4) John's sister is 8 years less than twice his age. If John is 39, what age is his sister?

Answer:

T=10

Step-by-step explanation:

Answer:

t=10

Step-by-step explanation:

you multiply each side by 2.5 so 4*2.5= 10

Answer: 7

Step-by-step explanation:

The smaller number is 7.75.

An equation is a mathematical statement formed when two expressions are equated using an equal sign.

The equations are useful in determination of unknown parameters.

The equations are of various types, such as Trigonometric equations, quadratic equations.

The system of equations are used to solve complex problems.

Let the smaller number is x.

The larger number is 2 less than three times the smaller number

Then the larger number is 3x -2

The sum of the two numbers is 29

The sum is the output of the mathematical operation, Addition.

The equation formed is :

3x -2 + x = 29

Grouping the variables and the constants

4x = 31

Dividing both side of the equation by 4

x = 7.75

The value of the smaller number is obtained.

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In the given formula n is the number of years the loan is out for.

The answer would be C.

Answer:

[tex]\boxed{\sf C}[/tex]

Step-by-step explanation:

The formula for the payment on a loan is given:

[tex]\displaystyle P=PV \cdot \frac{i}{1-(1+i)^{-n}}[/tex]

n would represent the number of periods or years it will take to pay the loan back.

Answer:

S6tep-by-step explanation:

4^(11+8) = 4^19 is the solution

Answer:

c. (3x^2-1)(x-7)

Step-by-step explanation:

=(3x^3-21x^2)+(-x+7)

=-(x-7)+3x^2(x-7)

=(3x^2-1)(x-7)

Answer:

25 children

So , each child will get 25 pens and 7 pencils

You have to find the highest common factor of 125 and 175 which is 25 and then you have to multiply it by those two numbers to find how may pens and pencils will be given to 1 child

Hope this helps and pls mark as brianliest :)

Step-by-step explanation:

Let the other endpoint be (x,y)

Since, (1,6) is the midpoint between (9,1) and (x,y)

Therefore,

1=(9+x)/2

=> 2=9+x

=> x= -7

and,

6=(1+y)/2

=>12= 1+y

=> y=11

So, the other endpoint is ( -7, 11)

Answer:

Step-by-step explanation:

Let the coordinates of Endpoint 2 be

(x ,y)

The midpoint of the endpoints is given by

[tex](1,6) = ( \frac{9 + x}{2} , \frac{1 + y}{2} )[/tex]

Where x and y are coordinates of Endpoint 2

Comparing with the midpoint we have

[tex]1 = \frac{9 + x}{2} \\ 2 = 9 + x \\ \\ x = 2 - 9 \\ \\ x = - 7[/tex]

[tex]6 = \frac{1 + y}{2} \\ 12 = 1 + y \\ \\ y = 12 - 1 \\ \\ y = 11[/tex]

Therefore x = - 7 and y = 11

The coordinates of Endpoint 2 are

Hope this helps you

Answer:

221g

Step-by-step explanation:

561g divided by 33cm is how much 1 cm of rope would be so then you multiply that amount by 13

Answer:

335

Step-by-step explanation:

Factor the given binomial:

x - y = 5

xy = 14

x = y + 5

(y + 5)y = 14

y^2 + 5y - 14 = 0

(y + 7)(y - 2) = 0

y = -7 or y = 2

y = -7

xy = 14

-7x = 14

x = -2

y = 2

2x = 14

x = 7

Solutions:

x = -2, y = -7

x = 7, y = 2

For x = -2, y = 7

x^3 - y^3 =

= (-2)^3 - (-7)^3

= -8 - (-343)

= 335

For x = 7, y = 2

x^3 - y^3 =

= 7^3 - 2^3

= 343 - 8

= 335

Answer:

AB = DE

BC = EF

AC = DF

∠ABC = ∠ DEF

∠BAC = ∠EDF

∠BCA = ∠EFD

Step-by-step explanation:

As its congruent all the corresponding parts will be equal

Answer:

The range consists of all real numbers where y ≠ 0

Step-by-step explanation:

reciprocal parent function is y = 1/x

If y = 0, then 1 would have to be divided by a number to equal 0. This would require x to equal a number that can divide 1 to equal 0. Because this is not possible, y cannot be 0.  

Answer:

315.1° (1 d.p.)

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

6/13

Step-by-step explanation:

Of the 13 students who do not own a graphing calculator, 6 are girls.  The probability is 6/13.

Answer:

C

Step-by-step explanation:

In any circle the following ratios are always equal.

