Answer:
Step-by-step explanation:
As it is an isosceles trapezoid,
AB = CD
6z - 5 = 4z + 3
To find the value of z, isolate z.
Add 5 to both sides
6z = 4z + 3 + 5
6z = 4z + 8
Subtract 4z from both sides
6z - 4z = 8
2z = 8
Divide both sides by 2
z = 8/2
z = 4
AB = 6z - 5
= 6*4 - 5
=24 - 5
AB = 19
CD = 4z + 3
= 4*4 +3
= 16 +3
CD = 19
BC = 7z + 4
= 7*4 + 4
= 28 + 4
BC = 32
The function f(x)= x2 has been translated 9 units up and 4 units to the right to form The Function g(x). Which represents g(x)
Answer: The third choice is the answer.
Step-by-step explanation:
If the original function is x^2, then to translate it 4 units to the right you need (x - 4)^2, and if you want to translate it 9 units up you simply add +9 outside the parenthesis.
John gave half of his stamps to Jim. Jim gave half of his stamps to Carla. Carla gave 1/4 of the stamps given to her to Thomas and kept the remaining 12. How many stamps did John start with?
Answer: 64 stamps
Step-by-step explanation:
Let the number of stamps John started with be J.
After giving half to Jim, he would have J/2 left.
After giving half to Carla he would have J/4 left and Carla would also have J/4.
After Carla gave 1/4 to Thomas, she would keep (3/4)*(J/4) = 3J/16 stamps. We are given that this equals 12.
Therefore, 3J/16 = 12
Multiply both sides by 16:
3J = 192
Divide both sides by 3:
J = 64
To solve the equation below by completing the square, what is your first step?
3x2 + 18x = 21
Add 9 to each side of the equation.
Divide both sides of the equation by 3
Multiply both sides of the equation by 3
Add 81 to each side of the equation.
Step-by-step explanation:
well, for that I want the equation as simple a possible. especially do I want to have a pure "x²" term with "1" as the factor.
so, as I see that all terms in the equation are multiples of 3, my first step will be to divide both sides by 3.
leading to
x² + 6x = 7
Answer:
Answer:
The first step to solve the equation by completing the square 3x²+ 18x= 21 is multiply both sides of the equation by .
The factors of the equations 3x²+ 18x= 21 are 1 ,-7 .
Step-by-step explanation:
As given the equations
3x² + 18x = 21
Multiply both sides of the equation by .
Thus the equation becomes
Simplify the above
x² + 6x = 7
Adding 9 on both sides of the above equation
x² + 6x + 9 = 7 + 9
x² + 6x + 9 = 16
(As (a +b)² = a² + b² + 2ab
Thus (x+3)² = x² + 6x + 9 )
Put in the above
(x+3)² = 16
Taking square root on both side
√16 = ± 4
First take
(x + 3) = 4
x = 4 -3
x = 1
Second take
(x+ 3) = -4
x = - 4 -3
x = -7
Therefore the first step to solve the equation by completing the square 3x²+ 18x= 21 is multiply both sides of the equation by .
The factors of the equations 3x²+ 18x= 21 are 1 ,-7 .
Cos^2x + tan^2x cos^2x = 1
I need help verifying the trig function with steps.
Step-by-step explanation:
answer is provided in picture
the price of a mountain bike ids decreased from 150$ to 120$. by what percent is trhe price decreased
Answer: Answer below
Step-by-step explanation:
We start off by subtracting 120 from 150, since we want to find the amount it decreased and not what percentage is left.
150 - 120 = 30
We now divide it by 150 to get our percentage.
30/150 = 1/5
1/5 = 0.2 or 20%
Our answer is 20%.
Short Answer
1. A classroom contains 18 girls and 24 boys. Write the ratio of girls to boys in the classroom as
a fraction in lowest terms.
Solve the proportion. Check your solution.
18 : 24
6 : 8
3 : 4
3 boys to 4 girls is the answer
A semicircle has a diameter of 40 inches. What is its area in square inches to the nearest hundredth?
Answer:The area of semicircle is 628cm².Oct
Step-by-step explanation:
AREA=1/2 *πr² = 1/2 *3.14 * 20*20 = 314/100*10*20 = 314/100*200 =314*2 =628 cm²
Answer: The area of a square painting is 600 square inches.
Step-by-step explanation: Finding the length of all the sides of the square painting.
Tanxcosx/ sinx =1
I need help to prove this trig function with steps.
Step-by-step explanation:
answer is provided in picture
PLEASE HELP ASAP:((! For a given function ƒ(x), the operation 1∕2ƒ(x) will______? Question options:
A) stretch the graph vertically by a factor of 2.
B) stretch the graph horizontally by a factor of 2.
C) shrink the graph horizontally by a factor of 1∕2.
D) shrink the graph vertically by a factor of 1∕2.
Answer:
D
Step-by-step explanation:
Shrink the graph vertically by a factor of 1/2 :)
I got it right of the test
If jay ran 1 mile in 6 minutes on monday, 2 miles in 12 minutes on tuesday, and 3 miles in 18 minutes on wednesday, how many miles do you think he might run in 24 minutes on thurdsay?
please answer quick
Answer:
4 miles
Step-by-step explanation:
24/6=4 He ran one miles every six minutes
Rory is driving 584 miles to a family reunion she will drive half of the distance by herself the first day the second day Rory and her cousin will share the driving equally how many miles will her cousin drive?
Answer:
Her cousin will drive 142 miles
Write an equation of the line that passes through point (2,-4) and has the slope m= 1/2
y =
Answer:
tHe can discuss intelligently the current political affairs. Television is a machine that ought to be used intelligently. It is necessary to think intelligently before performing any action.
Step-by-step explanation:
Can someone help me with this question? I’ll mark you brainliest if you answer!!!
A. Translation
This type of translation is defined as moving the object in space by keeping its size, shape or orientation constant. In a translation, each point of the shape must be moved in the same direction and for the same distance. When you are doing a translation, the primary object is called the pre-image, and the object after the translation is called the image.
B. Rotation
This type of transformation has an object about a fixed point without changing its size or shape.
C. Reflection
A reflection is a transformation that reflects each point in the preimage across a line of reflection. It is a rigid motion so it preserves length and angle measure
A perpendicular bisector is a line (ray, segment) which cuts a line segment into two equal parts at90° angle
D. A transformation is a change in the position or size of an object Movements that do not change the size or shape of the object moved are called “rigid transformations” There are three types of rigid transformations: Translations, Reflections, and Rotations. These are more commonly referred to as Slides, Flips, and Turns.
Bob and Alice each have a bag that contains one ball of each of the colors blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and puts it into Alice's bag. What is the probability that after this process the contents of the two bags are the same
Answer:
1/3
Step-by-step explanation:
Alice can select any ball from her bag and it goes into Bob's bag. Then bob has 6 balls including two of one color.
Suppose they are {A,B,B,C,D,E}
Now Bob must draw one of the two balls of the same color (B) in order to have the same content of the two bags.
P(bags same content)= 2/6= 1/3
The probability that the bags content are the same= 1/3
32, 27, 29, 24, 26, 21, 23 , _____
Answer:
18
Step-by-step explanation:
21 - 3 = 18
Numbers 1, 3, 5, 7 go down in 3s
Numbers 2, 4, 6, and 8 go down in 3s
If you need further explanation, let me know!
- profparis
Answer:
18
Step-by-step explanation:
Let's first find out the pattern
32-27 = 5
29 - 27 = 2
29 - 24 = 5
24 - 26 = 2
26 - 21 = 5
21 - 23 = 2
23 - 18 = 5
Pattern = Subtract 5 , Add 2
Since at 23 - 18 = 5
Therefore the next one is subtract 5
Hence, 23 - 5 = 18
[RevyBreeze]
(PLEASE HELP!!)
Shayley wants to buy 20 bottles of water for her trip to the Grand Canyon. A pack of 45 water bottles costs $19.99, but one water bottle is priced at $1.50. Would it be cheaper for Shayley to buy the pack or the water bottles individually?
Answer:
it would be cheaper to buy a pack of 45.
Step-by-step explanation:
Shayley would spend $30 on 20 single bottles because 1.50 times 20 = 30
∠A and ∠B are complimentary. The measure of ∠A is 42 more than 3 times the measure of ∠B. Find ∠A
Answer:
78 Degrees
Step-by-step explanation:
Complimentary Angles add up to 90 degrees so the equation below solves for x and then finds angle A.
3x+42+x=90
4x=48
x=12
3(12)+42=78
Find the solution of the system of equations
Answer:
[tex]\boxed{\tt (-2,3)}[/tex]
Step-by-step explanation:
[tex]\tt -10x-5y=5\\ \underline{-4x+5y=23}\\-14x=28[/tex]
[tex]\tt x=-2[/tex]
[tex]\tt y=3[/tex]
[tex]\tt (x,y) --\: \boxed{\tt (-2,3)}[/tex]
~
What are the coordinates of the focus of the parabola? (0,2) (0,–2) (2,0) (–2,0)
The focus of the parabola is at the point (0, 2).
What is the focus of the parabola?A parabola's focus can be found on the side of the concavity, at the same distance from the vertex as from the directrix, and at the same distance from the vertex to the parabola's centre of gravity.
This is actually a great geometrical characteristic of the parabola and the way it may be built using its definition. all those lane sites whose distance from the directrix to the focus is equal.
Then, the focus must be at a distance of two units from the vertex, (0,0), in line with the parabola's axis of symmetry (x=0), and on the positive side of the y-axis (notice the directrix is on the negative side of the y-axis.
So, the focus of this parabola at the point (0, 2).
learn more about the parabola here:
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The art club had an election to select a president. 75% of the 60 members of the club voted in the election.How many members voted?
Answer:
45 people
Step-by-step explanation:
It appears that I know the answer to this question.
right circular cylinder has a radius of 5 cm and a height of 10 cm. What is the volume of this cylinder in terms of? (Pls help)
Answer:
250 pi
Step-by-step explanation:
volume = 5^2 x pi x 10 = 250 pi
Suppose you drop a ball from a height of 10 feet. After the ball hits the floor, it rebounds to a height defined by the recursive formula an = 0. 85an – 1. What is a1? feet What is the height the ball rebounds to after its third bounce? Round your answer to three decimal places. Feet.
The height the ball rebounds to after its third bounce with the initial height by 10 feet is 6.141 feet.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
Suppose you drop a ball from a height of 10 feet. After the ball hits the floor, it rebounds to a height defined by the recursive formula
[tex]\rm a_n = 0. 85\ a_{n - 1}[/tex]
a₀ = 10 feet
For n = 1, the height will be
[tex]\rm a_1 = 0. 85\ a_{0}\\\\a_1 = 0.85*10\\\\a_1 = 8.5[/tex]
For n = 2, the height will be
[tex]\rm a_2 = 0. 85\ a_{1}\\\\a_2 = 0.85*8.5\\\\a_2 = 7.225[/tex]
For n = 3, the height will be
[tex]\rm a_3 = 0. 85\ a_{0}\\\\a_3 = 0.85*7.225\\\\a_3 = 6.14125 \approx 6.141[/tex]
More about the Algebra link is given below.
https://brainly.com/question/953809
Answer:
First one is 10
The next is 6.141
Step-by-step explanation:
edg answer
Henry deposited $250 into a savings account that earns 1.9% simple interest. How much will his account be worth at the end of 10 years?
Answer:
$297.5
Step-by-step explanation:
I = Prt/100
I = Interest
P = Amount deposited initially
r = Rate
t = number of years
I = Prt/100
= 250 × 1.9 × 10 / 100
= 25 × 1.9
= 47.5
That is the interest
The total amount in his account will be Initial amount + interest
250 + 47.5
= $297.5
Select all of the equations that are true.
A.2/4=4/8
B..3/5=15/30
C.2/3=2/5
D.8/5=16/15
E.1/3=3/9
help me ASAP
Answer:
A.2/4=4/8 and E.1/3=3/9
Step-by-step explanation:
A is right because 4/2=2 and 8/4=2.E is right because 1*3=3 and 3*3=9.
What is the equation for g(x)g(x)g, left parenthesis, x, right parenthesis ? Choose 1 answer: Choose 1 answer: (Choice A) A g(x)=\left|x+0.2\right|g(x)=∣x+0.2∣g, left parenthesis, x, right parenthesis, equals, open vertical bar, x, plus, 0, point, 2, close vertical bar (Choice B) B g(x)=|x-0.2|g(x)=∣x−0.2∣g, left parenthesis, x, right parenthesis, equals, vertical bar, x, minus, 0, point, 2, vertical bar (Choice C) C g(x)=-0.2|x|g(x)=−0.2∣x∣g, left parenthesis, x, right parenthesis, equals, minus, 0, point, 2, vertical bar, x, vertical bar (Choice D) D g(x)=0.2|x|g(x)=0.2∣x∣
Answer:
How do the graphs of the functions f(x) = ()x and g(x) = ()x compare? The graphs are reflections of each other over the y-axis. The graph of g(x) shows exponential decay, while the graph of f(x) shows exponential growth.
Answer:
C
Step-by-step explanation:
Alex wants to pay off his credit card balance before he gets married. he decides to take the $2,300 out of his savings and apply it to his credit card debt of $5,390. the credit card has an apr of 16.5%. what will alex's minimum monthly credit card payment be in order to pay off his debt in 14 months? a. $109.40 b. $190.83 c. $244.15 d. $572.32
Answer:
I think C!
Step-by-step explanation:
I just took the test.
Alex's minimum monthly credit card payment will be $244.15.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Firstly calculate the remaining credit card balance after Alex applies his savings:
$5,390 - $2,300 = $3,090.
Calculate the monthly interest rate on the credit card: 16.5% / 12 = 0.01375.
Use the formula P = i / (1 - (1+r)⁻ⁿ) to calculate the minimum monthly payment.
i = the remaining balance = $3,090
r = the monthly interest rate = 0.01375
n = the number of months to pay off the balance = 14
Plugging in the values, we get:
P = 3090×(0.01375)/(1-(1+0.01375)⁻¹⁴)
= $244.15
Therefore, Alex's minimum monthly credit card payment will be $244.15.
To learn more on Equation:
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Find the volume for the regular pyramid.
V=
Answer:
Step-by-step explanation:
First is to find area of base triangle:
It is an equilateral triangle with one side at 4
Height is given by 4*sin60degree = 2*sqrt(3)
Area = 1/2 * side * height
= 1/2*2*sqrt(3)*4
= 4*sqrt(3)
Height of pyramid is at centroid of the base equilateral triangle
Length of angle bisector of the base equilateral triangle
= sqrt(4^2 - 2^2)
= sqrt(16-4)
= sqrt(12)
Centroid is at sqrt(12)/3 from the nearest side.
Consider right-angle triangle formed by top of pyramid and centroid:
Height^2 + (sqrt(12)/3)^2 = 4^2 - 2^2
Height^2 = 16 - 12 - 12/9 = 24/9
Height = (2/3)*sqrt(6)
Volume of pyramid = 1/3*base area*height
= 1/3*4*sqrt(3)*(2/3)*sqrt(6)
= (8/3)*sqrt(2)
= 3.77
9 + 4 to the third power x (20-8) / 2 + 6
1110.5 is the answer and your welcome
Two times the sum of a number and four increased by three is at most six less than the number. Evaluate this problem situation for values of the number
Answer:
x=2
Step-by-step explanation:
interpreting the problem...
2x+5×3›6-x
2x+12›6-x
2x+x›6-12
3x›6
x›2
you can confirm if this is really the correct solution to the problem
The roots of a quadratic equation are 4 and -5. Which quadratic equation has these roots?
Answer:
(x-4)(x+5) or x^2+x-20
Step-by-step explanation:
If a root of the function is 4, (meaning that when y=0, x=4) it can be rewritten as x-4.
The same goes for if a root is -5. it will simplify to x+5.
These are called factors of a quadratic equation.
Put together, they look like (x-4)(x+5). Using the FOIL method, that can be simplified to x^2+x-20
Answer:
Standard Form: [tex]y = x^2 + x - 20[/tex]
Factored Form: [tex]y = 1(x -4)(x +5)[/tex]
Step-by-step explanation:
Hello!
We can utilize the factored form of a quadratic to find the equation.
Factored Form of a Quadratic: [tex]y = a(x -h)(x - k)[/tex]
h and k are the rootsWe simply plug in the values of the roots and expand to find the equation. Replace "a" with 1.
Expand[tex]y = a(x +h)(x + k)[/tex][tex]y = 1(x -4)(x +5)[/tex][tex]y = 1(x^2 + x - 20)[/tex][tex]y = x^2 +x - 20[/tex]The quadratic equation [tex]y = x^2 + x - 20[/tex] has the roots 4 and -5.