A teacher bought 8 books at (p - 1500) each book and 2 pens at (p + 1000) each pen. If the teacher spent 53,000 altogether, how much money did he spend on the books?​

Answer:

N–1=Z+2 should be the solution.

Answer:

704 cm³

Step-by-step explanation:

Things to understand :

Solving :

Volume (prism) = Volume (rectangular prism) - Volume (cylinder)

Volume = LWH - πr²h

Volume = 5 x 13 x 13 - π x 3² x 5

Volume = 845 - π x  45

Volume = 845 - 141.3

Volume = 704 cm³

[tex] \boxed{\sf \: Answer : Volume \: of \: prism \: is \: 703.7 cm³}[/tex]

Step-by-step explanation:

Information about diagram- The diagram is a square prism with a circular hole in it.

Given:

length of prism (a) = 13cm

height of prism (h) = 5 cm

diameter of circle(d) = 6 cm

To find:

Volume of prism =?

Solution:

Formula that would be used,

[tex] \sf volume \: of \: square \: prism = {a}^{2} h[/tex]

[tex] \sf volume \: of \: cylinder = \pi {r}^{2} h[/tex]

Let's calculate the overall volume of prism,

Volume of prism(including volume of hole) V = a²h

[tex] V = a²h \\ V = {13}^{2} \times 5 \\ V = 845 \: {cm}^{3} [/tex]

To find out the volume circular hole we need to find the radius of hole, since the diameter of hole is given we can calculate the radius by multiplying 1/2.

[tex]r= \frac{d}{2} \\ r = \frac{6}{2} \\ r = 3 \: cm[/tex]

now calculate the volume of circular hole inside the prism,

Volume of circular hole(cylindrical shape) v= πr²h

[tex]v = \pi {r}^{2} h \\ v = 3.14× {3}^{2} ×5 \\ v = 141.3 \: {cm}^{3}[/tex]

The volume of given diagram of prism (V') = Volume of overall prism(V) - volume of circular hole(v)

[tex]V' = V- v \\ V' = 845 - 141.3 \: \\ V' = 703.7 \: {cm}^{3}[/tex]

Answer - Volume of prism is 703.7 cm³

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Answer:

B

Step-by-step explanation:

Answer:

D. Because the same answer

Step-by-step explanation:

Answer:

Ok hello my name is Christopher and I have already done this and the answer is (6,-7)

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Slope of a line, given two points : formatslope=y2−y1x2−x1=4−2−2−(−1)=2−1=−2

Answer:

The answer is choice c. This is because texts present the same facts in fiction or nonfiction life.

Step-by-step explanation:

remember, a probability is always desired cases over possible cases.

and the combination of the probabilities of two (or more) events means to multiply these probabilities.

the probability to get a specific number on the spinner is 1/4 (1 desired number over 4 possible numbers).

so, to get first a number less than 3 ... - that means, the only desired outcome is the number 2.

so,

1/4

to get 5 on the second spin ?

again,

1/4

the combination of both events into one delivers the probability of

1/4 × 1/4 = 1/16

Answer:

120 cm squared

Step-by-step explanation:

1.the bases in this case are in blue,these are not included in lateral surface area.

first we must find the area of the top & bottom squares.

(4x4=16)

Then the side rectangles

(11x4=44)

then We add,there are two squares and two rectangles included in the lateral surface area.So we can do 16x2=32 and 44x2=88.

now that we have all our measurements we can add these numbers

88+32=120 cm squared

Answer:

y = x/5280  

Step-by-step explanation:

y  miles =  x feet / 5280

160

Step-by-step explanation:

Due to the kite being a 2D Object you can just add the numbers of each side up to get to the answer 160. If I'm wrong then I'm sorry I hope this helped though!

Answer: 2/sqrt6

Step-by-step explanation:

tan theta=perpendicular/base so

cot theta =base /perependicular=sqrt2/2

while sin theta=perpendicular/hypotenous=2/x

here x is unkown to find it we will use pythagoras theorem

(hypoteneous)^2=(Base)^2+(perependicular)^2

                            =(sqrt 2)^2+(2)^2

                            =2+4

  (hypoteneous)^2=6

  hypotenous   =sqrt6

so

sin theta=2/sqrt6

Answer: 2.2 inches

Step-by-step explanation:

The maximum amount Simon Powell can borrow against his home is $130,000.

The maximum amount Simon Powell can borrow against his home can be calculated using the following formula:

Maximum amount that can be borrowed = (Current value of the home * Percentage of the market value that can be borrowed) - Mortgage balance …………………. (1)

Substituting all the relevant values into equation (1), we have:

Maximum amount that can be borrowed = ($350,000 * 0.80) - $150,000 = $130,000

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Two polygonal regions are similar with scale factor 7, if the area of the smaller region is 490 cm² then the area of the larger region would be 3430 cm²

An equation is an expression that shows the relationship between two or more numbers and variables.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Two polygonal regions are similar with scale factor 7. The area of the smaller region is 490 cm², hence:

Area of larger region = 7 * 490 cm² = 3430 cm²

Two polygonal regions are similar with scale factor 7, if the area of the smaller region is 490 cm² then the area of the larger region would be 3430 cm²

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Answer:

Below in bold.

Step-by-step explanation:

x^2 + y^2 - 8x + 12y + 40 = 0

x^2 - 8x + y^2 + 12y = -40

Complete the square on the x and y terms:-

(x - 4)^2 - 16 + ( y + 6)^2 - 36 = -40

(x - 4)^2 + (y + 6)^2 = -40 + 16 + 36

(x - 4)^2 + (y + 6)^2 = 12

So the centre is at (4, -6) and the radius is √12.

Answer:

The circle is centered at (4,-6) and has a radius of √12.

Step-by-step explanation:

The standard form for the circle equation is:

[tex](x-a)^2+(y-b)^2=r^2[/tex]

You have:

[tex]x^2+y^2-8x+12y+40=0[/tex]

First complete the square for the 'x' terms:

[tex](x^2-8x+40)+y^2+12y=0[/tex]

[tex](x^2-8x+16-16+40)+y^2+12y=0[/tex]

[tex](x^2-8x+16)+y^2+12y+24=0[/tex]

[tex](x-4)^2+y^2+12y+24=0[/tex]

The 'x' terms are now in standard form. Work on the 'y' terms by completing the square once again:

[tex](x-4)^2+(y^2+12y+36-36+24)=0[/tex]

[tex](x-4)^2+(y^2+12y+36)-12=0[/tex]

[tex](x-4)^2+(y+6)^2-12=0[/tex]

Add the 12 to the other side:

[tex](x-4)^2+(y+6)^2=12[/tex]

The circle is centered at x = 4, y = -6, and has a radius of √12.

Answer: -17/4

Step-by-step explanation:

The product and the sum of the functions will be 3x² - 6x - 24 and 4x + 2. The value of the function (f - g) at x = 4 is negative 18.

In mathematics, functions are everywhere and are necessary for constructing physical connections. A function is a statement, rule, or law that establishes the connection between two variables.

The functions are given below.

f(x) = x - 4

g(x) = 3x + 6

Then the product of the functions will be

(f × g)(x) = (x - 4)(3x + 6)

(f × g)(x) = 3x² -12x + 6x - 24

(f × g)(x) = 3x² - 6x - 24

Then the sum of the functions will be

(f + g)(x) = x - 4 + 3x + 6

(f + g)(x) = 4x + 2

Then the difference in the functions at x = 4 will be

(f - g)(4) = (x - 4) - (3x + 6)

(f - g)(4) = x - 4 - 3x - 6

(f - g)(4) = -2x - 10

(f - g)(4) = -2 (4) - 10

(f - g)(4) = -8 -10

(f - g)(4) = -18

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Answer:

x = 4.55

Step-by-step explanation:

Tan(75) = 17/x

3.73 = 17/x

x3.73 =17

x = 4.55

Answer:

Denice would have used 2.25 (or 2 1/4) yards of fabric for each bag.

Step-by-step explanation:

First, you have the 9 bags you are making and they all must be the same because they are identical, so you divide the nine bags by the four yards and I got an answer of 2.25 yards per bag. The answer can also be 2 1/4 as well.

Answer:

4 weeks

Step-by-step explanation:

Given information:

Given equation:

[tex]\sf b = 85 + w(10 + 8)[/tex]

(where b is the balance and w is the number of weeks)

To find the number of it will take to have a balance of $150, substitute b = $150 into the given equation and solve for w:

[tex]\implies \sf 85+w(10+8)=150[/tex]

[tex]\implies \sf 85+18w=150[/tex]

[tex]\implies \sf 85+18w-85=150-85[/tex]

[tex]\implies \sf 18w=65[/tex]

[tex]\implies \sf \dfrac{18w}{18}=\dfrac{65}{8}[/tex]

[tex]\implies \sf w=3.6111...[/tex]

[tex]\implies \sf w=4\:weeks[/tex]

Therefore, there will be $150 in the bank account 4 weeks from now.

Answer:

12/13

Step-by-step explanation:

36/39

Divide by 3

12/13

Answer:

C

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr = πd ( d is the diameter and d = 2r ) , then

C = πd = 3.14 × 26 = 81.64 in

Answer :

Explaination :

Here we are given with two equations,

So in order to calculate the number of hours (h). We would simply substitute the value of f in first equation. (i.e., keeping them equal)

>> 7h + 20 = 10h + 5

>> 10h - 7h = 20 - 5

>> 3h = 15

>> h = 15 / 3

>> h = 5

[tex]y=f(x)= \dfrac x 3 \\\\\text{Replace x with y and then solve for y,}\\\\~~~~x = \dfrac y 3\\\\\implies y = 3x \\\\\implies f^{-1}(x) =3x[/tex]

The r-value that represents the no or low correlation is 0.0

For a r value to show no correlation, then the r value must be 0 or close to 0

Since the r values are not given, then we can assume that the r value is 0

Hence, the r-value that represents the no or low correlation is 0.0

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Answer:

30 grames.

Step-by-step explanation:

5 x 6 = 30.

The coordinate of G is (3,6.5).

When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula.

The Coordinate of F is (1, 7)

The Coordinate of H is (5,6)

Since G is the midpoint. So, it divides the line FH in 1:1 part

Let coordinates of G be (x, y)

Now using Section Formula,

[tex]x= \frac{1*1+1*5}{2} \;\;\; and \;y= \frac{1*7+1*6}{2}[/tex]

x= 3 and y = 6.5

Hence the coordinate of G is (3,6.5)

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2000cm³.

The volume of any 3d shape is the length x height x width.

This case it is 25 x 10 x 8.