Answer:
Anita= 25 years old
Sumbo= 10 years old
Step-by-step explanation:
Start by forming 2 equations that represent the given information.
Let Anu's and Sumbo's ages be A and S respectively.
A= S +15 -----(1)
A² +S²= 725 -----(2)
Now, solve for A and S by substitution.
Substitute (1) into (2):
(S +15)² +S²= 725
Expand:
S² +2(S)(15) +15² +S²= 725
2S² +30S +225= 725
-725 on both sides:
2S² +30S -500= 0
Divide both sides by 2:
S² +15S -250= 0
Factorise:
(S +25)(S -10)= 0
S +25= 0 or S -10= 0
S= -25 (reject) or S= 10
Sumbo's age cannot be a negative value hence -25 is rejected.
Substitute S= 10 into (1):
A= S +15
A= 10 +15
A= 25
(correct answers only)
A sailfish is swimming after a herring in a straight line at 11.8 m/s and begins to accelerate at 6.39 m/s². How long does it take for the sailfish to reach the herring if it is 55.0 m away?
(unit=s)
According to second equation of kinematics
s=ut+1/2at²55=11.8t+1/2(6.39)t²110=23.6t+6.39t²6.39t²+23.6t-110=0Take positive value
t=2.7sAnswer:
2.7 s (1 d.p.)
Step-by-step explanation:
Use the Constant Acceleration Equations where:
s = displacement in metersu = initial speed in m/sv = final speed in m/sa = acceleration in m/s²t = time in s (seconds)Given:
s = 55 mu = 11.8 m/sa = 6.39 m/s²[tex]\begin{aligned}\text{Using }s & =ut+\dfrac{1}{2}at^2\\\implies 55 & =11.8t+\dfrac{1}{2}(6.39)t^2\end{aligned}[/tex]
Rearrange the equation to equal zero:
[tex]\implies 3.195t^2+11.8t-55=0[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Use the quadratic equation to solve for t:
[tex]\implies a=3.195, \quad b=11.8, \quad c=-55[/tex]
[tex]\implies t=\dfrac{-11.8 \pm \sqrt{11.8^2-4(3.195)(-55)} }{2(3.195)}[/tex]
[tex]\implies t=2.694780675, -6.388051411[/tex]
As time is positive:
[tex]\implies t=2.694780675... \:\text{s}[/tex]
[tex]\implies t=2.7 \: \text{s (1 d.p.)}[/tex]
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Helppp needed plx as fast as u can
Answer:
The answer is either 30 degrees or 36 degrees.
You need a protractor to measure it.
Most probably, the answer is 30 degrees.
BUT PLEASE MEASURE THE ANGLE WITH A PROTRACTOR!
Answer:
d. 60°
Step-by-step explanation:
Since the clock is a full circle, it has a degree span of 360°.
∴ every 5-min interval on the clock
= 360° ÷ 12 five min intervals
= 30°
∴ acute angle formed by clock in figure
= two 5-min intervals
= 60°
what is the slope of the line represented by the equation y = 4/5x -3?
Answer:
4/5
Step-by-step explanation:
Slope
Slope y-intercept of a line: y = mx + b
Where m is the slope and b is the y-intercept.
[tex]\sf y =\dfrac{4}{5}x-3\\\\\boxed{Slope = \dfrac{4}{5}}[/tex]
hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა
⊱┈────────────────────────┈⊰
[tex]\large \bold {ANSWER}[/tex]
[tex]\large \boxed { \large \sf \green{m = \frac{4}{5} }}[/tex][tex]\large \bold {EXPLANATION}[/tex]
This line is in slope-intercept form, y=mx+b, where m represents the slope and b represents the y-intercept.
So that we can conclude that the slope is 4/5.
(2-z)/z=((2-z)( ? ))/(z^2+z)
what is this? please
Answer:
The answer for "?" is z+1.
Step-by-step explanation: In order to solve this I recommend comparing the two equations and expanding them as much as possible, like so.
[tex](\frac{2-z}{z} =\frac{(2-z)(?)}{z^2+z} )=(\frac{2-z}{z} =\frac{(2-z)(?)}{z(z+1)} )[/tex]
Once you have the equations expanded to their maximum you can see what was added to the right side of the equation and what you need to add to the numerator in this case to make the two equations equal.
[tex](\frac{2-z}{z} =\frac{(2-z)(z+1)}{z(z+1)} )[/tex]
*Note: You can also check the solution by plugging in a number for z and checking to see that both side equal. For example if z = 3.
