pls help with this if it is not to hard for you to do ​

Answer:

20x - 5y= -5

6x- 5y= 9

14x= - 14

x= - 14by4= - 1

put value in equation2

6( - 1) - 5y= 9

- 5y= 9 plus 6

- 5y= 15

y= -15 by5= - 3

Answer:

The answer is option B

Step-by-step explanation:

To find the coefficient of the third term in

\((x + 5)^{7} \)

Rewrite the expansion in the form

\((a + x)^{n} \)

where n is the index

So we have

\( ({5 + x})^{7} \)

After that we use the formula

\(nCr( {a}^{n - r} ) {x}^{r} \)

where r is the term we are looking for

For the third term we are looking for the term containing x²

that's

r + 1 = 3

r = 2

So to find the coefficient of the third term

We have

\(7C2\)

Hope this helps you

first of all, the notation is wrong it should be \( {}^nC_r \text{ and more usual notation is } {n \choose k} \)

second, the

\((r+1)^{\text{th}} \text{ term } T_{r+1} \text{ in the expansion of } (x+a)^n \text{ is } {n \choose r}x^{(n-r)}a^r\)

here \( a=5 \text{ and } n=7 \text{ and for } 3^{\text{rd}} \text{ term } T_3, \quad r+1=3 \implies r=2 \)

so the coefficient of third term is, \({7 \choose 2}={7\choose 5}\)

an important property of binomial coefficient you should know:

\( {n \choose k}={n \choose {n-k}}\)

and if you interchange \( x \text{ and } a\)

only the "order" will get reversed. i.e. the series will start from back.

another thing, the \( k^{\text{th}} \text{ term from beginning, is the } (n-k+2)^{\text{th}} \text{ term from behind}\)

The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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Answer:

steps below

Step-by-step explanation:

(cosA-sinA+1) * cosA = cos²A - sinA cosA + cosA

                                 = (1 - sin²A) - sinA cosA + cosA + sinA - sinA

                                 = cosA + sinA + 1 - sinA cosA  -sin²A - sinA  ..Re-group

                                 = (cosA + sinA + 1) - sinA (cosA + sinA + 1)

                                 = (cosA + sinA + 1) * (1 - sinA)

(cosA-sinA+1) / (cosA + sinA + 1) = (1 - sinA) / cosA

The solution to given linear inequality, 6(x1.5) + 30 < 48, is x < 2

From the question, we are to solve the given linear inequality

The given linear inequality is

6(x1.5) + 30 < 48

First, we will write this inequality properly.

The inequality can be properly written as

6(1.5x) + 30 < 48

Now, we will solve the linear inequality

6(1.5x) + 30 < 48

Subtract 30 from both sides of the equation

6(1.5x) + 30 - 30 < 48 - 30

6(1.5x) < 18

Divide both sides of the inequality by 6

6(1.5x)/6 < 18/6

(1.5x) < 3
1.5x < 3

Divide both sides of the inequality by 1.5

1.5x/1.5 < 3/1.5

x < 2

Hence, the solution is x < 2

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Answer:

maximum height = 26 feet and minimum height = 8 feet  The main cable of a suspension bridge forms a parabola modeled by the  height in feet of the cable above the road, x is the horizontal distance in feet from the How long are the sides of the smaller window? A soccer ball is kicked into the air from the ground.

Step-by-step explanation:

Answer

The inequality describing the situation is

1.50 + 0.65x ≤ 15

Solving this,

x ≤ 20.77 miles

This means that with the amount she's willing to spend, she can travel no more than 20.77 miles with $15

Explanation

Flat fee for the ride is $1.50

Then each mile covered results in an extra expense of $0.65 per mile.

Cindy can spend no more than $15 on a ride.

If the maximum number of miles Cindy can go is x

Total amount for the ride for x miles

= (1.50 + 0.65x) dollars

This total amount cannot exceed $15

1.50 + 0.65x ≤ 15

We can then solve this inequality

1.50 + 0.65x ≤ 15

0.65x ≤ 15 - 1.50

0.65x ≤ 13.5

Divide both sides by 0.65

(0.65x/0.65) ≤ (13.5/0.65)

x ≤ 20.77 miles

Hope this Helps!!!

The intervals of each behavior of the function are given as follows:

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well, we can simply divide 210 by (3 + 4) and then distribute accordingly

\(\stackrel{James}{3}~~ : ~~\stackrel{John}{4} ~~ \implies ~~ \stackrel{James}{3 ~~ \cdot \frac{210}{3+4}}~~ : ~~\stackrel{John}{4~~ \cdot \frac{210}{3+4}} ~~ \implies ~~ \stackrel{James}{3 \cdot \frac{210}{7}}~~ : ~~\stackrel{John}{4 \cdot \frac{210}{7}} \\\\\\ \stackrel{James}{3(30)}~~ : ~~\stackrel{John}{4(30)} ~~ \implies ~~ \stackrel{James}{90}~~ : ~~\stackrel{John}{120}\)

Answer:

James- 90 and John- 120

Step-by-step explanation:

Since you want to divide 210 with a ratio of 3:4. It's easiest to first add your 3 and 4. This =7. Now you know you have to divide 210 by 7 before you give them to James and John. 210 divided by 7 = 30. Now do 30 times each ratio.

James has 30 x 3 and John has 30 x 4

this leaves you with 90 and 120

Answer:

We are 95% confident that the true proportion of U.S. adults who live with one or more chronic conditions is between 39.7% and 46.33%

Step-by-step explanation:

From the question we are told that

  The  sample  proportion is \(\r p = 43\%  = 0.43\)

   The  standard error is \(SE =  0.017\)

Given that the confidence level is 95%  then the level of significance is mathematically represented as  

      \(\alpha =  (100-95)\%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as

     \(E = Z_{\frac{\alpha }{2} } *  SE\)

=>    \(E = 1.96 *  0.017\)

=>     \(E = 0.03332 \)

Generally 95% confidence interval is mathematically represented as

      \(\r p -E <  p <  \r p +E\)

=>   \(0.43 -0.03332 <  p <  0.43 + 0.03332\)

=>    \( 0.39668 <  p <  0.46332\)

Converting to percentage

\( (0.39668 * 100)<  p <  (0.46332*100)\)        

\( 39.7\% <  p < 46.33 \%\)    

Answer:

-2.25

Step-by-step explanation:

If you want to convert -2\(1/4\) to a decimal you will want to split the fraction up to make it easier to work with.

\(-2 \frac{1}{4} = -2 + \frac{1}{4}\)

\(\frac{1}{4}\) is the same 1 divided by 4

So you will do

−2+(1÷4)

1 divide by 4 is 0.25 so you will do

-2+0.25 = -2.25

The Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.

Volume can be defined as the total quantity of a substance that a container can hold at a given period of time. Also, the volume of a container is measured in:

Based on the information provided in the table above, we can infer and logically deduce that the Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.

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Answer:

The value of x is equal to: 4.5%

Step-by-step explanation:

10% of = 10.582

105.82-10.582= 95.238

100-95.238= 4.762

4.762 is 4.5% of 105.82.

Answer:

\(\frac{a}{3} \frac{.}{.}\frac{3}{a} =1\)

Step-by-step explanation:

As we seen that the reciprocal of the a/3(a/3) provides the result as a product number that gives the output as 1 .

Also we know that two fractions number gives output 1 if they are the reciprocal or multiplicative inverse from each other.

So,  a/3(a/3

\(\frac{3a}{3a} \\\\it\ can\ be \ written \ as \\\frac{3}{a} \frac{.}{.}\frac{a}{3}=\ 1\)

Answer:

It is not D!!!

Step-by-step explanation:

Answer:

C. Vertex (−3, 3); Range 3 ≤ y ≤ ∞

Step-by-step explanation:

The graph of a quadratic function h(x) is symmetric about the axis of symmetry.

The axis of symmetry is a vertical line that divides the parabola into two congruent halves and passes through the vertex.

The axis of symmetry is the x-value of the vertex.

From the table of values, we can see that the y-values of function h(x) are symmetric either side of h(x) = 3. Therefore, the axis of symmetry is x = -3 and the vertex is (-3, 3).

The range of a function is the set of all possible output values (y-values).

From the table, we can see that the minimum y-value is y = 3, so the range of the function is therefore 3 ≤ y ≤ ∞.

Answer:

None of the given system of linear inequalities

Step-by-step explanation:

Given

\((x,y) =(3,-2)\)

Required

The line inequalities with the above solution

The first set of linear inequalities, we have:

\(y < -3\)

\(y \ge \frac{2}{3}x - 4\)

\(y < -3\) implies that the values of y is -4,-5.....

While \((x,y) =(3,-2)\) implies that y = -2

Hence, the first set is wrong

The second set of linear inequalities, we have:

\(y > - 2\)

\(y \ge \frac{2}{3}x - 4\)

\(y > - 2\) implies that the values of y is -1,0.....

While \((x,y) =(3,-2)\) implies that y = -2

Hence, the second set is wrong

The system of linear inequalities having the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4.

A system of linear inequalities is known to be a composition of  linear inequalities that can be found in the same variables.

The graph that is showing  y > -3; y ≥ 2/3x - 4

-2 > -3  is true

y ≥ 2/3x - 4

-2 ≥ -2  is true

Therefore,  y > -3; y ≥ 2/3x - 4 has the point (3, -2) in its solution set.

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Answer:

false

Step-by-step explanation:

The standard form of polynomial is x^2 + 9x - 1/10

To write the equation in standard form, look at the degree of highest term and then rewrite the equation in decreasing order of degree i.e. from highest to lowest.

The given polynomial is

⇒ x^2 + 9x - 1/10

The standard form of the polynomial is

⇒ x^2 + 9x - 1/10

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The value of the original quotient log(9) / log(2) is equivalent to the logarithm with base 2 and argument 9, which can be written as log(base 2) 9.

We may apply the quotient rule of logarithms, which asserts that: to rewrite the quotient of logarithms log(9) / log(2) as a single logarithm:

Log(base b) = log(a)/log(b) a

This rule can be written as follows: log(9) / log(2) = log(base 2) 9

As a result, log(9) / log(2) = log(base 2) can be used to replace the ratio of logarithms log(9) / log(2) with a single logarithm using base 2 and argument 9. 9

This can also be expressed as 2(log(9) / log(2)) = 2log(base 2) 9 = 9 in exponential notation.

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Note: The complete Question is : Rewrite the following quotient of logarithms as a single logarithm: log(9) / log(2)

Answer:

True

False

False

Step-by-step explanation:

Answer:

We have,

y - x^2 = 29 - (-5)^2

= 29 - 25

= 4

Therefore, y - x^2 = 4 when x = -5 and y = 29.

The depth of the river is 3.192 feet.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Since last year the depth of the river was 4.2 feet deep and year it dropped 24%. The depth will be:

= 4.2 - (24% × 4.2)

= 4.2 - 1.008

= 3.192 feet

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\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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Answer:

The different inequality symbols include

Step-by-step explanation:

< which means less than

< which means less than or equal to

> which means greater than

> which means greater than or equal to

A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

The equivalent exponential equations are given as follows:

\(2^{4x} = 2^{3(x - 3)}\)

The exponential expression for this problem is defined as follows:

\(2^{4x} = 8^{x - 3}\)

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)

Meaning that the correct option is given by the fourth option.

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