Joyce saved $150 on an item that was 35
%
off. What was the original price?



Write answer to the nearest cent.

The expression y3¹⁰ - 10y³ is a binomial polynomial.

In the given situation y3¹⁰ - 10y³ is a binomial polynomial as there are two terms in the expression.

Therefore, the expression y3¹⁰ - 10y³ is a binomial polynomial.

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Based on the scale factor of 1:6, if the area of the activity field is 21,600 square feet, the area of the playground is equal to 3,600 square feet.

Given the following data:

Scale factor = 1:6

Area of the activity field = 21,600 square feet.

A scale factor can be defined as the ratio of two (2) corresponding length of sides, area, or diameter in two similar geometric figures such as equilateral triangles, river, planets in our solar system, etc.

Let E represent the area of the elementary playground.

Let H represent the area of the high school activity field.

Therefore, a mathematical expression which relates the area of the elementary playground to the area of the high school activity field is given by:

E : H 1:6 = x : 21,600

Evaluating, we have:

1/6 = x/21,600

Cross-multiplying, we have:

6x = 21,600

x = 21,600/6

x = 3,600 square feet.

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Step-by-step explanation:

0.25(x+10) = 2+0.5(x-1)

0.25 * x + 0.25 * 10 = 2.05 * x - 2.05 * 1

0.25x + 2.5 = 2.05x - 2.05

0.25x - 2.05x = -2.05 - 2.5

-1.8x = - 4.55

x = -4.55/-1.8

x = 2.53777777778

The 3 device trackers and wireless charger purchased at $45.22 using a 15% discount coupon gives the price of one device tracker as $12.52

Number of device trackers = 3

The discount given by the coupon = 15% off the total purchase

Amount paid after using the coupon.= $45.22

Original price of the charger = $15.64

Let x represent the price of one device tracker, we have the following equation;

(1 - 0.15)×(3•x + 15.64) = 45.23

Which gives;

x = ((45.22/(1 - 0.15)) - 15.64)/3 = 12.52

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Answer:

Step-by-step explanation:

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answer it yo self

Answer:

Rectangular Cross Section Surface

Two or more expressions with an equal sign is Equation.-76(x-61)=x-89 is the equation for −76 times the difference between a number and 61 is equal to the number plus −89.

Two or more expressions with an equal sign is called as Equation.

The sentence −76 times the difference between a number and 61 is equal to the number plus −89. We have to express in the form of equation.

−76 times the difference between a number

Let the number be 'x', times means multiplication and difference is subtraction.

-76(x-61)

the number plus −89

x+(-89)

−76 times the difference between a number and 61 is equal to the number plus −89.

-76(x-61)=x+(-89)

-76(x-61)=x-89

Therefore -76(x-61)=x-89 is the required equation.

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Answer:

11.58 years

6.82 years

Step-by-step explanation:

Compound interest can be represented as: [tex]A=P(1+\frac{r}{n})^{nt}[/tex] where P = initial amount, r=interest rate, n=compounds in each time unit, t = time (usually years)

If you think about it the: [tex](1+\frac{r}{n}})^{nt}[/tex] represents the overall interest being applied to the principal amount.

This would have to be equal to 2, for it to be doubled, so let's set that equal to 2

[tex]2=(1+\frac{r}{n})^{nt}[/tex]

Now let's solve for "t", first let's take the log of both sides

[tex]log(2)=log([1+\frac{r}{n}]^{nt})[/tex]

Now let's use log properties, specifically the exponent one to rewrite

[tex]log(2)=nt *log(1+\frac{r}{n})[/tex]

Now divide both sides by the log(1 + r/n) and n

[tex]t=\frac{log(2)}{n*log(1+\frac{r}{n})}[/tex]

Our "n" is going to be the same for both equations, 12 since it's compounded monthly

The interest will be a bit different, but in the first case it will be 6% which is 0.06

[tex]t=\frac{log(2)}{12*log(1+\frac{0.06}{12})}[/tex]

simplifying this we get

[tex]t\approx11.581[/tex]

Rounding this we get: [tex]t=11.58[/tex]

Now let's do this to the other equation:

[tex]t=\frac{log(2)}{12*log(1+\frac{0.102}{12})}[/tex]

simplifying this we get:

[tex]t\approx 6.824[/tex]

approximately 6.82

Answer:

y = 3x + b

Step-by-step explanation:

slope intercept form is y = mx + b

y - y-coordinate   m - slope    b - y-intercept

The measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105

The diagram that completes the question is added as an attachment

From the diagram, we have

<1 + <2 = 180 degrees --- supplementary angles

Given that

<2 - <1 = 30 degrees

Add the above equations

So, we have

2<2 = 210

Divide both sides by 2

<2 = 105

Substitute <2 = 105 in <2 - <1 = 30

So, we have

105 - <1 = 30

Evaluate

<1 = 85

Also, we have

<3 = <1

<4 = <2

This means that

<3 = 85

<4 = 105

Hence, the measures of the angles are <1 = 85, <2 = 105, <3 = 85 and <4 = 105

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Answer:

53.13

Step-by-step explanation:

[tex]\tan \alpha=\frac{8}{6} \\ \\ \alpha=\arctan(8/6) \\ \\ \approx 53.13^{\circ}[/tex]

Answer:

53.13

Step-by-step explanation:

correct

Answer: 4 * 10^(-11) + 5 * 10^(-12)

Step-by-step explanation:

4.5E-11=

4.5 * 10^(-11)=

(4+.5) * 10^(-11)=

4 * 10^(-11) + 0.5 * 10^(-11) =

4 * 10^(-11) + 5/10 * 10^(-11) =

4 * 10^(-11) + 5 * 10^(-1) * 10^(-11) =

4 * 10^(-11) + 5 * 10^(-1+(-11)) =

4 * 10^(-11) + 5 * 10^(-1-11) = 4 * 10^(-11) + 5 * 10^(-12)

Based on the fact that out of 2,000 responses, 7/10 indicated that they would like the zoo to add a dome, the number of members who want a dome to be added to the zoo are 1,400 members.

To find the number of members of the zoo who want the dome to be added to the zoo, the following formula would help:

= Number of members that were surveyed by the zoo x Fraction of members who indicated yes to the dome being added

Solving for the number of members who want the dome added gives;

= 2,000 x 7/10

= 14,000 / 10

= 1,400 members

In conclusion, 1,400 members indicated yes to the dome.

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The scale factor of the graph image shown is 1.5, using the letters with prime as the original image

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying.

For the given graph the values with prime is assumed to be the the original shape while the the values without prime represent the factored image.

Taking a point of reference say s' and s. The coordinates of s' and the coordinates of s are ( 2, 4 ) ( 3, 6 ) respectively.

solving for the factor, assuming the factor is k

x axis

2k = 3

k = 3/2 = 1.5

y axis

4k = 6

k = 6/4 = 1.5

This factor works for other coordinates hence we say that the scale factor is 1.5

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Answer:

11.  17.7 units

12.  24.7 units

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.  

To find the perimeter of a polygon, sum the lengths of its sides.

Use the distance formula to find the length of each side.

[tex]\boxed{\begin{minipage}{4.7 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]

Given points:

Use the distance formula to find the length of each side of ABC:

[tex]\begin{aligned}AB & = \sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& = \sqrt{(2-(-2))^2+(5-1)^2}\\& = \sqrt{4^2+4^2}\\& = \sqrt{16+16}\\& = \sqrt{32}\end{aligned}[/tex]

[tex]\begin{aligned}BC & = \sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\& = \sqrt{(5-2)^2+(1-5)^2}\\& = \sqrt{3^2+(-4)^2}\\& = \sqrt{9+16}\\& = \sqrt{25}\\& = 5\end{aligned}[/tex]

[tex]\begin{aligned}AC & = \sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\& = \sqrt{(5-(-2))^2+(1-1)^2}\\ & = \sqrt{7^2+0^2}\\ & = \sqrt{49}\\ & = 7\end{aligned}[/tex]

To find the perimeter, sum the sides:

[tex]\begin{aligned}\sf Perimeter & = AB+BC+AC\\& = \sqrt{32}+5+7\\& = 4\sqrt{2}+12\\& = 17.7\;\sf units\;(nearest\:tenth)\end{aligned}[/tex]

Given points:

After plotting the given points, it is clear that the polygon is a parallelogram. As the opposite sides of a parallelogram are equal in length:

Therefore, we only need to find the length of two sides to calculate the perimeter.

Use the distance formula to find AB and BC:

[tex]\begin{aligned}AB & = \sqrt{(1-(-3))^2+(6-5)^2}\\& = \sqrt{4^2+1^2}\\& = \sqrt{16+1}\\& = \sqrt{17}\end{aligned}[/tex]

[tex]\begin{aligned}BC & = \sqrt{(3-1)^2+(-2-6)^2}\\& = \sqrt{2^2+(-8)^2}\\& = \sqrt{4+64}\\& = \sqrt{68}\end{aligned}[/tex]

Therefore, the perimeter of ABCD is:

[tex]\begin{aligned}\sf Perimeter & = 2(AB+BC)\\& = 2(\sqrt{17}+\sqrt{68})\\& = 6\sqrt{17}\\& =24.7\;\sf units\;(nearest\:tenth)\end{aligned}[/tex]

Answer:

Here both a & b are positive integers that are obtained from the expression (-a)(-b).

Step-by-step explanation:

It is given that a and b are both positive integers, therefore -a and- b are negative integers.

Now, using this we need to simplify the expression (-a)(-b);

Firstly, let us understand what are integers and types of integers;

The collection of whole numbers and negative numbers is known as an integer in mathematics.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers.

The inverse additives of the equivalent positive numbers are the negative numbers.

Now, let us understand what are positive and negative integers;

In fact, positive integers are a subset of the wider class of numbers known as integers.

Integers with a negative value are those that are less than zero. They exclude decimals and fractions.

