To answer this question, we need to evaluate each function in x=66, this way:
[tex]\begin{gathered} y=7(66) \\ y=462 \\ y=(66)^2-12(66)+84 \\ y=3648 \\ y=1.1317^{66} \\ y=3517.76 \end{gathered}[/tex]In this case, the function that has a greater value at x=66 is the one in the second option:
[tex]y=x^2-12x+84[/tex]please answer this question
Answer:
3
Step-by-step explanation:
Given expression:
[tex]\dfrac{(14^2-13^2)^{\frac{2}{3}}}{(15^2-12^2)^{\frac{1}{4}}}[/tex]
Following the order of operations, carry out the operations inside the parentheses first.
Apply the Difference of Two Square formula [tex]x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
to the operations inside the parentheses in both the numerator and denominator:
[tex]\implies \dfrac{((14+13)(14-13))^{\frac{2}{3}}}{((15+12)(15-12))^{\frac{1}{4}}}[/tex]
Carry out the operations inside the parentheses:
[tex]\implies \dfrac{((27)(1))^{\frac{2}{3}}}{((27)(3))^{\frac{1}{4}}}[/tex]
[tex]\implies \dfrac{(27)^{\frac{2}{3}}}{(81)^{\frac{1}{4}}}[/tex]
Carry out the prime factorization of 27 and 81.
Therefore, rewrite 27 as 3³ and 81 as 3⁴:
[tex]\implies \dfrac{(3^3)^{\frac{2}{3}}}{(3^4)^{\frac{1}{4}}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \dfrac{3^{(3 \cdot \frac{2}{3})}}{3^{(4 \cdot \frac{1}{4})}}[/tex]
[tex]\implies \dfrac{3^2}{3^1}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 3^{(2-1)}[/tex]
[tex]\implies 3^1[/tex]
[tex]\implies 3[/tex]
Given that,
→ ((14² - 13²)^⅔)/((15² - 12²)^¼)
Evaluating the problem,
→ ((14² - 13²)^⅔)/((15² - 12²)^¼)
→ ((196 - 169)^⅔)/((225 - 144)^¼)
→ (27^⅔)/(81^¼)
→ ((3³)^⅔)/((3⁴)^¼)
→ (3²)/3
→ 9/3 = 3
Therefore, the solution is 3.
Find the equation of the line that is perpendicular to y= -1 over 5x-3 and contains the point (1,2)
STEP - BY - STEP EXPLANATION
What to find?
Equation of a line.
Given:
Perpendicular equation; y=-1/5 x - 3
Point(1,2)
Step 1
Find the slope of the perpendicular line.
Comparing the line with y=mx + c
[tex]slope(m)=-\frac{1}{5}[/tex]Step 2
Determine thee slope of the new equation.
Slope of perpendicular lines have the following characteristic;
[tex]m_1m_2=-1[/tex]where m2 is the slope of the new equation.
[tex]\begin{gathered} -\frac{1}{5}m_2=-1 \\ \\ m_2=-1\times-\frac{5}{1} \\ \\ =5 \end{gathered}[/tex]Step 3
Find the intercept(c) using the formula below:
[tex]y=mx+c[/tex]Substitute x=1 y=2 and m=5
[tex]\begin{gathered} 2=5(1)+c \\ \\ c=2-5 \\ \\ =-3 \end{gathered}[/tex]Step 4
Form the equation of the line by substituting m=5 and c=-3 into the general equation.
[tex]y=5x+(-3)[/tex]ANSWER
y= 5x + (-3)
how much of each ingredient would you need to make an identical recipe that serves 8 people explain your reasoning
LITERS OF SODA
24 people calls for 4 liters of lemon soda
18 people calls for x liters of lemon soda
24 people = 4 liters
18 people = x
cross multiply
24x = 72
Divide both-side of the equation by 24
x = 3
18 peoples calls for 3 liters of soda
PINT OF SHERBET
24 people calls for 2 pint of sherbet
18 people calls for x pint of sherbet
24 people = 2 pint
18 people = x
cross-multiply
24x = 36
Divide both-side of the equation by 24
x =1.5
18 peoples calls for 1.5 pint of sherbet
CUPS OF RICE
24 peoples calls for 6 cups of rice
18 people calls for x cups of rice
24 people = 6 cups of rice
18 people = x
cross multiply
24x = 108
Divide both-side of the equation by 24
x=4.5
18 people calls for 4.5 cups of rice
Hence, 18 people calls for; 3 liters of soda, 1.5 pint of sherbet and 4.5 cups of rice
64 is 2/3percent of what number
We have to find the number x for which 64 is the 2/3.
