Complete the expressions that would make them a perfect square trinomial.
a.
x² – 8x+
b. x2 + 20x +
C.
x² – 16x +
d. x2 + 9x +
Answers
Answer:
a) 16
b) 100
c) 64
d) \(\frac{81}{4}\)\)
Step-by-step explanation:
Perfect square trinomial:
A perfect square trinomial has the following format:
\((x \pm a)^2 = x^2 \pm 2ax + a^2\)
a.
x² – 8x
\(x^2 - 8x = x^2 - 2ax\)
So 2a = 8, a = 4. Then
\(a^2 = 4^2 = 16\)
The perfect square trinomial is \(x^2 - 8x + 16\)
b. x2 + 20x +
2a = 20, so a = 10
\(a^2 = 10^2 = 100\)
The perfect square trinomial is \(x^2 + 20x + 100\)
C.
x² – 16x +
2a = -16, so a = -8.
\(a^2 = (-8)^2 = 64\)
The perfect square trinomial is \(x^2 - 16x + 64\)
d. x2 + 9x +
\(2a = 9\), so \(a = \frac{9}{2}\)
\(a^2 = (\frac{9}{2})^2 = \frac{81}{4}\)
The perfect square trinomial is \(x^2 + 9x + \frac{81}{4}\)\)
Related Questions
Find the radius of the sphere with the given volume.
Answers
Answer:
see below
Step-by-step explanation: 6 5 17 43
Volume of a sphere = 121.5 π mm³ Find r
Vol Sphere = (4π r³) / 3 solve for r
Vol Sphere × 3 = (4π r³)
(Vol Sphere × 3) / 4π = r³
∛((Vol Sphere × 3) / 4π) = r
∛((121.5 π mm³× 3) / 4π) = r the pi terms cancel
∛((121.5 mm³× 3) / 4) = r
∛((364.5 mm³) / 4) = r
∛((91.125 mm³) ) = r
4.5 = r
A laptop computer originally priced at $1,000 now sells for $1,300. What is the percent of increase?
Answers
Answer:
30% :))))))))))))))))))))))))))))
Answer:
The percent of increase is 30%
Step-by-step explanation:
These are my solution's
Increase = New Number - Original Number. ↓
1300 - 1000 = 300
Next,
% increase = Increase ÷ Original Number × 100.↓
300 divided by 1000 = 0.3 x 100 = 30%
Please mark as a brainiest if my answer was helpful.
Thx UwU
HELP ITS DUE TODAY!
A baker is baking a giant cookie in the shape of a equilateral triangle what is the area of the cookie if the base is 17 inches and the height is 10 inches
Answers
To find the length of one of the sides, we can use the Pythagorean theorem. Since this is an equilateral triangle, all sides are equal in length. Let's call the length of one side "x". We know that the height (which is also one of the sides) is 10 inches, so we can set up a right triangle with one leg being x/2 (half of one side) and the other leg being 10 inches. The hypotenuse (the other side of the equilateral triangle) is x.
Using the Pythagorean theorem:
(x/2)^2 + 10^2 = x^2
x^2/4 + 100 = x^2
100 = 3x^2/4
400/3 = x^2
x = sqrt(400/3)
Now that we know the length of one side, we can plug it into the formula for area:
A = (sqrt(3)/4) x (sqrt(400/3))^2
A = (sqrt(3)/4) x (400/3)
A = 100sqrt(3)/3
Therefore, the area of the giant cookie in the shape of an equilateral triangle with a base of 17 inches and a height of 10 inches is approximately 57.74 square inches.
Answer:
85 square inches.
Step-by-step explanation:
The area of a triangle can be found by the formula \(1/2bh\), assuming b is the base and h is the height.
If b is 17 inches and h is 10 inches:
\(1/2(17)(10)\)
\(1/2(170)\)
\(A = 85\)
Therefore, the area is 85 square inches.
Simplify: (12 - 7) + (10 x 3) + (3 + 2)
a)7
b)11
c)35
d)45
Answers
Answer:
none
Step-by-step explanation:
not sure but the answer is 40 cause 12-7=5 10x3=30 and 3+2=5 and 5+30+5=40
Answer:
\((12 - 7) + (10 \times 3) + (3 + 2) \\ \\ = 5 + 30 + 5 \\ \\ = 40 \: is \: none\)
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1. Find an exponential function of the form f(x) = ba^-1 + c that has the given horizontal asymptote and y-intercept and passes through P
y = 33; y-intercept 408; P(2, 93)
Answers
Answer:
\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)
Step-by-step explanation:
An exponential function of form f(x) = ba^(-x) + c has a horizontal asymptote of y = c as x approaches infinity, and a y-intercept of (0, b + c). We can use the given information to set up a system of equations and solve for the unknowns.
