using the definition of multiplication between two fractions
[tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\cdot c}{b\cdot d}[/tex]we obtain,
[tex]\frac{5}{3}\times-\frac{3}{4}=-\frac{5\cdot3}{3\cdot4}=-\frac{5}{4}[/tex]Add 28, 362, and 104. Choose the appropriate number for each place value in the sum. Hundreds Tens Ones Intro
ANSWER
[tex]494[/tex]EXPLANATION
We want to add the three numbers:
[tex]28,362,104[/tex]To do this, add the numbers in corresponding place values i.e. units to units, tens to tens, and hundred to hundred:
[tex]\begin{gathered} 28 \\ +362 \\ +104 \\ =494 \end{gathered}[/tex]That is the answer.
use a unit rate to find the unknown value.2/4=?/16the unknown value is?
Let x be the unknown value.
Therefore we have
[tex]\frac{2}{4}=\frac{x}{16}[/tex]So we can inform from the first term that the denominator is double the numerator, since this term is equal to second term with the unknown x, same applies there also.
So,
[tex]\begin{gathered} 2x=16 \\ x=\frac{16}{2}=8 \end{gathered}[/tex]This can be further confirmed by applying cross multiplication,
[tex]\begin{gathered} \frac{2}{4}=\frac{x}{16} \\ 16\times2=4x \\ x=\frac{16\times2}{4}=8 \end{gathered}[/tex]5x + 3y = 9
can you put it the following equation in slope-intercept form?
[tex]\framebox{Slope intercept: -$\dfrac{5}{3}$x+3}[/tex]
The slope intercept form of [tex]5x+3y=9[/tex] would be written as:
[tex]-\frac{5}{3} x+3[/tex]
how far does a person travel in ft? this word problem is a little confusing but i understood everything else before this question.
Given:
The vertical height is 30ft.
The angle of elevation is 30 degrees.
To find:
The distance travelled by the person from bottom to top of the escalator.
Explanation:
Let x be the slant distance.
Since it is a right triangle.
Using the trigonometric ratio formula,
[tex]\begin{gathered} \sin\theta=\frac{Opp}{Hyp} \\ \sin30^{\circ}=\frac{30}{x} \\ \frac{1}{2}=\frac{30}{x} \\ x=30\times2 \\ x=60ft \end{gathered}[/tex]Therefore, the distance travelled by the person from the bottom to the top of the escalator is 60ft.
Final answer:
The distance travelled by the person from bottom to top of the escalator is 60ft.
What is the vertex of the absolute value function below?
Step-by-step explanation:
come on !
the vertex is typically a corner or a (general or local) extreme value or turning point of the curve.
so, what can that point be ?
there is only one candidate : (4, 1).
that means x = 4, y = 1.
that is the 4th answer option.
in the figure, pr and qs are diameters of circle u. find the measure of the indicated arc
Step 1: Problem
Step 2 : Concept
QR = 136
PQS = 42 + 136 + 42 = 220
PS = 64 + 72 = 136
Triangle ABC , m∠A = 75°, m∠B = 65°, a = 23.5ftFind the length of the shortest side.Round to one decimal.
Given in triangle ABC , m∠A = 75°, m∠B = 65°, a = 23.5ft.
We have to find the third angle,
[tex]m\angle C=180-75-65=40[/tex]The shortest angle is angle C. So, the shortest side will be opposite to angle C.
Use the sine rule, to find the third side as follows:
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin C}{c} \\ \Rightarrow\frac{\sin75}{23.5}=\frac{\sin 40}{c} \\ \Rightarrow\frac{0.966}{23.5}=\frac{0.643}{c} \\ \Rightarrow0.0411=\frac{0.643}{c} \\ \Rightarrow c=\frac{0.643}{0.0411} \\ \Rightarrow c=15.6 \end{gathered}[/tex]Thus. the length of the shortest side is 15.6 ft.
The equation and graph of a polynomial are shown below. The graph reachesits minimum when the value of xis 4. What is the y-value of this minimum?--y= 2x2-16x + 30ys
We can find the y-value of the minimum using the graph or using the equation. Let's use the equation and evaluate it when x = 4.
