[tex]y +1 = 2x~~~...(i)\\\\y^2 = 3x -2~~~...(ii)\\\\\text{From equation (i):}\\\\y +1 = 2x \\\\\implies y = 2x -1~~~....(iii)\\\\\text{Substitute} ~y = 2x-1~ \text{in equation (ii):}\\\\(2x-1)^2 = 3x-2\\\\\implies 4x^2 - 4x +1 = 3x -2\\\\\implies 4x^2 -4x -3x +3 =0\\\\\implies 4x(x-1) -3(x-1)=0\\\\\implies (x-1)(4x-3)=0\\\\\implies x =1 ~\text{or}~ x = \dfrac 34\\\\\text{Substitute x = 1 in equation (iii):}\\\\y = 2 -1 =1\\\\[/tex]
[tex]\text{Substitute}~ x = \dfrac 34 ~\text{in equation (iii):}\\\\\\y = 2\left(\dfrac 34 \right) -1 = \dfrac 32 -1 = \dfrac 12\\\\\text{Hence,}\\\\(x,y) = (1,1)\\\\\text{And}\\\\(x,y) = \left(\dfrac 34 , \dfrac 12 \right)[/tex]
In the figure given, what is the (numerical) value of x?
(5a)
(4a)
I need help I don't understand
Answer:
2nd one
Step-by-step explanation:
I know this because I learned about this
at breakfast yusef drinks 16 ounces of water
Answer:
Step-by-step explanation:
K, but what's the question?
What is an equation of the line that passes through the points (-4, 2) and (-8, -3)
Answer:
a line through (-4,2) and (-8,-3) has slope = (2+3)/(-4+8) = 5/4 = (y-2)/(x+4)
cross multiply
5x +20 = 4y-8
5x -4y =-28
Step-by-step explanation:
Tres profesores compraron libros: uno de ellos pago $845 por 3 libros de Algebra, 5 libros de Geometría Analítica y 2 libros de Cálculo Diferencial. Otro pago $580 por 2 libros de Geometría Analítica, 4 libros de Algebra y 1 libro de Cálculo Diferencial. El último de ellos pago $605 por un libro de Algebra, 3 libros de Geometría Analítica y 3 de Cálculo Diferencial. ¿Cuál es el costo de cada libro según su tema?
Usando un sistema de ecuaciones, se encuentra que
$96.875 es el costo de un libro de Algebra.$23.125 es el costo de un libro de Geometría Analítica.$146.25 es el costo de un libro de Calculo Diferencial.Para el sistema, hay que:
x es el costo de un libro de Algebra.y es el costo de un libro de Geometría Analítica.z es el costo de un libro de Calculo Diferencial.$845 por 3 libros de Algebra, 5 libros de Geometría Analítica y 2 libros de Cálculo Diferencial, o sea:
[tex]3x + 5y + 3z = 845[/tex]
$580 por 2 libros de Geometría Analítica, 4 libros de Algebra y 1 libro de Cálculo Diferencial, o sea:
[tex]4x + 2y + z = 580[/tex]
$605 por un libro de Algebra, 3 libros de Geometría Analítica y 3 de Cálculo Diferencial, o sea:
[tex]x + 3y + 3z = 605[/tex]
Reemplazando la segunda equación en las otras duas:
[tex]z = 580 - 4x - 2y[/tex]
[tex]3x + 5y + 3z = 845[/tex]
[tex]3x + 5y + 3(580 - 4x - 2y) = 845[/tex]
[tex]-9x - y = -895[/tex]
[tex]9x + y = 895[/tex]
[tex]y = 895 - 9x[/tex]
[tex]x + 3y + 3z = 605[/tex]
[tex]x + 3y + 3(580 - 4x - 2y) = 605[/tex]
[tex]-11x - 3y = -1135[/tex]
[tex]11x + 3y = 1135[/tex]
[tex]y = 895 - 9x[/tex], por eso:
[tex]11x + 3(895 - 9x) = 1135[/tex]
[tex]-16x = -1550[/tex]
[tex]x = \frac{1150}{16}[/tex]
[tex]x = 96.875[/tex]
[tex]y = 895 - 9x = 895 - 9(96.875) = 23.125[/tex]
[tex]z = 580 - 4(96.875) - 2(23.125) = 146.25[/tex]
$96.875 es el costo de un libro de Algebra.$23.125 es el costo de un libro de Geometría Analítica.$146.25 es el costo de un libro de Calculo Diferencial.Un problema similar, que también envuelve un sistema de ecuaciones, es dado en https://brainly.com/question/24646137
the first term of an AP is 2,and the last term is 59.if the sum of the first terms is 610,Find the common difference
Answer:
d = 3
Step-by-step explanation:
The sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( a + l)
where a is the first term and l the last term
Here a = 2, l = 59 and sum = 610 , then
[tex]\frac{n}{2}[/tex] (2 + 59) = 610
[tex]\frac{n}{2}[/tex] × 61 = 610 ( divide both sides by 61 )
[tex]\frac{n}{2}[/tex] = 10 ( multiply both sides by 2 to clear the fraction )
n = 20
Then the sequence has 20 terms with a₂₀ = 59
The nth term of an AP is
[tex]a_{n}[/tex] = a + (n - 1)d
where d is the common difference , then
2 + 19d = 59 ( subtract 2 from both sides )
19d = 57 ( divide both sides by 19 )
d = 3
The equation 12x² + 4kx + 3 = 0 has real and equal roots, if
Answer:
[tex]k=\pm3[/tex]
Step-by-step explanation:
[...] if you can write the LHS as a perfect square, or if you can't spot a factorization of it right away, if and only if the discriminant [tex]\Delta = b^2-4ac[/tex] (or, if b is an even number, 1/4 of it) is zero.
I see it! I see it!
Stare at it for a while. First term is [tex]3(2x)^2[/tex], third term is [tex]3(1)^2[/tex], we are missing a double product, but we can play with k. For the LHS to be [tex]3(2x\pm1)^2 = 3(4x^2\pm4x+1) = 12x^2\pm12x+3[/tex] you just need [tex]4k= \pm12 \rightarrow k=\pm3[/tex].
I don't see it...
Then number crunching it is. Set the discriminant to 0, solve for k
[tex]\frac{\Delta}4 = 4k^2-12\cdot 3 =0 \rightarrow 4k^2=36 \\k^2 = 9 \rightarrow k=\pm3[/tex]
a wind up robot can travel 20m on a single wind. how many times will it need to wind to cover a distance of half a mile?
Which expression represents the word phrase?
Drag an expression into each box to match each word phrase
the quotient of a number and 12
the sum of a number and 12
the difference between 12 and a number
12 - P
12 + p
p-12
p/12
12p
12/p
Answer:
The difference between 12 and a number ➜ 12 - p
The sum of a number and 12 ➜ 12 + p
The quotient of a number and 12 ➜ [tex]\frac{p}{12}[/tex]
The expression in the box for the quotient of a number and 12, the sum of a number and 12 and the difference between 12 and a number are p/12 , 12 + p and p - 12.
What is an expression?Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.
If x and y are the arbitrary numbers.
And sum of the numbers are x + y,
difference of the numbers are x - y and
quotient of number x and y is x/y.
Here we have the expression and their representation,
the quotient of a number and 12 = p/12
the sum of a number and 12 = p + 12
the difference between 12 and a number = p - 12.
Therefore the expression in the box for the quotient of a number and 12,
the sum of a number and 12 and the difference between 12 and a number are p/12 , 12 + p and p - 12.
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find 50% of 20
Find the answer I need it for Get More Math
Answer:
10
Step-by-step explanation:
1/2 of 20 is 10
Answer:
10
Step-by-step explanation:
-
1.) -x + 5y = 49
X =
X - 4y = - 39
-
=
Answer: (1,10)
Step-by-step explanation:
Assuming these are the correctly written equations:
-x + 5y = 49, and
x - 4y = -39
I'll rewrite them:
5y = x + 49
y = (1/5)x + (49/5)
-4y = -x -39
y = (1/4)x + (39/4)
=====
I'll assume the question is to find the point these two lines intersect (?).
See the attached graph. They intersect at (1,10).
Find 1 2··31 1 22 1··22. Show your work
1 = 1 = 1 < 2 < 22
1 is equal to 1 is equal to 1 is less than 2 is less than 22
1 = 1 =1 < 2 < 22 1 1 1 1 1 hope help mark brain.....?
A sixth grade class has 12 boys and 24 girls.
For every 2 boys, there are 4 girls. Do you agree with this statement? Explain.
Answer:
Yes
Step-by-step explanation:
The best way to solve this question is to use ratios. The first ratio to make is 12:24. This represents how there are 12 boys for 24 girls. Ratios remain equivalent as long as both sides of the ratio are simplified by the same number. So, you can divide both sides by 6. When you divide both sides you get 2:4. Therefore, there are 2 boys for 4 girls.
