The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle.

Answer:

A1 5×3 = 15

A2 = 2×4= 8

an=I don't know that one

[tex]\bf{Swap \ sides \ 8x+2(x+6)=-28 }[/tex]

[tex]\bf{Expand \ 2(x+6): \ \ \ \ 2x+12}[/tex]

[tex]\mathrm{Set \ the \ variables \ using: \ \ \ a(b+c)=ab+ac}[/tex]

[tex]a=2,\:b=x,\:c=6[/tex]

[tex]=2x+2\cdot \:6[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:6=12[/tex]

[tex]=2x+12[/tex]

[tex]8x+2x+12=-28[/tex]

[tex]\mathrm{Add\:similar\:elements:\:8x+2x=10x}[/tex]

[tex]10x+12=-28[/tex]

[tex]\mathrm{Subtract\:}12\mathrm{\:from\:both\:sides}[/tex]

[tex]10x+12-12=-28-12[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]10x=-40[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}10[/tex]

[tex]\dfrac{10x}{10}=\dfrac{-40}{10}[/tex]

[tex]\mathrm{Simplify \ \dfrac{10x}{10}: \ \ x }[/tex]

[tex]\mathrm{Divide:}\:\dfrac{10}{10}=1[/tex]

[tex]=x[/tex]

[tex]\mathrm{Simplify \ \dfrac{-40}{10}: \ \ -4 }[/tex]

[tex]\rm{Apply \ the \ properties \ of \ fractions \ to \ fractions: \ \ \dfrac{-a}{b}=-\drac{a}{b}}[/tex]

[tex]=-\dfrac{40}{10}[/tex]

[tex]\rm{split: \ \dfrac{40}{10}=4 }[/tex]

[tex]\bf{x=-4 \ \ \to \ \ \ Answer }[/tex]

Answer:

2/3 or 0.66 repeated

Step-by-step explanation:

Since 2022 is only divisible by 1,2,4, and 5, the probability of getting a number that is a divisor of 2020 is 4/6, simplified to 2/3 or %0.66.

In ten years' time, the mass of tritium would become 406.87 g. That's almost half of the original mass.

The mass, Q, of a sample of Tritium (a radioactive isotope of Hydrogen), decays at a rate of 5.626% per year.

To make a graph, we need to establish which is the independent and dependent variables.

The independent variable (x-axis) is time in years and the dependent variable (y-axis) is the mass of tritium in grams.

At year 1,

726(1 - 0.05626) = 685.16 g

At year 2,

685.16 (1 - 0.05626) = 646.61 g

At year 3,

646.61 g (1 - 0.05626) = 610.23 g

The final graph is shown in the attached figure.

In ten years' time, the mass of tritium would become 406.87 g. That's almost half of the original mass.

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Answer:

6.28 ft

Step-by-step explanation:

using the formula [tex]\pi d[/tex] to find the circumference of the circle, you substitute the numbers. 3.14(2). 3.14 x 2 = 6.28 hence the answer

Answer:

Median: 21

Eric took the longest

Ed took 18 minutes longer than Mike

Oscar took the shortest amount of time to solve the puzzle

Step-by-step explanation:

The median is the middle amount of the numbers, line them up from smallest to largest and find the number in the middle...the largest number is the person who took the longest...subtract Ed's score (25) from Mike's score (4) to get the answer...and the smallest number is the person who took the shortest amount of time

Answer:

A parallel line is something that is equivalent on the other end. This mean if you cut a shape, a square for example, in half,the sides will be of equal length.

Answer:

a parallel line is diagonal

Answer:

f(3) = 1

Step-by-step explanation:

substitute x = 3 into f(x) , that is

f(3) = 3² - 4(3) + 4 = 9 - 12 + 4 = 1

Answer:

1

Step-by-step explanation:

Substitute 3 for x in your equation leaving you with (3)^2-4(3)+4.

9-12+4

-3+4=1

Given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

Note that: Area of a circle is expressed as;

A = πr²

Where r is radius and π is constant pi ( π = 3.14 )

Given that;

A = πr²

A = 3.14 × ( 35cm )²

A = 3.14 × 1225cm²

A = 3846.5cm²

Therefore, given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

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Answer:

So, cows heart best is faster than horse.

Step-by-step explanation:

Time and heartbeats are in direct proportion.

   p = kx

Where p is the beats per minute and x represents time in minutes

Now, to find the value of k, substitute p = 152 and x = 4

152 = 4k

  k = 152/4

  k = 38

[tex]\sf \boxed{p = 38x}[/tex]

Cow:  y = 65x

So, cows heart best is faster than horse

Answer:

[tex]x=\frac{3}{4},\:x=-1[/tex]

Keys:

For this problem, you need the quadratic formula(listed below).

When you see ± in a quadratic equation, you must know there is going to be at least 2 solutions.

