20% of 50 is found by multiplying the base (50) by the decimal equivalent of the percent (0.2). The calculation yields an amount of 10, which indicates that 20% of 50 is 10.
Calculating percents involves using the basic equation that relates the percent, the base (also called 'whole' or 'total'), and the amount (or 'part'). The equation can be represented as percent = (amount/base) imes 100. To find what is 20% of 50, we use this equation, where the percent is known (20%) and the base is known (50), but the amount is what we are looking for.
First, let's convert the percent to a decimal to make the calculation easier: 20% = 20/100 = 0.2. Then, we multiply the base (50) by the decimal form of the percent (0.2): 50 x 0.2 = 10. So, 20% of 50 is 10.
Therefore, the correct representation relating the Percent, Amount, and Base in this problem is option A) Percent=20%, Amount=50, Base=unknown, since we're calculating the amount based on the known percent and base.
Answer:
C.) percent= 20%, Amount=unknown, Base =50
Step-by-step explanation:
20% is the percent
50 is the amount
20% of 50 is the unknown. This is the amount.
20% of 50 = 0.2 × 50 = 10
Find the area of the shaded region
Answer: Second Option
[tex]P (-1.17 <z <1.17) = 0.7580[/tex]
Step-by-step explanation:
The shaded area corresponds to the interval
[tex]-1.17 <z <1.17.[/tex]
By definition, for a standard normal distribution the area under the curve in the interval (b <z <h) is equal to:
[tex]P (b <z <h)[/tex]
So in this case we look for:
[tex]P (-1.17 <z <1.17)[/tex]
This is:
[tex]P (-1.17 <z <1.17) = P (z <1.17) - P (z <-1.17)[/tex]
Looking at the standard normal table we have to:
[tex]P (z <1.17) = 0.8790\\P (z <-1.17) = 0.1210[/tex]
So:
[tex]P (-1.17 <z <1.17) = 0.8790- 0.1210\\\\P (-1.17 <z <1.17) = 0.7580[/tex]
What is the value of a?
Check the picture below.
notice, on the first 2 lines, we used the quadrilateral conjecture.
on the lines 3 and 4 we used the inscribed angle theorem.
line 5, if we add those 3 arcs, we end up with 427°, mind you that the surplus is arcYW or "b", since it's added twice by XW and YZ.
line 6, if we subtract a full circle from it, we have the surplus.
line 7, we simply subtract YW from XW, leaving the leftover of arc "a".
What is the point slope form of a line that has a slope of 3 and passes through the point (-1,4)
Answer:
y - 4 = 3(x- (-1) ---> y-4 = 3(x+1)
Step-by-step explanation:
y - 4 = 3(x + 1)
y - 4 = 3x + 3
y = 3x + 7
then plug in (-1,4)
4 = 3(-1) + 7
4 = -3 + 7
4 = 4
Point slope form looks like:
y - y₁ = m(x - x₁)
Answer:
Y-4=3[(x-(-1)]
Step-by-step explanation:
This answer is corect i got it right on my questions
an office worker earns R6400 per month. his monthly expenses are 1/5 for rent , 2/7 for car payment, 1/6 for insurance, 1/3 for other monthly living expenses and the rest he deposits into a savings account. how much does he save per month?
Answer:
The officer saves $91.45 per month
~Step-by-step explanation~
Ok this is how I do fractions and its not very good, but it works.
First I divided 6400 by 5, 6, and 7, (I didn't do 3 because you can just multiply the answer to 6 by 2.) the reason I divided these is to see how much 1 part of their fraction is worth. So in total I got 1066.66 (irrational number) for insurance which means I got 2133.32 for his monthly living ( had to multiply by 2). For his car payment I got 1828.57 (I divided and then multiplied by 2) and for his rent I got 1280. I added these all together to get the total he spends each month which was 6308.55, and I subtracted that from 6400 to figure out that he puts $91.45 in his savings account
Answer:
The answer is R91.43.
