For this question we will use the two points formula for the equation of a line:
[tex]y-8_{}=\frac{-8-8}{4-7}(x-7)\text{.}[/tex]Solving for y we get:
[tex]\begin{gathered} y-8=\frac{-16}{-3}(x-7), \\ y-8=\frac{16}{3}x-\frac{112}{3}, \\ y=\frac{16}{3}x-\frac{112}{3}+8, \\ y=\frac{16}{3}x-\frac{88}{3}. \end{gathered}[/tex]Answer:
[tex]y=\frac{16}{3}x-\frac{88}{3}.[/tex]write each degree measure in radians round to the nearest hundred 76 degrees 124 degrees and 149 degrees
Conversion from Degrees to Radians
One radian is equivalent to 180°
To convert from degrees to radians, we just multiply by the factor:
[tex]\frac{\pi}{180}[/tex]a) Convert 76 degrees to radians
[tex]76\cdot\frac{\pi}{180}=1.33\text{ rad}[/tex]b) Convert 124 degrees to radians
[tex]124\cdot\frac{\pi}{180}=2.16\text{ rad}[/tex]c) Convert 149 degrees to radians
[tex]149\cdot\frac{\pi}{180}=2.60\text{ rad}[/tex]Give the domain of y = ln x.
Remember that
[tex]y=\ln x=\log _ex\Leftrightarrow e^y=x[/tex]And e^y can have any value in the interval (0, infinite).
Therefore, the domain of ln(x) is
[tex]\text{domain(}\ln (x))=(0,\infty)[/tex]The answer is x in (0, infinite)
The graph shown below displays thechange in the number of hurricanes thatoccurred over time.Which statement is the best description ofthe association between these variables?Choose 1 answer:A) As time went by, the number of hurricanestended to increase.B) As time went by, the number of hurricanestended to decrease.C) There is no clear relationship between timeand the number of hurricanes thatoccurred.
From the graph, it can be observed that number of hurricanes decreases as well as increases with increase in time (year since 1970). All points are distributed over the graph. So specific relation between number of hurricanes and time (year since 1970) can not be determined.
Thus option C is correct.
The coordinates of the terminal point of the vector <9,4> with its initialpoint is at (-3, 2) is (a, b). State the value of a + 2b. *
Answer:
[tex]a+2b=18[/tex]Step-by-step explanation:
The vector in component form is given as:
[tex][/tex]Therefore, if the vector <9,4> has initial point at (-3, 2), to find the terminal point:
[tex]\begin{gathered} 9=x_2-(-3) \\ 4=y_2-2 \end{gathered}[/tex]Solve for x2 and y2.
[tex]\begin{gathered} x_2=9-3=6 \\ y_2=4+2=6 \end{gathered}[/tex]Terminal point (a,b) would be (6,6), hence the value of a+2b:
[tex]\begin{gathered} a+2b=6+2(6) \\ a+2b=18 \end{gathered}[/tex]The winter clothing drive has received donations of 15 coats, 27 pairs of gloves, 38 scarves, and 20 hats so far. Based on this data, what is a reasonable estimate of the probability that the next donation is not a pair of gloves? A: .54 B: .73C: .27 D: .37
we must add all the garments that are not gloves and divide them by the total
we add 15 coats, 38 scarves and 20 hats
[tex]15+38+20=73[/tex]and divide by the total
[tex]15+38+20+27=100[/tex][tex]\frac{73}{100}=0.73[/tex]so, the right option is B
c12334un567co89f(x)52241788794g(x)657929 l'12.3Use the table to evaluate the expression,(gºf)(3) =help (numbers)
Question:
Solution:
By definition of composition of functions, we have that:
[tex](g\circ f)(x)=\text{ g(f(x))}[/tex]Now, according to the table, if we evaluate above in x=3, we get:
[tex](g\circ f)(3)=\text{ g(f(3)) = g(2)=5}[/tex]so that, we can conclude that the correct answer is:
[tex](g\circ f)(3)=\text{5}[/tex]18 ÷ (-9)F. 9G. 2H. -2I. -9
We solve as follows:
[tex]\frac{18}{-9}=-2[/tex]So, the solution is h. -2
Find the product of the complex numbers. Leave your answer in polar form
Given: Two complex numbers below
[tex]\begin{gathered} z_1=2+2i \\ z_2=-3+3i \end{gathered}[/tex]To Determine: The product of the given complex numbers
