Answer: 15 goats
Step-by-step explanation:
h = hens - they have 2 legs
g = goats - they have 4 legs
The equations would be:
h + g = 19
2h + 4g = 68
To solve this, I personally prefer substitution, we're isolating h since we need to find g:
h + g = 19
h = 19 - g
Now that we have h, we can plug this into the second equation:
2h + 4g = 68
2(19 - g) + 4g = 68
38 - 2g + 4g = 68
2g = 30
g = 15
There are 15 goats.
Adding onto this, 19 - 15 = 4, so there are 4 hens.
Which expression is equivalent to \frac{r^9}{r^3}
Answer:
[tex]\sf r^6[/tex]
Step-by-step explanation:
Exponent law:[tex]\boxed{\bf \dfrac{a^m}{a^n}=a^{m-n}}[/tex]
In exponent division, if bases are same, subtract the powers.
[tex]\sf \dfrac{r^9}{r^3}=r^{9-3}=r^{6}[/tex]
On the day of his 18th birthday, David decided to start saving money regularly.
a) Starting on that day, he could save £ 60 on the same date every month.
How much would he have saved by the day before his 60th birthday?
b) David explored another option.
Starting on his 18th birthday, he could save £ 100 on the same date every year.
If he saved in this way, how old would he be by the time he saved £ 2000?
a) The person will save $15,120 by the day before his 60th birthday. b) David would have had £2000 when he is 37 years old.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
a) Let x be a number of months.
Now, we will find a number of years between 60 and 18 years.
There will be 42 years from 18th birthday to 60th birthday.
Now, we will convert 42 years into months.
42 × 12 = 504
In order to find the total amount saved in 504 months, we will substitute in expression:
30x = 30(504) = 15120
Hence, the person will save $15,120 by the day before his 60th birthday.
b) David starts saving £100 annually from his 18th birthday
We would save £2000 after
(2000/100) years = 20 years
Since his 18th birthday is the first of the 20 years and so he will save £950 for the next 19 years, which is
18 + 19 = 37 years old
Hence, David would have had £2000 when he is 37 years old.
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Kindly solve this question 6 too !!
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
[tex]~~~~~x = \dfrac{1}{2 - \dfrac 1{2-\dfrac{1}{2-x}}}\\\\\\\implies x = \dfrac{1}{2 - \dfrac 1{\dfrac{4-2x-1}{2-x}}}\\\\\\\implies x= \dfrac{1}{2 - \dfrac{2-x}{3-2x}}\\\\\\\implies x = \dfrac{1}{\dfrac{6-4x-2+x}{3-2x}}\\\\\\\implies x = \dfrac{3-2x}{4-3x}\\\\\\\implies 4x -3x^2 = 3-2x\\\\\\\implies 3x^2 -4x +3-2x = 0\\\\\\\implies 3x^2 -6x +3 = 0\\\\\\\implies 3(x^2 -2x +1) =0\\\\\\\implies x^2 -2x +1 = 0\\\\\\\implies (x-1)^2 = 0\\\\\\\implies x -1 = 0\\\\\\\implies x = 1[/tex]
Line I has a slope of -The line through which of the following pair of
13
points is perpendicular to l?
The points (2,6) (-4,-7) have a slope of 13/6 which satisfies the perpendicular condition option (B) is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The question is incomplete.
The complete question is:
Line L has a slope of -6/13. The line through which of the following pair of points is perpendicular to L?
A) (6,-4) (-7,2)
B) (2,6) (-4,-7)
C) (6,9) (-4,-4)
D) (13,-4) (-7,2)
Line L slope m = -6/13
If two lines are perpendicular:
(m)(m') = -1
(-6/13)(m') = -1
m' = 13/6
From the points given finding the slope of every point:
A) (6,-4) (-7,2)
[tex]\rm m' =\dfrac{2+4}{-7-6}[/tex]
m' = -6/13
B) (2,6) (-4,-7)
[tex]\rm m' =\dfrac{-7-6}{-4-2}[/tex]
m' = 13/6
Thus, the points (2,6) (-4,-7) have a slope of 13/6 which satisfy the perpendicular condition option (B) is correct.
