Question
Solve: 9(x - 1) - 13x = -3(x + 5).
Provide your answer below:
X =

The liters of 80% material is 2/3 liters.

The liters of the 50% solution is 1/3 liters.

Based on the information, the scientist is working with two different concentrations of hydrochloric acid (HCI).

Let x = volume of 80%

Let 1 -x =volume of 50%

Therefore, the expression to illustrate the information will be:

80x + 50 × (1 - x) = 70

80x + 50 - 50x = 70

30x = 70 - 50

30x = 20

Divide

x = 20/30

x = 2/3

Therefore there are 2/3 liters of 80% material

The liters for the 50% solution will be 2/3 subtracted from 1. The 2/3 implies that for the 80% material. This will be:

= 1 - 2/3

= 1/3

There are also 1/3 liters of 50% material.

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The sum of the first 31 terms of the arithmetic series is 114.

What is arithmetic series?

In mathematics, arithmetic series is the sequence of the number whose common difference between the two consecutive number is always constant. And the sum of the series is depend on the first term as well as on the last term.

According to the question, the given series is an arithmetic series. In the common difference is same.

The given series is:

4, 11, 18,....4, 11, 18,....4, 11, 18,....

To know the sum of the given series, first calculate the sum of the first three numbers. And later multiply by ten.

Using standard formula for the sum of the arithmetic series:

[tex]S_{3} =\frac{(first term + last term)}{2} = \frac{4+18}{2} =11[/tex]

Therefore to calculate the sum of the 31 terms:

s(31 terms) = 10(11) + first term = 110 + 4 = 114

Hence, the sum of the first 31 terms of the arithmetic series is 114.

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For the given problems we have:

1) The solution of the inequality is:

x ≤ 2

2) The absolute value equation has two solutions:

z= 2

z = -12

3) The correct matches are:

Remember that solving means to isolate the variable in one side of the expression.

1) We have the inequality:

-4x + 17 ≥ 9

-4x  ≥ 9 - 17

x ≤ -8/-4

x ≤ 2

This is the solution of the inequality.

2) We have the absolute value function:

|5 + z| + 3 = 10

|5 + z| = 10 - 3 = 7

We can decompose this into:

5 + z = 7

5 + z = -7

Then the two solutions are:

z = 7 - 5 = 2

z = -7 - 5 = -12

3) The correct matches here are:

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The quotient of 2.538 ×10^9 and 2.7×10^2 expressed in scientific notation is : 0.94 × 10^6.

Given:

2.538 × 10^ 9 and 2.7 × 10^ 2

We have to first of all formulate before determining the scientific notation

(2.538 × 10^ 9) ÷ (2.7 × 10^2)

Rewrite as fraction

2.538 × 10^9 ÷ 2.7 × 10^2

simplify

2.538 ÷ 2.7 × 10^ 9-2

=  2.538 ÷ 2.7 × 10^7

Convert the fraction to decimal

0.94 × 10^7

Now let express it in scientific notation

Scientific notation = 94 × 10^6

Therefore the scientific notation is 94 × 10^6.

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The correct question is:

What is the quotient of 2.538 ×10^9 and 2.7×10^2 expressed in scientific notation

Answer:

[tex]{ \tt{\% savings = \frac{savings}{total \: income} \times 100\%}} \\ \\ { \tt{ = \frac{720}{3000} \times 100\%}} \\ \\ = { \tt{24\%}}[/tex]

Answer:

24%

Step-by-step explanation:

[tex]\boxed{\sf Percent=\left(\dfrac{Value}{Total\:value}\right) \times 100}[/tex]

Given information:

Substitute the given values into the formula and solve for percent:

[tex]\begin{aligned}\implies \textsf{Percent} & =\dfrac{720}{3000} \times 100\\\\& = \dfrac{720\times 100}{3000} \\\\& = \dfrac{72000}{3000} \\\\& = \dfrac{72}{3} \\\\& = 24\% \end{aligned}[/tex]

Therefore, 24% of Tanisha's budget is savings.

