The width of a rectangle is 3 units less than the length. The area of the rectangle is 28 units. What is the width, in units, of the rectangle.

Answer:

  B.  The situation represents an arithmetic sequence because the successive values have a common difference of 20.

Step-by-step explanation:

(x, y) values appear to be ...

  (1, 10) . . . . 10 minutes played in the first game

  (2, 30) . . . 20 minutes played in the second game, adding 20 to the total

  (3, 50) . . . 20 minutes played in the third game, adding 20 to the total

From here, we can see that each additional game adds 20 minutes to the total (y), so the sequence is ...

  an arithmetic sequence because the successive values have a common difference of 20

56 students represents 100 % and

X boys represent 34%,

so x= 56•34/100= 19.04 so approximately 19 boys

56-19= 37 girls signed up.

Now 37 girls represent 100% and 31 girls represent x % ,

So x= 31•100/37= 83.78% about 84% of the girls attended

To find the percentage of girls who attended the auditions, calculate the number of boys and girls who signed up, and then determine the percentage of girls who attended. About 83.78% of the girls who signed up for the school play attended the auditions.

The question: 56 students signed up for the school play. About 34% were boys. At the auditions, only 31 girls attended.

Calculate the number of boys who signed up: 56 x 0.34 = 19 boys.

Find the number of girls who signed up: 56 - 19 = 37 girls.

Calculate the percentage of girls who attended auditions: (31 girls / 37 girls) x 100% = 83.78%.

Answer:

The system of inequalities is

[tex]y\leq x+3[/tex] and [tex]y\leq -2x+3[/tex]

The solution is the shaded green area

Step-by-step explanation:

step 1

Find the equation of the inequality A

The line is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line

Find the slope

(-3,0),(-4,-1)

m=(-1-0)/(-4+3)=1

The equation of the line is y=mx+b

we have

m=1

b=3 ----> the y-intercept (see the graph)

substitute

y=x+3 -----> equation of the solid line A

The equation of the inequality is

[tex]y\leq x+3[/tex] -----> inequality A

step 2

Find the equation of the inequality B

The line is solid and goes through the points 1, 1, 2, negative 1 and is shaded in below the line

Find the slope

(1,1),(2,-1)

m=(-1-1)/(2-1)=-2

The equation of the line is y=mx+b

we have

m=-2

b=3 ----> the y-intercept (see the graph)

substitute

y=-2x+3 -----> equation of the solid line B

The equation of the inequality is

[tex]y\leq -2x+3[/tex] -----> inequality B

therefore

The system of inequalities is

[tex]y\leq x+3[/tex] -----> inequality A

[tex]y\leq -2x+3[/tex] -----> inequality B

The solution is the shaded green area

The graph represents the system of inequalities y >= -x - 3 and y >= -3x + 4. This is concluded by observing the slopes, intercept points, and shading regions.

The system of inequalities represented by the graph you provided can be deduced by the slopes, intercept points, and the regions of shading. Given the information, the solid line that goes through the points (-3, 0) and (-4, -1) can be represented by the equation y >= -x -3. Since the line is solid and the area below the line is shaded, the inequality symbol includes an equal sign which means the line itself is part of the solution.

For the second solid line that goes through the points (1, 1) and (2, -1), it can be represented by the equation y >= -3x + 4. Similarly, because the line is solid and the region below this line is shaded, the inequality symbol includes an equal sign.

Therefore, the system of inequalities that the graph represents is y >= -x - 3 and y >= -3x + 4.

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8 Females have to leave the room which then it would be 22 males and 22 females which is a 1-1 ratio

A ratio shows us the number of times a number contains another number. The number of females who should leave the conference room is 8.

A ratio shows us the number of times a number contains another number.

The ratio of females to males in the room is 15 to 11, therefore, the numbers of female to male ratio can be represented by 15x to 11x.

The sum of the total number of people in the room is 52, and can be represented as,

15x + 11x = 52

26x = 52

x = 2

Thus, the number of females in the conference room is 30(15x=15×2), while the number of males in the conference room is 22(11x=11×2).

