May I please get help with this math problem. I have been trying many times to find all correct answers to each length.
Answers
To draw a triangle, you cannot take three random line segments, they have to satisfy the triangle inequality theorems.
0. Triangle Inequality Theorem One: the lengths of any two sides of a triangle must add up to more than the length of the third side.
Procedure:
• Evaluating the first values given: (adding the two smallest values)
[tex]5.2+8.2=13.4[/tex]Now, we have to compare this addition with the bigger value. As 13.4 > 12.8, these can be side lengths of a triangle.
• Evaluating the second values given: (adding the two smallest values)
[tex]5+1=6[/tex]Comparing this addition with the bigger value, we can see that 6 < 10, meaning that these values cannot be side lengths of a triangle.
• Evaluating the third values given: (adding the two smallest values)
[tex]3+3=6[/tex]Comparing, we can see that 6 < 15. Therefore, these cannot be side lengths of a triangle.
• Evaluating the final values given:
[tex]7+5=12[/tex]We can see that 12 < 13, so these cannot be side lengths of a triangle.
Answer:
• 12.8, 5.2, 8.2: ,can be side lengths of a triangle.
,• 5, 10, 1: ,cannot be side lengths of a triangle.
,• 3, 3, 15: ,cannot be side lengths of a triangle.
,• 7, 13, 5: ,cannot be side lengths of a triangle.
Related Questions
i need help solving this with the statements and reasons
Answers
Given that:
[tex]\bar{AB}\mleft\Vert \mright?\bar{DC}[/tex]To prove that:
[tex]\Delta ABE\cong\Delta\text{CDE}[/tex]We know that congruent parts of congruent triangles are congruent
[tex]\angle\text{AEB }\cong\angle CDE\text{ (vertically opposite angles)}[/tex]Given that E is the midpoint of AC, therefore,
[tex]\begin{gathered} EA=EC\text{ } \\ EB=ED \end{gathered}[/tex]By the SAS congruency theorem as illustrated above, it is sufficient to prove that the triangles are congruent
Go on the head 120 eggs delivered to her bakery she used to 98 eggs to bake cakes which equation can she use find the number of eggs r she has left
Answers
Yolanda has 120 eggs, but she used 98 eggs
r represents the equation for the number of eggs that she left:
To find this, subtract the total of eggs by the eggs used
Then, r = 120 - 98
Ingrid is preparing a budget. She is first calculating her income. She makes $2,000 a month as a tutor, but she is going to school to become a lawyer who will eventually make close to $10,000 a month. What is the BEST thing for Ingrid to do to prepare an accurate budget?A. She should use the difference between both incomes--$8,000.B. She should average both incomes and use $6,000.C. She should use her future income of $10,000.D. She should use her current income of $2,000.
Answers
Given:
Ingrid is preparing a budget. She is first calculating her income.
She makes $2,000 a month as a tutor.
And she is going to school to become a lawyer.
Eventually, she will make close to $10,000 a month
So, the best thing is to calculate her earnings when she becomes a lawyer.
So, the answer will be option A
She should use the difference between both incomes--$8,000.
I wanted to know if this is the right answer
Answers
Notice that angles 6 and 4 are alternate exterior angles, therefore:
[tex]m\measuredangle4=m\measuredangle6.[/tex]Answer: m<4=66.
Solve for x. Write the reasons next to each step.Submit723x+10
Answers
x = 26/3
Explanation:We would apply the mid-segment theorem:
The base of the smaller triangle = 1/2 (the base of the bigger triangle)
The base of the smaller triangle = 3x + 10
the base of the bigger triangle = 72
3x + 10 = 1/2(72)
Reason: Mid segment is parallel to the base of the large triangle. And it is equal to half the length of the base of the large triangle
simplifying:
3x + 10 = 72/2
3x + 10= 36
subtract 10 from both sides:
3x + 10 - 10 = 36 - 10
3x = 26
DIvide both sides by 3:
3x/3 = 26/3
x = 26/3
or x = 8 2/3
A cannery needs to know the volume-to-surface-area ratio of a can to find the size that will create the greatest profit. Find the volume-to-surface-area ratio of a can.Hint : For a cylinder, S = 2πr2 + 2πrh and V = πr2h.a. 1/2b. 2(r+h) / rhc. πr(2r + 2h − rh)d. rh / 2(r+h)
Answers
SOLUTION
[tex]Volume\text{ }of\text{ }can=\pi r^2h[/tex][tex]Surface\text{ }area\text{ }of\text{ }can=2\pi r^2+2\pi rh[/tex]The ratio can be established as shown below
[tex]\begin{gathered} \frac{\pi r^2h}{2\pi r^2+2\pi rh} \\ \frac{\pi r^2h}{2\pi r(r+h)} \\ \frac{rh}{2(r+h)} \end{gathered}[/tex]The correct answer is OPTION D
The confidence interval on estimating the heights of students is given as (5.4, 6.8). Find the sample mean of the confidence interval. A.6.8B.6.1C. 5.4D. 0.7
Answers
Solution
- The formula for finding the sample mean from the confidence interval is given below
[tex]\begin{gathered} \text{Given the Confidence interval,} \\ (A_1,A_2) \\ \\ \therefore\operatorname{mean}=\frac{A_1+A_2}{2} \end{gathered}[/tex]- Thus, we can find the sample means as follows
[tex]\begin{gathered} A_1=5.4 \\ A_2=6.8 \\ \\ \therefore\operatorname{mean}=\frac{5.4+6.8}{2} \\ \\ \operatorname{mean}=\frac{12.2}{2} \\ \\ \operatorname{mean}=6.1 \end{gathered}[/tex]Final Answer
The sample mean is 6.1 (OPTION B)
determine the number of real solutions for the following quadratic equation using the discriminate
Answers
Given equation:
[tex]y=x^2-3x-4[/tex][tex]a=1,b=-3,c=-4[/tex]Discriminant:
[tex]\begin{gathered} b^2-4ac \\ (-3)^2-4(1)(-4) \\ =9+16 \\ =25 \end{gathered}[/tex]Number of real solutions:
Since the discriminant is > 0 (that is ,it is a positive value)
Which of the following shows the division problem down below
Answers
Question:
Solution:
Synthetic division is a quick method of dividing polynomials; it can be used when the divisor is of the form x-c. In synthetic division, we write only the essential parts of the long division. Notice that the long division of the given problem is written as:
thus, the synthetic division of the given problem would be:
Writing 6 instead of -6 allows us to add instead of subtracting. We can conclude that the correct answer is:
A.
Find sin 2x, cos 2x, and tan 2x if tan x= -3/2 and x terminates in quadrant IV.
Answers
• sin 2x = -12/13
,• cos 2x = -5/13
,• tan 2x = 12/5
Explanation:Given that
[tex]\tan x=-\frac{3}{2}[/tex]Then
[tex]\begin{gathered} \sin2x=\frac{2\tan x}{1+\tan^2x} \\ \\ =\frac{2(-\frac{3}{2})}{1+(-\frac{3}{2})^2}=\frac{-3}{\frac{13}{4}} \\ \\ =-3\times\frac{4}{13}=-\frac{12}{13} \end{gathered}[/tex][tex]\begin{gathered} \cos2x=\frac{1-\tan^2x}{1+\tan^2x}=\frac{1-(-\frac{3}{2})^2}{1+(-\frac{3}{2})^2} \\ \\ =\frac{1-\frac{9}{4}}{1+\frac{9}{4}}=\frac{-\frac{5}{4}}{\frac{13}{4}}=-\frac{5}{4}\times\frac{4}{13}=-\frac{5}{13} \end{gathered}[/tex][tex]\begin{gathered} \tan2x=\frac{2\tan x}{1-\tan^2x}=\frac{2(-\frac{3}{2})}{1-(-\frac{3}{2})^2} \\ \\ =\frac{-3}{1-\frac{9}{4}}=\frac{-3}{-\frac{5}{4}}=-3\times\frac{-4}{5}=\frac{12}{5} \end{gathered}[/tex]Find the surface area of the cylinderA). 188.4 ft^2B). 226.08 ft^2C). 244.92 ft^2D). 282.6 ft^2
Answers
To solve this problem, we will use the following formula for the surface area of a cylinder:
[tex]A=2\pi rh+2\pi r^2,[/tex]where r is the radius of the base, and h is the height of the cylinder.
Substituting h= 10 ft, and r = 3 ft in the above formula, we get:
[tex]A=2\pi(3ft)(10ft)+2\pi(3ft)^2.[/tex]Simplifying, we get:
[tex]A=244.92ft^2.[/tex]Answer: Option C.
While reviewing the previous day’s arrest report, a police sergeant that seven suspects were arrested, all of whom had either one or two previous arrests. Including yesterday arrests, there were 16 total among them. How many suspects had had less than two prior arrests?
Answers
ANSWER :
EXPLANATION :
solve 6 + 5 on the sqr root of 249 - 2x = 7
Answers
ANSWER
x = 124
EXPLANATION
First we have to clear the term that contains x in the equation. In this case, this term is the second term. So we have tu subtract 6 from both sides of the equation:
[tex]\begin{gathered} 6-6+\sqrt[5]{249-2x}=7-6 \\ \sqrt[5]{249-2x}=1 \end{gathered}[/tex]Then, we have to eliminate the root. Note that in the expression inside the root there are two terms. To do this, we have to apply the "opposite" operation on both sides of the equation, which in this case is exponent 5:
[tex]\begin{gathered} (\sqrt[5]{249-2x})^5=1^5 \\ 249-2x=1 \end{gathered}[/tex]Now we do something similar to the first step. We want to leave on one side of the equation only the term that contains x and the rest on the other side. To do this we can either add 2x on both sides, or subtract 249 from both sides. We'll apply the first option because then we'll have a positive coefficient for x:
[tex]\begin{gathered} 249-2x+2x=1+2x \\ 249=1+2x \end{gathered}[/tex]However, we now have to subtract 1 from both sides of the equation:
[tex]\begin{gathered} 249-1=1-1+2x \\ 248=2x \end{gathered}[/tex]Finally, to find x, we have to divide both sides by 2:
[tex]\begin{gathered} \frac{248}{2}=\frac{2x}{2} \\ 124=x \end{gathered}[/tex]Hence, the solution to the equation is x = 124.
Erin is buying produce at a store. She buys c cucumbers at $0.89 each and a apples at $0.99 each. What does the expression 0.89c + 0.99a represent? The expression represents the
Answers
One cucumber costs $0.89, so with Erin buys "c" cucumbers, the price he will pay for the cucumbers is the unitary price (0.89) times the number of cucumbers ("c"), so the price is 0.89c.
One apple costs $0.99, so with Erin buys "a" apples, the price he will pay for the apples is the unitary price (0.99) times the number of apples ("a"), so the price is 0.99a.
Then, to find the final price Erin will pay, we just need to sum both prices: all the cucumbers and all the apples:
Final price = 0.89c + 0.99a
So the expression represents the final price (or cost) Erin will pay for all products.
Monica did an experiment to compare two methods of warming an object. The results are shown in thetable below. Which statement best describes her results?
Answers
The correct answer is,
The temperature using method 2 changed exponentially.
Use the give right triangle to find ratios. In reduced form, for sin A, cos A, and tan A
Answers
From the figure given, if theta = A
opposite = 28 and hypotenuse =53
substitute the values into the formula
[tex]\sin A=\frac{28}{53}[/tex][tex]\cos A=\frac{adjacent}{\text{hypotenuse}}[/tex][tex]\cos A=\frac{45}{53}[/tex][tex]\tan \theta=\frac{opposite}{adjacent}[/tex][tex]\tan A=\frac{28}{45}[/tex]8. Factor ()=63−252++60 completely given that x=3 is a zero of p(x). Use only the techniques from the lecture on 3.3 (synthetic division). Other methods will receive a score of zero. Be sure to show all your work (including the synthetic division).
Answers
Factor the polynomial
[tex]\begin{gathered} p(x)=6x^3-25x^2+x+60 \\ \text{Given that, }x=3\text{ is a zero} \end{gathered}[/tex]Using the synthetic division method to factorize the polynomial completely,
The resulting coefficients from the table are 6, -7, -20, 0
Thus the quotient is
[tex]6x^2-7x-20[/tex]Factorizing the quotient completely,
[tex]\begin{gathered} 6x^2-7x-20 \\ =6x^2-15x+8x-20 \\ =3x(2x-5)+4(2x-5) \\ =(3x+4)(2x-5) \end{gathered}[/tex]Therefore, the other two zeros of the polynomial are:
[tex]\begin{gathered} (3x+4)(2x-5)=0 \\ 3x+4=0 \\ x=-\frac{4}{3} \\ 2x-5=0 \\ x=\frac{5}{2} \\ \\ Therefore,t\text{he factors of the polynomial are:} \\ (x-3)(3x+4)(2x-5) \end{gathered}[/tex]In 1990, the cost of tuition at a large Midwestern university was $104 per credit hour. In 1998, tuition had risen to $184 per credit hour.
Answers
We have to find the linear relationship for the cost of tuition in function of the year after 1990.
The cost in 1990 was $104, so we can represent this as the point (0, 104).
The cost in 1998 was $184, so the point is (8, 184).
