Question 1

ASAP!!! ILL GIVE BRAINLIEST !

Alex17521 [72]

Answer:

1) 60

2) 60

3) 119

4) 59

Step-by-step explanation:

All triangle angles add up to 180 degrees. All lines with transversals add to 180 degrees. Use these rules and the measurements given to solve.

3 0

2 years ago

Suppose that LMN is isosceles with base LN suppose that M

ira [324]

Given:

In an isosceles triangle LMN, LM=MN.

$m\angle M=(3x+17)^\circ,m\angle L=(2x+36)^\circ$

To find:

The measure of the angles L, M and N.

Solution:

In triangle LMN,

$LM=MN$ (Given)

$m\angle N=m\angle L=(2x+36)^\circ$ (Base angles of an isosceles triangle are equal)

Now,

$m\angle L+m\angle M+m\angle N=180^\circ$

$(2x+36)^\circ+(3x+17)^\circ+(2x+36)^\circ=180^\circ$

$(7x+89)^\circ=180^\circ$

$(7x+89)=180$

On further simplification, we get

$7x=180-89$

$7x=91$

$x=\dfrac{91}{7}$

$x=13$

The value of x is 13. Using this value, we get

$m\angle L=(2(13)+36)^\circ$

$m\angle L=(26+36)^\circ$

$m\angle L=62^\circ$

Similarly,

$m\angle M=(3(13)+17)^\circ$

$m\angle M=(39+17)^\circ$

$m\angle M=56^\circ$

And,

$m\angle N=m\angle L$

$m\angle N=62^\circ$

Therefore, the measure of angles are $m\angle L=62^\circ,m\angle M=56^\circ,m\angle N=62^\circ$ .

5 0

3 years ago

$1500 is invested at a rate of 3% compounded monthly. Write a compound interest function to model this situation. Then find the

Marianna [84]

Answer:

Equation: $F=1500(1.0025)^{12t}$

The balance after 5 years is: $1742.43

Step-by-step explanation:

This is a compound growth problem . THe formula is:

$F=P(1+\frac{r}{n})^{nt}$

Where

F is future amount

P is present amount

r is rate of interest, annually

n is the number of compounding per year

t is the time in years

Given:

P = 1500

r = 0.03

n = 12 (compounded monthly means 12 times a year)

The compound interest formula modelled by the variables is:

$F=1500(1+\frac{0.03}{12})^{12t}\\F=1500(1.0025)^{12t}$

Now, we want balance after 5 years, so t = 5, substituting, we get:

$F=1500(1.0025)^{12t}\\F=1500(1.0025)^{12*5}\\F=1500(1.0025)^{60}\\F=1742.43$

The balance after 5 years is: $1742.43

3 0

3 years ago

Describe the graph that would be used to solve the equation –x2 + 4 = x + 2 using a system of equations. How will you use the gr

gayaneshka [121]

Answer:

The solutions are (-2 , 0) and (1 , 3)

Step-by-step explanation:

∵ -x² + 4 = x + 2

* y = -x² + 4 ⇒ is quadratic represented by parabola

The parabola open downward because coefficient of x² is negative

The x-coordinate of its vertex = -b/2a, where b is the

coefficient of x and a is the coefficient of x²

∴ x = 0/2(-1) = 0

∴ The y-coordinate of the vertex = (0)² + 4 = 4

∴ The maximum point of the parabola is (0 , 4)

∵ -x² + 4 intersects x-axis at y = 0

∴ -x² + 4 = 0 ⇒ -x² = -4 ⇒ x² = 4

∵ x² = 4

∴ x = ±√4 = ± 2

∴ the parabola intersects x-axis at -2 , 2

∵ y = x + 2 represented by a line its slope = 1

It intersects y-axis at 2

∵ x + 2 intersects x-axis at y = 0

∴ x + 2 = 0

∴ x = -2

∴ The parabola and the line intersect each other at

x = -2 and y = 0

To find all the point of intersection between the 2 equations we will solve them as a system of equations

∵ y= -x² + 4 and y = x + 2

∴ -x² + 4 = x + 2

∴ -x² + 4 - x - 2 = 0

∴ -x² - x + 2 = 0 ⇒ × -1

∴ x² + x - 2 = 0 ⇒ factorize

∴ (x + 2)(x - 1) = 0

∴ x + 2 = 0 ⇒ x = -2

∴ x - 1 = 0 ⇒ x = 1

* when x = -2 ⇒ y = -2 + 2 = 0 ⇒ (-2 , 0)

* when x = 1 ⇒ y = 1 + 2 = 3 ⇒ (1 , 3)

The solution graphically

3 0

3 years ago

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3 years ago

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