[tex]\frac{arc}{circumference}[/tex] = [tex]\frac{centralangle}{360}[/tex] , thus

[tex]\frac{48}{circum}[/tex] = [tex]\frac{60}{360}[/tex] = [tex]\frac{1}{6}[/tex] ( cross- multiply )

circumference = 6 × 48 = 288 cm → C

Answer:

The number of marbles in the first bag=  5  

The number of marbles in the second bag = 15

The number of marbles in the third bag = 10

Step-by-step explanation:

Given that

Total number of marbles= 30

Lets take, the number of marbles in the first bag= x

The number of marbles in the second bag = 3 x

The number of marbles in the third bag = 2 x

Therefore

The total number of marbles = x + 2 x + 3 x = 6 x

6 x = 30

[tex]x=\dfrac{30}{5}[/tex]

x= 6 marbles

We  can say that

The number of marbles in the first bag=  5  

The number of marbles in the second bag = 15

The number of marbles in the third bag = 10

Answer:

<

Step-by-step explanation:

Answer:

HL  and SAS

which agrees with the third option listed among your options

Step-by-step explanation:

Notice that you have two triangles (see attached image) which have a common side (marked in blue), sides YW and YZ (marked in green) congruent, and the angle in between also congruent.

Therefore we have two postulates than can be applied to prove that the triangles YWX and YXZ are congruent:

HL postulate : "congruent hypotenuse and a corresponding congruent leg " that corresponds to hypotenuses YW and YZ, and congruent leg which is the common segment YX.

and:

SAS postulate: "two sides and the included angle" which corresponds to sides YW, YX, and angle WYX on one triangle, and sides YX, YZ, and angle XYZ in the other triangle

Answer:

The most helpful function in an attempt to determine the time it takes for the dolphin to re-enter is h(x) = 2·(x - 1)·(x - 4)·(x - 6)

Step-by-step explanation:

For 2·x²·(x - 11) + 4·(17·x - 12)

h(5) = 2×5^2×(5 - 11) + 4×(17×5 - 12) = -8

For the function h(x) = 2·x·(x² - 11·x + 34) -48 we have;

h(5) = 2×5×(5^2 - 11×5 + 34) -48 = -8

For the function h(x) = 2·(x - 1)·(x - 4)·(x - 6) we have;

h(5) = 2×(5 - 1)×(5 - 4)×(5 - 6) = -8

For the function h(x) = 2·x³ - 22·x² + 68·x -48 we have;

h(5) = 2×5^3 - 22×5^2 + 68× 5  - 48 = -8

Given that the values of the function are all equal at x = 5, the function that will be most helpful in determining the time it takes for the dolphin to re-enter the sea after leaping out of the water is the function that is already factorized

Thereby where the value of the function h(x) at which the dolphin re-enters the the sea is h(x) = 0, we have the function h(x) = 2·(x - 1)·(x - 4)·(x - 6), readily gives the time values, x, as x = 1 second or 4 second or 6 second, therefore, the most helpful function is h(x) = 2·(x - 1)·(x - 4)·(x - 6).

Answer:

The correct option is;

[tex]h(x) = \sqrt[3]{x + 2}[/tex]

Step-by-step explanation:

Given that h(x) is a translation of f(x) = ∛x

From the points on the graph, given that the function goes through (-1, 1) and (-3, -1) we have;

When x = -1, h(x) = 1

When x = -3, h(x) = -1

h''(x) = (-2, 0)

Which gives  

d²(∛(x + a))/dx²= [tex]-\left ( \dfrac{2}{9} \cdot \left (x + a \right )^{\dfrac{-5}{3}}\right )[/tex], have coordinates (-2, 0)

When h(x) = 0, x = -2 which gives;

[tex]-\left ( \dfrac{2}{9} \cdot \left (-2 + a \right )^{\dfrac{-5}{3}}\right ) = 0[/tex]

Therefore, a = (0/(-2/9))^(-3/5) + 2

a = 2

The translation is h(x) = [tex]\sqrt[3]{x + 2}[/tex]

We check, that when, x = -1, y = 1 which gives;

h(x) = [tex]\sqrt[3]{-1 + 2} = \sqrt[3]{1} = 1[/tex] which satisfies the condition that h(x) passes through the point (-1, 1)

For the point (-3, -1), we have;

h(x) = [tex]\sqrt[3]{-3 + 2} = \sqrt[3]{-1} = -1[/tex]

Therefore, the equation, h(x) = [tex]\sqrt[3]{x + 2}[/tex] passes through the points (-1, 1) and (-3, -1) and has an inflection point at (-2, 0).

Answer: B

Step-by-step explanation:

Answer:

Volume of Burj Khalifa Prism = 4000 [tex]cm^2[/tex]

Volume of CN Tower Prism = 2671 [tex]cm^2[/tex]

Step-by-step explanation:

Given

Height of Burj Khalifa = 828 m

Height of CN Tower in Toronto = 553 m

Base of rectangular prism is a square with sides 10 cm [tex]\times[/tex] 10 cm.