Step-by-step explanation:
Monthly salary of the worker = R6400
The monthly expenses are 1/5 for rent that is [tex]\frac{1}{5}\times6400= 1280[/tex]
The car payment is 2/7 that is [tex]\frac{2}{7}\times6400= 1828.57[/tex]
The insurance is 1/6 that is [tex]\frac{1}{6}\times6400= 1066.67[/tex]
Few other monthly living expenses are 1/3 that is [tex]\frac{1}{3}\times6400= 2133.33[/tex]
We will total these values:
[tex]1280+1828.57+1066.67+2133.33=6308.57[/tex]
So, the amount that is saved per month = [tex]6400-6308.57=91.43[/tex]
The answer is R91.43.
If cos(x) = 0.5, then what is x?
Answer:
=60 the second option.
Step-by-step explanation:
Given the trigonometric ratio, we can find the value of the angle by simply finding the inverse of the given ratio.
If for example Cos ∅= a, then ∅=Cos⁻¹a
If Cos (x)= 0.5, then x= Cos⁻¹ 0.5
Cos⁻1 0.5=60°
The angle whose sine is 0.5 is ∅=60°
Answer: second option.
Step-by-step explanation:
You have that:
[tex]cos(x)=0.5[/tex]
Then, to find the value of "x", you need to apply Arccosine ( This is the inverse function of the cosine).
Therefore, applying this in the procedure, you get that the value of "x" is the following:
[tex]cos(x)=0.5\\\\x=Arccos(0.5)\\\\x=60\°[/tex]
You can observe that this matches with the second option.
Is PQR-XYZ? If so, name which similarity postulate or theorem applies.
80°
6
3/80
p5 R
A. Similar - AA
O
O
B. Similar - SSS
O
c. Similar - SAS
D. Cannot be determined
Answer:
D. Cannot be determined
Step-by-step explanation:
there is not enough information for you to answer this question. A picture would be helpful to answer this question, but there isn't one.
The correct option is,
D. Cannot be determined.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Since, We are given that two triangle PQR and XYZ are similar.
AA-Similarity postulate: Two angles of one triangle is equal to its corresponding angles of other triangle. Then, the two triangles are similar by AA postulate.
SSS similar: When three sides of two triangles are in the same ratio.
SAS similar: When two sides of two triangle are in the same ratio and one angle between two proportional sides of two triangles is congruent.
But we have not enough information by which we can determine triangle PQR and triangle XYZ is similar.
Hence, option D is true.
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I NEED HELP NOW
The graph shown is a scatter plot:
Which point on the scatter plot is an outlier?
Point A
Point B
Point C
Point D
Answer: The outlier in this scatter plot is Point D.
Step-by-step explanation:
The reason its Point D because its the only one that is the farest away from the rest of the points on the plot.
The reason why "Point D" would be the correct answer because the point is no where near the "trend" of the scatter plot.
When you look at the scatter plot, you would notice that there following a "trend" when the graph increases.
However, you would notice that point D is not really near there, therefore making it an outlier.
An outlier is pretty much something that is left out, and in this case, point D would be the outlier since it's left out of the typical growth of the scatter plot.
I hope this helps!Best regards,MasterInvestor25 points!!
Can postulates always be proven true?
Answer:
The basic answer to your question is that we have to start somewhere.
The essence of mathematics (in the sense the Greeks introduced to the
world) is to take a small set of fundamental "facts," called
postulates or axioms, and build up from them a full understanding of
the objects you are dealing with (whether numbers, shapes, or
something else entirely) using only logical reasoning such that if
anyone accepts the postulates, then they must agree with you on the
rest.
It can sometimes be proven.
Using the data: 2, 2, 3, 3, 3, 4, 5, 6, 6, 19
What is Q1 and Q3
3.5, 6.5
2, 10
3, 6
2, 5
Answer: Third Option
[tex]Q_1=3[/tex]
[tex]Q_3=6[/tex]
Step-by-step explanation:
Notice that we already have the data sorted from least to greatest.
