Jane is 7 years older than John.If the sum of their ages is 43.How old is Jane and how old is John​

Given :

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To find :

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Solution :

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We know,

[tex]{ \longrightarrow{\qquad \sf{ \pmb {\dfrac{1}{2 } \times (b_{1} + b_{2}) \times h = {Area_{(Trapezoid)} } }}}}[/tex]

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Now, Substituting the values :

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[tex]{ \longrightarrow{\qquad \sf{ {\dfrac{1}{2 } \times (2 + 6) \times h = {60 } }}}}[/tex]

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[tex]{ \longrightarrow{\qquad \sf{ {\dfrac{1}{2 } \times 8 \times h = {60 } }}}}[/tex]

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[tex]{ \longrightarrow{\qquad \sf{ {\dfrac{8}{2 } \times h = {60 } }}}}[/tex]

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[tex]{ \longrightarrow{\qquad \sf{ 4 \times h = {60 } }}}[/tex]

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[tex]{ \longrightarrow{\qquad \sf{ h = { \dfrac{60}{4} } }}}[/tex]

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[tex]{ \longrightarrow{\qquad \sf{ \pmb { h = {15} } }}}[/tex]

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Therefore,

Answer:

  (a)  3x² -5

Step-by-step explanation:

The shift down is accomplished by subtracting 5 from the function value. (Eliminates choices B and D.) The function graph is made narrower by a vertical expansion or a horizontal compression. Either way, the coefficient of the x² term will be greater than 1. (Eliminates choice C.)

The transformed function g(x) = 3x² -5 will be narrower and shifted down from the parent function.

Answer: The population would be a total of 8,800 people.

Step-by-step explanation: Currently speaking, a town's population is 1,100 people in total.  Since it doubles every 60 years, it would double 3 times in total, because 180 / 60 equals 3.  2 x 1,100, then 2 x 2,200, and then 2x 4,400, gives you 8,800.

Have a great day! :)

Answer:

39 + 5d

Step-by-step explanation:

First multiply 5 by 9 and 5 by d then subtract 6 from 45 (which you get from multiplying 5 by 9) and you get 39 and multiply 5 by d so you get 39 + 5d

let's solve:-

[tex]⇒5(9 + d) - 6(given \: equation) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ⇒by \: bodmas \: rule \: distribute \: 5 \: with \: 9 \: nd \: d \\ \\⇒ 45 + 5d - 6 (subtracting \: like \: terms) \: \: \: \: \: \: \: \: \\ \\⇒ 39 + 5d \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

Answer:

200000 x 1.05^3=231525

Step-by-step explanation:

X 1.05 because the price is increasing by 5% and ^3 because there are three years between 2014 and 2017

Answer:

8x11/2= 44 it's 44

Step-by-step explanation:

A=44 = LW = (2W-3)W = 2W^2 -3W

2W^2-3W -44 = 0

(2W-11)(W+4) = 0

2W-11 = 0

2W = 11

W = 11/2 = 5 1/2 meters

L=2W-3 = 11-3 = 8

8x11/2= 44

length = 8 m,  width = 5 1/2 m

Answer:

Bottom left

Step-by-step explanation:

The limit as x approaches infinity is 3, so there is a horizontal asymptote at 3. So eliminate top left and bottom right.

Also, the fraction 2/(x-1) is undefined when x=1 (since the denominator is 0), so there is a vertical asymptote at x=1. Eliminate top right

So, your answer is the bottom left graph.

Answer:

i think it it false, true, false

hope that's right lol

Step-by-step explanation:

Answer:

Step 3 is wrong

Step-by-step explanation:

[tex]x_1=\frac{-\left(-6\right)+14}{2\cdot \:5},\:x_2=\frac{-\left(-6\right)-14}{2\cdot \:5}[/tex]

is how she shouldve put it in

Answer:

C The Item cost more than mona was able to pay

Step-by-step explanation:

I took the test

The possible number of solutions to the equations in the system is 2. A solution is a collection of data designated to the unexplored variables.

A solution is a set of values assigned to the unknown variables that ensure the equation's equality.

To put it another way, a solution is a value or a set of values (one for each unknown) that, when substituted for the unknowns, makes the equation equal.

The given system of equation is;

[tex]x^2+y^2=9\\9x+2y=16[/tex]

The standard equation of the  circle is;

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]

On comparing the given equation with the standard equation;

The first equation shows the center is at origin(0,0). and radius is 3.

The second equation shows the given equation is a straight line.

As we know that the straight line can only intersect a circle at a maximum of 2 points.

Hence the possible number of solutions to the equations in the system is 2.

