A circle with center C has equation x²+y²- 2x + 10y-19 = 0
It can be shown that center C is (1,-5) and that the radius is √45.
Find the equation of the tangent to the circle at the point (7,-2), giving your answer in the form ax + by + c=0, where a, b and c are integers.

An equation of a line with slope(m) = 4/5 and y-intercept(b) = 1 can be formed as y = (4/5)x + 1.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

An equation of a line in slope-intercept form with slope(m) = 4/5 and

y-intercept(b) = 1 can be formed as y = (4/5)x + 1.

The graph of this line is attached below.

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Answer:

Vhc = 401.92 cm3

Step-by-step explanation:

Vcylender = Pi*r2*h

Vhalfcyldr = (Pi*r2*h)/2

then

h= 16cm

r = 8cm/2 = 4cm

then

Vhalfcylinder = ((3.14)*(4)2*16) / 2

Vhc = 401.92 cm3

There are 8 bags of basmati rice are there if a crate contains bags of basmati rice Which weigh 5 lb each and bags of jasmine rice.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

a crate contains bags of basmati rice Which weigh 5 lb each and bags of jasmine rice which weigh 3 pounds each.

The equation can be framed:

x + y = 20

5x + 3y = 76

After solving

By substitution method:

we get:

y = 12

x = 20 - 12 = 8

Thus, there are 8 bags of basmati rice are there if a crate contains bags of basmati rice Which weigh 5 lb each, and bags of jasmine rice.

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The true statement about n is (a) The value of n is 1/5 because (⁵√2)⁵ = 2¹ and (2¹/⁵)⁵ = 1, so ⁵√2 = 2¹/⁵

From the question, we have the following parameters that can be used in our computation:

Expression =  ⁵√2

Also from the question, we understand that the expression is to be expressed as

2ⁿ

This means that

⁵√2 = 2ⁿ

Re-express ⁵√2 using the law of indices

2ⁿ = 2¹/⁵

By comparison, we have

n = 1/5

This means that the value of n is 1/5

Hence, the true statement is (a)

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Answer:

1236

Step-by-step explanation:

The percentage of companies with revenue between 73 million and 87 million dollars is; 0.30

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

Population mean; μ = 80 million

Population standard deviation; σ = 18 million

The percentage of companies with revenue between 73 million and 87 million dollars is expressed as;

P(73 < X < 87)

z₁ = (73 - 80)/18

z₁  = -0.389

z₂ = (87 - 80)/18

z₂ = 0.389

Using probability between two z-scores, we have;

P(-0.389 < Z < 0.389) ≈ 0.30

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Distance is the measure from one point to another point. Given, any two points distance is [tex]\sqrt{(x1-x2)^{2} }+\sqrt{(y1-y2)^{2} }[/tex].

Midpoint is the mid-value of two points.

Midpoint = [ x₁+x₂/2 , y₁+y₂/2]

So, for the given centre (9, 10) and point on circle(7,4)

Centre = [tex]\sqrt{}[/tex](9-7)²+(10-4)²

= [tex]\sqrt{}[/tex]4+36

= 6.32

For the given centre (2,-6) and point on circle (1,10)

Centre = [tex]\sqrt{}[/tex](2-1)²+(-6-10)²

=[tex]\sqrt{}[/tex]1+256

=16.03

For  given centre (1,-5) and point on circle(-7,-13)

Midpoint = [ 1-7/2 , -5-13/2]

= [-3, -9]

For given centre(-2,0) and point  on circle(-9,-4)

Midpoint = [-2-9/2 , 0-4/2]

= [-5.5,-2]

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Given, center (9,10) and point on circle is (7,4) distance is 6.32. And center (2,-6) and point on circle (1,10) distance is 16.03.

Given center (1, -5) and point of circle(-7,-13) midpoint is (-3,-9). And center (-2,0) and point on circle (-9,-4) midpoint is (-5.5,-2).

