The equation for the height, h, in terms of the base, b, and area, A is [tex]h = \frac{2A}{b}[/tex]
Solution:
Given that area of a triangle is given by the formula:
[tex]A = \frac{1}{2}bh[/tex]
Where,
A is the area of triangle
b is the base of triangle
h is the height of triangle
We have to find the equation for height in terms of base and area
So we have to arrange the equation in such a way that height can be found by using area and base
Given formula is:
[tex]A = \frac{1}{2}bh[/tex]
Keep "h" alone in L.H.S and move the other terms to other side of formula
[tex]A = \frac{bh}{2}\\\\2A = bh\\\\h = \frac{2A}{b}[/tex]
Thus height is expressed in terms of base and area
Simplify m3 + m3
And
Simplify 10+3c+5d-7c+d
For this case we must simplify the following expressions:
[tex]m ^ 3 + m ^ 3\\10 + 3c + 5d-7c + d[/tex]
Expression 1:
[tex]m ^ 3 + m ^ 3 =[/tex]
They are similar terms so we can add.
[tex]2m ^ 3[/tex]
Expression 2:
[tex]10 + 3c + 5d-7c + d =[/tex]
We add similar terms taking into account that:
Equal signs are added and the same sign is placed.
Different signs are subtracted and the major sign is placed.
[tex]10 + 3c-7c + 5d + d =\\10-4c + 6d[/tex]
Answer:
[tex]m ^ 3 + m ^ 3 = 2m ^ 3\\10 + 3c + 5d-7c + d = 10-4c + 6d[/tex]
A doctor administers a drug to a 36-kg patient, using a dosage formula of 51 mg/kg/day. Assume the drug is available in a 300 mg per 5ml suspension or in 500 mg tablets. How many tablets should a 36-kg patient take every four hours?
what is 13% of 600?
Answer:
78
Step-by-step explanation:
600 times 13%
How to solve the following inequality -1 > -2(x - 4) -5(4x - 7)
Answer:
The solution of the inequality is:
[tex]x>2[/tex]
Step-by-step explanation:
Given inequality:
[tex]-1 >-2(x - 4)-5(4x-7)[/tex]
Solving the inequality.
Using distribution.
⇒ [tex]-1 >(-2x) +((- 4)(-2))+(-5\times4x)+((-5)(-7))[/tex]
⇒ [tex]-1 >-2x +8-20x+35[/tex]
Combining like terms
⇒ [tex]-1 >-2x-20x+35+8[/tex]
⇒ [tex]-1 >-22x +43[/tex]
Adding [tex]22x[/tex] both sides.
⇒ [tex]-1+22x >-22x +43+22x[/tex]
⇒ [tex]-1 +22x> 43[/tex]
Adding 1 both sides.
⇒ [tex]-1+1 +22x> 43+1[/tex]
⇒ [tex]22x>44[/tex]
Dividing both sides by 22.
⇒ [tex]\frac{22x}{22}>\frac{44}{22}[/tex]
⇒ [tex]x>2[/tex]
Thus, the solution of the inequality is:
[tex]x>2[/tex]
30 points Asap Recall that Seth's house is 17 miles from school. Which
location should Seth start off at to get to school faster
and how long will it take?
from the bus stop is faster, taking 17 minutes
from the bus stop is faster, taking 24 minutes
from his friend's house is faster, taking 15 minutes
from his friend's house is faster, taking 22.5 minutes
Answer: D
Step-by-step explanation: I just did the quiz
Answer: D
Step-by-step explanation:
Yeah the quiz was like, dud the answers D, so I was like okay it's D
The height ,h, in feet of a baseball that is popped up into the air is a quadratic function of the time,t, in seconds, since it was hit. An equation that may model this situation is h(t)=4+60t-16t^2. Answers the following questions accurately, rounding to two decimals places when needed.
Answer: [tex]4\ feet[/tex]
Step-by-step explanation:
The missing question is: "How high is the ball when it strikes the bat?"The exercise provides you the following Quadratic function:
[tex]h(t)=4+60t-16t^2[/tex]
You know that it represents the height (in feet) of the ball as a function of the time (in seconds) since the ball hit the bat.
Based on this, you can conclude that when the ball strikes the bat the time in seconds is:
[tex]t=0[/tex]
Therefore, in order to calculate the height in feet of the ball when it strikes the bat, you need to subsititute [tex]t=0[/tex] into the function and then evaluate.
