(Q2) Decide if the function is an exponential function. If it is, state the initial value and the base. y=5^x

Answer:

[tex]\large\boxed{\overline{QT}\cong\overline{AZ}}[/tex]

Step-by-step explanation:

[tex]\triangle QPT\cong\triangle ARZ\\\\\begin{array}{c|c}Q&A\\P&R\\T&Z\end{array}\Rightarrow\begin{array}{ccc}\overline{QP}\cong\overline{AR}\\\overline{PT}\cong\overline{RZ}\\\overline{QT}\cong\overline{AZ}\end{array}[/tex]

Answer:

First option.

Step-by-step explanation:

I drew the triangles to see it better. If two triangles are congruent the sides and the angles have the same length. Also, the order of the vertex is important. I put them as it is enunciated. So, watching the image the congruent sides are:

QT and AZ

QP and AR

PT and RZ

Then, the correct option is the first one.

Answer:  The correct options are

(B) [tex]x=\dfrac{11+\sqrt{61}}{2}.[/tex]

(D) [tex]x=\dfrac{11-\sqrt{61}}{2}.[/tex]

Step-by-step explanation:  We are given to select the values of x that are the roots of the following polynomial :

[tex]x^2-11x+15.[/tex]

The quadratic equation formed by the given polynomial will be

[tex]x^2-11x+15=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

we know that

the solution set of a quadratic equation [tex]ax^2+bx+c=0,~~a\neq 0[/tex] is given by

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]

From equation (i), we have

a = 1, b = -11  and  c = 15.

Therefore, the roots of equation (i) will be given by

[tex]x=\dfrac{-(-11)\pm\sqrt{(-11)^2-4\times1\times15}}{2\times1}\\\\\\\Rightarrow x=\dfrac{11\pm\sqrt{121-60}}{2}\\\\\\\Rightarrow x=\dfrac{11\pm\sqrt{61}}{2}.[/tex]

Thus, the roots of the given polynomial are

[tex]x=\dfrac{11+\sqrt{61}}{2},~~~~~x=\dfrac{11-\sqrt{61}}{2}.[/tex]

Options (B) and (D) are CORRECT.

Answer:

b and d

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

5/8 is equal to 5 divided by 8 and your dividing 5 so all the friends can have a equal amount. every friend would also get 5/8 of a apple

Every friend would get 5/8 parts of the total apple.

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, 8 friends want to share 5 apples equally. We need to find that what fraction will each person get,

Since, we have 5 apples, which is to be distributed to 8 persons,

To find the same, we will have to, divide 5 apples equally among 8 persons,

Therefore,

If we divide 5 by 8 then the faction of 5/8 of the whole is the part that each of the 8 friends going to have,

Hence, each friend would get 5/8 parts of the total apple.

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Answer:

11/6 or decimal 1.8333... + 4.9 = 6.733333....

Step-by-step explanation:

Simplify the following:

(3 + 2/3)/2

Express 4/6 in its lowest form by cancelling out gcd(4, 6) = 2 from the numerator and denominator. 4/6 = (2×2)/(2×3) = 2/3:

(2/3 + 3)/2

Put 3 + 2/3 over the common denominator 3. 3 + 2/3 = (3×3)/3 + 2/3:

((3×3)/3 + 2/3)/2

3×3 = 9:

(9/3 + 2/3)/2

9/3 + 2/3 = (9 + 2)/3:

((9 + 2)/3)/2

9 + 2 = 11:

(11/3)/2

11/3×1/2 = 11/(3×2):

11/(3×2)

3×2 = 6:

Answer:  11/6 or decimal 1.8333... + 4.9 = 6.733333....

Answer:

See below.

Step-by-step explanation:

This function g(x) = 3(4^x) - 5 is an exponential function since it has a variable as an exponent. It has a initial value of 3 and a multiplicative rate of change of 4. The function itself when x = 0 is y = -2.

i think the answer to this problem is49

Answer:

The volume of this right rectangular prism is 49 Cubic feet.

Step-by-step explanation:

Here, the data is given

Lenght (l) = 7 feet

Widht (b) = 2 feet

Height (h) = 3.5 feet

Now, The Volume of rectangular prism

= l × b × h

= 7 × 2 × 3.5 feet

= 7 × 7 feet

= 49 cubic feet

Thus, The volume of this right rectangular prism is 49 Cubic feet.