Step-by-step explanation:

solving for x₁ and x₂

[tex]4x^2+x=3\\4x^2+x-3=3-3\\4x^2+x-3=0\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot 4\left(-3\right)}}{2\cdot 4}\\[/tex]

[tex]1^2=1\\=\sqrt{1-4\cdot \:4\left(-3\right)}\\=\sqrt{1+4\cdot \:4\cdot \:3}\\=\sqrt{1+48}\\=\sqrt{49}\\=\sqrt{7^2}\\\sqrt{7^2}=7\\=7[/tex]

[tex]x_{1,\:2}=\frac{-1\pm \:7}{2\cdot \:4}\\x_1=\frac{-1+7}{2\cdot \:4},\:x_2=\frac{-1-7}{2\cdot \:4}\\[/tex]

solve for x₁

[tex]\frac{-1+7}{2\cdot \:4}[/tex]

[tex]=\frac{6}{2\cdot \:4}[/tex]

[tex]=\frac{6}{8}[/tex]

[tex]= \frac{6\div2}{8\div2}[/tex]

[tex]=\frac{3}{4}[/tex]

solve for x₂

[tex]\frac{-1-7}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{8}[/tex]

[tex]=-\frac{8}{8}[/tex]

[tex]=-1[/tex]

Hope this helps!

Answer:

y = 6x + [tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

I think take this with a grain of salt

Answer:

Equation: 2w + 2(2w) = 12

width = 2

length = 4

Step-by-step explanation:

Width is w

Length is 2 * width = 2w

Perimeter is 2w + 2l

Substitute 2w for L.

Perimeter is now 2w + 2(2w) = 12

Distribute the 2 to the parentheses.

2w + 4w = 12

Combine Like terms

6w = 12

Divide by 6 to solve for w.

w = 2

If w = 2, then the length = 4.

Answer: 36.9

Step-by-step explanation:

Answer: 363

Step-by-step explanation:

The common difference is 7, so the explicit formula is [tex]a_{n}=-92+7(n-1)[/tex].

Substituting in n=66,

[tex]a_{66}=-92+7(66-1)=\boxed{363}[/tex]

Answer:

Step-by-step explanation:

The volume of a cube is given by the formula :

a³ (where a is the side length )

So now we have to cube these lengths :

Part A :

(3x²y)³ =

(3x²y)(3x²y)(3x²y) =

(9x^4y²)(3x²y) =

27x^6y³ (This is now fully simplified so our final answer for a)

Part B:  

(5y²)³ =

(5y²)(5y²)(5y²) =

(25y^4)(5y²) =

125y^6 (This is now fully simplified so our final answer for b)

Hope this helped and have a good day

A particle moves along line segments from the origin to the points, work done is mathematically given as

W=184.5units

Considering line segments from (0,0,0)origin to (2,0,0) , (2,5,1) and (0,5,1) under the infulence of force

Generally,  the equation for force is mathematically given as

F = z2i + 5xyj + 2y2k

Therefore, Considering u*v

[tex]u * v = (u_1j+u_2j+u_3k) * (v_1i+v_2j+v_3k)[/tex]

[tex]u* v = u_1v_1(i * i) + u_1v_2(i * j)+u_1v_3(i * k) + u_2v_1(j * i) + u_2v_2(j * j)+u_2_3(j* k) + u_3v_1(k * i) + u_3v_2(k * j)+u_3v_3(k * k)[/tex]

Where

[tex]i * i = j *j=k * k=0[/tex]

Hence

[tex]u* v = u_1v_2k-u_1v_3j-u_2v_1k+u_2v_3i +u_3v_1j - u_3v_2i[/tex]

[tex]u = (u_1,u_2,u_3) = (0,5,1)\\\\v = (v_1,v_2,v_3) = (-3,0,0)[/tex]

The normal equation formed

-2y + 15z = 0

z= (1/5)y

Considering the level surface and differential surface area

h(x,y,z) = -y + 5z =0

[tex]dS = |grad(h)| dA[/tex]

In terms of the x and y coordinates of (2,0,0) and (2,5,1) and (0,5,1), we can state that the ranges are 0 to 3 and 5 respectively we have

[tex]0 \leq x \leq 2 \ and \ 0 \leq y \leq 5[/tex]

Using strokes theorem to evaluate

[tex]F = z2i + 5xyj + 2y2k[/tex]

[tex]curl \ F = 4yi+2zj+5yk = (4y,2z,5y)[/tex]

[tex]curl \ F * nds= \frac{1}{5}(-2z + 25y)\ dy \ dx[/tex]

In conclusion, The work done is

[tex]W=\int _CF *dr[/tex]

[tex]\int _C F * dr = \int \int curl \ F * n ds[/tex]

[tex]\int _C F *dr = \frac{123}{2}\int_0^3 \ dx[/tex]

[tex]\int _C F * dr = \frac{123*3}{2}[/tex]

W= 184.5units

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The graph that could represent the motion of the apple is graph B.

A graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.