So, you get:
[tex]h(0)=4+60(0)-16(0)^2\\\\h(0)=4[/tex]
A Chemist needs to mix a 20% acid solution with a 50% acid solution to obtain 15 liters of a 34% acid solution. How many liters of each acid solution must be used?
8 litres (amount of 20% solution needed) and 7 litres for (amount of 50% solution needed)
Step-by-step explanation:
Let consider ‘x’ for 20% acid solution and (15 – x) for 50% acid solution. And so, the equation would be as below,
20% in x + 50% in (15 – x) = 15 litres of 34%
Convert percentage values, we get
0.20(x) + 0.50 (15 – x) = 15 (0.34)
0.20 x + 7.5 – 0.50 x = 5.1
-0.3 x + 7.5 = 5.1
0.3 x = 7.5 – 5.1
0.3 x = 2.4
[tex]x = \frac{2.4}{0.3} = 8 litres (amount of 20 \% solution needed)[/tex]
Apply ‘x = 8’ value in (15 – x) we get,
15 – 8 = 7 litres
The value of 7 litres for (amount of 50% solution needed)
1/4÷5 equal what? Djdjjdjdjdjdjdjdjdd
Answer:
1/20
Step-by-step explanation:
Which of the following demonstrates how the 20 is calculated using the
combination pattern?
Answer:
D
Step-by-step explanation:
The diagram shows Pascal's triangle. Pascal's triangle is a triangular array of the binomial coefficients.
The entry in the [tex]n^{th}[/tex] row (start counting rows from 0) and [tex]k^{th}[/tex] column (start counting columns from 0) of Pascal's triangle is denoted by
[tex]C^n_k=\left(\begin{array}{c}n\\ k\end{array}\right)[/tex]
Coefficient 20 stands in 6th row, then n = 6 and in 3rd column, so k = 3.
Hence,
[tex]20=C^6_3=\left(\begin{array}{c}6\\ 3\end{array}\right)=\dfrac{6!}{3!(6-3)!}[/tex]
Someone please help! Thank you!
Answer:
The coordinates of point Q will be given by (11,-2)
Step-by-step explanation:
See the attached diagram.
Given that R is the midpoint of PS and Q is the midpoint of RS.
Therefore, the point Q divides the line PS in the ratio 3 : 1.
Now, coordinates of P are (8,10) and that of point S is (12,-6).
Therefore, the coordinates of point Q will be given by
[tex](\frac{3\times 12 + 1 \times 8}{3 + 1}, \frac{3 \times (- 6) + 1 \times 10}{3 + 1})[/tex]
= (11,-2) (Answer)
A potter works 4 days a week, makes 14 pots per day on average, and
charges $24 a pot. If she lowers her price to $16 a pot, by how many pots per
day on average must she increase her production to make the same amount
of money per 4-day workweek?
Final answer:
To maintain the same weekly revenue after reducing her pot price from $24 to $16, a potter working 4 days a week must increase her daily production from 14 pots to 21 pots, which is an increase of 7 pots per day.
Explanation:
The question involves a potter who initially makes 14 pots per day and works 4 days a week, charging $24 per pot. To find out by how many pots per day she must increase her production after lowering her price to $16 per pot, to make the same amount of money, we first calculate her current weekly revenue:
14 pots/day * $24/pot * 4 days = $1,344 per week.After reducing the price to $16 per pot, we need to determine how many pots per day she needs to sell to maintain the same weekly revenue of $1,344:
$1,344 / ($16/pot) / 4 days = 21 pots per day.Therefore, she needs to sell 7 more pots per day (21 pots - 14 pots) to maintain her weekly revenue.
What is the length of BE given that BD = 18 and figure ABCD is a
parallelogram?
Answer: D. 9
Step-by-step explanation: If BD is 18 then BE is 9
Answer:
can confirm that it is 9
Step-by-step explanation:
slay have a nice day!
How does graphing linear inequalities differ from graphing linear equations?
Explanation:
When the inequality symbol is replaced by an equal sign, the resulting linear equation is the boundary of the solution space of the inequality. Whether that boundary is included in the solution region or not depends on the inequality symbol.
The boundary line is included if the symbol includes the "or equal to" condition (≤ or ≥). An included boundary line is graphed as a solid line.
