Elizabeth is five-sixths the age of her
sister Nancy. If Elizabeth is ten years
old, how old is Nancy? Write an
equation
to calculate Nancy's age.

Answer:

The number would be 90

Step-by-step explanation:

140 + 10 - 90 = 60

90 - 30 = 60

60 = 60

Answer: 90

Step-by-step explanation:

Let's use x as a placeholder to the number we are trying to find

[tex]140+10-x=x-30[/tex]

Now we need to isolate x

Step 1) Simplify both sides

[tex]140+10-x=x-30\\150-x=x-30[/tex]

Step 2) Add 30 to both sides

[tex]150-x+30=x-30+30\\180-x=x[/tex]

Step 3) Add x to both sides

[tex]180-x+x=x+x\\180=2x[/tex]

Step 4) Divide both sides by 2

[tex]\frac{180}{2}=\frac{2x}{2} \\90=x[/tex]

Step 5) Sub our value into the original equation and solve

[tex]140+10-x=x-30\\140+10-90=90-30\\150-90=60\\60=60[/tex]

The circle is an illustration of intersecting chords.

The value of x is 4

The given parameters are:

This means that:

jn * nk = ln * nm

So, we have:

3 * x = 2 * 6

Divide both sides by 3

x = 2 * 2

Evaluate the product

x = 4

Hence, the value of x is 4

Read more about intersecting chords at:

https://brainly.com/question/13950364

Answer:

[tex] \dfrac{a}{a - 4} [/tex]

Step-by-step explanation:

You are subtracting fractions, so as usual with fraction subtraction, you need a common denominator. To get a common denominator, you need to factor each denominator.

[tex] \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{a^2 - 16} = [/tex]

Factor the right denominator. It is a difference of two squares.

[tex] = \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]

The left denominator is (a + 4). The right denominator is (a - 4)(a + 4). The LCD is (a - 4)(a + 4), so multiply the left fraction by (a - 4)/(a - 4).

[tex] = \dfrac{3a}{a + 4} \times \dfrac{a - 4}{a - 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{3a^2 - 12a}{(a - 4)(a + 4)} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]

Be careful when you do the subtraction of the numerators, 3a² - 12a minus 2a² - 16a. 3a² - 12a - (2a² - 16a). The minus of the subtraction changes each sign inside the parentheses, so you end up with 3a² - 12a - 2a² + 16a. Be especially careful with the +16a.

[tex] = \dfrac{3a^2 - 12a - (2a^2 - 16a)}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{3a^2 - 12a - 2a^2 + 16a}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{a^2 + 4a}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{a(a + 4)}{(a - 4)(a + 4)} [/tex]

[tex] = \dfrac{a}{a - 4} [/tex]

Answer:

5050

Step-by-step explanation:

sum of first n natural num. = [n(n+1)]/2

sum of first 100 natural num. = (100x101)/2 = 5050

Answer : The sum of 1 to 101 positive integer is 5050

5052 will be sum of 1 to 101 only positive integer

Answer:

teacher's age: 30

student's age: 15

Step-by-step explanation:

T = 15 + S

from above,

(T+15)/(s+15) = 3/2

by substitution,

(15+S +15)/(S+15) = 3/2

cross multiply,

2(S+30) = 3(S+15)

2S + 60 = 3S + 45

60 = S + 45

s = 15

T = 30

The quadratic equation that can be used to determine the thickness of the frame will be B. 3x² + 5x - 19.25 = 0

It should be noted that a quadratic equation simply means an algebraic expression of the second degree in x.

In this case, the quadratic equation that can be used to determine the thickness of the frame will be 3x² + 5x - 19.25 = 0

Learn more about equations on:

https://brainly.com/question/2972832

Answer:

The answer is C. 4x2 + 16x - 4.25 = 0.

Step-by-step explanation:

Answer:

1. (-3) and (-4)

2. (-5) and 6; vise versa

Answer:

Step-by-step explanation:

hello :

1)Two numbers have a product of 12 but their sum is -7 :

means :  xy=12 ....(*)

              x+y = -7 ....(**)

solve this system : use (**) you have   x = -y-7 put this value in (*)

so : (-y-7)y = 12

-y²-7y-12 = 0

y² +7y+12=0       a=1 b=7   and  c= 12

the discriminant  delta =b²-4ac        delta = 7²-4(1)(12) = 1

y1 = (-7-1)/2  = -4      and y2 =  (-7+1)/2 =-3

but x= -7-y

if :y =  - 4   x= -7-(-4) =-3

if : y=-3   x = -7-(-3) =-4

2) same method : xy=-30

                             x+y=1

Answer:

What is the question? Also, your answer looks a bit wrong  1 think t should be 1 oz

Step-by-step explanation:

For every 15 oz potatoes, Garry uses 0.5 oz less cheese than Heather. So Heather's cheesy potatoes have more cheese.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

For Gary's recipe of cheesy potatoes has 15oz of potatoes and 4oz of cheese.

