Answer:
Both functions must be linear. The y-intercepts of f(x) and g(x) must be opposites.
Step-by-step explanation:
First we need to solve.
h(x) = 10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16
It seems tricky at first but we know a couple things. When we add the factors of h(x) together we get j(x) = 7[tex]x[/tex] so we know that when we multiply 2 numbers together it should equal 10 but add up to 7.
Lets write the possible combinations of 10:
1 x 10 = 10
2 x 5 = 10
5 x 2 = 10
10 x 1 = 10
Now which combination will add or subtract to 7?
1 - 10 = 9 1 + 10 = 11
2 - 5 = -7 2 + 5 = 7 We can stop here!
2 and 5 are in our factor, so let's write it down.
(2x ) (5x ) We know there will one + and one - because the -16. If we had two + it would be positive 16, and is we had two - it would also be positive 16 because a - x - = +
Now the last number is 16. Let's find the possible combinations of 16.
1 x 16 = 16
2 x 8 = 16
4 x 4 = 16 We will stop here because we end up repeating posibilities.
Here is where we think critically. Whichever combination we choose has to be multiplied by 2 and 5 and end up equaling 12. I think 16 is too high so let's try 2 and 8.
2x * 2 = 4x 5x * 8 = 40x Now one is positive and the other is negative. Let's try each combination.
4x - 40x = -36x -4x + 40x = 36x Neither of those are 12x. So let's Try 4 and 4.
2x * 4 = 8x 5x * 4 = 20x One will be positive and the other will be negative. Let's try each combination.
8x - 20x = -12x -8x + 20x = 12x There is our combination! Remeber when you mutiply together you have to multiply the opposite factor. Here are the combinations:
(Ax + B )(Cx + D) = (Ax*Cx) + (Ax*D) + (B*Cx) + (B*D)
(Ax - B )(Cx + D) = (Ax*Cx) + (Ax*D) - (B*Cx) - (B*D)
(Ax + B )(Cx - D) = (Ax*Cx) - (Ax*D) + (B*Cx) - (B*D)
(Ax - B )(Cx - D) = (Ax*Cx) - (Ax*D) - (B*Cx) + (B*D)
So we have:
(2x + 4) (5x - 4)
Let's prove is and multiply it back out.
2x*5x - 2x*4 + 4*5x - 4*4
10[tex]x^{2}[/tex] - 8[tex]x[/tex] + 20
10[tex]x^{2}[/tex] + 12[tex]x[/tex] - 16 So we got it right!
Now let's see if they really add up to 7x.
(2x + 4) (5x - 4) which we now need to add together
2x + 4 + 5x - 4 Rearrange
2x + 5x + 4 - 4 Combine like terms
7x + 0 or 7x It works!
So our original functions are f(x) = 2x + 4 and g(x) = 5x - 4
Now to answer the question. Select 2 options.
Both functions must be linear. Yes, because an equation with only an [tex]x[/tex] will be a straight line, if we graph both functions they are both straight lines.
Both functions must be quadratic. No, because a quadratic equation is any equation that can be rearranged in standard form as [tex]ax^{2} + bx +c = 0[/tex] Neither f(x) or g(x) can be rearranged to fit that.
Both functions must have a y-intercept of 0. No, to find the y intercept we set x to 0 and solve for y.
2x + 4 = y 5x - 4 = y
2(0) + 4 = y 5(0) - 4 = y
0 + 4 = y 0 - 4 = y
y = 4 y = -4
Neither are 0.
The rate of change of either f(x) or g(x) must be 0. Let's find the rate of change for each equation.
