The system of linear inequalties that is represented by the graph is formed by the expressions y > 2 · x - 2 and x + 4 · y > - 12.
What system of inequalities generate the graph seen in the image?
Herein we have two inequalities generated by two linear functions whose form is described below:
f(x, y) > a (blue region) (1)
g(x, y) > b (red region) (2)
By direct comparison, we find that the limit of the red region is represented by the inequality y > 2 · x - 2. From the equation of the line we can derive an expression for the limit of the blue region:
Slope
m = [- 4 - (- 3)]/(4 - 0)
m = - 1/4
Intercept
b = y - m · x
b = - 3 - (- 1/4) · 0
b = - 3
Then, the inequation is represented by the linear equation:
y > - (1/4) · x - 3
4 · y > - x - 12
x + 4 · y > - 12
The system of linear inequalties that is represented by the graph is formed by the expressions y > 2 · x - 2 and x + 4 · y > - 12.
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What is 1/4 in feet?
Answer:
0.25 feet
7.62 centimeters
3 inches
Step-by-step explanation:
Not really a clear question-
Vicki and Tamra are working on their math homework together. Vicki has worked p problems, and Tamra has worked 4 times as many problems as Vicki. The expression shows how many problems they have worked altogether.
Answer:
p + 4p
5p
Step-by-step explanation:
Problems Vicki solved = p
Tamra worked 4 times as many problems as Vicki = 4 x p = 4p
total problems solved by both of them =4p + p
= 5p
Can someone please help me with this?
For each triangle shown below, determine whether you would use the Law of Sines or Law of Cosines to find angle x, and explain how you know which Law to use. Then find angle x to the nearest tenth.
NOTE: The perimeter of ABC-31
Given:
The figure of a triangle.
The perimeter of the triangle ABC is 31.
To find:
The value of x in the given triangle.
Solution:
Three sides of the triangle ABC are AB, BC, AC are their measures are [tex]3b-4,2b+1,b+10[/tex] respectively.
The perimeter of the triangle ABC is 31.
[tex]AB+BC+AC=31[/tex]
[tex](3b-4)+(2b+1)+(b+10)=31[/tex]
[tex]6b+7=31[/tex]
Subtract 7 from both sides.
[tex]6b=31-7[/tex]
[tex]6b=24[/tex]
[tex]b=\dfrac{24}{6}[/tex]
[tex]b=4[/tex]
Now, the measures of the sides are:
[tex]AB=3b-4[/tex]
[tex]AB=3(4)-4[/tex]
[tex]AB=12-4[/tex]
[tex]AB=8[/tex]
[tex]BC=2b+1[/tex]
[tex]BC=2(4)+1[/tex]
[tex]BC=8+1[/tex]
[tex]BC=9[/tex]
And,
[tex]AC=b+10[/tex]
[tex]AC=4+10[/tex]
[tex]AC=14[/tex]
Using the law of cosines, we get
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]
[tex]\cos A=\dfrac{(AC)^2+(AB)^2-(BC)^2}{2(AC)(AB)}[/tex]
[tex]\cos A=\dfrac{(14)^2+(8)^2-(9)^2}{2(14)(8)}[/tex]
[tex]\cos A=\dfrac{179}{224}[/tex]
Using calculator, we get
[tex]\cos A=0.7991[/tex]
[tex]A=\cos ^{-1}(0.7991)[/tex]
[tex]x=36.9558^\circ[/tex]
[tex]x\approx 37.0^\circ[/tex]
Therefore, the value of x is 37.0 degrees.
URGENT!!!!!!HELP NOW PLEASE!!!!!!!!!
Answer:
$2.96
Step-by-step explanation:
Here, we want to get the expected value
To get the expected value, we have to multiply each payout by its corresponding probability and add up for all
So what this mean is that the expected value is the summation of the products of each pay out and their probability
We have the expected value calculated as;
0(0.12) + 1(0.2) + 2(0.38) + 5(0.2) + 10(0.1)
= 0 + 0.2 + 0.76 + 1 + 1 = $2.96
Plsss can someone answer the bottom question
Answer:
30
Step-by-step explanation:
[tex]\frac{75}{100} = \frac{x}{40}\\\\Cross- multiply:\\\\\\75*40=100x[/tex]
3000 = 100x
x = 30
Another way:
75/100 is in reality 3/4
and 3/4 of 40 = 30
40/4 = 10
10 * 3 = 30
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Which of the following equations represents the graph shown?