Now, for the ratio to be 1:1, the number of males should be the same and the number of females should be equal to the number of males. Therefore, the number of females who should leave the conference room is,

Number of females who should leave conference room = Number of females before - Number of females after

Number of females who should leave conference room = 30 - 22 = 8

Hence, the number of females who should leave the conference room is 8.

Learn more about Ratios:

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Answer:

The triangle is rotated 360° ⇒ answer D

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or  

anti-clockwise around the origin

- If point (x , y) rotated about the origin by angle 360°

∴ Its image is (x , y)  the point itself

* There is no difference between rotating 360° clockwise or  

anti-clockwise around the origin

* Now lets solve the problem

∵ The vertices of the triangle ABC are:

  A is (-6 , 3) , B is (-5 , 7) , C is (-4 , 3)

∵ The triangle map onto itself

∴ A = A'

∴ B = B'

∴ C = C'

∴ The triangle is rotated 360° about the origin

D= 360

When you’re talking about rotation you go counterclockwise and each quadrant is another 90 degrees.

Answer:

15

Step-by-step explanation:

5 ! = 120

Since 5 ! = 5 × 4 × 3 × 2 × 1, then

5 × 3 = 15 is the greatest odd factor of 5 !

The greatest odd integer that is a factor of 5 factorial (5!) is 5. This is because the definition of factorial involves multiplying a number by every number below it until reaching 1 and 5 is the largest odd number within this range.

The greatest odd integer that is a factor of 5! (or 5 factorial) is 5. The factorial, represented by the symbol '!', is a function that multiplies a number by every number below it until it reaches 1. For example, 5! means 5 * 4 * 3 * 2 * 1. To find the greatest odd integer that is a factor of 5!, you simply need to identify the largest odd number that is a part of this multiplication, which is 5.

Let's clarify this with some simple math. Start from the number 5 itself, then move down: 5 (it's an odd number), 4 (it's even, exclude), 3 (it's odd, but less than 5), 2 (it's even, exclude), 1 (it's odd, but less than 5). Hence, the largest odd integer that is a divisor of 5! is 5.

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Answer:

[tex]\large\boxed{\left\{\begin{array}{ccc}y-17z=-15&(a)\\-2y+17z=13&(b)\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x-3y+5z=5&(1)\\4x-5y-7z=-5&(2)\\-6x+7y+2z=-2&(3)\end{array}\right\\\\\\\text{From (1) and (2)}\\\left\{\begin{array}{ccc}2x-3y+5z=5&(1)&\text{multiply both sides by (-2)}\\4x-5y-7z=-5&(2)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-4x+6y-10z=-10\\4x-5y-7z=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad y-17z=-15\qquad(a)[/tex]

[tex]\text{From (1) and (3)}\\\left\{\begin{array}{ccc}2x-3y+5z=5&(1)&\text{multiply both sides by 3}\\-6x+7y+2z=-2&(3)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}6x-9y+15z=15\\-6x+7y+2z=-2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-2y+17z=13\qquad(b)[/tex]

To determine the amount of milk needed for 36 servings of pancakes, multiply one and two-thirds cups of milk by the number of servings. This results in a total of 60 cups of milk required.

To find out how many cups of milk are needed for 36 servings of pancakes, when one serving requires one and two-thirds cups of milk, we use multiplication. We can make a conversion factor using our original recipe, likening it to a mathematical relationship or a stoichiometric relationship in chemistry. Here is the step-by-step calculation:

So, for 36 servings of pancakes, you would need 60 cups of milk.

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i would think teachers

False.

For a point to lie on the X-axis, the second number needs to be 0, not the first one.

When the first number is 0, the point is on the Y-Axis.

Answer:

A, E

Step-by-step explanation:

Remember SOH-CAH-TOA:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Therefore, we can say:

sin 20° = LN / 8

cos 70° = LN / 8

tan 70° = MN / LN

Only the first and last options are correct.

