Given the equation:
[tex]\text{ x}^2\text{ + 3x - 4 = 0}[/tex]To find x, since the equation is in the standard form of Quadratic Equation, we will be using the Quadratic formula:
[tex]\text{ x =}\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2-4ac}}{2a}[/tex]At,
[tex]ax^2\text{ + bx + c = 0}[/tex]Where,
a = coefficient at x² = 1
b = coefficient at x = 3
c = constant = -4
Let's plug in the values to find for x:
[tex]\text{ x =}\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2-4ac}}{2a}[/tex][tex]undefined[/tex]
I need help with math
we are asked to determine the area of a circle with a radius of 3 in. To do that we will use the following formula:
[tex]A=\pi r^2[/tex]Where "r" is the radius. Replacing the values we get:
[tex]A=(3.14)(3in)^2[/tex]Solving the operations:
[tex]A=28.26in^2[/tex]solving right triangle find the missing side. round to the nearest tenth number 10
Given a right angle triangle
As shown in the figure:
Side x is the opposite to the angle 68
Side 21 is adjacent to the angle 68
We will use the tan function to find x:
[tex]\begin{gathered} \tan 68=\frac{opposite}{adjacent} \\ \\ \tan 68=\frac{x}{21} \\ \\ x=21\cdot\tan 68=51.9768 \end{gathered}[/tex]Rounding to the nearest tenth
So, the answer will be x = 52
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. It takes Pam 45 minutes to drive to work and 60 minutes to drive home from work. Write the ratio of the time Pam spends driving home from work to the time she spends driving to work in three different ways.
1) Gathering the data
Pam -----> 45' to drive to work and 60' to drive home
2) Writing the ratio in 3 different ways:
[tex]\frac{d_H}{d_W}\text{ =}\frac{45}{60}\text{ =}\frac{3}{4}=0.75[/tex]3) So this ratio can be written as 45/60 or 3/4 or 0.75 since we write on the numerator and the denominator the amount of time spent commuting, and the second one is after simplifying and the last one as a decimal number.
in ABC,X is the centroid if XZ=3, What is AZ
In every triangle, the centroid divides each segment starting through a vertex and passing through it (that is, the segments AZ, BY and CW) in two parts, where one part (starting from the vertex) is two times the other part.
So we have the following relations:
[tex]\begin{gathered} AX=2\cdot XZ \\ CX=2\cdot XW \\ BX=2\cdot XY \end{gathered}[/tex]So using the value XZ = 3, we can find the value of AX:
[tex]\begin{gathered} AX=2\cdot XZ \\ AX=2\cdot3 \\ AX=6 \end{gathered}[/tex]Then, since the segment AZ is the sum of the segments AX and XZ, we have:
[tex]\begin{gathered} AZ=AX+XZ \\ AZ=6+3 \\ AZ=9 \end{gathered}[/tex]So the length of AZ is equal 9.
find u'(4) for[tex]u(x) = h( \sqrt{x} )[/tex]use the table in the picture to solve the equation.
The equation given:
[tex]u(x)=h(\sqrt[]{x})[/tex]We need to find u'(4).
This means you put in "4" into the function and see:
So, it becomes:
[tex]\begin{gathered} u(4)=h(\sqrt[]{4}) \\ u(4)=h(2) \end{gathered}[/tex]Now, we want u'(4), so we need h'(2).
Looking into row and column of table, we find
h'(x) and "2" ------------>> we get "2".
Hence,
[tex]u^{\prime}(4)=2[/tex]Which of the following is true for the relation f(x)=x^2+8
Answer: Both the equation and its inverse are functions.
Explanation
Given the equation:
[tex]f\mleft(x\mright)=x^2+8[/tex]we can use the vertical line test to determine if it is a function:
As no vertical line touches the graph, then it is a function. Additionally, the inverse function can be calculating by interchanging the x and y variables in the original function:
[tex]x=y^2+8[/tex][tex]x-8=y^2[/tex][tex]y=\sqrt{x-8}[/tex]If we do the same vertical test for the inverse function we will see that both are function.
A population increases by 4% each year. What is the annual growthfactor?
Answer
Explanation: A annual growth factor represents how quickly a value increases during an entire year. It is represented in the percentage unit % and there are some formulas to calculate the values as the example below
[tex]annual_{\text{ }}growth_{\text{ }}factor=\frac{change\text{ value}}{original\text{ value}}*100[/tex]As we can see from the question the population increases by 4% each year. The 4% is representing exactly how quick the population is increasing in a year.
Final answer: So the annual growth factor is 4%.
How do you keep the answers on your profile for studying????
Given:
Number of sample (n) = 50
mean = 300
standard deviation (s) = 47
confidence level = 95%
The margin of error (MOE) can be calculated using the formula:
[tex]\text{MOE = z }\times\text{ }\frac{s}{\sqrt[]{n}}[/tex]Where z is the z-score at the given confidence level
At 95% confidence level, the z-score is 1.960
The margin of error is thus:
[tex]\begin{gathered} \text{MOE =1.96 }\times\frac{47}{\sqrt[]{50}} \\ =\text{ 13.0277} \end{gathered}[/tex]The formula to calculate the confidence interval is:
[tex]\begin{gathered} CI=\operatorname{mean}\pm z\frac{s}{\sqrt[]{n}}^{} \\ CI\text{ = mean }\pm\text{ margin of error} \end{gathered}[/tex]Where :
[tex]\begin{gathered} \text{lower bound = mean - margin of error} \\ \text{upper bound = mean + margin of error} \end{gathered}[/tex]Substituting:
[tex]\begin{gathered} \text{lower bound = }300\text{ - 13.0277} \\ =\text{ 286.9723} \\ \approx\text{ 287} \\ \text{upper bound = 300 + 13.0277} \\ =\text{ 313.0277} \\ \approx\text{ 313} \end{gathered}[/tex]Hence, if we to randomly sample from this population 100 times. The probability of having a score between 287 and 313 is 0.95
if p(x)= x^4 + 3x^3 -2x^2 +4 and q(x) = x+1, then g(x) is a polynomial that equal p(x)/q(x). what is the remainder of g(x) when it is divided by (x-2)?answer choicesA. 22B.12C.-4D.6
Answer: The correct answer for the question is B.12
Reason:
We are going first to calculate g(x)= p(x)/q(x), where
[tex]p(x)=x^4+3x^3-2x^2+4\text{ }[/tex][tex]q(x)=x+1[/tex]obtaining that:
[tex]g(x)=x^3+2x^2-4x+4[/tex]Now we need to divide g(x) by (x-2), and find the remainde
Eliminate the parameter t. Find rectangular equation for the plane curve defined by the parametric equations
For this problem, we are given the value of x in the function of t, and the value of y in the function of t. We need to represent y in the function of f.
The first step is to isolate t on the x equation:
[tex]\begin{gathered} x=\sqrt{t}\\ \\ x^2=t\\ \\ t=x^2 \end{gathered}[/tex]Then we need to replace the expression for t on the right side of the function for y.
[tex]y=2x^2+4[/tex]The correct answer is the third one. The interval get decreased in half, because of the relation between x and t.
billy was given a Toblerone candy. what is the volume of the candy shaped like and equilateral triangular prism. h=9cm h=6cm and w=22cm
Explanation
Step 1
as this is a equilateral triangle, every side measures 9 cm
so, the volume of the prism is
[tex]\begin{gathered} \text{Volume}=\text{area of the trianlge}\cdot length \\ \text{Volume}=(\frac{base\cdot hegith}{2}\cdot\text{length)} \end{gathered}[/tex]then,Let
base=9 cm
heigth=6 cm
length=22 cm
now, replace.
[tex]\begin{gathered} \text{Volume}=(\frac{base\cdot hegith}{2}\cdot\text{length)} \\ \text{Volume}=(\frac{9cm\cdot6\text{ cm}}{2}\cdot\text{22 cm)} \\ \text{Volume}=(\frac{54cm^{^2}}{2})\cdot22 \\ Volume=594cm^3 \\ \end{gathered}[/tex]I hope this helps you
Which of the following is equivalent to the expression below? 54^x/6^x
Given:
An expression is:
[tex]\frac{54^x}{6^x}[/tex]Required:
Find the equivalent expression to the given expression.