[tex]\begin{gathered} y=2x^2-16x+30=2(4)^2-16(4)+30 \\ y=2\cdot16-64+30=32-64+30=-2 \end{gathered}[/tex]Hence, the y-value of the minimum is -2.What is the x-value of the solution to the system of equations shown below? 2x + y = 20 6x - 5y = 12
Given the equation system:
[tex]\begin{gathered} 1)2x+y=20 \\ 2)6x-5y=12 \end{gathered}[/tex]To solve the system and determine the value of x, first step is to write one of the equations in terms of y:
[tex]\begin{gathered} 2x+y=20 \\ y=20-2x \end{gathered}[/tex]Then replace this expression in the second equation
[tex]\begin{gathered} 6x-5y=12 \\ 6x-5(20-2x)=12 \end{gathered}[/tex]Now that you have an expression with only one unknown, x, you can calculate its value.
Solve the parenthesis using the distributive property of multiplication
[tex]\begin{gathered} 6x-5\cdot20-5\cdot(-2x)=12 \\ 6x-100+10x=12 \\ 6x+10x-100=12 \\ 16x=12+100 \\ 16x=112 \\ \frac{16x}{16}=\frac{112}{16} \\ x=7 \end{gathered}[/tex]4. What is 10% of 25? Type your answer using numbers only. Your answer
10% = 10/100 = 0.10
therefore:
[tex]25\times0.10=2.5[/tex]answer: 2.5
Please see attachment for question. I have also uploaded a example for reference.
A=$88,000
P=$70,586
r=9.8% (0.098)
[tex]88,000=70,586e^{(0.098)t}[/tex]Divide both sides by 70,586:
[tex]\begin{gathered} \frac{88,000}{70,586}=\frac{70,586}{70,586}e^{(0.098)t} \\ \\ \frac{88,000}{70,586}=e^{(0.098)t} \end{gathered}[/tex]Find ln of both sides:
[tex]\begin{gathered} \ln (\frac{88,000}{70,586})=\ln (e^{(0.098)t}) \\ \\ \ln (\frac{88,000}{70,586})=0.098t \end{gathered}[/tex]Divide both sides by 0.098:
[tex]\begin{gathered} \frac{\ln (\frac{88,000}{70,586})}{0.098}=\frac{0.098}{0.098}t \\ \\ \frac{\ln(\frac{88,000}{70,586})}{0.098}=t \\ \\ \\ t=2.25 \end{gathered}[/tex]Then, t is 2.25 yearsEvaluate the expression for the given variable values. (p+g) P-29 if p = 4 and q = 8-13-122024
We have the expression:
[tex]\frac{(p+q)^2}{p-2q}[/tex]We have to evaluate it for p = 4 and q = 8.
To do that, we replace the variables p and q with the given values and calculate:
[tex]\begin{gathered} f(p,q)=_{}\frac{(p+q)^2}{p-2q} \\ f(4,8)=\frac{(4+8)^2}{4-2\cdot8} \\ f(4,8)=\frac{12^2}{4-16} \\ f(4,8)=\frac{144}{-12} \\ f(4,8)=-12 \end{gathered}[/tex]Answer: The value of the expression when p = 4 and q = 8 is -12 [Second option]
find its volume. Use 3.14 as the approximate value of a25 m
we know that
the solid of the figure is a sphere
the volume of the sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]we have
pi=3.14
r=25 m
substitute
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot25^3 \\ V=65,416.67\text{ m\textasciicircum{}3} \end{gathered}[/tex]the volume of the sphere is 65,416.67 cubic meters4.
8 ft
8 ff
P = (4 X 8)
P=__ ft
A = (8 X 8)
A =
sq. ft
After multiplying the value of P is 32 ft and the value of A is 64 sq. ft.
In the given question we have to find the value of P and A.
The given expression for P is
P = (4 X 8)
The given expression for A is
A = (8 X 8)
In the given P representing the perimeter of square because the formula of perimeter is
P = 4* side
A representing the area of square because the area of square is
A = side*side
So the value of P
P = (4 X 8)
P = 32 ft
The value of A
A = (8 X 8)
A = 64 sq. ft
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Given v=7i - 5j and w=-i+j,a. Find project wv .b. Decompose v into two vectors V, and v2, where vy is parallel to w and v2 is orthogonal to w.
