

Kremena wants the final amount (A) to be $1,250. The final amount is the sum of the principal and the interest earned: A = P + I. Therefore, we rearrange the simple interest formula to calculate P:

P = (A - (I = A * r * t)) / (1 + r * t)

Here, I = A - P, which means:

P = A / (1 + r * t)

Plugging in the numbers:

P = $1,250 / (1 + 0.045 * 3)

P = $1,250 / 1.135

P ≈ $1,101

Therefore, Kremena must deposit approximately $1,101 today to have $1,250 in 3 years at a 4.5% simple interest rate.

Answer:4/3

Step-by-step explanation:24/18

Divide both the numerator and the denominator by their highest common  factor. i.e 6

24÷6/18÷6

⇒ 4/3

The value of fraction for 24 divided by 18 is,

⇒ 4 / 3

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ 24 divided by 18

Now, We can write as;

⇒ 24 divided by 18

⇒ 24 ÷ 18

⇒ 24 / 18

⇒ 4 / 3

Thus, The value of fraction for 24 divided by 18 is,

⇒ 4 / 3

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Answer:

The speed of the boat in still water is 12 km/hour.

Step-by-step explanation:

Given:

Boat goes 50 km downstream and 30 km upstream. The speed of the stream 3 km/hour.

Now, to find the speed of the boat in still water:

Let the speed of boat in still water be [tex]x km/hour[/tex].

The speed of the downstream be [tex]x+3[/tex]

And, the speed of the upstream be [tex]x-3[/tex]

And, now we find the time by putting the formula:

[tex]Time = \frac{Distance}{Rate}[/tex]

So, downstream time is:

[tex]downstream\ time = \frac{50}{x+3}[/tex]

So, upstream time is:

[tex]upstream\ time = \frac{30}{x-3}[/tex]

According to question:

Time upstream = Time downstream

[tex]\frac{30}{x-3} = \frac{50}{x+3}[/tex]

By cross multiplication:

[tex]30\times (x+3)= 50\times (x-3)[/tex]

[tex]30x+90=50x-150[/tex]

By taking variables in one side and taking numbers on the other side we get:

[tex]90+150=50x-30x[/tex]

[tex]240=20x[/tex]

Dividing both sides by 20 we get :

[tex]12=x[/tex]

Therefore, the speed of the boat in still water is 12 km/hour.

Answer:

[tex]\theta =2\pi k,\ \ k\in Z\ \\\text{or}\ \\\theta=-\dfrac{2\pi}{3}+2\pi k,\ \ k\in Z[/tex]

Step-by-step explanation:

Given:

[tex]\cos \theta-\sqrt{3}\sin \theta=1[/tex]

Divide this equation by 2:

[tex]\dfrac{1}{2}\cos \theta-\dfrac{\sqrt{3}}{2}\sin \theta=\dfrac{1}{2}[/tex]

Note that

[tex]\cos \dfrac{\pi }{3}=\dfrac{1}{2}\\ \\\sin \dfrac{\pi }{3}=\dfrac{\sqrt{3}}{2}[/tex]

So, the previous equation is

[tex]\cos \dfrac{\pi}{3}\cdot \cos \theta-\sin \dfrac{\pi}{3}\cdot \sin \theta=\dfrac{1}{2}[/tex]

Remind that

[tex]\cos x\cos y-\sin x\sin y=\cos (x+y),[/tex]

then

[tex]\cos \left(\dfrac{\pi}{3}+\theta\right)=\dfrac{1}{2}[/tex]

The solution of this equation is

[tex]\dfrac{\pi}{3}+\theta=\pm \arccos \dfrac{1}{2}+2\pi k,\ \ k\in Z\\ \\\dfrac{\pi}{3}+\theta=\pm \dfrac{\pi}{3}+2\pi k,\ \ k\in Z\\ \\\theta =2\pi k,\ \ k\in Z\ \text{or}\ \theta=-\dfrac{2\pi}{3}+2\pi k,\ \ k\in Z[/tex]

The slope of the given line with points (0, -3) and (-2, 5) is -4.

