We have the following:
[tex]\begin{gathered} y=7x+3 \\ y=6x+4 \end{gathered}[/tex]solving using substitution:
[tex]\begin{gathered} 7x+3=6x+4 \\ 7x-6x=4-3 \\ x=1 \end{gathered}[/tex]for y:
[tex]y=7\cdot1+3=7+3=10[/tex]The answer is (1, 10)
Let's test out the prediction! On the coordinate plane below, plot the points from your table in Slide 4 and sketch the graph.Table from slide 4: Bounce Height after Bounce 1. 92. 8.13. 7.294. 6.561
Answer
Check Explanation
Explanation
To do this, we will let the bounce be represented on the x-axis as x and the height after bounce plotted on the y-axis as y
So, the table looks like
x | y
1 | 9
2 | 8.1
3 | 7.29
4 | 6.561
So, we plot these points on a graph and sketch a line of best fit to pass through them
Hope this Helps!!!
solve the equation for all values of x by completing the square. x²+8x=-15
since (8/2)^2=16, we will add 16 in both sides of the equation, obtaining
[tex]x^2+8x+16=1[/tex]now, we factor the left side of the equation (it's a perfect square)
[tex](x+4)^2=1[/tex]then we have two options or x+4=1 or x+4=-1
solving both of the we have that the values for x are x=-3 and x=-5With the exception of column one, all amounts are in dollars. Calculate the annual interest rate on this loan. Give your answer to the nearest hundredth percent. Do not include the % sign in your response.
Given:
Amortization table is given
Let r be the annual rate of interest.
[tex]\frac{r}{12}\text{ be the monthly rate of interest.}[/tex]Second payment:
P= $259873.20 ; interest = $539.24
[tex]\text{Interest for the 2nd payment = }P(\frac{r}{12}\times\frac{1}{100})[/tex][tex]539.24=259873.20(\frac{r}{1200})[/tex][tex]\frac{539.24}{259873.20}\times1200=r[/tex][tex]r=\frac{647088}{259873.20}[/tex][tex]r=2.49[/tex]Therefore, the annula rate of interest is 2.49%
trig The last sub-problem of this section stumped me pls help
For this problem, we are given a triangle and we need to determine its height.
The distance of the UFO from point A is equal to the side c of the triangle, this side forms a right triangle with the height, where the height is the opposite cathetus from angle alpha and side c is the hypothenuse. We can use the sine relationship to determine the height, as shown below:
[tex]\begin{gathered} \sin(87.4)=\frac{h}{425.58}\\ \\ h=425.58\cdot\sin(87.4)\\ \\ h=425.58\cdot0.9989706=425.14 \end{gathered}[/tex]The height is approximately 425.14 km.
Use the table. What percentage of the people surveyed were teachers who wanted a later start time?
The Solution.
The percentage of the people survey that were teachers that voted yes to start later is
[tex]\text{ }\frac{\text{ number of teachers that voted YES}}{\text{ Total number of people surveyed}}\times100[/tex]Which is
[tex]\frac{20}{75}\times100=0.266667\times100=26.6667\approx26.67\text{ \%}[/tex]b. The percentage of the people surveyed that were teachers is
[tex]\frac{\text{ number of teachers surveyed}}{\text{ Total number of people surveyed}}\times100[/tex]Which is
[tex]\frac{30}{75}\times100=0.4\times100=40\text{ \%}[/tex]Hence, the correct answer are:
a. 26.67% b. 40%
Find the slope of the secant line for the g(x) = -20 SQRT x between x = 2 and x = 3
Given:
Equation of line is,
[tex]g(x)=-20\sqrt[]{x}[/tex]The slope of the secant line between x =a and x= b is calculated as,
[tex]\begin{gathered} m=\frac{f(b)-f(a)}{b-a} \\ m=\frac{f(3)-f(2)}{3-2} \\ m=\frac{-20\sqrt[]{3}-(-20\sqrt[]{2})}{1} \\ m=-20\sqrt[]{3}+20\sqrt[]{2} \\ m=20(\sqrt[]{2}-\sqrt[]{3}) \\ m=-6.36 \end{gathered}[/tex]Answer: slope of the secant line is m = -6.36
in the equation 4x^3=56, what is the value of x
The given equation is
[tex]4x^3=56_{}[/tex]First, we divide the equation by 4.
[tex]\begin{gathered} \frac{4x^3}{4}=\frac{56}{4} \\ x^3=14 \end{gathered}[/tex]At last, we take the cubic root on each side.
