rewrite 3 to the power of -7 using a positive exponant

Answer:

6+3n

Step-by-step explanation:

Answer: -24

Step-by-step explanation: negative times a negative is a positive times a negative is a negative

C) 537 square feet is the approximate surface area of this right prism with triangular bases.

The area or region that an object’s surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has. There are numerous shapes and dimensions in geometry, including spheres, cubes, cuboids, cones, cylinders, etc. Each form has its own volume and surface area.

Given, A right prism has a triangular base.

From the general formula of surface area

Surface area of triangle = 1/2 * base * height

The surface area of the rectangle = length * width

in our case,

Surface area of the triangle =  1/2 * base * height

Surface area of the triangle =  1/2 * 10 * 8.7

Surface area of the triangle =  1/2 * 87

The surface area of the rectangle = length * width

The surface area of the rectangle =  15 * 10

The surface area of the rectangle = 150

Since surface area of rectangle prism = 3 * area of rectangle + area of triangle * 2

Thus,

the surface area of rectangle prism =3 * 150 + 2 * 1/2 * 87

surface area of rectangle prism = 450 + 87 = 537

Therefore, 537 square feet is the approximate surface area of this right prism with triangular bases.

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Answer:

I don't know

Step-by-step explanation:

There is no expression here!

The length of the hypotenuse of an isosceles right triangle with leg lengths 5 cm will be 7 cm.

            The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between the three sides of a right triangle in Euclidean geometry. The areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse, according to this statement.

            The length of the leg of the given isosceles right triangle is 5 cm.

Using pythgorous theorem,

[tex](h^{2} ) = 5^{2} + 5^{2} \\h^{2} = 25 +25\\h^{2} = 50\\h = \sqrt{50} \\h = 7.07\\h = 7 cm[/tex]

Hence, The length of the hypotenuse will be 7 cm.

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Jamila is correct because glucose is a product, not a reactant, of photosynthesis. The correct option is C.

Jamila is right because glucose is a byproduct of photosynthesis rather than a reactant. In plants, a chemical process known as photosynthesis uses water, carbon dioxide from the atmosphere, and other reactants to produce glucose from the light energy from the sun. Plants' leaf cells are where this process takes place.

Based on the information presented above, it can be concluded that Jamila is right because glucose is a byproduct of photosynthesis rather than a reactant.

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The length of the skid marks is 336 feet

Since the formula s = √(21d) relates the speed (s) of the car and the length of skid (d).

If the car is traveling at 84 miles per hour, we can determine the length of the skid marks by substituting s = 84 into the formula and then solve for d. That is:

s = √(21d)

84 = √(21d)

84² = 21d

7056 = 21d

21d = 7056

d = 7056/21

d = 336 feet

Thus, length of the skid marks is 336 feet

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My brother, who is always pushing my buttons, keeps taking my things.

State-​ment ˈ : something stated: such as. : a single declaration or remark : assertion. : a report of facts or opinions. : the act or process of stating or presenting orally or on paper.

Here , the required answer is.

My brother, who is always pushing my buttons, keeps taking my things.

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Answer:

  ∠EHF = 99°

Step-by-step explanation:

Given ∠EHG = 176°, ∠EHF = (4y+107)°, and ∠FHG = (10y+97)°, you want the measure of angle EHF.

Angle EHG is the sum of its parts:

  ∠EHG = ∠EHG +∠FHG

  176° = (4y+107)° +(10y+97)° . . . . use the given values

  176 = 14y +204 . . . . . . . . . simplify, divide by °

  -28 = 14y . . . . . . . . . . subtract 204

  -2 = y . . . . . . . . . . divide by 14

  ∠EHF = (4y +107)° = (4(-2) +107)°

  ∠EHF = 99°

The general form of the equation for the given circle centered at O(0, 0) include the following: B. x^2 + y^2 − 41 = 0

Mathematically, the general (standard) form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²  

Where:

Next, we would determine the radius of this circle by using the distance formula as follows;

Radius, r = √[(4 - 0)² + (5 - 0)²]

Radius, r = √(16 + 25)

Radius, r = √41

Substituting the given parameters into the general form, we have;

(x - h)² + (y - k)² = r²  

(x - 0)² + (y - 0)² = (√41)²  

x² + y² = 41

x² + y²- 41 = 0

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Complete Question:

Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)?

a. x^2 + y^2 + 41 = 0

b. x^2 + y^2 − 41 = 0

c. x^2 + y^2 + x + y − 41 = 0

d. x^2 + y^2 + x − y − 41 = 0

Amount to be repaid for Bank A is $2,696.625 and Amount to be repaid for Bank B is $2,741.25. However, I will choose Bank B because it offers a lower interest rate.