B) Use the quadratic formula to find the roots of each quadratic function.
Which of the following is the solution to the compound inequality below?5 + x>3or6x +1 -29O A. x2 - 7or14X<-3O B. *)-2orx 5C. x22 or x<5OD. x 814or X-3O
we will need to solve the first inequality,
5+x>=-3 , we will subtract -5 from both sides and the solution is
x>=-2
for the second inequality
6x+1<-29, we will subtract 1 from bothe sides and get
x<-5
is your choice B
Please see photo checking my work I think it is all the students attending the college
Answer:
A population is the entire group that you want to draw conclusions about.
So, in this exercise, the population is all the students attending the college.
Solve the inequality below to determine and state the smallest possible value of x in the solution set. - 7(x + 4) + 3x < 8x - 2(2x - 2)
given the inequality :
- 7(x + 4) + 3x < 8x - 2(2x - 2)
so,
-7x - 28 + 3x < 8x - 4x + 4
combine like terms:
-7x + 3x - 8x + 4x < 28 + 4
-8x < 32
Divide both sides by -8
Do not forget to flip the inequality sign
so,
x > -4
so, The solution is the interval ( -4 , ∞ )
On the number line the solution will be :
The smallest possible interger of x = -3
The expression below is scientificnotation for what number?4.58x10^-2
Using the exponent rules, 10^-2 can be expressed as follows:
[tex]10^{-2}=\frac{1}{10^2}=\frac{1}{100}[/tex]Substituting into the expression in scientific notation, we get:
[tex]4.58\cdot10^{-2}=4.58\cdot\frac{1}{100}=\frac{4.58}{100}=0.0458[/tex]Andrew constructed a triangle so that the measurement of 1 and 2 were congruent. if angle 3 measured 70 degrees, what is the measure of angle 1?
Andrew constructed a triangle such that the measurements of angles m<1 and m<2 are congruent.
The above statement can be inferred from concept of congruency of triangles. The oppsoite sides of the two congruent angles in a traingles are also equal.
From the above statement we can deduce the type of a triangle that Andrew drew as follows:
[tex]\text{Andrew drew a isoceles triangle}[/tex]An isoceles triangle has two equal sides and angles i.e congruent sides and interior angles. Hence,
[tex]m\angle1\text{ = m}\angle2\ldots\text{ Eq1}[/tex]The following information is given for the third interior angle m<3 of the isoceles triangle:
[tex]m\angle3\text{ = 70 degrees}[/tex]We need determine the angle measure of the angle 1. Recall that the sum of interior angles of a triangle is given as follows:
[tex]m\angle1\text{ + m}\angle2\text{ + m}\angle3\text{ = 180 degrees }\ldots\text{ Eq2}[/tex]Substitute Eq1 into Eq2 as follows:
[tex]\begin{gathered} m\angle1\text{ + m}\angle1\text{ + m}\angle3\text{ = 180} \\ \\ 2\cdot m\angle1\text{ + m}\angle3\text{ = 180} \end{gathered}[/tex]Substitute the angle measurement of angle ( 3 ) in the expression above and solve for angle ( 1 ) as follows:
[tex]\begin{gathered} 2\cdot m\angle1\text{ + 70 = 180} \\ 2\cdot m\angle1\text{ = 110} \\ m\angle1\text{ = }\frac{110}{2} \\ \\ m\angle1\text{ = 55 degrees }\ldots\text{ Answer} \end{gathered}[/tex]In AUVW, VW = UV and mZU = 74º. Find mZV.
We will find the measure of angle V as follows:
*From theorem we have that angles that are opposite to congruent sides are congruent. So, Angle W will also have a measure o 74°. Now, we also have that the sum of all internal angles of a triangle add 180°, so the following is true:
[tex]U+V+W=180\Rightarrow74+V+74=180[/tex]Now, we solve for V:
[tex]\Rightarrow V=32[/tex]So, the measure of angle V is 32°.