[tex]z_1z_2=(2+2i)(-3+3i)[/tex][tex]\begin{gathered} z_1z_2=2(-3+3i)+2i(-3+3i) \\ z_1z_2=-6+6i-6i+6i^2 \\ z_1z_2=-6+6i^2 \end{gathered}[/tex]Please note that
[tex]\begin{gathered} i=\sqrt[]{-1} \\ i^2=(\sqrt[]{-1})^2_{} \\ i^2=-1 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} z_1z_2=-6+6i \\ z_1z_2=-6+6(-1) \\ z_1z_2=-6-6 \\ z_1z_2=-12+0i \end{gathered}[/tex]Let us convert the product to polar form
Please note that
[tex]\begin{gathered} if,z=x+iy,the\text{ polar form is} \\ z=r(\cos \theta+i\sin \theta) \\ \text{where} \\ r=\sqrt[]{x^2+y^2} \\ \tan \theta=\frac{y}{x} \\ \theta=tan^{-1}(\frac{y}{x}) \end{gathered}[/tex]Apply the conversion into the product we got
[tex]\begin{gathered} z_1z_2=-12+0i,x=-12,y=0 \\ r=\sqrt[]{x^2+y^2}=\sqrt[]{(-12)^2+0^2} \\ r=\sqrt[]{144+0} \\ r=\sqrt[]{144} \\ r=12 \\ \theta=\tan ^{-1}(\frac{0}{-12}) \\ \theta=\tan ^{-1}(0) \\ \theta=\pi \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} z_1z_2=r(\cos \theta+i\sin \theta) \\ r=12,\theta=\pi \\ z_1z_2=12(\cos \pi+i\sin \pi) \end{gathered}[/tex]Hence, the product of the complex numbers in polar form is
12(cosπ+isinπ)
My question is #9 but I am confused if it is true or false
Given data:
The first condition is AB=XY.
The second condition is BC=YZ.
The third condition is ∠B=∠Y.
Follow the above condition then, triangle ABC is congruent to the triangle XYZ by SAS.
Thus, the first statement is true.
ill give 50 points and brailets if u ansewr fast and ergent
The linear equation that models the cost as a function of the number of hours is:
y = 40*x + 20
How to write the equation?We know that a repair that takes two hours costs $100 and a repair that takes 6 hours costs $260.
Let's assume this is a linear equation, then:
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
slope = (y2 - y1)/(x2 - x1)
Here we have the two points (2, 100) and (6, 260), then the slope is:
a = (260 - 100)/(6 - 2) = 160/4 = 40
So our line is something like:
y = 40*x +b
To find the value of b we use the fact that our line passes trhough (2, 100), then:
100 = 40*2 + b
100 - 80 = b
20 = b
Then the linear equation is:
y = 40*x + b
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To estimate the height of a building, two students find the angle of elevation from a point (at ground levedown the street from the building to the top of the building is 30°. From a point that is 400 feet closer tothe building, the angle of elevation (at ground level) to the top of the building is 52°. If we assume thatthe street is level, use this information to estimate the height of the building.The height of the building isfeet.
Given:
ground to building top is 30 degrees.
Distance = 400 feet
The angle of elevation at is top of the building = 52 degrees.
Find-: Height of the building.
Sol:
For the triangle ABC
Perpendicular = Height
Base = x
Angle = 52
Use trigonometric formula:
[tex]\begin{gathered} \tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}} \\ \\ \tan52=\frac{H}{x} \\ \\ 1.2799=\frac{H}{x} \\ \\ x=\frac{H}{1.2799} \end{gathered}[/tex]For the triangle ABD is:
Perpendicular = Height
Base = x+400
Angle = 32
[tex]\begin{gathered} \tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}} \\ \\ \tan32=\frac{H}{x+400} \\ \\ 0.6249=\frac{H}{x+400} \\ \\ \end{gathered}[/tex]Put the value of "x" is:
[tex]\begin{gathered} 0.6249(x+400)=H \\ \\ 0.6249x+249.947=H \\ \\ 0.6249(\frac{H}{1.2799})+249.947=H \\ \\ 0.488H+249.947=H \\ \\ 0.512H=249.947 \\ \\ H=488.407 \\ \end{gathered}[/tex]So the height of the building is: 488.407 feet
-Quadratic Equations-write a standard form Quadratic Equation with the given solution.
