How many significant digits are in 26.04813?​

R' (6,-3)

Explanation

Step 1

Let

R(-2, 1)

S(-8, 2)

T(-4, 5)

the law for the translation is 8 units right and 4 units down,it meas you have to add 8 units to x coordinates , and subtract 4 units from y coordinates

Step 2

find the translation for R

so, the answer is C) R' (6,-3)

The value of x with the given condition is 10

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

D(7,2), E(1, 9), F(4,8), and G(x, 1),

Also, we have

DE || FG

This means that the lines DE and FG are parallel lines and they have equal slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

(9 - 2)/(1 - 7) = (1 - 8)/(x - 4)

Evaluate the difference

-7/6 = -7/(x - 4)

So. we have

x - 4 = 6

Evaluate

x = 10

Hence. the value of x is 10

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The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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Answer:

d) 4

For the second question, just plug in the x value and isolate the y value

Step-by-step explanation:

1. 9y=36-13x

y=4-13/9 x

4 is the y-intercept

Answer:

d and (- 4, 33 )

Step-by-step explanation:

Given

13x + 9y = 36

To find the y- intercept, substitute x = 0 into the equation and solve for y

13(0) + 9y = 36, that is

0 + 9y = 36

9y = 36 ( divide both sides by 9 )

y = 4 ← y- intercept

---------------------------------------------

Given

y = - 6x + 9 and (- 4, y) then substitute x = - 4 into the equation

y = - 6(- 4) + 9 = 24 + 9 = 33

Thus (- 4, 33 ) is the ordered pair

Based on the given information, the value of y is 5.

What is a cyclic polygon?

A cyclic polygon is a polygon that can be inscribed inside a circle in such a way that all of its vertices lie on the circumference of the circle. In other words, a cyclic polygon is a polygon that can be circumscribed by a circle.

In a polygon with n sides, the sum of its interior angles is given by the formula: (n - 2) * 180 degrees. Since this polygon is inside a circle, it must be a cyclic polygon, which means that its opposite angles add up to 180 degrees.

We are given that the opposite angles are 23y and 13y, so we can write:

23y + 13y = 180

36y = 180

y = 5

Therefore, the value of y is 5.

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Answer:

(a) 0
(b) 0
(c) 1
The function is not continous at x = 9

Step-by-step explanation:

To the left and right of the point x = 9, the graph would seem to continue at  f(x) = 0, however on the exact point x = 9 there is a hole in the graph allowing it to be equal to 1. Due to the hole in the graph, it is not continuous

Apologies if this is wrong its been a bit since I did calculus

Answer:

C.

Step-by-step explanation:

A. 4 - 2 = 2    not zero

B.

$50 in 1 account

$50 in another account

Not zero

C.

6 deg - 6 deg = 0 deg

This is zero

D.

$8 - $3 = $5

Not zero

Answer:

c

Step-by-step explanation:

Answer:

37.5

Step-by-step explanation:

To convert Ram's score from a maximum of 100 marks to a maximum of 75 marks, we can use the following proportion:

100 marks = 75 marks

50 marks = x

We can solve for x by cross-multiplication:

100x = 50*75

x = 50*75/100

x = 37.5

Therefore, Ram's score in a maximum of 75 marks will be 37.5 marks.

IQR offers a more accurate indicator of consistency than range since it is less impacted by outliers.

Due to Bus 18's smaller IQR, we can infer that it is more consistent than Bus 47.

An indicator of statistical dispersion used to describe the variability of a dataset is the interquartile range (IQR). It is derived by subtracting a dataset's 75th percentile (Q3) from its 25th percentile (Q1). When compared to other measures of variability like range, the IQR represents the middle 50% of the data and is less susceptible to outliers.

We must contrast the measurements of variability for the two buses in order to determine which one is more reliable. We can utilize range and interquartile range as measurements of variability. (IQR).

The range of a dataset is the difference between its maximum and minimum values.

The range for Bus 18 is 16 (22 - 6), whereas the range for Bus 47 is 24. (28 - 4).

