Answer:
y = 4, x = 0
y = 1, x = -1
Step-by-step explanation:
[tex]y = 3 {x}^{2} + 6x + 4[/tex]
[tex]y = - 3 {x}^{2} + 4[/tex]
[tex] \: [/tex]
Since both of them are equal to y, we can just equate them and solve.
[tex] \: [/tex]
[tex]3 {x}^{2} + 6x + 4 = - 3 {x}^{2} + 4[/tex]
[tex]3 {x}^{2} + 6x + 4 + 3 {x}^{2} - 4 = 0[/tex]
[tex]6 {x}^{2} + 6x = 0[/tex]
[tex]6x(x + 1) = 0[/tex]
[tex]6x = 0[/tex]
[tex]x = 0[/tex]
[tex] \: [/tex]
[tex]x + 1 = 0[/tex]
[tex]x = - 1[/tex]
[tex] \: [/tex]
[tex]for \: x = 0[/tex]
[tex]y = 3( {0})^{2} + 6(0) + 4[/tex]
[tex]y = 4[/tex]
[tex] \: [/tex]
[tex]for \: x = - 1[/tex]
[tex]y = 3( { - 1})^{2} + 6( - 1) + 4[/tex]
[tex]y = 1[/tex]
[tex] \: [/tex]
[tex]values \: of \: x \: and \: y \: for \: the \: system \: of \: equations \: are[/tex]
y = 4, x = 0
y = 1, x = -1
The system of equations has been solved and the solution set of the equation are (-1,1) and (0,4).
What is a system of equation?A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
The first equation given as,
y = 3x² + 6x + 4
The second equation given as,
y = -3x² + 4
Equate the value of y from both equation as,
3x² + 6x + 4=-3x²+4
3x²+3x²+6x+4-4=0
6x²+6x=0
6x(x+1)=0
x=0:x=-1
Put these values of x, in first equation,
y = 3(-1)^2 + 6(-1) + 4
y = 3 - 6 + 4
y=1
Put 0 on the place of x,
y = 3(0)^2 + 6(0) + 4
y = 0 +0+ 4
y=4
Thus, the system of equations has been solved and the solution set of the equation are (-1,1) and (0,4).
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10. A garden is to be surrounded by a paved
border of uniform width.
16 m
|-X-
L=16+X+x
L= 2x+16
W=14+x+x
W= 2x+14
14 m
a) Write a simplified expression for the
area of the border.
b) The border is to have an area of
216 m². Find the width of the border.
What type of graph is this ?
Step-by-step explanation:
this isn't a graph of a function, this is just a series of plotted points.
f(x) = 3x + 2
What is f(5)?
Answer:
17
Step-by-step explanation:
→ f(x) = 3x + 2
→ f(5) = 3(5) + 2
→ 15 + 2
→ 17 is the answer.
Answer:
F(5) = 17
Step-by-step explanation:
to solve, we just need to plug all values of x into 5 as shown
f(x) = 3x + 2
f(5) = (3*5) + 2
then following the format of PEMDAS (explained at footer) we solve the new equation
f(5) = (3*5) + 2
f(5) = 15 + 2
f(5) = 17
therefor F(5) is equal to 17
The PEMDAS format of solving equations:
the term Pemdas stands for the steps involved in solving an equation
Parenthasis (follow PEMDAS within these ( ) first untill in simplest form)
Exponents (such as x^y)
Multiply (any multiplication)
Devide (any devision)
Addition (any addition)
Subtraction (any subtraction)
hpe all this helps you ^^
convert 12 minutes 35 seconds to seconds
:_
Answer:
755s
Step-by-step explanation:
60*12+35=755
This is the way
Answer:
755 seconds
Step-by-step explanation:
1min = 60 sec
12 x 60 = 720
720+35 = 755
:)
Please help me with question 36. I don’t know the answer
Answer:
Period = [tex]\frac{\pi }{4}[/tex]
Amplitude = 4
Step-by-step explanation:
To find the answer, use the form acos(bx - c) + d:
a = -4
b = 8
c = 0
d = 0
The amplitude is the absolute value of a, so:
|a| = |-4| = 4
To find the period, use this equation:
[tex]\frac{2\pi }{b}[/tex]
Replace b with 8 in the formula and solve:
[tex]\frac{2\pi }{8} = \frac{\pi }{4}[/tex] Simplify
So, the period is equal to [tex]\frac{\pi }{4}[/tex]
Hope this helps!!
Complete the definition of the h(x) so that it is continuous over its domain.
