Ray Np is an angle bisector of angle MNQ and measure of Angle PNQ = 2x+1. Find the measure of angle MNQ. If The measure of MNQ=x^2-10. Find the value of x, and the appropriate measure of angle MNQ
Answers
Because ray NP bisects ∠MNQ, therefore
∠MNP = ∠PNQ = 2x + 1.
Therefore
∠MNQ = 2*∠PNQ = 2(2x + 1) = 4x + 2.
Because ∠MNQ is given as x² - 10, therefore
x² - 10 = 4x + 2
x² - 4x - 12 = 0
(x + 2 )(x - 6) = 0
x = -2, or x = 6
When x = -2,
∠MNQ = 4*(-2) + 2 = -6°
This answer is not acceptablle, therefore x = -2 should be rejected.
When x = 6,
∠MNQ = 4*6 + 2 = 26°
Answer: x = 6, and ∠MNQ = 26°
To find the measure of angle MNQ, we can set up an equation using the fact that ray NP is an angle bisector. Solving the equation gives us the value of x, and substituting that value back into the equation gives us the measure of angle MNQ.
Explanation:To find the measure of angle MNQ, we can use the fact that ray NP is an angle bisector of angle MNQ. This means that angle PNQ is half of angle MNQ.
We are given that angle PNQ = 2x + 1, so we can set up the equation 2x + 1 = (1/2)(x^2 - 10) to find the value of x.
Solving this equation, we get x = 5. Therefore, the measure of angle MNQ is 5^2 - 10 = 15 degrees.
Related Questions
Ricardo is constructing a line through point P that is perpendicular to line m. He has already constructed the arc shown.
He places his compass on point X to construct an arc.
What must be true about the width of the compass opening when Ricardo draws the arc?
It must be less than 1/2XY.
It must be equal to XY .
It must be equal to PX .
It must be greater than 12XY.
Answers
Answer:
It must be greater than 1/2XY.
Step-by-step explanation:
We draw an arc from point X below the arc that passes through X and Y. Keeping our compass the same width, we will draw another arc from point Y below, intersecting the first arc.
If the width of the compass is not set to more than 1/2XY, then the two arcs will not intersect and we will not complete our construction.
Perpendicular lines are lines that meet at 90 degrees.
The true statement about the width of the compass is that: (d) It must be greater than 1/2XY.
From the question, we understand that he has drawn arc XY already.
The next step is to draw an arc less than the width of XY, but greater than half width XY.
This will ensure that the arcs bisect one another.
Hence, the true option is (d).
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Number 28 plz?????!!?!???
Answers
64 - 4 divided by 4 is
60 div by 4 = 15. No, 65 is not correct.
Let's try again, following Order of Operations rules:
Anything within parentheses is done first, followed by exponentiation. After that it's mult. or div., and after that it's addn. or subtr.
8^2 - 4 divided by 2 + 2 = 65
Do 8^2 first; correct result is 64.
"-4 div by 2" is -2; adding 2 results in zero.
Then we have 64 = 65 (which is false.
Are you positive that the original problem included a '65,' not a '64?'
: A bookstore owner is conducting market research to forecast sales for the coming year. The bookstore is open 360 days a year and out of the 1,200 people who pass the store each day, 8% of them enter the store and make a purchase. The average amount of each sale is $18. What is the estimated amount of sales for the coming year?
Answers
Answer:
622,080
Step-by-step explanation:
thanks me later
If it takes Ashley 3 seconds to run from the batters box to first base at an average speed of 6.5 m/sec, what is the distance that she covers in that time?
Answers
Find a formula for the sum of the first n even positive integers.
b.prove the formula that you conjectured in part (a)
Answers
(a) The formula for the sum of the first n even positive integers is n(n+1) and (b) the formula has been proved with an example.
What is an arithmetic progression?Arithmetic progression is the sequence of numbers that has a fixed common difference between any two consecutive numbers.
For the given situation,
Part (a):
The sum of even numbers formula is obtained by using the sum of terms in an arithmetic progression formula.