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74 is the same as
radians.
Round to the nearest hundredth of a radian.
Answer:
1,29
Step-by-step explanation:
74*2pi/360
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Kylie borrowed a book from a library. The library charged a fixed rental for the book and a late fee for every day the book was overdue. The expression below shows the charges Kylie paid for the book when she returned it x days after the
due date:
2 +0.25x
What does the constant term of the expression represent?
The late fee for the book
The fixed rental for the book
The number of books borrowed
The number of days the book was overdue
Answer:
B - fixed rental for the book.
Since for everyday the book is late the fee is 0.25 multiplied by X, X is the days the book is not returned.
Thus, the constant would be 2, 2 is the constant whereby the rental for the book regardless of other variables.
What is the expression for f(x) when we rewrite 36^x•6^(x-2) as 6^f(x)?
Answer: 3x-2
Using the given information, the expression for f(x) is 3x - 2
Writing an expressionFrom the question, we are to determine the the value of f(x)
The given expression is
36^x•6^(x-2)
That is
[tex]36^{x} \times 6^{x-2}[/tex]
This can be expressed as
[tex]6^{2x} \times 6^{x-2}[/tex]
Applying one of the laws of indices, we get
[tex]6^{2x+x-2}[/tex]
= [tex]6^{3x-2}[/tex]
Since the expression was rewritten as
[tex]6^{f(x)}[/tex]
By comparison,
f(x) = 3x - 2
Hence, the expression for f(x) is 3x - 2
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the price of an mp3 player is increased by 8%to £52.92
what was the original price?
Answer:
49£Step-by-step explanation:
the price of an mp3 player is increased by 8%to £52.92
what was the original price?
52.92 = 108%
52.92 : 108 = 0.49
0.49 * 100 = 49£
-------------
check
49 * 1.08 = 52.92
the answer is good
PLS HELP
What is the relationship between \blueD{\angle a}∠astart color #11accd, angle, a, end color #11accd and \greenD{\angle b}∠bstart color #1fab54, angle, b, end color #1fab54?
Two angles whose sum is 180° are called supplementary angles. The correct option is C.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
In the given Image, ∠a and ∠b are supplementary angles to each other. Therefore, the correct option is C.
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A cone with radius 2 units is shown below. Its volume is 29 cubic units.
2
h
Find the height of the cone.
Use 3.14 for π and round your final answer to the nearest hundredth.
units
Answer:
It's very interesting 4
Please someone do this for me
Answer:
A = -12
B = -8
C = -4
Step-by-step explanation:
[tex]y=2x-8[/tex]
x = -2
[tex]y=2(-2)-8=-4-8=-12[/tex]
A = -12
x = 0
[tex]y = 2 (0)-8=-8[/tex]
B = -8
x = 2
[tex]y = 2 (2) -8 = 4-8 = -4[/tex]
C = -4
Hope this helps
please help need it asap
Answer:
195
Step-by-step explanation:
87+38+40=165
360-165=195
Hope this helps!
If not, I am sorry.
What is the missing fifth term in the
pattern below?
1, 8, 27, 64, ?