Explanation:
The given expression is:
[tex]\frac{54^x}{6^x}[/tex]Use the exponent property as:
[tex]\frac{a^m}{b^m}=(\frac{a}{b})^m[/tex][tex]\begin{gathered} \frac{54^x}{6^x}=(\frac{54}{6})^x \\ \frac{54^x}{6^x}=(9)^x \end{gathered}[/tex]Final Answer:
Option C is the correct answer.
mom's florist sells two dozen Rose's for 24.60. First flowers sells 6 Rose's for 7.50 which florist had the lower cost per rose?
We are to compare the cost of each rose sold by two florists.
Mom's florist sells ( n ) number of roses at a certain price ( S ) as follows:
[tex]\begin{gathered} n\text{ = 2 dozen roses ( 2}\cdot12=24\text{ )} \\ S\text{ = \$24.60} \end{gathered}[/tex]First florist sells ( k ) number of roses at a certain price ( M ) as follows:
[tex]\begin{gathered} k\text{ = 6 roses} \\ M\text{ = \$7.5} \end{gathered}[/tex]We will determine the cost price of each rose ( c ) sold by the two florist.
For Mom's florist:
We will take the ratio of the total cost ( S ) and the number of roses sold ( n ) as follows:
[tex]\begin{gathered} c_1\text{ = }\frac{S}{n} \\ \\ c_1\text{ = }\frac{24.6}{24} \\ \\ c_1=\frac{\text{\$1.025 }}{rose} \end{gathered}[/tex]For First florist:
We will take the ratio of the total cost ( M ) and the number of roses sold ( k ) as follows:
[tex]\begin{gathered} c_2\text{ = }\frac{M}{k} \\ \\ c_2\text{ = }\frac{7.5}{6} \\ \\ c_2=\frac{\text{\$}1.25\text{ }}{rose} \end{gathered}[/tex]Then we compare the cost prices ( c ) for roses sold by each florist:
[tex]\begin{gathered} c_1Hence,[tex]\text{Mom's florist has the lower cost per rose}[/tex]
Given a Selling Price of $153.60 and a Cost of $67.98 find the Markup price.
The markup is given as;
[tex]\begin{gathered} SP-CP \\ \text{Where SP=selling price, CP= cost price} \end{gathered}[/tex]Given that;
[tex]\begin{gathered} SP=\text{ \$153.60,} \\ CP=\text{ \$67.98} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} Markup\text{ price = }153.60-67.98 \\ Markup\text{ price = \$85.62} \\ \\ \end{gathered}[/tex]4 2/3 - 5/6= / \ 2/6 3/6
You have the following expression:
4 2/6 - 5/6
consider that 5/6 = 2/6 + 3/6, then:
4 2/6 - 5/6 = 4 2/6 - (2/6 + 3/6) = 4 2/6 - 2/6 - 3/6 = 4 3/6 = 4 1/2
Hence, the result is 4 1/2
Zack, a soup chef at a new restaurant, kept track of the first week's soup sales. Split pea Chicken noodle Cup 6 5 Bowl 4 3 What is the probability that a randomly selected soup was ordered in a cup and was chicken noodle? Simplify any fractions.
hello
to solve this question, we simply need to add (split pea + chicken noodle) in a cup and then proceed from there.
probability of ordering chicken noodles in a cup is
[tex]\begin{gathered} \text{split pea +ch icken noodles = 6+5=11} \\ ch\text{ icken noodles=}\frac{5}{11} \end{gathered}[/tex]the probabi
Sales representatives of a new line of computers predict that sales can be approximated by the function S(t) = 1200 + 540\n(31 + e),where t is measured in years. What are the predicted sales in 13 years? Round your answer to the nearest whole number.
We have the function
[tex]S(t)=1200+540\ln(31t+e)[/tex]And we want to evaluate S(13), therefore
[tex]\begin{gathered} S(13)=1200+540\ln(31\cdot13+e) \\ \\ S(13)=1200+540\operatorname{\ln}(403+e) \\ \\ \end{gathered}[/tex]Here we must use a calculator to get the result
[tex]\begin{gathered} S(13)=1200+540\operatorname{\ln}(403+e) \\ \\ S(13)=1200+540\cdot6.00566 \\ \\ S(13)=1200+3243.05587 \\ \\ S(13)=4443.05587708 \\ \\ S(13)=4443 \end{gathered}[/tex]The predicted sales in 13 years are 4443 computers
Use the properties of exponents to rewrite this expression. Then evaluate the rewritten expression for the given values to complete the statement.
