Answer:
The data that we have is:
f(x) = x + 5
g(x) = x^2 + 1
p(x) = g(x) + f(x) = (x^2 + 1) + (x + 5) = x^2 + x + 6.
q(x) = g(x) - f(x) = (x^2 + 1) - (x + 5) = x^2 - x - 4
We want to find p(x)*q(x)
well, we can replace:
p(x)*g(x) = (g(x) + f(x))*(g(x) - f(x))
Now, you can recall the relationship:
a^2 - b^2 = (a + b)*(a - b)
then we have that:
(g(x) + f(x))*(g(x) - f(x)) = g(x)^2 - f(x)^2
now we can replace g(x) and f(x) by the expressions that we know:
g(x)^2 - f(x)^2 = (x^2 + 1)^2 - (x + 5)^2
now we can simplify this:
(x^2 + 1)^2 - (x + 5)^2 = (x^4 + 2*1*x + 1^2) - (x^2 + 2*5*x +5^2)
= x^4 + 2*x + 1 - x^2 - 10x - 25
= x^4 - x^2 - 8*x - 24
p(x)*q(x) = x^4 - x^2 - 8*x - 24
Answer:
x^4+x^2-10x-24
Step-by-step explanation:
Please help me.. I'm very confused about this
Answer:
C
Step-by-step explanation:
1:draw a very simple Cartesian plane for the graph
2:label the quadrants 1-4 from top right round to bottom right as 4
3:then apply x>0 (1,2) is top right and y<0 is bottom right (-1,-2)
02.06A LC) Which number is not in scientific notation? 02.06A
the answer is (A) you cant have 11 it should be 1.1 x 10^22
Please help me someone
Answer:
260 cm^2
Step-by-step explanation:
The area of a parallelogram is given by this formula:
● A= b*h
b is the base and h is the heigth.
The heigth of this parallelogram is 13 cm and its base is 20cm.
●A= 13*20 = 260 cm^2
(TIMED PLEASE HELP!!) The area of the two triangles is given by the functions: Area of Triangle A: x2 + x Area of Triangle B: x2 – 3x Which function represents the sum of the areas of the two triangles? (a) 4x (b)–4x (c) x2 – 4x (d) 2x2 – 2x
Answer:
D
Step-by-step explanation:
Here, we are given the values of the areas of the two triangles and we want to find the sum of these areas
The sum can be found by adding the area of triangle A to the area of triangle B
That would be;
x^2 + x + x^2-3x = 2x^2 -2x
Answer:
d
Step-by-step explanation:
Barry also looks into the cost of repaying an easy access loan for $1000. The up-front cost of the loan is $3 for every $20 borrowed, plus the original $1000. How much will this loan cost Barry in interest.
Answer:
Barry has to pay back $1150
Step-by-step explanation:
We can set up an equation to help solve this problem
x is the amount he has to pay back
x=1000+3(1000/20)
1000/20 lets us know how many times he borrowed 20 dollars
x=1000+3(50)
x=1000+150
x=1150
Barry has to pay back $1150
If Barry also looks into the cost of repaying an easy access loan for $1000. The up-front cost of the loan is $3 for every $20 borrowed, plus the original $1000. Then Barry has to pay back $1150.
What is Equation?Two or more expressions with an equal sign is called as Equation.
We can set up an equation to help solve this problem
x is the amount he has to pay back.
x=1000+3(1000/20)
1000/20 lets us know how many times he borrowed 20 dollars
x=1000+3(50)
x=1000+150
x=1150
Hence, Barry has to pay back $1150.
To learn more on Equations click:
https://brainly.com/question/10413253
#SPJ5
PLZ HELP The slope of the graph of a direct variation function is 4. What is the equation of the function? y = 4 x + 1 y = 1/4 x y = -4 x y = 4 x
Answer:
y = 4x
Step-by-step explanation:
A direct variation is written in the form
y = kx where k is the constant of variation ( or the slope)
y = 4x
Answer:
d. y = 4 x
Step-by-step explanation:
A direct variation
1. has no y-intercept
2. has a constant positive slope.
Out of
y = 4 x + 1 [has y-intercept of +1]
y = 1/4 x [direct variation with a slope of 1/4, not 4]
y = -4 x [has a negative slope]
y = 4 x [direct variation with slope of 4]
I was at the store, and saw two sizes of avocados being sold. The regular size sold for $0.84 each. For what prices would the larger avocado be a better deal?
Answer:
The bigger avocado will be a better deal if the ratio of the sizes of the bigger one to the smaller one is less than the ratio of the prices of the bigger one to the smaller one.
Step-by-step explanation:
Given that two sizea of avocados are being sold, since the regular size is being sold for $0.84 each, let the price for the bigger avocado be $x.
Then note the following:
1. How bigger than the smaller avocado is the bigger one?
This would determine if the price for the bigger one is a bargain, or a mistake.
If for instance, the bigger avocado is double the size of the smaller one, then for any price, $x less that $1.68 (twice of $0.84), it is a bargain.
The bigger avocado will be a better deal if the ratio of the sizes bigger one to the smaller one is less than the ratio of the prices of the bigger one to the smaller one.
Answer:
The better deal cannot be decided as we were not the weights of the 2 avocados. However, we assume they are x is the price of the larger avocado and y the weight of the larger avocado. Therefore we calculate the price per pound of the larger avocado which is x/y. The weight of the smaller avocado is called z while the price od the smaller / regular avocado is $0.84.The price per pound of the smaller / regular avocado is calculated as 0.84/z. Therefore x/y<0.84/z will make buying the longer avocado a better deal. Also, x/y>0.84/z will make buying the smaller/ regular avocado a better deal.
Step-by-step explanation:
The better deal cannot be decided as we were not the weights of the 2 avocados. However, we assume they are x is the price of the larger avocado and y the weight of the larger avocado. Therefore we calculate the price per pound of the larger avocado which is x/y. The weight of the smaller avocado is called z while the price od the smaller / regular avocado is $0.84.The price per pound of the smaller / regular avocado is calculated as 0.84/z. Therefore x/y<0.84/z will make buying the longer avocado a better deal. Also, x/y>0.84/z will make buying the smaller/ regular avocado a better deal.
Use the quadratic form to solve 6x^2+3x+2=0.
Answer:
Hello!!...
I hope its helpful to you...
Between two whole which pairs of numbers does √5 lie on the number line?
Answer:
2, 3
Step-by-step explanation:
5 lies between 2 perfect squares 4 and 9.
√4 < √5 < √9
√4 = 2
√9 = 3
2 < √5 < 3
how to do this question plz answer me step by step plzz
Answer:
30, 85, 95, 150
Step-by-step explanation:
The angles of a quadrilateral add to 360
Let x be the smallest angle
x+55
x+65
x+120 are the other three angles
Add the 4 angles together and they sum to 360
x+x+55 x+65+ x+120 = 360
Combine like terms
4x+240 = 360
Subtract 240 from each side
4x+240-240 = 360 -240
4x = 120
Divide by 4
4x/4 = 120/4
x = 30
x+55= 30+55 = 85
x+65 = 30+65 = 95
x+120 = 30+120 = 150
Please answer this fast in two minutes now
Answer:
18.3Step-by-step explanation:
from cosines theorem:
t² = 11² + 14² - 2•11•14•cos87°
t² = 121 + 196 + 308•0.05236
t² = 333.12688
t = √333.12688
t = 18.2517... ≈ 18.3
Which of the following statements would be represented with P → Q? Question 14 options: A) x = 5 if and only if y = 9. B) x = 5, and 2x ≠ 8. C) x = 5, but y = 9. D) If x = 5, then 2x = 10.
======================================================
Explanation:
Writing [tex]P \to Q[/tex] is another way of saying "if P, then Q".
P and Q are placeholders. Instead of holding numbers, they hold statements. The statements can be anything you want (generally they should be something that can be verified).
The two statements are
P: x = 5
Q: 2x = 10
So the format "if P, then Q" turns into "if x = 5, then 2x = 10" after replacing P and Q with the proper definitions.
Side note: it might help to think of the "search and replace" feature in many word documents.
Please help I need to finish this before I can take my final
Options:
A) f(x), g(x), h(x)
B) g(x), f(x), h(x)
C) h(x), g(x), f(x)
D) g(x), h(x), f(x)
Answer: D
Step-by-step explanation: Plug in 0 for x and solve. Then plug in 4 for x and solve. Compare the results. Which function has the smallest difference in output? Which has the greatest difference in output?
After which transformation of △ABC would the image △A'B'C' not have the same area?
Answer:
. reflection across the y-axis followed by a rotation 90° clockwise about the origin
2. rotation 180° clockwise about the origin followed by a reflection across the line y = -x
Step-by-step explanation:
Dilation of △ABC rotation 180° clockwise about the origin followed by a reflection across the line y = -x,
Reflection across the y-axis followed by a rotation 90° clockwise about the origin.
