Answer:
c )
Step-by-step explanation:
To find equivalent inequalities, we are looking to isolate x on the left side.
a) x < 4 ✅
b) x -1 < 3 add 1 to both sides x -1 +1 < 3 +1 result x < 4 ✅
c) x + 1 < 4 subtract 1 from both sides x + 1 -1 < 4 -1 result x < 3 ❌
d) x - 2 < 2 add 2 to both sides x - 2 +2 < 2+2 result x < 4 ✅
show that (3*8*x)^7= 6^7*8^7*x^7
Answer:
(3*8*) ^*7*8*
Step-by-step explanation:
IM DONE TO SHOW YOU
Angelica says the tangent is the ratio of the length of the leg opposite angle A ∠ A over the length of the leg adjacent to angle A This means B C must have a length of 3 3 units A C must have a length of: 4 4 units. They can find the length of Latex A B using the Pythagorean Theorem and then use it to find the sine and cosine ratios. Graciella says that they cannot find the length of any side of the triangle and, therefore, cannot find the ratios for sine and cosine. Both students have errors in their reasoning. Identify the mistake Angelica made in her reasoning. Provide an example that shows why she is incorrect. Identify the mistake that Graciella made in her reasoning. Explain why she is incorrect. Find the ratios for the sine and cosine of angle A Explain your process.
Based on the trigonometry ratios and the Pythagorean theorem both of them were incorrect.
Cos A = 4/5; Sin A = 3/5
What is the Trigonometry Ratios?The Trigonometry ratios relates the length of the sides of a right triangles. They are given as:
Sine ratio, sin ∅ = opp/hypCosine ratio, cos ∅ = adj/hypTangent ratio, tan ∅ = opp/adj.What is the Pythagroean Theorem?If two sides of a right triangle are known the third side can be determined using the Pythagorean theorem, which is given as, c² = a² + b², where and b are legs, and c is the hypotenuse of the right triangle.
1. Given that tan A = 3/4, it is not necessarily true that BC MUST have a length of 3 units, and AC MUST have a length of 4 units, because:
If BC = 9 units and AC = 12 units, the it will give us the same tangent ratio as:
tan A = 9/12 = 3/4.
Therefore, Angelica's mistake is stating that BC MUST be 3 units, and AC MUST be 4 units.
2. Knowing two length of the sides of a right triangle is enough information needed to find the length of the third side using the Pythagorean theorem, so Graceilla is incorrect.
3. Find AC using the Pythagorean theorem:
AB = √(3² + 4²)
AB = 5 units.
Cos A = adj/hyp = AC/AB
Cos A = 4/5
Sin A = opp/hyp = BC/AB
Sin A = 3/5
Learn more about the trigonometry ratios on:
https://brainly.com/question/10417664
A system of equations is given below. To solve this system using substitution, which of the following equations could be used?
A. 2x-4x-6=8
B. 2x- (4x-6)=8
C. 2x+3(4x-6)=8
D. 2x-3(4x-6)=8
Which function is the inverse of f(x)=-5x-4
Hello!
Let's solve this question with the information given to us in the question.
We were given the function, f(x) = -5x - 4, or also known as y = -5x - 4
With the function we need to find the inverse of it.
We can simply flip the "x" and "y" variables in the function and solve.
Solve:
y = -5x - 4
Flip the "x" and "y" variables.
x = -5y - 4
Now, solve for "y".
x = -5y - 4
Add 4 to both sides of the equation.
x + 4 = -5y
Divide everything by -5 to get "y" by itself.
-1/5x - 4/5 = y
Therefore, the inverse of the function would be [tex]-\frac{1}{5}x -\frac{4}{5}[/tex]
Answer:
Your answer would be A). [tex]-\frac{1}{5}x -\frac{4}{5}[/tex]
Suppose you deposit $2,000 in a saving account that pays interest at an annual rate of 4% with interest compounded monthly. Answer the
following questions:
(a)Write a function that represents the amount of money in the account after t years
(b) How much money is going to be in the account after 5 years.
(c) How many years will it take for the account to go over $2,500?
The function that represents the amount of money in the account after t years is f(t) = $2000(1.0033^12t).
The money in his account in five years would be $2442.
The number of years it would take to have a value over $2500 is 6 years.
