Answer:
Step-the base is equal to length * width.
the formula for the volume of a rectangular prism becomes length * width * height.
the ratio of the volume of a three sided figure is the ratio of their corresponding sides cubed.
so if the ratio of their volumes is 125/64, then the ratio of their corresponding sides id 5/4 because 5^3 = 125 and 4^3 = 64.
since the base area is equal to length * widfth, then the ratio of the areas becomes 5^2 / 4^2 which is equal to 25/16.
the ratio of the base area becomes 25/16.
to confirm, use an example:
original prism has dimensions as shown below:
length = 20
width = 40
height = 60
volume = 20 * 40 * 60 = 48000
base area = 20 * 40 = 800
prims that has sides in a ratio of 5/4 to original prism is shown below:
length = 20 * 5/4 = 25
width = 40 * 5/4 = 50
height = 60 * 5/4 = 75
volume = 25 * 50 * 75 = 93750
base area = 25 * 50 = 1250
ratio of the volumes = 93750 / 48000 = 1.953125
ratio of the base areas = 1250 / 800 = 1.5625
125/64 = 1.953125
25/16 = 1.5625
the formulas work.
the ratio of the volume is 125/64
the ratio of the base area is 25/16by-step explanation:
volume = 20 * 40 * 60 = 48000
base area = 20 * 40 = 800
prims that has sides in a ratio of 5/4 to original prism is shown below:
length = 20 * 5/4 = 25
width = 40 * 5/4 = 50
height = 60 * 5/4 = 75
volume = 25 * 50 * 75 = 93750
base area = 25 * 50 = 1250
What is the value of x?
Enter your answer as a decimal to the nearest tenth in the box.
ft
B
29
27 ft
C
Answer:
23.6 ft
Step-by-step explanation:
In the right triangle, an acute angle, the hypotenuse, and an adjacent side are marked. We went to know the length of the adjacent side. The trig relation involved is ...
Cos = Adjacent/Hypotenuse
__
Filling in the given information, this relation tells us ...
cos(29°) = x/(27 ft)
Solving for x, we get ...
x = (27 ft)cos(29°) ≈ 23.614 ft
The value of x is about 23.6 ft.
A student graphs the functions f(x) = | x+3 | and g(x) = x2-2x+3 on the coordinate plane shown.
Which are the solutions of f(x) =g(x)?
A. -3 and 1
B. -1 and 1
C. 0 and 3
D. 3 and 6
The solutions are the intersection point of both graphs
The left side graph is y=|x+3|The right side top graph is x²-2x+3(Parabola)So there mUST be two solutions
The intersections are
(0,3)(3,6)The x values are solution
They are 0,3Option C
Answer:
C. 0 and 3
Step-by-step explanation:
The solutions of f(x) = g(x) are the values of the x-coordinates of the points where the two graphed functions intersect.
From inspection of the graph, the points of intersection are:
(0, 3)(3, 6)Therefore, the solutions are 0 and 3 (since they are the x-values).
Proof
[tex]\implies f(x) = g(x)[/tex]
[tex]\implies |x + 3| = x^2-2x+3[/tex]
We only need to take the positive form of |x+3| since we can see from the graph that g(x) intersects f(x) when |x+3| is positive:
[tex]\implies x + 3 = x^2-2x+3[/tex]
[tex]\implies x^2-3x=0[/tex]
[tex]\implies x(x-3)=0[/tex]
[tex]\implies x=0, 3[/tex]
Thus confirming that the solutions are when x = 0 and 3
About 2% of the students at a college with a population of 9,000 students have significant vision impairments. A polling organization took a random sample of 800 of these students. is the 10% conditon met?
Yes, 10(800) = 8,000, which is less than the total population
Yes, 10% of 800 = 80, which is less than the total population
No, 10(9,000) = 90,000, which is more than the sample
No, 10% of 9000 = 900, which is more than the sample
Answer:
total population: 9,000
10% of 9,000= 900 students
they only surveyed 800 students so Yes the 10(800)=8,000 which is less then 9,000 or Option A
PLEASE HELP
The volume of a right rectangular prism can be found by using the product 6(4)(18). Which expression could also be used to determine the volume of this prism?
6 + 4 + 18
2(6 + 4 + 18)
32(18)
4(6)(18)
Answer:
The last one is 4(6)(18).
Please give Brainliest
Answer:
4(6)(18)
Step-by-step explanation:
the last option is your right answer
Given circle O lies perfectly within square ABCD. If side BC = 6.84, then what is the area of the orange region?
What we get to know by looking at picture :
There are two figures: 1. square 2. circle inside it touching all square's wall.As O is center of circle (given) ∴ OP is radius of circleAs the sides are of square , therefore AB = BC = DC = AD[tex] \\ \\\\ [/tex]
To find :
Area of orange region[tex] \\ \\ \\ [/tex]
Given:
O is the center of the circle.ABCD is squareLength of BC is equal to 6.84.[tex] \\ \\ \\ [/tex]
Concept:
So as we can orange doesn't lies inside circle. And the wall of circle touches all four sides of circle. So first we have to find area of circle and then Area of square. And then we will subtract the ares. The result will be Area of orange part.
[tex] \\\\ \\ [/tex]
Solution:[tex] \\ \\\\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of circle: }}}[/tex]
[tex] \\ [/tex]
To find area of circle we need radius of it i.e Length of OP.
As BC = AB
∴AB = 6.84
As O is the center of square ∴it's center of circle too
Therefore:
AB = 2 OP6.84 = 2 OPOP = 6.84/2OP = 684/2 × 10OP = 342/10OP = 3.42[tex] \\\\ [/tex]
Now Let's find area :
[tex] \\\\ [/tex]
[tex] \star \boxed{ \rm Area~of~circle = \pi {r}^{2} }[/tex]
here :
r is the radius of circle.[tex] \\ [/tex]
[tex]: \implies\sf Area~of~circle = \pi {r}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times {3.42}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times {3.42}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times11.7\\\\\\: \implies\sf Area~of~circle = \dfrac{257.4}{7} \\ \\ \\ : \implies \boxed{ \orange{\tt{ Area~of~circle = 36.6 \{approx \}}}} \bf \dag[/tex]
[tex] \\ \\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of square: }}}[/tex]
[tex] \\\\ [/tex]
[tex] \star \boxed{ \rm Area~of~square = {side}^{2} }[/tex]
[tex] \\ \\ [/tex]
[tex]: \implies\sf Area~of~square = {side}^{2} \\ \\ \\ : \implies\sf Area~of~square = {6.84}^{2} \\ \\ \\ : \implies\sf Area~of~square = {6.84} \times 6.84 \\ \\ \\ : \implies \boxed{\tt{ \orange{Area~of~square = 46.8 \{aprox \}}}}\bf\dag[/tex]
[tex] \\ \\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of orange \: part: }}}[/tex]
[tex] \\ [/tex]
[tex] \star\sf \boxed{ \rm Area_{(orange \: part)} = Area_{(square)} - Area_{(circle)}}[/tex]
[tex] \\ \\ [/tex]
[tex]: \implies\sf Area_{(orange \: part)} = 46.8 - 36.6 \\ \\ \\ : \implies \boxed{ \blue{\tt{Area_{(orange \: part)} = 10.2}}}\bf\dag[/tex]
can someone tell me what letter or variable it is after the = sign, is it an K or R?
What is the slope of the line shown below?
1/6
Step-by-step explanation:
Answer:
B. 6
Step-by-step explanation:
(y1 - y2) ÷ (x1 - x2)
(6 - 3) ÷ (12 - (-6))
3 ÷ 18 = 6
hope this helps
have a good day
If the coordinates of point Q are (−12,√32), then what is the value of tan(m) ?
Vector components are expressed in the form (x, y). The measure of tan m given the coordinate Q is -√32/12
Direction of a vectorVector components are expressed in the form (x, y). Given the coordinates of point Q are (−12,√32), the measure of the angle is expressed as;
m = arctan(y/x)
m = arctan (-√32/12)
Take the tan of both sides
tan m = tan arctan(-√32/12)
tan m = -√32/12
Hence the measure of tan m given the coordinate Q is -√32/12
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5. M's class is having a give-away
here 3 of her lucky students will
ceive 500 classroom credits. She
ll pull names out of a hat and select
winners. Once a student wins, they
e not eligible to win again. There
e 75 total students in the class,
cluding you and your 2 best friends.
The probability that both I and my best friend get the 100 classroom credits is 0.06%.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Since Mr Q's class is having a give-away where his students can receive 100 classroom credits, he will pull names out of a hat and select two winners, and once a student wins, they are not eligible to win a second time, if there are 40 total people in the class, including me and my best friend, to determine what is the probability that both I and my best friend get the 100 classroom credits, the following calculation must be performed:
I = 1/40 = 0.025
my best friend = 1/39 = 0.02564
0.02564 x 0.025 = X
0.0006410 = X
X x 100 = 0.064
Therefore, the probability that both I and my best friends get the 100 classroom credits is 0.06%.
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A triangle has sides with lengths of 17 feet, 31 feet, and 36 feet. Is it a right triangle?
yes
no
Find pi using circumference of 78.5 and the radius is 5. Explain how you found pi.
Answer:
Pi is normally 3.14 but in this case it is 15.7
Step-by-step explanation:
78.5 divided by 5 = 15.7
5 x 3.14 = 15.7
Taking successive discounts of 15% off and then 25% off is the same as taking a one time discount of 40%. true or false
Answer:
False
Step-by-step explanation
Let's take the example starting number as 100
15% off of 100 gives us 85.
25% off of 85 is 63.45
40% off of 100 would be 60.
find the selling price of a $36 item after a 50% markup
Answer:
$54
Step-by-step explanation:
36 divided by 2= 18
$36+$18=$54
Part B: Your cell phone and tablet use the same account. The cell phone costs $0.10 for
each minute of use and the tablet costs $0.15 for every minute of use. Each month, you
want to only spend up to $450 and use less than 5,000 minutes on both of the devices.
Now, create a system of inequalities using the above information (use x and y as the
variables).
please help me ill mark you brainliest
The inequalities are x + y < 5000 and 0.10x + 0.15y ≤ $450 which shows each month, you want to only spend up to $450 and use less than 5,000 minutes on both of the devices.c
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
Let's suppose the total minutes for cell phone is x
and total minutes for tablet is y
Then total minutes will be:
x + y < 5000 (less than 5,000 minutes on both of the devices)
And total cost:
0.10x + 0.15y ≤ $450
Thus, the inequalities are x + y < 5000 and 0.10x + 0.15y ≤ $450 which shows each month, you want to only spend up to $450 and use less than 5,000 minutes on both of the devices.
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Need some help, thanks in advance!
Answer: = 3 acres per day
Showing Work
This is a fraction equal to
3 acres ÷ 1 days
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 1
3 acres ÷ 1
__________
1 days ÷ 1
=
3 acres
_____
1 day
=
3 acres
______
day
= 3 acres per day
Find the value of x.
8:5 = 1/x:1
Answer:x=61
Step-by-step explanation
856−5x3{131}=2
8(x−9)+5(5−18)+1(15−6x)=2
8x−72−65+15−6x=2
2x=122
x=61
sorry if i'm wrong
Please awnser my other question
Answer:
S = (-6, -1)
T = (-7, 4)
U = (-6, 9)
V = (-4, 4)
3. The FFA had a fundraiser by selling hot dogs for $1.50 and drinks for $2.00. Their total sales were $400.
a) Write an equation to calculate the total of $400 based on the hot dog and drink sales.
b) Graph the relationship between hot dog sales.
The equation that represents the total of $400 based on the hot dog and drink sales is $400= $1.50H + $2.00D
Using equation for expressionsThe amount sold for each hot dog = $1.50
The total number of hot dogs sold = H × $1.50
The amount sold for each drink = $2.00
The total number of drinks sold = D× $2.00
The total sales made was = $400
Therefore the equation that represents the total of $400 based on the hot dog and drink sales is;
$400= $1.50H + $2.00D
The relationship that exists between the hot dog sales is that the cost is the drinks is higher than the cost of the hot dog.
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What fraction is equivalent to the decimal number 0.90?(theres a line above the 0.90)
A. 10 over 11
B. 9 over 10
C 1 over 9
D 1 over 90
Answer:
B
Step-by-step explanation:
The number is in the tenths spot so you do 0.90 times 10 which gives you 9/10.
I have 25% off coupon. The items in my cart come to a total of $178.99. What will be my bill after my discount?
help with practice problem
Answer:
i think the answer is r=0.5 or r=−3/2−x^2
Step-by-step explanation:
-4r^2-4r=6
step 1. -4r(-4r)= 16r
16r-4r=6
step 2. 16r-4r=12r
12r=6
step 3. /12 on both sides
r= 0.5
It takes Greg and Nikki a total of 40 minutes to paint a room if they work together. If Greg works alone, he takes 18 minutes longer to paint he room than Nikki takes if she works alone. When x represents the number of minutes it takes Nikki to paint the room working alone, the situation is represented by this equation: Which value is a solution of the rational equation that must be discarded because of the context
Using the together rate, it is found that the value that must be discarded is given by x = -9.
What is the together rate?It is the sum of each separate rate.
In this problem, the rates are given as follows:
Together: [tex]\frac{1}{40}[/tex].Nikki's: [tex]\frac{1}{x}[/tex].Greg's: [tex]\frac{1}{x + 18}[/tex].Hence:
[tex]\frac{1}{x} + \frac{1}{x + 18} = \frac{1}{40}[/tex]
[tex]\frac{x + 18 + x}{x(x + 18)} = \frac{1}{40}[/tex]
[tex]x^2 + 18x = 80x + 720[/tex]
[tex]x^2 - 72x - 720 = 0[/tex]
Then, we have a quadratic function, with coefficients a = 1, b = -72, c = -720, so:
[tex]\Delta = (-72)^2 - 4(1)(-720) = 8064[/tex]
[tex]x_1 = \frac{72 + \sqrt{8064}}{2} = 80.9[/tex]
[tex]x_2 = \frac{72 - \sqrt{8064}}{2} = -9[/tex]
They cannot have a negative rate, hence the value that must be discarded is given by x = -9.
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Answer:
X = -10
Step-by-step explanation:
PLATO
Can someone help me to solve this question? Prove that the quadrilateral ABCD whose vertices are A(-2,-1), B(-2,-3), C( 5,6), and D(5,-1)is a trapezium.Find the area of trapezium ABCD. Also Can you tell how to find the height of trapezium with vertices without knowing the area? Thank you.
If the height of the trapezium is 7 units. Then the area of the trapezium will be 31.5 square units.
What is a trapezium?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.
The quadrilateral ABCD whose vertices are A(-2,-1), B(-2,-3), C( 5,6), and D(5,-1).
The lines AB and CD are parallel to the y-axis. Then the quadrilateral ABCD is a trapezium.
The height of the trapezium will be 7 units.
The area of the trapezium will be
Area = 1/2 (2 + 7) x 7
Area = 0.5 x 9 x 7
Area = 31.5 square units.
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Option 1: use the applet to construct circles for problems 1 & 2 or 3 & 4.
take a screenshot and insert them into your student companion.
1. circle a, with a diameter of
6 cm.
2. circle c, with a radius that is
equal to circle a's diameter.
3. circle b, with a radius of 5
cm.
4. circle d, with a diameter
that is equal to circle b's
radius.
Answer:
9
Step-by-step explanation:
Option 1: use the applet to construct circles for problems 1 & 2 or 3 & 4.
take a screenshot and insert them into your student companion.
1. circle a, with a diameter of
6 cm.
2. circle c, with a radius that is
equal to circle a's diameter.
3. circle b, with a radius of 5
cm.
4. circle d, with a diameter
that is equal to circle b's
radius.
find the zeros for 3x2-8=-2x
Answer:
Here is the answer ..hope it helps:)
In figure MNL, the value of x is:
Answer:
x=6
Step-by-step explanation:
Those are scalene triangles, if 9 is the base, then the other two sides will be congruent, so x=6.
Good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
No he is wrong
If he is referring to table only then correct else wrong
Always 2^x can't have less intercept.
After some while it will cross 5(x)².
You can observe it from graphs
I WILL GIVE BRAINLIEST! Draw the line of reflection that reflects ABC onto ABC prime
Answer:
put the line on y= -2
Step-by-step explanation:
The figure ABC is reflected along the line y = -2 and the new coordinated will be A(-2, -4), B (3, 0), and C (-2, -7).
What is reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.
Given:
The coordinates of the figure of ABC is given as A(-2, 0), C(-2, 3), and B(3, -4),
The new coordinates of A'B'C' are A(-2, -4), B(3, 0), and C(-2, -7),
If the given figure is reflected as y = -x,
Then, the coordination will change like (-y, -x),
Thus, the new coordinates of ABC will be A(-2, -4), B (3, 0), and C (-2, -7).
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Does anybody understand this? Been struggling with it for awhile. Use the rectangle to find the measure of the following angles. BAC=25
Answer:
∠CBA =90°; ∠CAD =65°; ∠ACD =25°; ∠CBD = 65°
∠BWA = 130°; ∠AWD = 50°
Step-by-step explanation:
The diagonals of a rectangle divide the figure into two pairs of congruent isosceles triangles. The figure is symmetrical about both the vertical and horizontal centerlines. Each corner angle of the rectangle is 90°. Of course, the sum of angles in any of the triangles is 180°.
__
The above descriptions tell you ...
∠ABD =∠ACD =∠BAC =∠BDC = 25°
∠CBA =∠BCD =∠CDA =∠DAB = 90°
∠CAD =∠CBD =∠ACB =∠ADB = 90° -25° = 65°
∠BWA =∠CWD = 180° -25° -25° = 130°
∠AWD = ∠BWC = 180° -65° -65° = 50°
HELP HELP HELP PLEASE PLEASE
Answer:
Fourth one
Step-by-step explanation:
You can find the x coordinate of the vertex (which is the axis of symmetry)
by calculating x = - b/ 2a
( when equation is arranged into y = a x^2 + bx + c form )
first one - -2/4 = 1/2
second one -2/ -4 = 1/2
third one - -2 / 4 = 1/2
fourth one - 2 / 4 = - 1/2 BINGO !