The formula to calculate the simple interest is;

I = PRT

Where;

P is principal

R is rate

T is time

Now, we are given that;

Bank A;

Principal amount; P = $2550

Interest rate; R = 11.5% = 0.115

Time; t = 6 months = 0.5 years

Thus;

I = (2550 * 0.115 * 0.5)

I = $146.625

Amount to be repaid = 2550 + 146.625

Amount to be repaid = $2,696.625

Bank B;

Principal amount; P = $2550

Interest rate; R = 7.5% = 0.075

Time; t = 12 months = 1 year

Thus;

I = (2550 * 0.075 * 1)

I = $191.25

Amount to be repaid = 2550 + 191.25 = $2,741.25

Thus, bank B offers a more favorable interest rate and as such would be the preferred bank.

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A parabola with focus of (-8, 6) and a directrix of y = 0. has the equation of the parabola as (x + 5)² =  8 (y - 3)

Quadratic equation = parabolic equation, when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The focus

F (h, k + p) = (-8, 6)

h = -8

k + p = 6

P in this problem, is the midpoint between the focus and the directrix

P = (6 - 0) / 2 = 3

p = 3

the vertex

v(h, k)

h = -8

k + p = 6, k = 3

v(h, k) = v(-8, 3)

substitution of the values into the equation gives

(x - h)² =  4P (y - k)

(x - (-8))² =  4 * 3 (y - 3)

(x + 5)² =  8 (y - 3)

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The population at p(8) is 51.65 million. Option C

We know that when we talk about mathematical models, they can be able to serve the purpose of being used for predication or for the purpose of explanation.

In this case we can be able to write the model function in the form; P=3.5(1.4)x. We know that x can be said to be the the amount of decades since 1800 and we are to find P when x = 8

Hence;

P = 3.5(1.4)^(8)

P =51.65 million

Then we would have about 51.65 million people.

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Achieving your goals is hard work. If they're aligned with your values and purpose, you're probably intrinsically motivated to keep going.

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Answer:

[tex]x=7, y=-4[/tex]

Step-by-step explanation:

[tex](4x+10y)+(-4x-7y)=-12+0 \implies 3y=-12 \implies y=-4 \\ \\ 4x+10(-4)=-12 \implies x=7 \\ \\ \therefore x=7, y=-4[/tex]

The function is best described by option B direct variation; k= 5/2.

When two variables are related in a way that one is a constant multiple of the other, this is referred to as direct variation.

The direct variation is given as follows y ∝ x.

The equation is thus of the form y = kx.

Using the given values in the table:

Consider x=-2 and y= -5

Substitute the values in y=kx.

-5 = -2k

Divide both sides of the equation by -2.

[tex]\frac{-5}{-2} = \frac{-2}{-2}k \\k =\frac{5}{2}[/tex]

The equation is [tex]y=\frac{5}{2} x[/tex] [ equation 1]

Check equation 1 for a different value in the table using the constant value k.

Let x= 4 and y = 10.

[tex]y = \frac{5}{2} x\\10 = \frac{5}{2} (4) \\10 = 10[/tex]

The equation holds true; hence the function is best described by direct variation; k = 5/2.

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The only expression that cannot be simplified using the quotient rule for exponents is; Option D: q⁻⁵r¹¹ / s⁷t⁻¹⁵

The quotient rule for exponents states that when dividing two numbers with exponents, the exponents can be subtracted when the bases are the same. For example, xᵃ/xᵇ = xᵃ⁻ᵇ

A) (3²)(9⁻¹)(2³)/(8⁵)(7⁻²)

This can be re-expressed in terms of factors as;

(3²)(3⁻²)(2³)/((2³)⁵)(7⁻²)

= (3²⁻²)/((2³)⁴(7⁻²))

= 1/(8⁴(7⁻²))

B) (4⁻²)(x⁻¹)/(4⁻¹)(x⁻²)

Using quotient rule, we have;

(4⁻²⁺¹)(x⁻¹⁺²)

= (4⁻¹x⁻¹)

C) (6x⁻⁸z²)(6⁵x⁻¹z²)

Using quotient rule, we have;

x⁻⁷/6⁴

D) q⁻⁵r¹¹ / s⁷t⁻¹⁵

We don't have any similar variable as numerator or denominator and as such this cannot be simplified using quotient rule of exponents.

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In 6 years, the car's depreciated value that Dan buys for £2,200 will be £1,474 under the straight-line depreciation method.

The straight-line depreciation is one of the depreciation methods in use.

Other depreciation methods include the sum-of-the-years' digits, the double-declining balance method, and the unit-of-production method.

Under the straight-line depreciation method, the same amount is used to reduce the value of the car.

The cost of the car when Dan buys it = £2,200

The annual rate of depreciation = 0.5% = 0.005

The depreciation period = 6 years

The annual depreciation under the straight-line method = £11 (£2,200 x 0.5%)

The depreciated value of the car after 6 years = £1,474 (£2,200 - £11 x 6)

Thus, Dan's car will be worth £1,474 after 6 years of depreciation.

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Answer:

the answer will be 6

Step-by-step explanation:

The term that describe point M in the diagram is centroid.

A triangle is a given shape which have three number of sides, and three measures of internal angles. Some types of triangle are; isosceles, equilateral, scalene, right angled etc.

Constructing an angle bisector to each of its internal angles will produce an intersecting point which is referred as centroid. The centroid of a triangle is a point where the medians of the triangle meet. The medians of a triangle are the straight lines that bisect each of its internal angle.

Therefore it can be deduced from the given diagram that the term that describes point M is centroid.

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The length of the diagonal between the two sides, given the measurement of each side, is 20.

When given the lengths of two sides, the diagonal can be found by summing the squares of the sides and then finding the square root of the sum of these two numbers.

The sum of the squares is therefore :

= 12 ² + 16 ²

= 12 x 12 + 16 x 16

= 144 + 256

= 400

Then find the square root of this sum as this is the length of the diagonal between the two sides :

= √ sum of squares of sides

= √ 400

= 20 units

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The relationships that represent functions include the following:

Table B.

Mapping diagram C.

In Mathematics, a function is typically used in mathematics for uniquely mapping an input variable (domain or independent value) to an output variable (range or dependent value).

This ultimately implies that, an independent value represents the value on the x-axis of a cartesian coordinate while a dependent value represents the value on the y-axis of a cartesian coordinate.

Since the independent value (3) has multiple dependent values, the relation does not represent a function. Additionally, the second table represents a function because the independent value) and dependent value have unique values.

Lastly, the first mapping diagram represents a function because the independent values and dependent values are uniquely mapped as follows;

4 ⇒ 0

5 ⇒ 2

6 ⇒ 2

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The volume of the cone is 12π or 37.70 cm²

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.

The volume of a cone is given by the equation

Volume of Cone = ( 1/3 ) πr²h

where r is the radius of the cone

h is the height of the cone

Given data ,

Let the volume of the cone be represented as V

Now , the equation will be

Let the length of the cone be S = 5 cm

Let the height of the cone be = H

Let the radius of the cone be R = 3 cm

From the Pythagoras theorem , S² = H² + R²

So, substituting the values in the equation , we get

Height of the cone H = √5² - 3²

Height of the cone H = √25 - 9

Height of the cone H = √16

Height of the cone H = 4 cm

Now , the volume of the cone = ( 1/3 ) πR²H

Substituting the values in the equation , we get

Volume of the cone V = ( 1/3 ) x π x ( 3 )² x 4

On simplifying the equation , we get

Volume of the cone V = 3 x 4 x π

Volume of the cone V = 12 π

Volume of the cone V = 37.70 cm²

Therefore , the value of V is 37.70 cm²

Hence , the volume of cone is 12π or 37.70 cm²

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The  ()₁ = −()₂ and obtain tension is T=11.20 kips.

When two or more real things come in contact with one another, forces are applied between them. We refer to these contact forces by various names depending on the objects in contact. We refer to the force as tension if one of the items in contact is a string, rope, cable, or spring.

Given

It appears that there are two design factors to take into account. The largest bending moment is one at point E. Once this information is understood, the size and material/joint choices for column DBE may be made (a decision regarding how deeply the steel column should be buried in the ground can be made later).

concrete dock to prevent failure at point E as a result of bending moment).

The maximum tension in the wire ADCF is the other metric we need to monitor. The column at point E's maximum bending moment can actually be reduced with proper cable tensioning.

Using an Excel spreadsheet to determine the necessary tension in the cable ADCF when the maximum bending moment at point E is minimised is one of the most crucial elements in solving this design problem.

The detailed solution is

:

∑ = 0:   − (3.75) + 3600 + 1200(6.5) = 0

Simplifying Eqn. we have

= (3.75) − 3600 − 7800

For x=1.5 ft, we have

()₁ = (3.75) − 3600(1.5) − 7800

For x=17.5 ft, we have

()₂ = (3.75) − 3600(17.5) − 7800

Therefore, the final solution for the problem becomes,

For the smallest max value of ,

we set ()₁ = −()₂ and obtain T=11.20 kips

Hence the  ()₁ = −()₂ and obtain T=11.20 kips.

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The amount earned on average each day is $160.

From the information, James worked for 12 consecutive days, during the first 6 days, James averaged $140 per day, his average wage for the next 5 days was $175, and for the last day, he earned $205.

It should be noted that average is also the mean. This will be calculated as:

(6 × $140) + ($175 × 5) + $205 / 12

= $840 + $875 + $205 / 12

= $1920 / 12

= $160

The average amount is $160.

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Answer:

To calculate Almaz's typing rate in words per minute, you can divide the number of words she typed by the number of minutes it took her.

First, you'll need to convert the number of hours Almaz spent typing into minutes. You can do this by multiplying the number of hours by the number of minutes per hour. There are 60 minutes in an hour, so if Almaz spent 3.5 hours typing, she spent 3.5 * 60 = <<3.5*60=210>>210 minutes typing.

Then, to calculate Almaz's typing rate, you can divide the number of words she typed by the number of minutes it took her: 9050 words / 210 minutes = <<9050/210=43>>43 words per minute.

So Almaz's typing rate was approximately 43 words per minute.

Step-by-step explanation:

Answer:

To find the number of times that Aria's commute is between 32 and 35 minutes, we need to find the probability that her commute time is between 32 and 35 minutes and then multiply that probability by the total number of commutes per year.

To find the probability that Aria's commute time is between 32 and 35 minutes, we need to find the area under the normal curve between those two values.

We can use the following formula to convert the values 32 and 35 to standard units:

z = (x - mean) / standard deviation

Plugging in the values, we get:

z1 = (32 - 28) / 4.5 = 0.89

z2 = (35 - 28) / 4.5 = 1.56

To find the area under the curve between these two values, we can use a standard normal table or a calculator to find the area between these two values. The result is approximately 0.22.

Multiplying this probability by the total number of commutes per year gives us the number of times that Aria's commute is between 32 and 35 minutes.

So the number of times that Aria's commute is between 32 and 35 minutes is approximately 262 * 0.22 = 57.24, which is about 57 times to the nearest whole number.

Step-by-step explanation:

The scale factor of dilation of the 10 cm by 10 cm picture to produce the 4 m by 4 m copy on the wall indicates that the dimension of the copy of the 1 cm by 1 cm box on the wall is 40 cm.

A scale factor is the factor or number of times by which the size of a pre-image is reduced or increased.

Possible parts of the question includes;

Dimensions of the picture = 10 cm × 10 cm

The dimensions of the wall = 4 m × 4 m

The dimensions of each box in the picture = 1 cm × 1 cm

The dimensions of each box on the wall are found as follows;

The linear scale factor of the picture to the copy of the picture on the wall is; 10 cm ≡ 4 m

Therefore; 1 cm ≡ (4/10) m = 0.4 m

1 centimeters is to 0.4 meters son the wall

10 cm on the picture is equivalent to 4 meters on the wall

Therefore;

(10 cm)/10 = 1 cm on the picture is equivalent to (4 m)/10 = 0.4 m on the wall

1 meters = 100 centimeters

The dimension of the box on the wall is therefore; 40 cm × 40 cm

The best correct option is; 40 cm

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The kite have a measure of the angle m∠WXY = 116°.

A kite is a quadrilateral which implies the sum of its interior angles is equal to 360°.A kite is symmetrical about its main diagonal and the angles where the adjacent pairs of sides meet are equal.

m∠XYW = 23°

m∠ZWY = 41°

m∠XYZ = 2 × 23° {main diagonal bisect m∠XWZ}

m∠XYZ = 46°

m∠XWZ = 2 × 41° {main diagonal bisect m∠XYZ}

m∠XWZ = 82°

m∠WXY = m∠WZY

2(m∠WXY) = 360° - (82° + 46°) {sum of interior angles of a quadrilateral}

2(m∠WXY) = 360° - 128°

2(m∠WXY) = 232° {divide through by 2}

m∠WXY = 232°/2

m∠WXY = 116°

In conclusion, the kite have the measure of the angle m∠WXY = 116°

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