Here, the speed of apple at time t is given by v=0 + at which is a straight line of slope a that passes through origin because constant is zero. At time t=0 its initial speed is 0 and it will increase constantly with time. Therefore, graph (B) is correct

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Answer:

2 Hours

Step-by-step explanation:

First you have to add up all the points which would be;

1 1/2 + 1 1/2+ 2 1/2+ 2 1/2= 8 hours

Then you have to divide by how many points to find the average;

8 hours divided by 4 points= 2 hours average

In total, she will practice 2 hours every day

Answer:

All rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, all rectangles have 2 pairs of parallel sides.

Step-by-step explanation:

a) T - Calories, 2000 - Minimum calories, 500 - Additional calories per exercise hour, b) We should consume 3500 calories to spend three hours exercising.

In this question we have a linear function where the independent variable is the exercise time (h), in hours, and the dependent variable is the calorie gain (T), in calories. The constant "2000" is the minimum calorie consumption and the constant "500" represents the amount of additional calories per each hour of exercise.

Now we proceed to respond the questions of the part a):

(i) T - Amount of calories needed, (ii) 2000 - Minimum calorie consumption, (iii) 500 - Amount of additional calories per hour of exercise.

b) And lastly we calculate the amount of calories by evaluating the function:

T = 2000 + 500 · 3

T = 2000 + 1500

T = 3500

We should consume 3500 calories to spend three hours exercising.

The statement is incomplete, the complete form is shown below:

You are trying to bulk up and gain muscle. Your trainer says that your daily calorie intake should increase based on the hours you spend exercising and can be represented by the following equation: T = 2000 +  500 · h

a) What does each part of this expression represent? (i) T = , (ii) 2000, (iii) 500, (iv) h

b) If you spend 3 hours exercising, how many calories should you consume?

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The theoretical probability of getting an odd number is 0.6, but the experimental probability was 0.5.

Probability of getting an odd number: 3/5 = 0.6 or 60%

The experimental probability is lower than the theoretical probability.

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Answer:

Answer in pic below

Step-by-step explanation:

The solution to the expression (-x³ + x² - x + 1) / (x - 1) using long division is (x² - 2x + 3) + (4 / (-x - 1))

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the expression:

(-x³ + x² - x + 1) / (x - 1)

Using long division:

= x² + (2x² - x + 1)/(-x - 1)

= x² - 2x + (-3x + 1)/(-x - 1)

= (x² - 2x + 3) + (4 / (-x - 1))

The solution to the expression (-x³ + x² - x + 1) / (x - 1) using long division is (x² - 2x + 3) + (4 / (-x - 1))

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Answer:

The line has no slope. I hope this helps

Answer:

wedg

Step-by-step explanation:

ed

Step-by-step explanation:

the sum of an infinite geriatric series with |r| < 1 is

s = a1/ (1 - r)

in our case we have

a1 = 8

12 = 8/(1 - r)

12(1 - r) = 8

1 - r = 8/12 = 2/3

-r = -1/3

r = 1/3

so, the first 4 terms (I added a5 too, just in case your teacher meant the NEXT 4 terms) are

a1 = 8

a2 = a1 × 1/3 = 8/3

a3 = a2 × 1/3 = 8/9

a4 = a3 × 1/3 = 8/27

a5 = a4 × 1/3 = 8/81

...

Answer:

[tex]8,\quad \dfrac{8}{3},\quad \dfrac{8}{9},\quad\dfrac{8}{27}[/tex]

Step-by-step explanation:

Sum to infinity of a geometric series:

[tex]S_\infty=\dfrac{a}{1-r} \quad \textsf{for }|r| < 1[/tex]

Given:

Substitute given values into the formula and solve for [tex]r[/tex]:

[tex]\implies 12=\dfrac{8}{1-r}[/tex]

[tex]\implies 1-r=\dfrac{8}{12}[/tex]

[tex]\implies r=1-\dfrac{8}{12}[/tex]

[tex]\implies r=\dfrac{1}{3}[/tex]

General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]

(where a is the first term and r is the common ratio)

Substitute the found values of [tex]a[/tex] and [tex]r[/tex]:

[tex]\implies a_n=8\left(\dfrac{1}{3}\right)r^{n-1}[/tex]

The first 4 terms:

[tex]\implies a_1=8\left(\dfrac{1}{3}\right)r^0=8[/tex]

[tex]\implies a_2=8\left(\dfrac{1}{3}\right)r^1=\dfrac{8}{3}[/tex]

[tex]\implies a_3=8\left(\dfrac{1}{3}\right)r^2=\dfrac{8}{9}[/tex]

[tex]\implies a_4=8\left(\dfrac{1}{3}\right)r^3=\dfrac{8}{27}[/tex]

Answer:

  y -6 = -5(x -3)

Step-by-step explanation:

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

__

You have been given ...

  m = -5

  (h, k) = (3, 6)

Putting the given values into the point-slope form gives the equation you want:

  y -6 = -5(x -3)

Answer:

The answer is 7

Step-by-step explanation:

To find the volume you multiply the width, height, and the length.

Length= 7/3

width= 3/3

height= 9/3

When you multiply you then have to simplify which is 7/1 or 7.

Mark this correct to help me gain!!