Answer:
x = 6, and x = 1
Step-by-step explanation:
If each expression equals y, the simplest approach would be to equate them;
x^2 - 5x + 7 = 2x + 1 => Isolate all the terms on one side
x^2 - 5x - 2x + 7 - 1 = 0 => Combine like terms
x^2 - 7x + 6 = 0 => solve using quadratic equation
x = ( - (- 7) + √( - 7)^2 - 4 * 1 * 6 )/ 2 * 1
= 7 + √25 / 2 = 7 + 5 / 2
= 6
x = ( - (- 7) - √( - 7)^2 - 4 * 1 * 6 )/ 2 * 1
= 7 - √25 / 2 = 7 - 5 / 2
= 2 / 2 = 1
For an exponential function of the form f(x)=a*b^x , what is the relationship between the base of the power, the expression f(x+1)/f(x) , and the common ratio of the corresponding geometric sequence?
The relationship between the base of the power, the expression f(x+1)/f(x), and the common ratio of the corresponding geometric sequence is that they are all equal.
To see this, let's first write out the function f(x) and f(x+1):
f(x) = a× \(b^{x}\)
f(x+1) = a×\(b^{x+1}\) = a×\(b^{x}\) × b
Now, let's find the expression f(x+1)/f(x):
f(x+1)/f(x) = (a×b^x × b) / (a×\(b^{x}\))
= b
So, the expression f(x+1)/f(x) is equal to the base of the power, b.
Next, let's consider the corresponding geometric sequence. A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant, called the common ratio. In this case, the common ratio is the base of the power, b.
So, the relationship between the base of the power, the expression f(x+1)/f(x), and the common ratio of the corresponding geometric sequence is that they are all equal to the base of the power, b.
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I need help ASAP....
Answer:
the third one
Step-by-step explanation:
I do not know 100% but I am pretty sure so good luck and plz let me know if I am wrong.
Set up the integral to find the volume in the first octant of the solid whose upper boundary is the sphere x² + y² +z? =4 and whose lower boundary is the plane z = 73 x. Use rectangular coordinates; do not solve.
The integral to find the volume in the first octant of the solid is expressed as ∭(0 ≤ x ≤ √(4 - y² - z²), 0 ≤ y ≤ √(4 - x² - z²), 73x ≤ z ≤ √(4 - x² - y²)) dx dy dz.
The integral to find the volume in the first octant of the solid is:
∭(0 ≤ x ≤ √(4 - y² - z²), 0 ≤ y ≤ √(4 - x² - z²), 73x ≤ z ≤ √(4 - x² - y²)) dx dy dzTo evaluate this integral, we need to determine the limits of integration for each variable.
For x, the lower limit is 0, and the upper limit is √(4 - y² - z²) to ensure x stays within the sphere.For y, the lower limit is 0, and the upper limit is √(4 - x² - z²) to ensure y stays within the sphere.For z, the lower limit is 73x to represent the plane z = 73x, and the upper limit is √(4 - x² - y²) to ensure z stays below the sphere.Thus, the integral becomes:
∭(0 ≤ x ≤ √(4 - y² - z²), 0 ≤ y ≤ √(4 - x² - z²), 73x ≤ z ≤ √(4 - x² - y²)) dx dy dzlearn more about Integral here:
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Which numbers have line symmetry?
2, 3, 4 7,8,9
Each pound of strawberries sells for $2.50 and each pound of raspberries sells for $3.75. Jack made $225 from selling a total of 65 pounds of strawberries and raspberries. Graphically solve a system of equations in order to determine the number of pounds of strawberries sold, x,x, and the number of pounds of raspberries sold, yy.
Given:
Selling price of each pound of strawberries = $2.50
Selling price of each pound of raspberries = $3.75
Total quantity = 65 pounds
Total sales = $225
To find:
The number of pounds of strawberries sold, and the number of pounds of raspberries sold graphically.
Solution:
Let x be the number of pounds of strawberries and y be the number of pounds of raspberries sold.
According to the question,
Total quantity : \(x+y=65\) ...(i)
Total sales : \(2.50x+3.75y=225\) ...(ii)
Table of values for equation (i) is
x y
0 65
65 0
Table of values for equation (ii) is
x y
0 60
90 0
Plot these point on coordinate plane and connect them by straight lines as shown in the below graph.
From the graph it is clear that both lines intersect each other at (15,50). So,
\(x=15, y=50\)
Therefore, the number of pounds of strawberries sold is 15 and the number of pounds of raspberries sold is 50.
The number of pounds of strawberries sold and the number of pounds of raspberries sold is 15 and 50
The calculation is as follows;here we assume the strawberries be x
and, the raspberries be y
Now
x + y = 65
It can be written as y = 65 - x
2.50x + 3.75y = 225
From the graph we can say that it should be 15 and 50.