Now to find Q1 and Q3 we can use the following formulas
For a set of data ordered from least to greatest of the form [tex]X_1, X_2, ..., X_n[/tex]
Where n is the total number of data
[tex]Q_1=X_{\frac{1}{4}(n+1)}[/tex]
In this case [tex]n=10[/tex]
So:
[tex]Q_1=X_{\frac{1}{4}(10+1)}[/tex]
[tex]Q_1=X_{2.75}[/tex]
Round the nearest whole and get:
[tex]Q_1=X_{3}[/tex]
[tex]Q_1=3[/tex]
For [tex]Q_3[/tex] we have:
[tex]Q_3=X_{\frac{3}{4}(n+1)}[/tex]
[tex]Q_3=X_{\frac{3}{4}(10+1)}[/tex]
[tex]Q_3=X_{8.25}[/tex]
Round the nearest whole and get:
[tex]Q_3=X_{8}[/tex]
[tex]Q_3=6[/tex]
The measure of central angle XYZ is 3pi/4 radians. What is the area of the shaded sector?
32pi units2
85 ..
96 ..
256 ..
Answer:
96π units²
Step-by-step explanation:
area of shaded sector (A) = area of circle × fraction of circle
A = πr² × [tex]\frac{\frac{3\pi }{4} }{2\pi }[/tex]
= 16² × [tex]\frac{3\pi }{8}[/tex]
= 256 × [tex]\frac{3\pi }{8}[/tex]
= 32 × 3π
= 96π units²
Answer:
Area of sector : 96 π unit².
Step-by-step explanation:
Given : The measure of central angle XYZ is 3pi/4 radians.
To find : What is the area of the shaded sector?
Solution: We have given central angle XYZ is 3pi/4 radians.
Area of sector : [tex]\frac{1}{2}[/tex] (radius)²* central angle.
Plug the values central angle = [tex]\frac{3\pi }{4}[/tex] , radius = 16 units.
Then ,
Area of sector : [tex]\frac{1}{2}[/tex] (16)²* [tex]\frac{3\pi }{4}[/tex].
Area of sector : [tex]\frac{1}{2}[/tex] * 256 * [tex]\frac{3\pi }{4}[/tex].
Area of sector : 128 * [tex]\frac{3\pi }{4}[/tex].
Area of sector : 32 * 3 π
Area of sector : 96 π unit².
Therefore, Area of sector : 96 π unit².
b is the midpoint of AC and E is the midpoint of BD if A(-9,-4) C(-1,6) and E(-4,-3) find the coirdinates of D
Answer:
Step-by-step explanation:
[tex]B=(\frac{-9-1}{2},\frac{-4+6}{2} ) (midpoint formula)\\B=(-5,1)\\\\Then using midpoint formula again,\\E=(-4,3)=(\frac{-5+x}{2} =-4,\frac{1+y}{2} =3)\\so \\x=-3\\y=5\\\\D=(-3,5)[/tex]:
whihc question is not a good survey question? dont you agree that the financial crisis is essentially over? on average how many hours do you sleep per day?
Answer:
The correct answer would be option A, Don't you agree that the financial crisis is essentially over.
Step-by-step explanation:
A survey questionnaire is a series of question which is set formally to be asked from a specific sample of a population to gather, analyze and interpret the data obtained from the sample population. So the questions in the survey must be structured, to the point, clear, short and straight. Survey questions are desirably closed ones and the ones which do not need much explanation by the person who is doing the survey. So the first question in this question require an explanation, and also the question is not structured, clear and to the point and thus is not a good survey question. Comparatively, the second question is more structured, clear and to the point and such questions are normally desirable in the surveys.
Answer:
See image
Step-by-step explanation:
Plato
Sin x + cos x = cos x/1-tanx + sin x/1-cot x. Verify the identity. Explain each step please!
Answer:
[tex]sinx+cosx=\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex] proved.
Step-by-step explanation:
[tex]sinx+cosx=\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex]
Taking R.H.S
[tex]\frac{cosx}{1-tanx}+\frac{sinx}{1-cotx}\\[/tex]
Multiply and divide first term by cos x and second term by sinx
[tex]=\frac{cosx*cosx}{cosx(1-tanx)}+\frac{sinx*sinx}{sinx(1-cotx)}[/tex]
we know tanx = sinx/cosx and cotx = cosx/sinx
[tex]=\frac{cos^2x}{cosx(1-\frac{sinx}{cosx} )}+\frac{sin^2x}{sinx(1-\frac{cosx}{sinx})}\\=\frac{cos^2x}{cosx-sinx}+\frac{sin^2x}{sinx-cosx}[/tex]
Taking minus(-) sign common from second term
[tex]=\frac{cos^2x}{cosx-sinx}-\frac{sin^2x}{cosx-sinx}[/tex]
taking LCM of cosx-sinx and cosx-sinx is cosx-sinx
[tex]=\frac{cos^2x-sin^2x}{cosx-sinx}[/tex]
We know a^2-b^2 = (a+b)(a-b), Applying this formula:
[tex]=\frac{(cosx+sinx)(cosx-sinx)}{cosx-sinx}\\=cosx+sinx\\=L.H.S[/tex]
Hence proved
Which proportion could be used to find the length of side b?
Answer:
B
Step-by-step explanation:
Using the Sine Rule in ΔABC
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
∠C = 180° - (82 + 58)° = 180° - 140° = 40°
Completing values in the above formula gives
[tex]\frac{a}{sin58}[/tex] = [tex]\frac{b}{sin82}[/tex] = [tex]\frac{8.4}{sin40}[/tex]
We require a pair of ratios which contain b and 3 known quantities, that is
[tex]\frac{b}{sin82}[/tex] = [tex]\frac{8.4}{sin40}[/tex]
OR
[tex]\frac{sin40}{8.4}[/tex] = [tex]\frac{sin82}{b}[/tex] → B
Answer:
B
Step-by-step explanation:
Simplify -4 1/4 - (9 1/2)
Answer:
-55/4
Step-by-step explanation:
-4 1/4 - (9 1/2)
Both the terms are given in whole fraction:
Change the terms into improper fraction
4*-4+1 = -17/4
2*9 + 1=19/2
Now,
-17/4 - 19/2
Now take the L.C.M of the denominator.
L.C.M of 4 and 2 is 4
Solve for numerator:
L.C.M (4) divided by denominator of first term will give quotient 1. Then 1 multiply by the numerator -17 will give us 1* -17 = -17
Then 4 divided by denominator of 2nd term will give us 2 as a quotient. Then quotient multiplied by numerator of 2nd term will give us 19*2 = 38
Therefore,
-17 - 38/4
= -55/4
The answer is -55/4....
The expression -4 1/4 - (9 1/2), is simplified to be expressed as -53/4
What is -4 1/4 - (9 1/2) after you simplify?To simplify the expression -4 1/4 - (9 1/2), we need to convert the mixed numbers to improper fractions and perform the subtraction.
First, let's convert the mixed numbers to improper fractions:
-4 1/4 = -4 + 1/4 = -4 * 4/4 + 1/4 = -16/4 + 1/4 = -15/4
9 1/2 = 9 + 1/2 = 9 * 2/2 + 1/2 = 18/2 + 1/2 = 19/2
Now we can substitute these values back into the original expression:
-15/4 - 19/2
To subtract fractions, we need a common denominator. The least common multiple (LCM) of 4 and 2 is 4, so we can rewrite the fractions with a common denominator of 4:
-15/4 - 19/2 = -15/4 - 38/4
Now we can subtract the fractions:
-15/4 - 38/4 = (-15 - 38)/4 = -53/4
Therefore, the expression -4 1/4 - (9 1/2) simplifies to -53/4.
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find the x and y intercepts for the equation 2x-5y=6
Answer:
X intercepts (3,0) Y (0, -6/5)
Step-by-step explanation:
X intercepts: -6-2x/5=0
5(-6-2/5)=0*5
-6+2x=0
-6+6+2x=0+6
2x=6
2x/2=6/2
x=3
Y intercepts: y=-6-2*0/5
y=6-2*0=6
6-2*0/5
6-0/5
6/5
Answer:
X= 5y/2+3
Step-by-step explanation:
First add 5y to both sides
2x-5y+5y=6+5y
2x=5y+6
Step 2
Divide both sides by 2
2x/2=5y+6/2
X=5y/2+3
Examine the following system of inequalities.
{y <−1/4x+4 and y>(x+4)^2
Which option shows the graph of the system?
Dotted linear inequality shaded above passes through (0, 4) & (4,5). Dotted parabolic inequality shaded below passes through (negative 6,4), (negative 4, 0) & (negative 2, 4).
Dotted linear inequality shaded below passes through (0, 4) & (4,3). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).
Dotted linear inequality shaded below passes through (0, 4) & (4,5). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).
