Ava, Lucas, and Maria are playing a game where they pass a pull-back toy to one another in a path that forms a right triangle. Ava sends the toy to Lucas. Then, Lucas sends the toy to Maria. Finally, Maria sends it back to Ava. The angle formed at Lucas' position measures 90° and the angle formed at Ava's position measures 40°. The distance from Ava to Lucas is 12 feet.

Ava is trying to determine the other measures of the triangle created by the toy's path. Give each distance in feet rounded to the nearest tenths place.

The distance from Maria to Ava is ___ feet.

The distance from Lucas to Maria is ___ feet.

The angle formed at Maria's position measures ___ degrees.

Answers

Answer 1

Using relations in a right triangle, it is found that

The distance from Maria to Ava is 15.66 feet.The distance from Lucas to Maria is 10.07 feet.The angle formed at Maria's position measures 50 degrees.

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this problem, the situation is modeled by the graph given.

First, we have to remember that the sum of the internal angles of a triangle is of 180º, hence:

The angle formed at Maria's position measures 50 degrees.

Then, for the distance from Maria to Ava, which is the hypotenuse:

[tex]\sin{50^\circ} = \frac{12}{h}[/tex]

[tex]h = \frac{12}{\sin{50^\circ}}[/tex]

[tex]h = 15.66[/tex]

Hence:

The distance from Maria to Ava is 15.66 feet.

Finally, for the distance from Lucas to Maria:

[tex]\sin{40^{\circ}} = \frac{d}{15.66}[/tex]

[tex]d = 15.66\sin{40^{\circ}} = 10.07[/tex]

The distance from Lucas to Maria is 10.07 feet.

To learn more about relations in a right triangle, you can take a look at https://brainly.com/question/10467648

Ava, Lucas, And Maria Are Playing A Game Where They Pass A Pull-back Toy To One Another In A Path That

Related Questions

A car salesman sells a 23000 car and makes a 1,265 cosmission. What is the cosmission rate?

Answers

Answer:

24265

Step-by-step explanation:

I think you just need to add the expressions 23000 and 1265

23000 + 1265

= 24265

Find the QT plzzzzzzz

Answers

Step-by-step explanation:

I didn't write language hope u get it

The product $ab = 1200$, $a$ is an integer, and $b$ is an odd integer. What is the largest possible value of $b$?.

Answers

ANSWER:

Largest possible value of b is:

75

Step-by-step explanation:

we are given that:

ab=1200

where a is an integer and b is an odd integer.

we know that product of odd numbers is always odd.

Now, 1200= 12×100

               = 2×6×10×10

              =2×2×3×2×5×2×5

It cannot be factorized further

Now, considering the product of all odd numbers

=3×5×5

=75

Now, if we multiply any other remaining number from the factorization of 1200, we will get a even number

Hence, The largest possible value of b is:

75

how do i calculate the original number from a percentage?

Answers

Answer:

shift the decimal point to the left two places.

Step-by-step explanation:

Example:

25%

=0.025

[tex]\huge\text{Please help!}[/tex]
Simplify:
[tex]\bold{(x^{2} +8xy+16y^{2})^{\frac{1}{3} } (x+4y)}^{\frac{1}{3} }[/tex]
Due today. No spam, and thanks! :)
[tex]\bold{M^ag^ic^al\:^}[/tex]

Answers

Answer:

x + 4y

Step-by-step explanation:

Hey there! First, we have to recall back laws of exponent.

[tex]\displaystyle \large{a^{\frac{m}{n}} = \sqrt[n]{a^m} }[/tex]

Now simplify the expressions in surds form.

[tex]\displaystyle \large{\sqrt[3]{x^2+8xy+16y^2} \cdot \sqrt[3]{x+4y} }[/tex]

From x²+8xy+16y², we can convert the expression to perfect square.

Perfect Square

[tex]\displaystyle \large{x^2+2xb+b^2 = (x+b)^2}[/tex]

Therefore, from the expression.

[tex]\displaystyle \large{x^2+8xy+16y^2 = (x+4y)^2}[/tex]

Thus:

[tex]\displaystyle \large{\sqrt[3]{(x+4y)^2} \cdot \sqrt[3]{x+4y}[/tex]

Because both have same surds, multiply them in one.

Surd Property I

[tex]\displaystyle \large{\sqrt[n]{x} \cdot \sqrt[n]{y} =\sqrt[n]{xy} }[/tex]

Therefore:

[tex]\displaystyle \large{\sqrt[3]{(x+4y)^2(x+4y)}[/tex]

Since both are like-terms and multiplying each other, we can apply one of exponent laws.

