Please help me
I will give brainlist
Answer:
69 degrees
Step-by-step explanation:
See attached image.
Is the solution shown below correct? explain. 9x 2=8x2 6x negative 8 x squared 3 x 2 = 0. x = startfraction negative 3 plus-or-minus startroot (3) squared minus (4) (negative 8) (2) endroot over negative 16 endfraction. x = startfraction negative 3 plus-or-minus startroot 9 minus (64) endroot over negative 16 endfraction. x = startfraction 3 plus-or-minus startroot 55 endroot i over 16 endfraction.
The correct solution of the given quadratic equation was found using the formula.
The given equation is:
[tex]9x+2=8x^{2} +6x[/tex]
[tex]8x^{2} +6x-9x-2=0[/tex]
[tex]8x^{2} -3x-2=0[/tex]....(1)
What is a quadratic equation?An equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where [tex]a\neq 0[/tex].
We can solve equation (1) by the formula
[tex]x=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]
So, [tex]x=\frac{3+-\sqrt{(-3)^{2} -4(8)(-2)} }{2(8)}[/tex]
[tex]x=\frac{-3+-\sqrt{73} }{16}[/tex]
Hence, the correct solution of the given quadratic equation was found using the formula.
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The vertices of PQR are P(6, 1), Q(3,5), and R(11, 11). The length of segment PR is √125 units. Use the coordinates and geometric reasoning to show that PQR is a right triangle.Explain your reasoning and show your work
Check the picture below, so hmm we know that much, and we can also more or less see that PR is the longest side, let's check the length of the other two sides
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{6}~,~\stackrel{y_1}{1})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{[3 - 6]^2 + [5 - 1]^2}\implies PQ=\sqrt{(-3)^2+4^2}\implies \boxed{PQ=5} \\\\[-0.35em] ~\dotfill\\\\ Q(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad R(\stackrel{x_2}{11}~,~\stackrel{y_2}{11})~\hfill QR=\sqrt{[11 - 3]^2 + [11 - 5]^2} \\\\\\ QR=\sqrt{8^2+6^2}\implies \boxed{QR=10}[/tex]
if that's true, the triangle is indeed a right-triangle, then hmmmm most likely using the pythagorean theorem PR² = PQ² + QR², let's check
[tex](\sqrt{125})^2~~ = ~~5^2~~ + ~~10^2\implies 125=25+100\implies 125=125~~\textit{\Large \checkmark}[/tex]
i need help with this
3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k
Where k is a constant.
Given that passes through the points (0, -2) and (2, 18).
a. Show that k = 2 and find an equation for C
b. Show that the line with equation y = x-2 is a tangent to C and find the coordinates of the point of contact.
a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have
[tex]\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt[/tex]
Evaluate the integral to solve for y :
[tex]\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt[/tex]
[tex]\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x[/tex]
[tex]\displaystyle y = x^3+2x^2+kx - 2[/tex]
Use the other known value, f(2) = 18, to solve for k :
[tex]18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}[/tex]
Then the curve C has equation
[tex]\boxed{y = x^3 + 2x^2 + 2x - 2}[/tex]
b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:
[tex]\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2[/tex]
The slope of the given tangent line [tex]y=x-2[/tex] is 1. Solve for a :
[tex]3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1[/tex]
so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).
Decide which of these points is correct:
[tex]x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1[/tex]
So, the point of contact between the tangent line and C is (-1, -3).
What is the sum of the geometric sequence 1, 3, 9, ... if there are 11 terms? (5 points) 29,524 55,987 87,381 88,573
Answer:
S₁₁ = 88573
Step-by-step explanation:
the sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{3}{1}[/tex] = 3 , then
S₁₁ = [tex]\frac{1(3^{11}-1) }{3-1}[/tex] = [tex]\frac{1}{2}[/tex] (177147 - 1) = [tex]\frac{1}{2}[/tex] × 177146 = 88573
a. YXZ
b. YZX
c. ZYX
d. XYZ
Answer:
The triangle which is congruent to triangle QRS is YXZ
Write the slope-intercept form of equation.
