Solve for x.

x + 0.60(15) = 0.80(x + 15)

Answer:

country a = 19,812 cars

country b = 6,604 cars

Step-by-step explanation:

a = country a

b = country b

the 2 eqations are:

a + b = 26,416

a = 3b

now substitute 3b for a in the first equation:

3b + b = 26,416

add the variables:

4b = 26,416

now divide 26,416 by 4 (26,416/4)

b = 6,604

so country b has 6,604 cars

to find country b, substitute the number of cars in country b (which is 6,604) in the second equation:

a = 3b

a = 3 × 6,604

a = 19,812

so country a has 19,812 cars

Yo sup??

cot(7π/6)=cot(π+π/6)

=cot(π/6)

=√3

Hope this helps

Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the trigonometric identity

cot x = [tex]\frac{1}{tanx}[/tex]

Consider tan([tex]\frac{7\pi }{6}[/tex] )

[tex]\frac{7\pi }{6}[/tex] is an angle in the third quadrant where tan > 0

Thus tan([tex]\frac{7\pi }{6}[/tex] ) = tan([tex]\frac{7\pi }{6}[/tex] - π ) = tan([tex]\frac{\pi }{6}[/tex] ) = [tex]\frac{1}{\sqrt{3} }[/tex]

Hence

cot([tex]\frac{7\pi }{6}[/tex] ) = [tex]\frac{1}{\frac{1}{\sqrt{3} } }[/tex] = [tex]\sqrt{3}[/tex]

Answer:

<ABC = 98.

Step-by-step explanation:

We know that the triangle is lying on a flat line, which is 180 degrees. We know that angle ABC and angle CBD are supplementary as they both use line ABD as their transversal.

Set up the equation (3 + 5x) + 82 = 180.

Solve for x, and you get 19.

Plug it back in to (3 + 5x), we get <ABC = 98.

Answer:

32 cups of water is needed to fill a 2 gallon water tank.

Step-by-step explanation:

Here, the amount of water to be filled in the fish tank = 2 gallons

The utensil to measure water   =  a measuring cup

Now, as we know:

1 quart  = 0.25 gallons

⇒ 4 pints =  1  gallons

⇒ 8 pints =  2 gallons

Also, 1 pint  = 0.5 quart

⇒ 2 pints =  1 quarts

⇒ 8 pints =  4 quarts

⇒ 16 pints =  8 quarts

Again,  1 cup = 0.5 pint

⇒ 2 cup  = 1  pint

⇒ 32 cup  = 16  pints

Hence, 32 cups of water is needed to fill a 2 gallon water tank.

Answer:

$366.66

Step-by-step explanation:

You start with a credit card balance of $1950. If you reduce this balance by 13% each month for 12 months, using the formula for geometric series (a(r^n)), your final balance at the end of 12 months will be approximately $452.98.

The student's question is asking about reducing a credit card debt balance by a fixed percent each month. In this case, the student is reducing their debt by 13% every month for 12 months. To get a clear picture, let's go through this step by step.

Initially, the credit card balance is $1950. In the first month, the student reduces the debt by 13% which is $253.5. So, the remaining balance at the end of first month would be $1950 - $253.5 = $1696.5

This process is repeated each month. For example, in the second month, the student reduces the new amount of $1696.5 by 13%. The debt will continue to decrease in this manner each month.

To calculate the balance at the end of 12 months, we would use the formula for geometric series: a(r^n), where 'a' is the initial amount of debt($1950), 'r' is the percentage (1 - 13% or 0.87) and 'n' is the number of months (12).

Your final balance at the end of 12 months would be $1950*(0.87^12) which approximately equals $452.98. Hence, by reducing your debt by 13% each month for 12 months, your balance will be approximately $452.98. But remember, maintaining steady payments and not adding to the balance by new purchases is also important in managing credit card debt.