Options:
101
125
128
202
250
Answer:
The answer would be 125, because 1*1 = 1 2*2*2= 8 and so forth
Step-by-step explanation:
I hope this helps
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Your equation:}[/tex]
[tex]\mathsf{1, 8, 27, 64, ?}[/tex]
[tex]\huge\textbf{LET'S CONVERT IT TO FOR EASIER}\\\\\huge\textbf{TO UNDERSTAND A WHOLE LOT}\\\\\huge\textbf{BETTER.}[/tex]
[tex]\mathsf{1^3, 2^3, 3^3, 4^3, ?}[/tex]
[tex]\huge\textbf{Notice the pattern?}\\\\\\\\\huge\textbf{So, that means your mystery number}\\\\\huge\textbf{has to be squared (also known as to the}\\\\\huge\textbf{power of 3}[/tex]
[tex]\huge\textbf{Breaking down the exponents}[/tex]
[tex]\mathsf{1^3}\\\mathsf{= 1\times1\times1}\\\mathsf{= 1\times1}\\\mathsf{= \bf 1}[/tex]
[tex]\mathsf{2^3}\\\mathsf{= 2\times2\times2}\\\mathsf{= 4\times2}\\\mathsf{= \bf 8}[/tex]
[tex]\mathsf{3^3}\\\mathsf{= 3\times3\times3}\\\mathsf{= 9\times3}\\\mathsf{= \bf 27}[/tex]
[tex]\mathsf{4^3}\\\mathsf{= 4\times4\times4}\\\mathsf{= 16\times4}\\\mathsf{= \bf 64}[/tex]
[tex]\huge\textbf{If you didn't notice that your}\\\\\huge\textbf{exponents went like 1,2,3,4.}\\\\\\\\\huge\textbf{so that your mystery number has to}\\\\\huge\textbf{be 5 squared}[/tex]
[tex]\mathsf{5^3}\\\\\huge\textbf{That is what I meant \& this should give}\\\\\huge\textbf{you your result to this question.}[/tex]
[tex]\mathsf{5^3}\\\mathsf{= 5\times5\times5}\\\mathsf{= 25\times5}\\\mathsf{=125}[/tex]
[tex]\huge\textbf{The result:}[/tex]
[tex]\huge\boxed{\mathsf{Option\ B. \ 125}}\huge\checkmark[/tex]
[tex]\huge\textbf{The outro}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
[tex]\huge\textbf{Signature}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]Giving brainliest
Determine the current temperature in degrees Fahrenheit if the current temperature is 32 degrees Celsius in Lima, Peru. Round the final answer to the nearest whole number.
32
56
90
103
Answer:
The answer is 90.
Thank you
Answer:
89.6
Step-by-step explanation:
The formula to convert Celsius to Fahrenheit is given by °F = °C × (9/5) + 32
F = [ C × (9/5) + 32 ]
Given that, C = 32
F = 32 × (9/5) + 32
F = 32 [ 1 + (9/5) ]
F = 32 [ 1 + 1.8 ]
F = 32 × 2.8
F = 89.6
X^2 + y^2 = 169 and y = -5 as a graph and where are the coordinates of intersection
Step-by-step explanation:
please mark me as brainlest
algebra 2 pls help ill give brainliest
Answer:
Step-by-step explanation:
What do the points on the line in quadrant I represent in terms of the situation
Answer:
The points present in the first quadrant are of the form (a, b) where a, b>0.
Step-by-step explanation:
The points present in the first quadrant are of the form (a, b) where a, b>0.
In the first quadrant both the abscissa and ordinate are positive.
In the second quadrant the abscissa is negative and ordinate is positive.
In the third quadrant both the abscissa and ordinate are negative.
In the forth quadrant both the abscissa is positive and ordinate are negative.
The examples of points in the first quadrant are (1,0), (2,3), (11,4) and many other.
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Answer: The y-coordinates in the first quadrant are positive. because y represents the profit made, positive y values signify profit. The points in quadrant I represent the baseball team making a profit.
Step-by-step explanation: Source - I took the test.
Which expressions are in simplest form? Check all that apply. 0 x²³+y³ 1 - 3 9-9 ·to -12 a² + b ² Which expressions are in simplest form ? Check all that apply . 0 x²³ + y³ 1 - 3 9-9 · to -12 a² + b ²
The expression that's in the simplest term will be -12a² + b².
How to illustrate the expression?It should be noted that an expression means a mathematical statement that has a minimum of two terms containing variables.
In this case, the expression that's in the lowest term will be -12a² + b². This is because it's can't be simplified further.
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Workers in an office of 40 staff were asked
their favourite type of take-away.
The results are summarised in the table.
Take-away
Pizza
Curry
Fish & chips
Kebab
Other
Frequency
9
6
11
10
4
Angle
a
b
с
d
e
What fraction of a person is one degree?
Give your answer in its simplest form.
Answer:
1/
Step-by-step explanation:
There are 360 degrees in a circle. There are 40 people in this survey. Each person is 9 degrees, so 1 degree is 1/9 of a person.
If students sit 4 per row on a rollercoaster, 6 students are left without a seat.
