The diagram shows a rectangle. The area of the rectangle is 310 m². Work out the value of w when 5x-9 is the length and 3x+7 is the another length
Answer:
w = 10
Step-by-step explanation:
First we take the two values for the breadth of the rectangle
So:
5x - 9 = 3x + 7
now we solve this equation as follows:
5x - 3x = 9 + 7
2x = 16
x = 8
now that we have found the value for x, we can substitute it in the equation, 5x - 9,or in the equation, 3x + 7.
when we substitute x in any of these equations, we get
5(8) - 9 = 31
3(8) + 7 = 31
now that we have the value for the breadth we can form the following equation:
31 × w = 310
31w = 310
w = 310/31 = 10
Answer:
10
Step-by-step explanation:
Firstly, we find the value of X
since 5X-9 and 3X+7 are lenghts
5X-9= 3X+7
5X-3X= 7+9
2X = 16
dividing bothsides by 2
2X/2= 16/2
X = 8
Hence,
5X-9= 5(8)-9= 40-9 = 31
3X+7=3(8)+7= 24+7= 31
To find the width
Area= lenght×width
310= 31×w
31w= 310
w= 310/31
W= 10
please help bro
i needa get my grade up and i don’t understand any of this … if you can explain how u got the answer that would be helpful but if not, then it’s fine i guess.
Answer:
7. 630
8. I'm not sure on this one-
9. 1331
Step-by-step explanation:
So for a rectangular prism the formula is l x w x h (length times width times height) Which would be 14 * 5 * 9 which equals 630
For the triangular prism, I forgot the formula
For the cube, you are given 1 number, 11, since it's a cube all lengths are the same so you do 11 to the power of 3 = 1331
At a music academy, a randomly selected group of people were asked which type of musical instrument they are learning to play. The results are displayed, by age, in the two-way frequency table.
String Woodwind Piano Total
Ages 15-19 11 3 7 21
Ages 20-24 9 10 17 36
Ages 25-29 16 6 7 29
Total 36 19 31 86
Based on the data in the table, which statement is true?
A.
P(learning a string instrument) ≠ P(ages 20-24)
B.
P(playing piano|ages 25-29) = P(ages 15-19|learning piano)
C.
P(ages 15-19|learning piano) ≠ P(ages 15-19)
D.
P(learning piano|ages 20-24) = P(learning piano)
P(ages 15-19|learning piano) = P(playing piano|ages 25-29) so option (B) must be correct.
What is a frequency table?A frequency table is a list of objects with the frequency of each item shown in the table.
The quantity of times that an event or value occurs is its frequency.
In other words, a frequency table is a table in which we have some data and their frequency.
Given the problem has been attached below,
It is clear that
Number of playing piano in the age of 25 - 29 = Number of playing piano in the age of 15 - 19
Hence it should be the correct answer.
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Circle O has secant lines AB and BD intersects circle O at points C and D. if AD=40 degrees and BC=120 degrees, find
Answer:
Angle AED: 40
Angle BEC: 105
Explanation:
1) To find Angle AED, you have to do arc BC minus arc AD then divide by 2.
120 - 40 = 80.
80 / 2 = 40
2) To find Angle BEC, you have to do arc BA + CD then divide by 2. But that's only angle CED. You'll have to double the number because BEA is vertical; then minus 360.
62 + 88 = 150
150 / 2 = 75
75 times 2 = 150
360 - 150 = 210
210 / 2 = 105
- You'll divide 210 by 2 because of the vertical angles of AED and BEC.
i need some help doing this
Write the equation for the graph of the line
shown.
My answer is y= 2x-1 but I’m not sure if it’s right
Answer: Hope this explains everything for you!
y= -2x+3
Step-by-step explanation:
y= 2x-1 is wrong
First, we will start by identifying the y-int, the y-int is when x is zero. The y-int is 3 since when x is 0, y is 3, (0,3).
y= 2x+3 (So that means -1 is actually 3)
Plus even if your slope is 2, since from the 2 points you go up 2 and run by 1, if you're not going to calculate it with 2 points, you need to see if its uphill, downhill, etc. (More info in the image below) The slope is actually negative meaning it is -2.
So the equation of the line is actually y= -2x+3
a is a common factor of 72 and 108
b is common multiple of 4 and 10
work out the highest possible value of a/b
Answer:
the value is 14
Step-by-step explanation:
because im just trying to get points
A perpendicular bisector crosses a line segment.which type of angle does it form with the segment
Answer: A right angle
Step-by-step explanation:
Perpendicular lines form right angles
Answer:
90 degree
Step-by-step explanation:
Triangle ABC is a right triangle. The length of one of the legs is 12 centimeters, and the length of the hypotenuse is 20 centimeters. What is the length of the other leg?