Johnathan works on IXL 5 nights per week. One week, he masters 7 skills. If he makes the sameamount of progress each night, how many skills does he master per night?Linear Equation:Solve:
In this problem
Divide total skills by the total night per week
so
7/5=1.4 skills per night
therefore
Let
x ----> number of night
y ----> total skills
so
y=(7/5)x ------> y=1.4xwhat does this mean i dont get it please help me thanks, :)
It means that you are supposed to group The like terms together and simplify them
you will find that 2t is the liketerm with -5t and -u is a like term with -6u
As a results we have
[tex] = 2t - 5t - u - 6u \\ = - 3t - 7u[/tex]
as indicated I have shown you the answer .
good luck
The mass of a typical comet is about 1 x 10¹3 kg, while the mass of a typical asteroid is about 3 x 10¹⁹ kg.
Approximately how many times the mass of a typical comet is the mass of a typical asteroid?
100,000 times
300,000 times
1,000,000 times
O 3,000,000 times
The mass of the typical comet is 3,000,000 times the mass of a typical asteroid which is the fourth option among the given options.
It is given in the question that:-
Mass of a typical comet = [tex]1*10^{13}kg[/tex]
Mass of a typical asteroid = [tex]3*10^{19}kg[/tex]
We have to find the how many times the mass of a typical comet is the mass of a typical asteroid.
Mass of a typical asteroid/ Mass of a typical comet is given by:-
[tex]\frac{3*10^{19}}{1*10^{13}}=3*10^6[/tex]
We can write [tex]3*10^6[/tex] as 3,000,000.
Hence, the mass of the typical comet is 3,000,000 times the mass of a typical asteroid which is the fourth option among the given options.
To learn more about mass, here:-
https://brainly.com/question/19694949
#SPJ1
Tina designed an electric skateboard that has a speed of 4 miles per hour. She wants to write a function that represents the distance the skateboard will travel over a given amount of time.Which is the dependent variable in this scenario?the skateboardthe speedthe time traveledthe distance traveled
ANSWER
The distance traveled
EXPLANATION
We want to identify the dependent variable from the scenario.
The dependent variable in a function is the variable that changes as a result of a change in the independent variable. This implies that it depends on the independent variable for its value.
From the scenario, the distance that the skateboard travels is dependent on the amount of time spent traveling.
Therefore, the dependent variable is the distance traveled.
A circle Is cut from a square piece of cloth as shown How many square inches of cloth are cut from the square 1,061.32in22,122.64in22,704.00in23,622.31in2
Answer: 2,122.64in².
Explanation
We want to know the measure of the circle in square inches, meaning that we have to calculate the area.
The area of a circle (A) is given by:
[tex]A=\pi r^2[/tex]where r represents the radius of the circle.
The diameter of the circle is a straight line that goes from one point of the circumference of a circle to an opposite point, passing through the center of the circle. The radius is half the diameter.
Based on the image, we can see that the circle is cut touching one point of each side of the square, meaning the diameter is what the side of the square measures:
Then, if the diameter is 52", then the radius is half that, 26".
Now, we can calculate the area:
[tex]A=\pi\cdot26^2[/tex][tex]A=3.14\cdot676[/tex][tex]A=2122.64in^2[/tex]Given the measure -845°, which answer choice correctly gives an angle measure coterminal with the given angle and on the interval,0 < 0 < 360
Given the measure -845° we can find its coterminal measure on the interval, [0,360) below
Explanation
For angles measured in degrees
[tex]\begin{gathered} β=α±360*k,where\text{ }k\text{ }is\text{ }a\text{ }positive\text{ }integer \\ -845°=\frac{-169}{36}π≈-4.694π \\ Coterminal\text{ }angle\text{ }in\text{ \lbrack}0,360°)range:\text{ 235\degree, located in the third quadrant.} \end{gathered}[/tex]Answer: Option A
I will send a picture of the problem and or question
The equivalency for grams to centigrams is:
1 gram = 100centigrams
To convert the units you can apply cross multiplication:
1gr_____100cgr
443gr____xcgr
[tex]\begin{gathered} \frac{100}{1}=\frac{x}{443} \\ x=443\cdot100=44300 \end{gathered}[/tex]This means that 443 grams equals to 44300 centigrams
*-*-*-*
The scale is done in a base of 10 and the grams are in its center with value 1.
To convert from smaller units to grater units you have to divide the given measurement by 10
And to convert from greater units to smaller units you have to multiply by 10.