Sum of Even Numbers Formula = n(n+1),
where n is the number of terms in the series.
Part (b):
Let us consider the even positive numbers,
2,4,6,8,10,.......
Now take first 5 positive numbers 2,4,6,8,10
By using the formula, n=5
Sum of n even positive integers = [tex]n(n+1)[/tex]
⇒ [tex]5(5+1)[/tex]
⇒ [tex]5(6)[/tex]
⇒ [tex]30[/tex].
Now add the first 5 positive numbers without the formula,
⇒ [tex]2+4+6+8+10=30[/tex]
Hence we can conclude, that the formula for the sum of the first n even positive integers is n(n+1) and the formula has been proved with an example.
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The formula for the sum of the first n even positive integers is S = n(n+1). This was derived by recognizing the pattern of the series and using the formula for the sum of an arithmetic series. The proof by induction confirms the validity of our formula.
Explanation:The problem asks us to find and prove a formula for the sum of the first n even positive integers. To find the formula, we recognize that the first n even integers can be represented as 2, 4, 6, ..., 2n. Hence, the sum S of the first n even integers can be written as S = 2 + 4 + 6 + ... + 2n. This is an arithmetic series with the first term a = 2 and the common difference d = 2. The sum of an arithmetic series can be given by the formula S = n/2 [2a + (n-1)d], substituting a = 2 and d = 2, we get S = n/2 [2*2 + (n-1)2] = n[2 + 2(n-1)], which simplifies to S = n(n+1).
To prove this formula, we use induction. For n=1, the sum is 2, which matches our formula 1(1+1) = 2. Assuming the formula holds for n = k, for n = k+1, the sum would include one more term, 2(k+1), so the new sum is S + 2(k+1) which upon simplification, verifies our formula for all n.
89.87 is 215% of what number
Answers
89.87 is 215% of approximately 41.8. This is found by converting 215% to a decimal (2.15) and dividing the given number (89.87) by this decimal.
Explanation:
The student's question relates to an application of percentages. To work out this problem, we must first understand that in this context, 215% is equivalent to 2.15 when transformed into a decimal. We then divide the given number, 89.87, by 2.15 to find the original value. The calculation would be as follows: 89.87 ÷ 2.15, which equates to approximately 41.8. Therefore, 89.87 is 215% of the number 41.8.
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prove that x-s-t is a factor of x^3 - s^3 -t^3 -3st(s+t)
Answers
To prove that (x-s-t) is a factor of the polynomial $x^3 - s^3 - t^3 -3st(s+t)$, we applied the factor theorem which states that (x-c) will be a factor of a polynomial if f(c) equals zero. By substituting x with (s+t) into the polynomial, we got a value of zero, confirming that (x-s-t) is indeed a factor.
Explanation:To prove that (x-s-t) is a factor of $x^3 - s^3 -t^3 -3st(s+t)$, we can use the factor theorem. According to the factor theorem, a polynomial f(x) has a factor (x-c) if and only if f(c) equals zero.
Given the polynomial $x^3 - s^3 - t^3 -3st(s+t)$, we substitute (x = s + t) into the polynomial, thus:
$f(s + t) = (s + t)^3 -s^3 -t^3 - 3st(s + t)$.
After simplifying the equation, we obtain:
$s^3 + 3s^2t +3st^2 + t^3 - s^3 - t^3 - 3st^2 - 3s^2t$.
When we cancel out the like terms, the result is 0. Therefore,
$(x - s - t)$ is a factor of the given polynomial $x^3 - s^3 -t^3 -3st(s+t)$. This proves our result according to the Factor theorem.
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1. What is the area of a parallelogram whose vertices are A(−1, 12) , B(13, 12) , C(2, −5) , and D(−12, −5) ?
2.
Each small square on the grid is 1 ft².
Which estimate best describes the area of this figure?
25 ft²
35 ft²
50 ft²
65 ft²
Answers
Kesia knows that 1/4=0.25. Explain how she could use this fact to determine the decimal equivalent of 5/8
Answers
[tex]0.25 = \frac{1}{4} = \frac{2}{8} [/tex]
[tex] \frac{5}{8} = \frac{2}{8} + \frac{2}{8} + \frac{1}{8} = \\ 0.25 + 0.25 + \frac{0.25}{2} = \\ 0.25 + 0.25 + 0.125 = 0.625 [/tex]
Answer:
0.625
Step-by-step explanation:
We are given that
Kesia knows =[tex]\frac{1}{4}=0.25[/tex]
We have to determine the decimal equivalent to [tex]\frac{5}{8}[/tex] using given decimal value.
[tex]\frac{5}{8}[/tex] can be written as
[tex]\frac{5}{8}=\frac{2}{8}+\frac{2}{8}+\frac{\frac{1}{4}}{2}[/tex]
[tex]\frac{5}{8}=\frac{1}{4}+\frac{1}{4}+\frac{\frac{1}{4}}{2}[/tex]
[tex]\frac{5}{8}=0.25+0.25+\frac{0.25}{2}[/tex]
[tex]\frac{5}{8}=0.50+\frac{0.25}{2}[/tex]
[tex]\frac{5}{8}=0.625[/tex]
Hence,[tex]\frac{5}{8}=0.625/tex]
Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. Helena has 17 cups of flour and 4.5 cups of sugar available for baking.
Which combination of loaves of bread and batches of muffins could Helena bake?
Answers
Answer:
Helen can make 2 loaves of bread and 4 batches of muffins.
Step-by-step explanation:
Let x be the number of loaves of bread
Let y be the number of batches of muffins
As per the given requirement of flour, the equation becomes:
[tex]3.5x+2.5y=17[/tex] .......(1)
As per the given requirement of sugar, the equation becomes:
[tex]0.75x+0.75y=4.5[/tex] .....(2)
Multiplying equation (1) with 0.3 and subtracting (2) from (1)
[tex]1.05x+0.75y=5.1[/tex] now subtracting (2) from this we get
=> [tex]0.3x=0.6[/tex]
So, x = 2
And as [tex]3.5x+2.5y=17[/tex] ; so substituting x = 2 here we get
[tex]3.5(2)+2.5y=17[/tex]
[tex]7+2.5y=17[/tex]
[tex]2.5y=17-7[/tex]
[tex]2.5y=10[/tex]
So, y = 4
Hence, there will be 2 loaves of bread and 4 batches of muffins.
What is the average rate of change of d(t) between 2 seconds and 6 seconds, and what does it represent? 128 m/s; it represents the average speed of the object between 2 seconds and 6 seconds 80 m/s; it represents the average speed of the object between 2 seconds and 6 seconds 128 m/s; it represents the average distance traveled by the object between 2 seconds and 6 seconds 80 m/s; it represents the average distance traveled by the object between 2 seconds and 6 seconds
Answers
Relationship B has a greater rate than Relationship A.
This graph represents Relationship A. Which equations could represent Relationship B?
Select each correct answer.
a) y = 3/4x
b) y = 0.6x
c) y = 1/4x
d) y = 2/3x
Answers
The equation (a) y = 3/4x, equation (b) y = 0.6x, equation (d) y = 2/3x are correct option because they have greater rate than A
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
We have;
Relationship B has a greater rate than Relationship A.
From the graph, the rate of A or slope will be:
A(m) = (4-2)/(8-4) = 2/4
A(m) =1/2 = 0.5
From the given option, the equation y = 3/4x, y = 0.6x, and y = 2/3x has a greater rate than A which is 3/4, 0.6, and 2/3 respectively.
Thus, the equation (a) y = 3/4x, equation (b) y = 0.6x, equation (d) y = 2/3x are correct option because they have greater rate than A
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Martin drives to work at a speed of 45 miles per hour. It takes him about 2 hours and 15 minutes to get to work. If gas costs $2.75 per gallon and Martin’s car gets 25 miles per gallon, about how much does Martin spend on gas to get to work?