Distance is the measure from one point to another point. Given, any two points distance is -

[tex]\sqrt{x_1^2-x_2^2} +\sqrt{y_1^2-y_2^2}[/tex]

Midpoint is the mid-value of two points. Midpoint = [(x₁+x₂)/2, (y₁+y₂)/2]

So, for the given center (9, 10) and point on circle(7,4)

Center = (9-7)²+(10-4)²

= 4+36

= 6.32

For the given center (2,-6) and point on circle (1,10)

Center = (2-1)²+(-6-10)²

= 1+256

= 16.03

For  given center (1,-5) and point on circle(-7,-13)

Midpoint = [ 1-7/2 , -5-13/2]

               = [-3, -9]

For given center (-2,0) and point  on circle(-9,-4)

Midpoint = [-2-9/2,0-4/2]

               = [-5.5,-2]

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Answer:

Step-by-step explanation:

Part A:

For number 1, the bus drives non-linear. It is not a constant rate but it is increasing.

For number 2, the bus is at a stopping point.

For number 3, the bus drives in a non-linear rate but it still increasing.

For number 4, the bus is at its last stop, the middle of the bus ride, the peak of the time.

For number 5, the bus comes to a non-linear decrease in the route. and eventually the end.  

Part B:  

The bus is increasing in numbers 1 and 3, and decreasing for number 5, and at a constant at numbers 2 and 4.  

Part C:  

The graph is non-linear, as the slope is not at a constant.

Answer:

Sorry i don't know. But i think this is a good priblem

Answer:

unexplainable

Step-by-step explanation:

does not make since

The 15th term of the given geometric sequence will be (C) 5/4096.

Mathematicians refer to a succession of non-zero numbers as a geometric progression or geometric sequence.

Each term after the first is derived by multiplying the previous term by a fixed, non-zero value called the common ratio.

So, the geometric sequence will be:

nth term formula: aₙ = a₁rⁿ⁻¹

Now, insert the values and calculate as follows:

aₙ = a₁rⁿ⁻¹

a₁₅ = 20(1/2)¹⁵⁻¹

a₁₅ = 20(1/2)¹⁴

a₁₅ = 20(1/16384)

a₁₅ = 20/16384

a₁₅ = 5/4096

Therefore, the 15th term of the given geometric sequence will be (C) 5/4096.

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Complete question:
Find the 15th term in the geometric sequence below. 20, 10, 5, 2.5, . . .

A.-25/4,096

B.-5/4,096

C.5/4,096

D.25/4,096

Answer:

Step-by-step explanation:

The area of each triangle is one-half the area of the rectangle. So, the area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.

The evaluated expression the quantity of 6 less than y, raised to the power of x is - 8. Therefore, the correct option is D.

The quantity of 6 less than y, raised to the power of x can be expressed as follows:

The verbal expression can be converted to a mathematical expression as follows:

(y - 6)ˣ

when

y = 4

x = 3

Therefore,

(y - 6)ˣ = (4 - 6)³

Therefore,

(4 - 6)³ = (-2)³

(-2)³ = -8

Therefore, the evaluated expression is -8.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{doubled}{\$9000}\\ P=\textit{original amount deposited}\dotfill &\$4500\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases}[/tex]

[tex]9000=4500\left(1+\frac{0.0725}{4}\right)^{4\cdot t} \implies \cfrac{9000}{4500}=\left(1+\frac{0.0725}{4}\right)^{4\cdot t} \\\\\\ 2=1.018125^{4t}\implies \log(2)=\log(1.018125^{4t})\implies \log(2)=t\log(1.018125^{4}) \\\\\\ \cfrac{\log(2)}{\log(1.018125^{4})}=t\implies 9.65\approx t\qquad \textit{about 9 years and 8 months}[/tex]

Answer:

30=t i think

Step-by-step explanation:

So basically what you do is since it is division you would multiply 5 by its self and you multiply on the other side because if you do something on one side you have to do it on another so that would leave you with 30=t

A resemblance While retaining shape, metamorphosis can alter both location and size.

When the sides of two figures are proportionate and the accompanying angles are congruent, the figures are said to be comparable.

Get the two triangles to face in the same direction, or in the same orientation, to check if they resemble one another. You accomplish this by turning one shape so that it is in alignment with the other. A rotation is the name given to such a change.

