The area of the two rectangles is given by the functions:

Area of Rectangle A: f(x) = 4x2 + 6x

Area of Rectangle B: g(x) = 3x2 – x

Which function represents the difference, h(x) = f(x) – g(x), in the areas of the rectangles shown?

h(x) = 7x2 – 5x
h(x) = x2 – 7x
h(x) = x2 + 5x
h(x) = x2 + 7x

Answer:

55

Step-by-step explanation:

So we have the expression:

\(6x-5\)

And we want to find the value when x is 10. So, substitute 10 for x:

\(=6(10)-5\)

Multiply:

\(=60-5\)

Subtract:

\(=55\)

And we're done!

Set flour =x and onions=y

We have

{ x + y = 3.25

{ 3x + 2y = 9

x= \(\frac{5}{2}\)

y=\(\frac{3}{4}\)

Good Luck

Answer:

1) consecutive interior angle

2)alternate interior

3)corresponding angles

4)alternate exterior angles

5)corresponding angles

Step-by-step explanation:

Answer:

7.74 yd²

Step-by-step explanation:

Answer:

7.74 yd²

Step-by-step explanation:

The shaded area can be calculated by subtracting the area of the circle from the area of the square.

Given:

Area of the square = side length × side length

                               = 6 × 6

                               = 36 yd²

Area of the circle = πr²

                             = 3.14 × 3²

                             = 28.26 yd²

Shaded area = area of square - area of circle

                      = 36 - 28.26

                      = 7.74 yd²

Answer:

Eliza reads a total of 204 pages in the three days combined.

Step-by-step explanation:

From the given information, we are being told that:

Eliza reads \(\dfrac{1}{7}\) of her book on Monday.

On Tuesday and Wednesday combined, she reads thrice as much as she read on Monday.

Let assume that; Tuesday = T and Wednesday = W

Then;

\(T + w = 3 ( \dfrac{1}{7})\)

The expression to determine the total number of pages is given as:

\(\large \dfrac{1}{7}r+3\left(\dfrac{1}{7}r\right)\)

where;

r = total number of pages in the book.

Assuming that Eliza book contains a total of 357 pages. How many pages does she read in the three days combined together.

i.e.

r = 357

Then;

\(\implies \large \dfrac{1}{7}(357)+3\left(\dfrac{1}{7}(357)\right)\)

\(\implies 51+3(51))\)

\(\implies 51+153\)

= 204 pages

Thus, Eliza reads a total of 204 pages in the three days combined.

Answer:

88

Step-by-step explanation:

Answer:

A carpenter has a 64cm strip of wood and another 80cm. If you want to cut them into the maximum number of equal pieces without wasting material. How long should each piece of wood be?

Answer:

9units²

Step-by-step explanation:

A triangle has 3 sides. Let the length of the three sides be a, b, c.

If the perimeter of the triangle is 18, then;

P = a+b+c

a+b+c = 18... 1

If the sum of the squares of the three side lengths is 128, this means;

a²+b²+c² = 128... 2

Since the triangle is also right angled, according to Pythagoras theorem;

c² = a²+b²... 3 (taking c as the hypotenuse)

Substitute equation 3 into 2;

(a²+b²)+c² = 128

c²+c² = 128

2c² = 128

c² = 128/2

c² = 64

c = √64

c = 8

Substituting c = 8 into 1

a+b+c = 18

a+b+8=18

a+b = 10 ...... 3

Substituting c = 8 into 2

a²+b²+c² = 128

a²+b²+8² = 128

a²+b²+64 = 128

a²+b²= 64..... 4

Solve equation 3 and 4 simultaneously;

a+b = 10

a²+b²= 64

From 4; a = 10-b

Substitute a = 10-b into 4;

(10-b)²+b² = 64

100-20b+b²+b² = 64

2b²-20b+100-64 = 0

2b²-20b+36 = 0

Divide through by 2:

b²-10b+18 = 0

b = 10±√10²-4(18)/2

b = 10±√100-72/2

b =( 10±√28)/2

b =(10±√4×7)/2

b = (10±2√7)/2

b = 5±√7

Hence b = 5+√7

If a+ b = 10

a+(5+√7 ) = 10

a = 10-(5+√7)

a = 10-5-√7

a = 5-√7

Area of the triangle A = 1/2 ab

A = 1/2 × (5+√7) × (5-√7)

A = 1/2 × (25-5√7+5√7-7)

A = 1/2 × (25-7)

A = 1/2 × 18

A = 9

Hence the are of the triangle is 9units²

9514 1404 393

Answer:

  (a) The function that is represented by the equation y=-10x+6 has a steeper slope and a greater y-intercept

Step-by-step explanation:

If we take the "steepness" of the slope to be the absolute value of the slope, then the line y=-10x +6 has a slope with a steepness of 10.