To learn more about the solution refer to the link;

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Answer:

The answer is B.63

Explanation:

63 is a composite number because a composite numbers is any positive number which is not a "prime number"

Answer:

■ Sales tax: $36.00

■ Cost/Price before ST: $719.99

■ Total Cost/Price including ST: $755.99

Step-by-step explanation:

Answer: $755.99

Step-by-step explanation: The first step in finding how much an item or product costs with tax is to take the price of the product and multiply it by the percentage of sales tax to find out how much the tax costs. The next step is to take this cost of the tax and add it to the original price of the product. This gives you your final cost. This gives us the following equations.

In this problem the sales tax is 5%, which is equal to 0.05

(719.99) (0.05) = 35.9995

35 + 719.99 = 755.9895

The answer we get from the equations is 755.9895. Rounding to the nearest penny, or hundredth space, gives us our final answer of $755.99

Which of the following methods would be the easiest to use to solve x²−6=0?

[tex] \tt \: {x}^{2} - 6 = 0 \\ \tt {x}^{2} = 6 \\ \tt \: x = \pm \sqrt{6} \\ \tt \: x = - \sqrt{6} , x = \sqrt{6} [/tex]

And done, Solved!

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

Which of the following methods would be the easiest to use to solve x²−11=0?

[tex] \tt {x}^{2} - 11 = 0 \\ \tt \: {x}^{2} = 11 \\ \tt \: x = \pm \sqrt{11} \\ \tt \: x = - \sqrt{11} , x = \sqrt{11} [/tex]

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

Which equation would be the best to solve by completing the square?

[tex] \tt {x}^{2} = 49 \\ \tt \: x = \pm7 \\ \tt \: x = - 7, x = 7[/tex]

Answer: 7 feet

Step-by-step explanation: I did it trust

The length measurement of the third side of the triangular playground whose two sides are 24 ft and 30 ft long should be more than 6 but less than 54.

Triangle inequality theorem of a triangle says that the sum of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

(a+b)>c

(b+c)>a

(c+a)>b

There is a triangular playground. The measurements of two sides of a triangular playground are 24 feet and 30 feet.

Suppose the length of the measurement of the third side of the triangular playground is c meters.

As the two sides are 24 ft and 30 ft long. Thus, by the triangle inequality theorem,

[tex]24+30 > c\\54 > c[/tex]

For the sides 24 ft and c ft,

[tex]24+c > 30\\c > 30-24\\c > 6[/tex]

Thus, the length measurement of the third side of the triangular playground whose two sides are 24 ft and 30 ft long should be more than 6 but less than 54.

Learn more about the triangle inequality theorem here;

https://brainly.com/question/26037134

Answer:

Es 711

Hope this helps!

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Answer:

same side interior angles

3. What are pair relation exists between angle 7 and angle 4?

Explanation :

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Part (a)

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Explanation:

Multiply by 1000 to go from km to meters.

This is because 1000 m = 1 km.

Multiplying by 1000 in scientific notation means we add 3 to the exponent 5. The 3 is because 1000 = 10^3.

So the [tex]3.84 \times 10^5 \text{ km}[/tex] becomes [tex]3.84 \times 10^8 \text{ meters}[/tex]

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

Part (b)

Answer in standard form:  960,000 seconds

Answer in scientific notation: [tex]9.6\times10^{5} \text{ seconds}[/tex]

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Work Shown:

[tex]\text{distance} = \text{rate}*\text{time}\\\\\text{time} = \frac{\text{distance}}{\text{time}}\\\\\text{time} = \frac{3.84 \times 10^8 \text{ meters}}{400 \ \text{ m}/\text{s}}\\\\\text{time} = \frac{3.84 \times 10^8}{4 \times 10^2} \text{ seconds}\\\\\text{time} = \frac{3.84}{4}*\frac{10^{8}}{10^2} \text{ seconds}\\\\\text{time} = 0.96 \times 10^{8-2} \text{ seconds}\\\\\text{time} = 0.96\times 10^{6} \text{ seconds}\\\\[/tex]

[tex]\text{time} = (9.6\times10^{-1})\times10^{6} \text{ seconds}\\\\\text{time} = 9.6\times(10^{-1}*10^{6}) \text{ seconds}\\\\\text{time} = 9.6\times10^{-1+6} \text{ seconds}\\\\\text{time} = 9.6\times10^{5} \text{ seconds}\\\\\text{time} = 960,000 \text{ seconds}\\\\[/tex]

To go from the scientific notation to standard form, move the decimal point 5 spaces to the right. The 5 is from the exponent.

Answer:

Mine was a fashion designer or a model. The model part died out because of my insecurities. But Fashion design is still something I am interested in,

Step-by-step explanation:

Answer:

8 mini muffins

Step-by-step explanation:

*Bolded is important*

1. To help you get a better feel of the wording, let me give you an example:

The Walmart Franchise costs 5$ each. If I have 10$, how much franchises can I buy? See, it becomes simpler. It's 2.

This is what it is asking here:

If he has $5.40, and he can buy 12 mini muffins, we just need to find the cost of these mini muffins to solve the second part.

2. Solve

To find the solution to this equation, I will give you another example.