Answer:
ok from looking at this equation we can we that every it goes 1 up and on over so
-x+2
Hope This Helps!!!
What is the domain of the square root function graphed below
Answer:
Dominio de una Raíz cuadrada
Cuando tenemos una raíz, para estudiar su existencia debemos saber que una raíz existe si y solo sí el radicando (lo que está dentro de la raíz) sea mayor o igual a cero.
Por lo tanto deberemos estudiar el signo de lo que se encuentra dentro de la raíz; y determinar las zonas positivas y las raíces que son las zona de existencia de la función raíz o dominio de esta función.
Step-by-step explanation:
qsy
the area of the rectangle is 48cm^2
show that x satisfies the equation x^2 + 7x -78 = 0
Answer:
No its doesn't satisfy the equation.
[tex]{ \bf{area = 2(l + w)}} \\ { \tt{48 = 2((x + 10) + (x - 3))}} \\ { \tt{24 = 2x + 7}} \\ 2x = 17 \\ x = 8.5 \\ \\ { \bf{in : \: {x}^{2} + 7x - 78 = 0 }} \\ x = 6 \: \: and \: \: - 13[/tex]
solve for x. Round to the nearest tenth, if necessary.
Answer:
25.1
Step-by-step explanation:
Sin=opposite/hypotenuse
Sinx=4.2/9.9
x=arcsin(4.2/9.9)
x=25.1 degrees rounded from 25.102
how do you solve 2x+320=425
Answer:
how to solve your problem
Step-by-step explanation:
2x320=425
subtract both 320 both from sides of the equation
2x+320-320=425-320
subtract numbers
2x=105
divide both sides of equation by the same terms
2x/2=105/2
simplify
x=105/2
answer is x=105/2
Anna, Bob and Chris are altogether 31 years old. How old will all three be altogether in three years time? (A)32 (B)34 (C)35 (D)37 (E)40
Answer:
40
Step-by-step explanation:
A+B+C = 31
Add 3 years to each age
A+3 +B+3 + C+3 = 31 +3+3+3
They will be
A+3 +B+3 + C+3 = 40
Answer:
it will be 40
Step-by-step explanation:
If they are altogether 31 years old now in 3 years we just add 9 thus it is 40
question 2 help pls
Answer:
[tex](\sqrt{x+3} )^{2} + 4^{2} = 5^{2}[/tex]
x + 3 + 16 = 25
x + 19 = 25
x = 6
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
Find the HCF of:
3x and 6x.
Answer:
3x
Step-by-step explanation:
We need to find the HCF of given two numbers .HCF is the Highest Common factor for two or more than two numbers . The given numbers are ,
[tex]\implies Numbers = 3x \ and \ 6x [/tex]
Let's factorise the numbers , we get .
[tex]\implies 3x = 3 \times x [/tex]
[tex]\implies 6x = 3\times 2 \times x [/tex]
The common factors are 3 and x . Therefore the HCF is 3 × x = 3x .
[tex]\implies\underline{\underline{ HCF = 3x }}[/tex]
Solve the system of equations.
−5x−3y−9=0
4x−18y−54=0
y=? x=?
Answer:
Step-by-step explanation:
Eq. 1 ) −5x−3y−9=0
Eq. 2) 4x−18y−54=0
there are two routes to solve this, Substitution or elimination, I'll go for the 2nd one because I can see that the y values are a multiple of each other :)
6 *( −5x−3y−9=0 )
Eq. 3) -30x -18y =54
subtract Eq. 2 from Eq. 3 :)
-30x -18y =54
-( 4x−18y=54)
-34x = 0
so according to the equations then x =0 but, that's not really a full answer, so now we should go back and try the other method, substitution,
then:
-5x = 9 +3y
x = - 9/5 + (-3/5)y
now plug that into Eq. 2
4( - 9/5 + (-3/5)y ) - 18y = 54
-36/5 + (-12/5)y -18y = 54
(-12/5)y - (90/5)y = 54+36/5
-(102/5)*y =270/5+36/5
-(102/5)y = 306/5
y = (-5/102)*(306/5)
y = -306/102
y = -3
then plug in for either equation
-5x-3( -3) = 9
-5x + 9 = 9
-5x = 0
x = 0
now we have the full answer
check it by plugging in both x and y into the 2nd equation
4(0) - 18(-3) = 54
54= 54
this seems good
Find end and mid point
Answer:
You already post your answer!
Step-by-step explanation:
Maybe you should get two points in order to find midpoint and endpoint!
or you should give other information!