Answer:

19.5

Step-by-step explanation:

The most appropriate choice for linear equation will be given by-

The cost of bench is $375

What is linear equation?

A one degree equation is called a linear equation.

Here,

Let the cost of the bench be $x

cost of garden table = $(x + 80)

Total cost of bench and garden table= $(x + x + 80)

                                                              = $(2x + 80)

By the problem,

                           2x + 80 = 830

                            2x = 830 - 80

                             2x = 750

                                x = [tex]\frac{750}{2}[/tex]

                                x  = $375
So,

The cost of bench is $375

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Using the z-distribution to test the hypothesis, we have that:

a) The null hypothesis is [tex]H_0: \mu = 50[/tex].

b) The p-value of the test is greater than 0.05, hence we do not reject the null hypothesis, meaning that the supplements did not have the intended effect.

At the null hypothesis, it is tested if there is not enough evidence that the mean was different, hence:

[tex]H_0: \mu = 50[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the mean was different, hence:

[tex]H_1: \mu \neq 50[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

In the context of this test, the parameters are given as follows:

[tex]\overline{x} = 54, \mu = 50, \sigma = 12, n = 16[/tex]

Hence the test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{54 - 50}{\frac{12}{\sqrt{16}}}[/tex]

z = 1.33.

Considering a two-tailed test, as we are testing if the mean is different of a value, with z = 1.33, the p-value of the test is of 0.1835, which is greater than 0.05, meaning that we do not reject the null hypothesis and the supplement did not change the mean.

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1) Let's solve that exponential equation

Converting the bases:

2) Since we are on the same base let's just calculate the exponents.

3) Blake has committed a mistake when He didn't apply the distributive property properly. He didn't multiply the 7 by 4. He subtracted the x variables wrongly and added -7 to -5.

When He started operating the exponents.

Examples of each survey question that relates to organic farm produce are as follows;

a) Dichotomous

Do you prefer organic farm produce?

Yes/No

b) Multiple choice

How many of your colleagues make use of organic farm produce

c) Rating scale

On a scale of 1 to 5, with 10 being happiest, how happy are you about our customer service?

1, 2, 3, 4, 5

d) Completion

Eating organic produce _______ improve my health

Will

Will not

e) Open-ended

Tell us why you prefer organic farm produce ___________

A survey involves the administration of questions or the examination of a process that is aimed at obtaining data with regards to a service, process or product.

a) Dichotomous questions are questions that can have only two possible responses. Such questions are used in a survey in which the two possible responses are stated such as Agree/Disagree, Yes/No, Fair/Unfair, True/False, or Cold/Hot. Based on the definition of the responses, the opinion of the responder is made clear

An example of a dichotomous question asked with respect to organic farm produce is 'Do you prefer organic farm produce?'

The possible responses are; Yes/No

b) Multiple choice survey question

Multiple choice questions provide the opportunity for a respondent to have more options to choose a response from. The multiple choice questions also allow researcher to obtain detailed information on the subject.

An example of multiple choice question is as follows;

How many of your colleagues make use of organic farm produce

c) Rating Scale

In rating scale survey questions the respondents are asked to select a rating of their experience in a response that offers a rating such as 1 to 10 or 1 to 100

An example of a rating scale question in a survey is as follows;

On a scale of 1 to 5, with 10 being happiest, how happy are you about our customer service?

1, 2, 3, 4, 5

d) Completion

Completion type question assesses the level of cognition on a subject matter

Example;

Eating organic produce _______ improve my health

e) Open–ended

Open–ended questions gives respondents the latitude to express themselves with regards to the question in written text in a detailed or in a brief response.

Example;

Tell us why you prefer organic farm produce ___________

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Answer:

  1.1

Step-by-step explanation:

You want the multiplier of the wholesale cost that makes the retail cost be 10% more.

The retail cost is said to be ...

   retail cost = (wholesale cost) + 10% × (wholesale cost)

  = (wholesale cost) × (1 +10%)

  = (wholesale cost) × 1.10

The retail cost is 1.10 times the wholesale cost.