Exponent Laws II

[tex]\displaystyle \large{a^m \cdot a^n = a^{m+n}}[/tex]

Therefore, we have [tex]\displaystyle \large{\sqrt[3]{(x+4y)^{2+1} } \to \sqrt[3]{(x+4y)^3} }[/tex]

Simplify the expression, we have cube expression inside the cube root. Therefore, we simplify as x+4y as we cancel cube and cube root.

Let me know if you have any questions through comments!

[tex]\bold{x + 4y}[/tex]

Explanation :-

[tex]{(x^{2} +8xy+16y^{2})^{\frac{1}{3} } (x+4y)}^{\frac{1}{3} }[/tex]

Rewriting it into the expression of [tex]a^{2} + 2ab + {b}^{2} [/tex],

[tex]x^{2} + 2x \times 4y + (4y)^{2})^{\frac{1}{3} }(x + 4y)^{ \frac{1}{3} }[/tex]

[tex] = > ((x + 4y)^{2})^{ \frac{1}{3} }(x + 4y)^{ \frac{1}{3} }[/tex]

Now multiplying the fractions as,

[tex] = > ((x + 4y))^{ \frac{2}{3} }(x + 4y)^{ \frac{1}{3} }[/tex]

Now as the bases of the fractions are same, we can multiply directly,

[tex] = > (x + 4y)^{ \frac{2}{3} + \frac{1}{3} }[/tex]

[tex] = > (x + 4y)^{ \frac{3}{3} }[/tex]

As when same numerator and denominator of a fraction is 1, so,

[tex] = > (x + 4y)^1[/tex]

As 1 can be neglected (since it has no specific need in the equation), so,

[tex] = > x + 4y[/tex]

Hence, the answer is [tex]\bold{x + 4y}[/tex]

What is the probability of rolling a 6-sided die and getting a 2 or an odd number? A. 7/12 B. 1/3 C. 5/6 D. 2/3

Answers

Answer: D: 2/3

Step-by-step explanation: the numbers you can get is 2, 1, 3, or 5, and the chance of rolling a certain number on a die is 1/6, so for 4 numbers it would be 4/6.

Tell me if I’m wrong

Sample space=6

Getting 2 or an odd no

E={2,1,3,5}|E|=4

Probability

p(E)

4/62/3

What is 1/5 of £ 40?
Give your answer in pounds (£).

Answers

Answer:

£ 8

Step-by-step explanation:

basic equation:

£40 * 1/5

£ 40/5

£ 8

∵ £ 8 is the 1/5 of £ 40

Answer:

We need to find the 1/5 value of £40.We can find the value by multiplying 1/5 by £40.

Solution:

[tex] = \frac{1}{ \cancel5} \times \cancel{40} \: {}^{8} £[/tex]

[tex] = 1 \times 8£[/tex]

[tex] = 8£[/tex]

A number cube with sides marked with
the numbers 1 through 6 is tossed on a
table. What is the probability that the
number obtained will be an even
number?
A. 1 in 6
B. 2 in 6
C. 1 in 2
D. 2 in 3

Answers

Answer:

C. 1 in 2

Step-by-step explanation:

even numbers are 0, 2, 4, 6 etc.
the even numbers in a number cube are
2, 4, 6
so there is 3 possible results
all the numbers in the number cube are 6 numbers
so it is 3/6 times we can get an even number
by simplifying 3/6 (dividing by 3) we get 1/2

Can someone solve this please

Answers

Answer:

53 secs

Step-by-step explanation:

Seven more than twice a number is equal to 25. Which of the following is the number? Use
algebra to find your answer and show your work.

(1) 7
(3) 12
(2) 9
(4) 15

ANY HELP IS APPRRECATED

Answers

Answer:

the answer is 9

Step-by-step explanation:

when doubled 9 is 18

18+7=25

Answer:

9

Step-by-step explanation:

9+9=18 18-9=9 9×2=18 18÷9=2 18÷2=9

Let f(x) = (1 − x2)2/3. Which type of non-differentiable point exists at x = 1?.

Answers

[tex]f(x)=(1-x^2)^{\frac{2}{3}}\implies \cfrac{df}{dx}=\cfrac{2}{3}(1-x^2)^{-\frac{1}{3}}\implies \cfrac{df}{dx}=\cfrac{2}{3\sqrt[3]{1-x^2}}[/tex]

when it comes to a rational expression, we can get critical points from, zeroing the derivative "and" from zeroing the denominator alone, however the denominator provides critical valid points that are either "asymptotic" or "cuspics", namely that the function is not differentiable or not a "smooth line" at such spot.

if we get the critical points from the denominator on this one, we get x = ±1, both of which are cuspics.  Check the picture below.

Q.2 The lengths of a triangle are 7 cm, 8 cm and 10 cm correct to the nearest cm. Work out maximum possible perimeter of the triangle.

Answers

Step-by-step explanation:

7+8+10=25cm is the possibile perimeter of this

triangle.

In a schedule of 7 classes. Ella has 2 elective classes. What is the ratio of elective to
non-elective classes in Ella's schedule?

Answers

0.4 The process is shown in the following picture

What is the circumference of a circle?
A. A line segment that goes from one edge of a circle to the other and passes through the center.
B. Aline segment that goes from the center to the edge of a circle.
C. The distance around the circle.
D. The diameter plus the radius.

Answers

Answer:

C The distance around the circle is the circumference

Step-by-step explanation:

For information:

A is the diameter

B is the radius

what is the percent of : 20 of 60

Answers

Answer:

our fraction is 33.333333333333/100, which means that 20/60 as a percentage is 33.3333%.

33.3333 I’m pretty sure that’s it I’m not 100% though

please help me hurry please

Answers

Answer:

y = root under 24 (evaluate it if necessary)

or y = 2 root 6

Step-by-step explanation:

Let the reference angle be x

for the triangle in left,

b = 6-4 = 2

Now,

taking x as refrence angle,

cosx = b/h

or, cosx = 2/h

again,

for the bigger triangle,

taking x as reference angle,

cosx = b/h

or, cosx = b/6

As we can see base of bigger triangle is equal to hypotenuse of triangle at the left,

Let's suppose its a

so, cosx = a/6 = 2/a

now,

a/6 = 2/a

or, a² = 12

now,

for bigger triangle, using pythagoras theorem,

h² = p²+b²

or, 6² = y² + a²

or, 36 = y² + 12

or, y² = 24

so, y = root under 24

can someone help me I'm doing my packet and the quest is hard

Answers

The answer would be y=-3/4x-3

256 heartbeats in 4 minutes

Answers

Answer:

64 beats per minute

Step-by-step explanation:

256 divided by 4

When adding polynomials are the exponents always added together?

Answers

Answer:

No

Step-by-step explanation:

Exponents are only added when polynomials are multiplied and only applies to like terms. You add the coefficients of the like terms instead.

For example:

[tex](x^2+3x+6)+(2x^2-4x+1)=(1+2)x^2-(3-4)x+(6+1)=3x^2-x+7[/tex]

Answer:

no

Step-by-step explanation:

The exponents are added when the the same coefficient is multiplied:

[tex]x^2(x^3) = x^5[/tex]

If you think about it:

x^2 = x * x    and     x^3 = x * x * x

so you get:

(x^2)(x^3) = x * x * x * x * x = x^5

But, when adding x's of the same power, you add a coefficient:

[tex]x^2 + x^2 = 2x^2[/tex], not [tex]x^2 + x^2 = x^4[/tex]

Always remember to only add exponents when the coefficient/variable is multiplied, not added.

And, when an exponent is put to an exponent, multiply them:

[tex](x^3)^3 = x^3^(^3^) = x^9[/tex]

Juan is making a delivery to a store. The total trip will be 450 miles. He is driving at a constant rate of 60 miles per hour. He has already driven 30 miles. How
much longer will it take him to get to the store?

Answers

60x + 30 = 450 when solved, it will take Juan 7 hours to get to the store.

Johann and Marta shopped at a vintage toy store. Johann bought 3 blue marbles and 5 green marbles and paid $11. Marta bought 4 blue marbles and 2 green marbles and paid $10. Which system of equations can be used to find the prices of the blue and green marbles? 3 x 5 y = 10. 4 x 2 y = 11. 3 x 5 y = 11. 4 x 2 y = 10. 5 x 3 y = 10. 4 x 2 y = 11. 5 x 3 y = 11. 4 x 2 y = 10.

Answers

Answer:

B. 3x+5y=11

   4x+2y=10

On Edge 2022

Hope this Helps :)

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

The system of equations can be used to find the prices of the blue and green marbles are,

[tex]3x+5y=11[/tex]

[tex]4x+2y=10[/tex]

Thus the option 2 is the correct option.

What is system of equation?

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

Given information-

Johann bought 3 blue marbles and 5 green marbles.

The total money paid by the Johann is $11.

Marta bought 4 blue marbles and 2 green marbles.

The total money paid by the Marta is $10.

Suppose the price of the blue marbles is [tex]x[/tex] and price of the green marbles is [tex]y[/tex].

As Johann bought 3 blue marbles and 5 green marbles and paid $11. Thus,

[tex]3x+5y=11[/tex]      .....1

Let the above equation is equation number 1.

As Marta bought 4 blue marbles and 2 green marbles and paid $10. Thus,

[tex]4x+2y=10[/tex]      .....2

Let the above equation is equation number 2.

Thus the equation 1 and 2 are the required set of the equation for the given problem.

Hence the system of equations can be used to find the prices of the blue and green marbles are,

[tex]3x+5y=11[/tex]

[tex]4x+2y=10[/tex]

Thus the option 2 is the correct option.

Learn more about the system of equations  here;

https://brainly.com/question/13729904

Put these numbers in ascensing (smallest to biggest) order:

1272, 231, 817, 376, 233, 46, 2319, 494, 73, 1101

Answers

46,73,231,233,376,494,817,1101,1272,2319
46, 73, 231, 233, 376, 494, 817, 1101, 1272, 2319

ILL GIVE YOU BRAINLIEST!! Solve `x^{2}-5x+6=0`
Which solution method would be more efficient?
-Factoring
-Taking the square root
-Quadratic formula

Show your work!

Answers

Answer:

Factoring

Step-by-step explanation:

[tex]x^2-5x+6=0[/tex]

[tex]x^2-2x-3x+6=0[/tex]

[tex]x(x-2)-3(x-2)[/tex]

[tex](x-3)(x-2)=0[/tex]

[tex]x=2[/tex] and [tex]x=3[/tex]

I hope this help!

(Take note that this explanation is not written by me. The creator of the equation is by someone else.)

can someone please explain to me how to do this?

Answers

Answer:

x=50

Step-by-step explanation:

Since Line AB and Line CD are parallel, Angle AFG is supplementary to Angle CGF. So then x+3x-20=180. Then you just solve for x.

Combine like terms-> 4x-20=180

Add 20 to both sides-> 4x=200

Divide both sides by 4-> x=50

Hope this helps!

Feel free to ask if you still don't understand something

In the figure, a || b. What is the value of x?

Answers

Answer:

x=40

Step-by-step explanation:

Looking at this problem, we can see that 3x+9=129

Subtract 9 on both sides:

3x=120

Divide by 3 on both sides:

x=40

Line c passes through points (1, 14) and (7, 7). Line d is perpendicular to c. What is the slope of line d?

I will give brainliest!! :D

Answers

Answer:

6/7

Step-by-step explanation:

Your first step will be to find the slope of Line C. Using the slope formula of [tex]\frac{y_{2}-y_1 }{x_2-x_1}[/tex], the slope of Line C is [tex]\frac{7-14}{7-1} = \frac{-7}{6}[/tex].

If Line D is perpendicular to C, that means the slope is the negative reciprocal of Line C. So, that means the slope is 6/7.

Question 9
Determine the slope of the linear function represented
by the following scenario:
Jose opens a savings account with $150. He plans to
save the $20 he earns each week mowing his
neighbor's lawn.
slope
y-intercept
Correctness

Answers

The slope of the linear equation is 20 and the y-intercept is 150

What is a Slope?

Slope measures how steep a straight line is. It is described as rise over run.

The slope of the linear equation can be found as follows;

He opens the account with $150 and he plans to save $20 each week. Therefore,

let

x = number of weeks

Therefore,

y = 20x + 150

where

y = amount in his account after x number of weeks.

Using the slope intercept equation,

Slope intercept equation:y =mx + c

where

m = slope

c = y-intercept

Therefore, the slope of the linear equation is 20 and the y-intercept is 150

learn more on slope here: https://brainly.com/question/8057577

What is the equation to 5z=60

Answers

Answer:12

Step-by-step explanation:

since the 5 is multiplyed by z you have to divide but since ur dividng you have to divide to the other side so it looks like this

z=60/5

Value of x is greater than or equal to 14.

Answers

Answer:

x ≥ 14

Step-by-step explanation:

Answer:

x ≥ 14

Step-by-step explanation:

The ≥ sign represents greater than or equal to, so x ≥ 14.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

The area of the parallelogram is 11 1/4 feet. Find the height.

Answers

Answer:

h = 5/2 or 2 1/2

Step-by-step explanation:

The formula to calculate the area of a parallelogram is given as Area of parallelogram = base × height square units

so A = bh

11 1/4 = 4 1/2(h)

h = 11 1/4/4 1/2

h = (45/4)/(9/2)

h = 5/2 = 2 1/2

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