When the inequality symbol does not include the "or equal to" condition (< or >), the boundary line is not included in the solution space, and it is graphed as a dashed line.
Once the boundary line is graphed, the half-plane that makes up the solution space is shaded. The shaded half-plane will be to the right or above the boundary line if the inequality can be structured to be of one of these forms:
x > ... or x ≥ ... ⇒ shading is to the right of the boundaryy > ... or y ≥ ... ⇒ shading is above the boundaryOtherwise, the shaded solution space will be below or to the left of the boundary line.
_____
Just as a system of linear equations may have no solution, so that may be the case for inequalities. If the boundary lines are parallel and the solution spaces do not overlap, then there is no solution.
_____
The attached graph shows an example of graphed inequalities. The solutions for this system are in the doubly-shaded area to the left of the point where the lines intersect. We have purposely shown both kinds of inequalities (one "or equal to" and one not) with shading both above and below the boundary lines.
West high schools population is 250 students fewer then twice the population of East High school the two schools have a total of 2858 students how many students attend the East high school
Answer:
1036 students
Step-by-step explanation:
Let the number of students at West High be "w" and the number of students at East High be "e"
West High population is 250 FEWER than TWICE of East High, we can write:
w = 2e - 250
Total students in both schools is 2858, so we can write 2nd equation as:
e + w = 2858
We can replace 1st equation in 2nd to get an equation in e, and find "e":
e + w = 2858
e + (2e - 250) = 2858
3e - 250 = 2858
3e = 2858 + 250
3e = 3108
e = 3108/3
e = 1036
Hence,
number of students attending East High School = 1036 students
Divide using synthetic division. ( x^4-12x^2-9)/(x+3)
Answer:
x^3 - 3x^2 - 3x + 9 + (-36/(x+3))
OR
x^3 - 3x^2 - 3x + 9 - (36/(x+3))
Step-by-step explanation:
First set the divisor equal to 0:
x + 3 = 0
Subtract 3 from both sides
x = -3
This is what you'll divide the dividend by in synthetic division.
Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:
x^4 + 0x^3 - 12x^2 + 0x -9
Coefficents: 1. 0. -12. 0 -9.
Please see the image for the next steps.
The remainder is -36. Put the remainder over the divisor and add it to the polynomial (shown in image)
-36/(x+3)
Divide using synthetic division the remainder is -36. Put the remainder over the divisor and add it to the polynomial -36/(x+3).
First set the divisor equal to 0:
x + 3 = 0
Subtract 3 from both sides
x = -3
This is what you'll divide the dividend by in synthetic division.
Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:
[tex]x^4 + 0x^3 - 12x^2 + 0x -9[/tex]
Coefficents: 1. 0. -12. 0 -9.
The remainder is -36. Put the remainder over the divisor and add it to the polynomial -36/(x+3).
ABCD is a parallelogram. If mZCDA = 75, then what is mZDAB?
Answer:
Therefore
m∠ DAB is 105°
Step-by-step explanation:
Given:
ABCD is a parallelogram. The diagram is not drawn to scale.
m∠CDA = 75°,
To FInd
m∠DAB = ?
Solution:
ABCD is a parallelogram.
AB || CD .......{opposite sides of a parallelogram are parallel}
∴∠CDA+∠DAB = 180°{SUM of the interior angles between parallel are supplementary}
substituting the values we get
[tex]75+m\angle DAB=180\\\\m\angle DAB =180-75=105\\\\m\angle DAB =105\°[/tex]
Therefore
m∠ DAB is 105°
Andrew is home one winter day studying for an exam. It is lunchtime and he is hungry. Instead of making a sandwich from roast beef in the fridge, he drives to Taco Bell and spends $4 for 2 tacos, a burrito and a Dr. Pepper. He reasons that he can make $10 per hour cutting lawns so he really saves $6 by going to Taco Bell rather than preparing his own meal. What's wrong with Andrew's argument?
Answer:
Andrew did not reason that he could save the $10 per hour he would make cutting lawns by preparing his own meal
Step-by-step explanation:
If Andrew cuts lawns for $10 per hour, he would have $4 more to save by preparing his own meal rather than spending the $4 at Taco Bell
Answer:
Instead of spending time making food, he drives and buys food by a total of $4.
Now, he is not considerating the amount of gas that he is spending by going to buy food and returning.
Also, he was not working, so he is not producing money at the beginning, so making his own lunch actually does not implies that he stops working and loses money.
