Answer:
The measure of the vertex angle is 94 degrees ⇒ A
Step-by-step explanation:
- In any triangle, the sum of the measures of its interior angle is 180°
- In the isosceles triangle, the two base angles are equal in measures
∵ In an isosceles triangle, the measure of the base angle = (2x + 5)
∵ The base angles of the isosceles triangles are equal in measures
∴ The measures of the base angles are (2x + 5), (2x + 5)
∵ The measure of the vertex angle = (5x - 1)
∵ The sum of the measure of the three angles = 180°
∴ (2x + 5) + (2x + 5) + (5x - 1) = 180
→ Add the like terms in the left side
∵ (2x + 2x + 5x) + (5 + 5 + -1) = 180
∴ 9x + 9 = 180
→ Subtract 9 from both sides
∴ 9x + 9 - 9 = 180 - 9
∴ 9x = 171
→ Divide both sides by 9 to find x
∴ x = 19
→ Substitute the value of x in the measure of the vertex angle to find it
∵ The measure of the vertex angle = 5x - 1
∴ The measure of the vertex angle = 5(19) - 1
∴ The measure of the vertex angle = 95 - 1
∴ The measure of the vertex angle = 94°
∴ The measure of the vertex angle is 94 degrees
hours each day.
Step-by-step explanation:
The given function models the number of cars that are put through a quality control test each hour at a car production factory.
The given function is
We need to find the number of hours does the quality control facility operate each day.
Rewrite the given function it factored form.
Taking out the common factors from each parenthesis.
The factored form of given function is c(t)=-(t-10)(t+2).
Equate the function equal to 0 to find the x-intercept.
Number of hours cannot be negative. So from t=0 to t=10 quality control facility operate the cars.
Therefore the quality control facility operates for 10 hours each day.
Answer:
Step-by-step explanation:
x intercepts are -3,-1
f(x)=-(x²+x+3x+3)=-(x²+4x)-3=-(x²+4x+4-4)-3=-(x+2)²+4-3
or f(x)=-(x+2)²+1
vertex is (-2,1)
so it is an inverted parabola with vertex (-2,1) and x-intercepts (-3,0) and (-1,0)
Answer:
3
Step-by-step explanation:
The number is 3.
Step-by-step explanation:
Finding the Number
To find the number, we have to translate the problem above to an algebraic equation. The algebraic equation refers to the statement of the equality of two algebraic expressions.
Equation:
Let "x" be the number.
4 is divided by a number - 4/x
3 divided by the number decreased by 2 - 3/x-2
"4 is divided by a number is equal to 3 divided by the number decreased by 2"
4/x = 3/x-2
Solution:
Cross multiply.
4/x = 3/x-2
x(3) = 4(x-2)
3x = 4x - 8
(Combine similar terms.)
3x - 4x = - 8
- x = - 8
- x/- 1 = - 8/- 1
x = 8
Final Answer:
8
Checking:
4/x = 3/x-2
4/8 = 3/8-2
1/2 = 3/6
1/2 = 1/2 ✔
Answer:
y=mx + b
the slope is -3,2
y= -0.67x + 5
this is what. i got i could be wrong, sorry if i am
Step-by-step explanation:
