What is the length of side BC of the triangle?
Enter your answer in the box.

Answer:

3:4

Step-by-step explanation:

We know this because the GCD of 21 and 28 is 7

so we divide both numbers by 7 and get 3 and 4

so the answer is 3:4

Answer:

8.2 minutes

Step-by-step explanation:

[tex] \ \frac{492}{60} = 8.2[/tex]

492 seconds = 8.2 minutes

Answer:

(-1,3)

y=5x+8 , y=-4x-1y=5x+8,y=−4x−1

Both sides have y on the left hand side so make the right hand side equal and solve for x

5x+8= -4x-15x+8=−4x−1

To solve for x , add 4x on both sides

9x+8=-19x+8=−1

Subtract 8 on both sides

9x=-99x=−9

Divide by 9 on both sides

x=-1x=−1

Now plug in -1 for x in the first equation and find out y

y=5x+8y=5x+8

y=5(-1)+8y=5(−1)+8

y=-5+8y=−5+8

y=3y=3

Ordered pair is (x,y) that is (-1,3)

Step-by-step explanation:

Mark me as brainliest plsss

Answer:

14 hours

Step-by-step explanation:

7h - 5(3h-8) = -72

7h - 15h + 40 = -72

-8h +40 = -72

-8h = -72 -40

-8h = -112

h = -112/ -8

h = 14

Answer:

Step-by-step explanation:

Negative numbers don't have real square roots since a square is either positive or 0. so it doesn't exist

Answer:

i

Step-by-step explanation:

the square root of  negative one is not real.

It is classed as an imaginary number denoted by  i , that is

[tex]\sqrt{-1}[/tex] = i

Using the unit rate, the missing values that completes the table are:

A = 5; B = 15; C = 40

Unit rate (m) = change in y/change in x.

5 minutes for 8 Blocks (5, 8) and 10 minutes for 16 blocks (10, 16)are given.

Unit rate (m) = (16 - 8)/(10 - 5) = 8/5

An equation that will define the function is, y = 8/5x. Use it to complete the table.

Find A (y) when x is 5:

y = 8/5(5) = 8

The value of A is: 5

Find B (x) when y is 24:

24 = 8/5(x)

5(24) = 8x

120 = 8x

120/8 = x

15 = x

The value of B is: 15

Find A (y) when x is 25:

y = 8/5(25) = 40

The value of C is: 40

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Gracie’s overtime rate of pay would be $635.06.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Gracie earns 17.25/h for a 37.5h week, plus extra for overtime.

For one hour she earns $17.25

For 37.5h she earns = 37.5h x 17.25

                                   = $646.87

The total money she earns = $646.87 + overtime pay

During store inventory, she worked 48.5h. Her gross earnings were $1,471.88.

= 48.5h x 17.25

= $836.625

So, $836.625 + overtime pay = $1,471.88

overtime pay = $1,471.88 - $836.625 = $635.06

Hence, Gracie’s overtime rate of pay would be $635.06.

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[tex]2^x-3^x=\sqrt{6^x-9^x}\\\\D:6^x-9^x\geq0 \wedge 2^x-3^x\geq0\\D: 6^x\geq 9^x \wedge 2^x\geq3^x\\D:x\leq0 \wedge x\leq 0\qquad(\text{if }a < b \text{ then } a^x < b^x\text{ for } x > 0 \text{ and } a^x > b^x \text{ for } x < 0 )\\D:x\leq 0\\\\(2^x-3^x)^2=6^x-9^x\\(2^x-3^x)^2=3^x(2^x-3^x)\\\\\text{We divide both sides by } 2^x-3^x \text{ assuming }2^x-3^x\not=0\Leftrightarrow x\not=0.\\\\2^x-3^x=3^x\\2^x=2\cdot3^x\\\ln 2^x=\ln (2\cdot3^x )\\x\ln 2=\ln 2+\ln 3^x\\x\ln 2=\ln 2+x\ln 3[/tex]

[tex]x\ln 2-x\ln 3=\ln 2\\x(\ln 2-\ln 3)=\ln 2\\x=\dfrac{\ln 2}{\ln 2-\ln 3}=-\dfrac{\ln 2}{\ln 3-\ln 2}=-\dfrac{\ln 2}{\ln \frac{3}{2}}\approx-1.7[/tex]

For [tex]x=0[/tex], our initial equation is obviously true.