[tex]\\\frac{2-3}{3} =-\frac{1}{3} \\\frac{(2-3)(3+1)}{3^2+3} =-\frac{1}{3}[/tex]
So, z+1 is the answer.
6 Solve each equation. Round to the nearest ten-thousandth. Check your answers.
2.
4x = 19
[tex]\huge\text{Hey there!}[/tex]
[tex]\text{4x = 19}\\\\\large\textbf{DIVIDE 4 to BOTH SIDES}\\\\\rm{\dfrac{4x}{4} = \dfrac{19}{4}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\rm{x = \dfrac{19}{4}}\\\\\rm{x = 19 \div 4}\\\\\text{x = 4.75}\\\\\rm{x \approx 4.7500}\\\\\\\huge\text{Therefore, the answer should be: \boxed{\mathsf{4.7500}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Solve 22x = 5.3 by graphing.
a x ≈ 0.3
b x ≈ 0.7
c x ≈ 1.2
d x ≈ 0.4
The solution is x ≈ 0.3 , Option A is the right Answer.
What is an Equation ?An Equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
To find the value of
22x = 5.3
A graph has to be plotted for the line
From the graph it can be clearly seen the point at which the line intersect x axis is x = 0.24 , which is approx equal to 0.3.
Therefore the solution is x ≈ 0.3 ,
Option A is the right Answer.
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The heights of the starting players on each of two basketball teams are shown in the table below.
Team A
Team B
Heights of Starters on Team A and Team B
70 in.
71 in.
72 in.
73 in.
75 in.
71 in.
68 in.
72 in.
70 in.
73 in.
Answer:
whats the question? please explain
Explain the order in which to simplify the following and then simplify it.
Answer:
16 x^14 / y^16
Step-by-step explanation:
Remember ' PEDMAS '
Parentheses
Exponents
Division
Multiplication
Addition
Subtraction
so do the stuff inside the parentheses to get
y^8 ^-2
4x^7
Now do the exponents ( the -2 one)
y^-16
4^-2 x^-14 then simplify
16 x^14 / y^16
Standard Form
Instructions: Rewrite the equation in proper Standard Form.
Equation: x - y = −3
Standard Form:
Check
Solve x: 30 pts if u can figure it out and the first one that sounds right gets brainiest answer
3x+99x=1188
Is this even possible to work out????
Please dont just type random letters Bec then there’s just no point of u being on here.. and ur wasting ur time! So please think about it
Answer:
x = 99
Step-by-step explanation:
3x + 99x = 12x
12x = 1188 divide 1188 ÷ 12
x = 99
Find the value of x.
Answer:
7x-1 + 2x-1 =7 ..... given
9x-2 = 7
9x = 9
x = 1
Step-by-step explanation:
This is the answer of the above condition.
Please mark as BRAINLIEST and THANK ME.
If the volume of the pyramid is 192 yd³; and the area of the base is 64 yd², what is the height measured in yards?
Answer:
177
Step-by-step explanation:
Which pairs of angles are congruent?
Answer:
b) angles 1 and 4 are congruent.
Hope it helps!
A bronze statue weighs 2400 N and has a base that is 4 m by ½ m. What is the pressure the statue exerts on the floor?
The pressure by the statue exerted on the floor will be 1200 N per square meter.
What is pressure?
The term pressure is defined as the force per unit area.
The formula is igven below.
P = F /A
A bronze statue weighs 2400 N and has a base that is 4 m by ½ m.
Then the base area will be
A = 4 x 1/2
A = 2 square meters
Then the pressure will be
P = 2400 / 2
P = 1200 N per square meter.
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A table lamp emits light in the shape of a hyperbola. If the hyperbola is modeled by the equation 25x2 – 144y2 + 3,600 = 0, which of the following equations represents the boundaries of the light?
y equals five twelfths x and y equals negative five twelfths x
y equals twelve fifths x and y equals negative twelve fifths x
y equals five thirteenths x and y equals negative five thirteenths x
y equals thirteen fifths times x and y equals negative thirteen fifths times x
Answer:
(a) y = 5/12x and y = -5/12x
Step-by-step explanation:
Given the equation of a hyperbola 25x² – 144y² + 3,600 = 0, you want the equations of the asymptotes.
Standard formDividing by 3600 and doing a little rearrangement, we have ...
(y/5)² -(x/12)² = 1 . . . . . standard form equation of a hyperbola
AsymptotesThe equation of the asymptotes is ...
(y/5)² -(x/12)² = 0
Solving for y gives ...