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A cone-shaped paper cup is being produced such that it holds 100 cm3 of liquid. the material that will be used to produce the cups cost 0.25 cents per cm2. let the cost be a function of r and the slant height of the cup be defined as s equals the square root of quantity r squared plus h squared period which of the following equations will help to determine the lowest cost? (hint: the base of the cup would not be included, since it is open.
The height of the cup that can be made from the least amount of paper is 17 cm.
A cone-shaped paper cup is to hold 100 cubic cm of water. Find the height and the radius of the cup that can be made from the least amount of paper.
Use the volume of a cone formula: (1/3)*pi*r^2*h = V; to find h in terms of r.
(1/3)*pi*r^2*h = 100
multiply equation 3 to get rid of the denominator
pi*r^2*h = 300
h = 300/(pi * r^2)
:
Using the surface area equation: SA = pi*r^2 + (pi*r*L), find L using r and h
L = \(\sqrt{h^{2} +r^{2} }\)
Substitute above for L in the SA equation
:
\(SA = \pi r^{2} + \pi r\sqrt{\frac{300}{\pi r^{2} } + r^{2} }\)
:
Using this equation in my TI83, the graph showed the minimum radius to occur at appox 2.37 cm
:
Find the height using this value:
h = 17 cm
Check solution by finding the volume
V = (1/3) * pi * 2.37^2 * 17
V = 99.994 ~ 100 cm
Hence , the height of the cup that can be made from the least amount of paper is 17 cm.
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The area of the base of right rectangular prism is 14 square inches. The height is 5 inches. What is the VOLUME of the prism?
Answer:
70
Step-by-step explanation:
your height is 14, Given
Your surface area for the top face is 14
the way to make 14 from two factors is 7 and 2
therefore your height is 5 your width is 7 and your depth is 2
ZA and 23 are supplementary angles. If m
ZB = (4x + 3)º, then find the measure of ZA.
Answer:
Since they are supplementary angles which add up to 180 degrees the measure of ZA must be 157 degrees.
Step-by-step explanation:
the u.s. department of transportation recently reported that 81.5% of u.s. airline flights arrived on time. find the probability that among 12 randomly selected flights exactly 10 arrive on time.
The probability that among 12 randomly selected flights, exactly 10 arrive on time is 0.1667
How do we calculate the probability?The probability that, among 12 randomly selected flights, exactly 10 arrive on time is 0.1667. This is calculated by using the binomial probability formula:
\(P(x) = nCx (p^x) (1-p)^{(n-x)}\)
Where:
n = 12 (number of flights)x = 10 (number of flights arriving on time)p = 0.815 (probability of one flight arriving on time)\(P(x) = 12C10 (0.815^{10}) (0.185)^2 = 0.1667\)
The probability that among 12 randomly selected flights, exactly 10 arrive on time is 0.1667
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Which type of tide occurred on June 8?
A spring tide
B neap tide
C) full tide
D) half tide
PLEASE HELP
Answer:
A) spring tide
Step-by-step explanation:
what is the approximate area of a circle with a radius of 11m?
ANSWER 22 PLEASE...
22. Determine if the triangles below are congruent. If yes, state which method.
a)
b)
d)
o
4
Answer:
a) yes ASA
b) yes SSS
c) yes SSS
d) yes HL
Step-by-step explanation:
Caron want to put up a glow in the dark contellation diplay in hi bedroom he need a pack of two ided tape which cot $12 the tar ticker cot $14 per pack and he want to buy 3 pack what i a good etimation of how much change Caron will get back if he give $75?
If Caron gives $75, he will get $21 as a change, when he buys a constellation display.
To estimate the amount of change Caron will get back, we need to calculate the total cost of the two-sided tape and the star stickers. The two-sided tape costs $12 and Caron wants to buy 3 packs of star stickers which cost $14 each, so the total cost of the star stickers is 3 * $14 = $42. The total cost of both the two-sided tape and the star stickers is $12 + $42 = $54.
If Caron gives $75, he will get $75 - $54 = $21 as change. This is a rough estimate of the amount of change Caron will get back, and it's always a good idea to have a little extra money in case the actual cost is slightly higher.
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100 POINTS!!!
3) Transitive Property of Segment Congruence.
Given: AB is congruent to JK, JK is congruent to ST.
Prove: AB is congruent to ST.
Transitive property of segment congruence states that if two segments are congruent to the same segment, then they are congruent to each other. Mathematically, it can be written as, if AB ≅ JK and JK ≅ ST, then AB ≅ ST.
In the given problem, it is given that AB is congruent to JK and JK is congruent to ST. Therefore, it can be concluded that AB is congruent to ST because of the transitive property of segment congruence, i.e., AB ≅ JK ≅ ST ⇒ AB ≅ ST.Let’s have a brief discussion on how transitive property of segment congruence holds true.
It is based on the fact that segments that are equal to the same segment are equal to each other. Therefore, if AB ≅ JK, then AB and JK have the same length. Similarly, if JK ≅ ST, then JK and ST have the same length. Now, since AB and JK have the same length, and JK and ST also have the same length, it can be concluded that AB and ST are also equal. Hence, AB ≅ ST is proved using the transitive property of segment congruence.
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Answer:
Step-by-step explanation:
B is congruent to JK
Defintion of transitive property of segment
Mr John leased two thousand fifty meter square of land from the city administration. He gave one eighth of his land to his brother. How many meters square did he have left?
Answer:
1793.75 m²
Step-by-step explanation:
Given that :
Total amount of land leased = 2050 m²
Fraction of land given to brother = 1/8
Amount of land given to brother :
1/8 * 2050 = 256.25 m²
Amount of land left :
2050 m² - 256.25 m²
= 1793.75 m²
simplify (z7z−5)−2.
A .−z14
B. 1 over z raised to the fourth power
C.−z4
D.1 over z raised to the second power
i did the work but i would just like some clarification im correct,
so if you would please provide what you think it is and explain so i can check my own work to make sure thank you
7( z - 1 )( z + 1 ) is the required solution.
What is roots of quadratic equations?
Quadratic equation's roots The roots of a quadratic equation are the values of the variables that fulfil the equation. In other words, if f() = 0, then x = is a root of the quadratic equation f(x). The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.
\((z\cdot \textcolor{7}z-5)-2\\\\(\textcolor{7}zz-5)-2\)
\((7\textcolor{z}\textcolor{z}-5)-2\\\\\left( 7\textcolor{z^{2}}-5\right) -2\)
\(7z^{2}\textcolor{-5}\textcolor{-2}\\\\7z^{2}\textcolor{-7}\)
\((z\cdot 7z-5)-2\\\\7\left( z^{2}-1\right)\)
\(7\left( z^{2}\textcolor{-1}\right)\\\\7\left( z^{2}+\textcolor{z}\textcolor{-z}-1\right)\)
\(7\left( z^{2}+z-z-1\right)\\\\7(z(z+1)-1(z+1))\)
\(7(z(z+1)-1(z+1))\\\\7(z-1)(z+1)\)
Hence, 7 (z - 1 )( z + 1 ) is the required solution.
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Yolanda decides the length of her square vegetable garden will be 17 ft. she calculates that the area of the garden is 34 ft squared 2. Determine if Yolanda's calculation is correct. Explain.
Answer: That is incorrect because the garden will be 17 ft by 17 ft meaning it will be 289 square feet.
Step-by-step explanation:
Use inverse trigonometric functions to solve the following equations. If there is more than one solution, enter all solutions as a comma-separated list (like "1, 3"). If an equation has no solutions, enter "DNE".Solve 7tan(θ)=−15 for θ (where 0≤θ<2π).θ=
ANSWER:
\(\theta=-1.13416,2.00743\)STEP-BY-STEP EXPLANATION:
We have the following function
\(\begin{gathered} 7\cdot\tan (\theta)=-15 \\ 0\leq\theta<2\pi \end{gathered}\)Solving for θ:
\(\begin{gathered} 7\cdot\tan (\theta)=-15 \\ \tan (\theta)=-\frac{15}{7} \\ \tan (\theta)=-\frac{15}{7} \\ \theta=\arctan (-\frac{15}{7}) \\ \theta_1=-1.13416 \\ \theta_2=2.00743 \end{gathered}\)5. Write an equation of a line in standard form for the given conditions. passes through (0,0) and is perpendicular to the line 2- y=6
Answer:
69
Step-by-step explanation:
a 30% sugar syrup is mixed with 10% sugar syrup.The result is 600 g of 15% sugar syrup. How many grams of each syrup are in the mixture?
Answer:
450g of 10% sugar syrup
150g of 30% sugar syrup
Step-by-step explanation:
150g of 30% sugar syrup
450g of 10% sugar syrup
Step-by-step explanation:
big brains yo hope this helps yall
How would an inscribed dodecagon compare to the area of a circle?
underestimate of the circle
overestimate of the circle
same as the circle
does not compare
Answer:
I think the answer is underestimate of the circle
Step-by-step explanation:
I believe it is underestimate because the dodecagon is inside the circle, therefore smaller than the circle. It wont fill the circle completely so that is why i think it is underestimate. I hope this helps, if not I am really deeply sorry!!!!!
Can someone please help me with this question please answer it correctly and please explain.
A jar contains nickels and dimes. There is a total of 25 coins in the jar. The value of the coins is $1.75. How many nickels and how many dimes are in the jar?
Answer:
15 nickels and 10 dimesStep-by-step explanation:
Dimes - d, dime = 10c, total dimes = 10dNickels - n, nickel = 5 c, total nickels = 5n$1.75 = 175 cEquations:
d + n = 2510d + 5n = 175Multiply the first equation by 5 and subtract from the second one:
10d + 5n - 5d - 5n = 175 - 1255d = 50d = 10Find n:
n = 25 - d = 25 - 10 = 15a cylindral drill with radius 5 cm is used to bore a hole through the center of a sphere with radius 10 cm. find the volume of the ring-shaped solid that remains.
The volume of the ring-shaped solid that remains after drilling is 3961.73cm³.
The radius of the cylindrical drill is 5cm and the radius of the sphere is found to be 10cm.
After drilling,
The radius of the of the sphere will act as a hypotenuse to the triangle where the base is the radius of the cylinder and the perpendicular is the height of the cylinder.
So, we can say,
Height H of cylinder = √(10² - 5²)
Height H of cylinder = 8.66 cm.
The volume V of the ring shape remaining,
V = Volume of sphere - volume of cylinder
V = 4/3πR³ - 1/3πr²H
R is the radius of sphere and r is the radius of cylinder,
Putting values,
V = 4/3π(10)³ - 1/3π(5)²8.66
V = 3961.73 cm³.
So, the volume that remains is 3961.73cm³.
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please help asap XD
Using the congruent theorem,
a. ∠XBC will be equal to ∠AXY as the lines are parallel to each other for which the angles are corresponding to each other.
b. ∠BXC = 70°
Define congruent angles?Equal amounts of angles are referred to as congruent angles. As a result, congruent angles are those whose measures are the same. They can be found anywhere, including in isosceles triangles, equilateral triangles, and situations where a transversal joins two parallel lines.
Here in the question,
∠AXY = 55°
XY ║ BD
XB = XC
a.
So, from the figure:
∠XBC will be equal to ∠AXY as the lines are parallel to each other for which the angles are corresponding to each other.
So, ∠XBC = ∠AXY =55°
b.
Now,
In ΔXBC, XB = XC
So, ∠XBC = ∠XCB = 55°.
As per angles in a triangle,
∠XBC + ∠XCB + ∠BXC = 180°
⇒ ∠BXC = 180 - 55 - 55
⇒ ∠BXC = 70°
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How many solutions does the following equation have?
Answer:
Step-by-step explanation:
-9(z-8)=-9z-72
<=> 9z-72=--9z-72
zthuộc R ( vì có 2 vế bằng nhau)
Who was the first lady
Answer:
While the title was not in general use until much later, Martha Washington, the wife of George Washington, the first U.S. president (1789–1797), is considered to be the inaugural first lady of the United States. During her lifetime, she was often referred to as "Lady Washington".
plz can i get brainliest
Answer:
there are many first lady's but because you said was like past tense the last first Lady was Melania Trump. the current first Lady is Jill Biden! I hope this helps!!♡♡
Solve For X. Solve similar triangles (advanced)
The value of x in the given similar triangles ADB and BCE is 4.5.
To solve for x in the given similar triangles ADB and BCE, we can set up the proportion of corresponding sides:
In triangle ADB, we have:
AB/BD = x/DE
Substitute the given values:
3/4 = x/6
Now, cross-multiply and solve for x:
3 * 6 = 4x
18 = 4x
x = 18/4
x = 4.5
So, the value of x is 4.5.
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Y
2
0
A
с
B
o'
D
Which point is located at
(11.2)
The point that is located at the ordered pair (4, -2) is given as follows:
Point B.
How to define the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
In which the coordinates are given as follows:
x is the x-coordinate.y is the y-coordinate.On the coordinate plane, we have that:
x is the horizontal coordinate.y is the vertical coordinate.Hence the coordinates for this problem are given as follows:
A(-2, 4), B(4, -2), C(-4, 2) and D(2, -4).
Missing InformationThe graph is given by the image presented at the end of the answer.
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2x(3x -5) -3(x -3) for x = 2
SIMPLIFY THE FOLLOWING
Answer:
-15
Step-by-step explanation:
go to the picture okay
Answer: 7
Step-by-step explanation:
2x(3x-5) -3(x-3)2(2)(3(2)-5) -3(2-3) First you substitute 2 for all the x's. The twos in . parentheses represent multiplication.4(6-5) -3(2-3) Second, you multiply 2 by 2, which equals 4, . and multiply 3 by 2, which equals 6. 4(1) -3(-1) Next, you solve the problems in the . parentheses, which is 6 minus 5 is 1, and 2 . minus 3 is -14-(-3) Next, you multiply 4 by 1, which is 4, and . multiply 3 by -1.4+3 Since two negatives make a positive, the . equation changes to 4 plus 3.7 Finally, you add 4 plus 3 and get 7.P.S: Sorry about the random periods. I had to put them in to format it like that.
Can someone explain this lol thanks Find the volume of the rectangular
prism.
4
3
9
[?] units