Looking at the triangle, the reference angle is 30 degrees. The hypotenuse of the triangle is c. The opposite side of the triangle is 7 and the adjacent side is a.
We would determine the hypotenuse, c by applying the sine trigonometric ratio which is expressed as
Sin# = opposite side/hypotenuse
Sin 30 = 7/c
cSin30 = 7
c = 7/Sin 30 = 7/0.5
c = 14
We would determine the adjacent side, a by applying the tangent trigonometric ratio which is expressed as
Tan# = opposite side/adjacent side
Tan 30 = 7/a
aTan30 = 7
a = 7/Tan 30 = 7/0.5774
c = 12.12
Help with this personal finance problem
Answer: Take home pay
75.49%
$1,283.39
Step-by-step explanation:
Gross pay
$1,700.00
ChevronIncome taxes
10.95%
$186.09
Federal Income Tax
12%
$123.27
Iowa State Tax
6.25%
$62.82
ChevronFICA taxes
7.16%
$121.72
Social Security
5.8%
$98.65
Medicare
1.36%
$23.07
ChevronPre-tax
6.4%
$108.80
Commuter Parking
6.4%
$108.80
Post-tax
0%
$0.00
Take home pay
75.49%
$1,283.39
What is the inverse of the following statement? "If a shape has four sides, then it is not a triangle." If a shape has four sides, then it is a triangle. If a shape is not a triangle, then it has four sides. If a shape does not have four sides, then it is a triangle. If a shape is a triangle, then it does not have four sides.
"If a figure has four corners, it is not triangular," as opposed to "If a figure doesn't have four corners, it is a triangle."
If p, then q must follow.
If q is correct, then p should be true as well.
If p is not present, then q is not present.
If it isn't q, it isn't p.
An examination of all available choices,
a. Because the condition is "triangle" and the conclusion is "it has three sides," it is true.
b. It is incorrect since the condition and conclusion are inverted.
c. It's incorrect since a triangle has three sides.
d. It is incorrect since it is not an if-then form of the statement.
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True or false: 8 is an integer
The answer is true
the number 8 is a whole number
so
is an integer
a number that can be written without a fractional component is an integer
A natural number is an integer greater than 0
Plot points between and beyond the x-intercepts and the vertical asymptote. Evaluate the function.
Let's determine the values of f(x) based on the given x-values using the following function:
[tex]\text{ f\lparen x\rparen = }\frac{\text{ x}^2\text{ + x - 42}}{\text{ x - 7}}[/tex]At x = -9,
[tex]\text{ f\lparen-9\rparen= }\frac{(-9)^2\text{ + \lparen-9\rparen- 42 }}{-9\text{ - 7}}\text{ = }\frac{81\text{ - 9 - 42}}{-9\text{ - 7}}\text{ = }\frac{30}{-16}\text{ = -}\frac{15}{8}\text{ \lparen Simplified\rparen}[/tex]At x = -8,
[tex]\text{ f\lparen-8\rparen = }\frac{(-8)^2\text{ + \lparen-8\rparen - 42}}{-8\text{ - 7}}\text{ = }\frac{64\text{ - 8 - 42}}{-8\text{ - 7}}\text{ = }\frac{14}{-15}\text{ = -}\frac{14}{15}[/tex]At x = -1,
[tex]\text{ f\lparen-1\rparen = }\frac{(-1)^2\text{ +}(-1)\text{ - 42}}{-1\text{ - 7}}\text{ = }\frac{1\text{ - 1 - 42}}{-1\text{ - 7}}\text{ = }\frac{-42}{-8}\text{ = }\frac{21}{4}\text{ \lparen Simplified\rparen}[/tex]At x = 15/2,
[tex]\text{ f\lparen}\frac{15}{2})\text{ = }\frac{(\frac{15}{2})^2\text{ + \lparen}\frac{15}{2})\text{ - 42}}{\frac{15}{2}\text{ - 7}}\text{ = }\frac{\frac{225}{4}+\frac{30}{4}\text{ - }\frac{168}{4}}{\frac{30}{4}\text{ - }\frac{28}{4}}\text{ = }\frac{225\text{ + 30 - 168}}{30\text{ - 28}}\text{ = }\frac{87}{2}[/tex]At x = 10,
[tex]\text{ f\lparen10\rparen = }\frac{(10)^2\text{ + \lparen10\rparen - 42}}{\text{ 10 - 7}}\text{ = }\frac{\text{ 100 + 10 - 42}}{10\text{ - 7}}\text{ = }\frac{68}{3}[/tex]In Summary,
At x = -9, f(-9) = -15/8
At x = -8, f(-8) = -14/15
At x = -1, f(-1) = 21/4
At x = 15/2, f(15/2) = 87/2
At x = 10, f(10) = 68/3
Question 2020 points) Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c(X) = 3x2 - 234x + 57, where x is the number of watches repaired. How many watches must he repair to have the lowest cost? A) 28 watches B) 57 watches C) 30 watches D) 39 watches
We need to now when c'(x) = 0, to find the minimum of the functions that is the lowest cost, so we have that the minimum of c(x) is
[tex]x\text{ = 39 }[/tex]So the answer is: D) 39.
