Find the length of BC

Answer:

1. B) x = 6

2. No solutions

3. D) x = 4​

4. A) x = -4

Step-by-step explanation:

1. -4x + 8 = -3x + 2

8 = x + 2  ==> add 4x on both sides to move x to one side of the equation

x = 6  ==> subtract 2 on both sides

B. x = 6

2. 9x - 7 = 5x - 19

4x - 7 = -19 ==> subtract 5x on both sides to move x to one side of the

                        equation

4x = -12  ==> add 7 on both sides to isolate x

x = -3  ==> divide 4 on both sides

x = -3 isn't one of the options, so problem 2 has no solutions.

3. 2x - 7 = 5x - 19

-7 = 3x - 19  ==> subtract 3x on both sides to move x to one side of the

                        equation

12 = 3x  ==> isolate x by adding 19 on both sides

x = 4  ==> divide both sides by 3

D. x = 4​

4. -7x + 3 = -3x +19

3 = 4x + 19  ==> add 7x on both sides to move x to one side of the equation

-16 = 4x  ==> subtract 19 on both sides to isolate x

x = -4  ==> divide both sides by 4

A. x = -4

The two expressions that could represent the dimension of the rectangle are x + 2 and x - 7

The area of a rectangle can be represented by the product of its length and width. The formula for the area is given by:

A = l x w

where A is the area, l is the length and w is the width.

If the area is given by the expression x^2 - 5x - 14, then the two expressions for the dimensions can be determined by getting the factors of the expression.

x^2 - 5x - 14 = (x + 2)(x - 7)

Therefore, the dimensions of the rectangle can be expressed as x + 2 and x - 7.

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Answer:

Each pound of sugar costs $0.64

Step-by-step explanation:

4x = 2.56     Set up the equation. Divide both sides by 4 to isolate the x.

 x = 0.64

Answer:

Step-by-step explanation:

A triangle adds up to 180 degrees. Thus the answer to this question is

90°, 45°, and 45°.

90°+45°+45° = 180°

Answer:

90°, 45°, and 45°

Step-by-step explanation:

pls tell me if wrong have a good day/night<3

Answer:

Let's assume Holly invested x dollars in the first account that earns 5% interest and (500-x) dollars in the second account that earns 7.5% interest.

The interest made from the first account after 3 years is x * 0.05 * 3 = 0.15x

The interest made from the second account after 3 years is (500-x) * 0.075 * 3 = 0.225(500-x)

The total interest made is 0.15x + 0.225(500-x) = 100.50

Expanding and solving for x, we get:

0.15x + 112.5 - 0.225x = 100.50

-0.075x = -12

x = 160

So, Holly invested $160 in the first account and $340 in the second account.

The least common denominator of the fractions 1/4,1/2, and 3/4 is 4.

What is the least common denominator?

The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator. The smallest number that may be used as the denominator to produce a group of comparable fractions that all have the same denominator is known as the lowest common denominator.

All integers and mixed numbers (mixed fractions) must first be converted into fractions before attempting to identify the least common denominator. Next, determine the denominators' lowest common multiple (LCM). This value corresponds to the lowest common denominator (LCD). Then, using the same LCD denominator, you can write each phrase as an equivalent fraction.

Given 1/4, 1/2, 3/4

We are asked to find the least common denominator.

LCD of the given fractions is the LCM of the denominators 4,2,4.

LCM = 4

Therefore the least common denominator of the given fractions is 4.

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Answer:

y = 3x + 9

Step-by-step explanation:

Point-slope form: y - y₁ = m(x - x₁)

y - 3 = 3(x - 4)

y - 3 = 3x - 12

y = 3x + 9

The length of arc CD is 92.69

From the given circles we know that:

Circle E = Circle H

GF = CD = 28

∠CED = 75°

Arc CD?

We can imagine an imaginary radius line here are:

GH = FH = CE = DE

However we have no idea the length of the radius line of both circles.