Answer:

22

Step-by-step explanation:

8 - (-14)

keep, change, change

8 + 14 = 22

Answer:

6

Step-by-step explanation:

-14 is smaller than -8.  We subtract -14 from -8, obtaining +14 - 8, or +6.

The positive difference between -8 and -14 is 6.

considering the diagram,the top part is a triangle with the base of 3.2m and height of 2.2m. since the triangle 8s is a right angle triangle. we use Pythagoras theorem to solve for the hypotenus

Final answer:

The length of the wire connecting the tops of two poles of heights 3.8m and 6m, and spaced 3.2m apart is approximately 3.9 meters when calculated using the Pythagorean theorem.

Explanation:

To calculate the length of the wire connecting the tops of two poles of different heights, we can use the Pythagorean theorem.

This theorem states that in a right angle triangle, the square of the length of the hypotenuse (the wire) is equal to the sum of the squares of the lengths of the other two sides (the distances between the tops of the poles and the ground).

Let's denote:

Pole A as the shorter pole with a height of 3.8m

Pole B as the taller pole with a height of 6m

The distance between the two poles as 3.2m

The difference in height between the two poles is 6m - 3.8m, which is 2.2m. Thus, we have a right triangle where one leg is 3.2m (distance between poles) and the other leg is 2.2m (height difference between poles).

Applying Pythagorean theorem:

c² = a² + b²

c² = 3.2² + 2.2²

c² = 10.24 + 4.84

c² = 15.08

c = √15.08

c ≈ 3.9m

Therefore, the length of the wire is approximately 3.9 meters.

Answer:  The correct answer is:  [B]:

_________________________________________

                " [tex]\frac{-3}{ x}[/tex] " .

_________________________________________

Step-by-step explanation:

_________________________________________

Note:  A number; "divided by a variable" ; is Not a "polynomial" .

Answer choice:  [B]:  " [tex]\frac{-3}{ x}[/tex] " ;  

         is a "number;  divided by a "variable" ;  and as such, is Not a "polynomial".

_________________________________________

Answer:

[tex]r= 2(cos(\theta) + 3sin(\theta))[/tex]

Step-by-step explanation:

To convert an equation of rectangular shape to polar form use the following equivalences

[tex]x=rcos(\theta)[/tex]

[tex]y=rsin(\theta)[/tex]

[tex]x^2 + y^2=r^2[/tex]

In this case we have the following equation.

[tex](x-1)^2 + (y-3)^2=10[/tex]

First we expanded the expression

[tex](x-1)^2 + (y-3)^2=10\\\\(x^2 -2x +1) +(y^2 -6y + 9) = 10\\\\\\x^2 +y^2 -2x -6y = 10-9-1\\\\x^2 +y^2 -2x -6y = 0[/tex]

Now we know that [tex]x^2 + y^2=r^2[/tex], [tex]x=rcos(\theta)[/tex] and [tex]y=rsin(\theta)[/tex]

So

[tex]r^2 -2rcos(\theta) -6rsin(\theta) = 0\\\\r^2 - 2r(cos(\theta) + 3sin(\theta))=0\\\\r^2 = 2r(cos(\theta) + 3sin(\theta))\\\\r= 2(cos(\theta) + 3sin(\theta))[/tex]

Answer:

[tex] {32}^{ \frac{1}{2} } {x}^{ \frac{5}{2} } {y}^{ \frac{3}{2} } = \sqrt{32 {x}^{5} {y}^{3} } = (4 \sqrt{2} )( {x}^{2} \sqrt{x} )(y \sqrt{y} ) = 4 {x}^{2} y \sqrt{2xy} [/tex]

The simplification of the expression 10.26 - 1.9 x 3.7 + 0.1, using proper order of operations, gives the result of 3.33.