identify the standard form of the complex number. 13(cos343°+i sin343°)
Answer:
12.43 - 3.8i
Explanation:
The standard form of a complex number is a + bi
In this case, the number is
13(cos(343) + isin(343))
Multiplying 13 by both expressions inside the parenthesis, we get
13cos(343) + i(13)(sin343)
13(0.95) + i(13)(-0.29)
12.43 + (-3.8)i
Therefore, the standard form of the number is
12.43 - 3.8i
This is for a test review I need help with. Which graph matches the quadratic equation
Okay, here we have this:
Considering the provided equation, we are going to identify which graph matches the quadratic equation, so we obtain the following:
To do this, then first we will identify which direction the parabola opens and what its center is, from there we will be able to identify the correct graph, then we have:
Then let us remember that the vertex of the parabola of the form y=ax^2+bx+c in its x coordinate is equal to -b/2a, applying:
[tex]x_v=-\frac{2}{2(-1)}=\frac{-2}{-2}=1[/tex]And replacing with this value in the function:
[tex]\begin{gathered} f(x)=-x^2+2x \\ f(1)=-1^2+2(1) \\ f(1)=-1+2 \\ f(1)=1 \end{gathered}[/tex]Finally we obtain that the vertex of the function is (1, 1).
According to the vertex finally found, we obtain that the correct option is option D, since it is the only graph that has the vertex of the function located at this point.
did I mess up on any of the steps?( I was trying to turn 8x-4y=20 into slope intercept form)
In the second step, 8x was subtracted from both sides of the equation. This should give us
- 4y = 20 - 8x
- 4y = - 8x + 20
Dividing both sides of the equation by - 4, it becomes
- 4y/- 4 = - 8x/- 4 + 20/- 4
y = 2x - 5
The step was actually wrong though the final answer was correct
By following your step, the final answer should be y = 2x + 5 and this is wrong
WILL GIVE BRAINLYEST AND 30 POINTS ANSWER ASAP
5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 are multiplied. How many significant digits should the product have?
5
3
2
1
5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 multiply all the terms. There will be 9 significant digits in the final result.
Given that,
5.2187 x 10^−3, 2.05 x 10^7, and 3.40 x 10^3 multiply all the terms.
We have to find how many digits should be significant for the product.
Multiplication is the action of adding a number to itself for the specified number of times. For instance, 3 × 4 denotes the addition of 3 to itself 4 times, and the opposite is true for the other number.
The multiplication of the given numbers is
=5.1287 × 10⁻³ × 2.05 × 10⁷ × 3.40 × 10³
=5.1287 × 2.05 × 3.40 × 10⁽⁻³⁺⁷⁺³⁾
= 35.747039 × 10⁽⁻³⁺⁷⁺³⁾
= 35.747039 × 10⁷
= 3.5747 × 10⁸
Given that the digit "3" comes before the decimal and the number "10" has a power of 8. As a result, there are 9 significant digits in total (8 + 1).
Therefore, There will be 9 significant digits in the final result.
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Write 0.0000215 in scientific notation.
Given:
The number is:
[tex]=0.0000215[/tex]Find-:
The scientific notation
Explanation-:
The scientific notation is:
[tex]\begin{gathered} =0.0000215 \\ \\ =\frac{0.0000215}{10000000} \end{gathered}[/tex]So, the scientific notation is:
[tex]\begin{gathered} =\frac{0.0000215}{10000000} \\ \\ =215\times10^{-7} \end{gathered}[/tex]somone answer pleaseeeeeee
Answer:
C.) 2^10
Step-by-step explanation:
You would add the exponents which in this case are 3 and 7 getting 10 as your exponent.
Answer: C)
Step-by-step explanation: If you do 2^3 x 2^7 = 1024 also 2^10 = 1024
What line gets the proportionality between y and x of 4/3
Line B has the proportionality of 4/3.
What is meant by the term proportionality?In algebra, the equality of two ratios. In the term “ a/b = c/d, a and b are proportional to c and d. A proportion has been typically used to solve a problem with one of its four unknown quantities. It is solved by multiplying each numerator even by opposite denominator and trying to equate the product to the numerator and denominator of the other denominators and numerators. Proportionality refers to any relationship that always has the same ratio. TFor the given question;
The proportionality for the following lines are-
Line A = change in y/change in x = 4/1Line B = change in y/change in x = 4/3Line C = change in y/change in x = 1/2Thus, line B has the proportionality of 4/3.
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The perimeter of a square I must be greater than 102 inches but less than 138 inches find the range of the possible side lengths that satisfy these conditions hit the perimeter of the square is given by P equals 4S or S represent the length of the side explain your answer in interval notation used decimal forms for numerical value
The Solution:
Given:
[tex]\begin{gathered} 102We are required to find the range of a side (s).
[tex]102<4s\text{ or }4s<138[/tex]So,
[tex]\begin{gathered} 102<4s \\ \\ 4s>102 \\ \\ s>\frac{102}{4} \\ \\ s>\frac{51}{2} \\ \\ s>25.5 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} 4s<138 \\ \\ s<\frac{138}{4} \\ \\ s<\frac{69}{2} \\ \\ s<34.5 \end{gathered}[/tex]Therefore, the correct answer is (25.5, 34.5)
which graph represents the solution to the system of linear inequalities x>3 and y < or equal to 2
EXPLANATION
The system that represents the solutions to x>3 and y≤ 2 is the OPTION A
What is the area of a rectangular floor that is 7 feet - 3 inches long and 4 feet - 2 inches wide
SOLUTION
The area of the rectangular floor is obtained by the formula
[tex]\text{Area}=\text{Length x width}[/tex]From the question we have
[tex]\begin{gathered} \text{lenght}=7\text{feet}-3\text{inches } \\ \text{width}=4\text{feet - 2inches } \end{gathered}[/tex]Convert the value to the same dimentions in inches
[tex]\begin{gathered} 1\text{ foot =12 inces } \\ \text{the } \\ 7\text{ f}eet=12\times7=84inches\text{ } \\ \text{The 7 f}eet-3inches=84+3=87inches\text{ } \end{gathered}[/tex]Similarly, for the other dimenstion, we have
[tex]\begin{gathered} 4\text{feet}=12\times4=48\text{inches } \\ \text{Then} \\ 4\text{ fe}et-2inches=48inches+2inches=50inches\text{ } \end{gathered}[/tex]The substitute into the formula for area, we have
[tex]\text{Area}=50\times87=4350inches^2[/tex]Hence
The Area of the rectangular floor is 4350in²
out of 100 students, 27 are taking calculus, 26 are taking French, and 13 are taking both calculus and French. If a student is picked at random, what is the probability that the student is taking calculus or French? write your answer in fraction form
Determine the probability for taking calculus.
[tex]P(C)=\frac{27}{100}[/tex]Determine the probability for taking French.
[tex]P(F)=\frac{26}{100}[/tex]Determine the probability for taking calculus and French.
[tex]P(F\text{ and C)=}\frac{13}{100}[/tex]Determine the probability for taking Calculus or French.
[tex]\begin{gathered} P(C\text{ or F)=P(C)+P(F)-P(C and F)} \\ =\frac{27}{100}+\frac{26}{100}-\frac{13}{100} \\ =\frac{27+26-13}{100} \\ =\frac{40}{100} \\ =\frac{2}{5} \end{gathered}[/tex]So answer is 2/5.
How much fencing is needed to enclose a circular pond with a diameter of 8.5 feet
Answer:
C = 8.5π or 26.7035
Step-by-step explanation:
Perimeter/circumference = 2πr, where r=radius
Diameter=2r
8.5/2 = 4.25
4.25 = r
C = 2π(4.25)
C = 8.5π or 26.7035
find the slope and the y intercept y=5x-3what is the slope what is the y intercept
The y-intercept is the point where the graph of the equation crosses the y-axis. This happens when x = 0. If we replace x = 0 into the equation we get the y-intercept:
[tex]\begin{gathered} y=5x-3 \\ x=0 \\ y=-3 \end{gathered}[/tex]The y-intercept is -3
Then, this equation is written in the slope-intercept form. The general form is:
[tex]y=ax+b[/tex]Where b is the y-intercept and a is the slope. If we look at the equation and compare it to the general form we can see that a = 5 and b = -3 (b is the same value we obtained before for the y-intercept)
So, the slope is 5.
The slope is the variation of y respect of x
It is a branch of mathematics concerned with analyzing the chance that particular event will occur. .
Given:
It is a branch of mathematics concerned with analyzing the chance that particular event will occu
Required:
Which branch
Explanation:
probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.