We will use Law of Cosines to find the length of the radius line by taking GHF as a, isosceles triangle:

GF² = GH² + FH² - 2 GH FH cos H

28² = 2GH² - 2GH² cos 75°

28² = 2GH² (1 - cos 75)...(i)

Remember that:

Cos (A+B) = cos A cos B - sin A sin B

cos 75° = cos (30 + 45)°

cos 75° = cos 30 cos 45 - sin 30 sin 45

cos 75° = (√3/2)(√2/2) - (1/2)(√2/2)

cos 75° = √6/4 - √2/4

cos 75° = 1/4 (√6 - √2)

cos 75° = 0.921 ... (ii)

We subtitute equation (ii) into equation (i)

784 = 2GH² (1 - 0.921)

2GH² = 784 / (0.079)

GH = 70.78 = ED = EC

The length of arc CD is:

Arc CD = 75°/360° 2πr

Arc CD = 75°/360° 2π.ED

Arc CD = 92.69

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The number of pencils that each person has is given as follows:

The number of pencils that each person has is obtained by a system of equations, for which the variables are given as follows:

They have a total of 65 pencils, hence:

x + y = 65.

Ana has double Maria's amount plus 10 pencils, hence:

x = 2y + 10.

Replacing x = 2y + 10 on the first equation, Maria's amount is obtained as follows:

2y + 10 + y = 65

3y = 55

y = 55/3

y = 18.

Hence Ana's amount is given as follows:

x = 65 - 18 - 47.

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The histogram, time series, box plot, stem and leaf, and frequency polygon.

Dot plots, stem and leaf graphs, histograms, box plots, ogive graphs, and scatter plots are all used to graph numerical data. The dot plot: Stem and leaf: The stem represents the first digit of the number in these graphs, while the leaf/leaves indicate the second digit (s). A histogram or a polygon graph should be used for scores that fall on an interval or ratio scale. A bar is centered above each score (or interval) in a histogram, with the height corresponding to the frequency of that score or interval and the width according to the true boundaries of that score or period.

Scatterplot. Scatter plots are effective for displaying accurate, dense data visualizations, relationships, and groupings between variables.

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Answer:

1

Step-by-step explanation:

[tex]\cos \left(\arccos \left(\frac{3}{5} \right)+\arcsin(-\frac{4}{5} \right)=\cos(\arccos(3/5))\cos(\arcsin(-4/5))-\sin(\arccos(3/5))\sin(\arcsin(-4/5)) \\ \\ =(3/5)\cos(\arcsin(-4/5))-(-4/5)(\sin(\arccos(3/5)) \\ \\ =(3/5)(3/5)-(-4/5)(4/5) \\ \\ =1[/tex]

The instantaneous voltage across a capacitor is |2cos(155°)| sin(106t + 25° - angle(2 cos(155°))).

The instantaneous voltage across a capacitor is given by the equation:

vC(t) = vC(0) + 1/C * ∫i(t)dt

Since i(t) = 8 sin(106t + 25°), we can find the integral using the formula for the integral of a sine function:

∫i(t)dt = -8/106 cos(106t + 25°)

So,

vC(t) = 2 cos(155°) - 8/106 ∫ cos(106t + 25°)dt

vC(t) = 2 cos(155°) - 8/106 sin(106t + 25°)

The magnitude of vC(t) is positive, and the angle should be in the range of -180° to 180°. The final answer is in sine form, so we can write:

vC(t) = |2 cos(155°)| sin(106t + 25° - angle(2 cos(155°)))

where angle(2 cos(155°)) is the angle of 2 cos(155°).

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the value of X must be more than 8.

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.

Call the number x, please. Since we know that adding 6 to it will result in a number smaller than 14, x + 6 14.

We obtain x = 14 - 6 = 8 by deducting 6 from both sides.

Therefore, x must be greater than 8.

We can use the following method to find the another in one is given.

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The numeric values for the function f(x) are given as follows:

1. At x = 3: -5.

2. At x = -2: -25/3.

3. At x = 6: -3.

4. At x = 1: -19/3.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

In this problem, we have a piecewise function, which has different definitions based on the input of the function.

However, all the values at which we want to obtain the numeric value are greater than -4, hence the definition is given as follows:

f(x) = 2x/3 - 7.