The value of the expression in the options is (a) three raised to the sixth power divided by six raised to the fifteenth power

The expression is given as

A fraction with six raised to the negative third power in the numerator and the quantity three raised to the negative second power times six squared end quantity in the denominator and the entire fraction is cubed.

Rewrite the expression properly

So, we have

[6^-3/(3^-2 x 6^2)]^3

Apply the law of indices to the expression

So, we have

[6^-3/(3^-2 x 6^2)]^3 = [6^(-3 - 2)/(3^-2)]^3

Evaluate the difference

[6^-3/(3^-2 x 6^2)]^3 = [6^-5/(3^-2)]^3

Apply the change of power rule

[6^-3/(3^-2 x 6^2)]^3 = [3^2/6^5]^3

Evaluate the product of exponents

[6^-3/(3^-2 x 6^2)]^3 = 3^6/6^15

In words, the result is (a) three raised to the sixth power divided by six raised to the fifteenth power

Hence, the value of the expression is (a)

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    Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.

How to determine a line's equation from two points:

Using the slope formula, determine the slope.

To find the y-intercept (b), use the slope and one of the points.

You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).

y = -x/3 + 5 is the equation that depicts the line that crosses through the coordinates (-6, 7) and (-3, 6).

3 Answers What is the slope of the line passing through (- 7 2 and 6 7? by Certified Tutors

The slope of the equation would be nine.

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Total expenses = $289 + $361 + $433 + $217 = $1300

Percentage of money spent on rent:

(Money spent on rent)/(Total expenses) = $361/$1300 = 0.2777 ≈ 28%

Therefore 28% of total expenses are for rent

To write  3.656 X 10^-5 in standard form 0.00003656

What is Standard Form ?

A mathematical item's canonical, normal, or standard form refers to how the object is typically expressed mathematically in both mathematics and computer science. It is frequently the one that offers the most straightforward illustration of the thing while yet enabling distinctive identification.

Move the decimal in the number that many spaces to the right when multiplying a number by 10 to the power of a positive exponent

(for example, (10)^3)).

For example, 4.5x(10)^3=4500.

Move the decimal in the number (the absolute value of) that many spaces to the left when multiplying a number by 10 to the power of a negative exponent

(for example, (10)^4)).

For example, (4.5x10)^4=(0.00045)

Move the decimal five spaces to the left for (3.656x 10)^-5:

0.00003656

Hence , 0.00003656 is Standard form of  (3.656x 10)^-5

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Steve's new credit card balance at the end of the month and after making the minimum monthly payment will be $519.39.

A credit card balance is an amount the cardholder owes to the credit card issuer at the end of a credit period.

The credit card balance consists of purchases, finance charges, and repayments.

Credit card's APR = 11.99%

Credit limit = $1,800

Minimum monthly payment = 6.5%

Purchase at the beginning of the month = $550

Credit card interest for the month = $5.50 ($550 x 11.99% x 1/12)

New balance = $555.50

Minimum payment = $36.11 ($555.50 x 6.5%)

Balance after the minimum payment = $519.39 ($555.50 - $36.11)

Thus, If he buys $550 in school supplies at the beginning of the month, Steve’s new balance at the end of the month is $555.50, which he can reduce to $519.39 by making the required minimum monthly payment.

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We are to solve using completing the square:

1/4x² + x + 1/4 = 0

Let's collect like terms:

1/4x² + x = -1/4

Divide both sides by the coefficient of x-squared:

x² + 4x = -1

Take half of the coefficient of x, square it, then add to both sides:

x² + 4x + 4 = -1 + 4

factor the left side of the equation:

(x + 2)² = 3

Take the root of both sides;

x + 2 = ±√3

Add 2 to both sides:

x = ±√(3) - 2

x = -2 + √3 or x = -2 - √3

herefore, the correct option is B, which is x = -2 + √3 or x = -2 - √3

The formula to show the height and time an object is in the air :

when the object hits the ground the height will become 0

so, put h(t) = 0

and simplify :

