x subtract 2 x subtract 2 multiply 3 in expression

6a. The equation for the graph is y = 2√(x + 5).

6b. The equation for the graph is y = -|x + 1| + 5

In Mathematics and Geometry, the standard form of a square root function can be modeled as follows;

y = a√(x - h) + k

Part 6a.

Next, we would determine value of a as follows;

4 = a√(-1 + 5) + 0

4 = a√4

4 = 2a

a = 2

Therefore, the required square root function is given by;

y = 2√(x + 5)

Part 6b.

Since the line representing the absolute value function has a y-intercept at (0, 4) and vertex at (-1, 5), the absolute value equation for the graph is given by:

y = a|x - h| + k

y = -|x + 1| + 5

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Find the attachment of the histogram of the given data below.

Male adults,

Class boundary,

Class width,

The frequency distribution of the data will be:

Class                                  Class boundaries                      Frequency

61-65                                       6.5-65.5                                       3

66-70                                      65.5-70.5                                      4

71-75                                        70.5-75.5                                      11

76.80                                      75.5-80.5                                      3

81-85                                       80.5-85.5                                      2  

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Answer:

the 8 is the in the tenth place

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

20/3

Step-by-step explanation:

Every nth term takes the form of  a + n*d, where a is the first  term.

So 7th term = (54 = a + 7d), 13th term = (94 = a + 13d).

equate them both:

94 - 13d = 54 - 7d

40 = 6d

d = 40/6

Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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To show that the point (å, ä) is on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ), we need to demonstrate two things: that the point lies on the line segment, and that it is equidistant from the endpoints.

1. Determine the midpoint of the line segment:

  - The midpoint coordinates (\(x_{mid, y_{mid\)) can be found using the midpoint formula:

    \(x_{mid\) = (x1 + x2) / 2 and \(y_mid\) = (y1 + y2) / 2, where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

    In this case, we have (x1, y1) = (Ů, ü) and (x2, y2) = (ĝ, ġ).

2. Calculate the midpoint coordinates:

  - Substitute the values into the midpoint formula to find (x_mid, y_mid).

3. Find the slope of the line segment:

  - Use the slope formula: slope = (y2 - y1) / (x2 - x1).

    Apply the formula to the endpoints (Ů, ü) and (ĝ, ġ) to determine the slope of the line segment.

4. Determine the negative reciprocal of the line segment's slope:

  - Take the negative reciprocal of the slope calculated in the previous step. The negative reciprocal of a slope m is -1/m.

5. Write the equation of the perpendicular bisector:

  - Using the negative reciprocal slope and the midpoint coordinates (\(x_{mid\), \(y_{mid\)), write the equation of the perpendicular bisector in point-slope form: y - \(y_{mid\) = \(m_{perp\) * (x - \(x_{mid\)), where \(m_{perp\) is the negative reciprocal slope.

6. Substitute the point (å, ä) into the equation:

  - Replace x and y in the equation of the perpendicular bisector with the coordinates of the point (å, ä). Simplify the equation.

7. Verify that the equation holds true:

  - If the equation is satisfied when substituting (å, ä), then the point lies on the perpendicular bisector.

By following these steps, you can demonstrate that the point (å, ä) lies on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ).

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The expression that can be used to show the relationship between the number of days and the total dollars (t) he spends is t = 30d

The equation:

Total = cost per day × number of days

t = 30 × d

t = 30d

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The equation for the polynomial in this problem is given as follows:

\(y = \frac{1}{16}(x^4 - 17x^2 + 16)\)

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

The roots for this problem are given as follows:

Hence the polynomial is:

y = a(x + 4)(x + 1)(x - 1)(x - 4)

y = a(x² - 16)(x² - 1)

\(y = a(x^4 - 17x^2 + 16)\)

When x = 0, y = 1, hence the leading coefficient a is given as follows:

a = 1/16.

Thus the equation is:

\(y = \frac{1}{16}(x^4 - 17x^2 + 16)\)

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The solution of the given expression will be 9/16.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²

= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²

= 9/16

Hence, The solution of the given expression will be 9/16.

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a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

It is B. A Cylinder.

Answer:

6x

Step-by-step explanation:

6xy and 18x²

6x(y) and 6x(3x)

HCF =6x

Answer:

RIGHT

Step-by-step explanation:

Note: You missed to add the answer choices, so I am solving the overall procedure to determine the radius of the cylinder so that you could easily figure out the right choice.

Answer:

The radius of the cylinder:

Step-by-step explanation:

The volume of a cylinder is represented by the formula

V=πr²h

here

The radius of the cylinder can be computed using the formula of the volume of a cylinder

V = πr²h

r² = V / πh

Taking square roots

\(r\:=\:\sqrt{\frac{v}{\pi \:h}}\)

Thus, the formula of the radius of the cylinder.

\(r\:=\:\sqrt{\frac{v}{\pi \:h}}\)

Therefore, the radius of the cylinder:

Answer:

x=−12

Step-by-step explanation:

Let's solve your equation step-by-step.

7(x+3)=5x−3

Step 1: Simplify both sides of the equation.

7(x+3)=5x−3

(7)(x)+(7)(3)=5x+−3(Distribute)

7x+21=5x+−3

7x+21=5x−3

Step 2: Subtract 5x from both sides.

7x+21−5x=5x−3−5x

2x+21=−3

Step 3: Subtract 21 from both sides.

2x+21−21=−3−21

2x=−24

Step 4: Divide both sides by 2.

2x

2

=

−24

2

x=−12

Answer:

x=−12

Answer:X=-12

Step-by-step explanation:Simplify both sides of the equation

7(x+3)=5x−3

(7)(x)+(7)(3)=5x+−3(Distribute)

7x+21=5x+−3

7x+21=5x−3

Subtract 5x from both sides

7x+21−5x=5x−3−5x

2x+21=−3

Subtract 21 from both sides

2x+21−21=−3−21

2x=−24

Divide both sides by 2

2x/2=-24/2

X=-12

Answer:

−61

Step-by-step explanation:

Let's solve your equation step-by-step.

6(x+11)=−300

Step 1: Simplify both sides of the equation.

6(x+11)=−300

(6)(x)+(6)(11)=−300(Distribute)

6x+66=−300

Step 2: Subtract 66 from both sides.

6x+66−66=−300−66

6x=−366

Step 3: Divide both sides by 6.

6x/6 = -336/6

x= −61

The range for the given inequality is 43 ≤ c(b) ≤ 99.25

The range is the difference between the largest and smallest data points in a set of numerical data.

Given that, A coach is buying new soccer balls for the team. The total cost can be found using this function c(b)=6.25b+5.50. The coach needs to buy at least 6 balls, but no more than 15.

The cost for at least 6 balls = 6.25x6+5.5 = 43

The cost for not more than 15 balls = 6.25x15+5.5 = 99.25

Therefore, we can say that, the cost should be not less than $43 or more than $99.25

Hence, the range is 43 ≤ c(b) ≤ 99.25

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Answer:

C

Step-by-step explanation:

For these types of problems, its important that we focus on the base as well as the lengths of the base and any other given lengths.

Here, the net has a base that forms a square with side lengths of 8mm.

So automatically, we can eliminate choices a and d as both have a base that is a triangle rather than a square.

We've also noticed that the base has a length of 8mm

If we look at B and C closely, we can tell that B has base lengths of 10mm while C has base lengths of 8mm.

So C is the correct answer choice.

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The equation given in slope-intercept form does not represent the graph because the y-intercept of the graph is equal to 4 while the y-intercept of the equation is equal to 5.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the information provided regarding the equations and graphs, the y-intercept are as follows:

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Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

To test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.

Claim: p = 0.80

Opposite: p ≠ 0.80

The test is a two-tailed z-test.

Sample proportion (p) = 374/445 = 0.8404

Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)

z = 2.53 (rounded to 2 decimals)

Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.

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The statement "The range of F(x) = log base x is the set of all negative real numbers" is false.

