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Kay [80]
3 years ago
6

What is the value of x?

Mathematics
1 answer:
NemiM [27]3 years ago
4 0
Alternate interior angles are congruent.  Therefore, set the two angles equal to each other and solve for x. 

3x+4= 115
3x+4 -4 = 115 -4

3x =  111
x= 111/3---> 37. Therefore, x = 37. 

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Three lizards eat 63 grams of food each day. How many grams of food would you expect 5 lizards to eat
zhenek [66]

Answer: 105 grams

Step-by-step equation: they each eat 21 grams a day

3 0
3 years ago
Elena surveyed her classmates to see how many like to make jewelry. When she asked 20 of her classmates, 50 percent said they li
nordsb [41]

10 students of Elena's classmates like to make jewellery.

<u>Step-by-step explanation:</u>

Let total no.of classmates who liked the jewellery = x

Here, in the given problem, given she asked her classmates '20'. So, it clearly shows that total number of students/classmates = 20. Also, in that, 50% said like to make jewellery. Now find 'x' as below,

                    x = 50 \% \text { of } 20

                    x = \frac{50}{100} \times 20

                    x = 10

Hence, the total number of classmates who liked to make Jewellery = 10

5 0
3 years ago
One and two third minus two and two third
jeyben [28]

Answer:

1 \frac{2}{3} - 2\frac{2}{3}  = -1

Step-by-step explanation:

1\frac{2}{3} - 2 \frac{2}{3\\} \\\\\frac{5}{3} - \frac{8}{3} = \frac{-3}{3} \\ \\\frac{-3}{3} = -1

Hope this helps! :)

3 0
3 years ago
Given the circle with the equation (x + 1)2 + y2 = 36, determine the location of each point with respect to the graph of the cir
kati45 [8]
\bf \textit{equation of a circle}\\\\ &#10;(x- h)^2+(y- k)^2= r^2&#10;\qquad &#10;center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad &#10;radius=\stackrel{}{ r}\\\\&#10;-------------------------------\\\\&#10;(x+1)^2+y^2=36\implies [x-(\stackrel{h}{-1})]^2+[y-\stackrel{k}{0}]^2=\stackrel{r}{6^2}~~~~&#10;\begin{cases}&#10;\stackrel{center}{(-1,0)}\\&#10;\stackrel{radius}{6}&#10;\end{cases}

so, that's the equation of the circle, and that's its center, any point "ON" the circle, namely on its circumference, will have a distance to the center of 6 units, since that's the radius.

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad &#10;A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{1})\qquad \qquad &#10;%  distance value&#10;d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}&#10;\\\\\\&#10;\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(1-0)^2}\implies d=\sqrt{(-1+1)^2+1^2}&#10;\\\\\\&#10;d=\sqrt{0+1}\implies d=1

well, the distance from the center to A is 1, namely is "inside the circle".

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad &#10;B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6})\\\\\\&#10;\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(6-0)^2}\implies d=\sqrt{(-1+1)^2+6^2}&#10;\\\\\\&#10;d=\sqrt{0+36}\implies d=6

notice, the distance to B is exactly 6, and you know what that means.

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad &#10;C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})&#10;\\\\\\&#10;\stackrel{distance}{d}=\sqrt{[4-(-1)]^2+[-8-0]^2}\implies d=\sqrt{(4+1)^2+(-8)^2}&#10;\\\\\\&#10;d=\sqrt{25+64}\implies d=\sqrt{89}\implies d\approx 9.43398

notice, C is farther than the radius 6, meaning is outside the circle, hiking about on the plane.
3 0
3 years ago
Read 2 more answers
Find the probability that the senator was in the Democratic party, given that the senator was returning to office.
shutvik [7]

Answer:

The probability that the senator was in the Democratic party, given that the senator was returning to office is 0.4715.

Step-by-step explanation:

The complete question is:

Sophia made the following two-way table categorizing the US senators in 2015 by their political party and whether or not it was their first term in the senate.

                   Democratic         Republican         Independent        Total

First Term           11                          28                        11                     50

Returning           33                         26                        11                     70

Total                   44                         54                        22                  120

Find the probability that the senator was in the Democratic party, given that the senator was returning to office.

Solution:

The conditional probability of an event <em>A</em> given that another event <em>X</em> has already occurred is given by:

P(A|X)=\frac{P(A\cap X)}{P(X)}

The probability of an event <em>E</em> is given by the ratio of the number of favorable outcomes to the total number of outcomes.

P(E)=\frac{n(E)}{N}

Compute the probability of selecting an US senator who is a Democratic and was returning to office as follows:

P(D\cap R)=\frac{33}{120}=0.275

Compute the probability of selecting an US senator who was returning to office as follows:

P(R)=\frac{70}{120}=0.5833

Compute the conditional probability, P (D | R) as follows:

P(D|R)=\frac{P(D\cap R)}{P(R)}

            =\frac{0.275}{0.5833}\\\\=0.4714555\\\\\approx 0.4715

Thus, the probability that the senator was in the Democratic party, given that the senator was returning to office is 0.4715.

4 0
3 years ago
Read 2 more answers
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