Simplfy the equation by using discrimination rule :

The general form of quadratic equation is : ax² + bx + c

and the roots are express a s :

On compare the given equation with the general equation we get :

a = -16, b = 48 and c = 50

Substitute the value and simplify :

TO find the zeros of a quadratic function we should factorize the function

So we have to find numbers that multiplied are -20 and added are -1. So we get -5 and 4

so the zeros of the function are 5 and -4

Given that equation

1) [tex]x^{2} - 2x - 2[/tex]  using the general quadratic equation, x = 1

2)[tex]x^{2} -6x -4[/tex] using the general quadratic equation, x= [tex]\frac{6 - \sqrt{20} }{2}[/tex]

According to the question, given that

1) [tex]x^{2} - 2x - 2[/tex]

2)[tex]x^{2} -6x -4[/tex]  

this equation cannot be factored but using general quadratic equation. we solved it easily.

When asked to solve a quadratic equation that you just can’t seem to factor (or that just doesn’t factor), you have to employ other ways of solving the equation, such as by using the quadratic formula. The quadratic formula is the formula used to solve for the variable in a quadratic equation in standard form.

Given a quadratic equation in standard form ax2 + bx + c = 0,

[tex]x = \frac{- b - \sqrt{b^{2} - 4 ac } }{2a}[/tex] and  [tex]x = \frac{- b + \sqrt{b^{2} - 4 ac } }{2a}[/tex]

solve [tex]x^{2} - 2x - 2[/tex] = 0, you first say that a = 1, b = –2, and c = 2. The a, b, and c terms simply plug into the formula to give you the values for x:

    1) [tex]x^{2} - 2x - 2[/tex]    

 [tex]x = \frac{- (-2) + \sqrt{(-2)^{2} - 4 (1)(1) } }{2(1)}[/tex]

[tex]x = \frac{2 + \sqrt{4 -4} }{2}[/tex]

x = [tex]\frac{2}{2}[/tex]

[tex]x = 1[/tex]

and    [tex]x = \frac{- (-2) - \sqrt{(-2)^{2} - 4 (1)(1) } }{2(1)}[/tex]

         [tex]x = \frac{2 - \sqrt{4 -4} }{2}[/tex]

         x = [tex]\frac{2}{2}[/tex]

         [tex]x = 1[/tex]

equation  [tex]x^{2} - 2x - 2[/tex]  and x= 1

2)[tex]x^{2} -6x -4[/tex]  

solve [tex]x^{2} - 6x - 4[/tex] = 0, you first say that a = 1, b = –6, and c = 4. The a, b, and c terms simply plug into the formula to give you the values for x:

[tex]x^{2} -6x -4[/tex]  

[tex]x = \frac{- (-6) + \sqrt{(-6)^{2} - 4 (1)( 4) } }{2(1)}[/tex]

[tex]x = \frac{6 + \sqrt{36 - 16} }{2}[/tex]

x = [tex]\frac{6 \sqrt{20} }{2}[/tex]

and    [tex]x = \frac{- (-6) - \sqrt{(-6)^{2} - 4 (1)(4) } }{2(1)}[/tex]

         [tex]x = \frac{6 - \sqrt{36 - 16} }{2}[/tex]

         x = [tex]\frac{6 - \sqrt{20} }{2}[/tex]

equation  [tex]x^{2} - 6x + 4[/tex]  and x= [tex]\frac{6 - \sqrt{20} }{2}[/tex]

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The equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

Here, we are given a circle with center D and equation as-

[tex]x^{2}+ y^{2}+2x -8y + 8 =0[/tex]

Comparing this to the general form of equation of a circle which is  [tex]x^{2}[/tex] + [tex]y^{2}[/tex]+ 2gx + 2fy + c = 0, we get-

g = 1, f = -4 and c = 8

thus, the center of the circle is (-1,4) and radius =[tex]\sqrt{ (1+16-8)}[/tex] = 3

Now, since PT is a tangent to the circle, DP will e perpendicular to PT.