We need an interval so we have to find one. Let's use 1 and 2 for x, but we have to solve for y to get the coordinate.
f(x[tex]_{1}[/tex]) = 2x + 4 f(x[tex]_{2}[/tex]) = 2x + 4 g(x1) = 5x - 4 g(x2) = 5x - 4
x[tex]_{1}[/tex] = 1 x[tex]_{2}[/tex] = 2 x
y[tex]_{1}[/tex] = 2(1) + 4 y[tex]_{2}[/tex] = 2(2) + 4 y
y[tex]_{1}[/tex] = 2 + 4 y[tex]_{2}[/tex] = 4 + 4 y
y[tex]_{1}[/tex] = 6 y[tex]_{2}[/tex] = 8 y
( 1 , 6 ) ( 2 , 8 ) ( 1 , 1 ) ( 2 , 6 )
Rate of change formula is:
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Now we just plug in for each function.
f(x) = 2x + 4 g(x) = 5x - 4
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex] = [tex]\frac{8 - 6}{2 - 1}[/tex] = [tex]\frac{2}{1}[/tex] = 2
You can see the rate of change is not 0 for either function.
The y-intercepts of f(x) and g(x) must be opposites. Yes, we solved for the y intercepts earlier.
To find the y intercept we set x to 0 and solve for y.
2x + 4 = y 5x - 4 = y
2(0) + 4 = y 5(0) - 4 = y
0 + 4 = y 0 - 4 = y
y = 4 y = - 4
4 and - 4 are opposites, so this statement is also true.
"the sum of a number and 4."
answer?
Answer:
4+x
Step-by-step explanation:
[tex]Let\: the\:unknown\:number\:be \:x\\\\= x +4[/tex]
Answer:
x + 4
Step-by-step explanation:
The sum - '+'
Of a number - 'x'
And four - '4'
The sum of a number and 4 would be 'x + 4'.
Hope this helps.
(-6)(-2x – 4y); x = 1, y = 3
Answer:
First, you have to substitute your x and y.
This looks like
(-6)(-2 - 12) because you multiplied (-2)(1) and (-4)(3)
Then, you have to do what's in the parenthesis because of order of operations.
(-6)(-14)
The answer is 84 I believe.
Please answer ASAP! Describe how you would graph a figure that is translated by (x - 4, y + 2). I will pick you as brainliest!
Answer:
the answer is 3820
Step-by-step explanation:
first you do 28 +38 which is 393 and then you do 383_jals which is 69, please mark me as brainiest
Clare had $110 in her saving. She wanted to buy an MP3 player for $ 118 what is the difference between how much money Clare had and how much she needed
Answer:
$8
Step-by-step explanation:
We want to find the difference between the money Clare has and the money she needs.
Difference means subtract, so we should subtract the amount of money she has from the amount she needs.
money needed - money she has
She has $110 and she needs $118 to purchase the MP3 player.
$118 - $110
Subtract 110 from 118.
$8
The difference between the money Clare has and the money she needs is 8 dollars.
If a and b are real numbers, then (a + b)2 = a2 + b2 Provide a counterexample for the statement.
a = 0 and b = 1
a = 1 and b = 0
a = 1 and b = 2
a = 0 and b = 0
Answer:
a = 1 and b = 2
Step-by-step explanation:
Input the counterexample into the formula.
(a + b)² = a² + b²
(1 + 2)² = 1² + 2²
(3)² = 1 + 4
9 ≠ 5
This proves that the statement is false.
how to put -7/9 and -4/9 and 1/9 and 1/2 on a number line from least to greatest
Step-by-step explanation:
Take the LCM of the denominators:
=> LCM = 18
=> -7/9 x 2/2 = -14/18
=> -4/9 x 2/2 = -8/18
=> 1/9 x 2/2 = 2/18
=> 1/2 x 9/9 = 9/18
When the number is negative, the greater the number, the smaller it is.
So, -14 is smaller than -8.
< = smaller than
=> -14/18 < -8/18 < 2/18 < 9/18
=> -7/9 < -4/9 < 1/9 < 1/2
Answer:
-7/9, -4/9, 1/9, 1/2
There's no change as this list is already from smallest to largest
==========================================================
Explanation:
We can get each denominator to 18 as this is the LCD (lowest common denominator)
-7/9 = -14/18 ... multiply top and bottom by 2
-4/9 = -8/18 ... multiply top and bottom by 2
1/9 = 2/18 ... multiply top and bottom by 2
1/2 = 9/18 ... multiply top and bottom by 9
We now have to sort this list {-14/18, -8/18, 2/18, 9/18}
Which is the same as sorting {-14, -8, 2, 9} since we can focus solely on the numerators. This only applies when the denominators are the same.
The list {-14, -8, 2, 9} is already sorted from smallest to largest. Think of a number line. We would have -14 as the left most value, then -8 is next, followed by 2 and then 9.
So the original list of fractions {-7/9, -4/9, 1/9, 1/2} is already sorted from smallest to largest.
--------------
An alternative is to use your calculator to see that
-7/9 = -0.78 approximately
-4/9 = -0.44 approximately
1/9 = 0.11 approximately
1/2 = 0.50
The order from least to greatest is
-0.78, -0.44, 0.11, 0.50
The -0.78 is smaller than -0.44 since its further away from 0
So the order would be
-7/9, -4/9, 1/9, 1/2
and there's no change from the original order your teacher gave you.
If the measure of an angle is 13º, find the measure of its supplement.
Answer:
167°
Step-by-step explanation:
The supplement of an angle will always be the measure of an angle, when added to the original, will equal 180°.
If we know the measure of 1 of these angles, we can easily find the measure of the other, assuming x is the missing angle measure.
[tex]13+x=180[/tex]
We can subtract 13 from both sides to get the value of x.
[tex]13+x-13=180-13\\\\x=167[/tex]
Hope this helped!
Answer:
167
Step-by-step explanation:
Supplementary angles add to 180
x+13 = 180
Subtract 13 from each side
x = 180-13
x =167
The supplement to 13 is 167
A sprinter runs 400 meters in 54 seconds. What is the runner’s average running rate in meters per second? (Round to the nearest tenth.)
Answer:
Step-by-step explanation:
400 meters/54 seconds = 7.407 meters per second. when rounded to the nearest 10th you would get 7.4
Answer - 7.4
it would be amazing if you show work please
Answer:
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex](1,\infty)[/tex]
Step-by-step explanation:
The domain of a function is the span of x-values it covers.
The range of a function is the span of y-values it covers.
From the graph, we can see that the domain stretches infinitely in both directions. Therefore, the domain is all real numbers.
In interval notation, this is:
[tex](-\infty,\infty)[/tex]
For the range, note that horizontal line at y=1.
The dotted line tells us that there is a horizontal asymptote there. In other words, y would never reach exactly 1.
Thus, our range would be all values greater than 1 (to positive infinity).
In interval notation, this is:
[tex](1,\infty)[/tex]
And we're done :)
Find the distance between the points (2,-9) and (-1,4)
Answer:
The answer is
[tex]\sqrt{178} \: \: or \: \: 13.34 \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(2,-9) and (-1,4)
The distance between them is
[tex]d = \sqrt{ ({2 + 1})^{2} + ({ - 9 - 4})^{2} } \\ = \sqrt{ {3}^{2} + ({ - 13})^{2} } \\ = \sqrt{9 + 169} \\ [/tex]We have the final answer as
[tex] \sqrt{178} \: \: or \: \: 13.34 \: \: units[/tex]Hope this helps you
Answer:
[tex]\sqrt{178}[/tex] ≈ 13.3
Step-by-step explanation:
Calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, - 9) and (x₂, y₂ ) = (- 1, 4)
d = [tex]\sqrt{(-1-2)^2+(4+9)^2}[/tex]
= [tex]\sqrt{(-3)^2+13^2}[/tex]
= [tex]\sqrt{9+169}[/tex]
= [tex]\sqrt{178}[/tex] ≈ 13.3 ( to 1 dec. place )
(5/2)x=5 please help me
Answer:
x=2.5
Step-by-step explanation:
2.5x=5
subtract 2.5 from itself and 5
x=2.5
What is the value of 3.5 (11) + 1.9 (11) + 1.6 (11)?
Answer:
77
Step-by-step explanation:
3.5(11)+1.9(11)+1.6(11)
3.5(11)=38.5
1.9(11)=20.9
1.6(11)=17.6
38.5+20.9+17.6
77
Name two lines in the diagram.