What is Dilation?Dilation is a process for creating similar figures by changing the size.
In transformation of △ABC,
Dilation of △ABC rotation 180° clockwise about the origin followed by a reflection across the line y = -x,
Reflection across the y-axis followed by a rotation 90° clockwise about the origin.
Hence, the image △A'B'C' not have the same area.
Learn more about Dilation here:
https://brainly.com/question/13176891
#SPJ5
Suppose we have a bag with $10$ slips of paper in it. Eight slips have a $3$ on them and the other two have a $9$ on them. What is the expected value of the number shown if we add one additional $9$ to the bag?
Using the standard calculation, the expected value is 46/11.
El largo de un rectángulo es 8 metros mayor que su ancho. Si el ancho del rectángulo es x metros, la expresión algebraica que representa su perímetro es: *
Answer:
La expresión algebraica que representa el perímetro del rectángulo es:
perímetro = 4x + 16
Step-by-step explanation:
La formula del perímetro de un rectángulo es:
p = 2(ancho + largo)
Entonces:
b = x + 8 primer ecuación
p = 2(x+b) segunda ecuación
x = longitud del ancho del rectángulo
b = longitud del largo del rectángulo
por tanto:
sustituyendo el valor de la primer ecuación en la segunda ecuación:
p = 2(x + (x+8))
p = 2(2x + 8)
p = 4x + 16
Usando conceptos de rectángulo, se encuentra que el perímetro está dado por:
[tex]P = 4x + 16[/tex]
El perímetro de un rectangulo de ancho a y largo l es dado por:
[tex]P = 2(l + a)[/tex]
En este problema, el ancho es de x metros, o sea, [tex]l = x[/tex], enquanto el largo 8 metros mayor que su ancho, o sea, [tex]l = x + 8[/tex]
Por eso, el perímetro es dado por:
[tex]P = 2(l + a)[/tex]
[tex]P = 2(x + x + 8)[/tex]
[tex]P = 2(2x + 8)[/tex]
[tex]P = 4x + 16[/tex]
Un problema similar que tambíen envolve el perímetro de un rectangulo es dado en https://brainly.com/question/21715963
Plz help me the question is in the picture below
Answer:
function 2
Step-by-step explanation:
To do this you would already know that the first function's slope is 1 since r represents the x in slope intercept form. 2 will just be 1/1.1 since if you do y2-y1/x2-x2 you get 1/1.1 as the slope so function 2 will have a greater slope
A shoemaker makes three new souls every four minutes another shoemaker made to souls every three minutes what was the difference in the number souls they made in an hour
Answer:
15 soulsStep-by-step explanation:
If a shoemaker makes three new souls every four minutes, the number of soles he will make in an hour can expressed as shown;
3 souls = 4 minutes
x souls = 1hour (60 minutes)
Cross multiplying to get the number of souls;
4 * x = 3 * 60
4x = 180
x = 180/4
x = 45souls
Hence the number of souls made by this shoemaker in an hour is 45 souls.
Similarly, If another shoemaker makes two new souls every three minutes, the number of soles he will make in an hour can expressed as shown;
2 souls = 3 minutes
y souls = 1hour (60 minutes)
Cross multiplying to get the number of souls;
3 * y = 2 * 60
3y = 120
y = 120/4
y = 30souls
Therefore the number of souls made by this shoemaker in an hour is 30 souls.
The difference in the number souls they made in an hour will be x - y where x = 45 souls and y = 30 souls.
x - y = 45 - 30
The difference is equal to 15 souls
What is x, if the volume of the cylinder is 768 pi cm3? Do not use units or commas in your answer.
Answer:
48
Step-by-step explanation:
We have that the volume of a cylinder is given by:
V = pi * (r ^ 2) * h
In this case we know the diameter, we know that the radius is half the diameter like this:
r = d / 2
r = 8/2
r = 4
Now we know that the V equals 768 pi
we replace and we have:
768 * pi = pi * (4 ^ 2) * h
768 = 16 * h
h = 768/16
h = 48
Therefore the value of x would be 48 cm
For each function, state the vertex and whether the function has a maximum or minimum value. Explain how you decided? f(x) = -(x + 1)^2 + 6
Answer:
maximum value at (- 1, 6 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
• If a > 0 then minimum value
• If a < 0 then maximum value
y = - (x + 1)² + 6
with (h, k) = (- 1, 6 ) and a = - 1
Thus vertex = (- 1, 6 ) and is a maximum
please answer this question now
Answer:
≈ 94.9 mi²
Step-by-step explanation:
The area (A) of Δ WXY can be calculated as
A = [tex]\frac{1}{2}[/tex] × WY × WX × sinW
∠ W = 180° - (40 + 21)° = 180° - 61° = 119°
Calculate WX using the Sine rule, that is
[tex]\frac{11}{sin21}[/tex] = [tex]\frac{WX}{sin40}[/tex] ( cross- multiply )
WX sin21° = 11 sin40° ( divide both sides by sin21° )
WX = [tex]\frac{11sin40}{sin21}[/tex] ≈ 19.73 mi , thus
A = 0.5 × 11 × 19.73 × sin119° ≈ 49.9 mi² ( to the nearest tenth )
Helps is needed
Malita wants to prove that the interior angles of any triangle sum to 180°. She draws a
line through one vertex parallel to the opposite side, and then she labels all the angles
formed.
Drag a statement to match each reason in Malita's two-column proof in the table
below.
Answer:
See explanations and diagram attached.
Step-by-step explanation:
1. angle 4 = angle 3, and angle 5 = angle 2 alternate interior angles with red line parallel to side opposite angle 1
3. angle 1 + angle 4 + angle 5 = 180 because these angles lie on a straight line.
Find the equation of the line that passes through (-1,5) and is perpendicular to y – 5x = 1.
The answer is
[tex]y = - \frac{1}{5} x + \frac{24}{5} [/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
y - 5x = 1
y = 5x + 1
Comparing with the above formula
The slope / m of the line is 5
Since the is perpendicular to y = 5x + 1 it's slope it's the negative inverse of y = 5x + 1
That's
Slope of the perpendicular line = - 1/5
Equation of the line using point (-1,5) is
[tex]y - 5 = - \frac{1}{5} (x + 1)[/tex]
[tex]y - 5 = - \frac{1}{5} x - \frac{1}{5} [/tex]
[tex]y = - \frac{1}{5} x - \frac{1}{5} + 5[/tex]
We have the final answer as
[tex]y = - \frac{1}{5} x + \frac{24}{5} [/tex]
Hope this helps you
Answer:
[tex]\huge\boxed{y=-\dfrac{1}{5}x+\dfrac{24}{5}\to x+5y=24}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
Let
[tex]k:y=m_1x+b_1;\ l:y=m_2x+b_2[/tex]
therefore
[tex]k||l\iff m_1=m_2\\k\perp l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
We have the equation of a line in the standard form. Convert it to the slope-intercept form:
[tex]y-5x=1[/tex] add 5x to both sides
[tex]y-5x+5x=1+5x\\\\y=5x+1\to m_1=5;\ b_1=1[/tex]
Calculate the slope:
[tex]m_2=-\dfrac{1}{5}[/tex]
Substitute the value of a slope and the coordinates of the given point (-1, 5) to the equation of a line:
[tex]y=m_2x+b[/tex]
[tex]5=\left(-\dfrac{1}{5}\right)(-1)+b[/tex]
[tex]5=\dfrac{1}{5}+b[/tex] subtract 1/5 from both sides
[tex]5-\dfrac{1}{5}=\dfrac{1}{5}-\dfrac{1}{5}+b[/tex]
[tex]\dfrac{25}{5}-\dfrac{1}{5}=b\\\\\dfrac{24}{5}=b\to b=\dfrac{24}{5}[/tex]
Final answer:
[tex]y=-\dfrac{1}{5}x+\dfrac{24}{5}[/tex]
convert to the standard form (Ax + By = C):
[tex]y=-\dfrac{1}{5}x+\dfrac{24}{5}[/tex] multiply both sides by 5
[tex]5y=(5)\left(-\dfrac{1}{5}x\right)+(5)\left(\dfrac{24}{5}\right)[/tex]
[tex]5y=-x+24[/tex] add x to both sides
[tex]x+5y=24[/tex]
Need help on these appreciate it
Answer:
Circle B:
[tex](x+4)^2+(y+3)^2=4[/tex]
Circle F:
[tex](x-4)^2+(y-1)^2=16[/tex]
Step-by-step explanation:
We can write the equation of a circle equation with center on (h,k) and radius r as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Then, we analyze the circle will have for the circle B:
- It has a center in x=-4 and y=-3.