The numeric values are found replacing the lone instance of x, hence:

1. At x = 3: 2(3)/3 - 7 = 2 - 7 = -5.

2. At x = -2: 2(-2)/3 - 7 = -4/3 - 7 = -4/3 - 21/3 = -25/3.

3. At x = 6: 2(6)/3 - 7 = 4 - 7 = -3.

4. At x = 1: 2(1)/3 - 7 = 2/3 - 7 = 2/3 - 21/3 = -19/3.

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Answer:

$5644.88

Step-by-step explanation:

Formula for Compound interest: P(1 + r/n)^nt

P: initial amount

r: Interest rate

n: number of times compounded pet t

t: time period (usually in years)

3460(1 + 0.085/1)^6 = 5644.8775806

Answer:

Let x be the number of animated DVDs Sammi borrowed and y be the number of superhero DVDs she borrowed.

The total number of minutes of all DVDs is 1,200, so we have:

90x + 120y = 1,200

And the total number of DVDs borrowed is 11, so we have:

x + y = 11

To solve this system of linear equations, we can use substitution method. Solving for y in the second equation, we get:

y = 11 - x

Substituting this expression for y into the first equation, we have:

90x + 120(11 - x) = 1,200

Expanding the right side, we get:

90x + 1320 - 120x = 1,200

Combining like terms, we get:

-30x = -120

Solving for x, we get:

x = 4

Since x is the number of animated DVDs, Sammi borrowed 4 animated DVDs. Substituting this value of x back into the expression for y, we have:

y = 11 - x = 11 - 4 = 7

So Sammi borrowed 7 superhero DVDs.

The solution means that Sammi borrowed 4 animated DVDs and 7 superhero DVDs, which lasted for a total of 1,200 minutes. This method was relatively simple and efficient, as it only involved solving for one variable and then using substitution.

Find the multiples of 8 and 12 (multiples of 8 = 8, 16, 24, 32; multiples of 12 = 12, 24, 36, 48) and select the lowest multiple that is precisely divisible by 8 and 12, which is 24.

The LCM of 8 and 12 is 24 regardless of the technique chosen. To obtain this number, the listing technique will display the first three multiples of 8 and the first two multiples of 24. The prime factor technique compares the two numbers’ prime factors and multiplies them together, omitting repeated factors.

The first approach to compute the least common multiple: This is the method we used previously; in other words, we write the initial multiples of each integer, record the common multiples, and pick the least common multiple.

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The change in demand is $15 per barrel.

Given is that the price of oil increases from 20 to 5 per barrel.

So we can write the change in demand as -

$20 per barrel - $5 per barrel

$15 per barrel

Therefore, the change in demand is $15 per barrel.

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The required solution of the quadratic equation is given as x = -2 and -5. Option D is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
x² + 7x + 10 = 0

Factorize the above expression,

(x + 5)(x + 2) = 0

Now,
x + 5 = 0  ; x + 2 = 0
x = -5        : x = -2

Thus, the required solution of the quadratic equation is given as x = -2 and -5. Option D is correct.

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The proportion that can be used to find the actual distance is given as [tex]\frac{10}{4} = \frac{x}{20}[/tex], and the correct option is A.

By scaling, we may create a drawing of an item that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape. Similar figures are those that have been scaled.

Given that the scale on a map shows that 10 kilometers is represented by 4 centimeters.

We are to find the proportion can be used to find the actual distance, x, represented by 20 centimeters on the map.

We have

4 centimeters on the map = 10 kilometers.

So, 1 centimeter on the map

[tex]1 cm = \frac{10}{4}[/tex]

Also, 20 centimeters on the map = x kilometers.

So, 1 centimeter on the map

[tex]1cm = \frac{x}{20}[/tex]

Equating the two expressions:

[tex]\frac{10}{4} = \frac{x}{20}[/tex]

Therefore, the proportion that can be used to find the actual distance is given as [tex]\frac{10}{4} = \frac{x}{20}[/tex], and the correct option is A.

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A statement could be used to describe the functions include the following: D. the domain of f(x) is (−∞, 0] while the domain of g(x) is [0, ∞).

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

Additionally, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By using interval notation, the domain of this function shown in the graph above can be written as follows;

Domain of f(x) = {-∞, 0}

Domain of g(x) = {0, ∞}

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(a) at least 4 people born in the same month,

(b) In order to ensure that at least two persons were born on the same day,

(a)

we have 37 people.

we want to know at least how many were born in the same month.

I would think that at least 4 people had to be born in the same month.

here's why.12 months in a year.

if every 12 people were born in a different month, then out of 37 people, at least 3 people were born in the same month.

first 12 people        1   2  3  4   5  6  7  8  9  10  11   12

second 12 people  1   2  3  4  5   6  7  8   9    10  11  12

third 12 people       1   2  3  4  5  6  7  8  9  10  11  12

remaining 1 person 1

we could have minimum 4 people that were born in the same month,

Hence,  at least 4 people born in the same month,

(b)

 Assuming that no one is born on Feb. 29 (leap day), how many people should be selected to guarantee that at least 6 were born on the same day, not considering the year?

there are 365 days in the year.

You could have 365 people where no two persons were born on the same day, assuming that everyone was born on a different day.

However, the 366th individual would have to share the same birthday as another member of the group.

In order to ensure that at least two persons were born on the same day, the group's minimum size would consequently need to be 366.

The complete question is -

(a) Among 37 people at least how many were born in the same month?

(b) Assuming that no one is born on Feb. 29 (leap day), how many people should be selected to guarantee that at least 6 were born on the same day, not considering the year?

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Whether the two ratios are 2: 3 and 2: 3 or a proportion

4: 6 and 12: 18

[tex]$\frac{4}{6}$[/tex]   and

[tex]$\frac{12}{18}=\frac{2}{3}$[/tex]   and

2/3

=2: 3 and 2: 3

Yes the given two ratios form a proportion.

The complete question is:

Check whether the given two ratios form a proportion or not: 4: 6  12: 18

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If Brenda plans to reduce her spending by $70 a month, the future value of this reduced spending over the next 12 years is $14710.5.

We are given that Brenda will be saving $70 every month for a period of 12 years.

So, the future value of the annuity formula will be used for the calculation of future value.

Future value = R [( (1 + i)^n - 1 ) / i], where R is the regular payment, i is the interest rate and n is the number of payments

Here R = monthly amount to be saved = $70

i = interest rate = 6/12 = 0.5%

n = Number of payments = 12 x 12 = 144 months

Future value=70 [( (1+0.5%)^144 - 1) / 0.5%] = $14710.5

Hence, the future value of this reduced spending over the next 12 years is $14710.5.

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The shape of Banana is taking the shape of a parabola.

a plane curve created when a point moves so that the distance between it and a fixed point or line is equal.

y2=4ax, where is the distance from the parabola's vertex to focus, is the standard equation for a normal parabola.

Several examples of parabolas in real life

The wheel stance in yoga resembles a parabola.

Banana's shape is beginning to resemble a parabola.

A parabola is emerging from the Rainbow.

Antennas with a parabolic dish are resembling a parabola.

Mirror's concave surface.

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here.

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The numeric value of the function for each case is given as follows:

5. f(-11) = 1841.

6. g(1/3) = 14.78.

7. h(-1/2) = -5/8.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

Hence item 5 is solved as follows:

f(-11) = -(-11)³ + 5(-11)² + 9(-11) + 4

f(-11) = 1841.

Item 6 is solved as follows:

g(1/3) = 3(1/3)³ + 6(1/3)² + 12(1/3) + 10

g(1/3) = 14.78.

Item 7 is solved as follows:

h(-1/2) = 9(-1/2)³ - 8(-1/2)² + 11(-1/2) + 8

h(-1/2) = -5/8.

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The number of different groups of 4 people that a company could send to a job site, which is 27,720.

In the context of this question, a company has 30 people and wants to send 4 people to a job site.

To find out how many different groups of 4 people they could make, we need to use the concept of permutation.

To find the number of permutations, we use the formula nPk, where n is the total number of objects (30 in this case) and k is the number of objects we want to arrange (4 in this case).

So, the number of permutations will be

=> 30P4 = 30!/(30-4)!.

This simplifies to

=> 30!/(26!) = 27,720.

Therefore, the company has 27,720 different groups of 4 people that they could send to a job site. This means that they can send 27,720 different combinations of 4 people from their 30 employees to a job site.

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