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Answer:

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (3n + 7)

Step-by-step explanation:

We require to find the first term a₁ and the common difference d

The n th term is given by 3n + 2, thus

a₁ = 3(1) + 2 = 3 + 2 = 5

a₂ = 3(2) + 2 = 6 + 2 = 8

d = 8 - 5 = 3

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], substitute values

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ (2 × 5) + 3(n - 1) ] = [tex]\frac{n}{2}[/tex] (10 + 3n - 3) = [tex]\frac{n}{2}[/tex] (3n + 7)

Answer:

Sn = (3/2)n² + (7/2)n

Step-by-step explanation:

Sn = (n/2)[2a + (n-1)d]

a = 3(1)+2 = 5

d = second term - 5 = 3(2)+2 - 5 = 3

Sn = (n/2)[2(5) + (n-1)(3)]

= (n/2)[10 + 3n - 3]

= (n/2)(7 + 3n)

Sn = (3/2)n² + (7/2)n

Answer:

y = 30

Step-by-step explanation:

If y varies directly with x, then you can make a ratio:

24/8

Simplify the ratio:

3/1

Y is always the first number/ on top in a ratio, that's where I get 24 over 8

3/1 means that y is triple x

so 10 * 3 is 30

Answer:

the answer is to 72 divided by 1/3 is 216

The result of the division 72 divide by 1/3 is : 216.

Here, we have,

given that,

What is 72 divide by 1/3

we know that,

72 divide by 1/3 is the same thing as 72 times 3/1.

i.e. 72 ÷ 1/3

=> 72 × 3/1

now, we know that,

So 72 x 3 = 216

=> 216/1

And 216 divided by 1 is 216.

so, we get,

Hence, The result of the division 72 divide by 1/3 is : 216.

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Answer:

x = 4.5.

Step-by-step explanation:

5(2x + 1) = 50

10x + 5 = 50

10x = 50 -  5

10x = 45

x = 4.5.

The midpoint of AB is point G

The complete question has been attached below. As you can see, we have a line segment which is defined as a part of a line that is bounded by two different points that are at the end of the segment. So here we know that:

Therefore, the midpoint can be calculated as:

[tex]M:midpoint \\ \\ \\ M=\frac{A+B}{2} \\ \\ M=\frac{-6+8}{2} \\ \\ M=1[/tex]

So the midpoint is [tex]M=1[/tex] that matches point G. Finally:

Conclusion: The midpoint of AB is point G

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The angles of a triangle always add to 180°. In the triangle with 35°, we know that the other angle is 55° since 180 - 90 - 35 = 55. Know we know that 55° angle, 60° angle and the unknown angle will add to 180° because they form a flat line. So 180 - 60 - 55 = 65. Next, we subtract 65° and 90° from 180° to get the last unknown angle, which is 25°. Lastly we subtract 25° from 180 because the x angle and the 25° angle form a a flat line. 180 - 25 = 155.

I believe the measure of angle x is 155°.

The required value of the exterior angle x = 155°

A figure of angle in triangles is shown in which the value of x is to be determined.

The angle can be defined as the one line inclined over another line.

From the image attached below From the orange triangle,
The sum of the interior angle of a triangle is 180°,
35 + 90 + z =180
z = 180 -90 - 35
z = 55
Now, the sum of the angle
z + y + 60 = 180
55 + y + 60 = 180
y = 180 -60 - 55
y = 65

Now angle x can be given as the sum of the remote angle is equal to exterior angle x.
35 + z + y = x
35 + 55 + 65 = x
x = 155

Thus, the required value of the exterior angle x = 155°

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The final price of a $1049 television on a 12% sale, with a 4.5% sales tax, is $964.66.

The final price on a $1049 television that is on sale for 12% off can be found by deducting the discount from the original price, and then adding the sales tax on the discounted price.

First, let's find the discount: 12% of $1049 is (12/100)*1049 = $125.88. So, the price after discount would be 1049 - 125.88 = $923.12.

Next, we need to add the 4.5% sales tax. Sales tax is calculated on the discounted price, so 4.5% of $923.12 is (4.5/100)*923.12 = $41.54.

Finally, we add the tax to the discounted price to get the final price: $923.12 + $41.54 = $964.66. So, the final price of the television is $964.66.

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The height of the redwood tree can be determined through trigonometry, using the tangent of the angles given and the distances provided. The height of the tree from point B is found to be 1.8 feet, and the total height of the tree from point A is found to be approximately 30.9 feet.

In this question, we can use trigonometry to solve the problem. From point B, we see two angles. The smaller angle, 85.8°, is the angle from the line extending to the tree and line AB, and the greater angle is 90°. Therefore, the angle between the line extending to the top of the tree and line AB is (90-85.8)= 4.2°.