-TheUnknownScientist

Answer:

The measure of arc KL is [tex]145\°[/tex]

Step-by-step explanation:

we know that

[tex]arc\ JK=arc\ KL=x\°[/tex]

so

[tex]2x+70\°=360\°[/tex] -----> complete circle

solve for x

[tex]2x=360\°-70\°[/tex]

[tex]2x=290\°[/tex]

[tex]x=145\°[/tex]

Answer:

8

Step-by-step explanation:

Given in the question a logarithm expression

[tex]125^(log_{5}2)[/tex]

We will use Exponent of Log Rule

[tex]b^(log_{b}k) = k[/tex]

here b = 5

         k = 2

Suppose

[tex]125^(log_{5}2) = x[/tex]

take cube root on both sides of this equation

[tex]\sqrt[ 3]{(125^(log_{5}2)}=\sqrt[3]{x}[/tex]

[tex]\sqrt[3]{(125)} ^(log_{5}2)=\sqrt[3]{x}[/tex]

[tex]5^(log_{5}2)}=\sqrt[3]{x}[/tex]

Now according to the rule

2 = ∛x

to remove cube root take cube on both side

x = 8

so [tex]125^(log_{5}2 )[/tex] = 8

Answer: Third option

Step-by-step explanation:

You have the function:

[tex]y=3*2^x[/tex]

Then, if the value of x increases by 1, you obtain:

-Rewrite the function:

[tex]y=3*2^{(x+1)}[/tex]

-Substitute values for x into the function and observe what happen to y. Then:

x=1

[tex]y=3*2^{(1+1)}=12[/tex]

x=2

[tex]y=3*2^{(2+1)}=24[/tex]  

x=3

[tex]y=3*2^{(3+1)}=48[/tex]  

The value of y is doubled.

Answer:

C=the value of x increases by 1, the value of y will double.

Step-by-step explanation:

Answer:

Choice C is correct

Step-by-step explanation:

The polar equation of the conic section is in standard form. The eccentricity is simply the coefficient of cos theta; thus e = 2

The eccentricity being more than 1 implies the conic section is a hyperbola.

To determine the directrix, divide 6 by 2 to obtain 3. The conic section opens to the left thus;

directrix; x = 3

Answer:

Choice C is correct

Answer:

c. 105 yd^2.

Step-by-step explanation:

First find the slant height (h) of each of the triangular walls:

tan 60 = h /  3.1

h = 3.1 tan 60

= 5.369 yds.

Area of each side = 3.1* 5.369

= 16.645

Total surface area of the pyramid

= 4 * 16.645 + 6.2^2

= 105.02 yd^2.

Answer:

Step-by-step explanation:

The original price of the bike helmet was $68.25, calculated by understanding that the $54.60 Kelly paid represented 80% of the original price after a 20% discount.

Kelly paid $54.60 for a bike helmet that was 20% off the original price. To find the original price of the helmet, we need to understand that the price Kelly paid is 80% of the original price, after the discount was applied. Therefore, the equation to find the original price (OP) is:

54.60 = 0.80 × OP

To solve for OP, we divide both sides of the equation by 0.80:

OP = 54.60 / 0.80

OP = $68.25

Thus, the original price of the bike helmet was $68.25.

Answer:

4 out of 22 = 4/22

Step-by-step explanation:

Answer:

The length is [tex]15\ ft[/tex]

The width is [tex]12\ ft[/tex]

Step-by-step explanation:

we know that

The area of rectangle is equal to

[tex]A=LW[/tex]

we have

[tex]A=180\ ft^{2}[/tex]

so

[tex]180=LW[/tex] -----> equation A

[tex]W=L-3[/tex] ------> equation B

substitute equation B in equation A and solve for L

[tex]180=L(L-3)[/tex]

[tex]180=L^{2}-3L[/tex]

[tex]L^{2}-3L-180=0[/tex]

using a graphing tool------> solve the quadratic equation

The solution is [tex]L=15\ ft[/tex]

see the attached figure

Find the value of W

[tex]W=15-3=12\ ft[/tex]

To find the dimensions of the rectangle given its area, we set up an equation using the length and width of the rectangle. Solving the equation will give us the dimensions. In this case, the length of the rectangle is 15 feet and the width is 12 feet.

To find the dimensions of the rectangle, let's assume the length of the rectangle is L feet. According to the problem, the width is 3 feet less than the length, so the width would be L - 3 feet. The area of the rectangle is given as 180 square feet, so we can set up the equation: L * (L - 3) = 180. Solving this equation will give us the dimensions of the rectangle.

Multiplying the binomials, we get L^2 - 3L = 180. Rearranging the equation, we have L^2 - 3L - 180 = 0. This is a quadratic equation that can be factored. Factoring, we have (L - 15)(L + 12) = 0. We can now solve for L by setting each factor equal to zero: L - 15 = 0 or L + 12 = 0. This gives us two possible solutions for L: L = 15 or L = -12.