For example if you have 1mg and want to convert it to grams you have to divide the value 3 times by 10, i.e. divide the value by 1000
[tex]\frac{1mg}{1000}=0.001g[/tex]If you want to convert 1 Kg into 1 decagram, multiply the value two times by 10, i.e. multiply it by 100
[tex]1\operatorname{kg}\cdot100=100\text{dag}[/tex]Write a quadratic function whose graph passes through (3,6) and has the vertex (-2,4) what is the value of Y
The representation of a quadratic eqauation in vertex form is
[tex]y=a(x-k)^2+h[/tex]The given vertex is,
[tex](k,h)=(-2,4)[/tex]And the given point through which the graph passes is,
[tex](x,y)=(3,6)[/tex]Substitute the values in the formula of quadratic equation.
[tex]\begin{gathered} 6=a(3-(-2))+4 \\ 6=a(3+2)+4 \\ 6=5a+4 \\ 5a=6-4 \\ 5a=2 \\ a=\frac{5}{2} \end{gathered}[/tex]Hence, the equation in vertex form will be,
[tex]\begin{gathered} y=\frac{5}{2}(x-(-2))+4 \\ y=\frac{5}{2}(x+2)+4 \end{gathered}[/tex]Find the probability that a dart hits one of the shaded areas. Thewhite figure is a rectangle. Be sure to show all work.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Get the angles of the hexagon
The internal angles of an hexagon is given as:
[tex]\begin{gathered} \frac{180(n-2)}{n} \\ n=6\text{ since hexagon has 6 sides} \\ So\text{ we have:} \\ \frac{180(6-2)}{6}=\frac{180(4)}{6}=\frac{720}{6}=120\degree \end{gathered}[/tex]Therefore each angle of the hexagon is 120 degrees.
STEP 2: find the length of the sides
We remove the right triangles as seen below:
Using the special right triangles, we have:
STEP 3: find the area of the extracted triangle above
[tex]\begin{gathered} b=1,h=\sqrt{3} \\ Area=\frac{1}{2}\cdot1\cdot\sqrt{3}=\frac{\sqrt{3}}{2}units^2 \end{gathered}[/tex]Since there are two right triangles, we multiply the area by 2 to have:
[tex]Area=2\cdot\frac{\sqrt{3}}{2}=\sqrt{3}[/tex]There are two triangles(both sides), therefore the total area of the shaded area will be:
[tex]\sqrt{3}\cdot2=2\sqrt{3}[/tex]STEP 4: Find the area of the whole hexagon
[tex]\begin{gathered} Area=\frac{3\sqrt{3}s^2}{2} \\ s=hypotenuse\text{ of the right triangle}=2 \\ Area=\frac{3\sqrt{3}\cdot4}{2}=6\sqrt{3} \end{gathered}[/tex]STEP 5: Find the probability
[tex]\begin{gathered} Probability=\frac{possible\text{ area}}{Total\text{ area}} \\ \\ Possible\text{ area}=2\sqrt{3} \\ Total\text{ area}=6\sqrt{3} \\ \\ Probability=\frac{2\sqrt{3}}{6\sqrt{3}}=\frac{1}{3}=0.3333 \end{gathered}[/tex]Hence, the probability that the dart hits one of the shaded areas is approximately 0.3333
Mr. and Mrs. Tournas know that their son will attend a college, in 14 years, that they estimate to cost approximately $250,000How much should they deposit now if they assume that they can earn 8.5% compounded annually?
Compound interest formula:
[tex]A\text{ = }P(1+i)^n[/tex]where:
A is the final amount, here = $250,000
P is the principal amount
i is the interest rate per year (in decimal form), here = 0.085
n is the number of years invested, here = 14
Replacing into the equation and solving for P, we get:
[tex]250000=P(1+0.085)^{14}[/tex][tex]\frac{250000}{1.085^{14}}=P[/tex]
P = $79,785.5
Following figure shows ABC with silencer the nearest 10th find AB in ABC
We have to find the length of AB.
We can use the Law of sines the tell us that the quotient between the sine of an angle and the length of the opposite side is constant for each of the three angles.
So we can write:
[tex]\begin{gathered} \frac{\sin(A)}{CB}=\frac{\sin(C)}{AB} \\ \frac{\sin(71\degree)}{6}=\frac{\sin(48\degree)}{AB} \\ AB=\frac{6\cdot\sin(48\degree)}{\sin(71\degree)} \\ AB\approx\frac{6\cdot0.743}{0.946} \\ AB\approx4.7 \end{gathered}[/tex]Answer: AB = 4.7
wich choice shows the correct solution to 2544÷8?
