Answer:
32, 45
Step-by-step explanation:
The closure property under subtraction is shown when the correct
result from the subtraction of polynomials is also a polynomial.
Response:
- The option that shows that polynomials are closed under subtraction is; <u>3·x² - 2·x + 5 will be a polynomial</u>.
<h3>How is the option that shows the closure property found?</h3>
The closure property under subtraction for the polynomials is condition
in which the result of the difference between two polynomials is also a
polynomial.
The given polynomials being subtracted is presented as follows;
(5·x² + 3·x + 4) - (2·x² + 5·x - 1)
Which gives;
(5·x² + 3·x + 4) - (2·x² + 5·x - 1) = 3·x² - 2·x + 5
Given that the result of the subtraction, 3·x² - 2·x + 5, is also a
polynomial, we have, that the option that shows that polynomials are
closed under subtraction is; <u>3·x² - 2·x + 5 will (always) be a polynomial</u>.
Learn more about closure property here:
brainly.com/question/4334406
Answer:
328 feet
Step-by-step explanation:
From a boat ont he lake, the angle of elevation to the top of a cliff is 11° 50'. If the base of the cliff is 1568 feet from the boat, how high is the cliff (to the nearest foot)
Step 1
Note that
that 11°50' is just 11 degrees and 50 minutes
60 minutes = 1 degree,
thus 50 minutes = x degree
50/60 degrees
= 0.83°
Hence: 11°50' = 11.83°.
Step 2
We solve using Trigonometric function of tan
tan theta = Opposite/Adjacent
theta = 11.83°
Adjacent = 1568 feet
Opposite = Height of the cliff = x
tan 11.83° = x/1568
Cross Multiply
x = tan 11.83 × 1568
x = 328.429195 feet
Approximately = 328 feet
The height of the cliff is 328 feet
The system of equations that models the given situation is given as follows:
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
- Variable x: Number of single lawns cut.
- Variable y: Number of front and back lawns cut.
He had 25 customers, hence:
x + y = 25.
He charges $15 for a single lawn and $25 for a front and back lawn, and made a total of $475, hence:
15x + 25y = 475
More can be learned about a system of equations at brainly.com/question/24342899
#SPJ1
Here’s the proof:
The triangle is an Isosceles Triangle. An Isosceles Triangle is a type of triangle that has 2 congruent sides. There is a Theorem called The Isosceles Triangle Theorem, in which states that if a triangle has 2 congruent sides, then it is an Isosceles Triangle, and the angles oppositely the congruent sides will be congruent. Therefore, we know that the triangle is Isosceles because it has 2 congruent sides, so the angles opposite those sides are congruent. We first need to find the angle measures.
1.) Finding the angle measures using the Triangle Sum Theorem. The Triangle Sum Theorem states that all 3 angles in a triangle must sum up to 180°. So, we can create an Algebraic equation to solve and figure out what the angle measures are of the two angles at the bottom of the triangle because they are opposite to the congruent sides.
Equation:
26+2x=180. We know that one angle measure is 26°, and we know the other 2 are angles are congruent, so we will call them X, and there are two of them, so we call them 2x.
26-26+2x=180-26
2x=154
2x/2=154/2
x=77.
Therefore, the angles measure 77°. To check that we can just plug them back into our equation:
26+2(77)=180.
180=180.
The angle measures are correct.
2.) Since we know the angle measures of the triangle, we can use the Alternate Exterior Angles Theorem, which states: if a transversal is intersected by two parallel lines, then the alternating exterior angles are congruent. We can see in the picture that the lane with the triangle on top and trapezoid at the bottom is a transversal (transversal=line intersected by two parallel lines). We can also see that the two lines with arrows are parallel because they are marked parallel with arrows. Therefore, we have a transversal intersected by two parallel lines, so the angles outside the parallel lines and and opposite each other are congruent.
We know that the two angles at the base of the triangle are 77°. The left base angle in the triangle is outside the parallel lines, so angle n or n° must also be 77° because they are both outside the parallel lines (exterior) and alternating from each other.
Therefore, n°=77°