Since we cannot have negative dimensions for a rectangle, we discard the negative solution. Therefore, the length of the rectangle is 15 feet. The width can be found by substituting this value back into the equation: Width = 15 - 3 = 12 feet. So, the dimensions of the rectangle are 15 feet by 12 feet.

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Hence, the lakes' altitudes varied by 40 feet. To sum up: Average: around -26.3 feet, Average: -18 feet , Zero mode and 30 to 40 ft.

The mean, a statistic of central tendency in mathematics, is the average of a group of numerical values. It is also frequently known as the geometric average. A set of values' mean is calculated by adding up all of the values and dividing the result by the amount of values in the set. The mean can be determined, for instance, if the set of values is 3, 5, 7, 9, and 11, by multiplying the values together and dividing them by the total amount of numbers: Mean = (3 + 5 + 7 + 9 + 11) / 5 = 7 .As a result, 7 represents the set's mean value.

given

The median altitude of the lakes is -18 feet because the middle number is -18.

Mode: To identify the mode, we search the collection for the number that pops up the most often. There is no mode because no number appears more than once in this instance.

Range: To get the range, divide the largest by the smallest number:

Maximum number - smallest number equals the range (-9) - (-49) = 40

Hence, the lakes' altitudes varied by 40 feet. To sum up: Average: around -26.3 feet, Average: -18 feet , Zero mode and 30 to 40 ft.

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Answer:

The answer is ellipse; 23° to the nearest degree ⇒ answer (d)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

- 9x² + 4xy + 5y² - 40 = 0

∵ A = 9 , B = 4 , 5 = 5

∴ B² - 4 AC = (4)² - 4(9)(5) = -164 < 0

∴ B² - 4AC < 0

∴ If a conic exists, it will be either a circle or an ellipse.

* To find the type of the graph lets check;

- If A and C are nonzero, have the same sign, and are not

 equal to each other, then the graph is an ellipse.

- If A and C are equal and nonzero and have the same

 sign, then the graph is a circle.

∵ A and C have same signs and are not equal

∴ The graph is an ellipse

* If we have term xy ⇒ B ≠ 0

∴ The graph is rotate by angle Ф

* To find the angle of rotation use the rule:

- cot(2Ф) = (A - C)/B

∵ A = 9 , B = 4 , C = 5

∴ cot(2Ф) = (9 - 5)/4 = 4/4 = 1

∴ tan(2Ф) = 1

∴ 2Ф = 45°

∴ Ф = 22.5° ≅ 23° to the nearest degree

* The answer is ellipse; with angle of rotation = 23°

HERE'S HOW TO DO IT :)

A composite figure is made up of several simple geometric figures such as triangles, rectangles, squares, circles, and semicircles.

To find the area of a composite figure, separate the figure into simpler shapes whose area can be found. Then add the areas together.

(SEE EXAMPLE ATTACHED)

HERES WHAT WE KNOW ABOUT COMPOSITE FIGURES:

Composite Figures. A figure (or shape) that can be divided into more than one of the basic figures is said to be a composite figure (or shape). For example, figure ABCD is a composite figure as it consists of two basic figures

let me know if i can help more :)

See the attached picture for the answers:

The price and demand are inversely proportional to each other, When the price is less, the demand is higher. When the price is high, the demand is low.

So , as given, the gasoline prices has been decreased from $2.00 per gallon to $1.40 per gallon, so now the demand will increase. The quantity of gasoline that will be in demand will increase.

Answer:

The quantity of gasoline demanded will increase.

Step-by-step explanation:

We are asked to find the change in demand of gasoline, when price of gasoline decreased from $2 per gallon to $1.40.

We know that quantity of a product demanded is inversely proportional to supply of the product.

This means that an increase in price will decrease the quantity demanded, while a decrease in price will increase the demand.

Since the price of gasoline is decreased by $0.60 per gallon, therefore, the quantity of gasoline demanded will increase.

Answer:

The Zebra Danios!

Step-by-step explanation:

The zebra danios

4/3 is greater than 1, making it an improper fraction. Suppose that fancy guppy's length is x, the danios' length would be 4/3 x, which, since it is an improper fraction, is greater than x.

Mark me brainlest please!

I take half-credit my cousin aswell helped!