[tex]\begin{gathered} \sqrt[3]{x^3}=\sqrt[3]{14} \\ x\approx2.41 \end{gathered}[/tex]Therefore, the value of x is 2.41, approximately.24 cm 12 cm find the volume of the figure and leave pi in the answer
Explanation:
The volume of a cone is one third the area of the base times the height of the cone:
[tex]V=\frac{1}{3}\pi r^2h[/tex]r is the radius of the base and h is the height.
In this problem, the radius is 12cm and the height is 24cm. The volume is:
[tex]V=\frac{1}{3}\pi\cdot12^2\cdot24=\pi\cdot\frac{144\cdot24}{3}=\pi\cdot\frac{3456}{3}=\pi\cdot1152[/tex]Answer:
The volume is V = 1152 π
Two markers A and B on the same side of a canyon rim are 56 feet apart. A third marker C, located across the rim. is positioned so that BAC = 69º and ABC = 51° Complete parts (a) and (b) below (a) Find the distance between C and A.
To answer this question, it will be helpful to have a drawing of the situation to find the asked distance:
With this information, it will be easier to have all the information to solve for the distance CA.
Therefore, to find the distance CA, we can apply the Law of Sines, in which we have to find the angle C. We know that the sum of the interior angles of a triangle is equal to 180. Then, we have:
[tex]mNow, we can apply the Law of Sines to find the distance CA:[tex]\frac{AC}{\sin(51)}=\frac{56}{\sin(60)}\Rightarrow AC=\frac{56\cdot\sin (51)}{\sin (60)}[/tex]Then, we have:
[tex]AC=50.2527681652ft[/tex]Then, to round to one decimal place, we have that AC is approximately 50.3 ft.
To find the distance between the two rims, we have:
Now, we can also apply the Law of Sines to find the distance CD (the distance between the two rims):
[tex]\frac{CD}{\sin(69)}=\frac{CA}{\sin(90)}\Rightarrow CD=CA\cdot\sin (69),\sin (90)=1[/tex]Then, we have:
[tex]CD=50.2527681652\cdot\sin (69)\Rightarrow CD=46.9150007363ft[/tex]Therefore, the distance between the two canyon rims (round to one decimal place) is 46.9 ft.
If we take 50.3 ft (for CA), instead, we have 47 ft.
Solve for the remaining angles and side of the two triangles that can be created. Round to the nearest hundredth:B = 30 .b = 6,a = 7AnswerHow to enter your answer (opens in new window) 2 PointsTriangle 1: (where angle A is acute):Triangle 2: (where angle A is obtuse):AA:C =C:C:
ANSWER:
Triangle 1:
A = 35.69°
C = 114.31°
c = 10.94
Triangle 2:
A = 144.31°
C = 5.69°
c = 1.19
STEP-BY-STEP EXPLANATION:
Given:
B = 30°, b = 6, a = 7
We calculate the angle A by means of the law of sines:
[tex]\begin{gathered} \frac{a}{\sin A}=\frac{b}{\sin B} \\ \\ \text{ We replacing} \\ \\ \frac{7}{\sin A}=\frac{6}{\sin30} \\ \\ \sin A=\frac{7}{6}\cdot\sin30 \\ \\ \sin A=\frac{7}{12} \\ \\ A=\sin^{-1}\left(\frac{7}{12}\right)\: \\ \\ A_{acute}=35.69\degree \\ \\ A_{obtuse}=144.31\degree \end{gathered}[/tex]We calculate the value of angle C, knowing that the sum of all internal angles is equal to 180°
[tex]\begin{gathered} \text{ Acute} \\ \\ 180=35.69+30+C \\ \\ C=180-30-35.69=114.31\degree \\ \\ \text{ Obtuse} \\ \\ 180=144.31+30+C \\ \\ C=180-30-144.31=5.69\degree \end{gathered}[/tex]Side c is also calculated with the law of sines, like this:
[tex]\begin{gathered} \text{ Acute} \\ \\ \frac{b}{\sin B}=\frac{c}{\sin C} \\ \\ \frac{6}{\sin(30)}=\frac{c}{\sin114.31} \\ \\ c=\frac{6}{\sin(30)}\cdot\sin114.31 \\ \\ c=\:10.94 \\ \\ \text{ Obtuse} \\ \\ \frac{7}{\sin(A)}=\frac{c}{\sin(C)} \\ \\ c=\frac{6}{\sin(30)}\sin(5.69) \\ \\ c=1.19 \end{gathered}[/tex]Therefore;
Triangle 1:
A = 35.69°
C = 114.31°
c = 10.94
Triangle 2:
A = 144.31°
C = 5.69°
c = 1.19
An office uses paper drinking cups in the shape of a cone, with dimensions as shown.-23 in.4 in.To the nearest tenth of a cubic inch, what is the volume of each drinking cup?A. 2.5B. 7.9C. 23.7D. 31.7
According to the formula for volume of a cone and rounding to the nearest tenth of cubic inch, we find out that the volume of each drinking cup is 7.9 cubic inch. Thus, option B is correct.
From the given figure, we have
Diameter of the cone-shaped cups, d = [tex]2\frac{3}{4}[/tex] in = 2.75 in
Height of the cone-shaped cups, h = 4 in
We have to find out the volume of each drinking cup.
Since, d = 2.75 in (Given), we can say that
The radius of the cone-shaped cups, r = [tex]\frac{1}{2}*2.75[/tex]
=> r = 1.375 in
We know that the volume of a cone can be represented as -
[tex]V = \frac{1}{3} \pi r^{2}h[/tex]
Putting the value of radius, r and height, h in the above equation of volume of the cone, we get
Volume, [tex]V = \frac{1}{3} \pi r^{2}h[/tex]
=> [tex]V = \frac{1}{3}\pi (1.375)^{2}*4\\= > V = 7.919 in^{3}[/tex]
Thus, using the formula for volume of a cone and rounding to the nearest tenth of cubic inch, we find out that the volume of each drinking cup is 7.9 cubic inch. Thus, option B is correct.
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Answer:According to the formula for volume of a cone and rounding to the nearest tenth of cubic inch, we find out that the volume of each drinking cup is 7.9 cubic inch. Thus, option B is correct.
Step-by-step explanation:
limit using L'Hopital's rule . I just want to make sure if my answer is correct or not?
In order to use L'Hopital's rule, it is necessary to rewrite the limit as the quotient of two functions. Notice that:
[tex]\begin{gathered} 6x^{\sin (4x)}=e^{\ln (6x^{\sin (ex)})^{}} \\ =e^{\sin (4x)\cdot\ln (6x)} \end{gathered}[/tex]Since the exponential function is a continuous function, then:
[tex]\lim _{\text{x}\rightarrow0}e^{\sin (4x)\cdot\ln (6x)}=e^{\lim _{x\rightarrow0}\sin (4x)\cdot\ln (6x)}[/tex]Find the following limit using L'Hopital's rule:
[tex]\lim _{x\rightarrow0}\sin (4x)\cdot\ln (6x)[/tex]Write the function as a fraction:
[tex]\lim _{x\rightarrow0}\frac{\ln (6x)}{(\frac{1}{\sin (4x)})}[/tex]Use L'Hopital's rule to rewrite the limit as the limit of the quotient of the derivatives:
[tex]\begin{gathered} \lim _{x\rightarrow0}\frac{(\frac{1}{x})}{(-\frac{4\cos(4x)}{\sin^2(4x)})}=\lim _{x\rightarrow0}-\frac{\sin ^2(4x)}{4x\cdot\cos (4x)} \\ =\lim _{x\rightarrow0}\sin (4x)\cdot\frac{\sin(4x)}{4x}\cdot\frac{-1}{\cos (4x)} \\ =\lim _{x\rightarrow0}\sin (4x)\cdot\lim _{x\rightarrow0}\frac{\sin(4x)}{4x}\cdot\lim _{x\rightarrow0}\frac{-1}{\cos (4x)} \\ =0\cdot1\cdot-1 \\ =0 \end{gathered}[/tex]Therefore:
[tex]\lim _{x\rightarrow0}6x^{\sin (4x)}=e^0=1[/tex]Hello can someone help me in this pls i need it today now PLS i will give 25 points
Answer:
Look below
Step-by-step explanation:
Convert -8/5 into a decimal
-8/5 = -1 3/5 = -1.6
Solve the given expression for x = -18:5x/3 - 2
ANSWER
[tex]-32[/tex]EXPLANATION
We want to solve the given expression for x = -18:
[tex]\frac{5x}{3}-2[/tex]To do this, substitute the given value of x into the expression and simplify. That is:
[tex]\begin{gathered} \frac{5(-18)}{3}-2 \\ \frac{-90}{3}-2 \\ -30-2 \\ \Rightarrow-32 \end{gathered}[/tex]That is the answer.