9x + 3y = 27
slope intercept form: y = mx + b [ where m is slope and b is y-intercept ]
[tex]\dashrightarrow \ \sf9x + 3y = 27[/tex]
[tex]\dashrightarrow \ \sf 3y = 27 -9x[/tex]
[tex]\dashrightarrow \ \sf y = \dfrac{27 -9x}{3}[/tex]
[tex]\dashrightarrow \ \sf y = -3x + 9[/tex]
Here, the "slope is -3" and "y-intercept is 9"
Slope intercept form:-
y=mx+bNow convert
9x+3y=273y=-9x+273y=3(-3x+9)Cancel 3
y=-3x+9Please ANSWER
Amy is wrapping a present
that is a rectangular prism.
The height is 18 inches, the
width is 16 inches and the
length is 20 inches. What is the
least amount of wrapping
paper, in square inches, that
Amy needs to wrap the
present
The least amount of wrapping paper that Amy needs to wrap the present is 1936in².
What is Surface Area?Surface area is simply the amount of space covering the outside of a 3-dimensional object.
The surface area of a rectangular prism is expressed;
A = 2( wl + hl + hw )
Given the data in the question;
Height of the rectangular prism h = 18inWidth w = 16inLength l = 20inSurface area of the rectangular prism A = ?To determine the least amount of wrapping paper that Amy needs to wrap the present in the shape of a rectangular prism, we substitute our given values into the expression above.
A = 2( wl + hl + hw )
A = 2( (16in×20in) + (18in×20in) + (18in×16in) )
A = 2( 320in² + 360in² + 288in² )
A = 2( 968in² )
A = 1936in²
Therefore, the least amount of wrapping paper that Amy needs to wrap the present is 1936in².
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There are two mechanics who work on cars. For each mechanic, the relationship between x, the number of hours worked, and y, the total cost, in dollars, is described below. • The equation y = 36x represents the total cost charged by Mechanic A for the number of hours worked. The graph shown below represents the total cost charged by Mechanic B for the number of hours worked.
Answer:
B
Step-by-step explanation:
if you divide the 2/88 you should get a price of 44. So Mechanic B charges $44 while Mechanic A charges $36. Subtract 44-36 and get 8. Since Mechanic B charges more, it would give you the answer listed in B.
The equation satisfies option B, Mechanic B charges $8 more per hour then mechanic A.
What is graph?a collection of all points whose coordinates satisfy a given relation (such as a function) a diagram that represents the variation of a variable in comparison to that of one or more other variables, such as a series of one or more points, lines, line segments, curves, or areas
The fundamental subject of graph theory is graphs.
Given the Equation for cost charged by Mechanic A
y = 36x
where y = total cost and x = hours worked
graph shows the total cost charged by Mechanic B
from graph we the coordinates (0, 0) and (2, 88)
when x = 0, y = 0 and when x = 2, y = 88
the equation satisfy the condition is
y = 44x
cost for one hour for Mechanic A
y = 36x (x = 1)
y = $36
cost for one hour for Mechanic B
y = 44x (x = 1)
y = $44
Mechanic B is $8 more than Mechanic A
Hence Mechanic B charges $8 more per hour then mechanic A.
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find the value of the variable
Answer:
x=5
Step-by-step explanation:
6:5
x:4, so x =5
The side also looks a little bigger than 4.
Hope it Helps
Annual snowfall (in inches):
20, 16, 20, 17.5, 19.5, 18, 23
Mean =
Median =
What is the mean and the median?
Answer:
Mean is all the numbers add up and divide how many number were there. The Median is to line up all in order and the middle on.
Step-by-step explanation:
Answer:
Mean =19.142857142857
Median =19.5
Step-by-step explanation:
How to solve and the answer.
Answer:
The answer is 20
Step-by-step explanation:
There's two ways in which you can do this. The first one, and the simpliest one is finding the derivative of the equation P(x). After finding the derivative, set the dy/dx to be zero (so set the derivative to be zero). Then solve for x. This should give you the point at which there's no increase or decrease in the value of P, thus meaning the point at which its the maximum.