The student's question asks to simplify a mathematical expression. To accomplish this, we use the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

The given equation to simplify is 10.26 - 1.9 x 3.7 + 0.1. First, perform the multiplication: 1.9 x 3.7 = 7.03. Substitute this value into the expression to get 10.26 - 7.03 + 0.1. Then, perform subtraction and addition from left to right. This will result in 3.23 + 0.1 = 3.33. Therefore, the simplified result of the expression 10.26 - 1.9 x 3.7 + 0.1 is 3.33.

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Answer:

The radius of circle L is [tex]7.8\ in[/tex]

Step-by-step explanation:

Remember that a line that passes through the center divide the circle into two equal parts

YV=VM=6 in

VL is perpendicular to YM

so

The triangle VLM is a right triangle

The radius is equal to LM ----> hypotenuse of the triangle VLM

Applying the Pythagoras Theorem

[tex]LM^{2}=VM^{2}+VL^{2}[/tex]

substitute the given values

[tex]LM^{2}=6^{2}+5^{2}[/tex]

[tex]LM^{2}=61[/tex]

[tex]LM=7.8\ in[/tex]

Answer:

Slope: 5/3

Y - intercept: -2/3

Step-by-step explanation:

The slope is the coefficient of the x term, so that is 5/3. The y - intercept is the number being added to the x term, which is -2/3.

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut point with the "y" axis

We have the following equation:

[tex]y = - \frac {5} {3} x- \frac {2} {3}[/tex]

So we have to:

[tex]m = - \frac {5} {3}\\b = - \frac {2} {3}[/tex]

Answer:

The slope is[tex]- \frac {5} {3}[/tex]and the intersection with "y" is [tex]- \frac {2} {3}[/tex]

Answer:

Where are the followings

Step-by-step explanation:

A valid FICO credit score ranges from 300 to 850. A score outside this range is not valid. Key components of a FICO score include credit mix and the impact of new credit, both accounting for 10% of the score respectively.

When it comes to determining what is not a valid FICO credit score, it's important to understand that FICO scores range from 300 to 850. Any score that is not within this range would be considered invalid. Components that make up a FICO score include payment history, amounts owed, length of credit history, new credit, and credit mix. Credit mix refers to the variety of credit types you have, such as credit cards, retail accounts, installment loans, finance company accounts, and mortgage loans, and makes up 10% of your FICO score. Regarding new credit, opening a new account can temporarily lower your score because it reduces the average age of your accounts, which also accounts for 10% of your FICO score.

Two common myths are that opening a new retail credit card is always good for your credit score and that it hurts your score to comparison shop for loans. In reality, opening a retail credit card can lower your score initially, though responsibly managing your new credit can eventually have a positive effect. When it comes to loan comparison shopping, FICO provides a grace period for hard inquiries that are related, bundling them into a single inquiry if they occur within a 14 to 45-day span, depending on the type of credit. This is designed to not penalize consumers who are responsibly shopping for the best rates.

Answer:

$150

Step-by-step explanation:

Given

The graph with speed over speed limit on x-axis and amount of ticket on y-axis. In order to find the answer a person must know how to translate or read graphs.

As it is given in the question that the person is charged based on the extra miles over the speed limit. If the speed limit was 50 mph and the driver was driving at 61 mph, then the number of miles over the speed limit

=> 61-50

=> 11 miles

So, we have to look for 11 on x-axis and then we look for the y-axis's intercept that intersects with 11.

So, in the given graph, the value 11 of x-axis intercepts with the $150 on y-axis.

So the fine will be $150 ..

Answer:

1

Step-by-step explanation:

These numbers have no common factors. The only comon factor they have is one. Therefore, the GCF of 117, 19, and 110 is one.