Find the coordinates of the
midpoint M. *
A(-4,-8) and B(-1,4)
Please provide an explanation
Answer:
M(-5/2, -2)
Step-by-step explanation:
Add the x-coordinates & divide by 2.
Add the y-coordinates and divide by 2.
x-coordinates: -4, -1
(-4 + (-1))/2 = -5/2
y-coordinates: -8, 4
(-8 + 4)/2 = -4/2 = -2
M(-5/2, -2)
Solve the equation. Where necessary, indicate when the equation has no solution or is an identity.
5(2X + 8) - 5x = 5(5x + 6)
Answer:
x=0.5
Step-by-step explanation:
10x-40-5x=2x+30
5x+10=25x
10=20x
x=0.5
How to solve ,step by step
Answer:
gradient = slope = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{rise}{run}[/tex]
Slope intercept Form equation : y = mx + b
m = slope or gradient
b = y - intercept ( where the line crosses the y = axis)
x and y = are place holders for a coordinate pair that makes the equation true
c) y = -6x + 8
The -6 is the m. It's the slope or gradient.
the + 8 is the b. It's the y- intercept.
d) y = 4
This is a horizontal line. It intercepts the y-axis at 4.
That means the 4 is the y-intercept.
There is no x. That means the slope is 0. The line rises 0 as it runs left to right.
e) y -4x= 0
equation needs to be is standard form y = mx + b.
add 4x to both sides in order to isolate the y variable.
y = 4x + 0.
The slope or gradient is 4. The y - intercept is 0. The line crosses through the origin.
f) y -x = -8
Add x to both sides.
y = x - 8
There is one x. That means the gradient is 1. The y-intercept is the -8
g) y + 3x = 7
Subtract 3x from both sides.
y = -3x + 7
-3 = gradient. 7 = y-intercept.
h) y + [tex]\frac{1}{2}[/tex]x = -4
Subtract [tex]\frac{1}{2}[/tex]x from each side.
y = -[tex]\frac{1}{2}[/tex]x - 4
One last thing. If you are presented with an equation without a y, the gradient is 'undefined'.
example : x = 4
This a vertical line passing through 4 on the x-axis. There is no 'b' because its not crossing the y-axis.
Why is it 'undefined' ?
As the line rises it, it does not 'run' left or right. [tex]\frac{rise}{0}[/tex] . Zero can never, ever be in the denominator. Denominators can't be zero. That is why we say it's 'undefined'.
Hope this helps.
the sum of three consecutive terms of an arithmetic progression is 24, find the middle term?
Answer:
Therefore,
Middle term = 8
Sequence,
a-d, a, a+d = 8-6, 8, 8+6
= 2,8,14
Step-by-step explanation:
Answer:
The middle term is 8
Step-by-step explanation:
The middle term is 8.
Which is the value of this expression {jk^-2/j-1k-3}3, when j=-2 and k=-1?
Answer:
-9
Step-by-step explanation:
{-2*-1^-2/-2-1*-1-3}3
= -9
Answered by GAUTHMATH
In which section of the number line is 32−−√?
where's the number line?
maybe u can attach it at the comments:)
Answer:
Section B
Step-by-step explanation:
. Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. population mean math score parents college grads. population mean math score parents high school grads. _____ _____ b. What is the point estimate of the difference between the means for the two populations
Answer:
Following are the responses to the given question:
Step-by-step explanation:
For point a:
Following are the null and alternative hypotheses:
[tex]H_0 : \mu_1 \leq \mu_2\\\\H_1 : \mu_1 > \mu_2[/tex]
For point b:
By using the Excel we obtained the output of the 2 sample t-test that is defined in the attached file.
These point estimately are the difference among the mean for the two populations:
[tex]\to \mu_{\bar{x_1}-\bar{x_2}} = \mu_{\bar{x_1}}-\mu{\bar{x_2}} ={\bar{x_1}-\bar{x_2}}=573-491=82[/tex]
# By selling 5 oranges, a shopkeeper gains the selling price of 1 orange. Find his profit percentage.
O 50%
O 25%
O 15%
O 20%
profit from selling 5 oranges is 20%
Profit percentage of selling 5 oranges, a shopkeeper gains the selling price of 1 orange is equals to 25%.
What is profit?" Profit is defined as difference of cost price from selling price when the selling price of a product is greater than its cost price."
