Meena’s father’s present age is six times Meena’s age. Five years from now she will be one-third of her father’s present age. What are their present ages?

Answer:

The answer is B.

Step-by-step explanation:

The function F(x) = x would be the “parent function”. Meaning the +4 we see in G(x) would be a translation, because the function is not multiplied.

if you have ever seen the formula y = mx + b then you should be able to see that +4 would be referencing b in the linear equation, and because m is the same in both lines, we can say that the two functions only change is b, because b represents the y-intercept, if b was 0 in f(x)=x and was 4 in g(x)=x+4, the graph would be shifted 4 units up.

if you want to learn how to understand functions and linear equations, I recommend using khan academy. It is really helpfull in explaining topics of math.

The equation of the new graph g(x) is expressed as g(x) = 4^x + 6

The standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.

Translations is a transformation technique that changes the position of an object from one point on the plane to another.

Given the function f(x) = 4^x

If the function is shifted 6 units up, the function g(x) is derived by adding 4 to the function f(x). The resulting function is given as;

g(x) = f(x) + 6

g(x) = 4^x + 6

Hence the equation of the new graph g(x) is expressed as g(x) = 4^x + 6

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The new price after the price increase of Nu 40 will be Nu 840.

The price of a pant after n Nu 40 price increases will be:

= 800 + 40

= 840

The expected weekly sales as a function of the number of price increases will be:

= n - 1) × 800

= (30 - 1) × 800

= 29 × 800

= 23200

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The image point of (4,-2) after the transformations given is; (2,1).

It follows from the task content that the point given is (4, -2) which first reflects over the y axis and hence, renders the new image to be; (4, 2) after which it undergoes a dilation of with dilation factor, 1/2 and hence, the image point is; (2,1).

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Answer:

$0.75, which is

75 cents

Step-by-step explanation:

First add the cost of all the items.

1.25 + .50 + 3.95

= 5.70

To find 10% of 5.70, change the percent to a decimal and multiply.

10% is .10

5.70 × .10 = .57

The tax is 57 cents. This can be written as $0.57



The fill up are:

5. ∠B ≅ ∠B

6. AA Similarity Postulate          

7.   a/c = c/a

8. a² = cx

9. ∠CDA ≅ ∠BCA

10. ∠A ≅ ∠A

11. ΔCBA ~ ΔDBA  

The above answers shows that:

5. Reflexive Property

6. AA Similarity Postulate

7. Polygon Similarity Postulate

8. Cross Multiply and Simplify

9. All right angles are Congruent

10. Reflexive Property

11. AA similarity Postulate

To prove the above:

Note that the full proof of the Pythagorean theorem is that:

We are given: Δ ABC as a right triangle, with a right angle at ∠C.

Then the  Prove: A²+B² =C²

Therefore, If you follow the theories above, you will see that the answers given are correct.

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Answer:

Step-by-step explanation:

1) Separate terms with roots from terms without roots.

[tex]x^2+4=\sqrt[\frac{1}{2} ]{4+1}[/tex]

2) Simplify 4 + 1 to 5.

[tex]x^2+4=\sqrt[\frac{1}{2} ]{5}[/tex]

3) Invert and multiply.

[tex]x^2+4=5^2[/tex]

4)  Simplify  [tex]5^2[/tex] to 25.

[tex]x^2+4=25[/tex]

5) Subtract 4 from both sides.

[tex]x^2=25-4[/tex]

6) Simplify 25 - 1 to 24.

[tex]x^2=21[/tex]

7)  Take the square root of both sides.

[tex]x=\pm\sqrt{21}[/tex]

Answer:

A

Step-by-step explanation:

[tex]\sqrt{x^{2}+4}-1=2\\\sqrt{x^{2}+4}=3\\x^{2}+4=9\\x^{2}=5\\x=(plus/minus) \sqrt{5}[/tex]

Answer:

option D

Step-by-step explanation:

[tex]\sf 5\dfrac{3}{6}=\dfrac{33}{6}\\\\2\dfrac{1}{3}=\dfrac{7}{3}[/tex]

LCM of  6 , 3 = 6

[tex]\sf \dfrac{33}{6}-\dfrac{7}{3}=\dfrac{33}{6}-\dfrac{7*2}{3*2}\\[/tex]

           [tex]\sf =\dfrac{33}{6}-\dfrac{14}{6}\\\\=\dfrac{33-14}{6}\\\\= \dfrac{19*3}{6*3=\dfrac{57}{18}}\\\\=3\dfrac{3}{18}[/tex]

Answer:

22 cm.

Step-by-step explanation:

Volume =  πr^2 h  =  π 6^2 * 11

So to double the volume

Height will be 2*11 = 22 cm.

Taking a quotient, we will see that she can make 7 bowls of cereal (and some leftover milk).

