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2 years ago

How do I solve this problem?

Mathematics

1 answer:

Sergeu [11.5K]2 years ago

6 0

Answer:

$EF=7.6\ units$

$EG=15.9\ units$

$m$

Step-by-step explanation:

step 1

Find the measure of side EF

we know that

In the right triangle EFG

$tan(61.4\°)=\frac{FG}{EF}$

$EF=\frac{FG}{tan(61.4\°)}$

$EF=\frac{14}{tan(61.4\°)}$

$EF=7.6\ units$

step 2

Find the measure of side EG

we know that

In the right triangle EFG

$sin(61.4\°)=\frac{FG}{EG}$

$EG=\frac{FG}{sin(61.4\°)}$

$EG=\frac{14}{sin(61.4\°)}$

$EG=15.9\ units$

step 3

Find the measure of angle G

wee know that

$m>E+m$ -----> by complementary angles

we have

$m$

substitute

$61.4\°+m$

$m$

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Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.

xxTIMURxx [149]

Answer:

Option A: b must equal 7 and a second solution to the system must be located at the point (2, 5)

Step-by-step explanation:

The complete question is

Tom determines that the system of equations below has two solutions, one of which is located at the vertex of the parabola.

Equation 1: (x – 3)2 = y – 4

Equation 2: y = -x + b

In order for Tom’s thinking to be correct, which qualifications must be met?

A: b must equal 7 and a second solution to the system must be located at the point (2, 5).

B: b must equal 1 and a second solution to the system must be located at the point (4, 5).

C: b must equal 7 and a second solution to the system must be located at the point (1, 8).

D: b must equal 1 and a second solution to the system must be located at the point (3, 4).

step 1

Find the vertex of the quadratic equation

The general equation of a vertical parabola in vertex form is

$y=a(x-h)^2+k$

where

(h,k) is the vertex

we have

$(x-3)^{2}=y-4$

$y=(x-3)^{2}+4$

The vertex is the point (3,4)

step 2

Find out the value of b in the linear equation

we know that

If the vertex is a solution of the system of equations, then the vertex must satisfy both equations

substitute the value of x and the value of y of the vertex in the linear equation

$y=-x+b$

For x=3, y=4

$4=-3+b\\b=7$

$y=-x+7$

step 3

Find out the second solution of the system of equations

we have

$y=(x-3)^{2}+4$ -----> equation A

$y=-x+7$ ----> equation B

solve the system of equations by graphing

Remember that the solutions are the intersection points both graphs

The second solution of the system of equations is (2,5)

see the attached figure

therefore

b must equal 7 and a second solution to the system must be located at the point (2, 5)

5 0

3 years ago

Read 2 more answers

2/7 • 9 1/10 Please help

nordsb [41]

$\frac{2}{7} * 9 \frac{1}{10} = \frac{2}{7} * \frac{91}{10} = \frac{2~*~91}{7~*~10} = \frac{182}{70} = 2 \frac{42}{70} = 2 \frac{3}{5}$

3 0

3 years ago

Read 2 more answers

Reflect triangle stu across line st which of these is a valid reason why the image u will coincide with j

hjlf

Answer:

4. None of the above

Step-by-step explanation:

Reflection is a type of transformation that can be used to change the orientation of a given figure or shape without changing it size and shape.

When triangle STU is reflected across ST, the image U coincides with J because the two are on the opposite side and at the same distance from ST. Therefore, J is like the image of U.

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3 years ago

50 POINTS!!! WILL MARK BRAINLIEST!!! CORRECT ANSWERS PLS 1 HOUR LEFT

Brut [27]

Answer:

○ 3

○ y + ½ = 3(x - 2)

○ Multiply both sides of the equation by 3. The Standard Form of the equation is 12x - 2y = 24.

○ 5x - 3y = 15

○ y = ½x + 5⁄2

Step-by-step explanation:

Find the rate of change [slope]:

-y₁ + y₂\-x₁ + x₂ = m → (-1, 1) and (-2, -2)

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

__________________________________________________________

According to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting this coordinate into the formula with their CORRECT SIGNS:

(2, -½) → y + ½ = 3(x - 2)

__________________________________________________________

We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it:

-3[4x - ⅔y = 8] → -12x + 2y = -24

** They should have multiplied by -3 instead of 3 because that negative is hooked up to everything in the fraction, but since the exercise gave you 12x - 2y = 24, go with 12x - 2y = 24.

__________________________________________________________

If you would take a look at this graph real closely, you will see that this graph intersects the y-axis and x-axis at ENDPOINTS, so to find the x-intercept, you simply plug in zero for y: 5x = 15, and you will know right away that x is set to equal 3, which is what you see in the graph, (3, 0). Now, to find the y-intercept, you simply plug in zero for x: -3y = 15, and you will know right away that y is set to equal -5, which is what you see on the graph as well, (0, -5). With that being said, you have your answer.

__________________________________________________________

y - 3 = ½(x - 1)

y - 3 = ½x - ½

+ 3 + 3

_____________

y = ½x + 2½

* 2½ = 5⁄2

I am joyous to assist you anytime.

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2 years ago

C=a+8 the variable A represents the number of events attended, and the variable C represents the total cost. What is the total c

Nitella [24]

If a is the number of events, then a = 1. Plugging in 1 for a in the equation $C=a+8$ , you get $C=1+8=9$ .

Total cost is $9.

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3 years ago