Therefore [tex]x\in\left\{-\dfrac{\ln 2}{\ln \frac{3}{2}},0\right\}[/tex].

Answer to the miscellaneous equation, is x=0 and x=-1.71

Miscellaneous equation are the equations which are not polynomial

The question can be solved by:

Factorising Splitting the terms to find the required solution

Completing the squares, etc

2ˣ - 3ˣ = √(6ˣ - 9ˣ)

Squaring both sides,

2²ˣ+3²ˣ -2.2ˣ.3ˣ=2ˣ.3ˣ - 3²ˣ

2²ˣ+2.3²ˣ -3.2ˣ.3ˣ=0

Factorising the terms,

2ˣ(2ˣ-3ˣ) -2.3ˣ(2ˣ-3ˣ)=0

(2ˣ-3ˣ)(2ˣ-2.3ˣ)=0

Equating the braces to zero,

Either,

2ˣ=3ˣ

x=0

or

2ˣ=2.3ˣ

Taking log on both sides

xln2=ln2+xln3

x=ln2/(ln2-ln3)

  =-1.71

Therefore, x=0 and x=-1.71 is the only solution

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Answer:

1073

Step-by-step explanation:

it's simple addition

Answer: A

Step-by-step explanation:

[tex]\frac{dy}{dx}=\frac{1+x}{xy} \\ \\ y \text{ } dy=\frac{1+x}{x} \text{ } dx \\ \\ y \text{ } dy= \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \int y \text{ } dy=\int \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \frac{y^{2}}{2}=\ln \left| x \right|+x+C[/tex]

Substituting in the initial condition,

[tex]\frac{(-2)^{2}}{2}=\ln \left|1 \right|+1+C\\\\2=1+C\\\\C=1[/tex]

So,

[tex]\boxed{\frac{1}{2}y^{2}=\ln \left|x \right|+x+1}[/tex]

Answer:

[tex]\textsf{A.} \quad \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]

Step-by-step explanation:

To solve the differential equation:

Rearrange the given equation to get all the terms containing y on the left side, and all the terms containing x on the right side:

         [tex]\dfrac{dy}{dx}=\dfrac{1+x}{xy}[/tex]

[tex]\implies y\dfrac{dy}{dx}=\dfrac{1+x}{x}[/tex]

[tex]\implies y\:dy=\dfrac{1+x}{x}\:dx[/tex]

[tex]\implies y\:dy=\dfrac{1}{x}+\dfrac{x}{x}\:dx[/tex]

[tex]\implies y\:dy=\left(\dfrac{1}{x}+1\right)\:dx[/tex]

Integrate both sides:

[tex]\displaystyle \implies \int y\:dy=\int \left(\dfrac{1}{x}+1\right)\:dx[/tex]

[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+C[/tex]

Find the value of C using the given values of x and y:

when x = 1, y = -2

[tex]\implies \dfrac{1}{2}(-2)^2=\ln|1|+1+C[/tex]

[tex]\implies 2=0+1+C[/tex]

[tex]\implies C=1[/tex]

Substitute the found value of C:

[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]

Answer:

the answer would be 23/13 - 15/13i

Step-by-step explanation:

The result of the complex expression (10 – 4i) ÷ (5 + i) is [tex]\frac{23}{13} - i\frac{15}{13}[/tex] .

Given, complex expression  (10 – 4i) ÷ (5 + i)

Complex roots: When the roots are complex in nature then they appear in complex conjugate pair.

Complex roots: a ± ib

Complex number pair : a ± ib

i = iota(imaginary number)

a = real part

b = imaginary part

Value of iota :

[tex]i = \sqrt{-1}\\ i^2 = -1[/tex]

Complex expression :  (10 – 4i) ÷ (5 + i)

Apply rationalization,

Use formula [tex](a^2 - b^2) = (a+b)(a-b)[/tex].

[tex]\frac{ (10 - 4i) }{(5 + i)} \times \frac{5-i}{5-i} \\\\= \frac{(10 - 4i) \times (5-i) }{(5+i)(5-i)} \\\\=\frac{50 -30i -4}{5^2 - i^2}\\ \\= \frac{46 - 30i}{25 +1 } \\\\= \frac{46 - 30i}{26} \\\\[/tex]

[tex]= \frac{23}{13} - i\frac{15}{13}[/tex]

The real part is positive and imaginary part is negative.

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Option D is correct the face value is the price that must be paid to the issuer to buy it at the time it is issued.

If the bond issuer doesn't default, face value, also known as par value, is the sum that is paid to a bondholder at the bond's maturity date. Bonds offered on the secondary market do, however, change in response to interest rates.

Therefore Option D is correct the face value is the price that must be paid to the issuer to buy it at the time it is issued.

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Answer: 23.476 = 20+3+0.4+0.07+0.006

Step-by-step explanation:

I think you were supposed to write down the choices but I will guess the answer is this one:

23.476 = 20+3+0.4+0.07+0.006

Hope I helped!

Inequalities help us to compare two unequal expressions. The correct option is B.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

The solution to two systems of inequalities in the region where the area of the two inequalities overlaps. As it can be observed in this case that the overlap area is B.

Hence, the correct option is B.

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A percentage is a way to describe a part of a whole. The amount that Kelly will pay for the dress is $33.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given Kelly wants to buy a dress that costs $40.00. She has a coupon for 25% off, and there is a 10% sales tax. Therefore, the amount she will pay is,

25% of $40.00 is,

0.25 × $40 = $10

After using the coupon, the sale price is,

$40 - $10 = $30

The 10% tax on the sale price is,

0.10 × $30 = $3

The final price is $

$30 + $3 = $33

Hence, the amount that Kelly will pay for the dress is $33.

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All the transformations for which A and B would be congruent are; Translation, Reflection, and Rotation.

A congruence transformation is defined as a movement of shape such that it can produce a shape that is congruent to the original.

There are three types of congruence transformation;

1. Translation

2. Reflection

3. Rotation

Given;

Shape B is made by applying a single transformation to shape A.

Hence, All the transformations for which A and B would be congruent are; Translation, Reflection, and Rotation.

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Answer:

[tex]\fbox {See below} \downarrow[/tex]

Step-by-step explanation:

Question 1 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(4x^{3})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 4(3)x^{3-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 12x^{2}}[/tex]

Question 2 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{2}{x^{4}})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(2x^{-4})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 2(-4)x^{-4-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = -8x^{-5}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = -\frac{8}{x^{5}}}[/tex]

Question 3 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3\sqrt{x})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3(x)^{\frac{1}{2}})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 3(\frac{1}{2})x^{\frac{1}{2}-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2}x^{-\frac{1}{2}}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2\sqrt{x}}}[/tex]

Question 4 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{3}{\sqrt{x}})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{-\frac{1}{2}})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 3(-\frac{1}{2})x^{-\frac{1}{2}-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2}x^{-\frac{3}{2}}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2x\sqrt{x}}}[/tex]

Question 5 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{x^{3}}{4})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{1}{4}(3)x^{3-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = \frac{3}{4}x^{2}}[/tex]

Question 6 :

[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{5})}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 3(5)x^{5-1}}[/tex]

[tex]\mathsf {\frac{dy}{dx} = 15x^{4}}[/tex]

The equation is y = 250(0.89)^x and the decay rate is 11%.

The initial value will be:

= 250(0.89)^x

= 250(0.89^0)

= 250

The decay rate will be:

= 1 - 0.89

= 0.11

= 11%

In conclusion, the equation is y = 250(0.89)^x and the decay rate is 11%.

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Assessing the given Venn diagram and the data related to it, we can answer the required question:

Q1. How many people were surveyed = 86.

Q2. What is the probability that a customer chosen at random:

a) takes salt P(S) = 46/85.

b) takes both salt and vinegar P(S ∩ V) = 13/85.

c) takes salt or vinegar or both P(S ∪ V) = 66/85.

The number of people who take salt chips n(S) = 46.

The number of people who take vinegar chips n(V) = 33.

The number of people who takes both n(S ∩ V) = 13.

The number of people who take neither n((S ∪ V)') = 19.

Therefore, the total number of people surveyed n(U) = n(S) + n(V) - n(S ∩ V) + n((S ∪ V)') = 46 + 33 - 13 + 19 = 85.

The number of people who takes salt or vinegar or both n(S ∪ V) = n(U) - n((S ∪ V)') = 85 - 19 = 66.

The probability that a customer chosen at random takes salt P(S) = n(S)/n(U) = 46/85.

The probability that a customer chosen at random takes both salt and vinegar P(S ∩ V) = n(S ∩ V)/n(U) = 13/85.

The probability that a customer chosen at random takes salt or vinegar or both P(S ∪ V) = n(S ∪ V)/n(U) = 66/85.

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Step-by-step explanation:

0.000672, 6.72×10⁵, 67.2×10‐⁴, 672×10⁴

Scientific notation is a way of writing numbers that looks like the following:

[tex]a\times10^n[/tex]

For instance, we can write 2930 in scientific notation.

First, write all the given values in scientific notation:

Now, let's compare the values of n, and organize the numbers from least to greatest:

[tex]6.72\times10^{-4}[/tex]

[tex]6.72\times 10^{-3}[/tex]

[tex]6.72\times10^5[/tex]

[tex]6.72\times 10^6[/tex]

Finally, rewrite all the numbers as their given format:

[tex]0.000672[/tex]

[tex]67.2\times 10^{-4}[/tex]

[tex]6.72\times10^5[/tex]

[tex]672\times 10^4[/tex]

[tex]0.000672[/tex]

[tex]67.2\times 10^{-4}[/tex]

[tex]6.72\times10^5[/tex]

[tex]672\times 10^4[/tex]

This is not a good minimum quota for this survey. For us to have a good minimum quota, there must be equality. i,e 50% for cell phone respondents and 50% for landline respondents.

Survey methodology is the study of the sampling of discrete units or groups from a population and the procedures used to gather survey data, including the design of questionnaires and approaches for increasing survey response rates and precision.

A good minimum quota for this survey should be 50% for cell phone respondents and 50% for landline respondents.

It implies that the quota for cell phone respondents should be 10% lower and 10% higher for landline respondents.

For us to answer Part D, kindly provide or repost the complete question since we cannot see any link added.

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The correct answer is option B which is ( 5 / 3)

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division

The value will be calculated as:-

[tex]5\times \dfrac{1}{3}[/tex]  =  [tex]\dfrac{5}{3}[/tex]

1.67  = 1.67

Therefore the correct answer is option B which is ( 5 / 3)

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See the graph in the image.

Answer:

17.50 × 0.35 = 6.13

Step-by-step explanation:

Answer:

That would be $11.37

Step-by-step explanation:

First Multiply the discount and the original price

17.50(0.35)=  6.125 = 6.13

Use that answer and subtract it from the original price

17.50 - 6.13 = 11.37

Answer: In the first week, Micah bought 11 gallons of gas,

and in the second week, he bought 8 gallons of gas

Step-by-step explanation:

In the first week, Micah bought x gallons of fuel at $2.39/gallon

In the second week, he bought (x - 3) gallons at $2.49/gallon

Formulating an equation and solving for x gallons of fuel:

x × 2.39 + (x - 3) × 2.49 = 46.21

2.39x + x × 2.49 − 3 × 2.49 = 46.21

2.39x + 2.49x − 7.47 = 46.21

4.88x − 7.47 = 46.21

4.88x = 53.68

[tex]\frac{4.88x}{4.88} = \frac{53.68}{4.88}[/tex]

x = 11

Therefore,

In the first week, Micah bought 11 gallons of gas

In the second week, he bought (11 - 3) = 8 gallons of gas

Answer:

0.4 bottles can be filled

Step-by-step explanation:

divide the amount that is present by the max amount

the bottle can only hold 5.55 millimeters; therefore the max amount would be 5.55 millimeters.

the amount that is present is 2.22 millimeters.

[tex]\frac{222 millimeters}{555 millimeters} = 0.4[/tex]

0.4 bottles

if the given values are 555 and 222 then the answer is still .4

Answer:

0.4 bottles can be filled

Answer:

m∠M=98º

Step-by-step explanation

Sum of interior angles;

  3x-16+x+6+x = 180

                   5x = 180-6+16

                   5x = 190

                      x = 38º

Angle M;

      m<M= 3x - 16 = 3(38)-16= 98º

      m∠M=98º

Answer:

<M = 98

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

< M + < N + < O = 180

3x-16 + x + x+6 = 180

Combine like terms

5x - 10 = 180

Add 10 to each side

5x-10 + 10 = 180+10

5x = 190

Divide by 5

5x/5 = 190/5

x=38

We want to find <M

<M = 3x-16  = 3*38 -16 = 114-16 =98