We know that for each bowl, she needs 1/2 cups of milk.

And we also know that she has a total of (3 + 3/5) cups of milk.

To know how many bowls she can make, we need to take the quotient between the total that she has and the amount that she needs for each bowl:

(3 + 3/5)/(1/2)

We can rewrite the total as:

3 + 3/5 = 15/5 + 3/5 = 18/5

Then the quotient becomes:

(18/5)/(1/2) = (18/5)*2 = 36/5 = 35/5 + 1/5 = 7 + 1/5

So she can make 7 bowls of cereal (and some leftover milk).

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Answer:

well I don't get the question

Answer is C as all other choices are even numbers therefore make the equation non-integer.

Answer:

C)7

Step-by-step explanation:

Due to the fact that all other options are even numbers so it Wii make the equation non-integer.

The  statements that are correct  about right triangle QRS are:

A right triangle posses  a right angle which is in opposite direction to the  hypotenuse.

Considering the right angle triangle, it can be deduced that Side opposite ∠Q is RS not RQ,  and  Adjacent side to ∠Q is QS.

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The distance between the points (-8, -3) and (-2, -5) is √40 units

Using distance formula,

d = √(x₂ - x₁)² + (y₂ - y₁)²

Therefore, using (-8, -3) and (-2, -5).

x₁ = -8

x₂ = -2

y₁ = -3

y₂ = -5

d =  √(-2 + 8)² + (-5 + 3)²

d = √(6)² + (-2)²

d = √36 + 4

d = √40

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Applying the linear pair theorem and the sum of interior angles of hexagon, we have:

Angle 7 = 92°

Angle 1 = 107°

According to the linear pair theorem/postulate, when two angles lie on a straight line, the sum of their measures equals 180 degrees.

Angle 7 lie on a straight line with 88°, therefore, applying the linear pair theorem, we have:

Angle 7 + 88 = 180

Subtract both sides by 88

Angle 7 + 88 - 88 = 180 - 88

Angle 7 = 92°

Also, using the linear pair theorem, we have:

Angle 5 = 180 - 64

Angle 5 = 116°

Angle 3 = 180 - 57

Angle 3 = 123°

Sum of interior angles of hexagon equals 720°, therefore:

Angle 1 + angle 3 + angle 5 + angle 7 + 118 + 164 = 720°

Plug in the known values

Angle 1 + 123 + 116 + 92 + 118 + 164 = 720

Angle 1 + 613 = 720

Subtract both sides by 613

Angle 1 + 613 - 613 = 720 - 613

Angle 1 = 107°

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Answer:

[tex]\text{Midpoint} = (1, \; 1)[/tex]

Step-by-step explanation:

[tex]M = (x_M, \; y_M)[/tex]

[tex]M = \left(\dfrac{x_1 + x_2}{2}, \; \dfrac{y_1 + y_2}{2}\right)[/tex]

[tex]M = \left(\dfrac{0 + 2}{2}, \; \dfrac{4 + -2}{2}\right)[/tex]

[tex]M = \left(\dfrac{2}{2}, \; \dfrac{2}{2}\right)[/tex]

[tex]M = (1, \; 1)[/tex]

Answer: (1, 1)

Step by Step Explanation:

The midpoint formula is (x + x/2 ,  y + y/2)

If you plug in the coordinates it looks like this

( 0 + 2/2  ,  4 + (-2)/2)

That turns into this:

(2/2  ,  2/2)                              

Which gives you the final answer of (1, 1)          

Answer:

Slope: 1

Y-intercept: -1

Step-by-step explanation:

The line touches the y-axis at -1, and using rise over run for the slope, it would be 1, since you go up 1 unit and move to the right 1 unit. 1/1 which is our rise/run would be 1 and that would make the slope 1.

I hope it helps! Have a great day!

bren~

14 of the $1.50/lb type will you need to obtain the desired mixture.

According to the statement

Chocolate A that sells for $1.50/lb

Chocolate B that sells for $6.50/lb

Then in equation form the quantity of mixture will

A + B = X

then

$1.50A + $6.50(10) = X

1.50A + 65 = X -(1)

after solving the equation the value of a and b will become

A = 14.

So, 14 of the $1.50/lb type will you need to obtain the desired mixture.

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Answer:

Step-by-step explanation:

sin(90-a)=cos

cos = angle adjacent

theta=BC/CA

The joint relative frequency is 21%.

Joint relative frequency can be described as the ratio of the frequency of data in a certain category to the total number of data points in that category.

The joint relative frequency for teachers who teach math and not English = number of teachers who teach maths and not English / total number of teachers

(22 / 104) x 100 = 21%

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Answer:

  C.  f(x) = 2x⁴ +6x³ +22x² +54x +36

Step-by-step explanation:

You can use Descartes' rule of signs and the y-intercept to help you select the correct answer.