Similarity refers to two figures that share the same shape but differ in size. A rigid motion and a rescaling make up a similarity transformation. To put it another way, a similarity transformation may change both location and size while maintaining shape.

Let the given points be G(-2, 3), H(4, 3), I(4, 0) and J(1, 0), K(6.-2), L(1, -2).

A resemblance While retaining shape, metamorphosis can alter both location and size.

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Answer:

  not similar

Step-by-step explanation:

You want to know if ∆GHI ~ ∆JKL when they are defined by coordinates G(-2, 3), H(4, 3), I(4, 0) and J(1, 0), K(6.-2), L(1, -2).

Corresponding angles of similar triangles are congruent, and corresponding sides are proportional.

Here, angle G is an acute angle less than 45°, while corresponding angle J is an acute angle greater than 45°. These corresponding angles in the similarity statement are not congruent, so the similarity statement is false.

__

Additional comment

Side ratios in ∆GHI are 3 : 6 : 3√5 = 1 : 2 : √5.

Side ratios in ∆JKL are 2 : 5 : √29.

For comparison purposes, we like to list them shortest to longest.

These ratios are different, so even if the order of the vertices were straightened out, the triangles still would not be similar. If the triangles had the same side length ratios, the vertex order for a proper similarity statement would be ∆GHI ~ ∆KLJ.

Answer:

2x³ + 3x² - x + 10

Step-by-step explanation:

2x³ - 2x² + 4x + 5x² - 5x + 10

2x³ + 3x² - x + 10

The critical values and shecht the rejection reglues for a theo-tall tent, in a Z procedure with significance level isterse is (-1.812,1.812).

[tex]$\alpha=0.07$[/tex] This is two tailed lest

critical values are [tex]$\pm 1.812$[/tex]

What is critical values ?

A critical value is a value used as a cut-off to indicate the beginning of a zone where the test statistic from a hypothesis test is unlikely to decrease. In hypothesis testing, the crucial value and the resulting test statistic are compared to decide whether or not the null hypothesis has to be rejected.

For hypothesis testing, the crucial value graphically separates the graph into the acceptance region and the rejection zone. A test statistic's statistical significance should be verified. We will learn more about the critical value in this article, including its types, formula, and calculation method.

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Answer:

No

Step-by-step explanation:

1 = 2(-5) - 9

1 = -10 - 9

1 ≠ -19, therefore that point does not lie on the line

The probability that the Yankees will lose when they score 5 or more runs is equal to 0.2766.

What is Conditional Probability?

From the question, we know that the probability that the Yankees will win a game is 0.53.

[tex]\implies P(W)=0.53[/tex]

Also, then the probability that the Yankees will lose a game is given as,

[tex]P(L)=1-P(W)\\\implies P(L)=1-0.53\\\implies P(L)=0.47[/tex]

It is also given that, the probability that the Yankees will score 5 or more runs is 0.48.

[tex]\implies P(A)=0.48[/tex]  -----(1)

So, the probability that the Yankees will score less than 5 runs is,

[tex]P(S)=1-P(A)\\\implies P(S)=1-0.5\\\implies P(S)=0.5[/tex]------(2)

We also know the probability that the Yankees will win and score 5 or more runs is 0.42.

[tex]\implies P(B)=0.42[/tex]

Also, then the probability that the Yankees will lose or score less than 5 runs is given as,

[tex]P(C)=1-P(B)\\\implies P(C)=1-0.42\\\implies P(C)=0.58[/tex]

Next, the probability that the Yankees will lose and score less than 5 runs is,

[tex]P(D)=0.42+0.5-0.58\\\implies P(D)=0.34[/tex]

Now, the required probability is the probability that the Yankees will lose and score 5 or more runs.

It can be calculated using the conditional probability formula, [tex]P(M/N)=\frac{P(M\cap N)}{P(N)}[/tex]

So, the required probability  that the Yankees will lose and score 5 or more runs is given as,

P(they score 5 or more runs / probability that they lose game) = P(they lose and score 5 or more runs) / P(they lose the game)

[tex]\implies P(E)=\frac{0.47-0.38}{0.47} \\\implies P(E)=0.2766[/tex]

Therefore, the probability that the Yankees will lose when they score 5 or more runs is equal to 0.2766.

