Quadrilateral A'B'C'D' is a translation of quadrilateral ABCD. What is
the length of B'C?

In a parallelogram, opposite sides are equal. Therefore, AB = CD.

5x * 3 = 15 * x

15x = 15

x = 1

Therefore, the value of x is 1.

To find the area of parallelogram ABCD, we can use the formula A = base x height, where the base is the length of side AB and the height is the perpendicular distance between side AB and the opposite side CD. Since the height of parallelogram ABCD is given as 6, we need to find the length of side AB.

From the given information, we know that AB = 5x * 3, where x = 1. Therefore, AB = 15. Now we can calculate the area of parallelogram ABCD as:

A = base x height

A = 15 x 6

A = 90 square units

Therefore, the area of parallelogram ABCD is 90 square units.

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Answer:

369 cans

Step-by-step explanation:

Add the two numbers of cans collected by each:

Alan:   154 cans

Betty:  215 cans

Total:  369 cans

Answers:

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

Work Shown:

[tex]15 \text{ m} = (15 \text{ m})*\frac{100 \text{ cm}}{1 \text{ m}} = 1500 \text{ cm}\\\\\\1.6 \text{ km} = (1.6 \text{ km})*\frac{1000 \text{ m}}{1 \text{ km}}*\frac{100 \text{ cm}}{1 \text{ m}} = 160,000 \text{ cm}\\\\\\467 \text{ mm} = (467 \text{ mm})*\frac{1 \text{ cm}}{10 \text{ mm}} = 46.7 \text{ cm}[/tex]

Each conversion fraction is set up to cancel out any unit that isn't "centimeters".

Side notes:

Answer:

$8812.50

Step-by-step explanation:

To calculate the simple interest earned on Mia's investment, we can use the formula:

I = Prt

where I is the interest earned, P is the principal amount invested, r is the interest rate as a decimal, and t is the time in years.

Plugging in the values, we have:

I = $7500 * 0.035 * 5

I = $1312.50

The total amount Mia has after 5 years is the sum of her original investment and the interest earned:

$7500 + $1312.50 = $8812.50

slope found by rise over run or m = (y2 - y1) / (x2 - x1)

orientation is important to not mix either values order.

( 9 - 21) / ( -1 - 5) => ( -12 ) / ( - 6 )

negatives cancel and simplify to find

m = 2

Answer:

yes

Step-by-step explanation:

8. The depth of the water is solved to be = 2.9 cm (one decimal place).

9 The ratio r: s =√3 : 2.

The  depth of water is calculated by first using Pythagoras theorem to get the level between water level 7 cm and water level when completely full which is 10 cm

= √(10² - 7²)

= √(100 - 49)

= √51

The next step is to subtract from the radius

= 10 - √51

= 2.8586 cm

= 2.9 cm

9. The length of diagonal of a cube is given by the formula

= (√3)·s

The diameter of the sphere is equal to length of diagonal of a cube.

radius of a sphere = diameter / 2

r = (√3)*s / 2

r / s = √3 / 2

hence the ratio is

r : s = √3 : 2

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complete question is attached

The expression that equals 2D−3C in standard form is -2s² - 11s - 7

Algebraic expressions are defined as expressions that are composed of coefficients, variables, terms,  factors and constants.

From the information given, we have that;

D=1−s^2 −s and C=3+3s,

To determine the expression for 2D - 3C

substitute the values of the expressions, we get;

2(1-s² - s) - 3(3 + 3s)

expand the bracket

2 - 2s² - 2s - 9 -9s

collect the like terms or factors, we get;

-2s² - 2x - 9s - 9 + 2

Add or subtract the values

-2s² - 11s - 7

Hence, the expression is -2s² - 11s - 7

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Completing the equation below by writing an expression equivalent to the length of a, the leg of a right triangle is given below

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Hence, the complete equation according to this theorem is given above.

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nonononononononnnono

The lower bound for the weight 21.58 g correct to 2 decimal places is 21.57 g. This is because the next smallest value based on the rounding is obtained rounding down the number in second decimal place, which is 5.

To find the lower bound for the weight 21.58 g correct to 2 decimal places, we need to consider the next smallest number that can be represented to 2 decimal places.

Since the second decimal place is 8, the next smallest number is obtained by rounding down the number in the second decimal place, which is 5. Therefore, the lower bound for 21.58 g correct to 2 decimal places is: 21.57g

Note that the weight could be more precise than what we are given, but to represent it to 2 decimal places we have to make an assumption about the last digit.

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Answer:

6ft

Step-by-step explanation:

area of trapezoid formula: 1/2h(a+b)

height=x

x/2(4+8)=36

x/2*12=36

2 and 12 will get cancelled

6x=36

x=36/6

x=6

hope it helped!!!

Option (D) Between 5.1 and 5.3 is the correct answer fore the question where 5.2 on the number line would be located.