Answer:
x² + 49 = 0
Explanation:
An equation with the form (x - a)(x - b)= 0 has as a solutions x = a and x = b.
In this case, the solutions are x = 7i and x = -7i, so the equation will be:
(x - 7i)(x - (-7i)) = 0
(x - 7i)(x + 7i) = 0
Now, we need to apply the distributive property, so:
x(x) + x(7i) - 7i(x) - 7i(7i) = 0
x² + 7xi - 7xi - 49i² = 0
x² - 49i² = 0
Since, i² = -1, we get:
x² - 49(-1) = 0
x² + 49 = 0
Therefore, the quadratic equation in standard form is:
x² + 49 = 0
This is the standard form of the given quadratic equation is [tex]x^{2} +49=0[/tex]
Quadratic Equation-It is a type of equation in which the maximum power a variable can hold is 2 and the variable cannot be 0
The solution of the given equation are x=7i and x=-7i
we can write the equation as (x-7i)(x-(-7i))=0
as (An equation in the form of (x-a)(x-b)=0 is having x=a and x=b as their solution)
(x-7i)(x+7i)=0
According to the distributive property
(Distributive property-It states that A(B+C)=AB+AC)
x(x)+x(7i)-7i(x)-7i(7i)=0
[tex]x^{2}[/tex]+7xi-7xi-49[tex]i^{2}[/tex]=0
[tex]x^{2}[/tex]-49[tex]i^{2}[/tex] =0
since,([tex]i^{2}[/tex]=-1),we get:
[tex]x^{2}[/tex]+49=0
hence, the quadratic equation in standard form is
[tex]x^{2}[/tex]+49=0
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Identify the percent, amount, and base in this problem.
What percent of 80 is 40?
Step-by-step explanation:
well its going to be like this
80%/100 and 40/x
now to find the x you have to do cross products.
so 80% times 40
3200
the divide it by 100.
32
there you go
32 percent of 80 is 40
which of the following sets of numbers could represent the three sides of a triangle. 4,7,1212,16,284,12,137,13,22
ANSWER
4, 12, 13
EXPLANATION
The sum of any 2 sides of a triangle must be greater than the measure of the third side.
For these options we have to check which set of numbers follow this rule:
[tex]\begin{gathered} 4+7>12 \\ 11>12\text{ }\rightarrow\text{ false} \end{gathered}[/tex][tex]\begin{gathered} 12+16>28 \\ 28>28\text{ }\rightarrow\text{ false} \end{gathered}[/tex][tex]\begin{gathered} 4+12>13 \\ 16>13\text{ }\rightarrow\text{ true} \\ 12+13>4 \\ 25>4\text{ }\rightarrow\text{ true} \\ 4+13>12 \\ 17>12\text{ }\rightarrow\text{ true} \end{gathered}[/tex][tex]\begin{gathered} 7+13>22 \\ 20>22\rightarrow\text{ false} \end{gathered}[/tex]The third set of numbers could represent the three sides of a triangle
Which two parallelograms have the same area? Figure 1 Figure 2 18 cm 4 cm 13 cm 1 1 15 Figure 4 cm Figure 3 11 cm 5 cm 6 cm 1 112
Figure 1 Area = 4 x 15 = 60 cm²
Figure 2 Area = 3 x 18 = 54 cm²
Figure 3 Area = 6 x 11 = 66 cm²
Figure 4 Area = 12 x 5 = 60 cm²
Answer:
Therefore area of figure 1 and 4 are equal
The mid point between T(-2,6) and J (-5,1)
To find the midpoint between two points wee need to apply the following formula:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ y_m\text{ = }\frac{y_1+y_2}{2} \end{gathered}[/tex]Where (x1,y1) are the coordinates of the first point, (x2,y2) are the coordinates of the second point and (xm,ym) are the coordinates of the mid point. In this case the first point is T and the second point is J. If we apply the formula we should find the coordinates of the midpoint between them.
[tex]\begin{gathered} x_m\text{ = }\frac{-2-5}{2} \\ x_m\text{ = }\frac{-7}{2} \\ x_m\text{ = -3.5} \end{gathered}[/tex][tex]\begin{gathered} y_m\text{ = }\frac{6+1}{2} \\ y_m=\frac{7}{2} \\ y_m\text{ = 3.5} \end{gathered}[/tex]The coordinates of the midpoint are (-3.5, 3.5).
what is the domain of this exponential function? 1) { x | x > 0 }2) { x | x < 0 }3) { x | x ≤ 0 }4) { x | x ≥ 0 }5) all real numbers
Option 5 is the correct answerr.
