7^1 in expanded form​

Answer:

27

Step-by-step explanation:

FE is tangent to the circle with center D at point E and DE is radius.

[tex] \therefore FE \perp DE \implies m\angle FED = 90\degree [/tex]

DE = x

DF = x + 18

FE = 36

By Pythagoras theorem:

[tex] DF^2 = DE^2 + FE^2 [/tex]

[tex] (x+18)^2 = x^2 + 36^2 [/tex]

[tex] x^2 + 36x + 324= x^2 + 1296[/tex]

[tex] 36x + 324= 1296[/tex]

[tex] 36x = 1296-324[/tex]

[tex] 36x = 972[/tex]

[tex] x = \frac{972}{36}[/tex]

[tex] x =27[/tex]

The value of x from the given figure, which is radius of a circle is 27 units.

From the given figure, FE=36 units, DE=x units and FD=x+18 units.

Tangent and radius of a circle meet at 90°. If we draw a radius that meets the circumference at the same point, the angle between the radius and the tangent will always be exactly 90°.

Using Pythagoras theorem, we have

FD²=FE²+DE²

⇒ (x+18)²=36²+x²

⇒ x²+36x+324=1296+x²

⇒ 36x=1296-324

⇒ 36x=972

⇒ x=972/36

⇒ x=27 units

Hence, the value of x from the given figure, which is radius of a circle is 27 units.

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Answer:

[tex]\frac{1}{10}[/tex]

Step-by-step explanation:

If you originally have [tex]\frac{2}{5}[/tex] of your garden reserved for carrots, are taking [tex]\frac{1}{4}[/tex] of the carrot space ( [tex]\frac{2}{5}[/tex] ) for strawberries, then the total amount of your garden left for strawberries will be  [tex]\frac{2}{5}\cdot\frac{1}{4}[/tex]

[tex]\frac{2}{5}\cdot\frac{1}{4} = \frac{2}{20}[/tex]

[tex]\frac{2}{20}[/tex] simplifies down to [tex]\frac{1}{10}[/tex].

Hope this helped!

Answer:

8⋅(3a+9b−5c)

Step-by-step explanation:

The equation in a simple form by using the greatest common factor is

8 ( 3a + 9b -5c ).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The greatest common factor is the largest positive number which can be divided into given numbers evenly.

The expression will be simplified as below:-

E = 24a + 72b - 40c

Take the number 8 common from the expression.

E = 8 ( 3a + 9b -5c ).

Therefore, the equation in a simple form by using the greatest common factor is 8 ( 3a + 9b -5c ).

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Answer:

t=3 years

Step-by-step explanation:

t=log1.05E250

t= time in years

E= ending balance.

Interest=5% per year

Ending balance=$289.41

Note: write Log 1.05 as written in the question

t= log1.05 E/250

=log1.05 (289.41 / 250)

=Log 1.05 (1.15764)

=Log (1.15764) / log (1.05)

= 0.0636 / 0.0212

=3

Therefore,

t=3 years

Answer: -5a²b⁵c³

Step-by-step explanation: 5ab⁴c can be thought of as 5a¹b⁴c¹ and in the second part of the problem, since there is no coefficient on -a¹b¹c², we can give it a coefficient of 1.

Now simply multiply the coefficients

and add the exponents to get -5a²b⁵c³.

Answer:

Keiko would pay $30 a month at bank A.

Keiko would pay $15 a month at bank B.

Both bank A and bank B combined would be $45 a month.

Step-by-step explanation:

Answer:

Actually, this is equal to 1.

Step-by-step explanation:

Hello, please consider the following.

First of all, we assume x and y different from 0.

[tex]xy=4\\\\y=\dfrac{4}{x}\\\\x=\dfrac{4}{x}\\\\\text{So}\\\\y'(x)=\dfrac{-4}{x^2}\\\\y''(x)=\dfrac{-4*(-2)}{x^3}=\dfrac{8}{x^3}\\\\x''(y)=\dfrac{8}{y^2}\\\\\text{So, we can conclude}[/tex]

[tex]\dfrac{d^2y}{dx^2}\cdot \dfrac{d^2x}{dy^2}=\dfrac{8}{x^3}\cdot\dfrac{8}{y^3}\\\\=\dfrac{64}{(xy)^3}\\\\\text{We replace xy by 4}\\\\=\dfrac{64}{4^3}\\\\=\dfrac{64}{64}\\\\=\large \boxed{\sf \bf \ 1 \ }[/tex]