What is the future value of the account?The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsf(t) = $2000(1.0033^60) = $2442
f(6) = $2000(1.0033^72) = 2535.41
To learn more about future value, please check: https://brainly.com/question/18760477
You want to buy a new computer for $1500. You only have $500 right now, so you decide to deposit the money into an account yeilding 5% interest compounded monthly, how long until you have enough to buy the computer
Answer:
Twenty-two months (a year and ten months)
Step-by-step explanation:
First, we have to find how much is 5% of 500
500 x 0.05 = 25
Next, you add it to 500
so after the first month, you will have $525
Then, we have to find 5% of 525
525 x 0.05 = 26.25
meaning that after the second month, you'll have $551.25
We keep on repeating these steps until we reach the desired amount.
month three:
$551.25 x 0.05 = 27.5625
551. 25 + 27.5625 = 578.8125
month four:
578.8125 x 0.05 = 28.940625
578.8125 + 28.940625 = 607.753125
month five:
607.753125 x 0.05 = 30.38765625
607.753125 + 30.38765625 = 638.14
month six:
638.14 x 0.05 = 31.91
638.14 + 31.91 = 670.05
month seven:
670.05 x 0.05 = 33.51
670.05 + 33.51 = 703.55
month eight:
703.55 x 0.05 = 35.18
703.55 + 35.18 = 738.73
month nine:
738.73 x 0.05 = 36.94
738.73 + 36.94 = 775.67
month ten:
775.67 x 0.05 = 38.78
775.67 + 38.78 = 814.45
month eleven:
814.45 x 0.05 = 40.72
814.45 + 40.72 = 855.17
month twelve:
855.17 x 0.05 = 42.76
855.17 + 42.76 = 897.93
month thirteen:
897.93 x 0.05 = 44.90
897.93 + 44.90 = 942.83
month fourteen:
942.83 x 0.05 = 47.14
942.83 + 47.14 = 989.97
month fifteen:
989.97 x 0.05 = 49.50
989.97 + 49.50 = 1039.47
month sixteen:
1039.47 x 0.05 = 51.97
1039.47 + 51.97 = 1091.44
month seventeen:
1091.44 x 0.05 = 54.57
1091.44 + 54.57 = 1146.01
month eighteen:
1146.01 x 0.05 = 57.30
1146.01 + 57.30 = 1203.31
month nineteen:
1203.31 x 0.05 = 60.17
1203.31 + 60.17 = 1263.48
month twenty:
1263.48 x 0.05 = 63.17
1263.48 + 63.17 = 1326.65
month twenty-one:
1326.65 x 0.05 = 66.33
1326.65 + 66.33 = 1392.98
month twenty-two:
1392.98 x 0.05 = 69.65
1392.98 + 69.65 = 1462.63
month twenty-three:
1462.63 x 0.05 = 73.13
1462.63 + 73.13 = 1535.76
So your final answer would be that it would take twenty-two months (a year and ten months) to have enough money to buy the computer.
p.s. sorry for the super long answer, I wanted to make sure you had the complete process. hope this helped!
x^2+x-20=0
please help me otu
Answer x=2.7
Step-by-step explantion
x^2 +x-20=0
combine like terms.. so x^2 AND X TURN INTO X^3
X^3-20=0
THE SUBTRACT 20 FROM EACH SIDE
X^3=20
x=2.7
:)
In the figure below, find x. Assume that segments that appear to be tangent are tangent. Round to the nearest tenth.
Check the picture below.
Help 111111111111111
Answer:
6/11
Step-by-step explanation:
[tex]p(number \: less \: than \: 4) = \frac{3}{11} [/tex]
[tex]p(odd \: number) = \frac{5}{11} [/tex]
[tex]p(number \: \: less \: than \: 4 \: and \: odd) = \frac{2}{11} [/tex]
Now we know that
[tex]p(aUb) = p(a) + p(b) - p(anb)[/tex]
[tex]p(getting \: number \: less \: than\: 4 \: or \: odd \: number) = [/tex]
[tex] = \frac{3}{11} + \frac{5}{11} - \frac{2}{11} [/tex]
[tex] = \frac{6}{11} [/tex]
I hope it helped you
Stacy performed an experiment in which she rolled a six-sided die multiple times. The results are shown below
Based on the results above, predict the number of times a 3 would be rolled if Stacy performs the experiment a total of 480 times.
Answer:
5/9
Step-by-step explanation:
Let the probability of getting a multiple of 3 is "A"
Let the probability of getting an even number is "B"
Total number of outcomes=36
Total number of favourable outcomes of either a multiple of 3 or an even number are
(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)
That is we have 20 favourable outcomes
Hence, Probability=\frac{\text{favourable outcomes}}{\text{total number of outcomes}}Probability=
total number of outcomes
favourable outcomes
Therefore, after substituting the values we get
probability=\frac{20}{36}probability=
36
20
After simplification we will get
probability=\frac{5}{9}probability=
9
5
could someone help me super super quick?