For the given vector v=7i - 5j and w=-i+j,
projwv = 6i - 6j
v1 = 6i -6j
v2 = i +j
Vector:
A quantity that has both magnitude and direction are called vector. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude.
a) projwv is the projection of v onto w. Use the following equation:
projwv = [(v•w)/((magnitude(w))2)] w
v•w = (7*-1) + (-5*1) = -12
(magnitude w)^2 = ([tex]\sqrt{1^{2} + 1^{2}}[/tex])^2 = 2
projwv = ((-12)/2)(-i + j)
= 6i - 6j
b) The two components of the decomposed v will add to create the original vector v. v1 that is parallel to w will be the same as the projection of v onto w.
v = v1 + v2
v2 = v - v1 = (7i - 5j) - (6i -6j) = i +j
You can check that v2 is orthogonal by taking the dot product (v2•w). This equals 0.
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Find the volume.The measures are 4 yd, 3 yd, and 5 yd.
178.98 yd³
Explanation:The shape consists of a cone and a cylinder. So we would find the volume of each and sum them together.
Volume of a cone = 1/3 πr²h
r = radius = 3 yd
h = height = 4 yd
let π = 3.14
Volume of the cone = 1/3 × 3.14 × 3 × 3 × 4
Volume of the cone = 37.68 yd³
Volume of a cylinder = πr²h
r = radius = 3 yd
h = height = 5 yd
Volume of a cylinder = 3.14 × 3 × 3 × 5
Volume of a cylinder = 141.3 yd³
Volume of the shape = Volume of the cone + Volume of a cylinder
Volume of the shape = 37.68 + 141.3
Volume of the shape = 178.98 yd³
What is the ones place and the hundredths place for 48.26
The first number before the decimal point is the ones place.
48.26
ones = 8
The second number after the decimal point is the hundredths place:
48.26
hundredth: 6
Hello hope you are doing well. Can you help me with this please
To find Mario's current grade is to find the average of all his grades for the first quarter.
The average of his grade for the first quarter is the mean which is 70 percent.
Also, 70 percent is equivalent to a C minus
how do you find the sum of 3+15+75+.....+46875 using the Sn formula
3+15+75+.....+46875
a1 = first term = 3
If we multiply the first term by 5, we obtain the second term.
3 x 5 = 15
15x 5 = 75
75x 5= 375
375x5= 1875
1875x5=9375
9375x5= 46875 (7th term) n=7
So,
r= 5
Apply the formula:
an= a1 * r^(n-1)
an= 3 * 5 (n-1)
Sum
Sn = a1 (1 -r^n) / 1- r
S(7) = [3 (1 - 5^7)] / 1-5
S(7) = [3 (1-78,125)] /-4
S(7) = 58,893
A) This graph represents Function or non function?B) is it discrete or Continuous?Because of you count dots or measure lines?The domain is:The range is:
A) It's a function because each point of x has a point on y.
B. It's a discrete functions because you can't see a continuous line.
C. Domain (-3,6)
D. Range (0,3)
* C and D if each square is equivalent to 1 unit.
A person can join The Fitness Center for $50. A member can rent the tennis ball machine for $10 an hour. Write a linear function to model the relationship between the number of hours the machine is rented (x) and the total cost (y).
(a) write a equation for this problem
(b) what is the initial value
(c) Determine the cost for renting the tennis ball machine for 2 hours? for 5 hours? and 0 hours?
(d) How many hours did a member rent the tennis ball machine if the total cost was $130?
a) An equation for the given problem is;
b) The initial value for the given problem is;
c) The number of hours that a member rented the tennis ball machine if the total cost was $130 is; 4 hours
How to solve a Linear equation model?The general formula for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
a) Base price for joining the fitness center is $50 and as such this can be said to be the y-intercept. Then, the tennis ball machine is rented for $10 per hour.