Answers
2.25 * 45 = 101.25 miles to work
101.25 / 25 = 4.05 gallons of gas
4.05 * 2.75 = $11.14 total cost of gas
What number can you add to 7√ to get a rational number?
Answers
The number that can be added to √7 to get a rational number is -√7.
What are rational numbers?A number of the form a/b where a and b are integers and b ≠ 0 is called a rational number.
The given number is √7.
√7 is an irrational number.
Note that the square root of prime numbers is irrational, therefore, to get a rational number by addition, the only way is to add the negative reciprocal of the given irrational number.
The negative reciprocal of √7 is -√7, therefore, add -√7 to √7:
√7 + (-√7) = 0 (a rational number).
Hence, the number that can be added to √7 to get a rational number is -√7.
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please help me out with this simple question I REALLY NEED THIS :((((((((
Answers
WILL MARK BRAINLIEST!!
Write log3 6 as a logarithm of base 2.
log base 2 of 3 over log base 2 of 6
log base 2 of 6 over log base 2 of 3
log base 3 of 2 over log base 6 of 2
log base 6 of 2 over log base 3 of 2
Answers
Using the change-of-base formula:
log3(x)=logb(x)/logb(a)
to write log3(6) as a logarithm of base 2: a = 3, x = 6, b = 2:
log3(6)=log2(6)/log2(3)
hope this helps ^-^
Answer:
Option 2 - log base 2 of 6 over log base 2 of 3
Step-by-step explanation:
Given : Expression [tex]\log_3 6[/tex]
To find : Write the expression as a logarithm of base 2?
Solution :
Expression [tex]\log_3 6[/tex]
Applying the change-of-base formula,
[tex]\log_a(x)= \frac{\log_b(x)}{\log_b(a)}[/tex]
On comparing, a = 3, x = 6, b = 2
Substitute in the formula,
[tex]\log_3 (6)= \frac{\log_2(6)}{\log_2(3)}[/tex]
Therefore, Option 2 is correct.
Option 2 - log base 2 of 6 over log base 2 of 3
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit? 20.6 units 22.7 units 25.6 units 27.6 units
Answers
we know that
the perimeter of a polygon is the sum of the length sides
in this problem we have a triangle
so
the polygon has three sides
Let
[tex]A(-5,4)\\B(1,4)\\C(3,-4)[/tex]
the perimeter is equal to
[tex]P=AB+BC+AC[/tex]
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance AB
[tex]A(-5,4)\\B(1,4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(4-4)^{2}+(1+5)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]dAB=6\ units[/tex]
Step 2
Find the distance BC
[tex]B(1,4)\\C(3,-4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(-4-4)^{2}+(3-1)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{68}[/tex]
[tex]dBC=8.25\ units[/tex]
Step 3
Find the distance AC
[tex]A(-5,4)\\C(3,-4)[/tex]
substitutes the values in the formula
[tex]d=\sqrt{(-4-4)^{2}+(3+5)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(8)^{2}}[/tex]
[tex]d=\sqrt{128}[/tex]
[tex]dAC=11.31\ units[/tex]
Step 4
Find the perimeter
the perimeter is equal to
[tex]P=AB+BC+AC[/tex]
substitutes the values
[tex]P=6+8.25+11.31=25.56\ units=25.6\ units[/tex]
therefore
the answer is
[tex]25.6\ units[/tex]
What is the Solution of the following system?
{-3x -2y = -12
{9x + 6y= -9
Imagine those two bracket things are one big one connecting both equations, and the answers are A (2,1) B No Solutions C (-2, -1) D Infinitely Many Solutions
@Emma11234
Answers
One of the methods we can use to solve the system is the elimination method. In this method we multiply one of the equations with a certain value, such that when the this equation is added to the other one, one of x or y cancels out:
Notice that we can eliminate the variable y by multiplying the first equation by 3, and adding it to the second equation:
the system becomes:
-9x-6y=-36
9x+6y=-9
adding the left hand sides, and the right hand sides of the equations we have:
0=-45, which is not true. This means that the system has no solutions because all the operations we used are valid, but the result is absurd.
