Solve the following story problem.
The perimeter of a rectangle is 60 inches. The length is four times the
width.
What are the length and width of the rectangle?
Define your variables.
X =
Equation 1
y =
Equation 2
What is the length?
what is the width?

Answer:

the price with the offer is going to be 1.59$

Step-by-step explanation:

\( \frac{x}{5.30} = \frac{70}{100} \)

\(100(x) = 70(5.30)\)

\(100(x) = 371\)

\( \frac{100(x)}{100} = \frac{371}{100} \)

\(x = 3.71\)

\(70\% \: \: \: of \: \: \: 5.30 \: \: \: is \: \: \: 3.71\)

\(5.30 - 3.71 = 1.59\)

Answer:

maybe false

have a great day

true

Explanation:

you can use a2 +b2=c2 to find it

In a dilation, all side lengths of the figure are multiplied by the same scale factor, which can be any positive real number. So, if we have a triangle RST with side lengths 4 cm, 5 cm, and 8 cm, any numbers obtained by multiplying these lengths by the same scale factor would be the side lengths of dilation of triangle RST.

For example, if we multiply each side length by 2, we would get the triangle RST' with side lengths 8 cm, 10 cm, and 16 cm. If we multiply each side length by 3, we will get the triangle RST'' with side lengths 12 cm, 15 cm, and 24 cm. And so on.

Therefore, the side lengths of dilation of triangle RST could be any set of positive real numbers that are obtained by multiplying the side lengths of RST by the same scale factor.

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Answer:

The scale factor is 1/2

Step-by-step explanation:

The coordinates of Point G are (4,6) and the coordinates of Point G' are (2,3). To get from 4 to 2 and 6 to 3, you have to multiply by 1/2. Therefore, the scale factor is 1/2.

Answer:

B

Step-by-step explanation:

If the numerator is one, the denominator is going to be the same value as a normal positve interger.

Answer:

A

Step-by-step explanation:

If z = 10, y = 9, and x = 8, it would fit the fact that z > y and y > x.

If we divide 1 by the variables, then it would be 1/10, 1/9, and 1/8. Imagine this as a pie. 1/8 would be the biggest slice then because it is cut into less pieces. 1/9 would be the second biggest slice because it is cut into less pieces than 1/10. Therefore, A is the correct answer.

I hope this helps and please mark this as brainliest!

The correct option is D, the range is (-6, ∞)

The range is the set of the possibe outputs of the function, to identify it on a graph, we need to look at the vertical axis on the graph.

Here, the minimum value (in the horizontal axis) is at: y = -6, with an asymptotic behavior, so we never reach that actual value.

In other hand, we can see that the graph keeps going up, so we don't have a maximum.

Then the range of this function is written as:

(-6, ∞)

For the given options, the correct one is D.

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Answer:

Hey there!

3(2 - x) - 2(6x - 8)

6-3x-12x+16

6-15x+16

-15x+22

Hope this helps :)

Answer:

Grace is correct. The other two made mistakes while distributing the negative sign. Chelsea failed to distribute the negative sign to the second term of the second expression. Roan failed to distribute the negative sign to both terms of the second expression.

Answer:

Step-by-step explanation:

y equals x times 5 is the answer because 2 times 5 is 10 and so on and so forth hope this helps :D

Answer:

Fist if all u will draw ur Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Secondly u will draw ur Parallel lines or angle.

Answer:

a c e

Step-by-step explanation:

Answer:

Total = 36%

Step-by-step explanation:

Given

Company A = 0.15

Company B = 21%

Required

Determine the total revenue

Total is calculated as thus:

Total = Company A + Company B

Total = 0.15 + 21%

Represent 0.15 as %

Total = 0.15*100% + 21%

Total = 15% + 21%

Total = 36%

Answer:

I think it is 0.5

Step-by-step explanation:

32²×8²×16² = 16777216

64²×4³×128 = 33554432

16777216 ÷ 33554432= 0.5

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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Answer:

$55.88

Step-by-step explanation:

Step 1: 51.50 times 8.5% = 4.3775

Step 2: Add 51.50 plus 4.3775

Step 3: 55.8775 round to the hundreth place.

