MATHEMATICS HIGH SCHOOL

A local hamburger shop sold a combined total of 688 hamburgers and cheeseburgers on Thursday. There were 62 fewer cheeseburgers sold than hamburgers How many hamburgers were sold on Thursday?

Answers

Answer 1

Answer:

Answer:

626

Step-by-step explanation:

So 62 fewer right so 688 combined- 62 cheeseburger =626 hamburger

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0.3(y+2)=1.7+(8-y) solve the following equation

Answers

Answer:

y = 7

Step-by-step explanation:

0.3y+0.6 = 9.7 - y

0.3y+y = 9.7 -0.6

1.3y = 9.1

y= 7

sorry it had an error

Find the vertex, focus, directrix, and focal width of the parabola. x = 4y2.

Answers

- Vertex : ( 0, 0 ).
- Focus: ( p/2, 0 );
y² = 1/4 x
y² = 2 p x ⇒ 2 p = 1/4
p = 1/8
p/2 = 1/16
F ( 1/16, 0)
- Directrix:
x = - p/2 x
x = - 1/16 x
- The focal length:
2 p = 2 · 1/8 = 1/4

Answer:

The vertex is (0,0), focus of the parabola is $((1)/(16),0)$ , directrix of the parabola is $y=-(1)/(16)$ , focal width is $(1)/(4)$ .

Step-by-step explanation:

The given equation of parabola is

$x=4y^2$

It can be written as

$y^2=(1)/(4)x$ ....(1)

The general equation of parabola is

$(y-k)^2=4p(x-h)$ ... (2)

Where, (h,k) is vertex, (h+p,k) is focus, y=h-p is directrix and |4p| is focal width.

On comparing (1) and (2), we get

$h=0,k=0$

The vertex is (0,0).

$4p=(1)/(4)$

$p=(1)/(16)$

Focus of the parabola is

$(h+p,k)=(0+(1)/(16),0)=((1)/(16),0)$

Therefore focus of the parabola is $((1)/(16),0)$ .

Directrix of the parabola is

$y=h-p=0-(1)/(16)=-(1)/(16)$

Directrix of the parabola is $y=-(1)/(16)$ .

Focal width is

$|4p|=|4* (1)/(16)|=(1)/(4)$

Focal width is $(1)/(4)$ .

In a biological lab, the cell growth rate of two different organisms is tracked and recorded each week. Given the growth rate, the number of organisms can be determined using the following equations: s(x) = 100 + 23x
m(x) = 90(1.2x)

Complete the table of values.
x 100 + 23x 90(1.2x)
0
1
2
3
4
5
Use the table to determine at approximately which point the number of cells will be the same for each organism.
Graph the system of equations, and show the point of intersection.
Explain what the points graphed for each line represent.
Explain how you can determine the solution to the equation 100 + 23x = 90(1.2x) using the graph from part c.
Find the point(s) of intersection, and explain what the intersection represents in the context of the problem.

Answers

wow that's too much work!!! is this a table or printout?

s(x) = 100 + 23xs(x) = 100 + 23x

m(x) = 90(1.2x)

How do i find the fourth side of quadrilateral if three sides are given?

Answers

The length of a fourth side of a quadrilateral cannot be directly calculated from just the lengths of the other three sides. Additional information like the quadrilateral type, or types of angles within the quadrilateral, would be needed to calculate the length of the fourth side.

In mathematics, specifically geometry, the length of the fourth side of a quadrilateral (a shape with four sides) cannot be directly determined just by knowing the lengths of the three other sides. This is because a quadrilateral can be of multiple shapes such as squares, rectangles, parallelograms, trapezoids, etc., each having different properties.

However, if you have additional information like the types of angles within the quadrilateral or if it's a specific type of quadrilateral (rectangle, square, etc.), then you could possibly calculate the length of the fourth side.

For example, in a rectangle, opposite sides are equal so if you know three sides and know it's a rectangle, then the fourth side would be equal to the opposite side.

Without any additional information, there isn't a simple formula that can be used to directly calculate the length of the fourth side of any arbitrary quadrilateral.

Learn more about the topic of Quadrilateral here:

brainly.com/question/29934440

#SPJ11

Answer:

$\mathrm{Well,\ just\ by\ knowing\ the\ length\ of\ sides,\ you\ won't\ be\ able\ to\ calculate\ the}\n\mathrm{fourth\ side,\ unless\ you\ know\ that\ is\ an\ especial\ type\ of\ quadrilateral\ (for}\n\mathrm{example:\ rectangle,\ parallelogram,\ rhombus,\ square,\ etc).\ You\ will\ also\ need}\n\mathrm{the\ two\ unknown\ angles\ between\ those\ three\ sides.\ You\ will\ get\ what\ I\ mean\ if}\n\mathrm{you\ look\ the\ below\ diagram:}$

$\mathrm{Of\ course,\ you\ won't\ know\ how\ far\ the\ points\ A\ and\ D\ are\ unless\ you\ know}\n\mathrm{\angle B\ and\ \angle\ C.\ }$

$\mathrm{This\ concept\ works\ for\ triangles\ too.\ You\ can't\ find\ the\ third\ side\ of}\n\mathrm{a\ triangle\ only\ by\ knowing\ the\ length\ of\ the\ other\ two\ sides.\ You\ need\ to\ know}\n\mathrm{the\ angles\ between\ the\ two\ given\ sides.}$

A complex number, (a + bi), multiplied by (2 + 3i) and added to -i gives the product of (-11 + 5i) and (1 – i).a = and b =

Answers

Answer:

Hence, we have:

a= 3 and b= 4

Step-by-step explanation:

It is given that:

A complex number, (a + bi), multiplied by (2 + 3i) and added to -i gives the product of (-11 + 5i) and (1 – i).

i.e.

$(a+ib)(2+3i)-i=(-11+5i)(1-i)\n\ni.e.\n\na(2+3i)+ib(2+3i)-i=-11(1-i)+5i(1-i)\n\ni.e.\n\n2a+3ai+2bi+3bi^2-i=-11+11i+5i-5i^2$

Since, we know that :

$i^2=-1$

Hence, we have:

$2a+3ai+2bi-3b-i=-11+11i+5i+5\n\ni.e.\n\n(2a-3b)+i(3a+2b-1)=-11+5+11i+5i\n\ni.e.\n\n(2a-3b)+i(3a+2b-1)=-6+16i$

i.e. we have:

$2a-3b=-6---------(1)$

and

$3a+2b-1=16\n\ni.e.\n\n3a+2b=16+1\n\ni.e.\n\n3a+2b=17------------(2)$

On multiplying equation (1) by 2 and equation (2) by 3 we get:

$13a=39\n\ni.e.\n\na=3$

on putting the value of a into equation (1) we get:

$2* 3-3b=-6\n\ni.e.\n\n6-3b=-6\n\ni.e.\n\n-3b=-6-6\n\ni.e.\n\n-3b=-12\n\ni.e.\n\nb=4$

(a+bi)(2+3i)-i=(-11+5i)(1-i)
2a+3ai+2bi+3bi²-i=-11+11i+5i-5i²
2a+(3a+2b-1)i-3b=-11+16i+5
(2a-3b)+(3a+2b-1)i=-6+16i
Therefore; we have the next system of equations:
2a-3b=-6
3a+2b-1=16

Finally, the system of equations is:
2a-3b=-6
3a+2b=17
We can solve this system of equations by reduction method
2(2a-3b=-6)
3(3a+2b=17)
----------------------
   13a=39 ⇒a=39/13=3

3(2a-3b=-6)
-2(3a+2b=17)
----------------------
   -13b=-52 ⇒ b=52/13=4

Answer: a=3;    b=4

Are the graphs of the lines in the pair parallel? Explain.Find the slope of a line parallel to 5x + 2y = 6

Answers

To make it easier turn this equation into a slope. To do that you must get "y" by itself on one side of the equal sign. The "y" have to be positive. Then plot it out. Enter the "x" (1 for example) in the equation and solve to get "y". Then use the ordered pair to plot out the slope. Then you find a coefficient of "x" that matches the one in this equation and plot that out. If it's parallel then it's right. :)

The gradient of the line is - 2.5

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