A logarithmic function is a mathematical function that represents the logarithm of a number with respect to a given base. In other words, it is a function that relates a number to its logarithm. The general form of a logarithmic function is: f(x) = logₐ(x)

Here,
The natural logarithm function, ln(x), and the common logarithm function, log base 10 (x), both have domains of all positive real numbers, and their ranges are all real numbers. However, the logarithm function with base x, where x is a positive real number greater than 1, has a domain of all positive real numbers and a range of all real numbers. The logarithm function with base x, where x is a positive real number between 0 and 1, has a domain of all positive real numbers and a range of all negative real numbers.

Therefore, the statement is true only for the logarithm function with a base between 0 and 1, but false for the logarithm function with a base greater than 1.

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Answer:

magnesium >potassium

Step-by-step explanation:

Magnesium deficiency is frequently associated with hypokalemia. Concomitant magnesium deficiency aggravates hypokalemia and renders it refractory to treatment by potassium. Herein is reviewed literature suggesting that magnesium deficiency exacerbates potassium wasting by increasing distal potassium secretion.

h = hours till they're 58 miles apart

Check the picture below.

so they're travelling in opposite directions, however the combined distances is 58 miles at say "h" hours, by the time that happend Hopi has been walking "h" hours and Brittany has also being walking "h" hours too.

Since the combined distance is 58 miles than if Hopi has covered "m" miles then Brittany covered the slack of "58 - m".

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Hopi&m&15&h\\ Brittany&58-m&14&h \end{array}\hspace{5em} \begin{cases} m=(15)(h)\\\\ 58-m=(14)(h) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{substituting on the 2nd equation}}{58-(\stackrel{m}{15h})=14h}\implies 58=29h\implies \cfrac{58}{29}=h\implies \boxed{2=h}\)

a)95% confidence interval for the population mean birth weight in these hospitals is (3078.9358,3221.0642).

(b)The P-value is 0.0068.

To test the null hypothesis and the alternative hypothesis, all analysts employ a random population sample. The null hypothesis typically states that two population parameters are identical; for instance, it can claim that the population mean return is equal to zero.

A strategy for determining how reliably one may extrapolate observed results in a study sample to the larger population from is provided by hypothesis testing, a procedure used to assess the strength of the evidence from the sample and give a framework for doing so.

C.I=x-t(alpha/2)xs/sqrt{n}

=3150+_2.01*250/sqrt{50}

=(3078.9358,3221.0642)

b) P value =P(t<-2.83)+P(t>2.83)

use calculator

                 =0.0034+0.0034

                  =0.0068

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The form of the sum of the cubes identity is a^3 + b^3 = (a + b) [ a^2 - ab + b^2 ]

Consider the two terms a and b

The cubes of the terms are a^3 and b^3

Sum of the cubes of the two terms is

a^3 + b^3

Where a is the first variable

b is the second variable

Factorize the sum of the cubes of the terms

a^3 + b^3 = (a + b) [ a^2 - ab + b^2 ]

Here a^3 + b^3 is the product of the ( a + b) and  [ a^2 - ab + b^2 ].Here the sign of the ( a + b) and  [ a^2 - ab + b^2 ] will be always same.

Therefore, the result is (a + b) [ a^2 - ab + b^2 ]

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The lengths a and d are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For length a, we have that it is the hypotenuse of a right triangle, in which the side length 6 is adjacent/opposite to an angle of 45º(which has the same sine and cosine), hence:

sin(45º) = 6/a

\(\frac{\sqrt{2}}{2} = \frac{6}{a}\)

\(\sqrt{2}a = 12\)

\(a = 6\sqrt{2}\)

Length d is opposite to an angle of 30º, while the adjacent length is of 4, hence it is obtained as follows:

tan(30º) = d/4

\(\frac{\sqrt{3}}{3} = \frac{d}{4}\)

\(d = \frac{4\sqrt{3}}{3}\)

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Answer: 2.0431

Step-by-step explanation:

\(\log_{8} 70=\frac{\log 70}{\log 8} \approx 2.0431\)