The line y -36 - 8(x -4) has a slope with a steepness of 8, so the first line is steeper.

The line y=-10x+6 has a y-intercept of 6. The line y-36 =8(x -4) has a y-intercept of 4, so the first line has a higher y-intercept.

The appropriate description of the two lines is ...

  The function that is represented by the equation y=-10x+6 has a steeper slope and a greater y-intercept

SSS is the correct response because two triangles are considered to be congruent when all three of their respective sides and all three of their corresponding angles have the same measure.

Triangles that really are precisely the same in size and shape are said to be congruent. The symbol is in the term congruent. Two triangles are said to have been congruent when the three sides as well as three angles of one triangle have the identical dimensions as the three sides as well as three angles of another triangle.

Write the names of the vertices as shown below, starting with triangle DAB and triangle BCD.

AB = CD

DA = BC

The sides BD are identical in both triangles, so,

BD = BD

Since the triangles DAB and BCD have the same three sides, we may infer that they are congruent using the SSS property of a congruent triangle.

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Answer:

x=−1

x=−1.5

:DDDD

Answer:

B. -h

Step-by-step explanation:

Additive inverses are two numbers that add to 0.

h + (-h) = 0

-h is the additive inverse of h since h and -h add to 0.

Answer: B. -h

Answer:

-h

Step-by-step explanation:

The additive inverse of a number simply means that same number, but with an opposite sign. For example:

Additive inverse of 9 = -9

Additive inverse of -2 = 2

Additive inverse of -(-6) = -6

Additive inverse of -(+4) = 4

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b. This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

To find the equation for the tangent plane to the graph of the function f(x, y) = 2e^x - y at a given point (x0, y0), we need to calculate the partial derivatives of f with respect to x and y at that point.

The partial derivative of f with respect to x, denoted as ∂f/∂x or fₓ, represents the rate of change of f with respect to x while keeping y constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y or fᵧ, represents the rate of change of f with respect to y while keeping x constant.

Let's calculate these partial derivatives:

fₓ = d/dx(2e^x - y) = 2e^x

fᵧ = d/dy(2e^x - y) = -1

Now, we have the partial derivatives evaluated at the point (x0, y0). Let's assume our point of interest is (a, b), where a = x0 and b = y0.

At the point (a, b), the equation for the tangent plane is given by:

z - f(a, b) = fₓ(a, b)(x - a) + fᵧ(a, b)(y - b)

Substituting fₓ(a, b) = 2e^a and fᵧ(a, b) = -1, we have:

z - f(a, b) = 2e^a(x - a) - (y - b)

Now, let's substitute f(a, b) = 2e^a - b:

z - (2e^a - b) = 2e^a(x - a) - (y - b)

Rearranging and simplifying:

z = 2e^a(x - a) - (y - b) + 2e^a - b

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b.

This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

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Answer:

Step-by-step explanation:

x=5

Mark is 12 years old now,in 4 years time he will be 16.

Let Mark's present age be m years and Jane's present age be n years.

10 years ago, Jane was twice as old as Mark is now.

So, we get an equation

n - 10 = 2m               ...........(1)

In two years Jane will be three times as old as Mark is now.

So, we get an equation

n + 2 = 3m                   ............(2)

We need to find Mark's age after 4 years.

From equation (1),

n = 2m + 10                 .........(3)

Substitute the value of n in equation (2),

(2m + 10) + 2 = 3m

2m + 12 = 3m

m = 12

After 4 years Mark's age would be,

m + 4 = 12 + 4

         = 16 years

Therefore, in 4 years time Mark will be 16.

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Answer:

-4

Explanation:

Given any quadratic function of the form:

Its discriminant is obtained by using the formula:

Comparing our given equation with the form of a quadratic above, we have:

Therefore, the discriminant will be:

The value of the discriminant for the given quadratic is -4.