We can find the length of PD using the distance formula as we know P(4,6) and D(-1,4)

= [tex]\sqrt{(4+1)^{2} +(6-4)^{2} }[/tex]

= [tex]\sqrt{(5)^{2} +(2)^{2} }[/tex]

= [tex]\sqrt{25 +4 }[/tex]

=[tex]\sqrt{29}[/tex]

Thus, in triangle, PDT by using Pythagoras theorem, we will have-

[tex]PT^{2} + DT^{2} = PD^{2}[/tex]

since DT is the radius of the circle, DT = 3

⇒ [tex]PT^{2} + 3^{2} = (\sqrt{29}) ^{2}[/tex]

[tex]PT^{2} + 9 = 29[/tex]

[tex]PT^{2} = 29 - 9[/tex]

[tex]PT^{2} = 20[/tex]

[tex]PT = \sqrt{20}[/tex]

Thus, we've proved that the length of PT is [tex]\sqrt{20}[/tex] units.

Now, the circle with center P, passing through T will have radius = [tex]\sqrt{20}[/tex]

so r = [tex]\sqrt{20}[/tex] and (h,k) = (4,6)

Thus, the equation of the circle will be-

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]

[tex](x-4)^{2} + (y-6)^{2} = (\sqrt{20}) ^{2}[/tex]

[tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

Thus, the equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

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Answer: B. (5√3)

Step-by-step explanation: In a 60-30-90 triangle, the hypotenuse is 2x, and the long is x√3. Solve for x by setting 2x=10, which you would get 5. Then, you can plug 5 for x in x√3 to get 5√3.

The cost of the present is $20.67

Given,

The cost of the present = x

Amount given by cousin = $13.78

Amount given by cousin is 2/3 of x.

That is,

13.78 = 2/3 of x

Lets find x

13.78 = 2/3 × x

13.28 = 2x/3

Multiply with 3 on both sides

13.78 × 3 = (2x/3) × 3

We get,

41.34 = 2x

Divide 2 on both sides

That is,

41.34/2 = 2x/2

We get,

x = 20.67

Here, x is the cost of the present

Therefore, the cost of the present is $20.67

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When we write an inequality in the form:

In a number line, we can draw it, mark the endpoints (1 and 5) and then we highlight the parts at which the x is, which is in the middle:

Notice that we marked the endpoints as empty dots, which indicates that the endpoints are not included in the interval.

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

The value of k given that both points lie on a line passing through the origin is 48.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Since both points lie on a line which passes through the origin, we can logically deduce the following points:

Point (x, y) = (0, 0)

Substituting the given points into the formula, we have;

Slope, m = Δy/Δx

Slope, m = (-2 - 0)/(-12 - 0)

Slope, m = -2/-12

Slope, m = 1/6

At point (-12, -2) and (k, 8), we have:

1/6 = (8 - (-2))/(k - (-12))

1/6 = (8 + 2)/(k + 12)

1/6 = 10/(k + 12)

k + 12 = 10(6)

k + 12 = 60

k = 60 - 12

k = 48

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An equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) = 72.2 .

As given in the question,

Pierce is making a rectangular frame for a photo collage.

Perimeter of a rectangular frame is equal to 72.2 inches.

Length of the rectangular frame is equal to 20.3 inches

Perimeter of the rectangle = 2(length + width) __(1)

Let x inches be the width of the frame

Equation with x width of the frame is given

2(20.3 + x) = 72.2

Therefore, an equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) =72.2.

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SOLUTION

Given the question in the image, the following steps can be used to get x

Step 1: Explain the concept of equal arcs in a circle

If a circle is divided into arcs, then each arc is a minor arc and they all sum up to be equal to the total angles in the circumfference of the circle which is 360 degrees.

Step 2: Explain the breakdown of the minor arcs in the circle

It can be seen that the minor arcs divided the circle into three parts which are two equal arcs and a 70 degrees arc. This implies that:

Step 3: Find x

Hence, the value of x in the given circle is 145 degrees