Solve the system of equations 3x + y = 3 and 7x + 2y = 1.

1. Solve for the variable y in the first equation:     y = 3 − 3x

2. Substitute the value for y into the second equation:  7x + 2(3 − 3x) = 1

3. Solve for x: x =

Answer:

Step-by-step explanation:

Rhombus is a two dimensional shape. So it doesn't have volume.

Area of rhombus = (pq)/2

Here p & q are the diagonals

Answer:

The answer to your equation is -47.

Step-by-step explanation:

Follow the order of operations. First do 9*5=45, and 6*-2 to get -12. Next, just finish the equation from left to right to get -47.

Answer:

B

Step-by-step explanation:

I think the answer is B as it is on the positive side.

Answer:

t = -24*log(2/3)

Step-by-step explanation:

The expression is:

V = 22,500*10^(-t/12)

Replacing with V = 10,000 and isolating t, we get:

10,000 = 22,500*10^(-t/12)

10,000/22,500 = 10^(-t/12)

4/9 = 10^(-t/12)

(2/3)² = 10^(-t/12)

2*log(2/3) = -t/12

-12*2*log(2/3) = t

t = -24*log(2/3)

Answer:

The number of years after purchase at which Vishal's car will be worth $10,000 is [tex]Log_{10}\left (\frac{9}{4} \right )^{12}[/tex]  years

Step-by-step explanation:

The relationship is given as follows

Value, V of the car = 22500×[tex]10^{-t/12}[/tex]

Therefore, when the car is $10,000 we will have

$10,000 = 22,500×[tex]10^{-t/12}[/tex]

Which will give;

[tex]\frac{10000}{22500} =\frac{4}{9} = 10^{-\frac{t}{12}}[/tex]

Hence;

[tex]Log\frac{4}{9} = Log(10^{-\frac{t}{12}} )[/tex]

Therefore;

[tex]-\frac{t}{12}\times Log_{10} 10 = Log\frac{4}{9}[/tex]

[tex]\because Log_{10} 10 = 1, \ we \ have; \ -\frac{t}{12} = Log_{10}\frac{4}{9}[/tex]

Which gives;

[tex]t = -12 \times Log_{10}\frac{4}{9} \ or \ t = Log_{10}\left (\frac{4}{9} \right )^{-12}[/tex]

[tex]\therefore t = Log_{10}\left (\frac{9}{4} \right )^{12}[/tex] years

Evaluated, the above equation becomes t = 4.226 years

Therefore, the number of years after purchase at which Vishal's car will be worth $10,000 = [tex]Log_{10}\left (\frac{9}{4} \right )^{12}[/tex]  years.

Answer:

its B

Step-by-step explanation:

i got it right on USA TEST PREP

Answer:

The answer is 52°

Step-by-step explanation:

58°+70°+x=180

128°+x=180°

180°-128°

=52°

Answer:

The answer is 2; use the remainder only

Step-by-step explanation:

The question is asking how much water would be left over, not how much each bottle will get. There is a remainder of 2, so that means there will be 2 ounces left

Answer:

2.25

Step-by-step explanation:

5=15 and d8=170=which of the following is closest to the value of fb

The value of b is closest to (2) 2.25

An exponential function is represented as:

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

[tex]f(5) = 15[/tex] means that:

[tex]ab^5 = 15[/tex] ---- equation (1)

[tex]f(8) = 170[/tex] means that:

[tex]ab^8 = 170[/tex] ---- equation (2)

Divide equation (2) by equation (1)

[tex]\frac{ab^8}{ab^5}= \frac{170}{15}[/tex]

Divide common factors

[tex]b^3= 11.33[/tex]

Take the cube root of both sides

[tex]b= \sqrt[3]{11.33}[/tex]

Evaluate the expression

[tex]b= 2.246[/tex]

2.246 can be approximated to 2.25

Hence, the value of b is closest to (2) 2.25

Read more about exponential functions at:

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Answer:

d t(x), because an increasing exponential function will eventually exceed an increasing quadratic function

Step-by-step explanation:

t(x) joins the ordered pairs:

(0, 1) (1, 3) and (3, 27)

p(x) joins the ordered pairs:

(0, 2) (1, 3) (3, 11) (5, 27) and (6, 38)

After t(x) and p(x) intersection, t(x) increases in a greater amount than p(x)

Answer: he is correct

Step-by-step explanation:

Answer:

D, 10.28

Step-by-step explanation:

2+2+3.14x2/2+3.14x2/2=10.28

Answer:

10.28 in

Step-by-step explanation:

r = 2in/2 = 1in

P = 2π·r + 2·l

= 2×3.14×1in + 2×2in

= 6.28in + 4in

= 10.28 in

Answer:

The answer is 11 Hope this helps ;)

Step-by-step explanation:

The triangle LMN is a scalene triangle, and the area of the triangle LMN in the coordinate plane is 4 square units.