Thank you

Answer:

[tex]P(Blue) = 0.3[/tex]

Step-by-step explanation:

Given

Red = 5

Blue = 3

Orange = 2

Required

Probability that the first marble is Blue

First, the total number of marble has to be calculated;

[tex]Total = Red\ Marble + Blue\ Marble + Orange\ Marble[/tex]

[tex]Total = 5 + 3 + 2[/tex]

[tex]Total = 10[/tex]

The probability of Blue being the first is calculated as thus;

[tex]P(Blue) = \frac{n(Blue)}{Total}[/tex]

[tex]P(Blue) = \frac{3}{10}[/tex]

[tex]P(Blue) = 0.3[/tex]

Hence, the required probability is 0.3

Answer:

4m + 2m = 6m

Step-by-step explanation:

Answer:

[tex] -\frac{1}{40} [/tex]

Step-by-step explanation:

To evaluate [tex] -\frac{3}{8} - (-\frac{7}{20}) [/tex], start by opening the bracket.

When opening the bracket, we would be multiplying negative sign by negative sign, which equal positive sign.

Thus,

[tex] -\frac{3}{8} + \frac{7}{20} [/tex]

Solve further by performing addition operation to make both fractions one

The common denominator of 8 and 20 is 40,

[tex] \frac{5(-3) +2(7)}{40} [/tex]

[tex] \frac{-15 + 14}{40} [/tex]

[tex] \frac{-1}{40} = -\frac{1}{40} [/tex]

The answer of given expression in simplest form is:     [tex]\dfrac{-1}{40}\\[/tex]

The given expression is:

[tex]-\dfrac{3}{8} - (-\dfrac{7}{20})[/tex]

Multiplying negative sign with negative sign will result in positive sign of the latter term.

The simplification will be done as follows:

[tex]\\-\dfrac{3}{8} - (-\dfrac{7}{20})\\\\= -\dfrac{3}{8} + \dfrac{7}{20}\\\\=\dfrac{-3 \times 5 + 7 \times 2}{40}\\\\= -\dfrac{1}{40}\\[/tex]

In the above process, we the lcm of 8 and 20 was taken which is equal to 40.

Thus, the simplest form of the given expression is [tex]\dfrac{-1}{40}\\[/tex].

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Answer: B.) 1 and 111 only

Real, rational

Step-by-step explanation: Real is an encompassing terms when defining numbers as it includes all integers, whole, rational and irrational numbers. Therefore 75% belondmgs to a category of real numbers.

75% which is equivalent to 75/100 is a rational number as it can be written in the form p/q . where both p and q are integers and q is not 0. This also means 75% is not an irrational number.

75% = 0.75 is neither a whole number nor an integer as it contains decimal.

75% is not a natural number as natural numbers are counting numbers starting from 1.

Answer:

[tex]3\sin\theta+2\cos\theta=\dfrac{17}{5}[/tex]

Step-by-step explanation:

Given that,

The value of [tex]\tan\theta=\dfrac{3}{4}[/tex]

We know that, [tex]\tan\theta=\dfrac{\text{perpendicular}}{\text{base}}[/tex]

[tex]H^2=B^2+P^2[/tex]

H is hypotenuse

[tex]H^2=3^2+4^2\\\\H=5[/tex]

[tex]\sin\theta=\dfrac{P}{H}\\\\=\dfrac{3}{5}[/tex]

And, [tex]\cos\theta=\dfrac{B}{H}=\dfrac{4}{5}[/tex]

So,

[tex]3\sin\theta+2\cos\theta=3\times \dfrac{3}{5}+2\times \dfrac{4}{5}\\\\=\dfrac{9}{5}+\dfrac{8}{5}\\\\=\dfrac{17}{5}[/tex]

So, the value is 17/5.

Answer:

797.42

Step-by-step explanation:

Given the Output of a linear regression data using R;

From the result table;

Intercept = 72.807562

Gradient or slope = 0.009792

General form of a linear equation:

y = mx + c

Where y = response variable ; x = explanatory variable ; c = intercept and m = gradient / slope

Hence, the regression equation becomes :

y = 0.009792x + 72.807562

Using these regression results, what is the estimated repair cost on a car that has 74,000 miles on it?

x = 74,000

y = 0.009792(74000) + 72.807562

y = 724.608 + 72.807562

y = 797.42

Answer:

The estimated repair cost on a car that has 74,000 miles on it is $797.42.

