First we need to factorate the number 40:
[tex]40=2\cdot2\cdot2\cdot5[/tex]The possible numbers we can create using these factors are 2, 4, 5, 8, 10 and 20.
So If the product of the two factors (let's call them 'a' and 'b') is 40 and the sum is 14, we have:
[tex]\begin{gathered} a\cdot b=40 \\ a+b=14 \\ \\ \text{From the second equation:} \\ b=14-a \\ \\ \text{Using this value of b in the first equation:} \\ a(14-a)=40 \\ 14a-a^2=40 \\ a^2-14a+40=0 \end{gathered}[/tex]Using the quadratic formula to solve this equation, we have:
[tex]\begin{gathered} a_1=\frac{-b+\sqrt[]{b^2-4ac}}{2a}=\frac{14+\sqrt[]{196-160}}{2}=\frac{14+6}{2}=10 \\ a_2=\frac{-b-\sqrt[]{b^2-4ac}}{2a}=\frac{14-6}{2}=4 \\ \\ a=10\to b=14-10=4 \\ a=4\to b=14-4=10 \end{gathered}[/tex]So the factors which product is 40 and the sum is 14 are 4 and 10.
Question 3: 11 ptsArating for the school bus, Bruce records the colors of all cars passing through an intersection. The tablethe results. Estimate the probability that the next car through the intersection will be black. Express youras a percent. If necessary, round your answer to the nearest tenth.
To find the probability that the next car through the intersection will be black divide the number of black car by the total number of cars.
The total number of cars is the sum of the number of cars of each color, which is 58.
[tex]P=\frac{9}{58}=0.155[/tex]Expressed as a percent it is 15.5%.
It means that the correct answer is the last choice.
7-Which beans are the better deal? O Kidney Beans $1.18 per Ib Lima Beans $2.13 for 2 lbs 7b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 07 00, so if answer is 43 cents, its 043 or 43, if there is a dollar amount ke 1.50, do not add zeros in front) Your answer
Kidney $1.18 per 500g
Lima. $ 2.13. Per 2 lbs= 1000g
Then
Kidney = 1.18 x 1 lb
Lima = 2.13/2= 1.065 x 1 lb
So ANSWER IS :Better deal Is LIMA BEANS
Part 7b
UNIT PRICE for better deal is
LIMA BEANS , At $1.065 per lb
wich statement explain how Andy could prove what kind of quadrilateral this is ?
The first step is to locate the points to find what kind of quadrilateral this is.
The next step is to find the lengths of the diagonals, if both have the same length then the quadrilateral is a rectangle, if the don't the quadrilateral is a parallelogram.
When looking at the picture is easy to determine that the quadrilateral is a parallelogram, but the statement that could prove what kind of quadrilateral this is is C. Find the lengths of the diagonals to show that the quadrilateral is a parallelogram.
?What is the factored form of x6 - 9?O(x + 3)(x – 3)(x5 + 3)(x – 3)o(x3 + 3)(x2 - 3)o(x3 + 3)(x3 - 3)+DONE
Answer:
[tex]\lparen x^3+3)\left(x^3-3\right)[/tex]Explanation:
Given the expression
[tex]x^6-9[/tex]It can be rewritten as
[tex]x^{2\cdot3}-3^2=\lparen x^3)^2-3^2[/tex]Use the formula
[tex]a^2-b^2=\left(a+b\right)\left(a-b\right)[/tex]to get
[tex]\lparen x^3+3)\left(x^3-3\right)[/tex]which is the factored form of the given expression.
Answer:
It's Option D
Step-by-step explanation:
edge
What plus Ten equals thirty two
What plus Ten equals thirty two is equivalent to
x + 10 = 32
10 is adding on the left, then it will subtract on the right
x = 32 - 10
x = 22
what is the best estimate for the value of the expression? [tex] ( \frac{34}{8} - \frac{16}{3}) - \frac{14}{9} [/tex]A. -3B.[tex] - 2 \frac{1}{2} [/tex]C. 7D. [tex]7 \frac{1}{2} [/tex]
-95/34
Explanation:
[tex](\frac{34}{8}-\frac{16}{3})-\frac{14}{9}[/tex]Simplify the expresssion:
[tex]\begin{gathered} \text{LCM for the one in the bracket is 24} \\ \frac{34(3)-8(16)}{24}-\frac{14}{9} \\ \frac{102-128}{24}-\frac{14}{9} \\ =\text{ }\frac{-26}{24}-\frac{14}{9} \end{gathered}[/tex][tex]\begin{gathered} \frac{-26(3)\text{ -14(8)}}{72} \\ =\text{ }\frac{-78-112}{72}=\text{ }\frac{-190}{72} \\ =\frac{-95}{36} \end{gathered}[/tex]None of the options has this value.
There is likely an error in question.
HiI’m bad at math I decided to practice but get confused Not is not assignment
Solution
Name an acute angle for which each of the angles are associated in terms of trig ratios:
Trigonometry ratios include sine, cosine and tangent
The associated angles interms of relation to acute angle is which of them is equivalent
[tex]sin150=sin30[/tex][tex]tan225=tan45[/tex][tex]cos300=cos60[/tex]1. Given that f(x)=x²-4 and that g(x)=√√x-1:
A. State (f-g)(x) and (fog)(x).
B. State
and determine its domain.
C. Determine whether each of the following functions is odd, even, or neither odd nor
even: f(x)=x²-4, g(x)=√√x-1.
D. State (g/f)(x) and find all vertical asymptotes.
Please show work! Thank you so much!
Given the functions are,
[tex]f(x)=x^2-4\\g(x)=\sqrt[3]{x-1}[/tex]
Then the subtraction of functions is given by,
[tex](f-g)(x)=f(x)-g(x)=x^2-4-\sqrt[3]{x-1}[/tex]
Again,
[tex](f\circ g)(x)=f(g(x))=f(\sqrt[3]{x-1})=(x-1)^{2/3}-4[/tex]
And,
[tex]\left(\frac{f}g{}\right)(x)=\frac{f(x)}{g(x)}=\frac{x^2-4}{\sqrt[3]{x-1}}[/tex], it exists when x not equals to 1.
So domain of the function is all real number except 1.
Since, [tex]f(-x)=(-x)^2-4=x^2-4=f(x)[/tex], then the function is an even function.
Since [tex]g(-x)=\sqrt[3]{-x-1}[/tex], so it is neither odd function nor even function.
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CWhich of the following is the inverse of F(x)=2x+3?COAa 4520-19B.0 с.OD.103765PREVIOUSG Search or type URI(3,0)(15,0)3YSUBMIT
We have to find the inverse of the function f(x) = 2x + 3.
We can find the inverse function as:
[tex]\begin{gathered} f(f^{-1}(x))=x \\ 2f^{-1}(x)+3=x \\ 2f^{-1}(x)=x-3 \\ f^{-1}(x)=\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]From the options we can see that the slope has to be positive, so we can discard optiosn B and C.
Then, we can check option A:
- It has a y-intercept of -1.5, which is equal to -3/2.
- The x-intercept is (3,0), what indicates that it increases 0.5 units of y per unit increase in x. This corresponds to a slope of 0.5 or 1/2.
Then, as both characteristics match with the equation of the inverse, the right representation is option A.
Answer:
The inverse is f^-1(x) = 1/2*x - 3/2 [Option A]
For which graph is the parent function y = x2
Answer:
Answer d
Step-by-step explanation:
Make sure to get another answer + can you make sure if there is answer choices, please and thx
Rushdoors,
LSPLASH DOORS
:)
Type the correct answer in each box. Use numerals instead of words. If necessary, use/ for the fraction bar(s).The equation of a circle is given.2+ y²+6x+10y+18=0Determine the center and radius of the circle.) and the radius of the circle isunits.The center of the circle is at (ResetNext
ANSWER
[tex]\begin{gathered} center=(-3,-5) \\ r=4 \end{gathered}[/tex]EXPLANATION
Given;
[tex]x^2+y^2+6x+10y+18=0[/tex]The standard equation of circle of a circle centered at (h,k) with radius r is;
[tex](x-h)^2+(y-k)^2=r^2[/tex]Re-write the given equation in the standard form, we have;
[tex]\begin{gathered} x^{2}+y^{2}+6x+10y+18=0 \\ x^{2}-6x+(\frac{6}{2})^{2}+y^{2}+10y+(\frac{10}{2})^{2}=-18+9+25 \\ (x-3)^2+(y-5)^2=4^2 \end{gathered}[/tex]Hence, h=-3, k=-5, radius is 4
Express the number in scientific notation 6,340,000,000
Solution:
The number is given below as
[tex]6,340,000,000[/tex]Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form
Concept:
count the number from the last number and then stop in front of the first number 6 and then multiply in powers of 10
The general form of a scientific notation is given below as
By applying the concept, we will have
[tex]\begin{gathered} 6,340,000,000=6.34\times1,000,000,000 \\ 6,340,000,000=6.34\times10^9 \end{gathered}[/tex]Hence,
The final answer is
[tex]6.34\times10^9[/tex](10) When using substitution to solve this system of equations, what is the result of the first step? Eq#1 y = 6x + 3 Eq#2 x + 2y = 5
Given data:
The first equation given is y = 6x + 3.
The second equation given is x + 2y = 5.
Subsitute (6x+3) for y in second equation.
[tex]x+2(6x+3)=5[/tex]Thus, the first option is correct.
Perform the indicated operation 2 3/4-(-1 1/2) show all the work and give your answer as a fraction
2 3/4-(-1 1/2)=
2 3/4 + 1 1/2=
(2+1) (3/4 + 1/2)=
3 + 5/4=
3 + 1 1/4=
4 + 1/4=
4 1/4 or 17/4 or 4.25
13. You have $19.50 to buy subs for a party. Each sub costs $5.10. Estimate how many subs you can buy. Is your estimate too little or too much?
Let N be the number of subs, then we can write the following relationship:
[tex]5.10\cdot N=19.5[/tex]That is, this equality gives us the number of subs we can buy. If we move 5.10 to the right hand side, we have
[tex]\begin{gathered} N=\frac{19.50}{5.10} \\ N=3.82 \end{gathered}[/tex]this means that we can buy 4 subs approximately.
how does a to the 4 b to -5 over c to -3 d to the 6th get simplified?
Given the expression
[tex]\frac{a^4b^{-5}}{c^{-3}d^6}[/tex]To simplify the expression above, we convert all negative indices to positive indices
Applying the rule of indices
[tex]a^{-x}=\frac{1}{a^x}[/tex]Applying the rule to the given expression gives
[tex]\begin{gathered} \text{Where b}^{-5}=\frac{1}{b^5}\text{ and} \\ c^{-3}=\frac{1}{c^3} \end{gathered}[/tex]Substitute the above deduction into the given expression
[tex]\begin{gathered} \frac{a^4b^{-5}}{c^{-3}d^6}=a^4\times\frac{1}{b^5}\times\frac{1}{\frac{1}{c^3}}\times\frac{1}{d^6} \\ \text{Where }\frac{1}{\frac{1}{c^3}}=c^3 \\ =a^4\times\frac{1}{b^5}\times\frac{1}{\frac{1}{c^3}}\times\frac{1}{d^6}=a^4\times\frac{1}{b^5}\times c^3\times\frac{1}{d^6} \\ =\frac{a^4c^3}{b^5d^6} \\ \frac{a^4b^{-5}}{c^{-3}d^6}=\frac{a^4c^3}{b^5d^6} \end{gathered}[/tex]Hence, the simplified form is
[tex]\frac{a^4c^3}{b^5d^6}[/tex]complete the function table for the given domain and plot the points on the graph f(x)=2^x-7x. 0. 1. 2. 3. 4. f(x) . . . . graph
we have the following:
[tex]f(x)=2^x-7[/tex]replacing:
[tex]\begin{gathered} f(0)=2^0-7=1-7=-6;(0,-6)^{} \\ f\mleft(1\mright)=2^1-7=2-7=-5;(1,-5) \\ f\mleft(2\mright)=2^2-7=4-7=-3;(2,-3) \\ f(3)=2^3-7=8-7=1;(3,1) \\ f(4)=2^4-7=16-7=9;(4,9) \end{gathered}[/tex]x 0 1 2 3 4
f(x) -6 -5 -3 1 9
For the data shown in the plot below identify a point apart from the main cluster
(8, 7) or (8.5, 7.5)
See explanation below
Explanation:From the graph, there are two points away from the main clusters.
This is because their distance compared to other points is far apart. The main cluster is where most of the points are located
The two points are (x, y): (8, 7) and (8.5, 7.5)
In the absence of options, you can pick any of the points as the point that is apart from the cluster.
A house addition is in the shape of a semicircle (a half-circle) with a radius of 9 ft. What is itsarea?
We find its area as follows:
[tex]A=\frac{1}{2}\pi r^2[/tex][This is the equation for the area of a circle divided by 2] Now, we replace the radius:
[tex]A=\frac{1}{2}\pi(9)^2\Rightarrow A=\frac{81}{2}\pi\Rightarrow A\approx127.23[/tex]So, the area of the semi-circle is approximately 127.23 squared feet.