That is, all real numbers
A zebra and a giraffe are having a race, 300 yards from a row of trees (the starting line) to the edge of a stream (the finish line). When they start evenly, the zebra wins the race by 50 yards.They decide to race again, but in the second race the zebra has to start 50 yards behind the row of trees (350 yards from the finish line), while the giraffe starts at the usual starting line. The zebra and the giraffe always run at the same speeds from race to race. Who wins the second race? Explain your reasoning.
A zebra and a giraffe are having a race, 300 yards from a row of trees (the starting line) to the edge of a stream (the finish line). When they start evenly, the zebra wins the race by 50 yards.
They decide to race again, but in the second race the zebra has to start 50 yards behind the row of trees (350 yards from the finish line), while the giraffe starts at the usual starting line. The zebra and the giraffe always run at the same speeds from race to race. Who wins the second race? Explain your reasoning.
we have that
The speed is equal to divide tthe distance by the time
speed=d/t
t=d/speed
The zebra and the giraffe always run at the same speeds from race to race.
so
Race 1
Zebra ------> t=300/speed1
giraffe ----> t=(300-50)/speed2 -----> t=250/speed2
where t is the finishing time of the zebra
equate both equations
300/speed1=250/speed2
300/250=speed1/speed2
1.2=speed1/speed2
speed1=1.2speed2
that means ----> the spped of the zebra is 1.2 times the speed of the giraffe
Race 2
Zebra ----> t1=350/(1.2speed2) ------> t1=292/speed2
Giraffe ----> t2=300/speed2 ------> t2=300/speed2
compare the times
t1 < t2
that means
the zebra wins the race 2Which number is the solution of n/3 = - 12
-36 is the solution to the given equation
Here, we want to find the value of n that solves the equation
We simply cross-multiply here
We have;
[tex]n\text{ = 3 }\times\text{ -12 = -36}[/tex]Answer:
Step-by-step explanation:
1. The answer is -36 because -36/3=12.
Find θ for the given trigonometric function. cos θ= 0.8317
Take the inverse cosine of both sides:
[tex]\begin{gathered} cos^{-1}(cos(\theta))=cos^{-1}(0.8317) \\ so: \\ \theta=33.726 \end{gathered}[/tex]Answer:
33.726
use synthetic division to find the awnser write the quotient and write any remainders in fraction form (3x^3-x^2-9x+5)÷(x-2)
The given expressions are
[tex]\begin{gathered} 3x^3-x^2-9x+5 \\ x-2 \end{gathered}[/tex]We have to use the coefficients only to divide. Remember that the number 2 must multiply all the numbers in the quotient. The synthetic division would be:
x3 x2 x
| 3 -1 -9 5
2 | 6 10 2
3 5 1 7
Notice that the remainder is 7, the quotient would be the coefficients under the line.
The quotient is[tex]3x^2+5x^{}+1[/tex]Notice that the quotient doesn't include the number 7 because that's the remainder.
The remainder is 7.We can express the quotient, the remainder, and the divisor as follows:[tex]\frac{3x^3-x^2-9x+5}{x-2}=3x^2+5x+1+\frac{7}{x-2}[/tex]You have 2 different savings accounts. For Account A, the simple interest earned after months is $. For Account B, the simple interest earned after months is $. If the interest rate is % for Account A and % for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
Question content area bottom
Part 1
Account A has a principal of $
enter your response here. (Round to the nearest dollar as needed.)
The principals of each account are given as follows:
Account A: $250.Account B: $400.The account that earned the most interest in the first month was Account A.
How to obtain the balance using simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.The interest accrued after t years is given as follows:
I(t) = Prt.
For Account A, the simple interest earned after 9 months is $6.94, considering a rate of 3.7%, hence the principal is obtained as follows:
6.94 = P x 0.037 x 9/12 (as the time is given in years)
0.02775P = 6.94
P = 6.94/0.02775
P = $250.
Then the interest during the first month was of:
I(1/12) = 250 x 0.037 x 1/12 = $0.77.