A measure of variability that is less impacted by outliers than the range is the interquartile range (IQR). It is determined as the difference between a dataset's third and first quartiles (Q3 and Q1, respectively).

The IQR is 16 for Bus 18 (Q3 - Q1 = 22 - 6)

IQR offers a more accurate indicator of consistency than range since it is less impacted by outliers. Due to Bus 18's smaller IQR, we can infer that it is more consistent than Bus 47.

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To know if the equation of this line k(x) = 3x - 6 is true, you should determine its slope and then write the equation in slope-intercept form.

In Mathematics, the y-intercept of any graph generally occur at the point where the value of "x" is equal to zero (x = 0), which is -6 in this scenario.

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

y = mx + c

Where:

Making slope (m) the subject of formula, we have the following:

Slope, m = (y - c)/x

Slope, m = (0 - (-6))/2

Slope, m = (0 + 6)/2

Slope, m = 6/2

Slope, m = 3.

For the equation of this line, we have the following:

y = mx + c

y = k(x) = 3x - 6 (True)

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Applying the relations given, considering equivalent angles, the trigonometric measures for the angles are given as follows:

The sine of 240º can be written as follows:

sin(240º) = sin(180º + 60º).

Applying the first relation given on the second line, we have that:

sin(180º + 60º) = -sin(60º)

It is known that sin(60º) = sqrt(3)/2, hence the sine of 240º is given as follows:

sin(240º) = -sin(60º) = -sqrt(3)/2.

The cosine of 225º can be written as follows:

cos(225º) = cos(180º + 45º).

Applying the second relation given on the second line, we have that:

cos(180º + 45º) = -cos(45º)

It is known that cos(45º) = sqrt(2)/2, hence:

cos(225º) = -cos(45º) = -sqrt(2)/2.

The tangent of 225º can be written as follows:

tan(225º) = tan (180º + 45º).

Applying the third relation given on the second line, we have that:

tan(180º + 45º) = tan(45º)

It is known that tan(45º) = 1, hence:

tan(225º) = tan(45º) = 1.

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The equation of each line that satisfies the given conditions are:

1. y - 2 = 5/2(x - 3)

2. y - 4 = m(x + 3)

3. y = -3x + 5

1. Given the points, (3, 2) and (5, 7), find the slope (m):

Slope (m) = change in y / change in x = (7 - 2)/(5 - 3)

m = 5/2

Write the equation in point-slope form by substituting m = 5/2 and (a, b) = (3, 2) into y - b = m(x - a):

y - 2 = 5/2(x - 3)

2. Given:

A point = (-3, 4)

Slope (m) = 2

Substitute (a, b) (-3, 4), and m = 2 into y - b = m(x - a):

y - 4 = m(x + 3) [equation of the line]

3. Given:

Slope (m) = -3

Y-intercept (b) = 5

Substitute m = -3 and b = 5 into the equation y = mx + b:

y = -3x + 5

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Answer:

a = 3

Step-by-step explanation:

First start writing out the binomial expansion of \((ax + 1)^7\)

\([1^7] + [7C1 * 1^6 *(ax)] + [7C2*1^5*(ax)^2]+[7C3*1^4*(ax)^3]\)

as you can see from this, the last bracket will produce our \(x^3\) term

\(7C3*1^4*a^3x^3 \\35a^3x^3\\35a^3 = 945\\a^3 = 27\\a = 3\)

Hope this helps, let me know if you have any questions :)

Angles at the center of a circle add up to 360 degrees.

The measure of angle GEH in the circle is (d) 116 degrees

The given parameters are:

\(\mathbf{\angle FEG = 64^o}\)

Since line FH is the diameter of the circle;

It means that:

\(\mathbf{\angle FEG + \angle GEH = 180^o}\) --- By angle on a straight line theorem

Substitute 64 for FEG

\(\mathbf{64 + \angle GEH = 180^o}\)

Subtract 64 from both sides

\(\mathbf{\angle GEH = 180^o - 64}\)

Evaluate like terms

\(\mathbf{\angle GEH = 116^o}\)

Hence, the measure of angle GEH in the circle is (d) 116 degrees

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Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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First, calculate the price of the car WITH the tax rate.

8.5% → 0.085

$5900 × 0.085 = $501.50

Add the tax, to the original price.

$5900 + $501.50 = $6401.50

Next, get the 15% downpayment

15% → 0.15

$6401.50 × 0.15 = $960.225

Rounding off to the nearest cent, the downpayment is equal to $960.23.

The value of the missing side lengths x and y are 5√2 and 5 respectively.

The figure in the image is a right triangle.

Angle θ = 45 degree

Hypotenuse = x

Opposite to angle θ = y

Adjacent to angle θ = 5

To solve for side x and side y, we use the trigonometric ratio.

Note that:

Cosine = adjacent / hypotenuse

tangent = opposite / adjacent

Solving for x:

Cosine = adjacent / hypotenuse

Plug in the values

cos( 45 ) = 5/x

x = 5 / cos( 45 )

x = 5√2

Solving for side y:

tangent = opposite / adjacent

Plug in the values

tan( 45 ) = y/5

y = tan( 45 ) × 5

y = 5

Therefore, the value of side length x is 5 units.

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Answer:

54/10= 5,4 but if you want to a simple broken number it is 27/5

Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

Question 2

\(23=p \cdot 250\)

Question 3

\(p=\frac{23}{250}=0.092\)

Answer:

The car will travel  525 miles on 15 gallons of gas.

Step-by-step explanation:

Given that car can travel 35 miles using 1 Gallon of gas.

so

Unit rate = 35 miles per gallon

Thus,

The number of miles a car can travel in 15 gallons = 15 × 35

                                                                                    = 525 miles

Thus, the car will travel  525 miles on 15 gallons of gas.

Answer:

k = \(\frac{1}{9}\)

Step-by-step explanation:

Using the discriminant

Δ = b² - 4ac

For a repeated real solution then

b² - 4ac = 0

Given

16x² - \(\frac{8}{3}\) x + k = 0

with a = 16, b = - \(\frac{8}{3}\) , c = k

(- \(\frac{8}{3}\) )² - ( 4 × 16 × k) = 0

\(\frac{64}{9}\) - 64k = 0 ( subtract \(\frac{64}{9}\) from both sides )

- 64k = - \(\frac{64}{9}\) ( divide both sides by - 64 )

k = \(\frac{1}{9}\)

The two angles are related in that they are supplementary angles

Supplementary angles would add tuo to 180 degrees according to the angle Theorem.

Adding the two given angles :

These angles are supplementary

The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.

Hence, the angles are related as they are supplementary angles .

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Answer:

seriously,I think the answer is 10 hundred thousand

Step-by-step explanation:

10*100000=1000000

The lengths of the segments x and y in the right triangles are x = 6√2 and y = 12√2

The given shape is the right-angled triangle

Such that

We have angles = 30 degrees and 45 degrees

The measure of y can be calculated using the following sine ratio

sin(45) = y/24

Make y the subject

So, we have

y = 24 * sin(45)

When evaluated, we have

y = 12√2

The length x is calculated as

sin(30) = x/y

So, we have

x = y * sin(30)

This gives

x = 12√2 * 1/2

Evaluate

x = 6√2

Hence, the value of x in the triangle is 6√2

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Answer:

Step-by-step explanation:

the sum of the interior angles of a triangle is 180°,

x is an opposite angle, same value

so

180 - (55 + 55) =

180 - 110 =

70°

-------------------

check

55 + 55 + 70 = 180

the answer is good

Answer:

15.757 im not sure but i came up with that one.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

|5| = 5

Step-by-step explanation:

Absolute value can be seen as the distance between a number and zero. It is always a positive number. 5 is 5 units away from 0. |5| = 5, and |-5| would also be 5. It's important not to get absolute value confused with opposites.