The slope is the rate of change of the y-axis with respect to the x-axis. We can also think of slope as the rise over run. The slope of a line also describes the amount of angle a line forms from the positive x-axis.

From the given graph we can determine two points when x = 0 , y = -3 and when x = -2 , y = 5.

∴ The points of the given line are (0, -3) and (-2, 5).

We know the slope of a line is rise over run which is (y₂ - y₁)/(x₂ -x₁).

Therefore the slope of the given line is,

= (5 + 3)/(-2 - 0).

= 8/-2.

= -4.

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Answer:

250 students

Step-by-step explanation:

Another way of saying this is:

40% of all six-grade students are 100 of them.

So,

40% of total is equal to 100

We can translate this into an algebraic equation and solve for the total number of students.

Let total number of students be "t"

Also, note "of" means "multiplication" and "is" means "equal"

Lets translate word equation to algebraic:

"40% of total is equal to 100"

40% * t = 100

Converting percentage to decimal by dividing by 100, we have:

40% = 40/100 = 0.4

Now, we have:

0.4 * t = 100

We can now solve for t:

[tex]0.4 * t = 100\\t=\frac{100}{0.4}\\t=250[/tex]

Hence,

the total number of students is 250

Answer:

250 students

Step-by-step explanation:

Answer:

Step-by-step explanation:

You need to divide 74308 divided by 52 which equals 1429.

Answer:

I would say the answer is 90 degrees

Answer:

360-48-42-90-48-42=90°

Answer:

i think maybe 600k?

Step-by-step explanation:

To find out how much more interest is paid on a $195,000 home with a 20% down payment and a balance financed with a 30-year mortgage at 6% compared to 3.5%, one must calculate the total interest for each rate over the 30-year period and then compare the two totals.

To determine the difference in the amount of interest paid over the life of a 30-year mortgage because of different interest rates, we need to calculate the total interest for both scenarios. With a $195,000 home and a 20% down payment, the amount to be financed is $156,000 (since 20% of $195,000 is $39,000, and $195,000 - $39,000 = $156,000).

For the 6% mortgage rate, the monthly payment can be found using the formula for a fixed-rate mortgage, which is P[r(1+r)^n]/[(1+r)^n-1], where P is the principal ($156,000), r is the monthly interest rate (0.06/12), and n is the number of payments (360). Similarly, we calculate the monthly payment for the loan at 3.5% interest.

Once the monthly payments are determined, we can calculate the total payment over 30 years for each rate by multiplying the monthly payment by 360. The difference between the two total payments will give us the additional interest paid due to the higher interest rate.

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Answer:

9x+15  is the simplified version.

   7

Step-by-step explanation:

Distribute 3 into the parenthesis.

3x+3+2

 2 1/3

Simplify the problem.

3x+5

2 1/3

Convert the mixed number into an improper fraction.

3x+5

7/3

Multiply the denominator to the numerators of the complex fraction.

3x(3)+5(3)

7  ×3

3

9x+15

   7

Answer: 14/3 or 4 2/3

Step-by-step explanation:

you need 7 servings of 2/3 of a cup of cream

so, multiply the two values

7x2/3=14/3 or 4 2/3

Answer:

About 5 cups

Step-by-step explanation:

7×2/3

4.6666666667

you round up to 5 or put 4.6 repeated

Answer:

25

Step-by-step explanation:

To calculate rate, divide the number of cans by the time to get "Cans per minute".

300/15min = 20/min

Let m represent minutes and c for cans.

We write an equation for the problem:

c = 20m

We want to know the time for 500 cans, so substitute 500 for c.