A group of researchers are interested in the possible effects of distracting stimuli during eating, such as an increase or decrease in the amount of food consumption. To test this hypothesis, they monitored food intake for a group of 44 patients who were randomized into two equal groups. The treatment group ate lunch while playing solitaire, and the control group ate lunch without any added distractions. Patients in the treatment group ate an average of 52.1 grams of biscuits, with a standard deviation of 45.1 grams, and patients in the control group ate an average of 27.1 grams of biscuits, with a standard deviation of 26.4 grams. Do these data provide convincing evidence that the average food intake (measured in grams of biscuits consumed) is different for the patients in the treatment group? Assume that conditions for inference are satisfied.
Using the t-distribution, it is found that since the p-value of the test is of 0.0302, which is less than the standard significance level of 0.05, the data provides convincing evidence that the average food intake is different for the patients in the treatment group.
At the null hypothesis, it is tested if the consumption is not different, that is, if the subtraction of the means is 0, hence:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternative hypothesis, it is tested if the consumption is different, that is, if the subtraction of the means is not 0, hence:
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
Two groups of 22 patients, hence, the standard errors are:
[tex]s_1 = \frac{45.1}{\sqrt{22}} = 9.6154[/tex]
[tex]s_2 = \frac{26.4}{\sqrt{22}} = 5.6285[/tex]
The distribution of the differences is has:
[tex]\overline{x} = \mu_1 - \mu_2 = 52.1 - 27.1 = 25[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{9.6154^2 + 5.6285^2} = 11.14[/tex]
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]t = \frac{25 - 0}{11.14}[/tex]
[tex]t = 2.2438[/tex]
The p-value of the test is found using a two-tailed test, as we are testing if the mean is different of a value, with t = 2.2438 and 22 + 22 - 2 = 42 df.
Using a t-distribution calculator, this p-value is of 0.0302.Since the p-value of the test is of 0.0302, which is less than the standard significance level of 0.05, the data provides convincing evidence that the average food intake is different for the patients in the treatment group.
A similar problem is given at https://brainly.com/question/25600813
The angle measurements in the diagram are represented by the following expressions.
Answer:
114 degrees
Step-by-step explanation:
6x+12=3x+63
-3x -12 -3x -12
3x=51
x=17
6(17) +12 = 114
f(c)=x²-3x
find f (-8)
Answer:
88Step-by-step explanation:
Given function:
f(x) = x² - 3xFind f(-8):
f(-8) = (-8)² - 3(-8) = 64 + 24 = 88f(-8)
(-8)²-3(-8)64+2488dividing 0.68÷0.6936
Answer:
0.9804
Step-by-step explanation:
0.68 ÷ 0.6936 = 0.98039215686275
Definition: The points where a graph intersects the x-axis are called it’s __.
Answer:
zeroes or x-intercepts
Step-by-step explanation:
PLEASEEEEE HELP…
In Exploration 3.1.2 you went through a procedure that helped you see how a formula
with n compounds per year relates to the formula for compounding continuously. Select
the appropriate answers to model what you did in the exploration.
Annual growth Rate
A (t) = P(1 + r)
n compounds per year
nt
A () = (1+ a)
a =
[Select]
n
let z = -
7
A (t) = P(1 + [b])"
b = (Select)
let n = ar
Ict
C =
[Select)
A (0) P(1)
110) - P{(x - 2)
+
2
The growth amount is given by the growth rate the duration of the growth
and how the rate is applied to each period.