Answer: B. No solutions.
Remark:
we could have noticed that the coefficients of x and y in both equations are proportional. (-3*(-3)=9, -2*(-3)=6)
In such situations, if the numbers in the right hand side are also proportional, then the solution has infinitely many solutions,
if not, as in our case, the system has no solution.
Which set of statements always have the same truth value
A) Conditional and Converse
B) Conditional and Inverse
C) Inverse and Contrapositive
D) Conditional and Contrapositive
Answers
The set of statements always have the same truth value will be Conditional and Contrapositive i.e. Option [tex](D)[/tex] .
What is Conditional and Contrapositive?
Conditional and Contrapositive : If the conditional statement is “If P then Q.” Then converse of the conditional statement is “If Q then P.” The contrapositive of the conditional statement is “If not Q then not P.” The inverse of the conditional statement is “If not P then not Q.”
So,
As per given options,
Option [tex](B)[/tex] and [tex](C)[/tex] have inverse, so they have nothing to do with inverse.
Now,
So, according to the above mentioned definition,
Option [tex](D)[/tex] Conditional and Contrapositive is the correct option.
Hence, we can say that the set of statements always have the same truth value will be Conditional and Contrapositive Option [tex](D)[/tex] .
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Formula for calculating commission
Answers
Commission is calculated by multiplying sales revenue by the commission rate; this incentivizes sales, aiming to balance salary, commission, and overall business objectives like profitability and customer satisfaction.
The formula for calculating commission is usually based on the sales revenue multiplied by the commission rate. If, for example, a sales employee sells $10,000 worth of products and the commission rate is 5%, the calculation would be $10,000 x 0.05 = $500.
Commissions serve as a motivational tool in sales. They provide sales employees with an incentive to increase sales, as their earnings are directly linked to the success of their efforts. Optimal sales volume, profitability, and customer satisfaction are central to a well-balanced compensation plan that incorporates both a base salary and a commission structure.
PLEASE HELP ME :( I DONT UNDERSTAND! A teacher already had a certain number of canned goods for the food drive. Each day of the food drive, the class plans to bring in 10 cans. The total number of canned goods for 10 is 205. Assume the relationship is linear. Find and interpret the rate if change and the initial value.
Answers
The graph of the function B is shown below. If B(x) = -1, then what is x?
A. -1
B. 1
C. 2
A is NOT The answer, the answer is either B or C!!!
Answers
Evaluate the integral of the quotient of the sine of x and the square root of the quantity 1 plus cosine x, dx.
Answers
Answer:
[tex]-2\sqrt{1+\cos(x)}+C[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus[tex]\boxed{\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))}[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:
[tex]\displaystyle \int \dfrac{\sin(x)}{\sqrt{1+\cos(x)}}\;\text{d}x[/tex]
To evaluate the given integral, we can use the method of substitution.
Integration by substitution is a way of integrating a function of a function by simplifying the integral. To integrate by substitution, write part of the function in terms of u, where u is some function of x.
Use the substitution u = 1 + cos(x).
Start by differentiating u with respect to x:
[tex]\begin{aligned}u&=1+\cos(x)\\\\\dfrac{\text{d}u}{\text{d}x}&=0-\sin(x)\\\\\dfrac{\text{d}u}{\text{d}x}&=-\sin(x)\end{aligned}[/tex]
Now rearrange the equation for du/dx to get dx on its own:
[tex]\text{d}u=-\sin(x)\:\text{d}x[/tex]
[tex]\text{d}x=-\dfrac{1}{\sin(x)}\:\text{d}u[/tex]
Substitute everything into the original expression:
[tex]\begin{aligned}\displaystyle \int \dfrac{\sin(x)}{\sqrt{1+\cos(x)}}\;\text{d}x&=\int \dfrac{\sin(x)}{\sqrt{u}}\cdot -\dfrac{1}{\sin(x)}\:\text{d}u\\\\ &=\int -\dfrac{1}{\sqrt{u}}\:\text{d}u\end{aligned}[/tex]
Simplify the integral and evaluate:
[tex]\begin{aligned}&=\displaystyle \int -u^{-\frac{1}{2}}\:\text{d}u\\\\&=\dfrac{-u^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+C\\\\&=\dfrac{-u^{\frac{1}{2}}}{\frac{1}{2}}+C\\\\&=-2\sqrt{u}+C\end{aligned}[/tex]
[tex]\textsf{Finally, substitute $u=1+\cos(x)$ back in:}[/tex]
[tex]=-2\sqrt{1+\cos(x)}+C[/tex]
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At a charity bike rally, 2/3 of the student population of Heartsworth Middle School participated. If there are 1,200 students in Heartsworth, how many participated?