+ Type a messageSend2Help Mark use completing the square with the algebra tiles to convert this standard form equation to vertexform. Draw the tiles using this method and show the algebraic steps that take you from this equation to itsequivalent vertex form. Then state the vertex.014Show Your WorkCorrect answer y=xThis assignment has been submitted and is no longer editable.Client time: 5/13/2021, 6:06:10 PM (America/Los_Angeles)Server time: 5/13/2021, 6:06:10 PM (-70.44)Missing.omeos StommKB
From the image.
we have
1 y
1 x^2
6 x
8 (1squares)
We can write the standard equation as
[tex]y=x^{2^{}}+\text{ 6x +8}[/tex]But we need to express it in vertex form y = a(x-h)^2 + k where (h,k) is the vertex
to complete the squares we need to express the equation as
y = (x^2+6x+8+__)-___
to complete the square we need to add +1 inside the parenthesis and -1 outside
y = (x^2+6x+8+1)-1
We can express the equation
y = (x+3)^2 -1
[tex]y=(x+3)^2-1[/tex]find the probability of obtaining five heads when flipping five coins. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
1/32
Explanation:In an experiment, we can only get head or tail:
Probability of getting a head = 1/2
Probability of obtaining five heads when flipping five coins:
[tex]\begin{gathered} \text{Probability = (1/2)}^{number\text{ of flips}} \\ \text{Probability = (1/2)}^5 \\ \end{gathered}[/tex][tex]\text{Probability = 1/32}[/tex]Find the surface area of this cone. I think the inside is hollow? Im not sure what to do with this problem to be honest
Let us start this problem by analyzing the area we want to calculate
.
To calculate the surface area we will divide the are in two parts:
[tex]\text{ The total area = Area of the base + area of the inner and outer cone}[/tex]The area of the base:
The area of the base can be calculated as the difference between the areas of the to disks , as follows:
[tex]\begin{gathered} \text{ Area of the base=Area of the outer disk - area of the inner disk} \\ =\pi(12)^2-\pi4^2 \\ \\ =128\pi \\ \end{gathered}[/tex]Where we use twice the formula for the area of a circle pi*radius^2, for the outer disk the radius is 12 and for the inner disk the radius is 4.
The lateral area of the two cones, the outer and the inner
Now we will calculate the lateral area of a cone (that is we will not include the base) this area is illustrated by the following draw:
The lateral area of a cone can be calculated using the next formula
[tex]\text{ Lateral area of a cone=}\pi r\sqrt{h^2+r^2}[/tex]Where h is the height of the cone, and r is the radius of the base, for the bigger cone we know from the figure that the height is 6 ft and the radius is 12 ft, for the smaller cone we also know from the figuere that the height is 3 ft and the radius is 4 ft. Therefore we can calculate:
[tex]\begin{gathered} \text{ Lateral area of the bigger cone= }\pi12\sqrt{6^2+12^2} \\ \\ =12\pi\sqrt{180} \end{gathered}[/tex]and
[tex]\begin{gathered} \text{ Lateral area of the smaller cone= }\pi4\sqrt{3^2+4^2} \\ \\ =4\pi\sqrt{25} \\ \\ =20\pi \end{gathered}[/tex]Finally, putting all the areas together we find that:
[tex]\begin{gathered} \text{ The total area= The area of teh base+ the lateral area of the two cones} \\ \\ =128\pi+12\sqrt{180}\pi+20\pi \\ \\ =148\pi+12\sqrt{180}\pi \\ \\ =148\pi+72\sqrt{5}\pi \end{gathered}[/tex]a chemical company makes two brands of antifreeze. the first brand is 45% pure antifreeze and the second brand is 70% pure antifreeze. in order to obtain 170 gallon of a mixture that contains 65% pure antifreeze how many gallons of each brand of antifreeze mudt be used
Answer:
The first brand is 34 gallons
The second brand is 136 gallons
Explanation:
Let x represent the first brand, and
y represent the second brand
The total number of gallons of mixture to be obtained is 170, so
x + y = 170 .................................................................................(1)
And
45% of x + 70% of y = 65% of (x + y)
0.45x + 0.7y = 0.65(x + y)
0.45x - 0.65x = 0.65y - 0.7y
0.2x = 0.05y
Divide both sides by 0.05
4x = y ...........................................................................................(2)
Solving (1) and (2) simultaneously
Using (2) in (1)
x + 4x = 170
5x = 170
Divide both sides by 5
x = 170/5 = 34
Put x = 34 in (2)
4(34) = y
y = 136
A car company charges $42.50 per day to rent a car in 10 since for every mile driven Lydia wants to rent a car knowing that she plans to drive 225 miles and she has at most a $150 to spend
Explanation:
d: number of days.
m: number of miles.