The correct selections are;
a = n[tex]\displaystyle b = \frac{1}{x}[/tex]c = x·r[tex]\displaystyle \lim_{x \to \infty} \left(1 + \frac{1}{x} \right)^x \to 1[/tex]Reasons:
First part;
The given formula for the annual growth rate is; [tex]A(t) = \mathbf{P \cdot \left(1 + r)^t}[/tex]
[tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{r}{[a]} \right)^{n \cdot t}}[/tex]
Where;
P = The principal
r = The rate per period
n = The number of compounding per period
t = The number of periods
In the above formula, we have that the number of compounding per periods = n
Therefore;
a = nWhich gives the fraction of the interest applied to each period as [tex]\displaystyle \frac{r}{n}[/tex]
Which gives;
[tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{r}{n} \right)^{n \cdot t}}[/tex]
Second part;
When [tex]x = \displaystyle \frac{n}{r}[/tex], we have; [tex]A(t) = \mathbf{P \cdot \left(1 + [b])^{n \cdot t}}[/tex]
[tex]\displaystyle A(t) = P \cdot \left (1 + \frac{r}{n} \right)^{n \cdot t}[/tex]
Therefore;
[tex]\displaystyle b=\frac{r}{n}[/tex]
[tex]\displaystyle \frac{1}{x} = \frac{1}{\left(\frac{n}{r} \right)} =\frac{r}{n}[/tex]
Which gives;
[tex]\displaystyle b=\frac{r}{n} = \mathbf{\frac{1}{x}}[/tex]
[tex]\displaystyle \underline{ b = \frac{1}{x} }[/tex]
Third part;
Where, n = x·r, and [tex]\displaystyle A(t) = \mathbf{P \cdot \left (1 + \frac{1}{x} \right)^{[c] \cdot t}}[/tex]
We have;
[tex]\displaystyle x= \frac{n}{r}[/tex]
[tex]\displaystyle \frac{1}{x}=\frac{r}{n}[/tex]
[tex]\displaystyle A(t) = P \cdot \left (1 + \frac{1}{x} \right)^{[c] \cdot t} = \mathbf{P \cdot \left (1 + \frac{r}{n} \right)^{[c] \cdot t}}[/tex]
Which gives;
c = n = x·r
c = x·rFourth part;
If x is a really large number, we have; [tex]\displaystyle \mathbf{\left(1 + \frac{1}{x} \right)^x}[/tex]
Where x approaches ∞, we have;
[tex]\displaystyle \frac{1}{\infty}=0[/tex]
Which gives;
[tex]\displaystyle \displaystyle \left(1 + \frac{1}{x} \right)^x= \left(1 + \frac{1}{\infty} \right)^\infty = \displaystyle \left(1 + 0\right)^\infty = 1 ^\infty = 1[/tex]
[tex]\displaystyle \underline{\lim_{x \to \infty} \left(1 + \frac{1}{x} \right)^x \to 1}[/tex]Learn more about growth rate formula here:
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Guys please help asap i don't want to fail
Consider the sequence shown.
Answer:
The answer is option D
Step-by-step explanation:
f (n)=-2. (-5)^n-1. Jesus loves you
With the following cards, {blue, green, yellow, blue, red, pink} LaTrice created a sample space. From her chart what is the probability of NOT drawing a red card at all?
The probability of her NOT drawing a red card are very likely
What two words make the contradion "there's"
A. There are
B. There is
C. That is
D. There has
Answer:
C: There is
Step-by-step explanation:
Hope this helps!
Mark as Brainliest if it does.
Lia has 72 green grapes that are shared equally between 8 of her friends. Darrel adds 41 green grapes to his share. How many grapes does Darrel have in all
Darrel has 50 grapes in all.
Lia has 72 green grapes, and she shares them equally between 8 friends. To find out how many grapes each friend receives, divide the total number of grapes by the number of friends:
Number of grapes each friend receives = 72 / 8 = 9
Now, Darrel adds 41 green grapes to his share, so the total number of grapes he has is:
Total grapes for Darrel = Number of grapes Darrel received initially + Additional grapes added by Darrel
Total grapes for Darrel = 9 + 41 = 50
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There are 60 students eating lunch in the cafeteria five-tenths of them brought lunches from home. How many students brought lunches from home?
Answer: 30 Hope this helps please mark brainliest! Thanks!
Step-by-step explanation:
Five tenths=5/10=50%=1/2
So basically it's 30 out of 60 students brought lunch from home.
So the answer is 30!
Systems of elimination for
2w-3q=8
3w-7q=7
i guess is by multiplying 3by the first equation and multiply 2by the second equation
A jacket usually sells for $68.00. If the jacket is 40% off, and sales tax is 6%, what is the total price of the jacket, including tax?
Answer:
$ 43.25
Step-by-step explanation:
68 - 40% = 40.8
40.8 + 6% = $ 43.25
Which two integers is 129 between?
Answer:
128 130
Step-by-step explanation:
128 129 130
There are 32 students in your class. After voting for the class representative, Alan received 3 times as many votes than David. How many votes did Alan receive?
Answer:
alan received 24 votes
Step-by-step explanation:
bark
Cherries cost $4.35 per pound and onions cost $0.98 per pound. Lacey has $21.45 to spend. How many pounds of cherries can Lacey afford if she
has to buy 3 pounds of onions?
Answer:
Lacey could afford 4.25lb of cherries
Step-by-step explanation:
Cost of onions= 3 lb x 0.98/1=2.94
21.45-2.94=18.48$
1 lb=4.35
18.48 x 1lb of cherries/4.35=4.25lb of cherries.
Hope I helped please mark brainliest it means a lot to my progression and thanks! <3
What is the equation of the parabola? If correct will award brainliest, scam answers will be reported!
Answer:
Equation of parabola: y = a(x-h)2 + k or x = a(y-k)2 +h, but the simple version is y2 = 4ax.
Step-by-step explanation:
