Please help, easy geometry work

In this question, we have to find an equation for two lines, depending on the input x, which creates the following piecewise function for this graph:

[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]

Equation of a line:

The equation of a line is given by:

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

In which m is the slope and b is the y-intercept(value of y when x = 0).

This situation:

x between 0 and 10:

From here, we can take two points (t,y). I will take (0,0) and (10,10).

From point (0,0), we get that when [tex]x = 0, y = 0[/tex], which means that the y-intercept is [tex]b = 0[/tex], thus:

[tex]y_1 = mt[/tex]

To find the slope, when we have two points, it is given by change in y divided by change in t, so:

Change in t: 10 - 0 = 10

Change in y: 10 - 0 = 10

Slope: [tex]m = \frac{10}{10} = 1[/tex]

Thus, the first definition is:

[tex]y_1 = t, 0 \leq t < 10[/tex]

x between 10 and 20:

I will take the points (10,10) and (20,0).

First, we find the slope:

Change in t: 20 - 10 = 10

Change in y: 0 - 10 = -10

Slope: [tex]m = \frac{-10}{10} = -1[/tex]

Thus:

[tex]y_2 = -t + b[/tex]

For the intercept, we have point (20,0), which means that when [tex]t = 20, y = 0[/tex]. So

[tex]0 = -20 + b[/tex]

[tex]b = 20[/tex]

Thus, the second definition is:

[tex]y_2 = -t + 20, 10 \leq t \leq 20[/tex]

Write an equation for the graph.

We use the two definitions, that is:

[tex]y = y_1, 0 \leq t \leq 10, y_2, 10 \leq t \leq 20[/tex]

So

[tex]y = t, 0 \leq t \leq 10, -t + 20, 10 \leq t \leq 20[/tex]

A similar question can be found at https://brainly.com/question/16024991

Answer:

55 Gallons

Step-by-step explanation:

143 - (8)(11)

143 - 88

143 -  88

55 gallons

Answer:

42 green marbles

Step-by-step explanation:

sum the parts of the ratio, 7 + 2 = 9 parts

Divide the number of marbles by 9 to find the value of one part of the ratio.

54 ÷ 9 = 6 ← value of 1 part of the ratio , then

7 parts = 7 × 6 = 42 ← number of green marbles

Answer:

A. (2,5), (3,6), (6,9)

Step-by-step explanation:

In order to be a function, all inputs (x values) must go to only one output (y value). List A is the only list that obeys this rule. Therefore, List A is a function.

Answer:

40 coats don't have hoods

Answer:

the value of c is 70

Answer:

F.  m/10.

Step-by-step explanation:

10 miles = 1 inch

1 mile = 1/10 of an inch so

m miles = m/10 inches.

Answer:

y = (-x-1)/2

Step-by-step explanation:

x1 = -3

y1 = 1

x2 = -1

y2 = 0

now

m = rise/run = (y2-y1)/(x2-x1) = (0-1)/(-1+3) = -1/2

so

y = mx + b

0 = -1/2(-1) + b

or, 0 = 1/2 + b

or, 0-1/2 = b

so, b = -1/2

so

y = mx + b

y = -x /2+ -1/2

or, y = (-x-1)/2

Replace x with -11 and solve:

Y = (-11)^2 + 11

(-11)^2 = 121

Y = 121 + 11

Y = 132

Answer: 132

Answer:

132

Step-by-step explanation:

y = x^2 +11

Let x = -11

y = (-11)^2 +11

  = 121+11

  = 132

Answer:

Step-by-step explanation:

It's given in the question,

[tex]2^x=3^y=12^z[/tex]

[tex]2^x=12^z[/tex]

[tex]\text{log}2^x}=\text{log}12^z}[/tex]

[tex]x\text{log2}=z\text{log12}[/tex]

[tex]x=\frac{z\text{log}12}{\text{log2}}[/tex]

[tex]3^y=12^z[/tex]

[tex]\text{log}3^y}=\text{log}12^z}[/tex]

[tex]y\text{log}3}=z\text{log}12}[/tex]