Answer: 16 centimeters
Step-by-step explanation:
We will use the Pythagorean theorem to solve. The c variable is the hypotenuse, the a and b variables are the legs.
a² + b² = c²
12² + b² = 20²
144 + b² = 400
b² = 256
b = [tex]\sqrt{256}[/tex]
b = 16
The length of the other leg is 16 centimeters.
Answer:
The other leg is 16 cm long.
Explanation:
Use the Pythagorean theorem:
[tex]c^2=a^2+b^2[/tex],
where:
[tex]c[/tex] is the hypotenuse, and [tex]a[/tex] and [tex]b[/tex] are the other two sides (legs).
Let [tex]a=12[/tex] [tex]cm[/tex]
Rearrange the equation to isolate [tex]b^2[/tex]. Plug in the values for [tex]a[/tex] and [tex]c[/tex], and solve.
[tex]b^2=c^2-a^2[/tex]
[tex]b2=(20 cm)^2-(12 cm)^2[/tex]
Simplify.
[tex]b^2=400 cm^2-144cm^2[/tex]
[tex]b^2=256 cm^2[/tex]
Take the square root of both sides.
[tex]b=\sqrt{256cm^2}[/tex]
Simplify.
[tex]b=16[/tex] [tex]cm[/tex]
PLEASE HELPP! RIGHT ANSWERS ONLY!!!
Answer:
[tex] \large {\boxed{ \sf{y = 2x + 5}}}[/tex]
Step-by-step explanation:
Suppose the slope of the line is k.
So,
[tex] \large {\bold {k = \frac{7 - ( - 1)}{1 - (3)} = \frac{7 + 1}{1 + 3} = \frac{8}{4} = 2 }}\\ [/tex]
So the line:
[tex] \large \bold{ \frac{y - 7}{x - 1} = k = 2 } \\ [/tex]
[tex] \: [/tex]
So,
[tex] \large \bold{y - 7 = 2(x - 1)}[/tex]
[tex]\large \bold{y - 7 = 2x - 2}[/tex]
[tex]\large \bold{y = 2x - 2 + 7}[/tex]
[tex]\large \bold{y = 2x + 5}[/tex]
[tex]{\rule{200pt}{4pt}}[/tex]
[tex] \large \bold{-N} \frak{unx-}[/tex]
What does 0 = 0 mean regarding the solution to the system?
There are no solutions to the system because the equations represent parallel lines.
There are no solutions to the system because the equations represent the same line.
There are infinitely many solutions to the system because the equations represent parallel lines.
There are infinitely many solutions to the system because the equations represent the same line.
Answer:
There are infinitely many solutions to the system because the equations represent the same line
Simplify the expression given below.
(17^14)^20
A. 289^34
B. 289^280
C. 17^280
D. 17^34
Answer: Heyaa! ^^
When you simplify (17^14)^20 Your Answer is
C. 17^280Step-by-step explanation:
Multiply the exponents in (17^14)^20And Simplify!!Hopefully this helps you!
Eliminate the parameter:
x = 2cost-1 y = 3sint+ 4
Answer:
Hi,
Step-by-step explanation:
[tex]\left\{\begin {array} {ccc}x&=&2*cos(t)-1\\y&=&3*sin(t)+4\\\end{array}\right.\\\\\\\left\{\begin {array} {ccc}\dfrac{x+1}{2}&=&cos(t\\\dfrac{y-4}{3}&=&sin(t)\\\end{array}\right.\\\\Squaring\\\\\boxed{(\dfrac{x+1}{2})^2+(\dfrac{y-4}{3})^2&=1}\\[/tex]
The curve is an ellipse having (-1,4) as center and half-axis (2 and 6)
Express your answer in simplest a+ bi form. (8+5i)(3+2i)-(4+i)(4-i)
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \:(8 + 5i)(3 + 2i) - (4 + i)(4 - i)[/tex]
[tex]\qquad \sf \dashrightarrow \:[( 8 \sdot3) + (8 \sdot2i) + (5i \sdot3) + (5i \sdot2i)] -[( 4 \sdot4) + (4 \sdot - i) + (i \sdot4) + (i \sdot - i)][/tex]
[tex]\qquad \sf \dashrightarrow \:[24+ 16i + 15i+ 10i {}^{2} ] -[16 - 4 i+ 4i - i {}^{2} ][/tex]
[tex]\qquad \sf \dashrightarrow \:[24+ 31i+ 10 {}{( - 1)} ] -[16 - ( - 1){}^{} ][/tex]
[tex]\qquad \sf \dashrightarrow \:[24+ 31i - 10 {}{} ] -[16 + 1{}^{} ][/tex]
[tex]\qquad \sf \dashrightarrow \:[14+ 31i {}{} ] -[17{}^{} ][/tex]
[tex]\qquad \sf \dashrightarrow \: - 3+ 31i {}{} [/tex]
I hope you understood the procedure ~
Solve the logarithmic equation algebraically ?