Answer:
60
Explanation:
Given the below expression;
[tex](11j^{-3}k^{-2})(j^3k^4)[/tex]Applying the product rule, we'll have;
[tex]\begin{gathered} 11j^{-3+3}k^{-2+4} \\ =11j^0k^2 \\ =11k^{2^{}} \end{gathered}[/tex]Let's go ahead and evaluate the above expression when k = 7;
[tex]\begin{gathered} 11\ast(7)^2 \\ =11+49 \\ =60 \end{gathered}[/tex]the scale of a rectangular City Park measures 10.0 CM with by 5.0 CM length the scale of the drawing is 1.0 cm = 4.5 m what is the actual length of the part
it is given that
1 cm = 4.5 m
the width of the city is 10 cm = 10 x 1 cm = 10 x 4.5m = 45 m
so the length of the city is 5 cm = 5 x 1 cm = 5 x 4.5 m = 22.5 m
actual length of the city is 22.5 m
A native wolf species has been reintroduced into a national forest. Originally 200 wolves were transplanted. After 3 years, the population had grown to 270 wolves. If the population grows exponentially, how many wolves will be there in 10 years
we can find the value of 1.35
270=200(1+r)
where r is the common ratio of each term
we need to clear r
[tex](1+r)=\frac{270}{200}[/tex][tex]r=1.35-1[/tex][tex]r=.35[/tex]to find this formula exponentially
we use
PW=P0(1+r)^n
the formula can we use for this problem will be
[tex]PW=P0\mleft(1.35\mright)^n[/tex]where
PW is the new population of wolves
P0 the original population of wolves
n=the years
[tex]PW=200(1.35)^{10}=4021[/tex]4021 wolves will be there in 10 years
I need help on 5 I skipped this class and don’t know any of this
When you have a line like the one in the opcion C you must know that the angle is 180º
When you have two perpendicular lines like the option B the angle is 90º
Knowing that the angle which is approximalety 72º will be an angle smaller so the answer is DReggie recorded the number of pages he read each day for five days.!!ROUND YOUR ANSWER TO THE NEAREST TENTHS!!
Given:
Mean, x = 32
number of data, n = 5
From the plot, we have the following:
Number of pages Frequency
25 2
32 1
36 1
42 1
Sum up the distance between each data point and the mean using the absolute value and divide by the number of data(n).
To find the measn absolute devialtion, apply the formula:
[tex]\text{MAD}=\frac{\Sigma|x_i-x|}{n}[/tex]Thus, we have:
[tex]\text{MAD=}\frac{|25-32|+|25-32|+|32-32|+|36-32|+|42-32|}{5}[/tex]Solving further:
[tex]\begin{gathered} \text{MAD}=\frac{|-7|+|-7|+|0|+|4|+|10|}{5} \\ \\ \text{MAD}=\frac{7+7+0+4+10}{5} \\ \\ \text{MAD}=\frac{28}{5} \\ \\ \text{MAD}=5.6 \end{gathered}[/tex]Therefore, the mean absolute deviation of the data is 5.6
ANSWER:
5.6
-X + 9y = 363x + 3y = 42How do I solve using the elimination method
Given:
-x + 9y = 36 .......(1)
3x + 3y = 42 ........(2)
The equations can be solved using elimination method.
Multiply equation (2) by 3.
[tex]9x+9y=126\ldots\ldots(3)[/tex]Now, subtract equation (1) from (3).
[tex]\begin{gathered} 9x+9y-(-x+9y)=126-36 \\ 9x+9y+x-9y=90 \\ 10x=90 \\ x=\frac{90}{10}=9 \end{gathered}[/tex]Put x=9 in equation (1) and solve for y.
[tex]\begin{gathered} -9+9y=36 \\ 9y=36+9 \\ 9y=45 \\ y=\frac{45}{9} \\ y=5 \end{gathered}[/tex]Therefore, x=9 and y=5.
Correct0It takes Kim 7 hours to proof a chapter of Hawkes Learning Systems Introductory Algebra book and it takes Harding 2 hours. How long would it take them workingtogether? (Round your answer to two decimal places.)