Answer:  

-2x^3 + 2x^(1/2)

Step-by-step explanation:

step one- plug in the values of each in f(x) - g(x)

x^(1/2)-x - (2x^3-×^(1/2)-x) ; g(x) is in parentheses bc we need to distribute the negative

x^(1/2)-x-2x^3 + x^(1/2) + x ; combine like terms (letters with the same exponents) ; the x's cancel, and the x^(1/2) + x^(1/2) combine to form 2x^(1/2); the -2x^3 remains

you should get

-2x^3 + 2x^(1/2)

Answer:

[tex]f(x) - g(x) = 2(\sqrt{x}-x^3)[/tex]

Step-by-step explanation:

We have the functions

[tex]f(x)= x^{\frac{1}{2}}-x[/tex]  and   [tex]g(x) = 2x^3-x^\frac{1}{2}-x[/tex]

The operation [tex]f (x) -g (x)[/tex] is the subtraction of the function f(x) minus the function g(x). Thus

[tex]f(x) - g(x) = x^{\frac{1}{2}}-x -(2x^3-x^\frac{1}{2}-x)[/tex]

Simplifying the expression we have left that:

[tex]f(x) - g(x) = x^{\frac{1}{2}}-x -2x^3+x^\frac{1}{2}+x[/tex]

[tex]f(x) - g(x) = 2x^{\frac{1}{2}}-2x^3[/tex]

[tex]f(x) - g(x) = 2(\sqrt{x}-x^3)[/tex]  Because [tex]x^{\frac{a}{n}} = \sqrt[n]{x^a}[/tex]

Answer:

see explanation

Step-by-step explanation:

1

Given

y - 4 = 5(x + 2) ← distribute parenthesis

y - 4 = 5x + 10 ( add 4 to both sides )

y = 5x + 14 → B

Subtract y from both sides

0 = 5x - y + 14 ( subtract 14 from both sides )

- 14 = 5x - y → C

--------------------------------------------------

2

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 5 and c = 1, thus

y = 5x + 1 → A

Answer: 10pi

Step-by-step explanation:

C=2*pi*r

C=2*pi*5

C=10*pi (exact)

This is exact if u want numbers, you’ll have to round-off and you can just put 10xpi into a calculator If u want to see.

Answer:

C = 31.42

Step-by-step explanation:

radius = 5

C = 2 π r

C = 2 · π · 5

C = 31.41593

then you round so it equals 31.42 instead

Answer:

3x-8y=-16

The y intercept is;

(0, 2)

-5x-10y=7

The y intercept is;

(0, -0.7)

Step-by-step explanation:

The y-intercept refers to the point where the graph of an equation intersects or crosses the y-axis. At this point, the corresponding value of x is 0.

From the first equation given;

3x-8y=-16

Substitute x with 0 in the equation and solve for y;

3(0) -8y = -16

-8y = -16

y = 2

The y intercept is thus;

(0, 2)

From the second equation;

-5x-10y=7

Substitute x with 0 in the equation and solve for y;

-5(0) - 10y = 7

-10y = 7

y = -0.7

The y intercept is thus;

(0, -0.7)

Answer:

see the attached figure

Step-by-step explanation:

The best unit of measurement that represent each description in the attached figure

Answer:

Step-by-step explanation:

Miles

1. Distance traveled on a bike ride

2. Length of the border between Texas and Oklahoma

3. Distance around a lake.

Feet

1. Distance traveled by a base ball.

2. Height of a mature tree

Inches

1. Diagonal of a computer screen

2. Diameter of a basket ball

3. Width of a sheet of a paper.

Answer:

292.5 miles

Step-by-step explanation:

Ok so what you want to do is multiply 4.5 and 65 together.

She travels at 65 miles per hour and she travels for 4.5 hours

Recall that

[tex]\cos\dfrac\pi6=\dfrac{\sqrt3}2[/tex]

[tex]\sin\dfrac\pi6=\dfrac12[/tex]

Then

[tex]2\sqrt3+2i=4\left(\dfrac{\sqrt3}2+\dfrac12i\right)=4\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)=4e^{i\pi/6}[/tex]

Answer:

y = -5x + 21

Step-by-step explanation:

The perpendicular slope is opposite of the inverse.  The inverse of 1/5 is 5/1, and the opposite of that is -5/1.

So m = -5.

Then use point-slope form:

y + 4 = -5 (x - 5)

If you wish, convert to slope-intercept form:

y + 4 = -5x + 25

y = -5x + 21