Ratio of potatoes to cheese in Gary's recipe = 15/4

Heather's recipe of cheesy potatoes has 10 oz of potatoes and 3 oz of cheese.

Ratio of potatoes to cheese in Heather's recipe = 10/3

Multiplying with 1.5 in numerator and denominator

Ratio of potatoes to cheese in Heather's recipe = 15/4.5

Thus, for every 15 oz potatoes heather uses 4.5 oz of cheese.

Hence, In Heather's recipe amount of cheese is 0.5 oz more than Garry's recipe per 15 oz. of potatoes.

Learn more about ratio here:

brainly.com/question/13419413

#SPJ2

Answer:

i believe the last one would be 9 for the number of hours kevin works.

Step-by-step explanation:

[tex]\\ \rm\Rrightarrow -42z^2=14z[/tex]

[tex]\\ \rm\Rrightarrow 42z^2=-14z[/tex]

[tex]\\ \rm\Rrightarrow 3z^2=-z[/tex]

[tex]\\ \rm\Rrightarrow 3z=-1[/tex]

[tex]\\ \rm\Rrightarrow z=-1/3[/tex]

Answer:

[tex] - \frac{844}{29} z[/tex]

Step-by-step explanation:

I hope to help

Answer:

1/2 of the  bar is left

Step-by-step explanation:

1/12 x2= 2/12

2/12+ 1/3=2/12+4/12

6/12=1/2

Answer:

23/42

Step-by-step explanation:

2/7 = 12/42

1/6 = 7/42

12/42 + 7/42 = 19/42

42/42 - 19/42 = 23/42

The volume of the pyramid with a square base, where the perimeter of the base is 14 m and the height of the pyramid is 8.8 m is 35.9 m³

First, we shall determine the determine the area of the square base. This is shown below:

P = 4L

14 = 4L

Divide both sides by 4

L = 14 / 4

L = 3.5 m

Now, the area is obtained as follow

A = L²

A = 3.5²

A = 12.25 m²

Finally, we shall determine the volume of the pyramid. Details below:

V = ⅓Ah

V = ⅓ × 12.25 × 8.8

V = 35.9 m³

Thus, we can conclude that the volume of the pyramid is 35.9 m³

Learn more about volume of pyramid:

https://brainly.com/question/21864491

#SPJ1

Answer:

Below.

Step-by-step explanation:

To find the volume of the silo find the volum of the hemisphere with radius of 15 feet and add the volume of the cylinder with a radius of 15 feet and a height of (100 - 15) = 85 feet.

The total volume = 1/2 * 4/3 π (15)^3  + π (15)^2 * 85

= 67151.5 ft^3.

Step-by-step explanation:

find the volume of a sphere with a radius of 15 ft and divide by 2 (because there is only half a sphere on top of the silo).

then add the volume of a cylinder with a radius of 15 ft and a height of 85 ft (because we need to deduct the radius of the sphere from the total height to get the height of the cylinder itself).

Answer:

While resting, his heart rate is at 60 bpm. After sprinting, his heart rate is at 130bmp. The difference is 130 - 60 = 70

Step-by-step explanation:

i hope this helps

The correlation coefficient of the given data about time and heart rates is 0.98.

A correlation coefficient is a statistical measure of the degree to which changes to the value of one variable expect change to the value of another.

We have been given time and heart rates of students in Mrs. Anderson's health class and we have to find the value of correlation coefficient.

The formula by Karl Pearson to calculate correlation coefficient is as under:

Correlation coefficient=

=∑(x-x bar)(y-y bar)/[tex]\sqrt{sum(x-x bar)^{2} } \sqrt{sum(y-y bar)^{2} }[/tex]

We have to calculate figures required to fill in the formula which are:

∑(x-x bar)(y-y bar)=350

∑[tex](x-x bar)^{2}[/tex]=44.67

∑[tex](y-y bar)^{2}[/tex]=2872.25

Correlation coefficient=350/[tex]\sqrt{44.67} \sqrt{2872.25}[/tex]

=350/6.68*53.59

=350/357.98

=0.977

After rounding off to nearest hundred it will be 0.98.

Hence the correlation coefficient of the data about time and heart rate is 0.98.

Learn more about correlation coefficient at https://brainly.com/question/4219149

#SPJ2

Answer:

least common denominator=6

Step-by-step explanation:

For the fractions, 1/3 and 1/6th, 3*2=6. making the fraction 2/6 and leaving the other the same 1/6th.

Answer: 144 degrees, 136 degrees

Question 1:

The first x should be 144 because a straight line should equal 180, so you just subtract the (left angle or 36 degrees) with 180 to get the opposite angle.

Question 2:

For the second x, add the 2 interior angles and subtract it by 180 or the total sum of the interior angles.

49 + 87 = 136

180 - 136 = 44

Then follow the same steps in the first question.

180 - 44 = 136

Answer:

D.

Step-by-step explanation:

1) if the points (1;-1) and (4;0) belong to the line, then

2) the equation of this line is 3y-x=-4;

3) the inequality is 3y-x≤-4.

Answer:

D [-1,3] and R [5,27]

Step-by-step explanation:

I explained the process of finding the domain and range in your previous questions therefore I will only give you the answer for this one.

D [-1,3] or [tex]-1\leq x\leq 3[/tex]

R [5,27] or [tex]5\leq y\leq 27[/tex]

Answer:

Step-by-step explanation:

Given equation,

⇒ 5x - 6 = 3x - 8

Subtracting 3x from both sides :

⇒ 5x – 6 – 3x = 3x – 8 – 3x

⇒ 2x – 6 = – 8

Adding 6 to both sides we get :

⇒ 2x – 6 + 6 = – 8 + 6

⇒ 2x = – 2

Dividing both sides by 2 we get :

⇒ 2x/2 = – 2/2

⇒ x = – 1

Therefore,

Answer:

[tex]\sf \boxed{\bold{x=-1}}[/tex]

Solving Stepwise:

[tex]\dashrightarrow \sf 5x-6=3x-8[/tex]

add 6 on both sides

[tex]\dashrightarrow \sf 5x-6+6=3x-8+6[/tex]

simplify

[tex]\dashrightarrow \sf 5x=3x-2[/tex]

subtract both sides by 3x

[tex]\dashrightarrow \sf 5x-3x=3x-2-3x[/tex]

simplify

[tex]\dashrightarrow \sf 2x=-2[/tex]

divide both sides by 2

[tex]\dashrightarrow \sf \dfrac{2x}{2} =\dfrac{-2}{2}[/tex]

simplify

[tex]\dashrightarrow \sf x =-1[/tex]

Check for the answer:

insert x = -1

[tex]\hookrightarrow \sf 5(-1)-6=3(-1)-8[/tex]

[tex]\hookrightarrow \sf -5-6=-3-8[/tex]

[tex]\hookrightarrow \sf -11=-11[/tex]

Answer:

The answer is 7.

Step-by-step explanation:

7 + 2 is 9.

9 x 3 =27

27 - 7 =20.

Since the original number is 7 then we add 7 to 20.

7 + 20 = 27.

So, the number he started with is 7.

Answer:

Part A: No. Based on the scatter plot, r = 0.01 is not an accurate value for this data, because 0.01 means pratically no corrlation, while the points on the graph are moderately correlatedPart B: you must describe a scenary where a variable is the cause of the number of strawberries picked. See below, the example of rainfall.

Explanation:

1. Part A:

Since the points in the scatter plot show a moderated upward trend, you must expect a correlation coefficient close to ± 0.5. A correlation coefficient of 0.01 is too close to 0, which would mean that the points are almost not correlated at all.

The correlation coefficients, r, measure the strength of the correlation of two variables and they can have values from - 1 to  1.

r = - 1 is  a perfect negative correlation: the points will adjust perfectly to a line with negative slope.r =  + 1 is a perfect positive correlation: the points will ajdust perfectrly to a line with positive slope.r = 0 means that the variables are not correlated at all.

Hence, the closer to zero, the worse the correlation is, and that is what r = 0.01 means, but the graph shows other thing.

Therefore, the calculated value of r = 0.01 is not accurate for t his scatter plot.

2. Part B.

A causal relationship means that the expllanatory variable (the independent variable) is the cause of the dependent variable.

Hence, you must find a reasonable variable that can be the cause of the number of strawberries picked.

I could imagine the amount of rainfall the week before of harvest.

Thus, the scenario could be:

Amout of rainfall in mm (x)         Number of strawberries picked (y)

      100                                                     20

        50                                                     40

        25                                                     80

        12.5                                                  160

        6.25                                                 320

The amount of rainfall is the cause of the number of strawberries picked, and you could find a model (function) that relates both variables.

Answer:

Yes.

Step-by-step explanation:

Yes. They are normal

Answer:

$6.14.

Step-by-step explanation:

$30.70×20%

there will be after the tax and discount.