Step 4: Skylar spent $55.88 after tax

Using the Pythagorean Theorem, it is found that:

The Pythagorean Theorem is a geometry axion relates the length of the sides \(l_1\) and \(l_2\), which are the separated by the angle of 90º, of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:

\(h^2 = l_1^2 + l_2^2\)

For the netting, it is found that:

Hence the measure c, representing the length of the bar, is calculated as follows:

c² = 8² + 3.5²

c = sqrt(8² + 3.5²)

c = 8.73 ft.

The amount of netting needed is the area of the entire goal, composed by:

Hence:

A = 12 x 8.73 + 2 x 1/2 x 8 x 3.5 = 132.76 ft².

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The magnetic field generated by the wires at the point (x=4m, y=4m) carrying identical currents of 90A out of the page is 2.50 x \(10^{-6\) T or 2.50 μT.

Hence option b is correct.

According to the given information,

We can use the Biot-Savart Law to calculate the magnetic field generated by these wires at the given point.

Using the formula, we get:

B = (μ0/4π) I [(sinθ1 + sinθ2) / 2] / d,

Where,

μ0 is the permeability of free space (4π x \(10^{-7}\) T m/A),

I is the current (90 A),

θ1 and θ2 are the angles between the wire and the vector pointing from the wire to the given point,

And d is the distance between the wires (8 m).

To find θ1 and θ2, we can use Trigonometry:

θ1 = sin inverse (y/d)

   = sin inverse (4/8) = 30°

θ2 =  sin inverse [(y-d)/d]

     =  sin inverse [(4-8)/8]

     = -30°

Substituting these values into the formula, we get:

B = (4π x \(10^{-7}\) T m/A) 90 A [(sin30° + sin(-30°)) / 2] / 8 m

B = 2.50 x \(10^{-6\)  T

   = 2.50 μT

Therefore, the correct option is (b) 2.50 x  \(10^{-6\)  T (or 2.50 μT).

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The complete question is attached below:

Answer:

inverse of 5/9(F-32)

Step-by-step explanation:

m11=54°

m8=117°

m7=63°

Step-by-step explanation:

a) m2=m12 (corresponding angles)

m12=126°

180=m12+m11 (supplementary angles equal 180)

180=126+m11

m11=54°

b) m14=m8. (corresponding angles)

m8=117°

C) m7=180-m8 (supplementary angles equal 180)

m7=180-117

m7=63°

Answer:

See below ↓↓↓↓

Step-by-step explanation:

a) Area of circle with radius 10 units

b) Circumference of circle with diameter 7 units

c) Diameter of circle with area 121π square units

d) Area of circle with circumference 20π units

Area of circle with radius 10 units is 314 square units,

Circumference of circle with diameter 7 units is 22 square units,

Diameter of circle with area 121π square units is 22 units and

Area of circle with circumference 20π units is 314 square units

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

a) Area of circle with radius 10 units

A = πr²

A = 3.14 x (10)²

A = 3.14 x 100

A = 314 sq. units

b) Circumference of circle with diameter 7 units

C = πd

C = 3.14×7

C = 21.98 units

c) Diameter of circle with area 121π square units

A = πr²

121π = πr²

r = √121 = 11 units

d = 2r = 2 x 11 = 22 units

d) Area of circle with circumference 20π units

C = 2πr

20π = 2πr

r = 10 units

A = πr²

A = 3.14 x (10)²

A = 3.14 x 100

A = 314 square units

Hence, Area of circle with radius 10 units is 314 square units, Circumference of circle with diameter 7 units is 22 square units, Diameter of circle with area 121π square units is 22 units and Area of circle with circumference 20π units is 314 square units