We then can calculate the slope as:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{184-104}{8-0} \\ m=\frac{80}{8} \\ m=10 \end{gathered}[/tex]We can write the equation in slope-point form using the slope m = 10 and the point (0,104):
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-104=10(x-0) \\ y=10x+104 \end{gathered}[/tex]We can then write the cost c as:
[tex]c=10x+104[/tex]We then can estimate the cost for year 2002 by calculating c(x) for x = 12, because 2002 is 12 years after 1990.
We can calculate it as:
[tex]\begin{gathered} c=10(12)+104 \\ c=120+104 \\ c=224 \end{gathered}[/tex]Now we have to calculate in which year the tuition cost will be c = 254. We can find x as:
[tex]\begin{gathered} c=254 \\ 10x+104=254 \\ 10x=254-104 \\ 10x=150 \\ x=\frac{150}{10} \\ x=15 \end{gathered}[/tex]As x = 15, it correspond to year 1990+15 = 2005.
Answer:
a) c = 10x + 104
b) $224
c) year 2005.
State the rational number represented by each letter on the number line as a decimal.
Answers
The rational number represented by the letter D is -43/100 and by the letter R is -46/100.
What is rational number?
A rational number is one that can be written as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.
Here the number line is divided into 10 division with equal distance.
Each division is of the distance 0.01
So, the decimal number represented by letter D is -0.43 and by the letter R is -0.46.
To convert decimal number into rational number,
-0.43 = -43/100
-0.46 = -46/100
Therefore, the rational number represented by each letter on the number line as a decimal are D = -43/100 and R = -46/100.
To know more about the rational number, click on the link
https://brainly.com/question/12088221
#SPJ13
please help ………………. …………. ………… i already have the answer for part A but im having trouble with Parts B and C
Answers
In part B we must perform the following operation:
[tex](5a^3+4a^2-3a+2)+(a^3-3a^2+3a-9)[/tex]The key here is to group the terms according to the power of a they have:
[tex](5a^3+4a^2-3a+2)+(a^3-3a^2+3a-9)=(5a^3+a^3)+(4a^2-3a^2)+(-3a+3a)+(2-9)[/tex]Then, we can use the distributive property of the multiplication but in reverse:
[tex]b\cdot a+c\cdot a=(b+c)\cdot a[/tex]If we do this in each of the terms between parenthesis we get:
[tex]\begin{gathered} (5a^3+a^3)+(4a^2-3a^2)+(-3a+3a)+(2-9)= \\ =(5+1)a^3+(4-3)a^2+(-3+3)a-7 \\ (5+1)a^3+(4-3)a^2+(-3+3)a-7=6a^3+a^2-7 \end{gathered}[/tex]Then the answer for part B is:
[tex]6a^3+a^2-7[/tex]In part C we must simplify:
[tex](4y^3-2y+9)-(2y^3-3y^2+4y+7)[/tex]Here is important to remember that a negative sign before a parenthesis means that you have to change the sign of all the terms inside it. Then we have:
[tex](4y^3-2y+9)-(2y^3-3y^2+4y+7)=4y^3-2y+9-2y^3+3y^2-4y-7[/tex]Now we can do the same thing we did in part B, we group the terms according to the powers of y:
[tex]4y^3-2y+9-2y^3+3y^2-4y-7=(4y^3-2y^3)+3y^2+(-2y-4y)+(9-7)[/tex]Then we apply the distributive property in reverse:
[tex]\begin{gathered} (4y^3-2y^3)+3y^2+(-2y-4y)+(9-7)=(4-2)y^3+3y^2+(-2-4)y+2 \\ (4-2)y^3+3y^2+(-2-4)y+2=2y^3+3y^2-6y+2 \end{gathered}[/tex]Then the answer for part C is:
[tex]2y^3+3y^2-6y+2[/tex]4-10x = 3+5x subtract 4 from both sides
Answers
S={1/15}
1) Solving that expression
4-10x = 3+5x Subtract 4 from both sides
4-4-10x=3-4+5x
-10x =-1+5x Subtract 5x from both sides, to isolate x on the left side
-10x -5x = -1 +5x -5x
-15x=-1 Divide both sides by -15 to get the value of x, not -15x
x=1/15
S={1/15}
Determine whether 17y = 3x − 19 is quadratic or not. Explain.No; there is no x2 term, so a = 0.No; there is no x-term, so b = 0.No; there is no constant term, so c = 0.Yes; it can rewritten in the form y = ax2 + bx + c.
Answers
The standard form of quadratic equation is given as,
[tex]ax^2+bx\text{ + c = 0 where a }\ne\text{ 0}[/tex]The equation is given as,
[tex]17y\text{ = 3x - 19}[/tex]Therefore,
[tex]\text{From the given equation x}^2\text{ is not present and also a = 0.}[/tex]Thus the given equation is not a quadratic equation.
Part I: Domain and Range-identify the domain and range of each graph. Problem / Work Answe 2+ 6+ 2+ 1. Week 15 Homework Packet pdf 2003
Answers
Domain is the set of input values,
In the graph x axis show the domain
Where the x values is lies at -2,-1,0,1,2
Sothe domain will be :
[tex]\text{Domain =-2}\leq x\leq2[/tex]Range is the set of output values,
In the graph the value of function at y axis is : 0,2,4,6,8-2,-4.....
So, the range will be :
[tex]\text{Range = -}\infty\leq y\leq\infty[/tex]Determine the solution to the given equation.4 + 3y = 6y – 5
Answers
Answer:
[tex]y=3[/tex]Explanation:
Step 1. The expression we have is:
[tex]4+3y=6y-5[/tex]And we are required to find the solution; the value of y.
Step 2. To find the value of y, we need to have all of the terms that contain the variable on the same side of the equation. For this, we subtract 6y to both sides:
[tex]4+3y-6y=-5[/tex]Step 3. Also, we need all of the numbers on the opposite side that the variables are, so we subtract 4 to both sides:
[tex]3y-6y=-5-4[/tex]Step 4. Combine the like terms.
We combine the terms that contain y on the left side of the equation, and the numbers on the right side of the equation:
[tex]-3y=-9[/tex]Step 5. The last step will be to divide both sides of the equation by -3 in order to have only ''y'' on the left side:
[tex]\begin{gathered} \frac{-3y}{-3}=\frac{-9}{-3} \\ \downarrow\downarrow \\ y=3 \end{gathered}[/tex]The value of y is 3.
Answer:
[tex]y=3[/tex]The high school soccer booster club sells tickets to the varsity matches for $4 for students and $8
for adults. The booster club hopes to earn $200 at each match.
what does the slope mean in terms of the situation?
Answers
8y= -4x +200
y= -1/2x +25
Slope = -1/2
In a film, a character is criticized for marrying a woman when he is three times her age. He wittily replies, "Ah, but in 21 years time I shall only be twice her age." How old are the man and the
woman?
Write a linear function that models the total monthly costs for each option for x hours of court rental time.
Answers
The age of man is 63 years and the age of women is 21 years.
Given that, a character is criticized for marrying a woman when he is three times her age.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let age of man be x and the age of women be y.
Now, x=3y ---------(1)
In 21 years time man will be twice her age.
x+21=2(y+21)
⇒ x+21=2y+42
⇒ x-2y=21 ---------(2)
Substitute equation (1) in (2), we get
3y-2y=21
⇒ y = 21
So, x=3y=63
Therefore, the age of man is 63 years and the age of women is 21 years.
To learn more about the linear system of an equations visit:
https://brainly.com/question/27664510.
#SPJ1
Complete each equation so that it has infinitely many solutions. 12x - x + 8 + 3x = __x + __ (__ are blanks)
Answers
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
What are a definition and an example of a linear equation?Linear formula first-degree algebraic equation with the variables y = 4x + 3 or similar (that is, raised only to the first power). Such an equation has a straight line for its graph.
-12-x=8-3x
Add what is to the right of the equal sign to both sides of the equation, then rewrite the equation as follows:-12-x-(8-3*x)=0
Take like variables away:-20 + 2x = 2 • (x - 10)
Solve: 2 = 0There is no answer to this equation.A constant that is not zero can never equal zero.x-10 = 0
On both sides of the equation, add 10:x = 10.
To Learn more about linear equation refer to:
https://brainly.com/question/14323743
#SPJ1
Brett colors 25% of the total shapes on his paper. He colors 14 shapes. How many total shapes are there on Brett’s paper?
Answers
Answer:
56 i think because if 25% = 1/4 and 14 is 25% you would need to multiply 14 by 4 to get 100% or 4/4
Blackgrass black graph is the of y=f(x) chose the equation for the red graph
Answers
The Solution:
The correct answer is [option A]
Given:
Required:
To determine the equation of the red graph if the black graph function is y = f(x).
The correctb
Liam's monthly bank statement showed the following deposits and withdrawals.If Liam's balance in the account was $62.45 at the beginning of the month, what was the account balance at the end of the month?
Answers
First, let's take the inital balance and add all the deposits:
[tex]62.45+32.35+63.09+98.79=256.68[/tex]Then, we'll take this amount and substract all the withdrawals:
[tex]256.68-114.95-79.41=62.32[/tex]This way, we can conclude that the account balance at the end of the month was $62.32