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what are we supposed to be solving

Answer:

Step-by-step explanation:

duh

Answer:

66 [tex]cm^{2}[/tex]

Step-by-step explanation:

Front: 6 x 5 = 30

Back:  6 x 4 = 24

Left side: 1/2 (3 x 4) =6

Right side: 1/2 ( 3 x 4) 6

Add

30 + 24 + 6 + 6 = 66

The value of slope for line equation 1 is -5/2. The value of slope for line equation 2 is 5/3.

A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

Here,

y=mx+c

where m is slope.

line equation 1,

y=-5/2x-5

m=-5/2

line equation 2,

y=5/3x

m=5/3

For line equation 1, the slope is equal to -5/2. For line equation 2, the slope is equal to 5/3.

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Write each decimal as a fraction or mixed number in simplest form

-0.14

= -14/100

= -7/50

_________________________

0.27

= 27/100

[tex]3x^2+x-10=\boxed{(x+2)(3x-5)}[/tex]

Answer:

hope it help

the last answer is 6

I showed you step by step. for any explanation write it in the comment

Answer:

Below

Step-by-step explanation:

These are both equations of lines.....one has slope =6 and the other has slope = 4   so they will cross at ONE point

By using the formula for area of rectangle, it can be calculated that-

a) Expression for total area = [tex]6^2 + 2 \times 6 + 24[/tex]

Total area = 72 square inches

b) Length of the figure =  9 inches

Breadth of the figure =  8 inches

What is area of a rectangle?

Area of a rectangle is the total space taken by the rectangle.

If l is the length of the rectangle and b is the breadth of the rectangle, then area of the rectangle is calculated by

Area = l [tex]\times[/tex] b

Side of the square = 6 inches

Area of the square = [tex]6^2[/tex] square inches

Length of white rectangle = 2 inches

Breadth of white rectangle = 6 inches

Area of white rectangle = [tex]2 \times 6 =[/tex] 12 square inches

Area of blue rectangle  = 24 square inches

Total area = [tex]6^2 + 2 \times 6 + 24[/tex] =

                     36 + 12 + 24 =

                     72 sq. inches

b) Let the breadth of the blue rectangle be b inches

Length of the blue rectangle = 2 + 6 = 8 inches

Total area = 8b square inches

By the problem,

[tex]8b = 24 \\b = \frac{24}{8}\\[/tex]

b = 3 inches

Length of the figure = 6 + 3 = 9 inches

Breadth of the figure = 2 + 6 = 8 inches

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The value of x from the parallelogram ABCD is 10.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Given that, ∠A=120-2x, ∠B=70+x, ∠C=105-x² and ∠D=40+4x.

The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary.

Here, ∠A and ∠D are consecutive angles

Now, 120-2x+40+4x=180

⇒ 160+2x=180

⇒ 2x=20

⇒ x=10

So, ∠A=120-2x=100, ∠B=70+x=80, ∠C=160-6x=100 and ∠D=40+4x=80

Therefore, the value of x is 10.

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"Your question is incomplete, probably the complete question/missing part is:"

The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary. Given the angle measures, prove that quadrilateral ABCD is a parallelogram by finding the value of x. ∠A=120-2x, ∠B=70+x, ∠C=160-6x and ∠D=40+4x.

The total commission that's earned will be $360.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, an employee who earns $12/hour, worked 37 hours this week, is paid a commission of $40 for each sale, and makes 9 sales during the same week. Employees receive commission, also referred to as a sales commission, based on the sales they generate. A sales commission is a payment made to an employee after they successfully complete a task, typically selling a predetermined volume of goods or services. Sales commissions are a common incentive used by employers to boost employee productivity. A commission can be paid instead of or in addition to a salary.

The total commissions will be:

= Amount of commission × Number of sales

= $40 × 9

= $360

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