Formula used
Profit percentage = [tex]\frac{Selling price - cost price}{cost price} (100)[/tex]
According to the question,
We know that,
Selling price = cost price + profit
Substitute the given condition in the selling price formula we get,
Selling price of 5 oranges
= Cost price of 5 oranges + Selling price of 1 oranges
⇒(S.P of 5 oranges) - (S.P of 1 oranges) = C.P. of 5 oranges
⇒S.P of 4 oranges = C.P of 5 oranges
⇒[tex]\frac{S.P}{C.P}=\frac{5}{4}[/tex]
Substitute the value in the formula to get profit percentage,
Profit percentage = [tex]\frac{5-4}{4}(100)[/tex]
= 25%
Hence, profit percentage of selling 5 oranges, a shopkeeper gains the selling price of 1 orange is equals to 25%.
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Can someone help me with this question please. I've been struggling.
Write the equation of the line of reflection
Answer:
y=-1
Step-by-step explanation:
Since we see an overlap, the line must cross through the original image.We can solve the equation of the line of reflection by realizing there is no slope because the reflection is parallel to the x-axis.Multiply and reduce to lowest form and convert into a mixed fraction:
a) 15 x 3/5
b) 4 x 1/3
c) 5/2 x 6
Answer:
a) 9
b)
[tex]1 \frac{1}{3} [/tex]
c) 15
Step-by-step explanation:
The first step is to cancel out the fraction's denominator if possible.
a)
[tex]15 \times \frac{3}{5} [/tex]
We can cancel the 5 out since 15 divided by 5 is 3. The answer that comes out is
[tex]3 \times \frac{3}{1} [/tex]
Since 3/1 is 3, we can now simplify the values:
[tex]3 \times 3 = 9[/tex]
b)
[tex]4 \times \frac{1}{3} [/tex]
4 is indivisible by three and gives a non-whole value. This is not what we need here.
Instead we should do the division rule and find the remainder.
In this case, 4 divided by 3 gives 1 with a remainder of 1.
[tex]4 \times \frac{1}{3} = \frac{4}{3} [/tex]
After we simplify the non-mixed fraction, we have to change it into a mixed fraction, which consists of a whole number and a fraction. We can split it into the following:
[tex] \frac{4}{3} = 1r1[/tex]
The r1 is just the remainder of the fraction. Since we cannot remove 1 from the remainder, we add it back into the fraction's denominator of 3. This gives:
[tex] \frac{4}{3} = 1 + \frac{1}{3} = 1 \frac{1}{3} [/tex]
c)
[tex] \frac{5}{2} \times 6[/tex]
For this part, we can cancel out 2 since 6 is divisible by 2. This gives:
[tex] \frac{5}{1} \times 3[/tex]
Since 5/1 is 5,
we can now solve part c:
[tex]5 \times 3 = 15[/tex]
The length of a rectangle exceeds its width by 3 inches. The area of the rectangle is 70
square inches. Find its dimensions. Hint: as in the example, use the equation for area,
A = lw.
Answer:
70= (x+3)
Step-by-step explanation:
the length of the rectangle its width by 3 inches, if the width is x,the length will be x+3. so A=LW= 70
To find= 70= (x+3)x
x= 7 or -10
In the diagram, what is AC?
find the DB =[tex]\displaystyle\bf \sqrt{17^2-8^2} =15[/tex] ; now find AD=AB-DB=21-15=6 .Then AC=[tex]\displaystyle\bf \sqrt{AD^2+CD^2} =\sqrt{6^2+8^2} =10[/tex]
Answer:
C
Step-by-step explanation:
Using Pythagoras' identity in both right triangles
To find BD
BD² + CD² = BC²
BD² + 8² = 17²
BD² + 64 = 289 ( subtract 64 from both sides )
BD² = 225 ( take the square root of both sides )
BD = [tex]\sqrt{225}[/tex] = 15
Then
AD = AB - BD = 21 - 15 = 6
To find AC
AC² = AD² + CD²
AC² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )
AC = [tex]\sqrt{100}[/tex] = 10 → C
CHECK THE IMAGE! FOR THE QUESTION
Answer:
A
Step-by-step explanation:
The side of a rectangle legnth x+2 and width x-5. WHich equation describes the area A of the rectangle in terms of x?
Answer:
[tex] {x}^{2} - 3x - 10[/tex]
Step-by-step explanation:
Area= length× width
[tex](x + 2)(x - 5) \\ {x}^{2} + 2x - 5x - 10 \\ {x}^{2} - 3x - 10[/tex]