Answers
(2÷3)×(1200)= 800
800 students participated at a charity bike rally
What are mathematics operations?
• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
It is given that :
there are 1200 students population of Heartsworth Middle School.
and, 2/3 of the student participated in a charity bike rally That is :
(2 x 1200)/ 3 = 2400/3 = 800 students
Therefore, 800 students participated at a charity bike rally.
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A club with 15 women and 12 men need to form a committee that consists of a president, a vice president, a secretary, and a treasurer. how many committees are possible…
a. if the committee must have two women and two men?
Answers
where [tex]\displaystyle{ C(n, r) = \frac{n!}{r!(n-r)!} [/tex], r! being [tex]1\cdot2\cdot...\cdot r[/tex].
Thus, 2 women out of 15 can be selected in a total of C(15, 2) many ways, and 2 men out of 12, can be selected in C(12, 2) many ways.
Any possible pair of women can be combined with any pair of men, thus there are a total of [tex]C(15, 2)\cdot C(12, 2)[/tex] many ways of forming the committee.
[tex]C(15, 2)\cdot C(12, 2)= \displaystyle{ \frac{15!}{2!13!}\cdot \frac{12!}{2!10!}= \displaystyle{ \frac{15\cdot14\cdot13!}{2!13!}\cdot \frac{12\cdot11\cdot10!}{2!10!}[/tex]
[tex]\displaystyle{ = \frac{15\cdot14}{2}\cdot \frac{12\cdot11}{2}=15\cdot 7\cdot6\cdot11= 6,930[/tex]
Answer: 6,930
(Fill in the blank )
Zero pairs are two numbers that ______ to get zero.
A. Subtract
B. Add
C. Divide
D. Multiply
Answers
B. Add
graph and solve the system
3x+6y-12= 0
x + 2y = 8
Answers
Y-intercept: 2
Slope: -1/2
Y-intercept:4
hope this helped :)
which overlapping triangles are congruent by ASa
Answers
How do I write the height h of the rectangle as a function of x.
Answers
(4x-x^2)-2x=2x-x^2
To write the height h of the rectangle as a function of x, you need to understand the relationship between the height and the other variables involved.
To write the height h of the rectangle as a function of x, you need to understand the relationship between the height and the other variables involved. In a rectangle, the height is typically perpendicular to the base.
So, if we assume that x represents the base length, then the height h can be written as a function of x using an equation.
For example, if the rectangle has a fixed width, the height can be calculated using the following equation: h = f(x), where f is the function that describes the relationship between the base length x and the height h.
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Tom went to his car in the morning and saw that a car or truck had bumped into it during the night, causing a lot of damage. What is the most likely outcome of this situation?
His finance company will reduce his interest.
His insurance company will lower his monthly payments.
His insurance company will pay for damages.
His finance company will increase his interest.
Answers
Answer:
His insurance company will pay for damages.
Step-by-step explanation:
An insurance is a form of contract that permits an individual to transfer the responsibilities of a financial loss to an insurance company. The company bears the risk of the financial loss. Small amount of money are collected from their clients and summed together to pay for losses that the client may encounter in the future. Insurance safeguards an individual and his property from losses, misfortune, hazards or theft. Covered losses are paid for by the insurance company thereby reducing the financial costs for the individual. Examples include auto insurance , health insurance, disability insurance, and life insurance.