Answer:

[tex]\large\boxed{M+T=-15r^2+2r+8}[/tex]

Step-by-step explanation:

[tex]M=-8r^2+11r-6\\T=-7r^2-9r+14\\\\M+T=?\\\\\text{Substitute:}\\\\M+T=(-8r^2+11r-6)+(-7r^2-9r+14)\\\\M+T=-8r^2+11r-6-7r^2-9r+14\qquad\text{combine like terms}\\\\M+T=(-8r^2-7r^2)+(11r-9r)+(-6+14)\\\\M+T=-15r^2+2r+8[/tex]

The expression that represents M + T is -15r^2 + 2r + 8

The equations for M and T are given as:

[tex]M=-8r^2 +11r -6[/tex]

[tex]T=-7r^2-9r+14[/tex]

The sum of M and T is represented as: M + T

This is then calculated as:

[tex]M+T=-8r^2 +11r -6-7r^2-9r+14[/tex]

Collect like terms

[tex]M+T=-8r^2 -7r^2+11r -9r-6+14[/tex]

Evaluate the like terms

[tex]M + T = -15r^2 + 2r + 8[/tex]

Hence, the expression that represents M + T is -15r^2 + 2r + 8

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Answer:

Step-by-step explanation:

In a parallelogram opposite angles are congruent. Therefore we have the equation:

10y - 29 = 7y +19               add 29 to both sides

10y = 7y + 48               subtract 7y from both sides

3y = 48              divide both sides by 3

y = 16

Answer:

B

Step-by-step explanation:

A transformation of T(a,b) in the equation would give this form:

[tex](x-a)^2+(y-b)^2=8[/tex]

So, T(4,3) means translation of 4 units in x and 3 units in y. Thus, we can write:

[tex](x-4)^2+(y-3)^2=8[/tex]

Expanding and rearranging, we get:

[tex](x-4)^2-(y-3)^2-8=0\\x^2-8y+16-y^2+6y-9-8=0\\x^2-y^2-8x+6y-1=0[/tex]

Answer choice B is right.

Answer:

B

x^2-y^2-8x+6y-1=0

Answer:

Expression is 12 - [tex]\frac{12}{z}[/tex].

Step-by-step explanation:

Given  : "12 less than the quotient of 12 and a number z."

To find : Write an algebraic expression .

Solution : We have given 12 less than the quotient of 12 and a number z."

According to question :

Let the quotient = Q

quotient of 12 and a number z.

quotient = [tex]\frac{12}{z}[/tex].

12 less than the quotient of 12 and a number z.

12 - [tex]\frac{12}{z}[/tex].

Therefore, Expression is 12 - [tex]\frac{12}{z}[/tex].

Answer:

The area left to build is [tex]\frac{704}{60}\ m^{2}[/tex]

Step-by-step explanation:

The question in English is

The area of a property in square meters, measures 704/5. A house is built that occupies 5/6 of the total area. Half of the remaining area is used to build a terrace, how much area is left to build?

we know that

The total area represent the fraction 6/6

A house represent the fraction 5/6 of the total area

The remaining area represent the fraction  (6/6)-(5/6)=1/6 of the total area

If half of the remaining area is used to build a terrace

then

the area of the terrace represent the fraction (1/6)/2=1/12 of the total area

therefore

The area left to build represent the fraction 1/12 of the total area

so

[tex](\frac{1}{12})\frac{704}{5} =\frac{704}{60}\ m^{2}[/tex]

Answer:

Tthe area of the shaded region is [tex](x^{2}-3x+36)\ unit^{2}[/tex]

Step-by-step explanation:

we know that

To find the area of the shaded region (blue region), subtract the area of the smaller rectangle from the area of the larger square

so

Find the area of the larger square

[tex]A=(x+1)^{2}=(x^{2}+2x+1)\ unit^{2}[/tex]

Find the area of the smaller rectangle

[tex]A=5(x-7)=(5x-35)\ unit^{2}[/tex]

Subtract the polynomials

[tex](x^{2}+2x+1)-(5x-35)=(x^{2}-3x+36)\ unit^{2}[/tex]

Answer:

168 minutes, or 2 hours, 48 minutes

Step-by-step explanation:

Set up a proportion and solve.

56 minutes is to 4 tires as 'x' minutes are to 12 tires

becomes

56/4 = x/12         solve for x...

[56(12)]/4 = x            (multiply both sides by 12 to get rid of the fraction)

672/4 = x                 (simplify  52(12) = 672)

168 = x                      (simplify 672/4 = 168)          

Answer: 40

Step-by-step explanation:

second train leaves 40 minutes after

Answer:

[tex]an = 2.5 + (n - 1)(-5)[/tex]

Step-by-step explanation:

we know that

The explicit formula for the nth term of an arithmetic sequence is given by the formula

[tex]an = a1 + (n - 1)r[/tex]

where

a1 is the first term

n is the term number

r is the common difference

In this problem we have

[tex]a1=2.5, r=-5[/tex]

substitute

[tex]an = 2.5 + (n - 1)(-5)[/tex]