You do this you are a pro
Answer:
$40
That was easy!!
Also marks me as a brainliest
F(-6)=-8f(-3)=-6Find the linear function
We have the coordinates of two points on the line, those are (-6,-8) and (-3,-6).
Using these two points we can find the slope of the line using the following equation:
[tex]m=\frac{-8-(-6)}{-6-(-3)}=\frac{-2}{-3}=\frac{2}{3}[/tex]Use one of these points and the slope in the point slope formula to find the linear function:
[tex]\begin{gathered} y-(-6)=\frac{2}{3}(x-(-3)) \\ y+6=\frac{2}{3}(x+3) \\ y+6=\frac{2}{3}x+2 \\ y=\frac{2}{3}x+2-6 \\ y=\frac{2}{3}x-4 \end{gathered}[/tex]It means that the linear function is:
[tex]f(x)=\frac{2}{3}x-4[/tex]please help me with this, I need the answer by tomorrow.
Step-by-step explanation:
First thing first we will use the alternate exterior angles theorem,
Since 67 and 23x-2 are alternate exterior angles, they are equal
[tex]67 = 23x - 2[/tex]
[tex]69 = 23x[/tex]
[tex]x = 3[/tex]
Answer:
x=3
Step-by-step explanation:
since 67 and 23x-2 are congruent angles, you can set them equal to each other and solve ~OR~ since 5x+98 and 23x-2 are supplementary angles you can add them and have that equal to 180.
First Option:
67 = 23x-2
-2 -2
65=23x
/23 /23
3=x
Second Option:
5x+98 + 23x-2 = 180
combine like terms
28x+96=180
-96 -96
28x=84
/28 /28
x=3
1Solve for Q: C = (3P+Q/7) - 2H help!
Answer:
Q=7(C+2H-3P)
Explanation:
Given the equation:
[tex]C=(3P+\frac{Q}{7})-2H[/tex]First, add 2H to both sides:
[tex]\begin{gathered} C+2H=(3P+\frac{Q}{7})-2H+2H \\ C+2H=3P+\frac{Q}{7} \end{gathered}[/tex]Subtract 3P from both sides:
[tex]\begin{gathered} C+2H-3P=3P-3P+\frac{Q}{7} \\ \implies\frac{Q}{7}=C+2H-3P \end{gathered}[/tex]Multiply both sides by 7:
[tex]\begin{gathered} \frac{Q}{7}\times7=7(C+2H-3P) \\ \implies Q=7(C+2H-3P) \end{gathered}[/tex]The equation solved for Q gives:
[tex]Q=7(C+2H-3P)[/tex]A triangular prism has the dimensions shown at theright. What is the volume of the prism? Round to thenearest tenth if necessary.
ok
1.- Calculate the area of the base
Area = 3 x 6/2
= 18/2
= 9 mm^2
2.- Calculate the volume
Volume = area of the base x height
Volume = 9 x 5.22
= 46.98 mm^3
Rounding to the nearest tenth
Volume = 47 mm^3
in your own words, explain how you know that equations 2x + 2 = 8 and 2x = 6 are the same and have the same solution
You have the following equations:
2x + 2 = 8
2x = 6
The previous equations are the same equation because you can subtract 2 both sides of the first equation, and in such a way you obtain the second equation. In fat, you have:
2x + 2 = 8 subtract 2 both sides
2x = 8 - 2
2x = 6
which is exactly the same second equation. This situation is enough to prove that both equations are equal and then have the same siolutions.
Les is shown for tix) and gix:Xf(x)хg(x)000-2111-1241"39بهاباد541613525529Which statement compares the graphs of f(x) and g(x) over the interval [0, 5]?89(A)The graph of f(x) always exceeds the graph of glx).10(B)The graph of g(x) always exceeds the graph of f(x).11(C)The graph of g(x) exceeds the graph of f(x) on the interval between x = 0 and x = 4, the graphsintersect at a point somewhere between x = 4 and x = 5, and then the graph of f(x) exceeds thegraph g(x).12 C13 a(D)14The graph of f(x) exceeds the graph of g(x) on the interval between x = 0 and x = 4, the graphsintersect at a point somewhere between x = 4 and x = 5, and then the graph of g(x) exceedsthe graph f(x).15 O314p
Answer:
The graph of f(x) exceeds the graph of g(x) on the interval between x=0 and x=4, the graphs intersect at a point somewhere between x=4 and x=5, and then the graph of g(x) exceeds the graph of f(x).
Explanation:
Given the function f(x) and g(x).
The two functions are plotted in the graph below.
f(x) with points from A to F and G(x) with points from G to H.