The second method is simply ploting a graph and finding the highest point.
(2y^2 – 3y + 1) = (y - 2)
Answer:
see below
Step-by-step explanation:
Move R side to the L side to get
2y^2 -4y +3 = 0
Use quadratic formula to find y = 1 +- i sqrt (2) / 2
PLEASEE HELPPPPPPP!!!!!!!!!!!
Answer:
6
Step-by-step explanation:
[tex]h \sqrt{28 } \\ \sqrt{28} = \sqrt{4 \times 7} \\ \sqrt{28} = \sqrt{4} \times \sqrt{7} \\ 2 \sqrt{7} \\ 8 \sqrt{7} - 2 \sqrt{7} = 6 \sqrt{7} [/tex]
hope this helps :D have a good day
Find the lateral area of the prism
Answer: 50, 208 mm²
Step-by-step explanation:
The lateral area is the surface area excluding the bottom, also known as the base. This means we will be solving for two rectangles and two triangles.
[The Rectangles]
They are both congruent, so I will do the following;
A = 2(L * W)
A = 2(7 mm * 24 mm)
A = 2(168 mm)
A = 336 mm²
[The Triangles]
The area of a triangle is [tex]\frac{B * H}{2}[/tex] However, they are both congruent. I will do the following;
A = B * H
A = 24 mm * 2,078 mm
A = 49,872 mm²
[The Total]
Lastly, I will add them together.
336 mm² + 49,872 mm² = 50, 208 mm²
120
∑ (3n-6)
n=1
Find the sum.
Answer:
21300
Step-by-step explanation:
120∑n=13n−4
Split the summation into smaller summations that fit the summation rules.
120∑n=1 3n−4=3120∑n=1 n+120∑n=1 −4
Evaluate
3120∑n=1 n.
21780
Evaluate
120∑n=1 −4 −480
Add the results of the summations.
21780−480
Subtract 480 from 21780.
21300
what are the angle measures of X and Z?
Answer:
m∠Z=146
m∠X=34
Step-by-step explanation:
Since this is an Isosceles Trapezoid, we can assume that m∠Z=m∠Y, because an isosceles trapezoid has two pairs of congruent angles, therefore m∠Z=146.
Since angle Y and Angle X are same side interior and line ZY║WX, we can assume that m∠X+m∠Y=180. Substitute values:
[tex]146+X=180\\Y=34[/tex]
please help, thank you if you do
Step-by-step explanation:
q3) if the given sequence is 1, 2, 4, 8, 16..., then it is not arithmetic one. The common ratio is 2: 16/8=8/4=4/2=2/1.
q4) if it is given -34; -64; -94; -124; -154..., then it is arithmetic sequence, where the difference is -64--34=-94--64=-124--94=-154--124= -30
i’ll mark Brainliest or whatever it is
Which expression is equivalent to m (n + p)?
O A. m X n + P
Ов. т Хр+п
OC, (m x n) + P
OD. (mx n) + (m xp)
m
O E. (m + n) x (m + p)
Answer:
A
Step-by-step explanation:
m( n+ p)
it's also known as m × n + p
HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]y=-\dfrac 14 x~~....(i)\\\\x+2y = 4~~...(ii)\\\\\text{Substitute}~~ y= -\dfrac 14 x ~~ \text{in equation (ii):}\\ \\ \\x+2\left(-\dfrac 14 x \right) = 4\\\\\implies 4x -2x = 16~~~~;\left[\text{Multiply both sides by 4} \right]\\\\\implies 2x = 16\\\\\implies x =\dfrac{16}2 \\ \\\implies x =8\\\\\text{Substitute x = 8 in equation (i);}\\\\y= -\dfrac 14 \cdot 8 = -2\\\\\text{Hence,}~ (x,y) = (8,-2)[/tex]
Answer:
[tex]y = - \frac{1 }{4} x \\ [/tex]
[tex]x + 2y = 4 \\ [/tex]
[tex]x + 2( - \frac{1}{4} x) = 4 \\ [/tex]
[tex]x + ( - \frac{2}{4} x) = 4 \\ [/tex]
[tex]x - \frac{1}{2} x = 4 \\ [/tex]
[tex] \frac{2x - 1x}{2} = 4 \\ [/tex]
[tex]2x - x = 8[/tex]
[tex]x = 8[/tex]
[tex]x + 2y = 4 \\ [/tex]
[tex]8 + 2y = 4[/tex]
[tex]2y = 4 - 8[/tex]
[tex]2y = - 4[/tex]
[tex]y = - 2[/tex]
Solve the following:
Answer:
-25
Step-by-step explanation:
What is the value of the expression when a = 3 and b = 5?