The given point (0, 36) is the y-intercept of the function. This tells you 36 is the constant in the polynomial, eliminating choices A and B.

Descartes' rule of signs tells you the number of positive real roots will be less than or equal to the number of sign changes in the coefficients when the function is written in standard form. The number of negative real roots will be the number of sign changes after the signs of odd-degree terms are reversed.

The given real roots are both negative. There are zero positive real roots, so all of the signs of the coefficients in the function must be the same (no changes). This eliminates choice D, and tells you C is the correct answer.

  f(x) = 2x⁴ +6x³ +22x² +54x +36

The system of inequalities can model Gabrielle’s situation is;

x + 2y ≤ 20

x + 2y ≤ 203x + 2y ≤ 21

It follows from the task content, that the inequalities which can be used to model Gabrielle's situation be determined.

By setting variables as follows;

Brownie:

Sugar = 1 cup

Eggs = 2

Cookie:

Sugar = 3 cups

Eggs = 2

x + 2y ≤ 20

x + 2y ≤ 203x + 2y ≤ 21

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Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which:

A(0) is the initial value.

r is the growth rate, as a decimal.

In this problem:

Her initial balance is of $300, hence . A(0)=300

The growth rate is of 15%, hence R =0.15

Then,

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = 300(1+0.15)^t\\A(t) = 300(1.5)^t\\[/tex]

It will reach $450 after t years, for which A(t) = 450, hence:

[tex]A(t) =300(1.15)^t\\450= 300(1.15)^t\\1.15^t=\frac{450}{300}\\\\1.15^t =1.5\\log(1.15)^t=log1.5\\t log 1.15 = log 1.5\\t = \frac{log1.5}{log1.15}\\\\ t =2.9[/tex]

It will take about 2.9 years for Emma's balance to reach $450

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The function type in the graph is a decreasing function.

It should be noted that a function is simply used to illustrate the relationship between variables.

In this case, the function type in the graph is a decreasing function. As the number in X axis increases, the value in the y axis is decreased.

This illustrates a decreasing function.

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You have fifteen blankets that each take up 557 cubic inches of space. In a 14-inch moving box, we can pack approximately 5 blankets.

The Volume that can take up by single blanket is 557 cubic inches.

The dimension of the moving box = 14 × 14 × 14

Hence, the volume of the moving box = 2744 cubic inches

The total number of blankets that can be packed in the given moving box = 2744/557 = 4.92 ≅ 5

Therefore, in a 14-inch moving box, there can be 15 blankets with 557 cubic inches of space of each can be packed.

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The standard deviation of the sampling distribution of the sample mean is also called standard error of the mean.

For the given question,

Standard error is a mathematical tool used in statistics to measure variability. The standard error of the mean (SEM) measures how much discrepancy is likely in a sample's mean compared with the population mean.The SEM takes the SD and divides it by the square root of the sample size. The SEM will always be smaller than the SD.

The standard error of the mean indicates how different the population mean is likely to be from a sample mean. You can decrease the standard error by increasing the sample size.

Standard error of the mean and standard deviation are both measures of variability used to summarize sets of data.  It helps you estimate how well your sample data represents the whole population by measuring the accuracy with which the sample data represents a population using standard deviation.

Hence we can conclude that the standard deviation of the sampling distribution of the sample mean is also called standard error of the mean.

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Answer: i know it

Step-by-step explanation: i know

Answer:

The prime factors of 13195 are 5, 7, 13 and 29. The largest prime factor of the number 600851475143 is 6857

Using natural logarithms properties, we will see that:

x = -1.596

Here we can use the property:

[tex]ln(a^b) = b*ln(a)[/tex]

Now we have the equation:

[tex]4^{x + 3 }= 7[/tex]

If we apply the natural logarithm in both sides, we get:

[tex]ln(4^{x + 3 })= ln(7)\\\\(x + 3)*ln(4) = ln(7)\\\\x + 3 = ln(7)/ln(4)\\\\x = ln(7)/ln(4) - 3 = log_4(7) - 3 = -1.596[/tex]

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Arc M P is a minor arc and measures 152°

Arc M L N is a major arc and measures 298° .

Given that NL and MK are diameters of circle J.  

 Size of arc MP is 62+90=152°, since MP is smaller than MLN

             then it is a minor arc. Hence the correct statement is:  

             M P is a minor arc and measures 152°.

Size of M L N is 360-62=298°, thus it is a major arc. Hence the

             correct statement is:

             MLN is  major arc and measures 298°.

Arc M P is a minor arc and measures 152°

Arc M L N is a major arc and measures 298° .

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Answer:

Complete the statements about circle J.

Arc M P is a

✔ minor arc

and measures

✔ 152

degrees.

Arc M L N is a

✔ major arc

and measures

✔ 298

degrees.

Step-by-step explanation:

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