What is the sum of the first 29 terms of the arithmetic sequence? −43,−35,−27,−19,... Enter your answer in the box. S29=
Answer: [tex]S_{29}[/tex] = 2001
Step-by-step explanation:
Since the sequence is an arithmetic sequence , it means that a common difference must exist.
Let the terms in the sequence be [tex]T_{1}[/tex] , [tex]T_{2}[/tex] , [tex]T_{3}[/tex] , [tex]T_{4}[/tex] , ...
Then common difference = [tex]T_{2}[/tex] - [tex]T_{1}[/tex] = [tex]T_{3}[/tex] - [tex]T_{2}[/tex] = 8
That is , the common difference (d) = 8
The formula for calculating sum of n terms is given by :
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n-1)d ]
Where ;
n = number of terms
a = first term
d = common difference
From the question :
n = 29
a = -43
d = 8
Substituting into the formula , we have
[tex]S_{29}[/tex] = [tex]\frac{29}{2}[/tex] [ 2{-43} + (29-1)(8) ]
[tex]S_{29}[/tex] = [tex]\frac{29}{2}[/tex] (-86 +224)
[tex]S_{29}[/tex] = [tex]\frac{29}{2}[/tex] ( 138)
[tex]S_{29}[/tex] = [tex]\frac{4002}{2}[/tex]
[tex]S_{29}[/tex] = 2001
Find the perimeter of the trapezoid.
Answer:
28
Step-by-step explanation:
The height of the trapezoid and the base length from point S to the height makes a right triangle. In fact, it is a 3, 4, 5 triangle and a pyth. triplet. So...
QS = 5 cm
And...
perimeter = 5+3+6+3+4 = 21 cm
answer: B
20% tip on a bill of 42.26
Answer:
(42.26/100)*120 = $50.712
Step-by-step explanation:
Answer: tip = 8.452
Step-by-step explanation:
Harold plans to buy a $95 Father's Day present for his father, and the holiday
falls on the third Sunday of June. He can afford to put it on layaway with a
20% down payment and $12 a month after that. If payments are due at the
beginning of each month, when should Harold make his first monthly
payment?
Answer:
December 1st
Step-by-step explanation:
Apex
Answer: December 1st
Step-by-step explanation:
Mathematics of personal finance sem 1
Convert (1, 1) to polar form.
A. (2,459
B. (1,459)
C.(2, 2259)
D.(72,459)
Polar form: (r,θ)
Using these formulas:
x²+y²=r²
tan(θ)=y/x
We have the point (1,1) in cartesian coordinates. We need to find r and θ to get it in polar form.
r²=1²+1²
r²=2
r=±√2
tan(θ)=1/1
tan(θ)=1
θ=π/4 radians or 45 degrees
Polar coordinates: (√2,π/4)
Those answer choices look strange. Are you sure these are the right answer choices?
Answer:
Step-by-step explanation:
The way I see it, (1, 1) corresponds to a point which is √2 units from the origin and has an angle of 45° (or π/4 radians).
Which of the following best describes the term induction?
O
A. Writing down the steps to solve a complicated math problem
B. Forming rules based upon observations and experiences
C. Starting with a given set of rules and figuring out what must be
true
O
D. Reducing the solution to a problem in lowest terms
Answer:
C. Starting with a given set of rules and figuring out what must be true . TRUE
Step by step explanation:
Mathematical Induction
Mathematical Induction is a mathematical technique which we can use to prove any given mathematical statement, result, theorem or corollary with help of induction.
Here, we assume the statement to be true for a smaller natural number (Usually 1) and then prove the statement to be true for ANY ARBITRARY NUMBER say k.
Now, from the given options:
A. Writing down the steps to solve a complicated math problem .
FALSE as the induction method is based on ASSUMPTION and INDUCTION.
B. Forming rules based upon observations and experiences .
FALSE as the induction method is based on ASSUMPTION and INDUCTION. We need to induce the needed statement or Result.
C. Starting with a given set of rules and figuring out what must be true .
TRUE as the induction method is based on ASSUMPTION and INDUCTION.
We try and find out the result with the given existing data.
D. Reducing the solution to a problem in lowest terms.
FALSE as the induction method is based on ASSUMPTION and INDUCTION.