Below you can understand more about areas of triangle

A triangle is a shape that has 3 sides and 3 angles

Check below on how to determine the triangle area

The coordinates are given as:

L = (1,-1)

M = (3,2)

N = (1,3)

Calculate the length of side NL using:

NL = √[(x2 -x1)^2 + (y2 - y1)^2]

So, we have:

NL = √[(1 -1)^2 + (3 + 1)^2]

NL = √16

NL = 4

The altitude MP is 2 units.

So, the area is:

Area = 0.5 * NL * MP

This gives

Area = 0.5 * 4 * 2

Evaluate the product

Area = 4

Hence, the area of the triangle is 4 square units

Read more about areas at:

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Answer:

x= -1

Step-by-step explanation:

1-3x=x²+6x+9

1-3x-x²-6x-9=0

-8-9x-x²=0

x²+9x+8=0

x²+8x+x+8=0

(x+8)(x+1)=0

x+8=0

x+1=0

sqrt 1-3(-8)=-8+3

sqrt 1-3(-1)=-1+3

5=-5

2=2

x≠8

x=-1

Answer:

Sure! But I need to see the questions to answer them.

~Lexi

Answer:

Sure I can.

Step-by-step explanation:

Just post what questions you need checking, and I'll try to the best I can.

Answer:

y = 5

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (7, 5) and (x₂, y₂ ) = (- 9, 5)

m = [tex]\frac{5-5}{-9-7}[/tex] = [tex]\frac{0}{-16}[/tex] = 0

This means the line is horizontal and parallel to the x- axis with equation

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (7, 5) and (- 9, 5) with y- coordinates 5, thus

y = 5 ← equation of line

Answer:

x=7 (if your teacher cares it could + or - 7)

Step-by-step explanation:

Okay, since it's a 90 degree triangle you can use the Pythagorean theorem

( a^2 + b^2 = c^2)

Since it's an isosceles triangle the other side is x because it's the same value.

x^2 + x^2= (7[tex]\sqrt{2}[/tex] )^2

Add the left side

2x^2= 7^2 + [tex]\sqrt{2}[/tex]^2 roots and square roots cancel each other out

So -> 2x^2= 49 x 2 =98

just solve for x.

x^2 = 98/2

x^2= 49

Square root both sides

x= 7

Answer:

12 months

Step-by-step explanation:

Your answer would be 1/8.

The probability for getting a tail one time would be 1/2 because there are only 2 sides of a coin. Since tossing one coin doesn't affect the outcome of tossing the other coins, the probability for getting a tail on all of the coins is 1/2 each. We want this to happen 3 times, so the answer would be 1/2 × 1/2 × 1/2 = 1/8.

I hope this helps!

Answer:

1/2 x 1/2 x 1/2 = 1/8

1/8

Step-by-step explanation:

Answer:

the graph  that represents the compound inequality –3 < n < 1 is the straight line from -3 to 1 in which there is a hollow circle in the -3 point and in the 1 point. This is because < means that the possible values of n is only greater than -3 exluding -3 and less than -1 excluding -1

Answer:

is d

Step-by-step explanation:

Answer:

4?

Step-by-step explanation:

Answer:

The mean is 15 so adding another 15 keeps the mean unchanged.

Step-by-step explanation:

To solve this problem, we first set up an equation to express the product of the numbers at the vertices of the square in terms of their sum. Then, we use this equation to find the values of the numbers on the edges of the square. The sum of all the numbers on the edges equals to 2 times the square root of 15.

Let's denote the four numbers on the edges of the square as a, b, a, b (since it's a square, opposite sides are equal). The products at the vertices are: ab (top left), ab (top right), ab (bottom right) and ab (bottom left).

So the sum of these numbers at the vertices is 4ab = 15. From here, we can solve the equation for ab, giving us ab = 15 / 4.

The problem asks for the sum of the numbers on the edges, which equates to 2a + 2b. As due to our current setup, a = b, we can simplify this to 4a or 4b. But we don't have a or b - we have ab. Because of this, we require a bit of algebra. We know that (a + b)^2 = a^2 + 2ab + b^2. In our case, where a = b, this can simplify to 4a^2. From here, we proceed with ab = 15/4 to replace 2ab in the equation with the latter, and then solve for a^2, followed by a.

The result is a=root(15/4). To get the sum of all the edges, we would then multiply this by 4, giving us 4*root(15/4) = 2root(15).

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The sum of the numbers on the sides of the square is calculated by doubling the number on the side 'a', adding to double the number of 'b'. With 'b' equals to 15 divided by four times 'a', the sums equals to 2a plus 2 times 15 divided by four times 'a'.