Answer:
Vertex form of a quadratic equation is y=a(x-h)2+k, where (h,k) is the vertex of the parabola
The vertex of a parabola is the point at the top or bottom of the parabola
Step-by-step explanation:
Different textbooks have different interpretations of the reference "standard form" of a quadratic function. Some say f (x) = ax2 + bx + c is "standard form", while others say that f (x) = a(x - h)2 + k is "standard form". To avoid confusion, this site will not refer to either as "standard form", but will reference f (x) = a(x - h)2 + k as "vertex form" and will reference f(x) = ax2 + bx + c by its full statement.
#1
y=a(x-h)²+ky=a(x²)+3Put (2,-5)
-5=2²a+3-5=4a+34a=-8a=-2Equation
y=-2(x-0)²+3#2
y=a(x-2)²Put (5,9)
9=a(5-2)²3²a=99=9a=1Equation
y=(x-2)²+0#3
y=a(x+3)²+2put (-1,14)
14=a(2)²+214=4a+24a=12a=3Equation
y=3(x+3)²+2#4
y=a(x-5)²-3Put (1,-8)
-8=a(-4)²-3-8=16a-316a=-5a=-5/16Equation
y=-5/16(x-5)²-3
Situation: Holly wants to save money for an emergency. Holly invests $800 in an account that pays an interest rate of 4%. A = P(1 + r)¹ P = amount of money invested r = interest rate percentage in decimal form How many years will it take for the account to reach $1,600? Round your answer to the nearest hundredth. Enter the correct answer. DONE
Answer:
t = 74.897 years
(about 74 years 11 months)
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 per year,
Then, solve the equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(16,000.00/800.00) / ( 365 × [ln(1 + 0.04/365)] )
t = ln(16,000.00/800.00) / ( 365 × [ln(1 + 0.00010958904109589)] )
t = 74.897 years
Summary:
The time required to get a total amount of $16,000.00 with compoundeded interest on a principal of $800.00 at an interest rate of 4% per year and compounded 365 times per year is 74.897 years.
(about 74 years 11 months)
Since it wasn't stated howmany times the interest is compunded I took the value of once a year.
Estimate the amount of the tip by rounding the bill to the nearest ten dollars before calculating.
15% tip on a bill of $551.60
The amount of the tip is approximately $
Answer:
$82.50
Step-by-step explanation:
This problem requires you round the given bill value, then compute a fraction of that rounded value.
__
RoundingWe want to round the bill value to the nearest $10. The digit to the right of the tens digit is 1, so we simply replace that and all digits to the right with zeros. (Had the ones digit been 5 or more, we would increment the tens digit before zeroing digits to its right.)
$551.60 rounded to nearest $10 is $550.00
__
Tip AmountThe amount of the tip is found by multiplying the bill by the tip rate.
$550 × 15% = $550 × 0.15 = $82.50
The amount of the tip is approximately $82.50.
_____
Additional comment
It is often relatively easy to compute a tenth or half of something in your head. We know that 15% = 10% + (1/2)(10%), and that 10% of $550 is $55.
Half of $55 is $27.50, so the tip amount will be $55.00 +27.50 = 82.50, a calculation you can do mentally.
Find the surface area of the square pyramid?
Answer:
C) 224 square centimeters.
Step-by-step explanation:
what is the quotient of 4 ÷ 1/4?
Answer:
16
Step-by-step explanation:
4 divided by 1/4 =
4/.25
16
What’s the volume for this shape?
Answer:
60 m^3
Step-by-step explanation:
3 x 4 x 5 = 60
The others are self explanatory
15
Janice had a total of 156 red and yellow beads in the ratio 6:7.
After she gave away an equal number of each type of beads, the
number of red and yellow beads left was in the ratio 3:7.
(a)Did the fraction of red beads that Janice had left increase,
decrease or remain the same?
B)How many yellow beads were given away?
Answer:
decrease because the ratio number is Less so multiply by 156 to each ratio to find your relationship between. hope this helps.
find the missing side of this triangle 6 x 10
Answer:
√136 units
Step-by-step explanation:
We are given that;
The provided triangle is a right triangle.The measure of the legs are 6 and 10 units.The hypotenuse of the right triangle is x units.Since the provided triangle is a right triangle, we can use pythogoras theorem to determine the missing side length of the triangle.
