Some months have 30 days, some months have 31 days; how many have 28?

Answer:

x = 3

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠QRT is an exterior angle of the triangle

∠RTS and ∠RST are the 2 opposite interior angles, thus

45x = 25x + 57 + x

45x = 26x + 57 ( subtract 26x from both sides )

19x = 57 ( divide both sides by 19 )

x = 3

Answer:

The oven mitts cost

$13.80

But, Cook-n-Serve buys from a wholesaler, so they receive a discount of 40%

This means that they pay

(1-0.4)*($13.80) = 0.6*($13.80) = $8.28 for each pair

The markup rate on cost is 60%

And they sell for

$13.80/$8.28 = 1.67 times the price

1.67*100% = 167%

The markup rate on selling price is  167%

Answer:

x = 6

Step-by-step explanation:

Given the 2 equations

x - y = 4 → (1)

x + y = 8 → (2)

Adding the 2 equations term by term eliminates the y- term

(x + x) + (- y + y) = (4 + 8), that is

2x = 12 ( divide both sides by 2 )

x = 6

Answer:

r = 3

Step-by-step explanation:

The common ratio r of a geometric sequence is the ratio between consecutive terms, that is

r = [tex]\frac{4}{\frac{4}{3} }[/tex] = 3

r = 12 ÷ 4 = 3

r = 36 ÷ 12 = 3

Answer:

1152

Step-by-step explanation:

First we need to find the area of the wall in square inches

8 ft = 8*12 = 96 inch tall

36 ft = 36 * 12 = 432 inches wide

The area = 96 * 432 =41472 in^2

Each ounce of paint cover 72 in^2 so divide by 72

41472/72 =576

We need 576 ounces to cover the wall

At 2 dollars per ounces

576*2 =1152 dollars to paint the wall

The coordinates of the point A before dilation is (-12,-12)

Answer:

2

Step-by-step explanation:

1/2 is the same as saying 0.5

0.5 x 4     is the same as saying      0.5 + 0.5 + 0.5 + 0.5

0.5 + 0.5 + 0.5 + 0.5 = 2

Answer:

0.009 units in the positive y direction.

Step-by-step explanation:

Vertical shift is simply the value of the constant.

In this case, if you expand the formula by multiplying 0.9 into the parentheses,

y = 0.9 sin [(π/3) - x] + (0.9)(0.01)

y = 0.9 sin [(π/3) - x] + 0.009

Here the value of the constant is 0.009 and it is positive, hence the vertical shift is 0.009 units in the positive y direction.

Answer:

[tex]36\ m[/tex]

Step-by-step explanation:

Let

x -----> the distance of Ana from the kite

we know that

Applying the law of sines

[tex]\frac{46}{sin(109\°)}=\frac{x}{sin(47\°)}\\ \\x=(46)sin(47\°)/sin(109\°)\\ \\x=35.58\ m[/tex]

round to the nearest meter

[tex]35.58=36\ m[/tex]

Answer: I make 15 dollars every week at my job

Step-by-step explanation: your x is likely representing a time like weeks and your y is most likely going to be the amount of something like money. so if x increases by one every time and y increases by 15 every time your scenario could be i make 15 dollars every week at my job.

All real numbers.

[tex]\boxed{TRUE}[/tex]

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

Expand: 4(a+2)=4a+8

Expand again: 14-2(3-2a)=4a+8

4a+8=4a+8

You subtract by 8 from both sides of an equation.

4a+8-8=4a+8-8

Simplify.

4a=4a

Then, subtract by 4a from both sides of an equation.

4a-4a=4a-4a

Finally, simplify.

4a-4a=0

0=0

True

All real numbers is the final answer.

Hope this helps you!

Have a nice day! :)

Answer:

The reflected point is (3,6)

Step-by-step explanation:

we know that

The reflection Ry = 5, means a reflection is across the line y= 5

we have

the point P(3,4)

Since the point P has y-coordinate  4, its distance to the line y= 5 is equal to 1 units (P is located 1 units down the line y=5).

therefore

The reflection of the y-coordinate will be 1 units above the line y=5, which is  equal to

5+1=6

Hence

the y-coordinate of the image is 6.

The reflected point is (3,6)

To reflect a point about the y-axis, negate the x-coordinate while keeping the y-coordinate the same.

In this question, you are given the point P(3,4) and asked to find Ry=5(P). The notation Ry=5(P) represents the reflection of point P about the y-axis. To reflect a point about the y-axis, you need to replace the x-coordinate with its opposite (negate it) while keeping the y-coordinate the same.

So, P(3,4) reflected about the y-axis becomes (-3,4). The x-coordinate changes from 3 to -3, but the y-coordinate remains the same at 4.

Therefore, Ry=5(P) is (-3,4).

Answer:

843.67

Step-by-step explanation:

896 is the original price

A 12% discount will be applied so what is 12% of 896 =.12(896)=107.52

So we started with 896 and we are taking off 107.52=896-107.52=788.48

So the price after the discount is 788.48.

Now to apply the tax which is 7%=.07  so we need to find 7% of 788.48=.07(788.48)=55.19 (This is the tax dollar amount to be added to the price before tax).

So Sara is paying 788.48+55.19=843.67

Answer:

843.67

Step-by-step explanation:

Take the original price and find the discount

896 * 12 %

896 * .12

107.52

The new price is the original price minus the discount

896-107.52

788.48

Now we need to find the tax on the sale price

788.48 * 7%

788.48 *(.07)

55.19

Add the sale price and the tax to find the total price

788.48 +55.19

843.67

The expressions (x-5)/(x+3) and 4/(x-3) can be rewritten with a common denominator of (x+3)(x-3) to become ((x-5)(x-3))/((x+3)(x-3)) and 4(x+3)/((x+3)(x-3)).

The expressions stated are: (x-5)/(x+3) and 4/(x-3). In order to rewrite these expressions with a common denominator, you need to multiply the denominators together to create a common denominator. Therefore, the common denominator would be (x+3)(x-3).

Next, each expression must be rewritten so that they have this common denominator. For the first expression, we multiply the numerator and denominator by (x-3) so we get: ((x-5)(x-3))/((x+3)(x-3)).

For the second expression, we multiply the numerator and denominator by (x+3) so we get: 4(x+3)/((x+3)(x-3)). So, the expressions rewritten with a common denominator are ((x-5)(x-3))/((x+3)(x-3)) and 4(x+3)/((x+3)(x-3)).

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To find a common denominator for the given expressions, multiply the denominators together. The expressions, rewritten with the common denominator, are [tex](x-3)*(x-5)/(x+3)(x-3)[/tex] and [tex]4*(x+3)/(x+3)(x-3).[/tex]

The goal here is to find a common denominator for the expressions x-5/x+3 and 4/x-3. A common denominator can be found by multiplying the denominators of both expressions together. So for these expressions, the common denominator would be [tex](x+3)*(x-3).[/tex]

Then you multiply the top and bottom of each fraction by the missing factor from the other denominator. The expressions rewritten with a common denominator would then be:

So the expressions with a common denominator are: [tex](x-3)*(x-5)/(x+3)*(x-3)[/tex]and [tex]4*(x+3)/(x+3)*(x-3).[/tex]

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Answer:

length=1.05m

perimeter=2.7m

Step-by-step explanation:

18900 in m^2=1.89 m^2

area=length*width

1.89=length*1.8 m

length=1.89÷1.8

length=1.05 m

perimeter=(l+w) 2

perimeter=(1.05+1.8)2

perimeter=2.85×2

perimeter=2.7 m

a. The rectangular backboard’s length in meters is 1.05 meters.

b. The perimeter of the total area in meters is 5.7 meters.

Given the following data:

Conversion:

10,000 [tex]cm^{2}[/tex] = 1 [tex]m^2[/tex]

18,900 [tex]cm^{2}[/tex] = X [tex]m^2[/tex]

Cross-multiplying, we have:

[tex]X = \frac{18900}{10000}[/tex]

X = 1.89 [tex]m^2[/tex]

a. To find the backboard’s length in meters:

Mathematically, the area of a rectangle is given by the formula;

[tex]A = LW\\\\1.89 = L(1.8)\\\\L = \frac{1.89}{1.8}[/tex]

Length, L = 1.05 meters.

b. To find the perimeter of the total area in meters:

Mathematically, the perimeter of a rectangle is given by the formula;

[tex]Perimeter = 2(L+W)[/tex]

Substituting the values into the formula, we have;

[tex]Perimeter = 2(1.05+1.8)\\\\Perimeter = 2(2.85)[/tex]

Perimeter = 5.7 meters

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Answer:

25 m

Step-by-step explanation:

Use the Pythagorean Theorem.

a^2+b^2=c^2

Or just know you are finding the hypotenuse and use c=sqrt(a^2+b^2)

If you were finding a leg use a=sqrt(c^2-b^2).

So sqrt(15^2+20^2)

=sqrt(225+400)

=sqrt(625)

=25

To find the midpoint, add the 2 x values together and divide by 2, then add the 2 Y values together and divide by 2.

(5-13)/2, (-4+12)/2

-8/2 , 8/2

-4,4

The answer is (-4,4)

ANSWER

[tex]p = - 3[/tex]

The completely factored form is

[tex](x + 1)(x - 1)( 3x - 1)[/tex]

EXPLANATION

The given polynomial expression is

[tex]3 {x}^{3} - {x}^{2} + px + 1[/tex]

Let

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

According to the Remainder Theorem, if f(x) is exactly divisible by x-1, then the remainder is zero.

This implies that:

[tex]f(1) = 0[/tex]

[tex]3 {(1)}^{3} - {(1)}^{2} + p(1)+ 1 = 0[/tex]

[tex]3 - 1 + p + 1 = 0[/tex]

[tex]3 + p = 0[/tex]

[tex]p = - 3[/tex]

When we substitute the value of p back into the function, f(x) we get:

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

We now perform long division as shown in the attachment.

We can factor the function to get:

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

We now split the middle term of the quadratic term and factor it completely to obtain:

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

[tex]f(x) =(x - 1)( 3x(x + 1) - 1(x + 1))[/tex]

[tex]f(x) =(x - 1)( 3x - 1)(x + 1) [/tex]

[tex]f(x) =(x + 1)(x - 1)( 3x - 1)[/tex]

Answer:

2 whole 1/4

Step-by-step explanation:

When forming a perfect square trinomial you need to "complete the square".

All of the steps to completing the square when solving an equation:

1.  The leading coefficient must be 1.  

2.  Divide b by 2.

3.  Square (b/2)

4.  Add (b/2)^2 to both sides to keep the polynomial balanced.

5.  You can now write the perfect square trinomial and solve.

x^2 - 3x  

-3/2

(-3/2)^2 = 9/4 = 2 1/4

Answer:

The answer is 2 1/4

Step-by-step explanation:

You are welcome.

Answer:

Step-by-step explanation:

X²=12x-40

X²-12x+40=0

a=1  and b= -12 and c = 40

delta = b² - 4ac

delta = (-12)² - 4(1)(40) = 144 - 160 = - 16 = (4i)² ....i² = -1

x1= (12-4i)/2 =6-2i

x1= (12+4i)/2 =6+2i

Answer:

Step-by-step explanation:

x^2 = 12 x-40

x² - 12x + 40 = 0

a = 1;  b = -12; c = 40

4ac - b² = 4*1*40 - (-12)² = 160 - 144 = 16

x = -b ± √4ac-b² i / 2a

 = -(-12) ± √ 16 i

          2 * 1

= (12 ± 4 i )/ 2

= 2( 6 ±  2i)

        2

=   6 ±  2i

Answer:

d.no change

Step-by-step explanation:

There will be no change in the quantity of products sold.

Option D will be the correct answer.

Given that the turnover is increased by 10 % when the price increases by 10 %.

Let us consider that the price of the product is x and the quantity sold is n numbers. Then the turnover t will be given as,

[tex]t = x\times n[/tex]

An increase in the price of the product is 10 % results in an increase in turnover by 10%. Hence the increased price is,

[tex]x' = x+\dfrac{10}{100}\times x[/tex]

[tex]x' = 1.1 x[/tex]

Hence new turnover will be,

[tex]t'= x\times n + \dfrac {10}{100} \times x\times n[/tex]

[tex]t'= 1.1\times x\times n[/tex]

The quantity sold can be calculated by dividing the new turnover by the increased price of the product. Thus, the new quantity of the product will be,

[tex]n' = \dfrac {t'}{x'}[/tex]

[tex]n' = \dfrac {1.1\times x\times n}{1.1\times x}[/tex]

[tex]n' =n[/tex]

We can see that the quantity of the product sold remains unchanged.

Hence option D will be the correct answer, there will be no change in the quantity of product sold.

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Answer:

That is < 3.

Step-by-step explanation:

It is the angle between the (dotted)  horizontal  from B and the line going B and C.

Answer:

Exponential growth is called growth because its curve increases really fast, so that's the main characteristic of exponential growth. I'm attaching an example of a function with exponential growth, which is the change of population size over time.

[tex]y=2^{\left(x-2\right)}+3[/tex]

To solve this problem, we need to start with the parent function of the exponential function, which is [tex]f(x)=a^x[/tex], where [tex]a[/tex] is the base. In our problem, [tex]a=2[/tex], so our parent function here is [tex]y=2^x[/tex]. Then, we need to perform some transformations to our parent function. Thus:

1. Vertical shrink:

A vertical shrink is a nonrigid transformation because the graph of the function get a distortion in the shape, so this transformation is as follows:

[tex]g(x)=cf(x)[/tex]

where [tex]c[/tex] in this problem equals 0.25 because:

[tex]y=0.25(2^x) \\ \\ y=\frac{1}{4}(2^x) \\ \\ y=\frac{2^x}{2^2} \\ \\ y=2^{(x-2)}[/tex]

2. Vertical shift:

The graph of the function [tex]y=2^{(x-2)}[/tex] get a vertical shift given by:

[tex]y=2^{(x-2)}+3[/tex]

So the graph is shifted 3 units up. So the result is the graph shown above.

Answer:

The answer is C

Step-by-step explanation:

Answer:

5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The geometric mean of 2 numbers a and b is

[tex]\sqrt{ab}[/tex]

Hence

The geometric mean of 5 and 10 is

[tex]\sqrt{5(10)}[/tex]

= [tex]\sqrt{50}[/tex]

= [tex]\sqrt{25(2)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{2}[/tex] = 5[tex]\sqrt{2}[/tex]

Answer:

7.071

Step-by-step explanation:

To find geometric mean of two numbers given , you multiply numbers then find the square root of the result.

For this question we have  the numbers given as 5 and 10. So multiply 5 by 10 then get the square root of the answer.

[tex]=5*10=50\\\\\\\\\sqrt{50} =7.071[/tex]

ANSWER

[tex]y = 2x - 8[/tex]

EXPLANATION

To find the equation of a straight line, we need the slope and a point on that line.

We were given the equation of another line that will help us determine the slope . The given line has equation:

[tex]y = 2x + 4[/tex]

This equation is of the form

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

where

[tex]m = 2 \: \: is \: the \: \: slope.[/tex]

Since our line of interest is parallel to this line, their slopes are the same.

The line also contains the point (3,-2).

So we substitute the slope and point into the slope-intercept formula:

[tex] - 2= 2(3)+ b[/tex]

[tex] - 2 =6 + b[/tex]

[tex] \implies \: b = - 2 - 6 = - 8[/tex]

The required equation is

[tex]y = 2x - 8[/tex]

Final answer:

The equation of a line parallel to y = 2x + 4 and passing through the point (3, −2) is y = 2x − 8.

Explanation:

To find the equation of a line parallel to line AB with the equation y = 2x + 4 that passes through the point (3, −2), we need to use the fact that parallel lines have the same slope. Line AB has a slope of 2, so our new line will also have a slope of 2. Now, we use the point-slope form of a line: y − y1 = m(x − x1), where (x1, y1) is the point the line passes through and m is the slope. Substituting our point and slope in, we get y − (−2) = 2(x − 3). Simplifying, we get y + 2 = 2x − 6, and after moving the 2 to the other side, the final equation in slope-intercept form is y = 2x − 8.

Answer:

Yhe equation that jas the steepest gradient is D

Step-by-step explanation:

look at the numbers infront of the 'x' without looking at the negative sign. The

larger the number the steeper the gradient. Negative gradient only means that it is a downward slope

Answer:

Step-by-step explanation:

D

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x-1}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\\text{We have the slope}\ m=\dfrac{1}{4}\ \text{and the y-intercept}\ (0,\ -1)\to b=-1.\\\\\text{Substitute:}\\\\y=\dfrac{1}{4}x-1[/tex]

Answer:

a = 80°

Step-by-step explanation:

Since PS and QR are parallel lines, then

a = 80° ( alternate angles )

Answer:

a = 80°

Step-by-step explanation:

Since PS and QR are parallel lines, then

a = 80° ( alternate angles )

Answer:

C = 58.88 degrees

Step-by-step explanation:

We can use the law of cosines to find the missing angle measurement

c^2 = a^2 +b^2 -2ab cosC

Rearranging and solving for cos C

2ab Cos C = a^2 +b^2 - c^2

Divide by 2ab

cos(C) =  a^2 + b^2 − c^2

             ------------------------

                         2ab

Substituting what we know  a = 31 b = 21   c = 27

                            31^2 + 21^2 - 27^2

     cos C        =  -----------------------------

                             2(31)(21)

      cos C = .516897081

Take the inverse cos on each side

cos^-1 cos C = cos ^-1 (.516897081)

C = 58.88 degrees