[tex]y=\frac{z\text{log12}}{\text{log}3}[/tex]

Now substitute the values in the equation,

[tex]\frac{1}{y}+\frac{2}{y} =\frac{1}{\frac{z\text{log12}}{\text{log}3}}+\frac{2}{\frac{z\text{log}12}{\text{log2}}}[/tex]

         [tex]=\frac{\text{log}3}{z\text{log}12}+\frac{2\text{log}2}{z\text{log}12}[/tex]                    

         [tex]=\frac{\text{log}3+\text{log}2^2}{z\text{log}12}[/tex]

         [tex]=\frac{\text{log}(3\times 2^2)}{z\text{log}12}[/tex]

         [tex]=\frac{\text{log}(12)}{z\text{log}12}[/tex]

         [tex]=\frac{1}{z}[/tex]

Hence proved.

Answer:

x is 7 and m<1 is 99°

Step-by-step explanation:

m<NMQ + m<MQN + m<QNM = 180°

[tex]{ \sf{(5x + 19) + (8x - 11) + (11x + 4) = 180}} \\ { \sf{24x + 12 = 180}} \\ { \sf{24x = 168}} \\ { \sf{x = \frac{168}{24} }} \\ \\ { \sf{x = 7}}[/tex]

m<1 = 180° - (11x + 4)

m<1 = 180° - 81°

m<1 = 99°

Using angle sum property

[tex]\\ \sf\longmapsto 5x+19+8x-11+11x+4=180[/tex]

[tex]\\ \sf\longmapsto 24x12=180[/tex]

[tex]\\ \sf\longmapsto 24x=180-12=168[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{168}{24}[/tex]

[tex]\\ \sf\longmapsto x=7[/tex]

Answer: [tex]4004.76\ ft[/tex]

Step-by-step explanation:

Given

inclination is [tex]\theta=75^{\circ}[/tex]

Mountain is [tex]h=3900\ ft[/tex] high

Cable is tied [tex]x=910\ ft[/tex] from the base of the mountain

From the figure, length of the shortest path is [tex]l[/tex]

It is given by using Pythagoras theorem

[tex]\Rightarrow l^2=3900^2+910^2\\\Rightarrow l=\sqrt{(3900)^2+(910)^2}\\\Rightarrow l=4004.76\ ft[/tex]

Answer:

The answer is X=28.

Answer:

125 sweets

Step-by-step explanation:

Let the total # of sweets the teacher bought be the variable, x.

We can set up this equation to find the # of sweets she bought:

40 · 3 + 5 = x

Because she gave 3 sweets each to her 40 students, we have to multiply these two numbers to get the # of sweets the teacher gave out.

120 + 5 = x

Then, since there's 5 extra sweets left, we can add it to the # of sweets the teacher gave out to get the total amount of sweets she bought.

125 = x

x = 125

125 sweets

Answer:

Total sweets = 125

Step-by-step explanation:

Number of sweets given to each student = 3

Number of sweets given to 40 students = 40*3 = 120

Number of sweets left with the teacher = 5

Total sweets = 120 + 5 = 125

please mark this answer as brainlist

Answer:

15

Step-by-step explanation:

(3x-1+2x+1)(3) -> 3 is the plug-in for x

3x-1+2x+1=5x

5*3=15

15

Answer:

15

Step-by-step explanation:

f(x) = 3x -1

g(x) = 2x+1

(f+g)(3)

find g(3) = 2(3)+1 = 6+1 = 7

Then find f(3) = 3(3) -1 = 8

f(3) + g(3) = 7+8 = 15

Step-by-step explanation:

From both the cases we can say that √n is either a natural number or an irrational number. Hence the correct option is (d)Either a natural number or an irrational number. Note: Before solving this type of question we should have proper knowledge of natural numbers, rational numbers and irrational numbers.

Answer:

2,080

Step-by-step explanation:

Two thousand and seventy is written as 2,070.

Ten more than 2,070 would be 2,080 as you're just adding on 10.