How do I solve these?If f(x)=3xsquared + 9x-4 then evaluate the following:f(1)=3x^2+9x-4f(x+h)=3x^2+9x-4
a) We need to evaluate when x = 1
f(1): this means we will replace x with 1 in the given function
[tex]\begin{gathered} f\mleft(x\mright)=3x^2+9x-4 \\ f\mleft(1\mright)=3(1)^2+9(1)-4 \\ f(1)\text{ = 3(1) + 9 - 4 = 3 + 9 - 4} \\ f(1)\text{ = 8} \end{gathered}[/tex]b) We need to evaluate the function when x = x + h
[tex]\begin{gathered} f\mleft(x\mright)=3x^2+9x-4 \\ f(x\text{ + h): we will replace x with x + h in the given function} \\ f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}[/tex]Expanding:
[tex]\begin{gathered} f(x\text{ + h) }=3(x^2+2xh+h^2)\text{ + 9(x + h) - 4} \\ f(x\text{ + h) }=3x^2+6xh+3h^2\text{ + 9x + 9h - 4} \\ \text{Since there are no like terms we can simplify, we can leave it in expanded form:} \\ f(x\text{ + h) }=3x^2+6xh+3h^2\text{ + 9x + 9h - 4} \\ \\ or\text{ the non expanded form:} \\ f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}[/tex]please explain briefly..limits and derivatives
The logarithmic-radical expression √[㏒ₐ f(x)] is true for 0 < f(x) ≤ 1. (Correct choice: D)
What is the domain of a logarithmic-radical function?
Logarithms are trascendent expressions whose domain is described below:
Ran (logₐ f(x)) = (0, + ∞)
Since 0 < a < 1, then we find the following feature: logₐ f(x) > 0 for 0 < f(x) ≤ 1.
In addition, the domain of radical functions is described below:
Dom (√f(x)) = f(x) ≥ 0
Therefore, the logarithmic-radical expression defined in the statement is true for 0 < f(x) ≤ 1.
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solve the system by subsitution method
Substitute Y = 3X - 6
in second equation
-15X + 5•(3X - 6) = -30
Now solve for X, cancel parenthesis
use a(b+c) = ab + ac
-15X + 15 X - 30 = -30
. -30 = -30
Then we see that, have infinite solutions
In consecuence, ANSWER IS
OPTION D) (x , 3x - 6 )
Double a number and add 12 and the result will be greater than 20. The number is less than 6. What is the number?
The following expression is equivalent to "double a number and add 12":
[tex]2x+12[/tex]since the result is greater than 20, we have the following:
[tex]\begin{gathered} 2x+12>20 \\ \Rightarrow2x>20─12=8 \\ \Rightarrow x>\frac{8}{2}=4 \\ x>4 \end{gathered}[/tex]the number is also less than 6. Then we have that:
[tex]4therefore, the number is 5There is 1/5 of a foot of ribbon left onthe spool. If Brittany cuts it into 3equal pieces, how long (in feet) willeach piece be?
We know that
• There is 1/5 of a foot of ribbon.
If Brittany cuts it into 3 equal pieces, we have to divide to find the length of each piece.
[tex]\frac{\frac{1}{5}}{3}=\frac{1}{15}[/tex]Therefore, each piece is 1/15 of a foot long.Identify the following series as geometric or arithmetic. Also identify the series as infinite or finite.5, 10, 20, 40, 80, 160, 320geometricarithmeticinfinitefinite
the series is geometric and finite
Explanation:Given:
5, 10, 20, 40, 80, 160, 320
To find:
if the series is arithmetic or geometric; infinite or finite
a) For a series to be arithmetic, it must have a common difference
common difference = next term - previous term
For the series to be geometric, it must have a common ratio
common ratio = next term/previous term
We need to check if it has a common difference or common ratio
let next term = 10, previous term = 5
common difference = 10 - 5 = 5
let next term = 20, previous term = 10
common difference = 20 - 10 = 10
The difference is not common, it is different
common ratio = next term/previous term
let next term = 10, previous term = 5
common ratio = 10/5 = 2
let next term = 20, previous term = 10
common ratio = 20/10 = 2
The ratio is common
As a result, the series is geometric
b) Infinite series cannot be counted and totaled. This is because they do not end
Finite series can be counted and summed up. This is because the series has an end.
The series is finite
Answer:
geometric
finite
Step-by-step explanation:
Correct on Odyssey.
:)
Which of the following equations does the graph below represent?
A. 2x + 2y = 8
B. -2x - 2y = 8
C. -2x + y = 8
D. -2x + 2y = 8
Answer: D
Step-by-step explanation:
The answer is D, as seen on the graph, the Y-Intercept is at Y = 4, and the gradient is 1, so according to the equation y = mx + c,
"m" must equal 1, and "c" must equal 4, so the equation needs to be:
y = x + 4.
In Option D, the equation can be rearranged to 2y = 2x + 8, dividing both the LHS and RHS by 2, we get y = x + 4.
This type of question can be tough at first, however it's just a matter of practice, keep practicing, keep working hard, and you'll be an expert in no time!