500 = 20m

Isolate m and solve:

m = 500/20

m = 25

It will take 25 minutes to put 500 labels.

domain: {-5, 1, 3, 7}; Yes, it is a function ⇒ 3rd answer

Step-by-step explanation:

Let us revise the relation and the function

∵ The relation is {(-5, 2), (7, 7), (3, 6), (1, 7)}

∴ The inputs are: -5 , 7 , 3 , 1

∴ The outputs are: 2 , 7 , 6

∵ The domain is the set of the inputs

∴ The domain of the relation is {-5 , 1 , 3 , 7}

∵ The input -5 has the output 2

∵ The input 7 has the output 7

∵ The input 3 has the output 6

∵ The input 1 has the output 7

∴ There are one output for each input

∴ The relation is a function

domain: {-5, 1, 3, 7}; Yes, it is a function

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Answer:

less

Step-by-step explanation:

5/10 is equal to one half, but 4/10 is less than one half

Answer:

D

Step-by-step explanation:

its like going from point A to point B and then back to point A

Answer:

6827 centimeters

Step-by-step explanation:

multiply length value by 100

A waterfall has a height of 1400 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 16 feet per second. The​ height, h, of the pebble after t seconds is given by the equation h equals negative 16 t squared plus 16 t plus 1400

h=−16t2+16t+1400. How long after the pebble is thrown will it hit the​ ground?

Answer

The pebble hits the ground after 9.8675 s

Step-by-step explanation:

Given

waterfall height = 1400 feet

initial velocity =  16 feet per second

The height, h, of the pebble after t  seconds is given by the equation.

[tex]h(t) = -16t^{2}+16t+1400[/tex]

The pebble hits the ground when  [tex]h = 0[/tex]

[tex]h=-16t^{2}+16t+1400[/tex] ---------------(1)

put [tex]h=0[/tex] in equation (1)

[tex]0=-16t^{2}+16t+1400[/tex]

[tex]-16t^{2}+16t+1400=0[/tex]

Divide by -4 to simplify this equation

[tex]4t^{2}-4t-350=0[/tex]

using the Quadratic Formula where

a = 4, b = -4, and c = -350

[tex]t=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]t=\frac{-(-4)\pm\sqrt{(-4)^{2}-4(4)(-350) } }{2(4)}[/tex]

[tex]t=\frac{4\pm\sqrt{16-(-5600) } }{8}[/tex]

[tex]t=\frac{4\pm\sqrt{16+5600 } }{8}[/tex]

[tex]t=\frac{4\pm\sqrt{16+5616 } }{8}[/tex]

The discriminant [tex]b^{2}-4ac>0[/tex]

so, there are two real roots.

[tex]t=\frac{4\pm12\sqrt{39 } }{8}[/tex]

[tex]t=\frac{4}{8}\pm\frac{12\sqrt{39 }}{8}[/tex]

[tex]t=\frac{1}{2}\pm\frac{3\sqrt{39 }}{2}[/tex]

Use the positive square root to get a positive time.

[tex]t=9.8675 s[/tex]

The pebble hits the ground after 9.8675 second

There are 152 men, 76 women and 38 children.

Step-by-step explanation:

Total persons = 266

Let,

men = m

women = w

children = c

According to given statement;

m+w+c=266    Eqn 1

m = 4c   Eqn 2

w = 2c   Eqn 3

Putting value of m and w from Eqn 2 and 3 in Eqn 1

[tex]4c+2c+c=266\\7c=266\\[/tex]

Dividing both sides by 7

[tex]\frac{7c}{7}=\frac{266}{7}\\c=38[/tex]

Putting c=38 in Eqn 2;

[tex]m=4(38)\\m=152[/tex]

Putting c=38 in Eqn 1;

[tex]w=2(38)\\w=76[/tex]

There are 152 men, 76 women and 38 children.

Keywords: linear equations, substitution method

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We can use the points (2, -2) and (4, -1) to solve.

Slope formula: y2-y1/x2-x1

= -1-2/4-(-2)

= -3/6

= -1/2

Point slope form: y - y1 = m(x - x1)

y - 2 = -1/2(x + 2)

______

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