Answer: Line BC and Line DE
Step-by-step explanation:
In geometry terms, we can say that for any set of two points, we always can find a line that passes through them.
For example, in the image, we can see two lines (but actually we could make more with those points)
We can see a line that connects points B and C, and we can call that line as:
Line BC
We also can see a line that connects the points D and E, we can call this line as:
Line DE
So the two lines are: Line BC and Line DE
Which equation represents exponential decay?
A. y = 160 (31)1
B. y= (3.1)
C. y = 10(0.13)
D. y = 100(1.03)*
Answer:
the answer is C
Step-by-step explanation:
because of you multiply by the decimals that less than 1, the number will decrease.
b mi
a mi
a. Perimeter:
b. Area:
What is the perimeter and the area?
Slope m = -5 y= intercept -4 What is the equation?
Answer:
[tex]\huge\boxed{y = -5x - 4}[/tex]
Write an equation in the format y = mx + b, or the slope-intercept formula, where:
m = slope
b = y-intercept
Plug in the values given:
y = (-5)x + (-4)
Simplify:
y = -5x - 4. This is the equation in slope-intercept form.
Answer: y=-5x-4
Step-by-step explanation:
Slope intercept form is y=mx+b
Since m represents slope you will plug in -5 because that is your slope.
Since b represents the y-intercept, you will plug in -4 after y=-5x
so therefore your equation is y=-5x-4
Tried my best to explain...
Find the sum. 5/6 + 4/9
Answer:
The answer is 23/18..
5/6+4/9=23/18.
Answer:
Exact Form:
23/18
Decimal Form:
1.27
Mixed Number Form:
1 5/18
Step-by-step explanation:
The perimeter of a parallelogram is 56 meters. The width of the parallelogram is 8 meters less than its length. The length of the parallelogram is . The width of the parallelogram is . Find the length and the width of the parallelogram.
Answer: 8 Because i do math and got 8
i’ve been trying to figure out this answer. it’s algebra. at first i got 76 but i’m pretty sure it’s wrong.
Answer:
36
Step-by-step explanation:
● 3[ (4-2)^5 -20]
● 3 ( 2^5 -20 )
● 3 (32-20)
● 3× 12
● 36
PLEASE HELP ASAP!!! NEED THEM ALL ANSWERED!!!
① Find the Value of x from the image and then find the indicated side length in each rhombus using the equation below:
✧ x = ▢
✧ AB = 5(24) - 87 = ▢
② Find the Value of x from the image and then find the indicated side length in each rhombus using the equation below:
✧ x = ▢
✧ RS = QR = 3(7) = ▢
③ Finish the statements:
✦ First: angle K + angle N = 180 (This one is complete)
✦ Second: x + 68 + 2x + 4 = 180 (This one is complete)
✦ Third: Combine Like Terms.....
✧ ▢ x + ▢ = 180
✦ Fourth: Subtract 72 from both sides!
✧ 3x = ▢
✦ Fifth: Divide both sides by three!
✧ x = ▢
(I don't need the steps, but feel free to show steps as well as the answers. And yes, the pictures are in order.)
Answer:
1) x = 24
AB = 33
AD = 33
2) x = 7
PS = 21
QR = 21
3) x = 36
K = 104
N = 76
Step-by-step explanation:
1) 5x-87 = x+9
4x = 96
x = 96/4
x = 24
AB = 5(24)-87 = 33
AD = 24 + 9 = 33
2) 4x - 7 = 3x
x = 7
PS = 4(7) - 7 = 21
QR = 3(7) = 21
3) x + 68 + 2x + 4 = 180
x = 36
K = 36 + 68 = 104
N = 2(36) + 4 = 76
What is greater 16/28 or 28/49
Answer:
They are equal.
Step-by-step explanation:
Step 1: Evaluate 16/28
16/28 = 0.571429...
Step 2: Evaluate 28/49
28/49 = 0.571429...
Step 3: Compare
0.571429... ? 0.571429...
0.571429... = 0.571429...