Furthermore, the expression given is (-a)(-b) which is the product of two negative integers.

=> (-a)(-b)

=> ab

Therefore, here both a & b are positive integers that are obtained from the expression (-a)(-b).

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Answer:

No, for a graph to be proportional it needs to go through the point (0.0)

Step-by-step explanation:

The Coordinates of the point D will be (-3, 3) and point E will be (0, 5) and point F will be (2, -2).

According to the statement

We have to find that the points of the coordinates.

So, For this purpose, we know that the

Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.

From the given information:

the coordinates of D, E, and F after a reflection over the y axis? Plot these points on the grid, and label them D′, E′ and F′.

Then

Coordinates of a point is given by (x,y)

And

Here, x represents the horizontal distance of the point from origin (0,0) and y represents the vertical distance of the point from origin.

Let's take an example of point D,

Horizontal distance of point D from origin x =-3 and vertical distance from origin y =3.

Then

Coordinates of the point D will be (-3, 3).

Coordinates of the point F will be (2, -2).

Coordinates of the point E will be (0, 5).

For more details please see the image below.

So, The Coordinates of the point D will be (-3, 3) and point E will be (0, 5) and point F will be (2, -2).

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Answer:

11.02

Step-by-step explanation:

Answer:

finish quesiton please <3

Step-by-step explanation:

Answer:

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Step-by-step explanation:

I've ok h l

The horizontal distance as a function of d can be given as h = √(d + 7200) (d - 7200).

It is given in the question that:

Height at which blimp is flying (AB)= 7200 feet

The slanted distance to the pagoda (BC) = d feet

The horizontal distance (AC) = h

Let the angle made between slanted distance and horizontal distance be θ.

So, cosθ = AC/BC

cosθ = h/d

and also, sinθ = AB/BC

sinθ = 7200/d

Now, we know from the first trigonometric identity that cos²θ = 1 - sin²θ.

=> (h/d)² = 1 - (7200/d)²

=> (h/d)² = (d² - 7200)/d²

=> h² = d² - 7200

=> h = √(d² - 7200)

=> h = √(d + 7200) (d - 7200)

Thus, the horizontal distance as a function of d can be given as h = √(d + 7200) (d - 7200).

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Answer:

[tex]y=-\frac{5}{3}x +\frac{8}{3}.[/tex]

Step-by-step explanation:

[tex]1. \ formula:\\ \frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1};[/tex]

2. according to the formula above:

[tex]\frac{x+2}{1+2} =\frac{y-6}{1-6}; \ = > \ \frac{x+2}{3} =\frac{y-6}{-5};[/tex]

3. finally, 5x+3y=8 ⇔

[tex]y=-\frac{5}{3}x +\frac{8}{3}.[/tex]

The number of apple trees the orchard have is 3533.

The apple orchard  has honey crisp trees and McIntosh trees.

The orchard has 1603 honey crisp trees.

It has 327 more McIntosh trees than honey crisp trees.

Therefore,

number of honey crisp trees = 1603

number of McIntosh trees = 327 + 1603

number of McIntosh trees = 1930

Therefore, the number of apples trees the orchard have can be calculated as follows:

number of apples trees = number of McIntosh trees + number of honey crisp trees

number of honey crisp trees = 1603

number of McIntosh trees = 1930

number of apples trees = 1930 + 1603

number of apples trees = 3533

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The farmer can 9 days more than 31 days.

given,

farmer buy 1000 pounds of hay

if cow eats 25 pounds of hay per day .

here, 25 x 31 =775

which is less than 1000 ,so that the farmer can feed the cow more than 31 days

1000-775=225

225/25=9

therefore the farmer can 9 days more than 31 days.

There are four basic properties of numbers: commutative, associative, distributive, and identity. You should be familiar with each of these.

distributive property ;

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

The commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.

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The relation can be written as a set of ordered pairs as: a. {(–3, 3), (0, 0), (2, –2)}.

A relation, in maths, is defined as a relationship between two variables, x and y, which are linked to each other.

The x-value and the y-value of each set of points in a relation is written as (x, y).

Thus, in the given relation that is represented by the graph below, we have the following set of ordered pairs representing each point on the graph: (–3, 3), (0, 0), and (2, –2).

Therefore, the relation can be written as a set of ordered pairs as: a. {(–3, 3), (0, 0), (2, –2)}.

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The charges which sum up to 0 are +7 charge and −7 charge.

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

Given:

two charges have a sum of 0

So, taking one by one the pairs of option are

+7 charge and +7 charge

=+ 14 charge

−7 charge and −7 charge

=-14 charge

−7 charge d +7 charge

=0 charge

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Step-by-step explanation:

f(g(x)) simply means that g(x) is embedded in f(x) as the input value for f(x).

f(g(x)) = 3(7x + 6) - 1 = 21x + 18 - 1 = 21x + 17

c. is the right answer

g(f(x)) is the other way around. f(x) is now the input value for g(x).

g(f(x)) = 7(3x - 1) + 6 = 21x - 7 + 6 = 21x - 1

a. is the right answer