Complete the point-slope equation of the line through (6,4)(6,4)left parenthesis, 6, comma, 4, right parenthesis and (7,2)(7,2)left parenthesis, 7, comma, 2, right parenthesis. use exact numbers.

Answer:

C.

Step-by-step explanation:

This is substitution method in solving simulteanous equations.

given y = 4x + 1

we will substitute y into 2y = -x-1

[tex]2(4x + 1) = - x - 1 \\ 8x + 2 = - x - 1 \\ 8x + x + 2 = - 1 \\ 9x + 2 = - 1 \\ 9x = - 1 - 2 \\ 9x = - 3[/tex]

Therefore the answer is C.

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Substituting the equation given into another equation will produce another equation. But which one?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\bf{2y=-x-1}[/tex] | substitute the required equation

[tex]\bf{2(4x+1)=-x-1}[/tex] | solve in terms of x

[tex]\bf{8x+2=-x-1}[/tex] | carry on solving

[tex]\bf{9x+2=-1}[/tex] | carry on solving

[tex]\bf{9x=-3[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                 [tex]\bf{=The\;third\;option}[/tex]

[tex]\LARGE\boxed{\bf{aesthetics\not1\theta 1}}[/tex]

Answer:

64 girls

Step-by-step explanation:

Number of boys in a classroom: 4

Total no. of students in the classroom: 12

Number of girls in 1 classroom: 12-4 = 8

Number of girls in 8 such classrooms: 8 × 8 = 64

Answer:

3 < x < 13

Step-by-step explanation:

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let x be the length of the unknown side.

Therefore, x will either be the longest side or one of the shorter sides.

Therefore:

   x < 5 + 8

⇒ x < 13

And:

   8 < 5 + x

⇒ 3 < x

So the range of possible values of the third side is greater than 3 and less than 13:   3 < x < 13

Answer:

(- 1, 1 )

Step-by-step explanation:

x + 5y = 4 → (1)

4x + 12y = 8 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x

- 4x - 20y = - 16 → (3)

add (2) and (3) term by term to eliminate x

0 - 8y = - 8

- 8y = - 8 ( divide both sides by - 8 )

y = 1

substitute y = 1 into either of the 2 equations and solve for x

substituting into (1)

x + 5(1) = 4

x + 5 = 4 ( subtract 5 from both sides )

x = - 1

As a check

substitute these values into the left side of both equations and if equal to the right side then they are the solution.

- 1 + 5(1) = - 1 + 5 = 4 = right side

4(- 1) + 12(1) = - 4 + 12 = 8 = right side

(- 1, 1 ) is the solution to the system of equations

Answer:

13

Step-by-step explanation:

Since triangles CBA and DBA are equal, their lengths would also be equal, thus, DB = 13 as CA = 13

Answer:

CAB = DAB

CA is equivalent to BD

The volume of a cylinder changes when you adjust the height or radius as the volume either increases or reduces.

Let's assume that the height and radius are 14cm and 7cm. The volume will be:

= πr²h

= 3.14 × 7² × 14

= 2154.04cm³

When the radius and height are reduced to 5cm and 9cm, the volume will be:

= πr²h

= 3.14 × 5² × 9

= 706.5cm³

This illustrates that the volume reduces when the height and radius reduces.

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Answer: C

Step-by-step explanation:

[tex]y=-2[/tex] is dotted and shaded below, so it represents [tex]y < -2[/tex].

Also, [tex]x+y=1[/tex] is shaded above, so it represents [tex]x+y < 1[/tex].

Answer:

She needs the starting amount of money to create an equation.

Step-by-step explanation:

The formula that she can use when she has the starting amount or the y-intercept is this one: f(t)=P(1+b)^t.

t=time

b=percent

P=starting value

The formula with the information given is: f(6)=P(1+3.75)^6

Hope this helps!

If not, I am sorry.

Answer:

Principal

Step-by-step explanation:

Since, the amount in the simple interest is,

Where, P is the principal amount,

r is the annual rate,

t is the time ( in years ),

Here, r = 3.75 %, t = 6 years,

Thus, By the above explanation,

It is clear that, we need the value of P, that is, principal to find the amount.

Choices for the measure of center that is best are: C. Rome data center is best described by the mean while that of New York data is best described by the median.

The measures of center include the mean and the median. Mean is best for a symmetrical data distribution while median is good for a skewed data distribution with an outlier.

The data for New work has an outlier, while that of Rome does not. Therefore, the best choices for the measure of center is: C. Rome data center is best described by the mean while that of New York data is best described by the median.

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The first few terms of a geometric sequence with first term [tex]a[/tex] and common ratio [tex]r[/tex] look like

[tex]a, ar , ar^2, ar^3, \ldots[/tex]

and so on. Notice that the [tex]n[/tex]-th term (where [tex]n[/tex] is a natural number) is [tex]ar^{n-1}[/tex].

For this particular sequence, the first term is

[tex]a=3[/tex]

and the fourth term is

[tex]ar^{4-1} = ar^3 = 1029[/tex]

Substitute [tex]a=3[/tex] into the second equation and solve for [tex]r[/tex].

[tex]3r^3 = 1029 \implies r^3 = 343 \implies r = \sqrt[3]{343} = \sqrt[3]{7^3} = 7[/tex]

Then the two terms between the 1st and 4th - i.e. the 2nd and 3rd terms - are

[tex]ar = 3\times7 = \boxed{21}[/tex]

and

[tex]ar^2 = 3\times7^2 = \boxed{147}[/tex]

Answer:

Term 2 is 21, and term 3 is 147.

Step-by-step explanation:

The geometric sequence is 3, 3r, 3r^2, 1029.

[tex]r = \sqrt[3]{ \frac{1029}{3} } [/tex]

[tex]r = \sqrt[3]{343} = 7[/tex]

So we have 3, 21, 147, 1029.

Answer:

43°

Step-by-step explanation:

Calculating for the measure of angle C using

[tex] \frac{sin18}{9} = \frac{sinc}{20} \\ sinc = \frac{sin18 \times 20}{9} \\ sinc = 0.6867 \\ c = \csc(0.6867) \\ c = 43.3869 \\ c = 43 \: degrees[/tex]

The x-coordinate of the altitude on EF is the same as the point D(4, 5) and by calculation, the height from D (1, 5) is also median from D (1, 5)

The height from D is perpendicular to EF

The slope of EF = (8 - 2)/(1 - 1) = ∞

Therefore, the side EF is parallel to the y-axis.

Therefore, the coordinates of the point of intersection of the altitude from D and the line EF is (1, 5)

The median is the midpoint of the side EF

The coordinates of the midpoint is found as follows;

[tex] \mathbf{ \left(1 + \frac{1 - 1}{2}, \: 1 + \frac{8 - 2}{2}\right)} = (1 ,5)[/tex]

Therefore;

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Answer:

Four units left and one unit up.

Step-by-step explanation
Adding -4 to each x-coordinate shifts the figure to the left 4 units.

Adding +1 to each y-coordinate shifts the figure up 1 unit.

The figure is moved ...

 four units left and one unit up

Answer:

2nd option

Step-by-step explanation:

x-4 = 4 left

y+1 = 1 up

2nd option

Answer:

20

Step-by-step explanation:

Rise over run

Answer:

m = 20

Step-by-step explanation:

Answer:

Step-by-step explanation:

plus 18 and subtract 4

We will use a combination formula to determine how many ways the prizes could be given out.

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” The combination means “Selection of things”, where the order of things has no importance.

The formulas nCk is popularly known as counting formula.

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Using the domain and range concepts, we have that:

Hence, considering the given graph:

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Answer:

4 radians

Step-by-step explanation:

Arc Length (Radians) = rθ

Given Arc Length XY  = 40cm and radius, r = 10cm,

we will substitute these 2 values into the formula to find θ.

(10)θ  = 40

θ = 40 / 10

= 4 radians

Answer:

A

Step-by-step explanation:

the length of arc XY is calculated as

arc = circumference of circle × fraction of circle

      = 2πr × [tex]\frac{0}{2\pi }[/tex] ( r is radius and Θ is central angle )

here arc = 40 and r = 10 , then

2π × 10 ×[tex]\frac{0}{2\pi }[/tex] = 40

20π × [tex]\frac{0}{2\pi }[/tex] = 40 ( cancel 20π and 2π by 2π )

10Θ = 40 ( divide both sides by 10 )

Θ = 4 radians

The step you would take to evaluate an expression is to follow the order of operation

Expressions are mathematical statements that involve variables, terms, coefficients and mathematical operators

Different expressions require different ways of solving

However, the general guide is that the order of operation must be followed

The order of operation is represented by the acronym BEDMAS

Which means

Bracket

Exponent

Division

Multiplication

Addition

Subtraction

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Answer:

Generally x means times so the best and not dummest option is 2 times

2x and 2 x is the same the 2 x is spaced out a little

Step-by-step explanation:

The area of the given composite figure is 74.24cm^2

The figure is made up of semi circle and rectangle

Area = area of semicircle + Area of rectangle

Area = 3.14(4)^2 + 3(8)

Area = 50.24 + 24

Area. = 74.24cm^2

Hence the area of the given composite figure is 74.24cm^2

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Answer:

7.5 ft

Step-by-step explanation:

1st drop = 60 ft

2nd drop = 60/2 = 30 ft

3rd drop = 30/2 = 15 ft

4th drop = 15/2 = 7.5 ft

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{z^{2}-8 }-\sqrt{6z-17}=0 \end{gathered}$}[/tex]

Simplify the left side. Yes n is a positive integer greater than x and a is a real number or a factor, then [tex]\bf{\sqrt[n]{a^{x} }=a^{\frac{x}{n} }. }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{(z^{2}-8)^{\frac{1}{2} }-\sqrt{6z-17}=0 } \end{gathered}$}[/tex]

If n is a positive integer greater than x and a is a real number or a factor, then [tex]\bf{\sqrt[n]{a^{x} }=a^{\frac{x}{n} }. }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{(z^{2}-8)^{\frac{1}{2} }-(6z-17)^{\frac{1}{2}} =0 } \end{gathered}$}[/tex]

Draw each side of the equation. The solution is the x value of the point of intersection.

[tex]\red{\underbrace{\overbrace{\boxed{\boldsymbol{\sf{\green{z=3}}}}} \ \ \to \ \ \ Answer}}[/tex]

Answer:

Step-by-step explanation:

[tex]\sqrt{z^2-8} -\sqrt{6z-17} =0\\\sqrt{z^2-8} =\sqrt{6z-17} \\6z > 17\\z > \frac{17}{6} \\z^2-8=0\\z^2 > 8\\so \\z < -\sqrt{8} \\or\\z > \sqrt{8} \\combining\\z > \frac{17}{6} \\again\\z^2-8=6z-17\\z^2-6z-8+17=0\\z^2-6z+9=0\\z^2-3z-3z+9=0\\z(z-3)-3(z-3)=0\\(z-3)(z-3)=0\\z=3[/tex]

The statistical goal of multiple regression analysis is to build a linear equation model that identifies the optimal weighted linear combination of independent variables in the study in order to optimally predict the reference variable.

Regression analysis is usually performed for one of two purposes. Predicting the value of the dependent variable of a person whose information about the explanatory variable is available, or estimating the effect of the explanatory variable on the dependent variable.

In multiple regression analysis, researchers can determine the strength of the relationship between the outcome (dependent variable) and multiple predictors, and the importance of each predictor in the relationship, often the effect of other predictors. It can be evaluated by statistically eliminating it.

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An expression is defined as a set of numbers, variables, and mathematical operations. The value of b for which the expression x² + bx + 18 can be factored is 9.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of b for which the given expression x² + bx + 18 can be factored is 9. This will make the expression factored as (x+3) and (x+6).

Thus, the value of b for which the expression x² + bx + 18 can be factored is 9.

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The correct options regarding the circle with endpoints of the longest chord at (4, 5.5) and (4, 10.5) are:

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The center is the midpoint of the chords, hence:

The radius is half the distance between the chords, hence:

[tex]r = 0.5\sqrt{(4-4)^2 + (10.5 - 5.5)^2} = 0.5 = 2.5[/tex].

Hence the equation is:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x - 4)^2 + (y - 8)^2 = 2.5^2[/tex]

[tex](x - 4)^2 + (y - 8)^2 = 6.25[/tex]

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Answer:

x =7

Step-by-step explanation:

2x+6 = 20

To solve this equation, you first need to subtract 6 from each side

2x+6-6 = 20-6

2x = 14

Then divide each side by 2

2x/2 = 14/2

x = 7

The value of x is 126.87° and the value of y is 53°.

An obtuse angle is an angle that is greater than 90° but lesser than 180° while an acute angle is an angle between 0-90°.

From the given information:

sin x° = 0.8

x = sin⁻¹ (0.8)

x = 53.13°

x + 53.1° = 180°

x = 180° -53.13°

x = 126.87°

If cos 127° = -cos y°,

-cos y = -0.6018

cos y = 0.6018

y = cos⁻¹ (0.6018)

y = 53°

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