Using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle, we can solve for h. Tan 4.2° = h/24.8 feet. Solving for h gives us h = 24.8 feet * tan 4.2°. Using a calculator, we find that h is approximately 1.8 feet.

Similarly, let's calculate the height from point A. From point A, the angle of elevation to the top of the tree is 10.4°. The distance from the tree to point A is the sum of the length of AB (24.8 feet) and the length from B to the tree (h/tan 85.8°). So, the total height of the tree is h (from point B) + distance from A to the tree * tan 10.4°. This calculation gives us h = 1.8 feet + (24.8 feet + 1.8 feet/tan 85.8°)*tan 10.4°. After doing the calculations, we find that the height of the tree is approximately 30.9 feet when rounded to one decimal place.

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Answer:

domain={0,3}

range={1,9}

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

hello :

the nth term is : Bn= B1×R^n-1

calculate B3  (when n=3)    R= -1/3   B1 = 54

B3 =54×(-1/3)^(3-1)

B3 =54×(1/9)=6

Knowing about geometric sequences we have that its third term will be given by 6

Geometric Progression (PG) is a numerical continuity in which the division of a term with its previous one, except the first, will result in a single value, the so-called ratio (q), that is: PG: (a1, a2, a3, a4, ..., an), where q = (a2/a1 = a3/a2 = a4/a3,.

Given that:

The formula of the term will be:

[tex]Bn= B1*R^n-1[/tex]

Calculated the B3 we have:

[tex]B3 =54*(-1/3)^{(3-1)}\\B3 =54*(1/9)=6[/tex]

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D. (-2,-1)

Hope it helps you.

Answer:

D

Step-by-step explanation:

Given the 2 equations

y = 2x + 3 → (1)

y = - [tex]\frac{1}{2}[/tex] x - 2 → (2)

Since both equations express y in terms of x, equate the right sides

2x + 3 = - [tex]\frac{1}{2}[/tex] x- 2

Multiply through by 2 to clear the fraction

4x + 6 = - x - 4 ( add x to both sides )

5x + 6 = - 4 ( subtract 6 from both sides )

5x = - 10 ( divide both sides by 5 )

x = - 2

Substitute x = - 2 into (1) for corresponding value of y

y = 2(- 2) + 3 = - 4 + 3 = - 1

Solution is (- 2, - 1 ) → D

Answer:

-7/4

Step-by-step explanation:

Did you mean -7?

Brandus bought a total of 7/12 pounds of meat by adding together 1/3 pound of ground turkey and 1/4 pound of ground beef.

To find out how much meat Brandus bought, you need to add the weights of the ground turkey and the ground beef. Brandus bought 1/3 pound of ground turkey and 1/4 pound of ground beef.

Convert the fractions to have a common denominator:

1/3 = 4/12 (multiply both the numerator and the denominator by 4)

1/4 = 3/12 (multiply both the numerator and the denominator by 3)

Add the two amounts:

4/12 + 3/12 = 7/12

Hence, Brandus bought 7/12 pounds of meat in total to make sausages.

Answer:

There will be 6 necklaces

Step-by-step explanation:

102/17 is 6

Answer:Juanita can make 6 bracelets.

Step-by-step explanation:

Divide 102 and 17 then you should get 6.

Answer: 3600

Step-by-step explanation:

Answer:

- 3

Step-by-step explanation:

hello:

-2-17+12-(-4)=(-2-17)+(12+4)= -19+16= -3

Answer:

-3

Step-by-step explanation:

-2-17+12-(-4)

From BODMAS, we begin witht the bracket

=-2-17+12+4

= -2-17+16

= -19+16

= -3

Second graph.

Hello! You haven't provided any relationship, but I found it on the internet and it is the table attached below. The point-slope form of the equation of a line is given by:

[tex]y=mx+b[/tex]

So:

[tex]y-Intercept: \\ \\ (0,b) \\ \\ \\ From \ the \ table: \\ \\ (0,b)=(0,46) \\ \\ So: \\ \\ b=46[/tex]

Finding the slope:

[tex]m=\frac{39-46}{1-0} \\ \\ m=-7[/tex]

So the equation of the line is:

[tex]y=-7x+46[/tex]

From the graphs, only option 2 and 4 have negative slope and only option 2 passes through [tex](0,46)[/tex]

Conclusion: Correct option is second graph.