On a number line, each number is represented by a point. The location of a number on a number line depends on whether it is greater than or less than other numbers.

In the case of 5.2, it is located between 5.1 and 5.3, as option D states. This is because 5.2 is greater than 5.1 but less than 5.3. Therefore, its location on the number line would be between the points representing 5.1 and 5.3.

A number line is a useful visual tool for understanding the relative position of numbers to each other, as well as for performing basic arithmetic operations. Option (D) Between 5.1 and 5.3 is the correct answer fore the question where 5.2 on the number line would be located.

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Answer:

113.75

Step-by-step explanation:

13$ x 8.75 h (45 minutes is 3/4 of an hour) = $113.75

keeping in mind that an hour has 60 minutes, so you're really getting paid $13 per 60 minutes, so now, 8 hours and 45 minutes is just 8*60 + 45 = 525 minutes.

[tex]\begin{array}{ccll} \$&minutes\\ \cline{1-2} 13 & 60\\ x& 525 \end{array} \implies \cfrac{13}{x}~~=~~\cfrac{60}{525} \\\\\\ \cfrac{ 13 }{ x } ~~=~~ \cfrac{ 4 }{ 35 }\implies 455=4x\implies \cfrac{455}{4}=x\implies 113.75=x[/tex]

The angle that VSR would correspond to, given that polygon ABCDE is congruent to polygon TVSRK, is 2. Angle C.

When polygons are said to be congruent, then it means that their sides are the same lengths, and they have the same angles which means that they are corresponding.

This therefore means that the angle at A in polygon ABCDE would be congruent to the angle at T in TVSRK.

This therefore means that the angle VSR would correspond to the angle C in ABCDE because S is the third letter in TVSRK and C is the third letter in ABCDE.

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The full question is:

Polygon ABCDE is congruent to polygon TVSRK. what do angle VSR correspond to _____?

1. Angle B

2. Angle C

3. Angle D

4. Angle A

Exercise 1: Yes, 1.908 x 10^17 is written in scientific notation.

Exercise 2: Yes, 0.325 x 10^-2 is written in scientific notation.

Exercise 3: No, 7.99 x 10^32 is not written in scientific notation. The decimal d must be between 1 and 10, not between 10 and 100.

Exercise 4: No, 4.0701 + 10 is not written in scientific notation. The correct format is d x 10^n.

Exercise 5: No, 18.432 x 5 is not written in scientific notation. The correct format is d x 10^n.

Exercise 6: No, 8x 10^-11 is not written in scientific notation. The correct format is d x 10^n.

Step-by-step explanation:

Equation of ellipse depends on the points

The points that lie on the horizontal axis is (0,8) and (4,8). They have a distance of 4, therefore a radius of 2

The points that lie on the vertical axis is (2,3) and (2,13)

They have a distance of 10, therefore a radius of 5

Since the vertical axis is bigger, we have a vertical ellipse which is the equation of,

[tex] \frac{(y - k) {}^{2} }{ {a}^{2} } + \frac{(x - h) {}^{2} }{ {b}^{2} } = 1[/tex]

Where a is the major radius

b is the minor radius

(h,k) is the center

Step 1: Finding the center

The center should be the midpoint of the horizontal vertices or vertical vertices

Let's use the horizontal vertices

[tex] (\frac{(0 + 4}{2} ) = 2[/tex]

[tex]( \frac{8 + 8}{2} ) = 8[/tex]

So the center is (2,8)

Step 2: Finding the major and minor radius

We already know it , a is 5

b is 2, so we as of now, have this equation

[tex] \frac{(y -8) {}^{2} }{25} + \frac{(x - 2) {}^{2} }{4} = 1[/tex]

This is the equation of the ellisoe

Step 3: Find the foci

The foci for a vertical ellipse should lie on the same line as the same line as the major vertices and center.

The equation for an ellipse foci that is vertical are

(x,y+c) and (x,y-c)

Where C is

[tex]c = \sqrt{ {a}^{2} - {b}^{2} } [/tex]

[tex]c = \sqrt{25 - 4} [/tex]

[tex]c = \sqrt{21} [/tex]

So our foci are

,,,

[tex](2,8 + \sqrt{21} )[/tex]

and

[tex](2,8 - \sqrt{21} )[/tex]

,

Answer:

x=-7/2 (exact form)

x=-3.5 (decimal form)

x=-3 1/2 (mixed number form)

Step-by-step explanation: :)

Answer:

Improper fraction: -31/30

Mixed number: -1   1/30

Step-by-step explanation:

If x = -5/6 and y = -2/5, we can start by replacing x and y in the equation x + 1/2y.

x+1/2y -> -5/6+1/2(-2/5)

Now we can start solving the equation:

According to the Order of Operations, we have to start with multiplication before addition. So, let's multiply 1/2 and -2/5. We get -2/10, which simplifies to -1/5.