If I like drinking water, and I can buy 2 Pools of water for 2 dollars, how much does each pool of water cost?

It costs $1, which is not hard to solve.

What did we do to get the answer of $1? We divided. We divided 2/2 to get one. We have to do the same in this case.

Money is x and muffins is m.

Hence the equation is:

y = x/m, or in this case,

y=5.40/12, which will give us the cost of the muffins.

5.4/12 = $0.45.

Now, since we know the cost, we can find the answer.

To find the total amount of muffins he can buy with $4, we have to

divide.

X is Money and C is Cost per muffin. Hence, the equation is:

y = x/c or,

y = 4/0.45 which equals 8.8888888888888889.

Now, you cant buy 8/9 of a muffin. You can only buy a whole.

So he can buy 8 muffins.

3. Confirm

Lets confirm that this is true for the first equation:

5.40/0.45= 12, which is what the equation states.

So 4/0.45 = 8.899 is how much he could buy, but he can only buy 8 because, again, you cant buy 8/9 of a muffin

y = 8.

The simplification of the given expression will be  [tex](-3x^2-15x-30)[/tex].

Given expression is

[tex]-3(x+2)^2 -3+3x[/tex]

By applying  [tex](a+b)^2=a^2+2ab+b^2[/tex]  we get

[tex]-3(x^2+6x+9)-3+3x[/tex]

Multiplying by -3 into the whole bracket we get

[tex]-3x^2-18x-27-3+3x[/tex]

[tex]-3x^2-18x-30+3x[/tex]

[tex]-3x^2-15x-30[/tex]

Thus the simplification of the given expression will be  [tex](-3x^2-15x-30)[/tex]

To know more about Simplification follow

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Answer:

B. –3x^2 – 15x – 30

Step-by-step explanation:

Answer:

between 3 and 4 around 3[tex]\frac{3\\}{4}[/tex]

Answer: 3.5

Step-by-step explanation:

You want to choose two numbers that have perfect roots. One above 14, and one below 14. The nearest two perfect roots to 14 is 9 and 16. We have the following inequality:

[tex]\sqrt{9} < \sqrt{14} < \sqrt{16}[/tex]

[tex]3 < \sqrt{14} < 4[/tex]

This means the square root of 14 is somewhere between 3 and 4. A good estimate would be 3.5

Step-by-step explanation:

[tex]y = \frac{2x}{5} [/tex]

crossmultiply

[tex]5y = 2x[/tex]

divide both side by 2, to make x alone

x = 5y / 2

pls give brainliest

Answer:

Step-by-step explanatio

may not be real numbers. Our final theorem in the section gives us an upper bound on the number

of real zeros.

Theorem 3.7. Suppose f is a polynomial of degree n ≥ 1. Then f has at most n real zeros,

counting multiplicities.

Theorem 3.7 is a consequence of the Factor Theorem and polynomial multiplication. Every zero c

of f gives us a factor of the form (x − c) for f (x). Since f has degree n, there can be at most n of

these factors. The next section provides us some tools which not only help us determine where the

real zeros are to be found, but which real numbers they may be.

We close this section with a summary of several concepts previously presented. You should take

the time to look back through the text to see where each concept was first introduced and where

each connection to the other concepts was made.

Connections Between Zeros, Factors and Graphs of Polynomial Functions

Suppose p is a polynomial function of degree n ≥ 1. The following statements are equivalent:

• The real number c is a zero of p

• p(c) = 0

• x = c is a solution to the polynomial equation p(x) = 0

• (x − c) is a factor of p(x)

• The point (c, 0) is an x-intercept of the graph of y = p(x)

3.2 The Factor Theorem and The Remainder Theorem 265

3.2.1 Exercises

In Exercises 1 - 6, use polynomial long division to perform the indicated

Answer : 6

Explanation : 6 Is The Smallest  Number Which Is The Sum Of 1, 2, And 3. Other Perfect Numbers Are 28, 496, And 8,128.

Answer: 6

Step-by-step explanation: is A Perfect Number

The translated function is:

g(x) = √(x - 3) - 9

The transformations used here are:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

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

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

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

So, if we have a translation of 3 units right and 9 units down, this would be written as:

g(x) = f(x - 3) - 9

Replacing f(x) by the actual function we get:

g(x) = √(x - 3) - 9

If you want to learn more about translations, you can read:

https://brainly.com/question/24850937

Answer:

180/15=12 12x6=72 12x8=96... 12, 72, 96?

Answer:

[tex]3x + 4y = 12 \\ 3x - 4y = 5 \\ 6x = 17 \\ x = \frac{17}{6} \\ 3 \times \frac{17}{5} - 4y = 5 \\ 51 \div 5 - 4y = 5 \\ \\ 10.2 - 5 = 4y \\ y = \frac{5.2}{4} [/tex]

Answer:

79-22=8h

Step-by-step explanation:

hope this helps!