Let's denote the numbers on the sides of the square as a, b, a, b, respectively. Hence, each vertex will be the product of a and b, making each vertex to be ab. Given that the total sum of these vertex is 15, we have 4ab = 15, which simplifies to ab = 15/4.

To find the total sum of the numbers on the sides of the square (the edges), we should sum up all a and b's. Therefore the sum will be 2a + 2b. Given that b = 15 / (4a), we can substitute b into the equation, simplifying to get the total sum = 2a + 2*(15 / (4a)). This is the solution to the problem.

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Answer:

13.) tanC=40/30

14.) tanA=21/20

15.) tanC=12/35

16.) tanX=30/40

17.) sinZ=12/37

18.) sinZ=30/50

Final answer:

Trigonometry focuses on the ratios between sides and angles of right-angled triangles. Ratios are used to maintain relationships between quantities in scaled models or mathematical problems. Practicing these calculations aids in mental math and practical applications.

Explanation:

Practice Writing Trig Ratios

Trigonometry involves understanding the relationship between the angles and sides of right angled triangles. These trigonometric ratios, which include sine, cosine, and tangent, are essential in connecting angles to their respective side lengths. They are ratios and thus dimensionless, meaning they have no units. These calculations become easier with practice, allowing one to approximate and compute them mentally.

When dealing with practical problems, such as scaling distances for a model or building, it is common to write proportions to maintain the relationships between lengths and widths. For example, if you have a scale that says 1 inch on the model represents 10 feet in reality (inches/feet = 1/10), you would write a ratio that respects this scale. Similarly, if comparing areas, you would establish a ratio outlining how one area relates to the other based on their respective dimensions.

It is also valuable to familiarize oneself with the functions of a calculator by experimenting with various operations such as squaring, square roots, trigonometric functions, and logs. This helps in comprehending the interconnectedness of these mathematical concepts and their practical application.

Answer:

1

Step-by-step explanation:

Let the number be X

condition

12 more than seven times the number

it can be represented numerically by using process given belwo

seven times the number will be 7 * X = 7X

12 more than 7X will be equal to 7X + 12

______________________________

This number (7X + 12) is equal to number plus 19

number plus 18 will be X + 18

therefore according to the question

7X + 12  = X + 18

=> 7X - X = 18 - 12

=> 6X = 6

=> X = 6/6 = 1 (Answer)

The number is 1.

Answer:True

Step-by-step explanation: The smaller triangle is half as small

The triangles are similar, so this is true.

The blue triangle has been enlarged by a scale of 2. It's 4 units up and 2 units to the right and the second larger triangle is 8 units up and 4 to the right, so it's 2 times bigger.

I hope this helps :)

To find out how many more pounds of apples Shannon bought compared to Bill, subtract the weight of Bill's apples from the weight of Shannon's apples. The most close estimate of how many more pounds Shannon bought is 2 1/4 pounds.

To find out how many more pounds of apples Shannon bought compared to Bill, we need to subtract the weight of Bill's apples from the weight of Shannon's apples.

Shannon bought 5 1/8 pounds of apples, which can be written as a mixed number as 5 + 1/8.

Bill bought 2 7/8 pounds of apples, which can be written as a mixed number as 2 + 7/8.

To subtract these mixed numbers, we can find a common denominator and then subtract the whole numbers and fractions separately.

Let's convert the mixed numbers into improper fractions and subtract:

The most closely estimate of how many more pounds of apples Shannon bought than Bill is 9/4 pounds or 2 1/4 pounds.

Answer:

a = 40 if simplified :)

Answer:

Dear mate your answer is 40...

Look at the attached picture ⤴

Hope it will help u....

Step-by-step explanation:

Step 1:  Factor

[tex]b^2 + 5b + 6[/tex]

[tex]b^2 + 3b + 2b + 6[/tex]

[tex](b + 3)(b + 2)[/tex]

Answer:  [tex](b + 3)(b + 2)[/tex]

(b + 2) (b + 3)

Step-by-step explanation:

b² + 5b + 6

Known :

a = 1

b = 5

c = 6

Asked :

Factorise b² + 5b + 6 = ...?

Answer :

p × q = c

p + q = b

So :

p × q = 6

2 × 3 = 6

p + q = 5

2 + 3 = 5

So, p = 2 & q = 3

So, factorise b² + 5b + 6 is (b + 2) (b + 3)

Hope it helpful and useful :)

The roles of three levels of craftspeople in a shoemaker’s shop are Master Craftsman, Journeyman and Apprentice.

The three levels of craftspeople you might find in a shoemaker’s shop and their duties are:

Master Craftsman: Oversees the entire shoemaking process, creates designs, and ensures quality.

Journeyman: Skilled worker who assists the master craftsman, carries out specific tasks like cutting leather or stitching, and trains apprentices.

Apprentice: Learns the trade under the guidance of the master craftsman and journeyman, performs basic tasks to gain experience.