Find a measurement of the complement for the angle 20
Given:
There are given that the angle is 20 degrees.
Explanation:
According to the concept:
The complementary angle is:
[tex]90^{\circ}-\theta[/tex]Then,
Put the value of an angle;
So,
[tex]\begin{gathered} 90^{\circ}-\theta=90^{\circ}-20 \\ =70^{\circ} \end{gathered}[/tex]Final answer:
Hence, the measure of the complement is 70 degrees.
6.4 times m minus 12 equals 45.6
Given
6.4 times m minus 12 equals 45.6
To find: The value of m.
Explanation:
It is given that,
6.4 times m minus 12 equals 45.6.
Then,
[tex]\begin{gathered} 6.4m-12=45.6 \\ 6.4m=45.6+12 \\ 6.4m=57.6 \\ m=\frac{57.6}{6.4} \\ m=9 \end{gathered}[/tex]Hence, the value of m is 9.
Crystal earns $4.75 per hour mowing lawns. A. write a rule to describe how the amount of money M earned is a function of the number of hours H that mowing lawns. B. l how much does crystal earn if she works 1 hour and 15 minutes?
Given:
Crystal earns $4.75 per hour mowing lawns.
Let the money earned = M
And the number of hours = H
So, the relation between M and H will be :
[tex]M=4.75\cdot H[/tex]B. how much does crystal earn if she works 1 hour and 15 minutes?
Time = 1 hours and 15 minutes
AS 1 hour = 60 minutes
So,
[tex]H=1+\frac{15}{60}=1+\frac{1}{4}=1+0.25=1.25[/tex]Substitute with H to find M
So,
[tex]M=4.75\cdot1.25=5.9375[/tex]So, she will earn $5.9375
SCC Library667737985Based on the graph of this normal distribution,a. The mean isb. The median isThe mode isd. The standard deviation isCheck Answer
The Solution.
From the graph,
a. The mean = 73
b. The median = 73
c. The mode = 73
d. The standard deviation (S.D) is;
[tex]S.D=73-67=6[/tex]936.1 ÷ 2.3how do i calculate this without a calculator
Using long division:
Move the decimal point in the divisor and the dividend 1 unit
For what values of x is the expression below defined?A.-5 x < 1B.5 > x -1C.5 > x > 1D.5 x 1
Given:
There are given that the expression:
[tex]\frac{\sqrt{x+5}}{\sqrt{1-x}}[/tex]Explanation;
First, let's notice that we need positives to numbers inside both roots.
So,
The root of a negative number is a math error.
Then,
With that information, let us analyze the options.
From option A:
If we add 5 to this inequality, we have:
[tex]\begin{gathered} -5+5\leq x+5<1+5 \\ 0\leq x+5<6 \end{gathered}[/tex]That means the number in the first root is positive.
Now, we want 1-x to be positive:
[tex]\begin{gathered} -5\leq x<1 \\ 5\ge-x>-1 \\ 1+5\ge1-x>1-1 \\ 6\ge1-x>0 \end{gathered}[/tex]So, it is positive:
Final answer;
Hence, the correct option is A.
Leila bought a sofa on sale for $268. This price was 33% less than the original price.What was the original price?
Let P be the original price.
Since $268 is 33% less than the original price, then $268 is equal to 67% of the original price:
[tex]268=\frac{67}{100}\times P[/tex]Then:
[tex]\begin{gathered} P=\frac{100}{67}\times268 \\ =400 \end{gathered}[/tex]Therefore, the original price was $400.
Answer: $356.44
Step-by-step Explanation: To find the original price of the sofa you need to multiply 33% by $268, but you need to turn the percent into a decimal, to do so you need to divide 33 by 100 & that is 0.33. So 0.33 x $268 is 88.44. After, you add both $268 and $88.44 to get the original price & that is $356.44.
Translate to a system of equations. Do not solve.Two angles are supplementary. One angle is 4 less than three times the other . Find the measures of the angles l.
Two angles are supplementary
That means they add to 180
x+y = 180
One angle is 4 less than three times the other
We know that is means equals and less than comes after
x = 3y-4
set up an equation for your exterior angle, then use multi-step equation steps to solve for y.A. 15B. 17.4C. 5D. 10
In any triangle, the sum of the interior angles of two vertices is equal to the exterior angle of the other vertex.
Using this property, we can write the following equation:
[tex]\begin{gathered} \text{ABC+BAC=ACD}_{} \\ (4y+8)+(5y+3)=146 \\ 9y+11=146 \\ 9y=146-11 \\ 9y=135 \\ y=\frac{135}{9} \\ y=15 \end{gathered}[/tex]The value of y is equal to 15, therefore the correct option is A.