Step-by-step explanation:

The statement: Im(formula = Repair.Costs ~ Miles.Driven, data = Dataset) implies that the variable "Repair.Costs" is the dependent variable and the variable "Miles.Driven" is the independent variable.

From the provided data the regression equation formed is:

[tex]\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}[/tex]

Compute the estimated repair cost on a car that has 74,000 miles on it as follows:

[tex]\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}[/tex]

                     [tex]=72.807562+0.009792\cdot 74000\\\\=72.807562+724.608\\\\=797.415562\\\\\approx 797.42[/tex]

Thus, the estimated repair cost on a car that has 74,000 miles on it is $797.42.

Answer: The inverse mass of the boat (B)

Step-by-step explanation:

The relationship between force, mass and acceleration is: [tex]F = ma[/tex]. So, the slope of the graph represents the inverse of the mass of the boat.

From the question, we understand that the graph is acceleration vs net force.

This means that, the points on the graph will be:

[tex](F_1,a_1)[/tex] and [tex](F_2,a_2)[/tex]

The slope (m) of a linear graph is:

[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, it will be:

[tex]m =\frac{a_2 - a_1}{F_2 - F_1}[/tex] ---- slope

Recall that:

[tex]F = ma[/tex]

Make mass (m) the subject

[tex]m = \frac Fa[/tex]

See attachment for further explanation

Hence, the slope of the graph represents (b) the inverse of the mass of the boat

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Answer:

D. True because the null space of an m x n matrix A is a subspace of [tex]$R^n$[/tex]

Step-by-step explanation:

A null space is also  the vector space.

We know that a null set satisfies the following properties of a vector space.

Now let [tex]$x,y \in Null (A), \alpha \in IR$[/tex] ,  then

[tex]A[\alpha x+y] = \alpha A(x)+ A(y) = \alpha . 0 + 0 = 0$[/tex]

Thus, [tex]$ \alpha x+y \in Null (A)$[/tex]

Hence, option (d) is true.

Answer:

A ' = (2, -3)

B ' = (1, -1)

See attached image below for the diagram

========================================================

Explanation:

Point A is originally at (-6, 9). It moves to A ' (2,-3) after applying the scale factor. This is because we basically multiply the scale factor (-1/3) by each coordinate of point A

-6 * (-1/3) = 2

9 * (-1/3) = -3

The negative scale factor is like a mirror in a way. Points in negative regions move to positive regions, and vice versa. Since |-1/3| = 1/3 is less than 1, this means the new point (2,-3) is closer to (0,0) compared to its original counterpart.

Point B follows the same idea

B(-3,3) moves to B ' (1, -1) after multiplying each coordinate by -1/3

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

Side note: The segment A'B' is 1/3 as long compared to segment AB.

Answer:

d. all of the above

Step-by-step explanation:

K-means clustering is a term used to describe a technique of vector quantization, that attempts to partition "n" observations into "k" clusters whereby each observation refers to the cluster with the closest mean which represents a model of the cluster.

This implies that the K-means algorithm recognizes the "k" number of centroids, and then assigns every data point to the closest cluster while the centroids remain as small as possible.

Hence, the following is required of K-means clustering:

1. defined distance metric

2. number of clusters

3. initial guess of centroids

Therefore, in this case, the correct answer is option D: All of the above.

Answer:

135°

Step-by-step explanation:

The supplement of an angle is the measure in which, when combined with the previous angle, will total up to 180°. Since we already know the measure of 1, we can easily find the supplement, assuming [tex]x[/tex] is the supplement of 45.

[tex]45 + x = 180\\\\x = 180-45\\\\x=135[/tex]

Hope this helped!

Answer: - A horizontal shift of 3 units to the left.

- A vertical dilation of factor 2.

- A vertical shift of 6 units down.

Step-by-step explanation:

Here we have 3 transformations:

I will start giving general cases for each transformation:

Horizontal shift.

When we have a function f(x), an horizontal shift to the right of N units (N positive) is written as:

g(x) = f(x - N)

So in our case, we have a shift to the LEFT of 3 units.

Vertical dilation/contraction.

A vertical dilation/contraction of factor A, is written as:

g(x) = A*f(x)

if A > 1, this is a dilation, if A < 1, this is a contraction.

In the case of our problem, we have A  = 2.

Vertical shift:

A vertical shift is written as:

g(x) = f(x) + N.

If N is positive, we have a shift of N units up, if N is negative, we have a shift of N units down.

in this case, N = -6.

Then the transformations are:

q(x) = 2*p(x -(-3)) - 6

- A horizontal shift of 3 units to the left.

- A vertical dilation of factor 2.

- A vertical shift of 6 units down.

Answer:

he makes $12 an hour

Step-by-step explanation:

Ed makes $6 in one hour.

To find out how much Ed makes in one hour, we can divide the total amount he makes in a 7 1/2 hour day by the number of hours in a day.

First, let's convert 7 1/2 hours to a mixed fraction.

7 1/2 hours = 7 + 1/2 = 14/2 + 1/2 = 15/2 hours.

Now, we can calculate how much Ed makes per hour by dividing the total amount he makes ($90) by the number of hours (15/2):

Amount per hour = $90 ÷ (15/2) = $90 × (2/15) = $6.

Therefore, Ed makes $6 in one hour.

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Answer:

13 cm, 84 cm, 85 cm

Step-by-step explanation:

Let the sides of triangle are be a, b, c

As per Pythagorean theorem:

Solving the quadratic equation we get:

Then:

Answer:

The cost of the dining set = $200

Step-by-step explanation:

Let

Cost of the dining set=x

Sixty percent of the cost of the dining set

= 60% of x

=60/100 * x

= 0.6x

One half the cost of the dining set decreased by $180.

=1 1/2 of x - 180

= 1.5 * x - 180

= 1.5x - 180

Sixty percent of the cost of the dining set is the same as one half the cost of the dining set decreased by $180

0.6x = 1.5x - 180

Collect like terms

0.6x - 1.5x = -180

-0.9x = -180

Divide both sides by -0.9

x= -180 / -0.9

=200

x= $200

Check:

0.6x

= 0.6(200)

=120

1.5x - 180

=1.5(200) - 180

= 300 - 180

=120

Answer:

64868 feet

Step-by-step explanation:

The deepest point as a negative 35,840 feet mark

The tallest point has a positive 29,028 feet mark

The difference between them:

Answer is 64,868 feet

Answer:

  3x -2y = -5

Step-by-step explanation:

Standard form is ...

  ax +by = c

where the leading coefficient (a, or b if a=0) is positive and a, b, c are mutually prime.

Multiplying the equation by 2 gives ...

   2y = 3x +5

We can subtract 2y+5 to get standard form:

  3x -2y = -5

Answer:

Option D is the correct option

Step-by-step explanation:

[tex] \sf{(5 + 3)j = 48}[/tex]

Distribute j through the parentheses

⇒[tex] \sf{5j + 3j = 48}[/tex]

Collect like terms

⇒[tex] \sf{8j = 48}[/tex]

Divide both sides of the equation by 8

⇒[tex] \sf{ \frac{8j}{8} = \frac{48}{8} }[/tex]

Calculate

⇒[tex] \sf{j = 6}[/tex]

Hope I helped!

Best regards!!

x+y+z=1

x=1/(y+z)

1/(y+z)-2y+3z=2  

1-2y²-2yz+3yz+3z²=2(y+z)

(1-2y²+yz+3z²)/2=y+z

z=(1-2y²+yz+3z²)/2 -y/1

z=(1-2y²+yz+3z²-2y)/2

Answer:

h = [tex]\frac{2A}{a+c}[/tex]

Step-by-step explanation:

Given

A = [tex]\frac{1}{2}[/tex](a + c)h

Multiply both sides by 2 to clear the fraction

2A = (a + c)h ( divide both sides by (a + c) )

[tex]\frac{2A}{a+c}[/tex] = h

Answer:

[see below]

Step-by-step explanation:

[tex]a = 1/2(a+c)h\\\\1/2(a+c)h = a\\\\2 * 1/2(a+c)h = a * 2\\\\h(a+c)=2a\\\\\frac{h(a+c)}{a+c}=\frac{2a}{a+c}; a \neq -c\\\\\boxed{h=\frac{2a}{a+c}; a \neq -c}[/tex]

Hope this helps.

Answer:

7y-15

Step-by-step explanation:

10y-3(y+5)

=10y-3y-15

=7y-15

Hope it helped :)

Answer:

-9/4, 2.1, -26/13, -13/8

Step-by-step explanation:

Answer: a. variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE

Step-by-step explanation:

The coefficient of determination is denoted by R square is the proportion of the variance in the dependent variable that is predictable from the independent variable.

Given:  dependent variable = TEST SCORE

independent variable = HOURS SPENT STUDYING

coefficient of determination = 0.43

That means variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE.

Hence, the correct option is a.