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Answer:

The rule depends on the scale factor.

Step-by-step explanation:

Hi there,

1) Many, I'd say mostly, dilations is centered at the origin (0,0) of the cartesian plane. Like the picture below.

2) So now, what's left to do is what is the scale factor? What coefficient that multiplies the original rectangle URST, will result the U'R'S'T'?

3) Since no coordinates, no options or any numerical value were given, then I've made one example.

Check below

If you do have the coordinates of each point then divide each coordinate this way

[tex]\frac{U'(x,y)}{U(x,y)}=\frac{R'(x,y)}{R(x,y)}=\frac{S'(x,y)}{S(x,y)}=\frac{T'(x,y)}{T(x,y)}=scale \:factor\\\frac{U'(-4,4)}{U(2,2)}\Rightarrow U'=2U\\(x,y)=D2(x,y)[/tex]

Answer:

you didn't put a picture

Step-by-step explanation:

Step-by-step explanation:

Given:

[tex] (x_1, \: y_1 ) =(2, \:3)\:\:\&\:\: (x_2, \: y_2) =(6, \:10)[/tex]

[tex]l(PQ) = \sqrt{ {(x_1 - x_2)}^{2} + {(y_1 - y_2)}^{2}} \\ \\ = \sqrt{ {(2 - 6)}^{2} + {(3 - 10)}^{2}} \\ \\ = \sqrt{ {( - 4)}^{2} + {( - 7)}^{2}} \\ \\ = \sqrt{16 + 49} \\ \\ = \sqrt{65} \\ \\ \therefore \purple{ \boxed{ l(PQ) = 8.06 \: units}}\\\\[/tex]

Let S be the mid-point of PQ.

[tex]\therefore S = \{\frac{x_1+x_2}{2}, \:\:\frac{y_1+y_2}{2}\} \\\\

= \{\frac{2 +6}{2}, \:\:\frac{3+10}{2}\} \\\\

= \{\frac{8}{2}, \:\:\frac{13}{2}\} \\\\

\therefore S= \{4, \:\:6.5\} \\\\[/tex]

Equation of line PQ is given as:

[tex] \frac{y-y_1}{y_1 - y_2}=\frac{x-x_1}{x_1 - x_2} \\\\

\therefore \frac{y-3}{3 - 10}=\frac{x-2}{2 - 6} \\\\

\therefore \frac{y-3}{-7}=\frac{x-2}{-4} \\\\

\therefore \frac{y-3}{7}=\frac{x-2}{4} \\\\

\therefore 4(y-3)=7(x-2)\\\\

\therefore 4y-12=7x-14\\\\

\therefore 7x-14 - 4y + 12=0\\\\

\red{\boxed {\therefore 7x-4y - 2 =0}} [/tex]

Answer:

length = square root of ((2-6)^2)+((3-10)^2) = square root (of) 16+49

square root of 65 =  8.062257748  = approx 8.1

midpoint = (x1+x2)/2  ,  (y1+y2)/2

= 2+6  /2  ,  3+10  /2

=8/2 , 13/2

= 4, 6.5 (midpoint)

equation= y=mx+c

m(gradient) = (y2-y1)/(x2-x1) or (y1-y2)/(x1-x2)

= so,  (3-10)/(2-6)  (y1-y2)/(x1-x2)- i normally use this one

= -7/-4 = 1.75

so y=1.75x+c

plug in the values from any one of them (2,3) or (6,10)

to get

for example:  3=1.75*2+c

3=3.5+c

-0.5=c

now we get the equation y=1.75x+(-0.5)

you always have to have a plus( +(-0.5)) since the equation is y=mx+c

The best scenario for an exponential function is Option B, as it describes a consistent percentage decrease annually, which is characteristic of exponential decay.

The situation that is best modeled by an exponential function is Option B, which describes the amount of a substance remaining after x years if it is decreasing at a rate of 25% annually. This exemplifies an exponential decay scenario where the rate of change of a quantity is directly proportional to its current value. Over time, the substance decreases by a consistent percentage, which is characteristic of exponential decay functions.

A key feature of exponential relationships is that they describe processes where the change at any given point is proportional to the current amount, which fits the description of a substance decreasing by a consistent percentage each year.

Answer:y=-24

Step-by-step explanation:

Move all terms not containing

y

to the right side of the equation.