3a+b−4
4
7
10
34
helppppp................................/
Answer:
pounds and ounces
Randomly pick 25 fish from the entire pond and weigh each of them
Step-by-step explanation:
Centimeters, feet and inches measure length, not weight.
To find the average weight of fish living in a large pond, the scientist will randomly pick 25 fish from all over the pond. Next, each fish will be weighed. The weight of all 25 fish will be added and the total will be divided by 25. This will give you the average weight of a fish living in the large pond.
2. In the last quarter of a high school basketball game,
you team is behind by 34 points. A field goal is 2 points
and a foul shot is 1 point. The coach doesn’t want the team
shooting any 3-point shots.
- Let x represent the number of field goals scored.
Let y represent the number of foul shots scores.
- Write and graph an inequality that models the
different numbers of field goals and foul shots
your team could score to win or tie the game.
(Assume that the other team scores no more points.
The inequality of the expression is a greater than inequality, and the required inequality is 2x + y > 34
How to determine the inequality?From the question, we have the following representations:
x represents field goalsy represents foul shotsA field goal has 2 points, while a foul shot has 1 point.
So, the number of points in a game is:
Score = 2x + y
The team is behind by 34 points.
So, the team must attain above 34 points
This means that the score must be greater than 34.
So, the inequality is:
2x + y > 34
See attachment for the graph of the inequality
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Juan's family and Ethan's family go to a food stand.
• Juan's family buys three hot dogs and four drinks for $18.50.
• Ethan's family buys five hot dogs and four drinks for $25.50.
What is the cost of one drink at the food stand?
Answer:
1 hotdog is $3.5.
1 drink is $2.
Step-by-step explanation:
18.50= 3x+4y(times 5)
25.50=5x+4y(times -3)
92.5=15x+20x
-76.5=-15x+-12y
16=-8y
2=y
18.50=3x+4(2)
10.50=3x+8
10.50=3x
3.5=x
The width w is less than 10 inches
Answer:
w - 10
Step-by-step explanation:
Substract 10 from W --> w - 10
Please help!!!
Danil, Gabriel and Hadley share some money in the ratios 3:5:9
The difference between the amount of money that Gabriel receives and the amount of
money that Hadley receives is 196 euros.
Work out the amount of money that Danil receives.
Answer:
Danil received 147 euros
Step-by-step explanation:
Let, Danil,Gabriel and Hardly share some money of 3x:5x:9x ratio then,
From the question,
9x - 5x= 196
or, 4x= 196
or, x = 196/4
or, x = 49 euros
Again,Danil received 3x share of money
=3*49
=147 euros
Answer:
Step-by-step explanation:
Ratio = 3 : 5 : 9
Money received by Danil = 3x
Money received by Gabriel = 5x
Money received by Hadley = 9x
Difference in the amount between Gabriel and Hadley = 196 euros
9x - 5x = 196
4x = 196
x = 196/4
x = 49
Money received by Danil = 3*49
= € 147
PLEASE HELP I WILL GIVE YOU 5 STARS AND BRAINLIEST
Answer:
224 ÷ 4 = 56
Step-by-step explanation:
14 × 4 = 56
56 × 4 = 224
224 ÷ 4 = 56
If he is choosing one event and one time how many options does he have for his birthday party?
Answer:
6 options
Step-by-step explanation:
hes got 3 event options
and 2 time slots so
3 times 2 is 6