Dotted linear inequality shaded above passes through (0, 4) & (4,3). Dotted parabolic inequality shaded below passes through (negative 6,4), (negative 4, 0) & (negative 2, 4).
Dotted linear inequality shaded below passes through (0, 4) & (4,3). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).
Step-by-step explanation:Hello! Let me help you to find the correct option to this problem. First of all, we have the following system of inequalities:
[tex]\left\{ \begin{array}{c}y< -\frac{1}{4}x+4\\y>(x+4)^{2}\end{array}\right.[/tex]
To solve this, let's write the following equations:
FIRST:[tex]y=-\frac{1}{4}x+4[/tex]
This is a linear function written in slope-intercept form as [tex]y=mx+b[/tex]. So, the slope [tex]m=-\frac{1}{4}[/tex] and the y-intercept is [tex]b=4[/tex]. Since in the inequality we have the symbol < then the graph of the line must be dotted. To get the shaded region, let's take a point, say, [tex](0, 0)[/tex] and let's test whether the region is above or below the graph. So:
[tex]y< -\frac{1}{4}x+4 \\ \\ Let \ x=y=0 \\ \\ 0<-\frac{1}{4}(0)+4 \\ \\ 0<4 \ True![/tex]
Since the expression is true, then the region is the one including point [tex](0, 0)[/tex], that is, it's shaded below.
SECOND:[tex]y=(x+4)^{2}[/tex]
This is a parabola that opens upward and whose vertex is [tex](-4,0)[/tex]. Since in the inequality we have the symbol > then the graph of the parabola must be dotted. Let's take the same point [tex](0, 0)[/tex] to test whether the region is above or below the graph. So:
[tex]y>(x+4)^{2} \\ \\ Let \ x=y=0 \\ \\ 0>(0+4)^2\\ \\ 0>16 \ False![/tex]
Since the expression is false, then the region is the one that doesn't include point [tex](0, 0)[/tex], that is, it's shaded above
____________________
On the other hand, testing points (0, 4) and (4,3) on the linear function:[tex]y=-\frac{1}{4}x+4 \\ \\ \\ \bullet \ (0,4): \\ \\ y=-\frac{1}{4}(0)+4 \therefore y=4 \\ \\ \\ \bullet \ (4,3): \\ \\ y=-\frac{1}{4}(4)+4 \therefore y=3[/tex]
So the line passes through these two points.
Now, testing points (negative 6,4), (negative 4, 0) & (negative 2, 4) on the parabola:[tex]y=(x+4)^2 \\ \\ \\ \bullet \ (-6,4): \\ \\ y=(-6+4)^2 \therefore y=(-2)^2 \therefore y=4 \\ \\ \\ \bullet \ (-4,0): \\ \\ y=(-4+4)^2 \therefore y=0 \\ \\ \\ \bullet \ (-2,4): \\ \\ y=(-2+4)^2 \therefore y=(2)^2 \therefore y=4[/tex]
So the line passes through these three points.
Finally, the shaded region is shown below.
Which graph best represents the solution to the following pair of equations? y = 2x − 10 y = −x + 18
Answer:(6,12)
Step-by-step explanation:
Please helpppppppppp me
Answer:
Please read explanation below.
Step-by-step explanation:
Let's go over what some of the symbols of inequalities represent:
[tex]>[/tex]: greater than
[tex]<[/tex]: less than
[tex]\ge[/tex]: greater than or equal to
[tex]\le[/tex]: less than or equal to
The symbol in the equation that is given to you is [tex]\ge[/tex]. It seems as though each of the answer choices have everything written as the same thing except for the description of the inequalities. Check the one that applies.
Which property was used to write the equation in step 2?
Step 1: 5(x-7) = 55
Step 2: 5x-35 = 55
Step 3: 5x = 90
Step 4: X= 18
A) distributive property
B) addition property of equality
C) subtraction property of equality
D )division property of equality
Answer:
A
Step-by-step explanation:
Given
5(x - 7) = 55, then using the distributive property, that is
a(b - c) = ab - ac, then
5x - 35 = 55
The property that was used to write the equation in step 2 is option A) distributive property
Given that,
5(x - 7) = 55So here we have to use the distributive property i.e.
a(b - c) = ab - ac,So,
5x - 35 = 55
Therefore we can conclude that The property that was used to write the equation in step 2 is option A) distributive property
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If you apply the changes below to the absolute value parent function, f(x) = |x|,what is the equation of the new function?