So 16/28 = 28/49
Divide: (5 + 4i) / (-3 – 2i)
Answer:
-23/13 - 2/13iStep-by-step explanation:
[tex]\frac{5+4i}{-3-2i}\\\\\mathrm{Apply\:complex\:arithmetic\:rule}:\\\\\quad \frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}\:=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}\\\\a=5,\:b=4,\:c=-3,\:d=-2\\\\=\frac{\left(5\left(-3\right)+4\left(-2\right)\right)+\left(4\left(-3\right)-5\left(-2\right)\right)i}{\left(-3\right)^2+\left(-2\right)^2}\\\\Refine\\=\frac{-23-2i}{13}\\\\[/tex]
[tex]\mathrm{Rewrite\:}\frac{-23-2i}{13}\mathrm{\:in\:standard\:complex\:form:\:}-\frac{23}{13}-\frac{2}{13}i\\[/tex]
Select the correct answer. Which term is a term in this expression? -3x - 7(x+4) OA x + 4 O B. -7 Ос. -3x OD. -3
Answer:
D. -3x
Step-by-step explanation:
Terms have the form k or kx^n, where k is a number, x is a variable, and n is a whole number.
-3x follows the above rule, so -3x is a term.
Answer:
D
Step-by-step explanation:
Hi...
Given that f(x) = x2 + x and g(x) = 3x + 1, find the value of g(f(-2)).
Answer:
7Step-by-step explanation:
[tex]f(x) = x^2 + x\\g(x) = 3x + 1\\\\g(f(-2)) = ?\\f(-2) =?\\[/tex]
To find f(-2) , Substitute -2 for x in the given equation ;
[tex]f(-2)= (-2)^2 +(-2)\\f(-2) = 4-2\\f(-2) = 2[/tex]
To find g(f(-2)) ;
[tex]g(f(-2))\\f(-2) =2\\\\= g(f(-2)) = g(2)\\[/tex]
To find g(2) , substitute 2 for x in the given equation
[tex]g(x) = 3x+1\\g(2) = 3(2)+1\\\\g(f(-2)) = 6+1\\\\g(f(-2))=7[/tex]
Value of g(f(-2)) is equals to 7.
What is composition function?"Composition function is defined as where two function combined together to create a new function. It is denoted by 'o'."
According to the question,
Given,
f(x) = x² + x
g(x) = 3x + 1
Substitute the value x=-2 in function f(x) we get,
f(-2) = (-2)² +(-2)
= 4 -2
= 2 ______(1)
Again substitute the value of x = f(-2) in g(x) to get composition function,
g(f(-2)) = 3f(-2) +1
Substitute the value f(-2) from (1) we have,
g(f(-2)) = 3(2) + 1
⇒ g(f(-2)) = 7
Hence, value of g(f(-2)) is equals to 7.
Learn more about composition function here
https://brainly.com/question/20379727
#SPJ2
What is the area of the rhombus
Answer:
[tex]Area \: of \: rhombus = \frac{pq}{2} [/tex]
Where p is diagonal 1 and q is diagonal 2
Step-by-step explanation:
Different formulas to find the area of a rhombus are:
Formulas to Calculate Area of RhombusUsing DiagonalsA = ½ × d1 × d2
Using Base and HeightA = b × h
Using TrigonometryA = b2 × Sin(a)
Area = d1×d2÷2
Help me please I’ll give brainliest PLEASE HELP ASSP
Answer:
fundamental orders of connecticut
Step-by-step explanation:
En un pastel que se quiere repartir a 5 personas, se logran generar 8 piezas al cortarlo, cual de las siguientes expresiones refleja esta acción: ⅕ ⅝ ¾
Answer:
La respuesta es 1/5.
Step-by-step explanation:
porque el 1 pastel se divide en 5 personas.
Espero que esto ayude.
Brad gets an allowance of $16 each week, and his younger sister Samantha gets an allowance of $9 each week. Brad saves one-half of his allowance, and Samantha saves two-thirds of her allowance. Suppose Brad started with $0 savings, and Samantha started with $40. How many weeks will it take until they have the same amount in savings?
