The value of 'y' in the isosceles trapezoid ABCD is 14 and this can be determined by using the properties of isosceles trapezoid.
Given :
ABCD is an isosceles trapezoid with legs AB and CD and base BC.If the length of AB is (7y - 4), the length of BC s (4y - 6) and the length of CD is (8y - 18).The two legs are of equal length In any isosceles trapezoid that means:
7y - 4 = 8y - 18
Add 18 on both sides in the above equation.
7y - 4 + 18 = 8y - 18 + 18
7y + 14 = 8y
Now, subtract 7y on both sides in the above equation.
7y + 14 - 7y = 8y - 7y
Simplify the above expression in order to get the value of 'y'.
y = 14
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Calculate each mountain path grade to the nearest percent. Path A for every 31 meters of horizontal distance, the vertical change is 11 meters Path B for every 4.25 meters of horizontal distance, the vertical change is 3 meters?
The grades of Path A and Path B are calculated by dividing the vertical change by the horizontal distance. Path A has a grade of approximately 35%, while Path B has a grade of approximately 71%.
Explanation:The grade of a path or road is calculated by taking the vertical rise and dividing it by the horizontal distance, typically expressed as a percentage. In Path A, the vertical change is 11 meters and the horizontal distance is 31 meters. Therefore, the grade of Path A is calculated as follows:
(11 / 31) x 100 = 35.48%So, Path A has a grade of approximately 35% when rounded to the nearest percent.
For Path B, the vertical change is 3 meters and the horizontal distance is 4.25 meters. Therefore, the grade of Path B is calculated as follows:
(3 / 4.25) x 100 = 70.59%So, Path B has a grade of approximately 71% when rounded to the nearest percent.
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find the average rate of change for the equation [1,6] f(x)=-ln(x)
The histogram shows the number of hours volunteers worked one week.
What percent of the volunteers worked 8 to 11 hours or 16 to 19 hours?
Enter your answer in the box.
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The larger triangle is a dilation of the smaller triangle with a center of dilation at
(2,???1)
.
What is the scale factor of the dilation?
A. 1/3
B. 1/2
C. 2
D. 3
HELP!!! BRAINLIEST ANSWER!!!!!!
Arnold and Jeremy are working on a rocket project for math class. Their job is to find the time it takes for a model rocket to reach its maximum height and how long it will take the rocket to return to Earth if the rocket’s parachute fails to deploy.
They are making calculations for three different rocket engines and each engine has a different initial velocity. They are a bit confused on how to make the calculations. Take a look at the information that they were given and show them how to set up the equations and solve for the times requested.
1. A model rocket is launched from the ground with an initial velocity of 160 ft/sec.
a. How long will it take the rocket to reach its maximum height?
b. Assume the model rocket’s parachute failed to deploy and the rocket fell back to the ground. How long would it take the rocket to return to Earth from the time it was launched?
since u already have a answer and brainly isn't letting me ask a question i have to ask it here...... how did you figure out what the max height was for the rocket.
The rocket will reach it's maximum height in 4.98 seconds.
The rocket would return to earth in 9.96 seconds from the time it was launched.
What are Equations of Motion?Equations of motion are the equations which relate quantities like velocity, displacement, time and acceleration.
There are three equations of motion, which are:
First equation of motion, v = u + at
Second equation of motion, s = ut + [tex]\frac{1}{2}[/tex] at²
Third equation of motion, v² = u² + 2as
where, u is the initial velocity, v is the final velocity, a is the acceleration, t is the time and s is the displacement.
(a) Given that a model rocket is launched from the ground with an initial velocity of 160 feet/sec.
So, u = 160 feet/sec. = 160 × 0.305 meter/second = 48.8 meter/sec.
At maximum height velocity will be equal to zero.
So, v = 0
Here value of the acceleration will be g, acceleration of gravity = 9.8 m/s². And the sign of g will be negative because motion is in upward direction against gravity.
So, a = -g = -9.8 m/s².
From first equation of motion,
v = u + at
0 = 48.8 + (-9.8)t
9.8 t = 48.8
t = 48.8 / 9.8
t = 4.98 seconds.
(b) If the model rocket’s parachute failed to deploy and the rocket fell back to the ground, the time taken to reach the ground from it's maximum height will be the same as the time taken to reach the maximum height from the ground.
So total time taken = 4.98 + 4.98 = 9.96 seconds
Hence, the rocket will reach it's maximum height in 4.98 seconds.
The rocket would return to the Earth from the time it was launched in 9.96 seconds.
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CAN SOMEONE HELP ME PLZ!!
The salesperson earn $172 in COMMISSION last week. How much money, in dollars, did he have in SALES last week?
The correct answer is $3,640 ($3,640 is really the answer). Explain step-by-step how to come to that answer or show your work.
can u find the volume of a cone?
The volume of a cone is 180 in3. find a function that models the height h of the cone in terms of its radius r.
Final answer:
The function modeling the height of the cone in terms of its radius, given the volume of 180 in³, is h(r) = 540 / (πr²).
Explanation:
The volume V of a cone with radius r and height h is given by the formula V = (1/3)πr²h, where π is Pi (approximately 3.14159). Given that the volume of the cone is 180 in³, we can solve for the height h in terms of the radius r.
Starting with the formula:
V = (1/3)πr²h
We plug in the volume:
180 = (1/3)πr²h
To solve for h, we rearrange the equation:
h = 3*180 / (πr²)
h = 540 / (πr²)
So the function modeling the height h of the cone in terms of its radius r is:
h(r) = 540 / (πr²)
Which statement is NOT always true?
A. The sum of two rational numbers is rational.
B. The product of two irrational numbers is rational.
C. The sum of a rational number and an irrational number is irrational.
D. The product of a nonzero rational number and an irrational number is irrational.
Statement B is the one that is NOT always true.
Explanation of which statement is not always true among given mathematical statements.
To determine which statement is not always true among the given options, let's analyze each one:
A. The sum of two rational numbers is rational - Always TrueB. The product of two irrational numbers is rational - Not Always True. For example, √2 multiplied by √2 equals 2, which is rational.C. The sum of a rational number and an irrational number is irrational - Always TrueD. The product of a nonzero rational number and an irrational number is irrational - Not Always True. For example, 1 (rational) multiplied by √2 (irrational) equals √2 (irrational).Based on the analysis,
Statement B is the one that is NOT always true.
Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 6, nothing otherwise. What is your expected value?
Final answer:
The expected value of the game where you pay $3.00 to roll a die and win $5.00 for rolling a 1 or a 6 is -$0.33 per roll, indicating a loss over time.
Explanation:
The problem is asking us to calculate the expected value of the game in which you pay $3.00 to roll a fair die with the potential of winning $5.00 for rolling a 1 or a 6. To find the expected value, we need to multiply the outcomes by their respective probabilities and then sum these products.
The probability of rolling a 1 or a 6 is 1/6 for each number, so the combined probability for these winning rolls is 1/6 + 1/6 = 1/3. The probability of rolling a 2, 3, 4, or 5 is therefore 2/3 since these are the non-winning rolls.
Let's calculate the expected value (EV):
Winning: (1/3) * $5.00 = $1.67
Losing: (2/3) * -$3.00 = -$2.00
Now we add the two values:
EV = $1.67 - $2.00 = -$0.33
Therefore, the expected value of playing the game is a loss of $0.33 per roll. This means that in the long run, you can expect to lose an average of $0.33 for each time you play this game.
A salesperson earns a weekly base salary plus a commission of 20% of all sales over the first $500. This situation can be represented by the expression 750+0.2(x-500). Which of the following describes the meaning of 0.2(x-500) for this situation?
a. total amount of sales
b. total amount of salary earned
c. total amount of sales after the first $500
d. total amount of commission earned
and example why it is the answer
Answer:
d. total amount of commission earned
Step-by-step explanation:
A salesperson earns a weekly base salary plus a commission of 20% of all sales over the first $500.
This situation can be represented by the expression [tex]750+0.2(x-500)[/tex]
0.2(x-500) means total amount of commission earned.
This is because firstly its given that 20% is commission so we have 0.2.
The x-500 represents the sales over $500, where x is total sales. Like the person sold $800 worth of items so he will get 20% commission on $300.
Prism A is similar to Prism B. The volume of Prism A is 2720 cm³.
What is the volume of Prism B?
PLEASE HELP
If a = 1, find the values of b, c, and d that make the given expression equivalent to the expression below.
Equivalent expressions are expressions with the same value.
The values of the variables are:
[tex]\mathbf{a = 1}[/tex] [tex]\mathbf{b = 9}[/tex] [tex]\mathbf{c = -2}[/tex] [tex]\mathbf{d = 4}[/tex]
The expression is given as:
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49}}[/tex]
Expand
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{3x^2 + 9x - 7x - 21}{-2x^2 +4x -6x + 12} \cdot \frac{2x^2 + 14x + 9x + 63}{6x^2 + 21x - 14x - 49 } }[/tex]
Factorize
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{3x(x + 3) - 7(x + 3)}{-2x(x -2) -6(x - 2)} \cdot \frac{2x(x + 7) + 9(x + 7)}{3x(2x + 7) - 7(2x - 7) } }[/tex]
Factor out the terms
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(3x - 7) (x + 3)}{(-2x -6)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{(3x - 7) (2x - 7) } }[/tex]
Cancel out 3x - 7
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(x + 3)}{(-2x -6)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) } }[/tex]
Factor out -2
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(x + 3)}{-2(x +3)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) } }[/tex]
Cancel out x + 3
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{1}{-2(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) }}[/tex]
Rewrite as:
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(2x + 9)(x + 7)}{ -2(x - 2)(2x - 7) } }[/tex]
Expand
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{2x^2 + 25x + 63}{ -4x^2 + 22x - 28}}[/tex]
Factorize again
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(2x+ 7)(x + 9)}{(2x + 7)(-2x + 4)}}[/tex]
Cancel out common factors
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{x + 9}{-2x + 4}}[/tex]
From the question, we have:
[tex]\mathbf{\frac{ax + b}{cx + d}}[/tex]
So, we have:
[tex]\mathbf{\frac{ax + b}{cx + d} = \frac{x + 9}{-2x + 4}}[/tex]
By comparison, we have:
[tex]\mathbf{a = 1}[/tex]
[tex]\mathbf{b = 9}[/tex]
[tex]\mathbf{c = -2}[/tex]
[tex]\mathbf{d = 4}[/tex]
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Write 7.4 as a mixed number and as an improper fraction. Do not try to simplify your answers.
It takes 40 ink cartridges and 200 pages to print a book, and it takes 30 ink cartridges and 80 pages to print a magazine.
Sarah wants to print books and magazines with at most 300 ink cartridges and 1200 pages. Let B denote the number of books she prints and M the number of magazines she prints.
Write an inequality that represents the condition based on the number of ink cartridges.
Write an inequality that represents the condition based on the number of pages.
Answer:
40B+30M≤300
200B+80M≤1200
Step-by-step explanation:
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Some steps to rewrite the expression x3 − 9x + x2 − 9 as a product of three factors are shown below:
Step 1: x3 − 9x + x2 − 9
Step 2: x3 + x2 − 9x − 9
Step 3: x2(x + 1) − 9(x + 1)
Which of the following best shows the next two steps to rewrite the expression?
Step 4: (x2 + 9)(x + 1); Step 5: (x + 3)(x + 3)(x + 1)
Step 4: (x2 − 9)(x + 1); Step 5: (x + 3)(x + 3)(x + 1)
Step 4: (x2 + 9)(x + 1); Step 5: (x − 3)(x + 3)(x + 1)
Step 4: (x2 − 9)(x + 1); Step 5: (x − 3)(x + 3)(x + 1)
Answer:
[tex](x+1)\cdot(x^2-9)[/tex]
[tex](x+1)\cdot(x-3)\cdot(x+3)[/tex]
Step-by-step explanation:
We can simplify the expression as follows:
[tex]x^3-9\cdot(x)+x^2-9[/tex]
[tex]x^3+x^2-9\cdot(x)-9[/tex]
we have a write the expression with a common factor of (x+1)
[tex]x^2\cdot(x+1)-9\cdot(x+1)[/tex]
[tex](x+1)\cdot(x^2-9)[/tex]
We can simplify (x²-9) as:
[tex](x-3)\cdot(x+3)=x^3-3\cdot(x)+3\cdot(x)-9[/tex]
Therefore the final form of the expression is:
[tex](x+1)\cdot(x-3)\cdot(x+3)[/tex]
The fourth option is the best option.
Choose the correct classification of 4x4 ??? 4x3 + 10x6.
4th degree trinomial
12th degree trinomial
3rd degree trinomial
6th degree trinomial
The polynomial [tex]\( 4x^4 - 4x^3 + 10x^6 \)[/tex] is classified as a 6th degree trinomial. The correct option is d) 6th degree trinomial.
To classify the polynomial [tex]\( 4x^4 - 4x^3 + 10x^6 \)[/tex]:
Identify the degree of each term:
- [tex]\( 4x^4 \)[/tex] has a degree of 4.
- [tex]\( 4x^3 \)[/tex] has a degree of 3.
- [tex]\( 10x^6 \)[/tex] has a degree of 6.
Determine the degree of the polynomial:
The degree of the polynomial is the highest degree of its terms, which is 6.
Count the number of terms: The polynomial has three terms.
Thus, the polynomial has 6th degree and number of terms trinomial.
The complete question is:
Choose the correct classification of [tex]4x^4-4x^3+10x^6.[/tex]
a) 4th degree trinomial
b) 12th degree trinomial
c) 3rd degree trinomial
d) 6th degree trinomial
The volume of a rectangular prism is 2x3+9x2-8x-36 with height x + 2. Using synthetic division, what is the area of the base?
we know that
The volume of a rectangular prism as
[tex]V=A*h[/tex]
where
V is volume
A is area
H is height
now, we are given
[tex]V=2x^3+9x^2-8x-36[/tex]
[tex]h=x+2[/tex]
now, we can find A
[tex]V=A*h[/tex]
[tex]A=\frac{V}{h}[/tex]
now, we can plug it
[tex]A=\frac{2x^3+9x^2-8x-36}{x+2}[/tex]
now, we can synthetic division method
so, we can write it as
[tex]A=\frac{2x^3+9x^2-8x-36}{x+2}=(2x^2+5x-18)[/tex]
so, the area of base is
[tex]=(2x^2+5x-18)[/tex].............Answer
what are the domain and range of the function f(x) = 4(3 square root 81)^x?{x| x is a real number}; {y| y > 0}{x| x > 4}; {y| y > 0}{x| x is a real number}; {y| y > 4}{x| x > 4}; {y| y > 4}
we are given
[tex]f(x)=4(3\sqrt{81} )^x[/tex]
Domain:
we know that domain is all possible values of x for which any function is defined
Here , since, x is only exponent
so, we can take any values of x
it will be defined for all values of x
so, domain is all real numbers
{x | x is a real number}
Range:
we know that
range is all possible values of f(x) or y
Since, there is no negative sign here
so, f(x) will always be positive and greater than 0
so, range is y>0
Answer: {x| x is a real number}; {y| y>0}
Step-by-step explanation:
Which is the appropriate solution to the system y = 0.5x + 3.5 and y = -2/3x+1/3 shown on the graph
The function y = 3.75 + 2.50(x - 3) can be used to determine the cost in dollars for a uber ride of x miles. What is the rate of change of the cost in dollars with respect to the number of miles? PLEASE EXPLAIN HOW YOU GOT YOUR ANSWER.
Multiple choices:
A. $3.75 per mile
B. $6.25 per mile
C. $4.75 per mile
D. $2.50 per mile
Abed says he has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is y = 3x – 1. Which could be the other equation? y = 3x + 2 3x – y = 2 3x – y = 1 3x + y = 1
Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 121212 inches. He will make the "X" by stretching red ribbon diagonally from corner to corner.
How many inches of ribbon will Peter need to make the "X"?
What is the value of h when the function is converted to vertex form?
Note: Vertex form is g(x)=a(x−h)2+k .
g(x)=x2−6x+14
Answer: The value of 'h' is 3.
Step-by-step explanation: Given that the vertex form of a function is given by
[tex]g(x)=a(x-h)^2+k~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the value of 'h' when the following function is converted to the vertex form.
[tex]g(x)=x^2-6x+14~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (ii), we have
[tex]g(x)=x^2-6x+14\\\\\Rightarrow g(x)=x^2-2\times x\times 3+3^2-3^2+14\\\\\Rightarrow g(x)=(x-3)^2-9+14\\\\\Rightarrow G(x)=(x-3)^2+5.[/tex]
Comparing it with the vertex form (i), we get
[tex]h=3.[/tex]
Thus, the value of 'h' is 3.
The value of h in the vertex form is -3.
How to find the value of h?
in the vertex form:
g(x)=a(x−h)^2 + k
h is the x-value of the vertex.
Remember that for the general quadratic equation:
y = a*x^2 + b*x + c
The vertex is at:
h = -b/2a
So in our equation:
g(x) = x^2 - 6x + 14
We will have:
h = -(-6)/2*1 = 3
h = 3
That is the value of h.
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What is the missing reason in Step 8? Pythagorean theorem definition of cosine substitution properties of multiplication
8.a2 = b2 – 2bccos(A) + c2 8.?
Pythagorean theorem is used only for the right angled triangles.
For ΔABC,
Cosine rule is
[tex] a^2=b^2 + c^2-2bc$ cosA $ [/tex]
[tex] b^2=a^2 + c^2-2ac$ cosB $ [/tex]
[tex] c^2=a^2 + b^2-2ab$ cosC $ [/tex]
Here we have used one of these formulae
Hence definition of cosine or Cosine rule is the right answer
Option 2) is the right answer
The missing reason in Step 8 is substitution of a² = b² – 2bc·cosA + c²
What is the law of cosines?The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
Given is a proof using triangles property and rule,
In △ ABC, BD ⊥ AC
Prove: the formula for the law of cosines, a² = b² + c² – 2bccos
Statements Reasons
1. In △ ABC, BD ⊥ AC 1. given
2. In △ ADB, c² = x² + h² 2. Pythagorean thm.
3. In △ BDC, a² = (b – x)² + h² 3. Pythagorean thm.
4. a² = b² – 2bx + x² + h² 4. prop. of multiplication
5. a² = b² – 2bx + c² 5. substitution
6. In △ ADB, cos(A) = x/6 6. def. cosine
7. ccos(A) = x 7. mult. prop. of equality
8. a² = b² – 2bccos(A) + c² 8. ?
9. a² = b² + c² – 2bccos(A) 9. commutative property
We are asked to find the reason used in step 8,
From step 5) we have, a² = b² – 2bx + c².......(i)
From step 7) we have, ccos(A) = x
So, by substituting ccosA for x in eq(i), we get the equation for step 8)
a² = b² – 2bc·cosA + c²
Hence, the missing reason in Step 8 is substitution of a² = b² – 2bc·cosA + c²
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y=f (x)=-4^x solve for f (x) when x = 3
Answer:
-64
Step-by-step explanation:
Plato/Edmentum users -64 is correct.
Subtract. (5z−3)−(3z−8) Enter your answer, in simplified form, in the box.
How to find side of triangle if two sides and one angle is known?