ANSWER:
318
STEP-BY-STEP EXPLANATION:
We have the following operation:
[tex]2544÷8[/tex]So the answer is 318
0.25(60) + 0.10x = 0.15(60 + x)
Answer: X = 120
Step-by-step explanation:
lol:
V = (−∞,∞)
X = 120
A train leaves a station and travels north at a speed of 175 km/h. Two hours later, a second train leaves on a parallel track and travels north at 225 km/h. How far from the station will theymeet?The trains will meet (?) away from the station(Type an integer or a decimal.)
Given,
The speed of first train is 175km/h.
The speed of second train is 225 km/h.
Consider, the time taken by first train to meet is x h.
The time taken by the second train to meet is (x-2) h.
The distance is calculated as,
[tex]\text{Distance}=\text{speed}\times time[/tex]At the meeting point the distance covered by both train is same,
So, taking the distance equation of both trains in equal,
[tex]\begin{gathered} 175\times x=225\times(x-2) \\ 175x=225x-450 \\ -50x=-450 \\ x=9 \end{gathered}[/tex]The first train meet to second train after distance,
[tex]d=175\times9=1575\text{km}[/tex]The second train meet to first train after distance,
[tex]d=225\times(9-2)=1575\text{ km}[/tex]Hence, both train meet after 1575 km from the station.
Based on your knowfedgs of the two data sets described below, would you espect a scatter plot describing the two data sets to have a positive, a negative, or nocorrelationduration of usage and the charge in the battery of a mobile phone
We expect the variable to have a negative correlation.
This means that the more we use the phone the lower the charge will be.
What is the domain for the following function? 2x . - 3 O A. (x+3) O B. {**-3) O c. {*#0 O D. all real number ers
Given,
y = 2x/x - 3
to solve this,
let's equate the denominator to 0
so,
y = 2x/0
this means undefined
recall,
Domain is the set of all possible values of x. Since the function is undeined when the denominator is zero, the domain is the set of all real numbers except the value which will make the denominator zero
so the domain for the function y = 2x/x - 3
is x is not equal to 3
therefore, the correct option is
[tex]A.\mleft\lbrace x\ne3\mright\rbrace[/tex]Directions:For questions 12-16 simplify using the given replacement valued. There should be no decimals, convert all decimals to fractions. (Do not change whole numbers)I need help with 14
14. Given:
[tex]\frac{3}{2}r-rs+4,r=\frac{6}{7},s=\frac{2}{3}[/tex]Substitute the value of r and s in the given problem.
We get,
[tex]\begin{gathered} \frac{3}{2}(\frac{6}{7})-(\frac{6}{7})(\frac{2}{3})+4=3(\frac{3}{7})-(\frac{2}{7})(2)+4 \\ =\frac{9}{7}-\frac{4}{7}+4 \\ =\frac{5}{7}+4 \\ =\frac{33}{7} \end{gathered}[/tex]Hence, the answer is
[tex]\frac{33}{7}[/tex]Q1 of the numbers 5, 8, 10, 11, 12, 15, 19, 20, 20, 24, 25
Answer
Q1 = 10
Explanation
To ontain the Q1, we need to first make sure the numbers are arranged in ascending or descending order.
5, 8, 10, 11, 12, 15, 19, 20, 20, 24, 25
Q1 is the number that occurs at the (N + 1)/4 position for the distribution.
N = Number of variables = 11
Q1 = (N + 1)/4
Q1 = (11 + 1)/4 = (12/4) = 3rd variable.
5, 8, 10, 11, 12, 15, 19, 20, 20, 24, 25
The 3rd variable = 10
Hope this Helps!!!
Answer:
10
Step-by-step explanation:
i'm drinking boba and am to lazy to explain.
Simplify the following expression.(12x-2.1)-(19x+6.9)
The given algebraic expression is
[tex](12x-2.1)-(19x+6.9)[/tex]To simplify this expression, we need to solve those parentheses in the first place, multiplying the sign in front of each of them.
[tex]12x-2.1-19x-6.9[/tex]Now, we reduce like terms. Remember that like terms are those who have the same variable, and those who don't have variables at all.
[tex]12x-19x-2.1-6.9=-7x-9[/tex]Therefore, the simplest form of the given expression is[tex]-7x-9[/tex]