Mathematics High School

Some spiders, dragonflies, and houseflies are kept in three separate enclosures. They have a total of 20 heads, 136 legs, and 19 pairs of wings.
Given that...
a spider has 8 legs and 0 pairs of wings
a dragonfly has 6 legs and 2 pairs of wings
a housefly has 6 legs and 1 pair of wings
Find the number of spiders, the number of dragonflies, and the number of houseflies.

Answers

Answer 1

Answer:

Number of Spiders: 8

Number of Dragonflies: 7

Number of Houseflies: 5

Step-by-step explanation:

s= spider

d= dragonfly

h= housefly

Heads:

20= s+d+h

Legs:

136= 8s+6d+6h

Wings:

19= 0s+2d+1h

Solve with substitution.

Divide the second equation by 2.

136= 8s+6d+6h

68= 3d+3h+4s

Set the last equation in terms of d.

19= 0s+2d+1h

d= [tex]\frac{19}{2} -\frac{1}{2}h[/tex]

Substitute what we just found (d) into the first and our new second equation. Simplify.

20= s+d+h

20= s+[tex]\frac{19}{2} -\frac{1}{2}h[/tex]+h

h+2s=21

68= 3d+3h+4s

68= 3([tex]\frac{19}{2} -\frac{1}{2}h[/tex])+3h+4s

3h+8s=79

Take both simplified equations and solve with elimination. Do this by multiplying the top equation by negative 3.

h+2s=21

3h+8s=79

-3h-6s=-63

3h+8s=79

2s=16

s=8

Plug in s=8 into the other equation.

h+2s=21

h+2(8)=21

h=5

Plug in h=5 into the last equation we rewritten.

[tex]d= \frac{19}{2} -\frac{1}{2} h[/tex]

[tex]d=\frac{19}{2} -\frac{1}{2}(5)[/tex]

d=7

(d,h,s)= (7,5,8)

Related Questions

how can i Find the volume of the following cylinder that the Radius of 1 cm Height of 8 cm

Answers

Answer:

Okay first you need to use the formula: V=[tex]\pi r^{2} *h[/tex]

All you need to do is plug in those numbers.

Like this: V= [tex]\pi *1^{2}*8[/tex]

which is = 25.13 [tex]cm^{3}[/tex]

Ta-da!! lol. Have a great day!

If 2x-3y=3 find 16^x/64^y

a. 4
b. 8
c. 16
d. 64

Answers

Answer:

D. 64

Step-by-step explanation:

Did you mean: if 2x−3y=3 what is 16x64y? That fraction equals 42x−3y, so the answer would be 43, which is 64.

D. 64

Express as a product of primes: dfrac24x26y2 x -3 y =3 simplify

Please help

??

:$):’jfidifkvk

Answers

Answer:

For the question a i think its b

Step-by-step explanation:

1. f(x) = x2
• vertex :
• opening of the graph :
• vertex is a ______ point
• equation of axis of symmetry (x=h) :
• range (y≥k) :

Answers

Answer:

Step-by-step explanation:

f(x) = x²

1. Vertex ( 0 ,0)

2) a > 0 , opening upward

3) minimum

4) Axis of symmetry : x = 0

5) Range: y ≥ 0

x m 1,5 m and 1,5 m

Answers

☆Answer :

x² = (1,5)² + (1,5)²

x² = 2,25 + 2,25

x² = 4,5

x = 2,1m

[tex]\bold{\underline{Solution : -}}[/tex]

[tex]\sf a^2 + b^2 = c^2[/tex]

[tex]\sf x^2 = (1.5)^2 + (1.5)^2 [/tex]

[tex]\sf x^2 = 2.25 + 2.25 [/tex]

[tex]\sf x^2 = 4.5 [/tex]

[tex]\sf x = \sqrt{4.5} \approx 2.1[/tex]

Divide 31.50 / 2.50 step by step. Write is out on paper if you can. :D

Answers

Answer:

12.6 you divide 31.50 by 2.50 pretend the decimal signs aren't there.

Answer each question below.
18.
(16)
ZW and ZY are supplementary. If m

Answers

Is there anymore words?

Answer:

I'm not answering but i can help you :)

Step-by-step explanation:

Supplementary angles are two angles whose measures add up to 180°.

The two angles of a linear pair, like ∠1 and ∠2 in the figure below, are always supplementary.

But, two angles need not be adjacent to be supplementary. In the next figure, ∠3 and ∠4 are supplementary, because their measures add to 180°.

Example 1:

Two angles are supplementary. If the measure of the angle is twice the measure of the other, find the measure of each angle.

Let the measure of one of the supplementary angles be a .

Measure of the other angle is 2 times a.

So, measure of the other angle is 2a.

If the sum of the measures of two angles is 180°, then the angles are supplementary.

So, a+2a=180°

Simplify.

3a=180°

To isolate a, divide both sides of the equation by 3.

3a3=180°3 a=60°

The measure of the second angle is,

2a=2×60° =120°

So, the measures of the two supplementary angles are 60° and 120°.