If they sit 6 per row, there are 3 rows left empty. How many students are
there?
An expression is defined as a set of numbers, variables, and mathematical operations. The total number of students is 54.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Let the number of columns in the rollercoaster be represented by x.
If students sit 4 per row on a rollercoaster, 6 students are left without a seat. Therefore, the number of students can be written as,
Total number of students = 4x + 6
If they sit 6 per row, there are 3 rows left empty. Therefore, the total number of students can be written as,
Total number of students = 6(x-3)
The total number of students can be written as,
4x + 6 = 6(x - 3)
4x + 6 = 6x - 18
2x = 24
x = 12
Now, the total number of students in the class are,
4x + 6 = 4(12) + 6 = 54
Hence, the total number of students are 54.
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determine which equation is parallel and perpendicular to jk
None of the equations are parallel or perpendicular to the line jk.
How to know equations that are parallel and perpendicular?The equation of a line can be interpreted as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
Parallel lines have the same slope(m).
Perpendicular line follows the principle below:
m₁ m₂ = -1Therefore, let's find equation of jk
(-5, 5)(1, -5)
m = -5 - 5 / 1 + 5 = -10 / 6 = - 5 / 3
using (1, -5)
-5 = - 5 / 3 (1) + b
b = -5 + 5 / 3 = -15 + 5 / 3 = -10 / 3
Therefore,
y = -5 / 3 x - 10 / 3
m = - 5 / 3
6x + 10y = 11
10y = -6x + 11
y = - 6 / 10 x + 11 / 10
y = - 3 / 5 x + 11 / 10
hence, m = - 3 / 5
5x - 3y = 8
3y = 5x - 8
y = 5 / 3 x - 8/3
m = 5 / 3
The equation
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OX and OY are two straight lines which intersect at an acute angle of 60°. OX = 4.5cm and OY = 5cm . The point M is on OX such that OM = 2MX Find a point P within the acute angle formed by OX and OY which is always the same distance from OX and OY and 3 cm from M.
Therefore the point P is at 3.46 cm from O and it lies on the angle bisector of ∠XOY
What is an Angle Bisector ?The ray that bisects the angle into half is called Angle Bisector.
It is given that ∠XOY = 60 degree
the length of OX = 4.5 cm
OY =5 cm
The point M is on OX such that
OM = 2 MX
so The M is at 3 cm from O
The point P lies in the acute angle such that the distance between point P and OX and OY is always same and at 3 cm from M
According to the angle bisector theorem converse states that if a point is in the interior of an angle and is at equal distance from the sides then it lies on the bisector of that angle.
As it can be seen from the image that a point equidistant from the rays , at 3 cm from M will be at
By Pythagoras Theorem
3² +3² = OP²
OP = 2[tex]\sqrt{3}[/tex] = 3.46 cm from O
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Select the table that lists all the factor pairs for 24
Answer:
1, 2, 3, 4, 6, 8, 12, and 24. Factors of 24 include negative numbers.
Step-by-step explanation:
An aircraft on a reconnaissance mission takes off from its home base and flies 550 miles at a bearing of s 46° e to a location in the sea. it then flies 483 miles from the sea at a bearing of s 55° w to another location. finally, the aircraft flies straight back from the second location to its base. what is the total distance it flies, rounded to the nearest mile? 2 vertical lines. top, point a (airport), point c below are marked on left line. point b marked on middle of right line. abc makes triangle. ab as c equals 5.5. bc as a equals 4.83. interior angle a 46 degrees. exterior angle b 55 degrees. a. 550 miles b. 1,033 miles c. 1,583 miles d. 1,692 miles e. 2,210 miles
The total distance it flies, rounded to the nearest mile is: d. 1,692 miles .
Total distanceFirst distance= 550 miles (given)
Second distance=483 miles (given)
Now let find the third distance
Let x represent the third distance
Hence:
x/sin79 = 550/sin55
x= 659.1
Now let calculate the total distance
Total distance=550+483+659.1
Total distance= 1692.1
Total distance= 1692 miles (rounded)
Therefore the correct option is d.
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Raj correctly determined that ray LH is the bisector of AngleGLI. Which information could he have used to determine this?