The total cost of the car 'y' is:
[tex]y=42.5d+0.1m[/tex]Lydia plans to drive 225 miles, this is m = 225. And she has $150 to spend, so we have to solve y ≤ 150.
The inequality to solve is:
[tex]\begin{gathered} y\le150 \\ 42.5d+0.1\cdot225\le150 \\ 42.5d+22.5\le150 \end{gathered}[/tex]Solving the inequality:
[tex]\begin{gathered} 42.5d+22.5\le150 \\ 42.5d\le150-22.5 \\ 42.5d\le127.5 \\ d\le\frac{127.5}{42.5} \\ d\le3 \end{gathered}[/tex]Lydia can afford 3 days at most.
Answers:
• Inequality: ,42.5d + 22.5 ≤ 150
,• d ≤ 3
what is 1 + 1 and two times 15
Solution
1 + 1= 2
2* 15= 30
f(x) = -x^2 + x + 13Find f(9)
To answer this question, we need to substitute the value of 9 into the quadratic function as follows:
[tex]f(9)=-(9)^2+9+13=-81+22\Rightarrow f(9)=-59[/tex]Therefore, the answer is f(9) = -59.
Hi I just need a quick and easy explanation for this question I’m having a bit of trouble
Using the properties of parallel lines and transversal we can calculate the value of ∠5 as 64° .
The two lines are parallel to one another and the intersecting line is the transversal to the parallel lines.
the two given angles whose values are given are
∠4 = 106-y
∠6 = 3y-10
Now we can clearly see that these two angles ∠4 and ∠6 are co-interior angles.
We know that co-interior angles are supplementary.
Hence ∠4 + ∠6 = 180°
now we will put the values in the equation:
or , 106-y + 3y-10 = 180 °
or , 96 + 2y = 180 °
or, 2y = 84 °
or, y = 42°
Therefore ∠4 = 106 - y = 106° - 42° = 64°
Now from the properties of parallel lines we can see that ∠4 and ∠5 are alternate angles.
Hence ∠4 = ∠5 = 64°
therefore the value of ∠5 is 64° .
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Need help with dilations mix
When you add/subtract values to the coordinates of a figure, its size doesn't change, you only move it to another location.
When you multiply the coordinates of a figure, you enlarge it, i.e. create a bigger figure proportional to the original one.
When you divide the coordinates of a figure, you reduce its size.
Since the figure was dilated and not moved, option F is incorrect.
To determine how much it was dilated select any point from the pre image and image and compare them.
For example
G (-2,1)
G'(-5,2.5)
To determine the coefficient used for the dilation divide the x-coordinate of the image point by the x-coordinate of the preimage point:
[tex]\frac{X_{G^{\prime}}}{X_G}=\frac{-5}{-2}=\frac{5}{2}[/tex]Now do the same to determine the coefficient used in the Y-coordinates:
[tex]\frac{Y_{G^{\prime}}}{Y_G}=\frac{2.5}{1}=2.5[/tex]2.5 expressed in fractions is 5/2
So the dilation made was (X,Y)→(2/5X,2/5Y)
The correct answer is E.
Find the equation of the axis symmetry:Find the x-intercept(s):and y-intercept(s):Find the coordinates of the vertex:
Step 1
Find the equation of the axis of symmetry
[tex]\begin{gathered} From\text{ the graph the zeroes are} \\ x=-2 \\ \text{and} \\ x=4 \end{gathered}[/tex][tex]\begin{gathered} \text{Hence the function is } \\ y=(x+2)(x-4) \\ y=x^2-4x+2x-8 \\ y=x^2-2x-8 \end{gathered}[/tex]The equation of symmetry is given as
[tex]\begin{gathered} x=\frac{-b}{2a} \\ b=-2 \\ a=1 \\ c=-8 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-(-2)}{2(1)} \\ x=\frac{2}{2}=1 \\ x=1 \end{gathered}[/tex]Step 2
Find the x-intercepts
[tex]\begin{gathered} \text{From the graph, the x-intercepts are}; \\ (4,0),(-2,0) \end{gathered}[/tex]Step 3
Find the y-intercepts
[tex]y\text{-intercept; (0,-8)}[/tex]Step 4
Find the coordinates of the vertex
[tex]The\text{ coordinates of the Vertex ; (1,-9)}[/tex]change these to decimals. 7%, 200%, .3%
the 7% means
7/100 = 0.07
[tex]7\text{ \% =}\frac{7}{100}=0.07[/tex]200 % means
200/100 = 2
and 0.3 % means
0.3/100 = 0.003