The given function is:
[tex]\begin{gathered} f(x)=x^2+x+1 \\ \text{Interval } \\ \lbrack0,6\rbrack \end{gathered}[/tex]Start by evaluating the function in the extreme values of the interval:
[tex]\begin{gathered} f(0)=0^2+0+1 \\ f(0)=1 \\ \text{And} \\ f(6)=6^2+6+1 \\ f(6)=36+6+1=43 \end{gathered}[/tex]The intermediate value theorem states: if a function f is continuous in an interval [a,b], and k is any number between f(a) and f(b), then there exists a number c between a and b such that f(c)=k.
As k=13 and it is between 1 and 43, then there is a number c such that f(c)=13.
Now, replace f(c) by 13 and solve for c:
[tex]\begin{gathered} 13=c^2+c+1 \\ \text{Subtract 13 from both sides} \\ 13-13=c^2+c+1-13 \\ 0=c^2+c-12 \end{gathered}[/tex]Let's find the factored form to find the c-values:
[tex]\begin{gathered} c^2+c-12=(c+4)(c-3) \\ \text{Then equal both factors to zero and solve for c} \\ c+4=0 \\ c=-4 \\ \text{and} \\ c-3=0 \\ c=3 \end{gathered}[/tex]As -4 is not in the interval, thus the value of c guaranteed by the theorem is c=3.
What is the value of x in the parallellogram below?
Given:
Side DC=
[tex]5x-6[/tex]Side AB=
[tex]9x-30[/tex][tex]\angle A=110\degree[/tex]Required:
The value of
[tex]x[/tex]Answer:
We know that the opposite sides of the parallelogram are equal.
Therefore,
side DC = side AB
[tex]\begin{gathered} 5x-6=9x-30 \\ 9x-5x=-6+30 \\ 4x=24 \\ x=6 \end{gathered}[/tex]Final Answer:
The value of
[tex]x=6[/tex]identifying calculate the area and perimeter for the fourth triangle
We have to calculate the area and perimeter of this triangle.
This is a right triangle because it has a right angle.
We can calculate the area as half the product of the two legs, sides a and b:
[tex]A=\frac{a\cdot b}{2}=\frac{7.9\cdot6}{2}=\frac{47.4}{2}=23.7[/tex]The perimeter is equal to the sum of the length of the three sides:
[tex]P=a+b+c=7.9+6+9.92=23.82[/tex]Answer:
Area: 23.7 cm²
Perimeter: 23.82 cm
Type: right triangle.
Eva measured the lengths of 5 local fields. she measured: 39 feet, 36 feet, 34 feet, 36 feet, 32 feet What was the median lenght of the fields, in the feet
Median: Middle number in a list of values. If there is an even number of values then average the middle two values together.
List: {32ft,34ft,36ft,36ft,39ft}
Therefore:
Median = 36ft
x - 2y + z = 4 x + y +z=2 3x + 3y + 3z = 14elimination method
To use elimination method we are going to multiply the first equation by -4 as:
(x - 2y + z)(-4) = 4(-4)
-4x + 8y - 4z = -16
Then, we can sum the equations as:
- 4x + 8y - 4z = -16
x + y + z = 2
3x + 3y + 3z = 14
0 + 12y + 0 = 0
So, we get the equation 12y = 0. It means that y is equal to 0
12y = 0
y = 0
Then, if we replace y by 0 on the initial equations, we get:
x + z = 4
x + z = 2
Since the sum of two numbers can't be 4 and 2 at the same time, the system doesn't have a solution.
Answer: the system doesn't have a solution.
Kate wants to buy some daisies for $6.99, some potting soil for $3.98, and a ceramic pot for $7.95. She has $20.00.Which number sentence represents the amount of change Kate receives back?
Given:
Kate wants to buy some daisies for $6.99, some potting soil for $3.98, and a ceramic pot for $7.95. She has $20.00
Required:
Amount of change Kate receives back?
Explanation:
We will add each expense
[tex]6.99+3.98+7.95=18.92[/tex]Now, amount of change Kate receives back is 20.00 - 18.92 = 1.08
Answer:
Hence, amount of change Kate receives back is 1.08
Questio 13 At a butcher shop, Hilda bought 7 11 lb of beef and some pork. She left with 18 25 20 number of pounds of pork she bought using a decimal. lb of meat. Exp
Hilda bought 7 13/25 lb of bee
simplify the ratio 41.6 to 28.8
We want to simplify the following ratio:
[tex]41.6\colon28.8[/tex]Let's multiply both numbers by 10, so we don't need to deal with decimals.
[tex]\frac{41.6}{28.8}=\frac{416}{288}[/tex]Now, let's factorize both numbers to get their greatest common factor
[tex]\begin{gathered} 416=2\times2\times2\times2\times2\times13=32\times13 \\ 288=2\times2\times2\times2\times2\times3\times3=2^5\times9=32\times9 \end{gathered}[/tex]The greatest common factor is 32. Divinding both numerator and denominator by 32, we have
[tex]\frac{416/32}{288/32}=\frac{13}{9}[/tex]Our simplified ratio is 13/9.
The operations that are on a circle are wrong, I need you to correct them, please.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as folloows:
[tex]\begin{gathered} Sample\text{ 1\rparen} \\ 3\text{ x 5 = 15 } \\ \text{3 + 5 = 8} \end{gathered}[/tex][tex]\begin{gathered} Sample\text{ 2 :} \\ \text{2 x 4 = 8} \\ \text{2 + 4 = 6} \end{gathered}[/tex][tex]\begin{gathered} Sample\text{ 3:} \\ 1\text{ x 10 = 10} \\ 1+\text{ 10 = 11} \end{gathered}[/tex][tex]\begin{gathered} Sample\text{ 4:} \\ -\text{ 5 x 7 = -35} \\ -5\text{ + 7 = 2} \end{gathered}[/tex]
PART TWO:
[tex]\begin{gathered} 1)\text{ }4\text{ x 6 = 24} \\ \text{ 4 + 6 = 10} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} 2)\text{ 3 x 2 = 6} \\ 3+\text{ 2 = 5} \end{gathered}[/tex][tex]\begin{gathered} 3) \\ 7\text{ x - 8 = -56} \\ 7\text{ + \lparen-8\rparen = 7 - 8 = -1} \end{gathered}[/tex][tex]\begin{gathered} 4) \\ -7\text{ x 3 = -21} \\ -7\text{ + 3 = -4} \end{gathered}[/tex][tex]\begin{gathered} 5) \\ 10\text{ x 11 = 110} \\ 10\text{ + 11 = 21} \end{gathered}[/tex][tex]\begin{gathered} 6) \\ -1\text{ x 3 = -3} \\ -1\text{ + 3 = 2} \end{gathered}[/tex][tex]\begin{gathered} 7) \\ -6\text{ x - 4 = 24} \\ -6\text{ + \lparen-4 \rparen = -6 - 4 = -10} \end{gathered}[/tex][tex]\begin{gathered} 8) \\ 7\text{ x 5= 35} \\ \text{7 + 5 = 12} \end{gathered}[/tex][tex]\begin{gathered} 9) \\ 5\text{ x 12 = 60} \\ 5\text{ + 12 = 17} \end{gathered}[/tex][tex]\begin{gathered} 10) \\ (-3)\text{ x \lparen -6 \rparen = -18} \\ (-3)\text{ + \lparen -6 \rparen = -3 - 6 = -9} \\ \end{gathered}[/tex]
5. Write the equation of the line in slope-intercept form given the following:Point (1, 4), slope6
You use the slope and the given point to find the equation of the line in slope-intercept form, as follow:
slope m=6
point (x,y)
x=1
y=4
A box with an open top has a square base and four sides of equal height. The volume of the box is 539 ft^3. The height is 4 ft greater than both the length and the width. If the surface area is 357 ft^2, what are the dimensions of the box?
A box with an open-top has a square base and four sides of equal height.
The volume of the box is 539 ft^3.
The surface area is 357 ft^2
Let H is the height, L is the length and W is the width.
The volume is given by
[tex]\begin{gathered} V=L\cdot W\cdot H \\ 539=L\cdot W\cdot H \end{gathered}[/tex]The height is 4 ft greater than both the length and the width.
[tex]W=L=H-4[/tex]The surface area is given by
find the missing interest earned. (round to the nearest cent as needed)
The compound interest is $625.41
Here, we want to calculate the missing amount, which is the interest earned
Mathematically, this is the difference between the amount that the compounding will yield and the principal
We can calculate the amount earned using the formula below;
[tex]A\text{ = P(1 + }\frac{r}{n})^{nt}[/tex]where;
P is the principal = $1,000
r is the interest rate = 7% which is same as 7/100 = 0.07
n is the number of times the interest is compounded per year
According to the question, the compounding is quarterly which means 4 times per year
so n = 4
t represents the number of years = 7
Substituting these values into the equation, we have;
[tex]\begin{gathered} A\text{ = 1000(1 + }\frac{0.07}{4})^{7\times4} \\ \\ A=1000(1+0.0175)^{28} \\ \\ A=1000(1.0175)^{28} \\ \\ A\text{ = 1,625.41} \end{gathered}[/tex]So now, we can get the compound interest using the formula below;
[tex]\begin{gathered} \text{compound interest = Amount - Principal} \\ \\ =\text{ 1,625.41-1000 = 625.41} \end{gathered}[/tex]Santa has a leak in Santa's fuel tank. Santa lost three gallons last week and five gallons this week. What number should Santa add to the amount Santa started with to find what Santa has left? (Hint: Santa will be adding a negative number.)
Solution:
According to the problem, consider the following amounts:
fuel leak last week = 3 gallons.
fuel leak this week = 5 gallons
then, the total fuel leak is 3 gallons + 5 gallons = 8 gallons.
Now, according to the hint given in the problem (Santa will add a negative number), we can say that the number Santa must add to the amount of fuel he started with to find the remaining fuel is:
- 8
So that, the correct answer is:
- 8
IfA={1,2,4 and B = {2, 4, 6, 8, 10), find A n B.{2,4}{1,2,4,6,8,10){1, 6, 8, 10){}
The set given:
A={1,2,4} and B={2,4,6,8,10}
A n B simply means A intersection B, that is; those elements that are in A and at the same time, are also in B.
Hence, A n B = { 2, 4}
You need to combine like terms first and fill in the follow definition to set up an equation to find the number of students in Mr. Bogue‘s house is a total number of students in eighth grade is 90.
Solution:
Given the initial equation;
[tex]b+1.5(b+2)+15+2b-9=90[/tex]Remove the bracket;
[tex]b+1.5b+3+15+2b-9=90[/tex]
Collect like terms;
[tex]\begin{gathered} b+1.5b+2b+3+15-9=90 \\ \\ 4.5b+9=90 \end{gathered}[/tex]ANSWER:
[tex]4.5b+9=90[/tex]Find the coordinates of the center, vertices, covertices, foci, length of transverse and cojugate axis and the equation of the asymptotes. Then graph the parabola.
The given equation is:
[tex]\frac{x^2}{9}-\frac{y^2}{49}=1[/tex]The equation matches the general equation of a hyperbola given by:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]Hence a=3 and b=7.
The center is at origin (0,0)
The vertices are at (3,0) and (-3,0)
The focii are:
[tex](\sqrt[]{58},0),(-\sqrt[]{58},0)[/tex]The equation of the asymptotes are:
[tex]y=\frac{7x}{3},y=-\frac{7x}{3}[/tex]There are no covertices since the hyperbola does not have covertices.
The graph is given below:
28 is equal to 4 more than 3 times a number. what is the number?
Let the number be m
The statement can be wriiten as
28 = 4 + 3p
solving this equation , we have
-3p = 4-28
-3p = -24
p = -24/-3
p=8
The number is 8
I NEED HELP IN UNDER 10 MINUTES, just tell me the X
Given the triangle ΔABC as shown below:
Required: value of x.
Step 1:
Using 30° as the focus angle, label the sides of the triangle.
Thus,
[tex]\begin{gathered} AB\Rightarrow hypotenuse \\ AC\Rightarrow adjacent \\ BC\Rightarrow opposite \end{gathered}[/tex]Step 2:
Evaluate the length x
[tex]\begin{gathered} \tan \text{ 30 = }\frac{opposite}{adjacent} \\ \tan \text{ 30 = }\frac{BC}{AC} \\ \text{but tan 30 = }\frac{\sqrt{3}}{3} \\ \text{thus,} \\ \frac{\sqrt[]{3}}{3}\text{ = }\frac{\sqrt[]{2}}{x} \\ x\times\sqrt[]{3}\text{ = }\sqrt[]{2}\text{ }\times\text{ 3} \\ \Rightarrow x\text{ = }\frac{3\sqrt[]{2}\text{ }}{\sqrt[]{3}}\text{ } \end{gathered}[/tex]Step 3:
Rationalize the denominator.
Thus,
[tex]\begin{gathered} \text{ }\frac{3\sqrt[]{2}\text{ }}{\sqrt[]{3}}\text{ }\times\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ =\frac{3\sqrt[]{2}\text{ }\times\sqrt[]{3}}{3} \\ =\frac{3\sqrt[]{6}\text{ }}{3} \\ \text{Thus, } \\ x=\sqrt[]{6}\text{ } \end{gathered}[/tex]Hence, the lenth of
When the coming interpretations in the garegression iscrete2-thecite of the difference of sumes the square afy and mail divided by 2.mesthesia afytheme of the difference of the sure times and also the suare of timesСсthe site of the difference of somes the square ar yandal cividest on the square of mythe difference of the cube aumes the square of yang al die by 2 times the square afyResetNetINTEO
Given the expression below,
[tex]\frac{(5y^2-7)^3}{(2y)^2^{}}[/tex]The correct interpretation is,
The cube of the difference of 5 times the square of y and 7 all divided by the square of 2 times y.
Answer is C.
Which of the values is not a solution to the inequality. 2x - 5 < 13 12 2
hello
the equation of the inequality given is
[tex]2x-5\le13[/tex]we'll do this in steps
step 1
collect like terms
to do this, take -5 to the right hand side of the equation to meet 13. note that the sign of the number crossing the inequailty sign must change
[tex]undefined[/tex]CalculatorWhat is the measure of angle P?13 cm5 cmEnter your answer as a decimal in the box. Round only your finalanswer to the nearest hundredth.12 cmR.MZP=12345
Step 1: Problem
Find the measure of angle P
Step 2: Concept
Apply cosine ratio formula
Step 3:
Given data
Hypotenuse = 13cm side facing right angle
Opposite = 12cm side facing given angle P
Adjacent = 5cm
[tex]\begin{gathered} \theta\text{ = p} \\ \cos \theta\text{ = }\frac{adjacent}{\text{Hypotenuse}} \\ \cos p\text{ = }\frac{5}{13} \\ \cos \text{ p = 0.3846153846} \\ p\text{ = }\cos ^{-1}\text{ 0.3846153846} \\ p\text{ = 67.380135} \end{gathered}[/tex]Step 4: Final answer
Angle
assume a sample is used to estimate a population proportion P. find the margin of error E that corresponds to the given statistics and confidence level. round margin of error to four decimal places99% confidence; n=6500, x=1950
SOLUTION
99% confidence; n=6500, x=1950
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places.
The margin of error is known to be the maximum likely difference between the point estimate of a parameter and the actual value of the parameter. For one population proportion, p, the margin of error is computed as follows:
Margin of Error =
[tex][/tex]I need help knowing how to find the answer to number 28.
we have that
In a kite the larger diagonal, divide the kite into two congruent triangles
that means
m
Remember that the sum of the interior angles in any quadrilateral must be equal to 360 degrees
so
360=18+62+2m360=80+2m2m2mm
so I think I got nine correct but 10-11 are part of the same problem and I'm not sure to go from here
Tell whether the ordered pair (-1, 3) is a solution of the system of linear equations.y= -7x -4y = 8x + 5
To determine if the ordered pair (-1, 3) is the solution of the system, we replace the values of the x-component and y-component in x & y respectively in each function, that is:
[tex](3)=-7(-1)-4\Rightarrow3=3[/tex][tex]3=8(-1)+5\Rightarrow3\ne-3[/tex]From these solutions, we can see that the ordered pair (-1, 3) is no solution for the system of linear equations given.
Dante divided 642 by 8 and wrote the quoitent as 8 remainder 2. What error did Dante Make? What is the correct answer?
the mistake dante made was a miscalculation in the quoitent
At an ice cream shop, jars of chocolate sauce are stored in boxes in the pantry. Each box contains 10 jars of chocolate sauce. A candy store employee uses 3 jars from one of the boxes to put on top of the ice-cream. Which function shows the relationship between y, the total number of jars of chocolate sauce remaining in the pantry, and x, the number of boxes in the pantry?A. y = 7xB. 10x + 7C. 10x - 3D. y = 10x
Variables:
y: total number of jars of chocolate sauce remaining
x: number of boxes
Each box contains 10 jars of chocolate sauce. Then, x boxes contain 10x jars
If 3 jars are used, the remaining jars are:
y = 10x - 3
A chef cooks 5/6 of a pound of pasta. She plans toserve 1/12 of a pound to each customer. How manycustomers can she serve?
hello
this is a simple algebraic question where we would use ratios to solve it
the chef intends to cook 5/6 pounds of pasta and plans to share it amongst x number of customers in ratio 1/12.
to find the number of customers, divide the quantity of the pasta by the ratio she intends to serve them with.
[tex]\begin{gathered} \text{number of customers }=\text{ }\frac{5}{6}\text{ / }\frac{1}{12} \\ \text{number of customers }=\text{ }\frac{5}{6}\times\frac{12}{1} \\ \text{number of customers }=\text{ }\frac{60}{6} \\ number\text{ of customers }=\text{ 10} \\ \end{gathered}[/tex]she's can serve a maximum of 10 customers.
i have AP calculus problems i need help withAt a certain instance, the length of a rectangle is 3 inches and is increasing at the rate of 1 inch per minute. At the same instant, the width is 2 inches and is decreasing at the rate of .5 inches per minute. Is the area increasing or decreasing?
Given
Length = 3 inches , dl/dt = 1 inch/minute
width = 2 inches , db/dt = -0.5 inch/minute
Find
Is the area increasing or decreasing?
Explanation
as we know , area = length * breadth
so ,
[tex]A=l\times b[/tex]differentiate with respect to t.
so ,
[tex]\frac{dA}{dt}=l\frac{db}{dt}+b\frac{dl}{dt}[/tex]now substitute the values,
[tex]\begin{gathered} \frac{dA}{dt}=3(-0.5)+2(1) \\ \\ \frac{dA}{dt}=-1.5+2 \\ \\ \frac{dA}{dt}=0.5\text{ }inch\text{ }per\text{ }minute \end{gathered}[/tex]therefore , area is increasing at the rate of 0.5 inch per minute
Final Answer
Hence , the area is increasing at the rate of 0.5 inch per minute.
3 fair coins are tossed. What is the probability that at least one is a tail (enter the probability as a fraction.)
First, you should find:
Probability of NOT getting a tail in 3 coin toss:
[tex](\frac{1}{2})^3=\frac{1}{8}[/tex]After that, you should find the probability of getting at least one tail in 3 fair coins tossed
[tex]1-\frac{1}{8}=\frac{8-1}{8}=\frac{7}{8}[/tex]Answer: 7/8
Draw a triangle with sides a=6 b=8 c=10 label vertices A B C number 3
The Solution.
The triangle to be drawn must be a right-angled triangle since it is link with trigonometric ratios. So, below is the right-angled triangle:
By Trigonometrical Ratios,
[tex]\sin A=\frac{opposite}{\text{Hypotenuse}}=\frac{6}{10}=\frac{3}{5}\text{ or 0.6}[/tex]Similarly,
[tex]\cos A=\frac{\text{Adjacent}}{\text{Hypotenuse}}=\frac{8}{10}=\frac{4}{5}\text{ or 0}.8[/tex]Also, by Trigonometrical Ratio,
[tex]\tan A=\frac{\text{opposite}}{\text{Adjacent}}=\frac{6}{8}=\frac{3}{4}\text{ or 0}.75[/tex]