AngleGLH Is-congruent-to AngleILM
mAngleKLM = 5mAngleILM
mAngleGLI = 2mAngleGLH
mAngleGLI = mAngleGLH + mAngleHLI
The information could he have used to determine this is C. ∠GLI = 2∠GLH.
What is an angle?An angle is formed from the intersection of two lines. The types of angles are acute, obtuse, and scalene.
∠GLI is bisected by LH, hence:
∠GLH = ∠HLI (definition of bisection)
∠GLI = ∠GLH + ∠HLI (angle addition)
∠GLI = 2∠GLH
The information that can be used to determine this is ∠GLI = 2∠GLH.
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Answer: its C
Step-by-step explanation: on edge
PLEASE HELP ASAP!!!! I HAVE THE ANSWERS BUT I NEED THE WORK FOR THESE THREE PLEASE ITS URGENT
Answer: The solution is x=7.
Step-by-step explanation: Using the segment addition posyulate we can find the measure of the segment. given it is 4, 5, 8.
Explanation:
Building proportional relationships
[tex]\sf \dfrac{XA}{XY} = \dfrac{XB}{XZ}[/tex]
21.
[tex]\sf \rightarrow \dfrac{5}{XY} = \dfrac{10}{18}[/tex]
[tex]\sf \rightarrow XY = \dfrac{5(18)}{10}[/tex]
[tex]\sf \rightarrow XY = 9[/tex]
Then find AY
[tex]\sf AY = XY - XA[/tex]
[tex]\sf AY = 9 - 5[/tex]
[tex]\sf AY = 4[/tex]
[tex]\hrulefill[/tex]
22.
[tex]\rightarrow \sf \dfrac{10}{25} = \dfrac{XB}{XB + 3}[/tex]
[tex]\rightarrow \sf 10(XB + 3) = 25XB[/tex]
[tex]\rightarrow \sf 10XB + 30 = 25XB[/tex]
[tex]\rightarrow \sf 25XB-10XB = 30[/tex]
[tex]\rightarrow \sf 15XB = 30[/tex]
[tex]\rightarrow \sf XB = 2[/tex]
Then find XZ
[tex]\sf XZ = XB + BZ[/tex]
[tex]\sf XZ = 2 + 3[/tex]
[tex]\sf XZ = 5[/tex]
[tex]\hrulefill[/tex]
23.
[tex]\sf \rightarrow \dfrac{4}{13} = \dfrac{XB}{26}[/tex]
[tex]\sf \rightarrow \dfrac{26(4)}{13} = XB[/tex]
[tex]\sf \rightarrow XB = 8[/tex]
Our school store buys a shipment of 1000
pencils for $65. If we sell each pencil for
10 cents, what is the markup percentage
of each pencil?
A. 28%
C. 54%
D. 65%
B. 43%
Answer:
54%
Step-by-step explanation:
65 / 1000 = 0.065. 0.10 / 0.065 = 1.538, so the markup would be C, 54%.
It Sami anual Compound interest is applied interest, what instead of anual compound will be the profit of an investor It Sami anual Compound interest is applied interest , what instead of anual compound will be the profit of an investor.
Answer:
it's helps with learning the difference of thr compound
Solve using a proportion.
Jasmine uses 4 inches of tape to wrap 5 presents. How many inches of tape will Jasmine use to wrap 15 presents?
A. 12 inches
B. 10 inches
C. 15 inches
D. 14 inches
Calculate the a) total tax rate, and b) sales tax.
The total tax rate and the sales tax will be given below.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Total selling price (TSP), State tax rate (STR), City tax rate (CTR), Total tax rate (TTR) and Sales tax (ST).
The table complete table is given below.
Item TSP STR CTR TTR ST
Clothing $81.39 3% 0% 3% $2.44
Cell phone $159.95 5% 0% 5% $7.99
MP3 player $195.55 4% 2% 6% $11.73
Computer $1599.75 4.88% 1.50% 6.38% $102.06
Take-out $49.85 8.13% 2.50% 10.63% $5.29
Pickup truck $38,526.42 6.50% 1.25% 7.75% $2985.79
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