Example 2:

Find m∠P and m∠Q if ∠P and ∠Q are supplementary, m∠P=2x+15, and m∠Q=5x−38.

The sum of the measures of two supplementary angles is 180°.

So, m∠P+m∠Q=180°

Substitute 2x+15 for m∠P and 5x−38 for m∠Q.

2x+15+5x−38=180°

Combine the like terms. We get:

7x−23=180°

Add 23 to both sides. We get:

7x=203°

Divide both sides by 7.

7x7=203°7

Simplify.

x=29°

To find m∠P, substitute 29 for x in 2x+15.

2(29)+15=58+15

Simplify.

58+15=73

So, m∠P=73°.

To find m∠Q, substitute 29 for x in 5x−38.

5(29)−38=145−38

Simplify.

145−38=107

So, m∠Q=107°.

At the local deli, David bought two ginger ales and two bagels for $6.60. Sumaiya bought four ginger ales and three bagels for $11.70.

Find the exact cost of one bagel and one ginger ale.

PLS HELP

Answers

Step-by-step explanation:

let the ginger ales be $x and the bagels $y.

Case 1, 2x+2y=6.60 x+y=3.30 ......1

Case 2, 4x+3y=11.70. .....2

1, x+y=3.30...×4

2, 4x+3y=11.70...×1

1, 4x+4y=13.20

2, 4x+3y=11.70

(-) (-) (-)

____________

y=1.50

____________

now, placing the value of y in equation 1,

x+y=3.30

x+1.50=3.30

x=1.80

therefore, the exact cost of one bagel and one ginger ale is $1.50 and $1.80 respectively.

If you are asking for the value of x, then x = not defined because dividing a value by 0 will always give you a non-defined answer. So, x can be equal to any number (there can be infinite values).

Next, if you want to prove that both the statements are true, then yes it's true because RHS = LHS = 0.

Check the 2 attachments for the steps.

______

RainbowSalt2222 ☔

Answer:

infinite number of solutions

Step-by-step explanation:

x - ([tex]\frac{x}{5}[/tex] + 60) = [tex]\frac{4}{5}[/tex] x - 60 ← distribute parenthesis on left by - 1

x - [tex]\frac{x}{5}[/tex] - 60 = [tex]\frac{4}{5}[/tex] x - 60 , collect like terms on left side

[tex]\frac{4}{5}[/tex] x - 60 = [tex]\frac{4}{5}[/tex] x - 60

Since expressions on both sides are equal then any value of x is a solution.

That is there is an infinite number of solutions

The school is 100 meters from Miguel's house.
The following describes the most recent trip.
He walked 75 meters towards school in 3
min. Miguel realized that he left his iPad at
home.
• He tumed around and walked home at the
same speed.
He spent 5 min. looking for his iPad.
• Then he walked all the way to school at 50
meters per minute.
Use the graph tool to create a graph that accurately
represents Miguel's walk.
yeah

Answers

Answer:

i don't knoe if we can do it without the graph

PLEASE HELP ME……………..

Answers

Answer: chrome

Step-by-step explanation: go to a new tab then search it up.

Weather report, pls help me y’all i don’t wanna fail this class i beg you plss

Answers

Answer:

4(x9)=3

Step-by-step explanation:

Define the sample space, S, of a fair coin being tossed once.

S=

A. {H, T}

B. {H, H}

C. {T, T}

Answers

Answer:

S = { H,T }

Step-by-step explanation:

Sample space is these two outcomes

The local softball field has a lemonade stand. The graph shows the amount that of money in the cash register of the lemonade stand

1. What is the y-intercept?

2.What dose the y-coordinate of the y-intercept of the function represent

3. What is the slope

4What dose the slope of the function represent

Answer:

the equations is y=x+3-1

Step-by-step explanation:

what is the greatest number of relative maximum that a polynomial of degree 15 can have? Select the right answer among them 1. 14 2. 6 3. 9 4. 7 5. 4

Answers

Answer:

Step-by-step explanation:

The greatest number of relative maxima it can have is 14.

So, the correct answer would be option (1) 14.

Use the concept of a polynomial defined as:

An expression that consists of exponents, variables, and constants and that is combining many different mathematical procedures:

Addition, subtraction, and multiplication is referred to as polynomial.

Given that,

The degree of polynomial = 15

The objective of this question determine the number of relative maxima it can have.

The number of relative maxima that a polynomial can have is equal to its degree minus 1.

In this case:

The polynomial is of degree = 15,

Hence,

The greatest number of relative maxima it can have is 15 - 1 = 14.

So, the correct answer would be option (1) 14.

To learn more about polynomials visit:

https://brainly.com/question/11536910

#SPJ3

two and twenty-seven hundredths

Answers

Twenty=20Twenty seven hundred hundreths=2700

Actual number

[tex]\\ \sf\longmapsto 202700[/tex]

Number in words=two hundred and two thousands and seven hundreds

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