Hope this helps :)

Answer:

Hello,

answer 22

Step-by-step explanation:

[tex]\dfrac{1}{j} +\dfrac{1}{k} =\dfrac{1}{3} \\\\\dfrac{k+j}{j*k} =\dfrac{1}{3} \\\\\\3k+3j=j*k\\\\k(3-j)=-3j\\\\k=\dfrac{3j}{j-3} \\\\k=\dfrac{3j-9+9}{j-3} \\\\k=3+\dfrac{9}{j-3} \\\\\\j-3\ must\ be \ a divisor\ of\ 9 ==> 1,3,9\\\\j-3=1 ==> j=4 , k=3+\dfrac{9}{1} =12\\\\j-3=3 ==> j=6 , k=3+\dfrac{9}{3} =6\\\\j-3=9 ==> j=12 , k=3+\dfrac{9}{9} =4\\\\\sum\ k=12+6+4=22\\[/tex]

The sum of all possible values for k is 22.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

1/j + 1/k= 1/3

Simplifying the fraction

(k+ j)/ kj= 1/3

3k + 3j = kj

k(3- j) = -3j

k = -3j/ (3- j)

k= 3j/ (j-3)

k = 3j + 9 - 9 / (j-3)

k = 3 + 9/ (j-3)

Since (j-3) must be divisor of 9.

j- 3 = 1---> j=4, k= 3 +9 = 12

j- 3 = 3---> j=6, k= 3 +9/3 = 6

j- 3 = 9---> j=12, k= 3 +9/9 = 4

So, The sum is = 12+ 6 + 4 = 22

Learn more about Fraction here:

https://brainly.com/question/10354322

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Answer:

x=3, y=5

Step-by-step explanation:

Answer:

Option C,

y² = 18x, since the graph opens right

Answered by GAUTHMATH

(v^3)(w^-3) / (-v^-6)(w^3)

(-v^9)(w^-3) / (w^3)

(-v^9)(w^-6)

ANSWER: Option 4

Hope this helps!

Answer:

Step-by-step explanation:

If you drew out the bell curve and put the values where they go, this would be a no-brainer that doesn't even need math to solve. However, we will use the formula and then the table for z-scores to find this answer.

We are looking for the probability that the number of calls falls between 19 and 67. The standard deviation is 8 and the mean is 43. The probability we are looking for is P(19 < x < 67), therefore we look for the probability first that number of calls is greater than 19:

[tex]z=\frac{19-43}{8}=-3[/tex] and from the table and to the right of the z-score, the probability that the number of calls is greater than 19 is .99865 (or 99.8%). Likewise,

[tex]z=\frac{67-43}{8}=3[/tex] and from the table and to the right of the z-score, the probability that the number of calls is greater than 67 is .00315.

Take the difference of these to get the probability that the number of calls falls between these 2:

.99865 - .00135 = .9973 or 99.7%

Answer:

1 [tex]\frac{1}{6}[/tex] pounds of candy

Step-by-step explanation:

Add together the fractions by creating a common denominator of 6:

[tex]\frac{5}{6} + \frac{1}{3}[/tex]

[tex]\frac{5}{6} + \frac{2}{6}[/tex]

= [tex]\frac{7}{6}[/tex]

Simplify into a mixed fraction:

= 1 [tex]\frac{1}{6}[/tex]

So, the girls had 1 [tex]\frac{1}{6}[/tex] pounds of candy

Answer:b

Step-by-step explanation:

Answer:

$8

Step-by-step explanation:

$96 divided by 12

Answer:

if Im correct it should be $8.40

Step-by-step explanation:

why well if you think of breaking down by say 1/4 of 168 all you do is divide 4 which is the whole amount by 0.2 which is the amount the father gave her so 4/0.2= 20 the you take your whole 168 and divide by 20 which the whole number for 0.2 the your answer should be this 168/20= 8.4 which then i assumed it was $8.40 hopefully that is correct hehe

Answer:

9 dam

Step-by-step explanation:

1 km = 100 dam

0.09 km = 0.09 × 100

              = 9 dam

∴ 0.09 km = 9 dam