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3 years ago

Please help me and explain it please questions 28

Mathematics

2 answers:

blagie [28]3 years ago

8 0

Answer:

.25*x +.10*y +.05*z

We have 1.35 which is the value of our coins.

Step-by-step explanation:

We need to multiply how much each coin is worth by the number of each type of coin we have.

If we have x quarters then we multiply x by .25 and we have y dime then we multiply y by .10 and we have z nickels then we multiply z by .05. To find out how much money we have, we add it all up

Our equations becomes

.25*x +.10*y +.05*z

We have x=3 or 3 quarters, y = 5 or 5 dimes and z=2 or 2 nickels

.25(3) + .10 (5) +.05(2)

.75+.50+.10

1.35

We have 1.35

klasskru [66]3 years ago

5 0

Answer:

$1.35

Step-by-step explanation:

x: quarter=$0.25

y: dime=$0.10

z: nickel=$0.05

so total amount of changes

= (0.25*x)+(0.10*y)+(0.05*z)

x=3, y=5, z=2

substituting into the eqn

total = (0.25*3)+(0.10*5)+(0.05*2)

= 0.75 + 0.5 + 0.1

= $1.35

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Find symmetric equations for the line of intersection of the planes. z = 4x − y − 13, z = 6x + 5y − 13

MArishka [77]

The intersection line of two planes is the cross product of the normal vectors of the two planes.

p1: z=4x-y-13 => 4x-y-z=13
p2: z=6x+5y-13 => 6x+5y-z=13
The corresponding normal vectors are:
n1=<4,-1,-1>
n2=<6,5,-1>

The direction vector of the intersection line is the cross product of the two normals,
vl=
i j k
4 -1 -1
6 5 -1
=<1+5, -6+4, 20+6>
=<6,-2,26>
We simplify the vector by reducing its length by half, i.e.
vl=<3,-1,13>

To find the equation of the line, we need to find a point on the intersection line.
Equate z: 4x-y-13=6x+5y-13 => 2x+6y=0 => x+3y=0.
If x=0, then y=0, z=-13 => line passes through (0,0,-13)

Proceed to find the equation of the line:
L: (0,0,-13)+t(3,-1,13)
Convert to symmetric form:
$\frac{x-0}{3}=\frac{y-0}{-1}=\frac{z-(-13)}{13}$
=>
$\frac{x}{3}=\frac{-y}{1}=\frac{z+13}{13}$

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3 years ago

You are flipping 3 coins trying to get all 3 to come up heads. If the first one comes up heads, what is the probability of all 3

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3 years ago

An isosceles triangle ABC with the base BC is inscribed in a circle. Find the measure of angles of it, if measure of arc BC = 10

Usimov [2.4K]

Answer:

The measures of the angles of the triangle are 51° , 64.5° , 64.5°

The measures of the angles of the triangle are 129° , 25.5° , 25.5°

Step-by-step explanation:

* Lets explain the meaning of the inscribed triangle in a circle

- If a triangle inscribed in a circle, then the vertices of the triangle lie

on the circumference of the circle and each vertex is an inscribed

angle in the circle subtended by the opposite arc

- Fact in the circle the measure of the inscribed angle is 1/2 the

measure of its subtended arc

* Now lets solve the problem

- Δ ABC is an isosceles with the base BC

∴ AB = AC

∴ m∠B = m∠C

- Δ ABC is inscribed in a circle

∴ ∠A is inscribed angle subtended by arc BC (minor or major)

# The measure of the minor arc is less than 180° and the measure of

the major arc is greater then 180° and the sum of the two arcs

equals the measure of the circle which is 360°

∴ ∠B subtended by arc AC

∴ ∠C subtended by arc AB

∵ The measure of the arc BC = 102°

- There is two cases in this question

(1) If the angle A subtended by the minor arc BC

(2) If the angle A subtended by the major arc BC

- Lets solve case (1)

∵ ∠A is an inscribed angle subtended by the minor arc BC

∴ m∠A = 1/2 the measure of the arc BC

∵ The measure of the arc BC is 102°

∴ m∠A = 1/2 × 102 = 51°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 51 + m∠B + m∠C = 180° ⇒ subtract 51 from both sides

∴ m∠B + m∠C = 129°

∵ m∠B = m∠C ⇒ isosceles Δ

∴ m∠B = m∠C = 129/2 = 64.5°

* The measures of the angles of the triangle are 51° , 64.5° , 64.5°

- Lets solve case (2)

∵ ∠A is an inscribed angle subtended by the major arc BC

∴ m∠A = 1/2 the measure of the arc BC

∵ The measure of the minor arc BC is 102°

∵ The measure of the circle is 360°

∴ The measure of the major arc = 360 - 102 = 258°

∴ m∠A = 1/2 × 258 = 129°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 129 + m∠B + m∠C = 180° ⇒ subtract 129 from both sides

∴ m∠B + m∠C = 51°

∵ m∠B = m∠C ⇒ isosceles Δ

∴ m∠B = m∠C = 51/2 = 25.5°

* The measures of the angles of the triangle are 129° , 25.5° , 25.5°

4 0

3 years ago