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3 years ago

Use the following image to answer the questions.

Mathematics

1 answer:

monitta3 years ago

8 0

(a.) The triangles presented in this problem are congruent. We can prove this using the AAA (angle-angle-angle) theorem of similarity. This states that if all three angles of a triangle are equivalent then the sides of the triangles are proportional. We know that all three angles of these triangles are the same since the image shows angle A = angle P, and angle B = angle Q, therefore, angle C = angle R.

(b.) Now that we know the triangles are similar and the sides are proportional, we can simply take a ratio of the sides to solve for x.

(3x+6)/24 = 28/32
3x+6 = (28/32)(24)
3x = 21 - 6
x = 15/3
x = 5

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Given the diagram below. If G is the circumcenter of ABC. DC = 16, GB = 21 and AZ = 19, find each measure.

Jlenok [28]

Answer:

Step-by-step explanation:

Properties of a circumcenter;

1). Circumcenter of a triangle is a point which is equidistant from all vertices.

2). Point where perpendicular bisectors of the sides of a triangle meet is called circumcenter of the triangle.

From the picture attached,

9). AG = GB = GC = 21

10). BC = 2(DC)

= 2×16

= 32

11). By applying Pythagoras Theorem in ΔGFB,

GB² = GF² + FB²

(21)² = GF² + (19)²

441 = GF² + 361

GF² = 441 - 361

GF = $\sqrt{80}$

GF = 8.9

12). By applying Pythagoras theorem in ΔGDB,

GB² = DG² + BD²

(21)² = (DG)² + (16)² [BD = DC = 16]

DG² = 441 - 256

DG = √185

DG = 13.6

7 0

3 years ago

I can’t figure this out, any help?

saveliy_v [14]

if the spinner is fair , it will land on green for 60 times , there are 24% chances for the spinner to land on purple ,For 1000 spins it will land 150 times on blue

<h3>What is Probability ?</h3>

Probability can be defined as the study to predict the likelihood of an event.

It has a range from 0 to 1.

Probability if the spinner is fair is 1/5 for each colour.

As it is spun 300 times

(1/5) * 300 = 60 times

So if the spinner is fair , it will land on green for 60 times.

(b) The probability of landing on purple theoretically is 60times , 20 % chances

but it can be seen from the data provided that for 300 spins , the spinner landed for 72 times

which is 24% , i.e. there are 24% chances for the spinner to land on purple.

(c)Theoretically blue has 20% chances 200 times , But it is seen in the data obtained that

for 300 spins the spinner is landing on blue for 45 times.

For 1000 spins it will land 1000*45/300 = 150 times.

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7 0

2 years ago

Solve x^2=18 where x is a real number

V125BC [204]

Answer:

x = ±3√2

or in decimal:

x = ±4.24

Step-by-step explanation:

x² = 18

x = ±√18

= ±√2√9

= ±3√2

6 0

3 years ago

Read 2 more answers

Is the median always sometimes or never one of the data values. explain

blondinia [14]

It can somteimes be one of the data values. When there's an odd set of numbers, the median will always be one of the data values. When there's a even set of numbers, the median will sometimes be one of the data values.
Even:
2, 3, 4, 5, 6, 7
Now, we need to find the number between 4 and 5, which is 4.5, 4.5 doesn't show up in the data set.
2,3, 5, 5, 6, 7
The middle of 5 and 5 is 5 since it's the same number. 5 does show up in the data set.
So, the median sometimes is one of the data values.

6 0

3 years ago

Read 2 more answers

candy that costs 31 cents per pound is mixed with candy that costs 46 cents per pound to obtain 50 pounds of candy that costs 40

photoshop1234 [79]

The amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.

<h3>How to form mathematical expression from the given description?</h3>

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For this case, we can assume the separate weights of each type of candies to be represented by variables.

Let we have:

x = weight (in pounds) of first type of candy whose cost is 31 cents per pound.
y = weight (in pounds) of second type of candy whose cost is 46 cents per pound.

x pounds of first type of candy is mixed with y pounds of second candy.

The weight of the mixture = x + y = 50 pounds

The cost of the mixture = 40 cents per pound = $40 \times 50 = 2000$ cents

Cost of the mixture = cost of x pounds of first candy+ cost of y pounds of second candy = $31x + 46y$
Thus, we get $31x + 46y =2000$

Therefore, we got a system of two linear equations as:

$x +y = 50\\31x + 46y =2000$

From first equation, we get:

$x = 50 -y$

Substituting this value in second equation, we get:

$31(50-y) + 46y =2000\\1550 + 15y = 2000\\15y = 450\\\\y = 450/15 = 30$

Putting this value of y in equation for x, we get:

$x = 50-y = 50-30 = 20$

Thus, the amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.

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2 years ago

Read 2 more answers