What is the pythogoras theorem and it's formula?Pythogoras theorem is a formula that is used to determine the missing side length of a right triangle, with the following given;
Two side lengths (Legs)A hypotenuse (Longest side)Pythogoras theorem is denoted as;
(c)² = (b)² + (a)²Where, "c" is the hypotenuse; "b" and "a" are the legs.
When we substitute the measure of the two legs and the hypotenuse of the triangle, we get;
(x)² = (10)² + (6)²Now, let's simplify the equation to determine the value of "x".
⇒ (x)² = 100 + 36 [Evaluating the squares]⇒ (x)² = 136 [Simplifying the right-hand-side]⇒ √(x)² = √136 [Taking square root both sides]⇒ x = √136 ≈ 11.66 units (2 d.p) [Taking square root both sides]The measure of the missing side is √136 units.
Learn more aobut pythogoras theorem: https://brainly.com/question/14056085
Answer:
136
Step-by-step explanation:
solve for x～
[tex]x {}^{2} - 5x + 6 = 0[/tex]
thankyou! :)
what three numbers give you 206 when multiplied
Answer:
1, 1, 206.Step-by-step explanation:
There are nothing else that can multiply to get to 206, so this is the answer.
Solve:
1 * 1 * 206= 1 * 206= 206.This is the only equation that can make 206 with 3 numbers.
1 dozen roses for $29.75 how much does one rose cost
Answer:
$2.48
Step-by-step explanation:
29.75/12 =2.479
solve this sum plsss
Step-by-step explanation:
the answer is in the attachment.
hope this helps you.
Find the limit of the function by using direct substitution. limit as x approaches zero of quantity x squared minus eight.
Answer:
-8
Step-by-step explanation:
lim x⇒0 (x²-8) = 0-8 = -8
Write a two-digit number ...
a
that has 9 tens and 1 ones;
.
Answer: 91
Step-by-step explanation:
9 tens= 90
1 ones= 1
90+1=91
HELP HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
The answer is C. A fraction is basically another way of writing division, and six divided by three is two.
if you invest $421 for 9 years at an interest rate of 4%, how much interest will you earn?
Step-by-step explanation:
421×9=3789 it is easy when you know your multiple choice
Solve by factoring:
a² = 25
Answer:
[tex]a=[/tex] ±[tex]5[/tex]
Step-by-step explanation:
[tex]a^{2} =25[/tex]
equal to zero
[tex]a^{2} -25=0[/tex]
factor: difference of squares
[tex](a+5)(a-5)=0[/tex]
first factor:
[tex]a+5=0\\a_{1} =-5[/tex]
second factor:
[tex]a-5=0\\a_{2} =5[/tex]
Hope this helps
Hanson and his classmates placed colored blocks on a scale during a science lab. The blue block weighed 8.1 pounds and the green block weighed 3.758 pounds. How much more did the blue block weigh than the green block?
This is for my younger brother
Answer:
4.342
Step-by-step explanation:
8.1 - 3.758 = 4.342
When you are trying to find the amount of difference between two values you subtract the value less than the other and there you go, the solution!
I hope it was as simple as that and that this helped!
What is9.3 to a fraction?
Answer:
9.3 = 93 / 10
Step-by-step explanation:
In an examination,33 1/3 percentage of the examinees passed.If 240 examinees failed,find the total number of the examinees!!
Answer:
[tex]SOLUTION:-[/tex]
[tex] \rm{passed \: percent = { \displaystyle{33 \frac{1}{3} \%} = \frac{100}{3}\% }}[/tex]
[tex]{ \displaystyle{ \rm{failed \: percent = \left( 100 - \frac{100}{3} \right)}\%}}[/tex]
[tex]\displaystyle{ \frac{3 \times 100 - 100}{3}\% }[/tex]
[tex]\displaystyle{ \frac{200}{3}\% }[/tex]
Let,x be the total number of examinees:-
We have,
[tex]\displaystyle{ \frac{200}{3}\% \: \rm{of \: x = 240} }[/tex]
[tex]\displaystyle{ \frac{200}{3} \times \frac{1}{100} \rm \: x = 240}[/tex]
[tex]\displaystyle{ \rm{x = \frac{240 \times 3 \times 100}{200} }}[/tex]
[tex]\displaystyle{ \rm{x = 360}}[/tex]
Hence,required number of examinees = 360 .