graph the system below2x-3y=-183x+y=-5

B. we just replace the vlues of t=1.5 and d=72

the rate of speed is 48 miles per hour

Check the picture below.

[tex]cos(\theta )=\cfrac{x}{10}\implies \stackrel{chain~rule}{-sin(\theta )\cdot \cfrac{d\theta }{dt}}=\cfrac{1}{10}\cdot \cfrac{dx}{dt} -sin(\theta )\cdot \cfrac{d\theta }{dt}=\cfrac{1}{10}(0.7)[/tex]

[tex]\cfrac{d\theta }{dt}=\cfrac{0.07}{-sin(\theta )}~\hfill \stackrel{\textit{when the ladder's bottom is 8ft, x = 8}}{sin(\theta )=\cfrac{8}{10}\implies sin(\theta )=\cfrac{4}{5}} \\\\\\ \cfrac{d\theta }{dt}=-\cfrac{0.07}{~~ \frac{4 }{5 } ~~}\implies \implies \cfrac{d\theta }{dt}=-0.07\cdot \cfrac{5}{4}\implies {\Large \begin{array}{llll} \cfrac{d\theta }{dt}=-0.0875~\frac{rad}{s} \end{array}}[/tex]

the rate is negative because the angle is decreasing as the ladder slides outwards.

The last term using factorization method to make the perfect square is 3 and the final expression is (x + 3)².

What is factorization method?

The factorization method is used for the quadratic based equation whose highest degree is either two or more than two. Depending upon the degree of the variable, the number of factors are calculated. And by substituting the calculated value to check whether the answer is correct or not.

According to the question, the given quadratic equation can be solved by performing factorization as well as by adding the half of the coefficient of the x-term to the given equation.

Therefore, the expression can be written as:

x² + 6x + 3² = 0

⇒(x + 3)² = 0

Hence, the last term by using factorization method to make the perfect square is 3 and the final expression is (x + 3)².

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Pi (π) is an irrational number that can be found by dividing the radius of a circumference by its diameter.

The digits of π considering the first 1,000 digital places are:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989

For k=2 for infinite solutions.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

4(4x + 1) = k(8x + 2)

Now, the equation should have infinite solutions

In consider the situation then we must put value of k such that LHS part become Equal to RHS.

Now, take k=2

4(4x + 1) = k(8x + 2)

LHS: 4(4x+1)= 16x+ 4

RHS: 2(8x+ 2)= 16x+ 4

Hence, k=2 for infinite solutions.

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Answer:

x = 3

Step-by-step explanation:

When twenty is reduced by one-third of a number, the result is 19. Find the number.

20 - 1/3x = 19

subtract 20 to both sides:

20 - 1/3x - 20 = 19 - 20

-1/3x = -1

multiply both sides by -3:

-3(-1/3x) = -1(-3)

x = 3

let j be justin, e for Eva and m for Emma. We get

so we get that, replacing all the variables

so we get that Eva has $20. therefore Justin has $27.5 and Emma has $15.5

The formula for determining the surface area of a sphere is expressed as

Surface area = 4 * pi * radius^2

From the information given,

surface area = 6

pi = 3.14

thus,

6 = 4 * 3.14 * radius^2

6 = 12.56radius^2

The formula for determining the volume of a sphere is expressed as

Volume = 4/3 * pi * radius^3

Thus,

Volume of sphere = 4/3 * 3.14 * 0.69^3

Volume of sphere = 1.38m^3

Answer:

[tex](x-1)^2+(y-9)^2=3^2[/tex]

Step-by-step explanation:

The standard form of the equation of a circle is:

[tex](x-a)^2+(y-b)^2=r^2[/tex]

Where a and b are the x and y, coordinates, and r is the radius.

So, you can just substitute the a and b values for the x and y values of the center to find the equation of the circle.

The lcm of the rational algebraic equation 6/x+x-3/4=2 be (24 -3x - 4x²) / 4x = 0.

The least common multiple is defined as the set of numbers with the least common multiple. The lowest positive integer with more than one factor in the set is HCF.

The given equation below as:

⇒ 6/x + x - 3/4 = 2

We must find the lcm of the rational algebraic equation.

⇒ 6/x + x - 3/4 = 2

Rearrange the term of 2 in the equation,

⇒ 6/x + x - 3/4 - 2 = 0

Take LCM in the above equation,

⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]

⇒ (24 + 4x² -3x - 8x²) / 4x = 0

Combine the likewise terms in the numerator,

⇒ (24 -3x - 4x²) / 4x = 0

Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.

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Answer:

B. the amount spent on grapes compared with the weight of the purchase

Given:

3.7284

The given number should be read as "three point seven two eight four.

Option D is the correct answer.

Answer:

y= -2x -7

Step-by-step explanation:

The equation of a line in slope-intercept form is given by y= mx +c.

Given that the slope is -2, we can substitute m= -2 into the equation.

y= -2x +c

The value of c can be found by substituting a point in which the line passes through into the equation. In this case, the point is (-4, 1).

y= -2x +c

When x= -4, y= 1,

1= -2(-4) +c

1= 8 +c

Subtract 8 on both sides:

c= 1 -8

c= -7

Substituting c= -7 into the equation:

y= -2x -7

Optional step:

To check our answer, we can substitute one coordinate and see if the other coordinate is the same as the given coordinate. For example, let's substitute the x-coordinate of -4 into the equation.

y= -2(-4) -7

y= 8 -7

y= 1

Since the y-coordinate is indeed 1, the equation above is correct.