For the second account, considering the parameters, the principal is obtained as follows:
13.80 = P x 0.023 x 18/12
0.0345P = 13.80
P = 13.80/0.0345
P = $400.
Then the interest during the first month was of:
I(1/12) = 400 x 0.023 x 1/12 = $0.767. (which is less than account A).
Missing InformationThe problem is:
"You have 2 different savings accounts. For Account A, the simple interest earned after 9 months is $6.94. For Account B, the simple interest earned after 18 months is $13.80. If the interest rate is 3.7% for Account A and 2.3% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer."
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Determine the number of significant figures in the measurement 77.09 m.Express your answer numerically as an integer.
Given:
The significant figures in 77.09 m are 4 because all the digits are necessary to denote the quantity.
Hence, 4 is the number of significant figures expressed in integer.
5. The table shows the amount of money, A, in a savings account after mmonths. Select ALL the equations that represent the relationship betweenthe amount of money, A, and the number of months, m.*number ofmonthsdollaramount51,20061,30071,40081,500
The center of dilation, the original point, and its image do not line up on the same ray. ** is this true or false?
ANSWER
FALSE
EXPLANATION
A dilation is a transformation that changes the size of an object. It could be an enlargement or a reduction.
The center of dilation is the point where the dilation rays come from. They pass through the original point as shown in the diagram below:
As we can see, point O is the center of dilation, point B is an image of point A and the ray that connects them is OB.
So, the center of dilation, the original point and its image actually line up on the same ray.
The statement is FALSE
Divide.(4x^3 + 8x ^2 +7x+ 10) = (2x+1)Your answer should give the quotient and the remainder.Quotient:Remainder:
The Solution.
The given polynomial is
[tex]\frac{4x^3+8x^2+7x+10}{2x+1}[/tex][tex]\begin{gathered} \text{The Quotient: 2x}^2+3x+2 \\ \text{The Remainder: 8} \end{gathered}[/tex]Hence, the correct answer is
[tex]undefined[/tex]A store sells a $400 microscope after a markup of 32%. What is the price of the microscope at the store?
O $128
O $272
O $528
O $672
Using the markup, the price of the microscope at the store is 528 dollars.
What is markup?Markup shows how much more a company's selling price is than the amount the item costs the company.
In other words, markup is the amount by which the cost of a product is increased in order to derive the selling price.
Therefore, the store sells A store sells a $400 microscope after a markup of 32%. The price of the microscope at the store can be calculated as follows:
markup = 32% of 400
markup = 32 / 100 × 400
markup = 12800 / 100
markup = $128
Therefore,
price of the microscope = 400 + 128
price of the microscope = $528
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1=1
what is the answer
Answer: After about 30 seconds of consideration I am proud to say that the answer is probably 1
:)
Tano went to a professional basketball game He spent $54.85 for a ticket S4 99 for a hot dog and $2 15 for a soda What is the total amount that he spent? Use mental math to find the sum. A S60.99 O B 961.00 O C 561.99 OD 96200
The total amount is calculated as the sum of the cost of the ticket, the cost of the hot dog, and the cost of the soda.
So, the total amount is:
[tex]54.85+4.99+2.15=61.99[/tex]Answer: $ 61.99
To answer it using mental math, we can add 0.85 and 0.15 and get 1, add 54 and 2 and get 56 and approximate 4.99 to 5.
Then, the sum 1 + 56 + 5 is equal to 62.00 but we need to subtract 0.01 because of the approximation. Therefore the final result is:
62.00 - 0.01 = 61.99
Las 25 22. Lines a and bare parallel and cut by the transversalt. Label each of the 7 unknown angles with the correct angle measure. 20 t
Explanation:
Angle b and the one that's 70º are vertical angles, so they are congruent.
Angles b and g are corresponding angles. They are congruent.
Angles g and e are vertical angles. They are congruent.
Angles a and b are supplementary - their measures add up 180º:
[tex]\begin{gathered} m\angle a+m\angle b=180º \\ m\angle a=180º-70º \\ m\angle a=110º \end{gathered}[/tex]Angles a and d are corresponding angles. They are congruent.
Angles c and a are vertical angles. They are congruent.
Angles d and f are vertical angles. They are congruent.
Answers:
• m∠a = 110º
,• m∠b = 70º
,• m∠c = 110º
,• m∠d = 110º
,• m∠e = 70º
,• m∠f = 110º
,• m∠g = 70º