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The mean score of 90, and percentile of Bob's score of 80, gives Bob's exam score as approximately 92.5%

The Z-Score of the 80th percentile is 0.8416

The formula for Z-Score is presented as follows;

\(z = \frac{x - \mu}{ \sigma} \)

Where;

\( \sigma = The \: standard \: deviation\)

\( \mu = The \: mean = 90\%\)

x = The given score

Taking the mean as a proportion, we have;

\( \sigma = \sqrt{\frac{\mu \cdot (1-\mu)}{n}}\)

Which gives;

\( \sigma = \sqrt{\frac{0.9 \times (1-0.9)}{100}}= 0.03\)

Therefore, when z = 0.8416, gives;

\(0.8416 = \frac{x - 0.9}{ 0.03} \)

x = 0.8416 × 0.03 + 0.9 ≈ 0.925

Therefore;

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Answer:

5/6 or 0.8333333333 (83%)

Step-by-step explanation:

So she landed 15 out of 18 so we are going to divide 15 by 18 (15/18) which gets us 5/6 or 0.8333333333 or 83%

Hopes this help ^-^

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

\(\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta\)

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

\(\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta\)

Simplify. The denominator uses the difference of two squares pattern:

\(\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta\)

Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

\(\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta\)

Split into two separate fractions:

\(\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta\)

Rewrite the two fractions:

\(\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta\)

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

\(\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=} \sec^2\theta - \sec\theta\tan\theta\)

Hence verified.

Answer:Difference

Step-by-step explanation:

The value of the expression (x != 7) && (x <= y) is: B. true

The expression is a combination of two logical conditions joined by the logical operator "&&" which means "and". The first condition "x != 7" checks if x is not equal to 7, which is true because x is 5. The second condition "x <= y" checks if x is less than or equal to y, which is also true because x is 5 and y is 7.

Since both conditions are true, the entire expression evaluates to true. The logical operator "&&" only returns true if both the conditions are true, else it will return false.

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\(\longrightarrow \sf The \: angle's \:measure \:is \:15⁰\)

Two angles are said to be complimentary if their sum is 90⁰. These angles are called compliment of each other.

\(\red{\leadsto}\:\)\(\textsf{let \: the \: angle \: be \:x } \)

\(\green{\leadsto}\:\)\(\textsf{Complimentary \:angle \:will \:be \:5x }\)\(\sf \)

\(\green{ \underline { \boxed{ \sf{Sum \: of \: complimentary \:angles = 90⁰}}}}\)

\(\begin{gathered}\\\implies\quad \sf x+5x = 90⁰ \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf 6x = 90⁰ \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf x = \frac{90}{6} \\\end{gathered} \)

\(\begin{gathered}\\\implies\quad \sf x = 15⁰\\\end{gathered} \)

Answer:

3/2

Step-by-step explanation:

3 x 1/2 can be written as 3/1 x 1/2

first, you multiply the numerators, 3 and 1, and you get 3.

then, you multiply the denominators, 1 and 2, and get 2.

Therefore, the answer is 3/2

The required value of the function is 2

In the case of a function from one set to the other, each element of X receives exactly one element of Y.

The given function is of the form :

g(x) = - x² - 7

Now let us find the required values.

g (-3) = - (-3)² - 7 = 2

g (-2) = - (-2)² - 7 = -3

g (1 ) = - ( -1 )² - 7 = -6

Hence the required value of the function is 2 at x = -3 .

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Answer:

30% and $30

Step-by-step explanation:

Well  240-168 is 72

72 is  30 percent of 240  because

240* x/100 = 72

24000x=7200

x=.3

.3 is percentage is 30%

We can check by doing

240*.3= 72

there is a 30% decrease

Next question

If the total price of something is 31.20 with a 4% tax we do

x * .04 + x = 31.20

because 4% added to the price of that object is 3.20

1.04x = 31.20

x= 30

we can check by doing

30*.04+ 30= 31.2