Answer:

APR, or annual percentage rate, is your interest rate stated as a yearly rate. An APR for a loan can include fees you may be charged, like origination fees. APR is important because it can give you a good idea of how much you'll pay to take out a loan.

Answer:

a rotation of 180° about point (0.5, -0.5) followed by a dilation of 0.5

Step-by-step explanation:

A sequence is arithmetic sequence when the first differences are all the same non-zero number.

An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a defined number. The common difference of the series, which is a constant value, is the same for all following pairs of terms.

As a result, a sequence can be said to be arithmetic if its first differences all contain the same non-zero value. For instance, the arithmetic sequence 3, 6, 9, 12, 15,... has a common difference of 3.

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Answer:

19

Step-by-step explanation:

If a=17, then:

2 + 17 = 19

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Have a great summer :)

Answer:

The answer to your problem is, D. $13,564.80

Step-by-step explanation:

We know it took her 4 years to pay this amount. Let's solve for the total amount she paid including the interest.

12,560 x 0.02 = 251.2 per year

251.2 x 4 = 1004.8 dollars for 4 years.

1004.8 + 12,560 = 13,564.8 dollars.

Thus the answer to your problem is, D. $13,564.80

Answer:

Step-by-step explanation:

Distribute 2/5 through the parentheses

2/5x-4/5=-1

multiply both sides by 5

2x-4=-5

move the constant to the right and change the sign

2x=-5+4

add the sum

2x=-1

divide both sides by 2

x=-1/2

Answer:

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Step-by-step explanation:

Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line.

The amount invested in bonds when total of 33,000 is being invested in a local bank is 13200.

Let the amount invested in bond = x

The amount invested in stocks is one half of the amount invested in bonds. This will be:

= 1.5 × x = 1.5x

Therefore, the expression will be:

Stock + Bond = 33000

1.5x + x = 33000

2.5x = 33000

Divide

x = 33000 / 2.5

x = 13200

The amount is 13200.

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The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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Answer:

0.17 per ounce

Step-by-step explanation:

To find the price per ounce, divide the price by the number of ounces.

price/ number of ounces

A 2 pound bag costs $5.44. We need to find out how many ounces are in 2 pounds.

Each pound has 16 punches. Therefore, 2 pounds will have 32 ounces (16 ounces * 2 pounds=32 ounces).

Now we can find the price per ounce by dividing the price by the number of ounces.

price/ounces

We know the bag is 2 pounds, which is equal to 32 ounces. We also know the bag costs $5.44

price= $5.44

ounces= 32 ounces

$5.44/ 32 ounces

$0.17 / ounces

The asparagus costs 0.17 per ounce.

The equivalent of 0.85 hectogram (hg) is 850 decigram (dg)

The measure is given as:

0.85 hg

As a general rule:

1 hectogram (hg) = 1000 decigram (dg)

So, multiply both sides of the above equation by 0.85

So, we have:

0.85 * 1 hectogram (hg) = 0.85 * 1000 decigram (dg)

Evaluate the product

0.85 hectogram (hg) = 850 decigram (dg)

Hence, the equivalent of 0.85 hectogram (hg) is 850 decigram (dg)

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Answer:

S = 14.14

Step-by-step explanation:

The area of a square is S*S or S^2.

So, if we know that the area of the square patio is 200, we can say that

S^2 = 200.

S = sqrt(200)

S = 14.14 ft.

Answer:

(Choice B) B 10 ( h + 3 + 5 j ) 10(h+3+5j)10, left parenthesis, h, plus, 3, plus, 5, j, right parenthesis

(Choice C) C 2 ( 5 h + 15 + 25 j ) 2(5h+15+25j)2, left parenthesis, 5, h, plus, 15, plus, 25, j, right parenthesis

Step-by-step explanation:

10h+30+50j

There are two answers

First answer

Factorise using 10 as common factor

10h+30+50j

=10(h+3+5j)

(Choice B) B 10 ( h + 3 + 5 j ) 10(h+3+5j)10, left parenthesis, h, plus, 3, plus, 5, j, right parenthesis

Second answer

Factorise using 2 as the common factor

10h+30+50j

=2(5h+15+25j)

(Choice C) C 2 ( 5 h + 15 + 25 j ) 2(5h+15+25j)2, left parenthesis, 5, h, plus, 15, plus, 25, j, right parenthesis

Answer: Choice B and C

Step-by-step explanation: