Answer:
9 inches and 15 inches
Step-by-step explanation:
The height of a trapezoid is 4 in.
Its area is 48 in^2.
Let a be one base and b be the second base.
One base is 6 inches longer than the other. This implies that:
a = 6 + b _________ (1)
The formula for the area of a trapezoid is given as:
[tex]A = \frac{1}{2}(a + b)h[/tex]
where h = height
From (1), we have that:
[tex]A = \frac{1}{2}(6 + b + b )h\\ \\A = \frac{1}{2}(6 + 2b )h[/tex]
We have that h = 4 and A = 48 in^2, therefore:
[tex]48 = \frac {1}{2}(6 + 2b) * 4\\ \\96 = 24 + 8b\\\\8b = 96 - 24 = 72\\\\b = 72 / 8 = 9 in[/tex]
=> a = 6 + 9 = 15 in
The bases are 9 inches and 15 inches long.
please tomorrow exam - John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three times as old as Alice. How old is Peter now?
Answer:
Peter is 20 years old
Step-by-step explanation:
John= 2(Peter's age) (j=2p)
Peter= (Alice's age + 5) (P= A+5)
Okay, so let's substitute the equations now:
John= 2(Alice + 5)
So the equation for 5 years from now is:
2(A+5) + 5 = 3a (because he is 3 times as old as alice)
so, let's solve for that equation:
2a + 10 + 5 = 3a
subtract 2a from both sides:
15= a
so, Alice is going to be 15 years old, so now we can solve for Peter's age:
P= A + 5
P= 15 + 5
P = 20
Peter is 20 years old
I hope this helps! :)
Please help me with my math question!!
Answer: A
Step-by-step explanation:
Using sohcahtoa you can figure out that the missing side length is 5.98 :)
4/9 divided by 5/2 I need help wit 15 more can anyone help ?
Answer:
8/45
Step-by-step explanation:
4/9 ÷5/2
Copy dot flip
4/9 * 2/5
Multiply the numerators
8
Multiply the denominators
45
Put the numerator over the denominator
8 /45
Answer:
[tex] = \frac{8}{45} [/tex]
Step-by-step explanation:
[tex] \frac{4}{9} \div \frac{5}{2} \\ \frac{4}{9} \times \frac{2}{5} \\ = \frac{8}{45} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
what is the product of (9+x)(9-x)
Answer:
81 - x^2
Step-by-step explanation:
this is a "special product," namely, the product of the sum and the difference of quantities 9 and x.
The product is the difference of two squares:
(9 + x)(9 - x) = 81 - x^2
Solve the following inequality:
7 < 6.4+3(-6x – 4.3)
Answer:
X < -0.84
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words.
Harry buys a boat in 2010. He plans on selling it in 2020. In 2010, the boat costs $20,000. The value of the boat depreciates over time
as is shown in the graph below, where the y-axis represents the value of the boat, in dollars, and the x-axis represents the number of
years since 2010.
Answer:
The initial value of the boat was $20,000
The percent decrease per year of the value of the boat is 10%.
The interval on which the value of the boat is decreasing while Harry has it is (0,10)
Step-by-step explanation:
It is given that the boat costs $20,000 in 2010 when x = 0. So, the initial value of the boat was $20,000.
Next, find the percent decrease per year of the value of the boat. Consider the general form of an exponential equation, y = a(b)x, where a is the initial value of the boat, b is the base of the exponent, x is the number of years after 2010, and y is the value of the boat, in dollars.
Consider the point (1 , 18,000) which lies on the graph of this situation. Substitute x = 1, y = 18,000, and a = 20,000 into the exponential equation and isolate b.
Recall that for exponential decay, b = 1 - r where r represents the decay rate. Substitute b = 0.9 into this equation and solve for r.
So, the decay rate is 0.1, and the percent decrease per year of the value of the boat is 10%.
Harry bought the boat in 2010, and plans on selling it after 10 years in 2020. Therefore, the interval on which the value of the boat is decreasing while Harry has it is [0, 10].
In the Soft Boulder Cafe each table has 3 legs, each chair has 4 legs and all the customers and the three members of staff have two legs each. There are four chairs at each table. At a certain time, three-quarters of the chairs are occupied by customers and there are 206 legs altogether in the cafe. How many chairs does the cafe have?
Answer:
32 chairs
Step-by-step explanation:
In the soft Boulder cafe they a chairs , table and customers and the 3 members staffs.
Each Table = 3 legs
Each Chairs = 4 legs
Each customer = 2 legs
Each members of staffs = 2 legs
4 chairs goes with each table. This means 4 × 4 = 16 legs of chairs for each 3 legs of table.
At a certain time 3/4 of the chairs are occupied by customers. That is 3 out of 4 chairs are occupied plus 6 tables . Therefore,
3 + 16 + 6 = 25 legs of table
206 legs altogether - the 6 legs of the staff(3 staffs has 6 legs)= 200 legs
This means 200 legs = 8 tables. Therefore,
8 tables requires 32 chairs
Write the quadratic function in the form f(x)=a(x-h)^2+k. Then, give the vertex of its graph. Finally, graph the function by plotting the vertex and four additional points, two on each side of the vertex. f(x)=-2x^2+16x-35
Answer:
[tex]f(x) = -2(x - 4)^2 -3[/tex]
Vertex = (4, -3)
Graph in the image attached, additional points:
(2, -11), (3, -5), (5, -5), (6, -11)
Step-by-step explanation:
The vertex of f(x) can be found using the formula:
[tex]x_{vertex} = -b/2a[/tex]
[tex]x_{vertex} = -16 / (-4)[/tex]
[tex]x_{vertex} = 4[/tex]
to find y_vertex, we use x_vertex in f(x):
[tex]f(x_{vertex}) = -2 * 4^2 + 16*4 - 35[/tex]
[tex]f(x_{vertex}) = -3[/tex]
So the vertex is (4, -3)
To write the function in the form [tex]f(x)=a(x-h)^2+k[/tex], we just need to calculate h = -b/2a and then find k:
[tex]h = -b/2a = -16/(-4) = 4[/tex]
[tex]f(x) = -2(x - 4)^2 + k = -2(x^2 - 8x + 16) + k = -2x^2 + 16x - 32 + k[/tex]
Comparing both forms of f(x), we have:
[tex]-32 + k = -35[/tex]
[tex]k = -3[/tex]
So we have:
[tex]f(x) = -2(x - 4)^2 -3[/tex]
Now let's find the four additional points.
Two points to the left: x = 3 and x = 2
[tex]f(3) = -2 * 3^2 + 16*3 - 35 = -5[/tex]
[tex]f(2) = -2 * 2^2 + 16*2 - 35 = -11[/tex]
Two points to the right: x = 5 and x = 6
[tex]f(5) = -2 * 5^2 + 16*5 - 35 = -5[/tex]
[tex]f(6) = -2 * 6^2 + 16*6 - 35 = -11[/tex]
solve for the width in the formula for the area of a triangle
Answer: [tex]\frac{2A}{h} = w[/tex]
Step-by-step explanation:
The formula for area of a triangle is [tex]A = wh\frac{1}{2}[/tex]
Now we have to isolate for w.
First multiply by the 2 which is the reciprocal of 1/2 to cancel it out.
[tex]2A = wh\\[/tex]
Now divide by h to isolate w.
[tex]\frac{2A}{h} = w[/tex]
A number line going from negative 8 to positive 8 in increments of 2. Which integer is the farthest to the left of 0?
Answer:
its 4-!
Step-by-step explanation:
trust me on this
Can someone please help me with the slope?
Answer:
1/2
Step-by-step explanation:
For each two units that this line moves to the right, it rises one. This means that it has a slope of 1/2. Hope this helps!
Which description best describes coplanar figures? A. They are contained in the same plane. B. They are not contained in the same plane. C. They lie in a straight line. D. They take up the same amount of space
The description that best describes coplanar figures is that they are contained in the same plane.
What are Coplanar figure?This is referred to as the points or lines that are known to be or lie on the same kind of plane.
Note that if for example, points P , Q , and S lie in the same plane C, then they are coplanar and thus The description that best describes coplanar figures is that they are contained in the same plane.
Learn more about coplanar figure from
https://brainly.com/question/9047265
3(x + 6) – 2(x – 4) > 5(x + 2)
Answer:
4 >x
Step-by-step explanation:
3(x + 6) – 2(x – 4) > 5(x + 2)
Distribute
3x+18 -2x+8 > 5x+10
Combine like terms
x +26 > 5x+10
Subtract x from each side
x+26-x > 5x-x+10
26 > 4x+10
Subtract 10 from each side
26-10 >4x+10-10
16 >4x
Divide each side by 4
16/4 >4x/4
4 >x
Here’s a graph of a linear function. Write the equation that describes that function. Express it in slope intercept form.
slope = 1/2, y intercept = 3
==============================================================
Work Shown:
Pick any two points you want on the line.
I'll pick the two points (0,3) which is the y intercept and also the point (2,4).
------
Find the slope of the line through (x1,y1) = (0,3) and (x2,y2) = (2,4)
m = (y2 - y1)/(x2 - x1)
m = (4 - 3)/(2 - 0)
m = 1/2 is the slope
slope = rise/run = 1/2
rise/run = 1/2 means rise = 1 and run = 2.
This means we go up 1 unit each time we move to the right 2 units.
-----
Since the slope is m = 1/2 and the y intercept is b = 3, we can say
y = mx+b
y = (1/2)x+3
this is the same as y = 0.5x+3 since 1/2 = 0.5
what is the product of -3xy^2 and (2x^2 - 4y)
Answer:
2 • (x2 - 2y)
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
2x2 - 4y
Step 2 : See below
Step 3 : See below
Pulling out like terms :
3.1 Pull out like factors :
Answer: 2 • (x2 - 2y)
Hope this helps.
What is HK? have any clue?
Answer:
As a relation between height and hypotenuse in right triangle GHJ, we have:
HK^2 = KG x KJ
=> HK = sqrt(KG x KJ) = sqrt(2 x 8) = sqrt(16) = 4
Hope this helps!
:)
What is the solution of the equation 6x - 3 = -51?
OA.
-9
OB.
-8
O c.
00
OD.
9
Answer:
x = -8
Step-by-step explanation:
6x - 3 = -51
Add 3 to each side
6x - 3+3 = -51+3
6x = -48
Divide each side by 6
6x/6 = -48/6
x = -8
Answer:
x = -8
Step-by-step explanation:
[tex]6x - 3 = -51?\\To - find-x- collect-like-terms.\\6x=-51+3\\6x =-48\\Divide-both-sides-of-the-equation-by-6\\\frac{6x}{6} = \frac{-48}{6} \\x = -8[/tex]
Find the exact value of x. (25)^(x-20)=((1)/(125))^(x)
Answer:
x = 8
Step-by-step explanation:
[tex] {25}^{(x - 20)} = \frac{1}{ {125}^{x} } \\ \\ {5}^{2(x - 20)} = \frac{1}{ {5}^{3x} } \\ \\ {5}^{2x - 40} = {5}^{ - 3x} \\ \\ 2x - 40 = - 3x ..(bases \: are \: equal \: \\ therefore \: exponents \: will \: also \: be \: equal)\\ 2x + 3x = 40 \\ 5x = 40 \\ x = \frac{40}{5} \\ \huge \purple{ \boxed{ x = 8}}[/tex]
Using factoring determine the zeros of f(x) = 4x + 11x – 3. The explain what the zeros
represent on the graph of f(x).
Answer:
Step-by-step explanation:
4x + 11x - 3 = 0
15x = 3
x = 5
5 is a zero of f(x).
On the graph of f(x), zeros represent the intercepts of the function with the y-axis.
How to find diameter when circumference is given?
Answer: divide by 3.14
Step-by-step explanation:
May You Please Help Me With This Problem
Answer:
x² + x - 8
Step-by-step explanation:
(f . g)(x) is same with (f(g(x))
so insert the g(x) equation into f(x) and change the x on it
f(g(x)) = g(x) - 2
f(g(x)) = (x² + x - 6) - 2 = x² + x - 6 - 2 = x² + x -8
so
(f.g)(x) is x² + x - 8
A company is evaluating a new reading program that is supposed to improve test scores. The box plots show the results of reading tests given before and after using the program. With this data, what is the most reasonable answer to the question: Does the program improve test scores 20 pts
Answer:
Yes, because the median test score increased 5 points.
Step-by-step explanation:
Answer:
Yes, because the median test score increased 5 points
good luck and have a great day
Five times a number which is 3 more than h. Write this as an expression.
｡☆✼★ ━━━━━━━━━━━━━━ ☾
So, let's start off with h
The expression needs to be '3 more than h'
This can be written as:
h + 3
The expression also needs to be 'five times' this value
This can be written as:
5(h + 3)
That would be your answer ^^
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
Step-by-step explanation: Let the number be x
5 times x = 3-h
5x =3-h
1)In an year the value of a motorcycle depreciates by 10% of its value at the beginning of that year.What is its value after two years if the purchased price was $7200?
2)When John Short increases the spend at which he motors from an average of 40mph to 50mph,the number of miles travelled per gallon decreases by 25%.If he travels 36 miles on each gallon when his average speed is 30 mph how many miles per gallon can he execpt at an average speed of 50mph?
Answer:1. $5760
Step-by-step explanation:
Answer:
the answer is 1,200 thats what i got
Step-by-step explanation:
Which rational number could be graphed between 0 and 1? A number line going from negative 5 to positive 3 in increments of 1.
A)Negative one-half
B)One-fourth
C)Three-halves
D)1.75
Answer:
d 1.75
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
cause that was the best option the other choice are all far away from between 0 and 1
Find the value of 5!
O A. 120
O B. 20
O C. 15
O D. 25
Answer:
A: 120
Step-by-step explanation:
5! means 5 factorial
the factorial of a number is the number times every whole number until 1
in this case,
5 * 4 * 3 * 2 * 1
5 * 4 = 20 , 3 * 2 * 1 = 6
20 * 6 = 120 (option A)
If this helps. please consider giving me brainliest.
Answer:
a 120
Step-by-step explanation:
Line CD passes through points C(3, -5) and D(6, 0) . what is the equation of the line CD in standard form?
Answer:
Option 2: 5x - 3y = 30
Step-by-step explanation:
Step 1: Find slope
(0-(-5))/(6-3) = 5/3
Step 2: Find b
y = 5/3x + b
0 = 5/3(6) + b
b = -10
Step 3: Write in slope-intercept form
y = 5/3x - 10
Step 4: Move x over
-5/3x + y = -10
Step 5: Multiply by -3 on both sides
5x - 3y = 30
And we have our final answer!
Given that 3m=2c-5k,express c in terms of k and m.
Answer:
The answer is
[tex]c = \frac{3m + 5k}{2} [/tex]
Step-by-step explanation:
You have to move all the unrelated terms to the other side :
[tex]3m = 2c - 5k[/tex]
[tex]3m + 5k = 2c[/tex]
[tex]2c = 3m + 5k[/tex]
Next you have to divide it by 2 :
[tex]c = \frac{3m + 5k}{2} [/tex]
how do I find the x
Answer:
6.8=x
Step-by-step explanation:
3x=20.4
x-6.8
Circle T is shown. Line segments T S, T R, T Q, and T P are radii. Lines are drawn to connect points S and R and points P and Q to form secants. Angles R T S and Q T P are congruent. What is true regarding two adjacent arcs created by two intersecting diameters? They always have equal measures. The difference of their measures is 90°. The sum of their measures is 180°. Their measures cannot be equal.
Answer: the sum of their measures is 180 degrees
Step-by-step explanation:
I just got it right
The angles R T S and Q T P are vertically opposite angles. So that they always have equal measures.
Circle :In given circle, T is center of circle .
and RP and SQ are diameter of circle which are intersecting at center T.
The diagram of circle is attached below.
In the diagram of circle, Angles R T S and Q T P are congruent.
So that, [tex]\angle RTS=\angle QTP\\\\[/tex]
Since, both diameter are crossing each other.
So that, Angles R T S and Q T P are vertically opposite angles.
Therefore, they always have equal measures.
Learn more about the diameter of circle here:
https://brainly.com/question/1649593