Answer:
20 weeks
Step-by-step explanation:
To be able to find the amount of weeks that it will take them to have the same amount, you can say that the amount that Brad saves each week for the number of weeks is equal to the amount that Samantha saves each week for the number of weeks plus the initial amount she has:
(16*1/2)*x=((9*2/3)*x)+40, where
x is the number of weeks
Now, you have to solve for x:
8x=6x+40
8x-6x=40
2x=40
x=40/2
x=20
According to this, the answer is that it will take them 20 weeks to have the same amount in savings.
Is it true that ƒ −(g − h) = (ƒ − g) − h? Explain why you believe the equation is true or provide a counterexample to show that it is not.
Answer:
The expression is false
Step-by-step explanation:
Given
[tex]f - (g - h) = (f - g) - h[/tex]
Required
True or False
To determine if the expression is true or false, we need to simplify both sides of the equation
[tex]f - (g - h) = (f - g) - h[/tex]
Start by opening the bracket on the right hand side
[tex]f - (g - h) = f - g - h[/tex]
Then open the bracket on the left
[tex]f - g + h = f - g - h[/tex]
Subtract f - g from both sides
[tex]f - g - (f - g) + h = f - g - (f - g) + h[/tex]
[tex]f - g - f + g + h = f - g - f + g - h[/tex]
[tex]f - f - g + g + h = f - f - g + g - h[/tex]
[tex]h \neq -h[/tex]
Hence;
The statement is false
To further check;
Assume f = 5; g = 4 and h = 3
[tex]f - (g - h) = (f - g) - h[/tex] becomes
[tex]5 - (4 - 3) = (5 - 4) - 3[/tex]
[tex]5 - 4 + 3 = 5 - 4 - 3[/tex]
[tex]2 \neq -2[/tex]
.......................
Answer:
1) when tomato patch is 6.5 feet the area is 191.75 sq.ft
2) when tomato patch is 7 feet the area is 217 sq.ft
3) when area is 338 sq.ft the tomato patch is 9.0778 feet
4) when area is 147.25 sq.ft the tomato patch is 5.543799 feet
Step-by-step explanation:
The given equation is :
3x^2 + 10x
Length of Tomato (in feet) x, 6.5 , x , 7
Patch Area of Vegetable Garden (in square feet) 338, x , 147.25, x
So we can find the missing terms with the help of the equation 3x^2 + 10x
Putting the values of x from the length of the tomato patch
1) 3x^2 + 10x= 3(6.5)²+ 10 (6.5)=126.75+ 65= 191.75 square feet
2) 3x^2 + 10x= 3(7)² +10 (7)= 147+70= 217 square feet
So the area of her vegetable garden for a variety of lengths of the tomato patch= 6.5 feet is 191.75 square feet
and for 7 feet is 217 square feet
Similarly we can find the length of the tomato patch from the area by again using the given equation 3x^2 + 10x
So when area = 338 square feet
The equation becomes
3x^2 + 10x= 338
Rearranging it : 3x^2 + 10x-338 =0
This is a quadratic equation and can be solved with the help of the formula.
Here a= 3, b= 10 and c= -338
x = -b±√b²- 4ac/2a
Putting the values of a,b,c we get
x= -10±√100+ 4056/6
x= -10± 64.467/6
x= 54.467/6 or -74.467/6 we ignore the negative value because the garden cannot have the negative area.
x= 9.0778 feet
Similarly repeating the same process would give
So when area = 147.25 square feet
The equation becomes
3x^2 + 10x= 147.25
Rearranging it : 3x^2 + 10x-147.25 =0
This is a quadratic equation and can be solved with the help of the formula.
Here a= 3, b= 10 and c= - 147.25
x = -b±√b²- 4ac/2a
Putting the values of a,b,c we get
x= -10±√100+ 1767/6
x= -10± 43.208/6
x= 33.208/6 or -53.208/6 we ignore the negative value because the garden cannot have the negative area.
x= 5.543799 feet