ANSWER
1.56 hours
EXPLANATION
If Kim reads 1 chapter in 7 hours, in 1 hour she would read,
[tex]\frac{1chapter}{7h}=\frac{1}{7}chapter/hour[/tex]Similarly, if Harding reads the same chapter in 2 hours, then in 1 hour he will read,
[tex]\frac{1chapter}{2h}=\frac{1}{2}chapter/hour[/tex]If they work together, in 1 hour they would read,
[tex]\frac{1}{7}chapter+\frac{1}{2}chapter=\frac{2+7}{2\cdot7}chapter=\frac{9}{14}chapter[/tex]If they read together 9/14 of a chapter in 1 hour, then they will read 1 full chapter in,
[tex]1chapter\cdot\frac{1h}{\frac{9}{14}chapter}=\frac{14}{9}h\approx1.56h[/tex]Hence, if they work together, they will read the chapter in 1.56 hours.
find the value or measure. Assume all lines that appear to be tangent are tangent. m(angle) FHG=
Assuming that the lines FG and HG are tangent, you need to remember that, by definition, when two tangents intersect outside a circle, the angle formed by them is the difference of the intercepted arcs divided by 2.
Then:
[tex]AngleFormedbyTwoTangents=\frac{(DifferenceOfInterceptedArcs)}{2}[/tex]In this case, you know that the angle formed by the tangents FG and HG is:
[tex]\angle FGH[/tex]And the Intercepted arcs are the following:
[tex]\begin{gathered} FH=97\degree \\ FIH \end{gathered}[/tex]By definition, a circle has 360 degrees; then you can find the measure of the arc FIH as following:
[tex]\begin{gathered} FIH=360\degree-97\degree=263\degree \\ \end{gathered}[/tex]
Knowing that, you can substitute values into the equation in order to find the measure of the angle FGH:
[tex]m\angle FGH=\frac{263\degree-97\degree}{2}=83\degree[/tex]The answer is: First option.
What slope line passes through (0,5) (3,17)
To calculate the slope we have to use the following formula
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]therefore, we have that
[tex]m=\frac{17-5}{3-0}=\frac{12}{3}=4[/tex]so the slope is 4
Given the ellipse (x−3)^2/4+(y−4)^2/25=1,Find the center point: List the four vertices
The equation of the ellipse of center (h, k) is
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]Its 4 vertices are
[tex](h,k+a)(h,k-a),(h+b,k),(h-b,k)[/tex]Since the given equation is
[tex]\frac{(x-3)^2}{4}+\frac{(y-4)^2}{25}=1[/tex]Then by comparing it with the form above
[tex]h=3,k=4[/tex][tex]b^2=4,b=2,-2[/tex][tex]a^2=25,a=5,-5[/tex]Then we can find the 4 vertices using the rule above
[tex](h,k+a)=(3,4+5)=(3,9)[/tex][tex](h,k-a)=(3,4-5)=(3,-1)[/tex][tex]\begin{gathered} (h+b,k)=(3+2,4)=(5,4) \\ (h-b,k)=(3-2,4)=(1,4) \end{gathered}[/tex]The 4 vertices are
(3, 9), (3, -1), (5, 4), (1, 4)
The center is (3, 4)
I'm not sure what I am supposed to do here can you help me?it also asks what is the left/right facesand top and bottom faces
Given:
The length of the prism = 5 ft.
The width of the prism = 1.5 ft.
The height of the prism = 1,25 ft.
The pole is in the shape of a rectangle with length =1.25ft and width =1.5 ft.
To find:
We need to find the area of both poles.
Explanation:
The area of both poles = 2 times the area of the rectangle with length =1.25ft and width =1.5 ft.
Consider the formula to find the area of the rectangle.
[tex]A=lw[/tex]Substiutitue l=1.25 and w=1.5 in the formula.
[tex]A=1.25\times1.5[/tex][tex]A=1.875ft^2[/tex]Multiply the equation by 2.
[tex]2A=2\times1.875ft^2[/tex][tex]2A=3.75ft^2[/tex]Final answer:
Rahul can save 3.75 square feet of aluminum per pole.
A. How many jars of peppermint candies are represented on the histogram?
By taking into account the number of jars of each bar, you can conclude that the number of jars are:
5 + 1 + 4 + 3 + 2 = 15
There are 15 jars
Factor f(x)= x2 - 13x - 168 ?
To factor the given equation, we would begin by taking all possible factors of -168. Next step is to identify which of these factors would add up to -13.
One pair of factors of -168 is 8 and -21. These also add up to -13