From the attached graph, the line of f(x) is above (exceeds) the line of g(x) in the interval between x= 1 to 4, the graph then intersects at a point between x=4 and 5, then g(x) exceed f(x).
Write a two-column proof
I just need the answer for question 7
The statements and reasons used in the two column method to prove the given statements are as follows;
6. ∠1 is equal to ∠3 by the substitution property and therefore;
∠1 ≅ ∠2 by the definition of congruent angles
7. ∠2 = ∠4 by subtraction and substitution properties of equality, therefore; ∠2 ≅ ∠4 by the definition of congruency
8. ∠5 = ∠8 by substitution, therefore ∠5 ≅ ∠8 by definition
What is the two column method in mathematics?The two column method makes use of two columns in which logical arguments and reasons are provided to support the statements that is required to be proven.
6. The two column method used to prove the statements are as follows;
Statement [tex]{}[/tex] Reason
∠2 ≅ ∠4 [tex]{}[/tex] Given
∠2 = ∠4 [tex]{}[/tex] Definition of congruency
∠1 ≅ ∠3 [tex]{}[/tex] Given
∠1 = ∠3 [tex]{}[/tex] Definition of congruency
∠1 + ∠2 = 90° [tex]{}[/tex] Angle addition property
∠3 + ∠4 = 90° [tex]{}[/tex] Angle addition property
∠1 + ∠2 = ∠3 + ∠4 [tex]{}[/tex] Substitution property of equality
∠1 + ∠2 = ∠3 + ∠2 [tex]{}[/tex] Substitution property of equality
∠1 = ∠3 [tex]{}[/tex] Subtraction property of equality
∠1 ≅ ∠3 [tex]{}[/tex] By definition of congruency
7. Statements [tex]{}[/tex] Reasons
∠1 ≅ ∠3 [tex]{}[/tex] Given
∠1 = ∠3 [tex]{}[/tex] Definition of congruency
∠1 and ∠3 are corresponding ∠s[tex]{}[/tex] Definition of corresponding angles
∠3 and ∠4 are linear pair ∠s [tex]{}[/tex] Definition of linear pair angles
∠1 and ∠2 are linear pair ∠s [tex]{}[/tex] Definition of linear pair angles
∠3 + ∠4 = 180° [tex]{}[/tex] Linear pair angles are supplementary
∠1 + ∠2 = 180° [tex]{}[/tex] Linear pair angles are supplementary
∠1 + ∠2 = ∠3 + ∠4 [tex]{}[/tex] Substitution property
∠3 + ∠2 = ∠3 + ∠4 [tex]{}[/tex] Substitution property
∠2 = ∠4 [tex]{}[/tex] Subtraction property of equality
∠2 ≅ ∠4 [tex]{}[/tex] Definition of congruency
Statement [tex]{}[/tex] Reason
∠5 ≅ ∠7 [tex]{}[/tex] Given
∠5 = ∠7 [tex]{}[/tex] Definition of congruency
∠5 ≅ ∠8 [tex]{}[/tex] Given
∠5 = ∠8 [tex]{}[/tex] Definition of congruency
∠7 ≅ ∠8 [tex]{}[/tex] Vertical angles theorem
∠7 = ∠8 [tex]{}[/tex] Definition of congruency
∠5 = ∠8 [tex]{}[/tex] Substitution property of equality
∠5 ≅ ∠8 [tex]{}[/tex] Definition of congruency
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PLEASE HURRY WILL MARK BRAINLIEST
which of the following represents a linear equation in slope intercept form of the line that passes through (4,-3) and (2,3)
Answer:
[tex]y = - 3x + 9[/tex]
Step-by-step explanation:
[tex]m = \frac{3 - ( - 3)}{2 - 4} = \frac{6}{ - 2} = - 3[/tex]
[tex]3 = - 3(2) + b[/tex]
[tex]3 = - 6 + b[/tex]
[tex]b = 9[/tex]
[tex]y = - 3x + 9[/tex]
What will be the new position of the given point (3, –5) after reflection across the y-axis?
Candy needs to know how much fertilizer to buy her garden at home. To help Candy find out how much fertilizer she needs for her garden, use the scale drawing below to determine the area of actual garden.
The relation between the draw and the real garden is 1 in to 4 ft so we can find the new sides with a rule of 3, so the long side will be:
[tex]x_1=\frac{7\cdot4}{1}=28[/tex]and the short side:
[tex]x_2=\frac{3.4\cdot4}{1}=13.6[/tex]So the real area will be:
[tex]\begin{gathered} A=28\cdot13.6 \\ A=380.8ft^2 \end{gathered}[/tex]