Now we have to do the addition: -5/6+(-1/5)

To add fractions together, we have to find a common denominator. We can do this by finding the LCM of the two denominators(Least common multiple).

6: 6, 12, 18, 24, 30, 36...

5: 5, 10, 15, 20, 25, 30, 35...

The LCM is 30.

-5/6 x 5/5 = -25/30 <-- the equivalent fraction of -5/6

-1/5 x 6/6 = -6/30 <-- the equivalent fraction of -1/5

-25/30 + (-6/30) = -31/30

The answer is -31/30 in improper fraction form, and -1 1/30 in mixed number form.

For the equation 3 = (g/-4) - 5, the value of g is g = -32.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given equation is -

3 = (g/-4) - 5

The equation contains a fractional component.

Simplify the equation to get the value of g.

First collect all the like terms -

g/-4 = 3 + 5

Then use arithmetic operation of addition -

g/-4 = 8

Then move the denominator of the fraction to right hand side of the equation -

g = 8 × -4

Then use arithmetic operation of multiplication -

g = -32

Therefore, the value of g is -32.

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Answer:

3/8

Step-by-step explanation:

1. If there are three parts green and 5 parts yellow, you can add them to find the total parts

2. 5+3 is 8

3. Then to find the green, which is three, we can divide it

4. 3 green parts/ total which is 8

5. 3/8

Answer:

~ generally is substituted by negation

Hence, option D (Even numbers are not divisible by 2) would be the correct answer.

Answer:

x^2 +4x +5

Step-by-step explanation:

2x^2 -x^2 will be x^2

3x+x is 4x

-4+9 is 5

The equation will be written as [tex]A = 325[1.004]^{12t}[/tex]. The time taken to reach $200 will be 10 years.

Compound interest is defined as the interest levied upon the interest. The formula to calculate the compound interest will be written as:-

[tex]A = P[1+\dfrac{r}{m}]^{rt}[/tex]

Given that Hassan places $325 into a savings account that offers a monthly compound interest rate of 4.7%.

The equation for the compounding on monthly basis,

[tex]A = 325[1+\dfrac{0.047}{12}]^{12t}[/tex]

[tex]A = 325[1.004]^{12t}[/tex]

The time will be calculated as:-

[tex]A = 325[1.004]^{12t}[/tex]

[tex]200 = 325[ 1.004]^{12t}[/tex]

log(0.615) = 12 x t x log(1.004)

12t = 121.77

t = 10 years

Therefore, the equation will appear as  [tex]A = 325[1.004]^{12t}[/tex]. It will take 10 years for the price to reach $200.

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Answer:

The values of x for which f(x) = g(x) are:

Step-by-step explanation:

To find all the values of x for which f(x) = g(x), equate the given functions:

[tex]\implies f(x)=g(x)[/tex]

[tex]\implies -x^2+5=-2x+2[/tex]

Rearrange the equation so that it is in the quadratic form ax²+bx+c=0:

[tex]\implies -x^2+5+2x-2=0[/tex]

[tex]\implies -x^2+2x+3=0[/tex]

Divide both sides by -1:

[tex]\implies x^2-2x-3=0[/tex]

Factor the quadratic equation:

[tex]\implies x^2-3x+x-3=0[/tex]

[tex]\implies x(x-3)+1(x-3)=0[/tex]

[tex]\implies (x+1)(x-3)=0[/tex]

To solve for x, apply the zero-product property:

[tex](x+1)=0 \implies x=-1[/tex]

[tex](x-3)=0 \implies x=3[/tex]

Therefore, the values of x for which f(x) = g(x) are:

We can check the solutions by substituting each found value of x into the functions.

[tex]f(-1)=-(-1)^2+5=4[/tex]

[tex]g(-1)=-2(-1)+2=4[/tex]

[tex]f(3)=-(3)^2+5=-4[/tex]

[tex]g(3)=-2(3)+2=-4[/tex]

As f(-1) = g(-1) and f(3) = g(3), this proves that the values of x for which f(x) = g(x) are x = -1 or x = 3.

Equate Both equatios and find x

The points are -1,3

Answer:

It would be 3.765 pounds. You have to do 7.53 x 10 to the -10= 0.000000000753. Then do 0.000000000753 x 5 billion to get 3.765.

Step-by-step explanation:

Answer:

f(-3) = 5

Step-by-step explanation:

f(-3) → x = -3

f(x) = -x+2

f(-3) = -(-3)+2

f(-3) = 3+2

f(-3) = 5

Answer:

5894 seconds

Step-by-step explanation:

Convert  1 hour 38 min 14 seconds to seconds​

1 hour = 3600 seconds

1 min = 60 seconds

38 mins = 60 x 38 = 2280 seconds

Now add all numbers together

3600 + 2280 + 14 = 5894 seconds

So, 1 hour 38 minutes 14 seconds is 5894 seconds.