(y/5)² = (x/12)²
y/5 = ±x/12 . . . . . . take the square root
y = ±5/12·x . . . . . . . matches the first choice
__
Additional comment
The equation of a hyperbola with vertices on the y-axis is often written as ...
y²/a² -x²/b² = 1
We have written it in the above form to better show the scale factors applied to x and y.
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You invest $1600 in an account paying 5.4% interest compounded daily. What is the account's effective annual yield? Write as a decimal.
Answer:
For a principle amount of $1600 and rate 5.4%, the effective annual yield is 5.55% if interest is compounded annually.
Step-by-step explanation:
Concept: The annual percentage yield (APY) or the effective annual yield is the real rate of return earned on an investment, taking into account the effect of compounding interest.
The principle amount is $1600, rate is 5.4% and period is 365 days. The formula to find yield is [tex]Y = (1+\frac{r}{n} )^{n} -1[/tex]. All the values are to be inserted in the formula. Here n = 365 and r = 5.4%.
[tex]Y=(1+\frac{0.054}{365} )^{365} -1\\Y=(1.000148)^{365} -1\\Y=5.55%[/tex]
The annual yield is 5.55%.
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if the figure forms the base of a right solid 110 centimeters high, find the surface area
Answer:
[tex]60200cm^{2}[/tex]
Step-by-step explanation:
(I am assuming that the units for the measurements in this question are all centimeters)
Surface area = 2 * (Area of Base) + (Perimeter of base)*(Height)
First, we'd need to solve for the area of the base by finding the area of the triangle and subtracting it from the area of the rectangle. The area of the rectangle is [tex]100 * 150 = 15000[/tex]. The area of the triangle is [tex]\frac{1}{2} * 120 * 90 = 5400[/tex]. (We can do this because it is a right triangle with leg lengths in the pattern of a 3-4-5 triangle.) Now, subtracting the area of the triangle from the rectangle, we get [tex]15000 - 54000 = 9600[/tex]. This is the area of the base.
Next, the perimeter of the base is [tex]100 + 150 + 90 + 120 = 460[/tex]. Multiplying this by the height, we get [tex]460 * 110 = 50600[/tex].
Finally, we add 9600 and 50900 to get [tex]9600 + 50900 = 60200[/tex].
Consider the function shown on the graph.
Answer:
C.) y = 3(x - 3)(x - 7)
For the function:
x intercept: (3, 0), (7, 0)vertex point: (5, -12)point: (8, 15)Writing equation:
y = a(x - h)² + k
15 = a(8 - 5)² - 12
15 = 9a - 12
9a = 15 + 12
9a = 27
a = 3
So the equation is:
y = 3(x - 5)² - 12
y = 3(x² - 10x + 25) - 12
y = 3x² - 30x + 63
y = 3(x - 3)(x - 7)
X -6,-3,0,3,6 y 0 1 2 3 4 which equation contains the coordinate parts given in the table
The linear equation that contains the coordinate parts in the given table is: y = 1/3x + 2.
How to Find the Equation of a Linear Equation?To find the linear equation that contains the coordinate parts in the table given, find the slope (m) and y-intercept (b), then substitute the values into y = mx + b.
Slope (m) using two coordinate parts, (0, 2) and (3, 3):
Slope (m) = change in y / change in x = (3 - 2)/(3 - 0)
Slope (m) = 1/3
y-intercept (b) = 2 [this is the value of y when x = 0)
Substitute the values into y = mx + b
y = 1/3x + 2.
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They brought a new plasma TV for $1800 he made a down payment for 500 and then find is the balance to the store unfortunately he was unable to make the first monthly payment and now pay 7% interest per month on the balance what is Vicks monthly interest payment
Answer:
Vicks monthly interest payment is $91
Step-by-step explanation:
Total: $1800
Down payment: $500 (already paid)
Current balance need to be paid:
$1800 - $500 = $1300
7% of $1300 is, 1300 x 0.07 = $91
PLEASEEEEEEEEEE HELPPPPPPPPPP!! IM SO CONFUSED HOW TO DO THIS!
Create a word problem that can be represented by this mathematical statement and solve your problem.
12! / 3! 9!