• Shift 4 units to the right.
• Shift 6 units up.
Answer:
Option B [tex]g\left(x\right)=\left|x-4\right|+6[/tex]
Step-by-step explanation:
we have
[tex]f\left(x\right)=\left|x\right|[/tex]
The vertex is the point (0,0)
If to the parent function apply
Shift 4 units to the right and Shift 6 units up
The rule of the translation is
(x,y) ------> (x+4,y+6)
so
The vertex of the new function is (4,6)
therefore
the equation of the new function is
[tex]g\left(x\right)=\left|x-4\right|+6[/tex]
Answer:
just entered the answer and it was |x-4|+6
hope that helps!
Step-by-step explanation:
Simplify the given equation.
5x + 2(x - 3) = -2(x - 1)
078-6--2X-2
7x - 6 = -2x + 2
7x - 3 = -2x - 1
Answer:
x = 8/9
Step-by-step explanation:
5x + 2(x - 3) = -2(x - 1)
Distribute on both sides.
5x + 2x - 6 = -2x + 2
Combine like terms on the left side.
7x - 6 = -2x + 2
Add 2x to both sides.
9x - 6 = 2
Add 6 to both sides.
9x = 8
Divide both sides by 9.
x = 8/9
bob spent 3/8 of his birthday money at a baseball game and 5/12 ona new bat and glove.what fraction of his birthday money did bob spend?
Answer:
19/24
Step-by-step explanation:
Since you are looking for the fraction he spend, you have to add 3/8 and 5/12 with one another. To do this you have to change those fractions to have the same denominators. so you multiply 3/8 by 3/3 to get 9/24 and you multiply 5/12 by 2/2 to get 10/24. You then add 9/24 with 10/24 to get 19/24. Since you cannot simplify this further, 19/24 is your answer.
Bob spent [tex]\frac{19}{24}[/tex] of his birthday money
What is fraction?"It is a number is expressed as a quotient, in which the numerator is divided by the denominator.""It is used to represent the part of the whole thing. "For given question,
Bob spent 3/8 of his birthday money at a baseball game and 5/12 on a new bat and glove.
We need to find the fraction of his birthday money he spent.
so we add given two fractions.
[tex]\frac{3}{8}+ \frac{5}{12}\\\\ =\frac{3\times 3}{8\times 3}+ \frac{5\times 2}{12\times 2}\\\\=\frac{9}{24}+ \frac{10}{24}\\\\=\frac{9+10}{24}\\\\ =\frac{19}{24}[/tex]
Therefore, Bob spent [tex]\frac{19}{24}[/tex] of his birthday money.
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Please help with this one question ASAP. (show steps if you can)
For this case we have that the area of the figure is given by the area of a rectangle plus the area of a square. By definition, the area of a rectangle is given by:
[tex]A = a * b[/tex]
According to the figure we have:
[tex]a = 9 \sqrt {2}\\b = 8 \sqrt {2} -2 \sqrt {2} = 6 \sqrt {2}[/tex]
So, the area of the rectangle is:
[tex]A = 9 \sqrt {2} * 6 \sqrt {2} = 54 (\sqrt {2}) ^ 2 = 54 * 2 = 108[/tex]
On the other hand, the area of a square is given by:
[tex]A = l ^ 2[/tex]
Where:
l: it is the side of the square
According to the figure we have:
[tex]l = 2 \sqrt {2}[/tex]
So:
[tex]A = (2 \sqrt {2}) ^ 2 = 4 * 2 = 8[/tex]
Finally, the area of the figure is:
[tex]A_ {t} = 108 + 8 = 116[/tex]
Answer:
116
What is the prime factorization of 31?
Enter your answer as a product of prime numbers, like 2 x 3, or as a single prime number, like 17.
Answer:
Step-by-step explanation:
31 is prime. It can't be factored. The way I'm reading the directions, you should enter 31.
Answer:
31
Step-by-step explanation:
The prime factorization of 31 is 1 x 31 = 31.