- It radius can be calculated from the distance from the center (x,y)=(-4,-3) to one of its points (x,y)=(-4, -1). Then, its radius is r=2.
Then, we can write the equation as:
[tex](x-h)^2+(y-k)^2=r^2\\\\h=-4\\k=-3\\r=2\\\\(x+4)^2+(y+3)^2=4[/tex]
we analyze the circle will have for the circle F:
- It has a center in x=4 and y=1.
- It radius can be calculated from the distance from the center (x,y)=(4, 1) to one of its points (x,y)=(0, 1). Then, its radius is r=4.
Then, we can write the equation as:
[tex](x-h)^2+(y-k)^2=r^2\\\\h=4\\k=1\\r=4\\\\(x-4)^2+(y-1)^2=16[/tex]
these polygons are similar. find the value of x
Answer:
20Option D is the correct option.
Step-by-step explanation:
As they are similar, correspondence sides are in common ratios:
[tex] \frac{x}{10} = \frac{10}{5} [/tex]
Apply cross product property
[tex]5x = 10 \times 10[/tex]
Multiply the numbers
[tex]5x = 100[/tex]
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{100}{5} [/tex]
Calculate
[tex]x = 20[/tex]
Hope this helps...
Best regards!!
PLEASE HELP ME GUYS!! In a complete sentence, describe the angle relationship between ∠DAE and ∠EAF. Then write and solve an equation based on the relationship you identified in order to find the measure of ∠DAE.
Answer:
Hey there!
Angle DAE and EAF are complementary angles, meaning that they add to 90 degrees.
Thus, we have 65+x=90
Solving for x we have 25.
Hope this helps :)
Which of the following equations have infinitely many solutions? Choose All that apply. A: 37x-37=37x-37 B: 74x-37=74-37 C: 73x-37=73x-37 D: x-37=x-37
Answer:
(A), (C) and (D).
Step-by-step explanation:
An equation will have infinite solutions if both sides of the equal sign are the exact same thing, for instance [tex]4x+4=4x+4[/tex]. (You can test this with any value of x and find that they all work!)
So to find the equations that have infinite solutions, we need to see which have the same exact sides.
[tex]37x-37 = 37x-37[/tex] have the same thing on each side: [tex]37x-37\\[/tex], so this has infinite solutions.
[tex]74x-37 = 74-37[/tex] does not have the same thing on each side, so it doesn’t have infinite solutions (it has 1)
[tex]73x-37 = 73x-37[/tex] has the same thing on each side: [tex]73x-37[/tex], so this has infinite solutions.
And finally, [tex]x-37=x-37[/tex] has the same thing on each side: [tex]x-37[/tex], so it has infinite solutions.
Hope this helped!
Answer:
question is not clear please send clear question
greatly appreciate help :) picture below
Answer:
The answer is None.
Step-by-step explanation:
I took the test on FLVS and I got the answer right.
I hope this helps. I am sorry if you get this wrong.
Answer:
None. Say the obtuse angle is 100 degrees. Since the sum of all angles in a triangle cannot be bigger than 180, it's not possible because 195 (100+95) is greater than 180 degrees.
Step-by-step explanation:
On the coordinate plane below, Point P is located at (2,-3), and point Q is located at (-4,4).
Find the distance between points P and Q Round your answer to the nearest whole number.
Answer:
Approximately 9 units.
Step-by-step explanation:
To find the distance between two ordered pairs, we can use the distance formula. The distance formula is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Let (2,-3) be x₁ and y₁ respectively, and let (-4,4) be x₂ and y₂, respectively.
[tex]d=\sqrt{(-4-2)^2+(4--3)^2} \\d=\sqrt{(-6)^2+(7)^2} \\d=\sqrt{36+49} \\d=\sqrt{85}\approx9[/tex]
Please answer this question now
Answer:
s = 11.4
Step-by-step explanation:
The following data were obtained from the question:
Angle S = 60°
Opposite S = s =?
Opposite U = u = 13
Opposite T = t = 5
Thus, from the data obtained from the question, we can calculate the value of s by using cosine rule as shown below:
s² = u² + t² – 2ut Cos S
s² = 13² + 5² – 2 × 13 × 5 × Cos 60
s² = 169 + 25 – 130 × 0.5
s² = 194 – 65
s² = 129
Take the square root of both side.
s = √129
s = 11.4
Therefore, the value of s is 11.4