Answer:
A=0
B=2
so we have our question, h (x) x^3, x<0.
a is equal to 0 since that answer was already given.
so now it would be srqt/x over 0 of 4
4 divided by 0 is 0
1/2x x>4
turns into 1/2x x>4/1
cross simplify
the answer to B is 2
Answer:
a=0
b=2
Step-by-step explanation:
Rectangle pqrs had vertices p(-4,3),q(-2,5),r(3,0) and s(1,-2). the diagonals of the rectangle bisect eachother. atwhich point do the diagonals intersect?
Answer:
Step-by-step explanation:
Green paint can be made by mixing yellow and blue paint in a 2 : 5 ratio
What fraction of the green paint is yellow paint? Give your answer in its
simplest form.
Answer:
4 : 10
Step-by-step explanation:
Answer:
2/7
Step-by-step explanation:
there's seven parts in green (2 yellow and 5 blue)
two of them are yellow
so 2/7 is the fraction
(seven is prime so it's already in simplest form.)
Help please! Will give brainliest!!!!!!!!!!!!!!
Answer:
a is the same aand b is the sane
20d + 0.7m = 235
Shelly spent $235 to rent a moving van. The equation above shows the relationship
between the number of days she rented the van, d, and the number of miles she drove
the van, m. If she rented the van for 3 days, how many miles did she drive the van?
The number of miles she drove the van for is 250 miles
Solving linear equationsFrom the question, we are to determine the number of miles Shelly drove the van
The given equation which shows the relationship between the number of days she rented the van, d, and the number of miles she drove the van, m is
20d + 0.7m = 235
Now, if she rented the van for 3 days, that is, d = 3
Putting the value of d = 3 into the equation to determine the value of m
We get
20(3) + 0.7m = 235
60 + 0.7m = 235
0.7m = 235 - 60
0.7m = 175
m = 175 / 0.7
m = 250
Hence, the number of miles she drove the van for is 250 miles
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Place (dlick and drag) one option from each of the lists below Into Its corresponding box to
create an equation of the line that passes through the polnt (1, "10) and is perpandicular to y=-1/3 x +5
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}}x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-1}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-1}\implies 3}}[/tex]
so we're really looking for the equation of a line whose slope is 3 and passes through (1 , 10)
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{10})\qquad \qquad \stackrel{slope}{m}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{3}(x-\stackrel{x_1}{1}) \\\\\\ y-10=3x-3\implies y=3x+7[/tex]
Alice, a 16-year-old, gave birth to a baby boy last year. how will this affect the likelihood that her 13-year-old sister, marie, will have a baby
Answer:
I think that the actions of older people/family members around you greatly influence that thoughts/actions of a younger child. Since Marie looks up to Alice, Marie probably thinks that having a child at such a young age is a good idea. Therefore if Alice gave birth at the age of 15, there is a high chance her younger sister will follow in her footsteps.
(I'm not sure how this relates to math)
There is estimated to be a population of approximately 85 mice on Farmer Jon's Farm, and the population is tripling each year. Does the scenario above represent exponential growth or decay? write an equation to represent the scenario.
Answer:
Exponential growth
Step-by-step explanation:
As it mentions that the population is tripling each year, we can clearly understand that it is exponential growth.
Equation
⇒ Let y be total population of mice and x the number of years
⇒ y = 85(3ˣ)
Hope it helps ~
Simplify the expression. Write your answer as a power.
The simplified expression is
Answer:
Answer = 6^7
Step-by-step explanation:
When multiplying expressions with exponent you add the exponents together. So here you would get 6^13/6^6. However you can simplify this farther since the base (6) is the same. When dividing expressions with exponents you subtract the exponents so the the answer would be 6^7.
Hope that helps! :)
Write a negative function h(x) with a y-intercept at "-4" with one solution
The required negative function h(x) with a y-intercept at "-4" with one solution is x + 4
Intercept of the equationThe y-intercept of an equation is the pint where the x-value of the function is 0, that is;
f(-4) = 0
Since the solution has one solution, hence it will be linear in nature
h(x) = x + 4
This gives the required negative function h(x) with a y-intercept at "-4" with one solution
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what is 9 - 3 dived by 1/3 + 1 =
4. The equation 2x = - 10 is modeled below.
What is the value of x makes the equation true?
Answer:
x = -5
Step-by-step explanation:
2x = -10 <== divide both sides by 2
/2 /2
x = -5
Check your work:
2x = -10
2(-5) = -10
-10 = -10
This statement is true
Hope this helps!
How can I find the x value?
How can I explain it?
PLEASE ANSWER THE QUESTION!!!
12x+16y=336
Please help me find y intercept the answer should be 28 but guide me on the steps
Shawna is going out of town for the day, so she asks a friend to watch her 3 dogs. She wants to leave
1/2 of a pound of food for each dog. If a can of dog food has 0.75 pounds of food, how many cans should Shawna leave?
Answer:
2cans
Step-by-step explanation:
1/2 = .5 so .5×3=1.5 and 1.5 ÷ .075 =2
Identify coordinate point B. (0, 2) (1, 5) (7, 3) (6, 7)
Answer:
i think 1.5 imagine a dot so its on 5 and 1 then you get 1.5 thats what i think
Step-by-step explanation:
pls dont get mad if i got it wrong D:
Answer:(1, 5)
Step-by-step explanation:
Yuuma applied the steps below to find the product of (–10.2)(–16.4).
Step 1: (–10.2)(–16.4) = (–16.4)(–10.2)
Step 2: = (–16.4)(–10) + (–16.4)(–0.2)
Step 3: = ____________
Step 4: = 167.28
Which expression correctly fills in the blank in Step 3?
(–164) + (–3.28)
164 – 3.28
(–164) + 3.28
164 + 3.28
Answer:
164+3.28
Step-by-step explanation:
(16.4)(10)+(16.4)(0.2)
164+3.28
167.28
I need help! its really hard to do
Mr. Brown picks out the time that appears the most to find the
. He arranges the times in increasing order and picks the middle value to find the
.
pls help (this is for a frend)
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$5\\ P=\textit{original amount deposited}\\ r=rate\to 1.25\%\to \frac{1.25}{100}\dotfill &0.0125\\ t=years\dotfill &\frac{1}{2} \end{cases} \\\\\\ 5 = (P)(0.0125)(\frac{1}{2})\implies \cfrac{5}{(0.0125)(\frac{1}{2})}=P\implies 800=P[/tex]
In Galton’s height data, the least-squares line for predicting forearm length (y) from height (x) is y = −0.2967 + 0.2738x.
Predict the forearm length of a man whose height is 72 in. Round the answer to three decimal places.
Using the line of best fit, it is found that the prediction of the forearm length of a man whose height is of 72 in is of 19.417 in.
What does the line of best fit state?It states that the predicted forearm length of a person of height x is given by:
y = -0.2967 + 0.2738x.
In this problem, the height is of x = 72 in, hence:
y = -0.2967 + 0.2738(72) = 19.417 in.
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The diameter of a circle is 42 ft. Find its area to the nearest whole number.
Answer:
5539 or 1764[tex]\pi[/tex]
Step-by-step explanation:
to find the area, we need the radius
The radius(R) is half of the diameter(D)
R = D/2
R = 42/2
R = 21
area of a circle(A) = pi x radius[tex]^{2}[/tex]
A = pi( which most times in a problem, equals 3.14) x 42[tex]^{2}[/tex]
A = 3.14 x 1764
A = 5538.96
A(when rounded) = 5539
How to find maximum and minimum values of a parabola
Answer:
Step-by-step explanation:
Finding max/min: There are two ways to find the absolute maximum/minimum value for f(x) = ax2 + bx + c: Put the quadratic in standard form f(x) = a(x − h)2 + k, and the absolute maximum/minimum value is k and it occurs at x = h. If a > 0, then the parabola opens up, and it is a minimum functional value of f.
A. 611.18 b. 431.59 c. 395.59 d. 1,042.37. ASAP PLEASEE
Answer:
A
Step-by-step explanation:
The table shows the results of rolling a number cube with sides labeled 1 through 6 several times.
What is the experimental probability of rolling a 3 or a 6?
Enter your answer as a fraction in simplest form in the box.
1 10
2 6
3 4
4 8
5 6
6 6
Total times die rolled =10+6+4+8+6+6=40
Times 3 and 6 appears
4+6=10Experimental probability
P(3 or 6)
10/401/40.25Answer:
[tex]\sf \dfrac{1}{4}[/tex]
Step-by-step explanation:
Experimental probability
Calculated by dividing the number of times an event happens by the total number of trials in an actual experiment.
[tex]\textsf{Experimental Probability} = \dfrac{\textsf{Number of times an event happens}}{\textsf{Total number of trials}}[/tex]
Total number of trials = 10 + 6 + 4 + 8 + 6 + 6 = 40
Total number of times rolling a 3 or a 6 = 4 + 6 = 10
[tex]\textsf{Experimental Probability of rolling 3 or 6} = \sf \dfrac{10}{4}=\dfrac{1}{4}[/tex]