Additional reading:

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Answer:

8

Step-by-step explanation:

65.29/8.23≈7.933

7.933 rounds to 8

Given the two numbers, let us simplify to find the value;

From the derived value, we can find which of the statements is true.

From the options, we can see that the only option that is entirely true is;

- The value of root 17 is less than 5, and the value of root 60 is greater than 7.

AA (or AAA) or Angle-Angle Similarity

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

We do not have 3 angles.

SAS or Side-Angle-Side Similarity

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.

We have two sides and 1 angle. But, two sides of a triangle are not in the same proportion of the two sides of another triangle

SSS or Side-Side-Side Similarity

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Letter D

We will find it as follows:

The volume of such a sphere is given by the expression found.

***

When we have a binomial at the power of a number, of the form:

We use Pascal's triangle to determine the expansion. Pascal's triangle is the following:

Each row can be used to calculate a specific power, in our case the binomial is at the power of three, and we will use the 4rth row to expand, that is:

As you can see, the numbers that accompany a & b are the ones found in the 4th row of Pascal's triangle. We also see that the "degree" o the expansion always sums 3, that is a^3 has an overall degree of 3, a^2b has an overall degree of 3, ab^2 has an overall degree of 3 & b^3 has an overall degree of 3.

***

If we, for example, wanted to expand (a + b)^4, we then would have the following:

*We would use the 5th row and get:

[Pascal's triangle expands to infinity. So, you in theory can manually expand any binomial at any power, but for big numbers, it will take a long time]

***

In our case, the binomial was:

And, its respective expansion is:

Answer:1234567.00 feet

Step-by-step explanation: feet are yummy

The best estimate for the product 9/10 x 5/11 is 1/2.

Product in Mathematics simply means a number that you get when you multiply. It is used to illustrate tye concept of multiplication

In this case, the estimate for 9/10 is 1 and the estimate of 5/11 is 1/2. Therefore, the product will be:

= 1 × 1/2

= 1/2

This shows the estimation.

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Solution:

Let the length and the width of the rectangular table be represented as L and W respectively.

Given that the length and the width have a ratio of 8 to 5, this implies that

If the width of the table is 40 in, the length of the table is evaluated as

Hence, the length of the table is 64 in.

The secant function is the reciprocal of the cosine function.

We can evaluate trigonometric functions of angles outside the first quadrant using reference angles as we have already done with the sine and cosine functions. The procedure is the same:

Find the reference angle formed by the terminal side of the given angle with the horizontal axis. The trigonometric function values for the original angle will be the same as those for the reference angle, except for the positive or negative sign, which is determined by x– and y-values in the original quadrant. (Figure) shows which functions are positive in which quadrant.

An even function is one in which f(-x) = f(x)

An even function is one in which f(-x) = - f(x)

Cosine and secant are even:

Therefore from the drop down the correct answer : secant function is EVEN

In this type of question, we will use the exponential equation

Where:

a is the initial amount

b is the factor of growth or decay

Since it is a half-life, then

b = 1/2 = 0.5

Since it is now 50 grams, then

a = 50

Since x is the number of years, then

x = 700

Substitute them in the rule above

It will be representing 0 grams after 700 years

The answer is A

solve for b:

Divide both sides by 12:

The argument of the polar coordinate is -45 degrees, which can be converted as,

Thus, the required point is D.

An equation which could be represented by the number line is: D. -5 + (-1) = -6.

A number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to compare or determine the difference between two numbers. Additionally, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.

From the number line shown above, we have:

Distance = -5 + (-1)

Distance = -5 - 1

Distance = -6.

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Yes, the numbers will be similar.

it will be true if the numbers were -3, 5, -16 and -10

Explanation:

The first list: -3, 5, 16 and -10

Arranging from least to greatest:

-10, -3, 5, 16

Arranging the same numbers from closest to zero to farthest to zero:

Let's use zero as our reference. Then start arranging towards the left and right side of it.

-10, -3, 0, 5, 16

Looking at the above: when we remove 0, we would have same answer as the arrangement from least to greatest:

-10, -3, 5, 16

The second list:

-3, 5, -16, -10

Arranging from least to greatest:

-16, -10, -3, 5

Arranging the same numbers from closest to zero to farthest to zero:

Let's use zero as our reference. Then start arranging towards the left and right side of it.

-16, -10, -3, 0, 5

Looking at the above: when we remove 0, we would have same answer as the arrangement from least to greatest:

-16, -10, -3, 5

Hence, fromt the above: if we arrange the same numbers from least to greatest and from closest to zero to farthest to zero, we would arrive at the same result.

It will take 4.9 days for 21 locust to eat 420 grams of grass

From the question, we have the following parameters:

Given that the amount of grass is constant at 420 grams

The given parameters can be represented using the following ratio

Ratio = Locust : Days

So, we have

Locust : Days = 30 : 7

When there are a total number of 21 locust eating the grass, then we have

21 : Days = 30 : 7

Express as fraction

Days/21 = 7/30

This gives

Days = 21 * 7/30

Evaluate

Days = 4.9

Hence, the number of days is 4.9 days

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Solution

For this case we can use the following formula:

And for this case

n= 4 compounded quarterly

t= 10 years

A= 200000

P=?

r=0.06

And we can solve for P and we got:

So then the final answer would be:

110252.5