Height of Burj Khalifa prism = 40 cm

828 m is represented as 40 cm

[tex]\Rightarrow 553 m[/tex] is represented as [tex]\frac{40}{828 } \times 553 = 26.71\ cm[/tex]

So, height of rectangular prism of CN Tower = 26.71 cm

Volume of a Prism is given by the Formula:

[tex]V=Area\ of\ Base \times Height[/tex]

Base is a square, so Area of base = [tex]Side^2[/tex]

Volume of Burj Khalifa Prism:

[tex]V_B=10^2 \times 40 = 4000\ cm^2[/tex]

Volume of CN Tower Prism:

[tex]V_C=10^2 \times 26.71 = 2671\ cm^2[/tex]

So, the answer is:

Volume of Burj Khalifa Prism = 4000 [tex]cm^2[/tex]

Volume of CN Tower Prism = 2671 [tex]cm^2[/tex]

Answer:

the other side lengths are 6m and 8m

Step-by-step explanation:

i did the quiz and got it right

Answer:

La altura de la pirámide es de 8.14 unidades.

Step-by-step explanation:

Hay una pirámide cuadrangular regular cuyas caras laterales forman un ángulo que mide 53º con la base y el área de la superficie lateral es 60. ¿Qué altura tiene?

Dado que el área de superficie lateral = 60

Tenemos

Área del triángulo equilátero = (√3 / 4) × a²

 (√3 / 4) × a² = 60

a² = 60 / (√3 / 4) = 80 · √3

a = √ (80 · √3) = 11.77 unidades

La altura inclinada = Altura de la superficie inclinada = a × sin (60) = 11.77 × sin (60)

La altura inclinada = 11.77 × sin (60) = 10.194 unidades

La altura de la pirámide = Altura inclinada × sin (ángulo de caras laterales con la base)

La altura de la pirámide = 10.194 × sin (53) = 8.14 unidades.

La altura de la pirámide = 8.14 unidades.

Answer:

-10=661.5

-1=6.7

0=4.0

1=2.4

2=1.4

8=0.1

(0,4)

Step-by-step explanation:

The y intercept is (0,4)

A function is a law that relates a dependent and an independent variable.

The function is g(x) = 4 (0.6)ˣ

The table shows the value of x

The value of g(x) at different value of x is

At x = -10

g(x) = 661.5

At x = -1

g(x) = 6.7

At x = 0

g(x) = 4

At x = 1

g(x) = 2.4

At x = 2

g(x) = 1.4

At x = 8

g(x) = 0.1

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Answer:

C

Step-by-step explanation:

The slope formula is y^2 - y^1 over x^2 - x^1    

hope this helps!

also the answer is just the inverse of that answer

Answer:

x=0    x=3

Step-by-step explanation:

F(x)=3x(2x-6)

Set equal to zero

0 =3x(2x-6)

Using the zero product property

3x =0   2x-6 =0

x =0     2x = 6

             x = 6/2

             x = 3

Answer:

x = 0 or x = 3

Step-by-step explanation:

Set the output to 0

0 = 3x(2x-6)

Set factors equal to 0.

3x = 0

x = 0

2x - 6 = 0

2x = 6

x = 3

Answer:

27

Step-by-step explanation:

3 cubed=3✖️3✖️3=27

Answer:

3³ = 3 × 3 × 3 = 9 × 3 = 27

Hope this helps you

Answer:

Correct option: Third one

Step-by-step explanation:

A polynomial is an expression in the form:

[tex]ax^n + bx^{n-1}+...+mx^1+n[/tex]

Where n is a non-negative integer number, and a, b, ... are real coefficients.

The first option is not a polynomial, because there is a non-integer number (5/2) in the exponent of y.

The second option is not a polynomial, because there is a negative integer number in the exponent (the fraction [tex]\frac{1}{x^2}[/tex] is the same as [tex]x^{-2}[/tex], and [tex]\frac{1}{5x}[/tex] is the same as [tex]0.2x^{-1}[/tex]).

The third option is a polynomial, because all numbers in exponent are non-negative integers.

The fourth option is not a polynomial, because there is a variable x in the exponent, so we don't know if the exponent is a non-negative integer number.

Answer:

Step-by-step explanation:

If a group of hikers finished hiking at an elevation of -5 the group started hiking at an elevation of 8, their initial feet will be -5 and their final feet will be 8.

Change in feet of the groups elevation = final feel - initial feet

Final feet = 8 feet

Change in feet of the groups elevation = 8 -(-5)

Change in feet of the groups elevation = 8+5

Change in feet of the groups elevation = 13

Answer:

There are six equilateral triangles in regular hexagons

Answer:

There are 6 equilateral triangles in a regular hexagon.

Step-by-step explanation:

A regular hexagon has 6 congruent sides and can be divided into 6 congruent equilateral triangles.

There are 6 equilateral triangles in a regular hexagon.

Answer:

The number of houses built in Town B is 56.

Step-by-step explanation:

We are given that in 2010, the number of houses built in Town A was 25 percent greater than the number of houses built in Town B.

Also, 70 houses were built in Town A during 210.

Let the number of houses built in Town B be 'x'.

So, according to the question;

Number of houses built in Town A = Number of houses built in Town B + 25% of the houses built in Town B

[tex]70 = x + (25\% \times x)[/tex]

[tex]70 = x(1+0.25)[/tex]

[tex]x=\frac{70}{1.25}[/tex]

x = 56

Hence, the number of houses built in Town B is 56.