Answers
x/3 = 3/4
x*4 = 3*3
4x = 9
x = 9/4
AC = AD+DC
AC = 4+x
AC = 4+9/4
AC = 16/4 + 9/4
AC = 25/4
AB^2 + BC^2 = AC^2
5^2 + y^2 = (25/4)^2
25 + y^2 = 625/16
y^2 = 625/16 - 25
y^2 = 625/16 - 400/16
y^2 = 225/16
y = sqrt(225/16)
y = 15/4
Related Questions
Suppose you travel at 60 mph for 222 miles. How many hours will it take you to reach your destination?
A.) 4.3 hours
B.) 4.5 hours
C.) 3.7 hours
D.) 1.05 hours
Answers
Divide 60 by 222 for the number of hours you will need to travel to get to your destination.
222/60= 3.7
"C" 3.7 hours <== the answer
I hope this helps!
~kaikers
Identify the vertical asymptote(s) of each function. Check all of the boxes that apply. f(x)=x-8/x^2-3x+2
x = -8
x = -2
x = -1
x = 1
x = 2
x = 8
Nevermind the answer was x=1 and x=2. If anyone is wondering how to do it you can put the denominator in desmos and where the 2 points hit the x axis is your answer.
Answers
[tex] \frac{x-8}{ x^{2} -3x+2} [/tex]
Now factorize the denominator:
[tex]\frac{x-8}{ x^{2} -x-2x+2}[/tex]
[tex]\frac{x-8}{ x(x-1) -2(x-1 ) }[/tex]
[tex]\frac{x-8}{ (x-1) (x-2 ) }[/tex]
Now put the denominator equals to zero:
[tex] (x-1) (x-2 ) = 0[/tex]
Now take each one of them separately to find the vertical asymptotes:
[tex]x-1 =0, x-2=0[/tex]
Ans: So there are TWO asymptotes:
1) x = 1.
2) x = 2.
-i
Answer:
x=1 and x=2
Step-by-step explanation:
A tiger in captivity is fed 13.5 pounds of food an elephant in captivity eats per day. Compare the function by comparing their rates of change.
Answers
SEE ATTACHED IMAGE.
The first thing that we are going to do in this case is to find the slope of the line for the function that simulates the amount of food of the elephant.
We have then:
m = (y2-y1) / (x2-x1)
Substituting any two points:
m = (625-125) / (5-1)
m = 125 pounds / day
125> 13.5
Answer:
The elephant eats more than the tiger daily.
Choose the correct simplification of the expression a to the 7th power times b to the 8th power all over a to the 4th power times b to the 4th power
Answers
[tex] \frac{ a^{7} b^{8} }{ a^{4} b^{4} } [/tex]
When you will simplify this fraction, you can divide the expressions. Based on the law of exponents when you divide like terms with different exponents, you can subtract the exponents of the denominator from the numerator.
So if you will simplify the equation:
[tex] \frac{ a^{7} b^{8} }{ a^{4} b^{4} } [/tex]
Subtract the following:
Exponents of a 7-4 and;
Exponents of b 8-4
Your answer should be
[tex] a^{3} b^{4} [/tex]
A stuntman jumps from a rooftop 315 ft off the ground. how long will it take him, falling freely, to reach the ground? (use the formula s = 16t2.)
Answers
We then have to replace:
s = 16 * t ^ 2
315 = 16 * t ^ 2
Clearing the value of t:
315 = 16 * t ^ 2
t1 = root (315/16)
t1 = 4.437059837
t2 = - root (315/16)
t2 = - 4.437059837
We ignore the negative root.
Answer:
it will take him, falling freely 4.43 s to reach the ground
The stuntman will take approximately 3.98 seconds to reach the ground when falling freely from a rooftop 315 ft high.
To calculate the time it takes for the stuntman to reach the ground when falling freely:
Given s = 315 ft and using the formula s = 16t^2, where s represents the distance and t represents time.Plug in the value of s into the formula: 315 = 16t^2.Solve for t by isolating the variable: t = sqrt(315/16) ≈ 3.98 seconds.HELP FAST PLEASE!!!
A telephone pole that is 14 ft. tall has fallen against a house. If the top of the telephone pole touches the house 8 ft. above the ground, what is the angle that the telephone pole makes with the ground?
29.7 degrees
55.2 degrees
60.3 degrees
34.8 degrees
Answers
From the given information , we can make a rough figure as shown in attachment.
Now in the given triangle we can use following formula of sin to get the angle,
[tex] sin x = \frac{Perpendicular}{opposite} [/tex]
We can see from the figure that:
perpendicular = 8 and opposite =14.
Plugging the given values in the formula for sin x,
[tex] sin x = \frac{8}{14} [/tex]
sin x = 0.5714
to find x we have to find sin inverse of 0.5714 ,
x = sin⁻¹(0.5714)
x=34.8 degrees.
Answer : the angle that the telephone pole makes with the ground is 34.8 degrees. option D
What is the area of a sector with a central angle of 3π5 radians and a diameter of 21.2 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
cm²
Answers
Area of a circumference=π*r²
for diameter=21.2 cm---------> r=10.6 cm
A=π*10.6²--------> A=π*112.36 -------> A=352.81 cm²
if 2π radians (full circumference) has an area of -----------------> 352.81 cm²
3π/5 radians-------------------------------------> X
X=[(3π/5)*(352.81)]/2π---------> X=105.84 cm²
the answer is 105.84 cm²
Multiply and simplify if possible.
√5x(√x - 5 √5)
Answers
x√5 - 25√x
This figure is made up of a quadrilateral and a semicircle.
What is the area of this figure?
Use 3.14 for pi. Round your final answer to the nearest tenth.
15.7 units²
17.9 units²
25.7 units²
31.4 units²
Answers
Answer:
Option B. 17.9 units²
Step-by-step explanation:
This figure consist of two figures
1). One quadrilateral
2). One semicircle
Now to get the area of total figure
= Area of triangle + area of semicircle
1). Area of quadrilateral = length × width
= √(3-1)²+(1-2)² × √(3-1)²+(1+3)² = √(4 + 1) ×√(4 + 16) = √5×2√5 = 10
2) Area of semicircle = (1/2)πr²
Radius of the circle = (1/2)√(3-1)²+(1+3)² = (1/2)√(4 + 16) = (1/2)(√20)
r = √5
Area of semicircle = (1/2).(π).(√5)² = (1/2).(3.14)(5) = 7.85
Area of the total figure = 10 + 7.85 = 17.85 ≈ 17.9 units²
Option B is the correct answer.
Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want to work over 65 hours per week combined. Jane is paid $12.50 per hour at her job, and Jack is paid $10 per hour at his. Neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. If they need to make a minimum of $750 per week before taxes, what is the maximum amount of hours that Jack can work per week according to these limits?
Answers
The inequality representing their combined pay would be
[tex]12.50x+10.00y \geq 750[/tex]. This is because Jane makes 12.50/hr, Jack makes 10.00/hr, and they want to make at least, so greater than or equal to, $750 combined.
The inequality representing their combined hours working would be
[tex]x+y \leq 65[/tex], since they do not want their combined hours to be over 65. In both of these inequalities, x represents the number of hours Jane works and y represent the number of hours Jack works.
To graph these, we solve both of them for y:
[tex]x+y \leq 65 \\ x+y-x \leq 65-x \\ y \leq 65-x[/tex]
[tex]12.50x+10.00y \geq750 \\12.50x+10.00y-12.50x \geq 750-12.50x \\10.00y \geq 750-12.50x \\ \frac{10.00y}{10.00} \geq \frac{750}{10.00} - \frac{12.50x}{10.00} \\y \geq 75-1.25x[/tex]
The attached screenshot shows what the graph looks like. Going to the point where they intersect, we see that the shaded region that satisfies both inequalities begins when Jane works 40 hours and Jack works 25.
Answer:
20
Step-by-step explanation:
just did it on study island
1. SCHOOL PLAY Marika and her three friends attended the school play. Tickets cost $5.75 each, and Marika paid for everyone. Find the totał cost of the tickets. Justify your answer by using the Distributive Property
Answers
explain how a table cn be used to find the rate of change?
Answers
The table lists the test scores William and Andre received on five math assessments William's scores 89 97 78 81 91 Andre's score 90 74 73 87 82
Which statement best describes the difference of the mean of the two sets?
A)It is equal to about 0.5 times the mean absolute deviation of either data set. B)It is equal to about 1 times the mean absolute deviation of either data set. C)It is equal to about 1.5 times the mean absolute deviation of either data set. D)It is equal to about 2 times the mean absolute deviation of either data set.
Answers
[tex]\frac{89+97+78+81+91}{5}=\frac{436}{5}=87.2[/tex]
To find his mean absolute deviation, find the absolute values of the differences between each data point and the mean; then find the average of these:
[tex]\frac{|89-87.2|+|97-87.2|+|78-87.2|+|81-87.2|+|91-87.2|}{5} \\ \\=\frac{1.8+9.8+9.2+6.2+3.8}{5}=\frac{30.8}{5}=6.16[/tex]
Now find the mean of Andre's data (again, add all of the data points together and divide by the number of data points):
[tex]\frac{90+74+73+87+82}{5}=\frac{406}{5}=81.2[/tex]
Find his mean absolute distance (find the absolute value of the difference between each data point and the mean, then average these):
[tex]\frac{|90-81.2|+|74-81.2|+|73-81.2|+|87-81.2|+|82-81.2|}{5} \\ \\=\frac{8.8+7.2+8.2+5.8+0.8}{5}=\frac{30.8}{5}=6.16[/tex]
Both mean absolute deviations are the same. The difference between the means of the two sets is
87.2-81.2=6.
6 is about 1 times the mean absolute deviation of either set.
Match the statements
1. m<2 = 122° and m<3 = 58°
If corresponding angles are equal, then lines are parallel.
2. 3 and 5 are supplementary angles
Exterior Sides in Opposite Rays
3. m<3 + m<5 = 180°
Given
4. 58° + m<5 = 180°
Second Substitution
5. m<5 = 122°
Definition of Supplementary Angles
6. m<2 = m5
First Substitution
7. l || m
Subtraction Property of Equality
Answers
1. m<2 = 122° and m<3 = 58° - C. Given
2. 3 and 5 are supplementary angles - E. Definition of Supplementary Angles
3. m<3 + m<5 = 180° - D. Second Substitution
4. 58° + m<5 = 180° - F. First Substitution
5. m<5 = 122° - G. Subtraction Property of Equality
6. m<2 = m5 - A. If corresponding angles are equal, then lines are parallel
7. l || m - B. Exterior Sides in Opposite Rays
The given geometry statements are matched with appropriate geometric principles, such as the definition of supplementary angles, substitution properties, and theorems related to parallel lines and angles.
To match the statements given with the correct reasons, we need to analyze the relationships between angles and understand the geometric principles involved.
Here are the matches:
1. m<2 = 122° and m<3 = 58° - C. Given
2. 3 and 5 are supplementary angles - E. Definition of Supplementary Angles
3. m<3 + m<5 = 180° - D. Second Substitution
4. 58° + m<5 = 180° - F. First Substitution
5. m<5 = 122° - G. Subtraction Property of Equality
6. m<2 = m5 - A. If corresponding angles are equal, then lines are parallel
7. l || m - B. Exterior Sides in Opposite Rays
The probable question may be:
Match the statements
1. m<2 = 122° and m<3 = 58°
2. 3 and 5 are supplementary angles
3. m<3 + m<5 = 180°
4. 58° + m<5 = 180°
5. m<5 = 122°
6. m<2 = m5
7. l || m
A. If corresponding angles are equal, then lines are parallel.
B. Exterior Sides in Opposite Rays
C. Given
D. Second Substitution
E. Definition of Supplementary Angles
F. First Substitution
G. Subtraction Property of Equality
Suppose the ages of cars driven by employees at a company are normally distributed with a mean of 8 years and a standard deviation of 3.2 years. What is the z score of a car that is 6 years old?
Answers
[tex]z=(6-8)\div 3.2=(-2)\div 3.2=-0.625[/tex]
Answer:
-0.625 is right
Step-by-step explanation:
:3 i did the test
Factor –7x3 + 21x2 + 3x – 9 by grouping. What is the resulting expression? (3 – 7x)(x2 – 3) (7x – 3)(3 + x2) (3 – 7x2)(x – 3) (7x2 – 3)(3 + x)
Answers
If you apply the distributive property in (3–7x²)(x–3), you obtain:
3x-9-7x²(x)+21x²
3x-9-7x³+21x²
When you order the expression, you have:
-7x³+21x²+3x-9
Then, the answer is (3–7x²)(x–3)
Explanation:
1) Given: -7x^3 + 21x^2 + 3x - 9
2) Group the first two terms and the second two terms:
[-7x^3 + 21x^2] + [3x - 9]
3) Extract common factor -7x^2 from the first group and common factor 3 from the second group:
-7x^2 [x - 3] + 3[x - 3]
4) Take common factor x - 3
(x - 3) (3 - 7x^2)
By commutative property that is equal to (3 - 7x^2) (x - 3)
Please if some one can help help ! Thank you !!
Answers
As compared to the equations in the 1st step the equations in the 4th step have this description.
The first equation in the first step has been multiplied by 2.
The second equation in the first step has been multiplied by 3.
Selection C is appropriate.
Choose as many answers as apply. Which of the following are sources of income? salary deductions part-time work odd jobs wishful thinking
Answers
Answer:
salary . part time work . odd jobs.
Step-by-step explanation:
For which interval is the function constant?
(0, 2)
(−∞, −6)
(2, ∞)
(−6, 0)
Answers
Answer:
(−6, 0)
Step-by-step explanation:
The section where the function is constant is where it is horizontal. This is from x = -6 to x = 0; in interval notation, this is (-6, 0).
A function assigns the value of each element of one set to the other specific element of another set. The function is constant in the interval (-6 to 0).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A function is known to be constant if the value of one of the variables is not changing the value of the other.
In the function as we can see that the value of y is not changing with the change in the value of x between x=-6 to 0, therefore, the function is constant in the interval (-6 to 0).
Learn more about Function:
https://brainly.com/question/5245372
The vertices of triangle jkl are j(-2,1), k(2,-3), and l(2 2). The triangle is reflected over the line y=x. Graph triangle jkl and triangle j’k’l’.
Answers
I have attached a picture of a question I am stuck on. It is about Riemann sums. I have attempted the question but did not get the correct answer :( Here is my work:
I see that this graph has the same area repeating 12 times.
I did (b - a)/n, or (12 - 0)/36, and found that the width of each rectangle should be 1/3. Because we are asked to find the area using "circumscribed angles," I will use right-endpoint rectangles on the first part of the graph that shows a decreasing interval from 0 to 1:
t = 1/3, r(t) = 2.01745506
t = 2/3, r(t) = 2
t = 1, r(t) = 1.45369751
These values for r(t) represent heights of the rectangles. I can add them and multiply by the width of each rectangle:
1/3(2.01745506 + 2 + 1.45369751) = 1/3(5.47115257) = 1.823717523
I can multiply the area by 12 to find the area under the entire function:
1.823717523 * 12 = 21.88461028
This is not an answer choice, so I clearly did something wrong! Can someone help me find my mistake?
Answers
Or, you could use u-substitution to get the exact area under the curve from [0, 12] - but I would do as the problem says. If you want me to that, DM me.
4.5x-7=20 i need help whats the answer
Answers
_____________________________________________________________
Your goal is to isolate x. By isolating the x-variable, you effectively receive the answer. In order to isolate x, you move the -7 term [Note: that the sign in front of a number signifies if it's positive or negative] as well as 4.5 behind the equality symbol. To do this, you do reverse operations to both sides. Start with -7.
The opposite of negative 7 is positive 7, therefore -7 + 7 = 20 + 7
-7 + 7 cancels each other out and 27 takes the place of 20. We now have: 4.5x = 27
Since you have to multiply 4.5 by x originally, you have to divide now. Divide 4.5 by itself and 27 by 4.5. This gives you 1 and 6. [Note that a 1 in front of a variable is like saying only that variable]
(1)x = 6, Therefore x is equivalent to 6.
Briefly check your work by taking the original equation and substituting x with 6. If 4.5(6) - 7 equals 20, 6 is our right answer. [Note: Solve with PEMDAS]
4.5 * 6 = 27
27 - 7 = 20.
In summary, x = 6 is correct.
Divide 9x^2-21x-20 by x-1
Answers
1) quotient: 9x - 12
2) remainder: - 32
Explanation:
I will use short division, which consists in using just the coefficients.
This is the full operation:
literal x^2 x 0
coefficient | 9 - 21 - 20
|
1 | 9 - 12
-------------------------------------
9 -12 - 32
Result:
1) quotient: 9x - 12
2) remainder: - 32
You can prove the result by multiplyin (9x - 12) times (x - 1) and then adding the remainder (-32).
=> (9x - 12) (x - 1) - 32 = 9x^2 - 9x - 12x + 12 - 32 = 9x^2 - 21x - 20 which proves the answer.
230 is equal to _____.
Answers
solution:
230 degree is 50 degrees past 180 degrees into the third quadrant where both sin and cos are negative.
Hannah is saving money for a car. She earns $160 each week working part time after school and on the weekends at Papa's Pizza. Hannah currently has $1,280 in savings. Her parents put $50 in her savings account each week and she saves one-half of her paycheck each week. Which expression represents the situation? (n represents the number of weeks)
Answers
Since we know that Hanna currently has $1,280 in her saving's account and each week she and her parents deposit $130 to the account, with [tex]n[/tex] representing the number of weeks, we can model the situation as follows:
[tex]f(n)=1280+130n[/tex]
Answer:
The answer is A because
Step-by-step explanation:
1,280 in savings
160n
2
Hannah saves each week
50n parents put in savings each week
thus,
1,280 + 160n/2+ 50n
1,280 + 80n + 50n
1280 + 130n
You really have to think this one through all the way. All the other answer choices are steps in finding the answer
Which is more 3 liters or 2997 millilliters
Answers
Name the property the equation illustrates.
A) Commutative Property of Addition
B) Inverse Property of Multiplication
C) Commutative Property of Multiplication
D) Associative Property of Addition
Answers
The commutative property of multiplication is the idea that you can multiply two numbers in any order to get the same result. So that's why order doesn't matter. The general format is x*y = y*x
For example, 2*3 = 6 and 3*2 = 6 so 2*3 = 3*2
One or both of the numbers can be a fraction.
Ishaan is 2 times as old as Christopher. 35 years ago, Ishaan was 7 times as old as Christopher. How old is Ishaan now?
Answers
C= Christopher's age
35 years ago means we have to subtract 35 from their current age. Ishaan minus 35 equals 7 times Christopher minus 35 years.
CHRISTOPHER'S AGE:
I - 35= 7(C-35)
substitute I=2C in for I
multiply 7 by all in parenthesis
2C - 35= 7C - 245
add 35 to both sides
2C= 7C - 210
subtract 7C from both sides
-5C = -210
divide both sides by -5
C= 42 Christopher's age
ISHAAN'S AGE:
I= 2C
substitute C=42 to find Ishaan's age
I= 2(42)
I= 84 Ishaan's age
CHECK:
Substitute answers in original equation
I - 35= 7(C-35)
84 - 35= 7(42-35)
49= (7*42)+(7*-35)
49= 294-245
49=49
Hope this helps! :)
One liter is approximately 1.06 quarts. Write a direct variation equation that relates x liters to y quarts. what is an equation
Answers
y = k * x
Where,
k: proportionality constant.
We have then that the equation for this case is:
y = 1.06 * x
That is to say:
k = 1.06
Answer:
an equation is:
y = 1.06 * x
PLEASE HELP!!!! NEED NOW!!! 20 pts
Explain how the Quotient of Powers was used to simplify this expression.
2 to the 5th power, over 8 = 2 to the 2nd power
By finding the quotient of the bases to be one fourth, and cancelling common factors
By finding the quotient of the bases to be one fourth, and simplifying the expression
By simplifying 8 to 2^3 to make both powers base two, and subtracting the exponents
By simplifying 8 to 2^3 to make both powers base two, and adding the exponents
Answers
If so like 8 it has the same base for [tex]2^{5}[/tex]
as they are both can be obtained by multiplying a certain number of 2s.
for example [tex] 8=2^{3}= 2*2*2 [/tex] which makes 8 can be obtained by multiplying three 2s.
in our example [tex] \frac{2^{5}}{8}=\frac{2^{5}}{2^{3}} = 2^{5} * 2^{-3} [/tex]
in this case, we can add the two powers as long as the basis are the same.
[tex] \frac{2^{5}}{8}=2^{5-3}=2^{2}=4[/tex]
I hope it make sense now ;)
Best Wishes