You have to multiply the number by 1 to find its prime factorization.
However, it is usually written as just 31.
What is the sum and classification of [tex]\frac{2}{5} + \sqrt{88}[/tex]
A- 9.78083151..., irrational
B - 9.78083151..., rational
C-13.38083151..., irrational
D- 13.38083151..., rational
Answer:
The answer is def. A.
Answer: OPTION A.
Step-by-step explanation:
By definition:
A number is Rational when it can be written as a simple fraction.
A number is Irrational when it cannot be written as a simple fraction.
Notice that:
[tex]\frac{2}{5}[/tex] is a Rational number.
[tex]\sqrt{88}=2\sqrt{2}[/tex] It is an irrational number.
Therefore, the sum of these numbers is an Irrational number:
[tex]\frac{2}{5} + \sqrt{88}=\frac{2}{5} + 2\sqrt{22}=9.78083151...[/tex]
After the expression (x^16)3/4is simplified as much as possible, x is raised to what exponent? a0
Answer:
12
Step-by-step explanation:
Given expression is:
[tex](x^16)^\frac{3}{4}[/tex]
By the rues of exponents, when there is exponent on exponent then the exponents are multiplied.
So,
[tex]= x^{16*\frac{3}{4}}\\ = x^{4*3}\\=x^{12}[/tex]
The exponent of x will be 12 after the simplification ..
solve the following equations:2x-5y-4 x+6y=15
Answer:
x= 3
y= 2
Step-by-step explanation:
The given equations are :
2x-5y = -4 equation 1
x +6y = 15 equation 2
We will multiply the equation:2 by 2
2(x+6y=15)
2x+12y=30 equation 3
Lets call this equation:3
Now we will use the elimination method:
Subtract equation 3 from equation 1:
2x-5y = -4
2x+12y=30
_________
-17y = -34
y= -34/-17
y = 2
Now put the value of y in any equation:
We will use equation 1
2x-5y = -4
2x-5(2)= -4
2x-10= -4
Move the constant to the R.H.S
2x= -4+10
2x=6
Divide both the terms by 2
x= 3
Therefore the solution set is (x,y){(3,2)}....
The cosine of 23° is equivalent to the sine of what angle
Answer:
So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).
(There are more values since we can go around the circle from 67 degrees numerous times.)
Step-by-step explanation:
You can use a co-function identity.
The co-function of sine is cosine just like the co-function of cosine is sine.
Notice that cosine is co-(sine).
Anyways co-functions have this identity:
[tex]\cos(90^\circ-x)=\sin(x)[/tex]
or
[tex]\sin(90^\circ-x)=\cos(x)[/tex]
You can prove those drawing a right triangle.
I drew a triangle in my picture just so I can have something to reference proving both of the identities I just wrote:
The sum of the angles is 180.
So 90+x+(missing angle)=180.
Let's solve for the missing angle.
Subtract 90 on both sides:
x+(missing angle)=90
Subtract x on both sides:
(missing angle)=90-x.
So the missing angle has measurement (90-x).
So cos(90-x)=a/c
and sin(x)=a/c.
Since cos(90-x) and sin(x) have the same value of a/c, then one can conclude that cos(90-x)=sin(x).
We can do this also for cos(x) and sin(90-x).
cos(x)=b/c
sin(90-x)=b/c
This means sin(90-x)=cos(x).
So back to the problem:
cos(23)=sin(90-23)
cos(23)=sin(67)
So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).
HELP ME WITH THIS QUESTION ✔
THANKS YOU !!
[tex]\text{Hey there!}[/tex]
[tex]\huge\text{Decimals, fractions, \& negatives are below 0!}[/tex]
[tex]2\dfrac{21}{30}\ = 2\times30+21 \ = 2\times 30 = 60+21= 81\rightarrow \dfrac{81}{30}[/tex]
[tex]2\dfrac{1}{2}\ = 2\times2+1=2\times2=4+1=5\rightarrow\dfrac{5}{2}[/tex]
[tex]-\dfrac{32}{40}=-\dfrac{32}{40}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer:}-\dfrac{32}{40}, \ 2\dfrac{1}{2}, \ 2\dfrac{21}{30}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]