Simplify: 2(5+3x)+(x+10)
First, do distributive property:
2(5+3x)+(x+10) Distribute the 2 to the 5 and the 3x; multiply them
10+6x+x+10 Since (x+10) would be 1 times x and 10, it's just x+10
Then, do communitive property:
10+6x+x+10 What we found in the last step, now combine the like terms
20+7x This is what you get since 10+10=20 and 6x+x=7x
The answer:
20+7x or 7x+20
Hope that helps!
Jenny goes to the shop.
She buys
• three cups for £1.24 each
three saucers for 95p each
• a teapot for £6.18
Jenny has £20 to spend. She also wants to buy some plates, which are £1.57 each
What is the greatest number of plates Jenny can buy?
Answer:
5
Step-by-step explanation:
1.24 times 3 = 3.72
.95 (the value of pence to a pound in decimal form) = 2.85
6.18 for the teapot
2.72+2.85+6.18=11.75
She now has £8.25 left (20-11.75).
8.25/1.57=the amount of plates she can buy: 5.25477707006, so 5 with some money left
Two adjacent supplementary angles are
∠ APW and ∠ WPZ
∠ ZPW and ∠ ZPB
∠ BPZ and ∠ WPA
∠ ZPB and ∠ APZ
Answer:
∠ZPB and ∠APZ are two adjacent supplementary angles
Step-by-step explanation:
we know that
Two angles are Adjacent when they have a common side and a common vertex
Two angles are supplementary if their sum is equal to 180 degrees
In this problem we have that
[tex]m\angle ZPB=90^o[/tex] ----> given problem
[tex]m\angle APZ=90^o[/tex] ----> given problem
so
[tex]m\angle ZPB+m\angle APZ=180^o[/tex]
∠ZPB and ∠APZ are supplementary angles
and
∠ZPB and ∠APZ have a common side (ZP) and a common vertex (P)
therefore
∠ZPB and ∠APZ are two adjacent supplementary angles
Answer: ∠ZPB and ∠APZ are two adjacent supplementary angles
Step-by-step explanation: Its the way the cookie crumbles.
2/5 (6-5p) simplified expression
Thank you
Answer:
12/5-2p
Step-by-step explanation:
2/5(6-5p)
12/5-10/5p
12/5-2p
The simplified form of the expression 2/5 (6 -5p) is 12 / 5 - 2p.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
2/5 (6 -5p)
Simplify the expression by solving bracket term,
(2/5) x 6 - (2/5) x 5p
12 / 5 - 2p
The simplified form of the expression 2/5 (6 -5p) is 12 / 5 - 2p.
To know more about Algebraic expression on:
https://brainly.com/question/19245500
#SPJ3
Factorize 10ab + 4a + 5b + 2
Answer:
10ab + 4a + 5b + 2
= 10ab + 5b + 4a + 2
= 5b(2a+1) + 2(2a+1)
= (5b+2)(2a+1)
A baker bought 4 gallons oficing to decorate cakes. He uses 4 % cups
of long to completely frost and decorate each cake. What is the
maximum number of cakes he can completely decorate? Explain your
thinking, hint: 16 cups = 1 gallon)
25 cakes can be completely decorated using 4 gallons of icing.
Step-by-step explanation:
Given:
4 gallons of icing
16 cups =1 gallon
No. of icing cups = [tex]4\times16[/tex] cups
=64 cups
No. of cups required to decorate and frost a cake= 4% of total no. of icing cups
= [tex]\frac{(4\times64)}{100}[/tex]
= 2.56
2.56 cups of icing is required to decorate each cake.
Maximum no. of cakes decorated = [tex]\frac{ (64\times1)}{2.56}[/tex]
= 25
25 cakes can be completely decorated using 4 gallons of icing.
Rita is hiking along a trail that is 14.3 miles long. So far she has hiked along one-tenth of the trail
How far has Rita hiked?
Rita has hiked miles
Just multiply the total length by the fraction:
14.3 * 1/10 = 1.43 miles
Answer:
1.43
Step-by-step explanation:
NOTE: This is the way I do it , other people may have a other/faster way to do it.
For this question you simpily have to divide 14.3 by 10:
1. Convert 14.3 into a mixed number - 14 3/10
2. Divide 14 by 10 - 1.4
3. Divide 3/10 by 10 - 3/100
4. Convert 3/100 into a decimal- 0.03
5. Add the two decimals - 0.03 + 1.4 = 1.43