Answer:x = 0.449
Step-by-step explanation:
You will find it in the screenshots! up there☝️
wright the follwing in decimlal form:25/8
Answer:
25/8 in decimal form is 3.125.
Step-by-step explanation:
I hope this helps! :)
Mieko bought 2 gallons of paint. she used 1/4 of the paint on her bedroom, 3 quarts on the hallway, and the rest of the paint in the living room. how many quarts of paint did mieko use in the living room?
The number of quarts of paint did mieko use in the living room is A = 3 quarts
Given data ,
Mieko bought 2 gallons of paint. she used 1/4 of the paint on her bedroom, 3 quarts on the hallway, and the rest of the paint in the living room
Now , on simplifying the equation , we get
Two gallons of paint is equal to 8 quarts (2 x 4 = 8)
Mieko used 1/4 of the paint on her bedroom, which is equal to 2 quarts (1/4 x 8 = 2)
She used 3 quarts of paint on the hallway
Thus, Mieko used a total of 2 + 3 = 5 quarts of paint on the bedroom and hallway
Therefore , she used 8 - 5 = 3 quarts of paint in the living room
Hence , the number of quarts is A = 3 quarts
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Find the value of x that makes line m parallel to line n.
Answer: x = 20
Step-by-step explanation:
If line m is parallel to line n, the two angles given will be congruent because they will be alternate exterior angles (which are congruent).
This means we will set them equal to each other and solve for x.
Given:
(4x - 23) = (2x + 17)
Add 23 to both sides of the equation:
4x = 2x + 40
Subtract 2x from both sides of the equation:
2x = 40
Divide both sides of the equation by 2:
x = 20
HELP
Select the correct answer from each drop-down menu.
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
The three-dimensional shape that this net represents is a
The surface area of the figure is
12 cm
12 cm
12 cm
square centimeters.
Reset
Next
The net represents a cube.
The net shows a cube with a side length of 12 cm, meaning its surface area is [tex]6(12)^{2}=\boxed{864 \text{ cm}^{3}}[/tex]
Answer:
cube864 cm²Step-by-step explanation:
The Platonic solid with six (6) square faces is the cube. Its surface area is the sum of the areas of the square faces. Each of those is the square of its edge length.
__
The 3-dimensional shape represented by the net is a cube.
The area of the cube is ...
6 × (12 cm)² = 6 × (144 cm²) = 864 cm²
The scatter plot shows the relationship between the saturation specific humidity, in grams per kilogram of air, and the ambient temperature, in degrees celsius, of the atmosphere. which type of relationship would best model this data?
By critically observing the scatter plot (see attachment), the type of relationship that would best model this data is positive nonlinear.
The types of relationship in a scatter plot.In Statistics, there are four (4) main types of relationship (association) in a scatter plot and these include the following:
Positive linear association.Negative linear association.No association (None).Non-linear association.By critically observing the scatter plot shown in the image attached below, we can logically deduce that the type of relationship that would best model this data is positive nonlinear because the change in one of the variables doesn't result in a constant change in other variables.
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2
3
4
5 6
미
8 9 10
What is the value of x in the equation 8x - 2y = 48, when y = 4
6
7
14
48
Answer:
x=7 ................................
Calculate the Theoretical probability of the following experiments.
Use a tree diagram to visualize your calculations. *** Note that these are independent experiments. Once she has removed a fruit, she will put it back in before removing a second fruit.***
Jane has a bag with 5 oranges, 4 grapefruits, and 3 apples.
What is the probability that she will NOT randomly take out two oranges in a row?
What is the probability that she will NOT randomly take out two grapefruits in a row?
What is the probability that she will NOT randomly take out two apples in a row?
What is the probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order?
The probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order is 0.2917.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
A.) The probability that she will NOT randomly take out two oranges in a row,
Probability = 1 - (5/12)² = 0.8264
B.) The probability that she will NOT randomly take out two grapefruits in a row,
Probability = 1 - (4/12)² = 0.8264 = 0.8889
C.) The probability that she will NOT randomly take out two apples in a row,
Probability = 1 - (3/12)² = 0.8264 = 0.9375
D.) The probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order,
Probability = (7/12) × (9/12) × (8/12) = 0.2917
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If the measure of arc AB is 50 degrees, what is the measure of angle ADB?
90 degrees
100 degrees
25 degrees
50 degrees
Answer:
25 degrees
Step-by-step explanation:
arc divided by 2 = angle
50/2=25
This table shows some values of an exponential function.
What is the function?