Now, the number of hours the machine is rented (x) and the total cost (y), then the equation is;
y = 10x + 50
b) The initial value is the price when x = 0 which is the y-intercept and as such it is $50.
c) The cost for renting the tennis ball machine for 2 hours is;
y = 10(2) + 50
y = $70
The cost for renting the tennis ball machine for 5 hours is;
y = 10(5) + 50
y = $120
The cost for renting the tennis ball machine for 0 hours is;
y = 10(0) + 50
y = $50
d) If total cost is $130, then we have;
130 = 10x + 50
10x = 80
x = 80/10
x = 8 hours
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what are the bounds of integration for the first integral ?
We are going to use the properties of definite integrals. Note that if c belongs to the interval [a,b] and is integrable in [a,c] and [c,b], then f is integrable in [a,b]. Moreover,
[tex]\int_a^cf(x)dx+\int_c^bf(x)dx=\int_a^bf(x)dx[/tex]Applying this property to the presented case, we obtain that
[tex]\begin{gathered} \int_a^bf(x)dx=\int_{-5}^9f(x)dx+\int_9^{13}f(x)dx-\int_{-5}^2f(x)dx \\ \int_a^bf(x)dx=\int_{-5}^{13}f(x)dx-\int_{-5}^2f(x)dx \\ \int_a^bf(x)dx=\int_2^{13}f(x)dx \end{gathered}[/tex]Note: Another way to interpret the exercise is to interpret the integral as the area under the curve.
Thus, the answer to the exercise is a= 2 and b = 13.
The value of China's exports of automobiles and parts (in billions of dollars) is approximately f ( x ) = 1.8208 e .3387 x , where x = 0 corresponds to 1998. In what year did/will the exports reach $7.4 billion?
We have the following equation:
[tex]f(x)=108208e^{0.3387x}[/tex]where x denotes the number of years after 1998.
By substituting the given information, we have that
[tex]7.4=1.8208e^{0.3387x}[/tex]and we need to find x. Then, by dividing both sides by 1.8208, we get
[tex]e^{0.3387x=}4.0641475[/tex]then by taking natural logarithm to both sides, we obtain
[tex]0.3387x=ln(4.0641476)[/tex]which gives
[tex]0.3387x=1.4022040[/tex]then, the number of years after 1998 is:
[tex]\begin{gathered} x=\frac{1.4022040}{0.3387} \\ x=4.13996 \end{gathered}[/tex]which means 4 years after 1998. Then, by rounding to the nearest year, the answer is 2002.
- 10x + 100y = 30-3x + 30y = 9
The given system is
[tex]\mleft\{\begin{aligned}-10x+100y=30 \\ -3x+30y=9\end{aligned}\mright.[/tex]First, we multiply the first equation by -3/10.
[tex]\mleft\{\begin{aligned}3x-30y=-9 \\ -3x+30y=9\end{aligned}\mright.[/tex]Then, we sum the equations
[tex]\begin{gathered} 3x-3x+30y-30y=9-9 \\ 0x+0y=0 \\ 0=0 \end{gathered}[/tex]According to this result, we can deduct that the system doesn't have any solutions because the lines represented by the equations are parallel.A is the set of even numbers greater than or equal to 4 and less than or equal to 8B=1-29, -25,-24, -22, -21, 22, 27(a) Find the cardinalities of A and B.n(A)=3(b) Select true or false.12 € A22 € B67 A-24 € BTruen(B) = 1FalseX%S3
Set A is composed of all the even numbers equal or greater than 4 and equal or less than 8 so set A is:
[tex]A=\lbrace4,6,8\rbrace[/tex]The cardinalities of A and B are equal to their number of elements so we have n(A)=3 and n(B)=7.
With both sets explicitly written we can complete the true or false table. The only thing to take into account is that the symbol ∈ means "belongs to" and that ∉ means "does not belong to".
The first statement of the table is:
[tex]12\in A[/tex]This is false because 12 does not belong to set A since it is not included in it.
The second statement is:
[tex]22\in B[/tex]As you can see 22 is in deed one of the elements of set B which means that this statement is true.
The third one is:
[tex]6\notin A[/tex]This statement is false because as we saw before 6 is an element of set A.
The last statement is:
[tex]-24\in B[/tex]As you can see -24 is one of the elements of set B so this statement is true.
AnswersFalse
True
False
True
Find x1) -4x=362) x+6=133) -9x=36
1) -4x=36
2) x+6=13
3) -9x=36
SolutionNumber 1[tex]\begin{gathered} -4x=36 \\ divide\text{ both sides by -4} \\ -\frac{4x}{-4}=\frac{36}{-4} \\ \\ x=-9 \end{gathered}[/tex]Number 2[tex]\begin{gathered} x+6=13 \\ collect\text{ the like terms} \\ x=13-6 \\ x=7 \end{gathered}[/tex]Number 3[tex]\begin{gathered} -9x=36 \\ divide\text{ both sides by -9} \\ -\frac{9x}{-9}=\frac{36}{-9} \\ \\ x=-4 \end{gathered}[/tex]why is this problem incorrect or correct?
Well, I would like to know more about this problem.
If you are solving an equation it is wrong because you are adding 10 units only in one side of the equation, that is a mistake.
If this is not a process to solve the equation it is correct, it does not matter if you are only adding 10 in one side.
5. Given the degree and zeros of a polynomial function, find the standard form of the polynomial.
Degree: 5; zero: 1, i, 1+i
The expanded polynomial is:
x5 +
x4+
x3 +
x2 +
x +
The equation of the polynomial equation in standard form is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2
How to determine the polynomial expression in standard form?The given parameters are
Degree = 5
Zero = 1, i, 1 + i
There are complex numbers in the above zeros
This means that, the other zeros are
Zeros = 1 - i and -i
The equation of the polynomial is then calculated as
P(x) = Leading coefficient * (x - zero)^multiplicity
So, we have
P(x) = (x - 1) * (x - (1 + i)) * (x - (1 - i) * (x - (-i)) * (x - i)
This gives
P(x) = (x - 1) * (x - 1 - i) * (x - 1 + i) * (x² + 1)
Solving further, we have
P(x) = (x - 1) * (x² - x + ix - x + 1 - i - ix + i + 1) * (x² + 1)
P(x) = (x - 1) * (x² - 2x + 2) * (x² + 1)
Evaluate the products)
P(x) = (x³ - x² + x - 1) * (x² - 2x + 2)
This gives
P(x) = x⁵ - 2x⁴ + 2x³ - x⁴ + 2x³ - 2x² + x³ - 2x² + 2x - x² + 2x - 2
Express in standard form
P(x) = x⁵ - 2x⁴ - x⁴ + 2x³ + 2x³ + x³ - 2x² - 2x² - x² + 2x + 2x - 2
Evaluate the like terms
P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2
Hence, the equation is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2
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Neals family spends $7,104 annually for food. Approximately what percent of their $34,910 annual net income is this amount?
Total income= $34910
Amount spent on food = $7104
[tex]\begin{gathered} \text{ \% of income spent on food =}\frac{\text{ Amount spent on food}}{\text{ Total income }}\text{ x 100} \\ =\frac{7104}{33910}\text{ x 100} \\ =20.95\text{ \%} \end{gathered}[/tex]The sides of a rectangle are in a ratio of 5:7 and the perimeter is 72. Find the area of the rectangle.
Since the sides of the rectangle are in ratio 5: 7
Insert x in the 2 terms of the ratio and find its perimeter using them
[tex]\begin{gathered} L\colon W=5x\colon7x \\ P=2(L+W) \\ P=2(5x+7x) \\ P=2(12x) \\ P=24x \end{gathered}[/tex]Equate 24x by the given perimeter 72 to find the value of x
[tex]24x=72[/tex]Divide both sides by 24
[tex]\begin{gathered} \frac{24x}{24}=\frac{72}{24} \\ x=3 \end{gathered}[/tex]Then the sides of the rectangle are
[tex]\begin{gathered} L=5(3)=15 \\ W=7(3)=21 \end{gathered}[/tex]Since the rule of the area of the rectangle is A = L x W, then
[tex]\begin{gathered} A=15\times21 \\ A=315 \end{gathered}[/tex]The area of the rectangle is 315 square units