10 points need help finding area
Answer:
8 un^2
Step-by-step explanation:
to find this answer you must find the area of the rectangle and then the triangle
the rectangles area is
2 * 3 = 6 un^2
the traingle is
2 * 2 * 1/2 = 2 un^2
now you add them
6 + 2 = 8 un^2
1. A water tank measuring 80 cm by 40 cm by 30 cm is completely filled with water. Water flows out of the tank at a rate of 4 per minute. At this rate, how long will the tank be completely drained out of water? 80 cm 40 cm 30 cm 1. A water tank measuring 80 cm by 40 cm by 30 cm is completely filled with water . Water flows out of the tank at a rate of 4 per minute . At this rate , how long will the tank be completely drained out of water ? 80 cm 40 cm 30 cm
Answer:
6.34 min to empty
Step-by-step explanation:
80 cm x 40 cm x 30 cm = 96000 cm^3
this volume represents 25.36 gallons of water (US)
25.36 gal / 4 gal/min = 6.34 min to empty
What is the value of the rational expression below when x is equal to 4?
Answer: letter B (answer is 2)
Step-by-step explanation:
what is 2/3 x 6/7 answer
Answer:
4/7
Step-by-step explanation:
2/3 × 6
7
4/7
and bro that's really it
There are 15 players on a volleyball team. Only 6 players can be on the court for a game. How many different groups of players of 6 players can the coach make, if the position does not matter? 720 810 5,005 3,603,600
The no. of different groups of players of 6 players , if the position does not matter is given by 5005 ,Option C is the right answer.
What is Combination ?Combination is a method of selection of items from a set of distinct objects , when the position doesn't matter .
It is given that
Total number of players = 15 = n
No. of players to be selected = 6 = r
The no. of different groups of players of 6 players , if the position does not matter is given by
[tex]\rm ^nC_r = \dfrac{n!}{r! (n-r)!}[/tex]
So
[tex]\rm ^{15}C_6 = \dfrac{15!}{6! (15-6)!}\\\\\rm ^{15}C_6 = \dfrac{15!}{6! (9)!}\\\\\\^{15}C_6 = \dfrac{15 * 14 * 13* 12 * 11 * 10 }{6 *5* 4 * 3 * 2*1}\\\\ ^{15}C_6 = 5005\\[/tex]
Therefore , The no. of different groups of players of 6 players , if the position does not matter is given by 5005
Option C is the right answer.
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Find the area of a circle with a diameter of 10 ft. ( = 3.14)
Answer:
78.5 ft² or25πStep-by-step explanation:
Find the area of a circle with a diameter of 10 ft.
Area of a Circle
A = π × r²
r = diameter : 2
10 : 2 = 5 ft (radius)
A = π × 5²
A = 3.14 * 25
A = 78.5 ft²
38. How much does Mike Carson earn every
day?
A. $89.33
B $76.80
C. $27.00
D. $9.60
39. Mike Carson takes home approximately
what percent of his gross pay?
A. 33%
B. 50%
C. 75%
D, 90%
40. Approximately what percent of total
carnings is deducted for city and state
withholding tax?
A. 3%
B. 10%
C. 15%
D. 25%
The ingredients for your braised greens cost 1.32. You sell it for $4. What is your contribution margin?
Your contribution margin is $2.68 considering the price of the braised ribs and the cost of the components.
Selling price per unit less variable cost per unit equals contribution margin, often known as dollar contribution per unit. The amount of sales income referred to as "Contribution" is the fraction that is not used to pay variable expenses and hence helps to cover fixed costs.
Given ingredients for your braised greens cost 1.32$ and sells at $4
We have to find contribution margin on that
The difference between a venture's variable costs and its selling price is the contribution margin:
= Selling price - Variable cost
The selling cost is $4 and the variable costs are $1.32.
Therefore Contribution margin is as follow:
= 4 - 1.32
= $2.68
Hence your contribution margin is $2.68 considering the price of the braised ribs and the cost of the components.
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A
True
False
P
Given the diagram as marked.
True or False: P is on the angle bisector of A
Answer:
False
Step-by-step explanation:
P is not necessarily on the angle bisector of angle A.
Attached is an example of a carefully constructed shape (so that it's easy to see the measurements):
Angle A measures 45° (again, for convenience)Point P is 4 units to the right of and 3 units above point A.Point P forms a right angle with two congruent line segments, each of which terminate on the rays extending from Point A, forming angle A.The lower point is 8 units to the right of point A; the upper point is 7 units to the right of and 7 units above point A.The length of the two line segments is 5 units, and thus they are congruent.Visually, point P is not on the angle bisector of angle A.
While having two adjacent congruent segments is necessary for P to be on the bisector of angle A, it is not sufficient. The segments on the rays from A to the end of those segments would also need to be a pair of congruent adjacent sides (forming a kite). For a kite, the diagonal from the point between one pair of adjacent congruent sides to the point between the other pair of adjacent congruent sides does form an angle bisector with both angles.