The exponential function of the table is y = 0.75(2)^x
How to determine the exponential function?From the table, we have the following points
(x,y) = (0,0.75) and (1,1.5)
An exponential function is represented as:
y = ab^x
At (0,0.75), we have:
0.75 = ab^0
a = 0.75
Substitute a = 0.75 in y = ab^x
y = 0.75b^x
At (1,1.5), we have:
1.5 = 0.75b^1
Evaluate
1.5 = 0.75b
Divide both sides by 0.75
b =2
Substitute b =2 in y = 0.75b^x
y = 0.75(2)^x
Hence, the exponential function is y = 0.75(2)^x
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In a random population, out of 500 people, 160 had blue eyes. In a group of 2500 people, how many would have blue eyes?
======================================================
Work Shown:
(160 with blue eyes)/(500 total) = (x with blue eyes)/(2500 total)
160/500 = x/2500
x = 2500*(160/500)
x = 800
------------
Another approach:
160/500 = 0.32 = 32% of the first group has blue eyes
Assuming this percentage is the same for any group, then,
32% of 2500 = 0.32*2500 = 800 people of the second group are estimated to have blue eyes, of the 2500 total.
The time in seconds, t, it takes for a specific object being dropped from a particular height in feet above sea level, h, to reach the ground can be found by the radical function t equals one fourth times radical h period At what height should you drop an object in order for it to reach the ground in 16 seconds?
Answer:
B.) 4,096 feet
Step-by-step explanation:
You were given a time, and time in the equation is represented by "t". To find the height, represented by "h", you just need to plug the given value in for "t" and simplify to find "h".
t = (1/4)√x <--- Original equation
16 = (1/4)√x <--- Plug 16 in "t"
64 = √x <--- Divide both sides by (1/4)
4,096 ft = x <--- Square both sides
The object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.
The equation is t=1/4 √x , where t is time in seconds and x is height in feet. To determine the height x at which an object should be dropped to reach the ground in 16 seconds, you can plug in the value of t=16 into the equation:
16 = 1/4 √x
Simplify the equation by multiplying both sides by 4:
4⋅16= √x
64= √x
Now, square both sides to isolate x:
64²=x
4096 = x
Therefore, to have the object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.
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What is the relationship between the values m and n plotted on the number
line below?
m
n
H
A. m = n
OB. m> n
OC. m
h
Answer:
C
Step-by-step explanation:
M is less than n because it comes before it in the number line
Find the center and radius of the circle whose equation is x2 + y2 + 8x - 2y + 15 = 0
(4, 1) r = 2
(-16, 1), r = 4
(-4, 1),
(-4, -1),
The equation represents a circle whose center is (-4, 1) and has a radius r = √2
How to find the center and radius of the circle?We have the equation:
[tex]x^2 + y^2 + 8x - 2y + 15 = 0[/tex]
We can rewrite this as:
[tex](x^2 + 8x ) + (y^2 - 2y ) + 15 = 0\\\\\\\\(x^2 + 8x + 16) - 16 + (y^2 - 2y + 1) - 1 + 15 = 0\\\\(x + 4)^2 + (y - 1)^2 - 16 - 1 + 15 = 0\\\\(x + 4)^2 + (y - 1)^2 = 2[/tex]
Where we just completed squares.
Comparing this with the general circle equation, we can see that the center is the point (-4, 1) and the radius is √2.
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What is the solution for x in the equation?
x-3/7=2x-25/7
Step-by-step explanation:
please mark me as brainlest
Answer: x = 4/3
Step-by-step explanation: I just answered the answer
Guys, can you please help me with The Question #47 of The Quadratic Relations for me, please? :)
Answer:
[tex]y=\dfrac{1}{2}(x+5)^2-3[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
Parent function
[tex]y=-x^2[/tex]
Reflected in the x-axis
[tex]-f(x) \implies y=-(-x^2)\implies y=x^2[/tex]
Compressed vertically by a factor of 1/2
Multiply the whole function by the given scale factor:
[tex]\dfrac{1}{2}f(x)\implies y=\dfrac{1}{2}x^2[/tex]
Translated 3 units down
Subtract 3 from the whole function:
[tex]f(x)-3 \implies y=\dfrac{1}{2}x^2-3[/tex]
Translated 5 units left
Add 5 to the variable of the function:
[tex]f(x+5) \implies y=\dfrac{1}{2}(x+5)^2-3[/tex]
To sketch the parabola
Vertex = [tex](-5, -3)[/tex]
Axis of symmetry: [tex]x = -5[/tex]
Plot points:
[tex]x=-9 \implies \dfrac{1}{2}(-9+5)^2-3=5 \implies (-9,5)[/tex]
[tex]x=-7 \implies \dfrac{1}{2}(-7+5)^2-3=-1 \implies (-7,-1)[/tex]
[tex]x=-3 \implies \dfrac{1}{2}(-3+5)^2-3=-1 \implies (-3,-1)[/tex]
[tex]x=-1 \implies \dfrac{1}{2}(-1+5)^2-3=5 \implies (-1,5)[/tex]