The horizontal asymptote is given as y = 33, so we have:
c = 33
The y-intercept is given as (0, 408), so we have:
b + c = 408
Substituting c = 33, we get:
b + 33 = 408
b = 375
So the function we're looking for is of the form:
\(\bold{f(x) = 375a^{-x}+ 33}\)
To find a, we use the fact that the function passes through P(2, 93):
93 = 375a^(-2) + 33
60 = 375a^(-2)
a^2 = 375/60
a^2 = 6.25
a = \(\sqrt{6.25 } =2.5\)
Therefore, the exponential function that satisfies the given conditions is:
\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)
Find the x and y- intercepts of 3x + 12y = 36.
Answers
Answer:
x intercept-
12,0
y intercept-
0,3
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s):
(12,0)
y-intercept(s):
(0,3)
Hello! Could someone please help explain how to solve this to me please and an answer would be nice! Thanks! :)
Answers
if we notice the tickmarks on the triangle, we can see the all sides are equal, namely is an equilateral triangle, and if all sides are equal, then all interior angles are equal as well.
Let's recall that the sum of all interior angles in a triangle is 180°, now if we divide that by 3, that gives us 60, namely each angle in the equilateral triangle is 60°, that means
\(10x=60\implies x=\cfrac{60}{10}\implies \boxed{x=6} ~\hfill 12y=60\implies y=\cfrac{60}{12}\implies \boxed{y=5}\)
Can someone give me the answers of the nexts excercises:
1) 4 more than p
2) 12 minus n
3) the quotient of n and 8
5) 23 less tha x
6) 2 more than twice a number
7) 9 minus a number
8) the product of a 5 and a number
9) the quotient of a number and 6
10) the total cost is the number of cans time $.70.
i will really thx you're help
Answers
Answers are in bold
p+412-nn/8skipping x-232n+2n-95nn/60.70n========================================================
Explanations:
"4 more than p" means we add 4 onto p. For instance, let's say we replace p with 10. This means "4 more than 10" would be 4+p = 4+10 = 14.Not much to say here. We subtract the two items.The term "quotient" is the result of dividing two numbers. The slash / symbol means "divide" and it also is used for fractions.Skipping.Similar to problem 1, but now we subtract since the result is smaller than x. For instance, let's say x = 30. Then 23 less than this is x-23 = 30-23 = 7.If n is some number, then twice that is 2n. We add on 2 more to get 2n+2 as the answer.Same idea as problem 2. "A number" stands in place of "n"."Product" means "result of multiplication". So we multiply 5 and the number to say 5 times n = 5*n = 5n. Similar idea to problem 3, but we use "a number" in place of "n".We multiply the number of cans (n) with the price per can (0.70) to get 0.70nProve that if a and b are positive integers,then there exists a unique integers q and r such that a=bq+r where 0≤r<b
Answers
Step-by-step explanation:
Correct option is
C
0≤r<b
If r must satisfy0≤r<b
Proof,
..,a−3b,a−2b,a−b,a,a+b,a+2b,a+3b,..
clearly it is an arithmetic progression with common difference b and it extends infinitely in both directions.
Let r be the smallest non-negative term of this arithmetic progression.Then,there exists a non-negative integer q such that,
a−bq=r
=>a=bq+r
As,r is the smallest non-negative integer satisfying the result.Therefore, 0≤r≤b
Thus, we have
a=bq1+r1, 0≤r1≤b
HELP HELP HELP! can someone please help me with this algebra 2 question?
Answers
The transformations that take the graph of f(x)=e^x to f(x)=(-e^x)-2 are a reflection about the x-axis and also by a vertical shift downward by 2 units.
HELP! Please explain
Answers
Answer:
∠1 = 110
Step-by-step explanation:
Vertically Opposite angles, means that when you have two parrallel lines, The angles opposite of each other are equal. So 4 = 2 on the bottom line.
This means angle 1 is equal to it's opposite angle, 110'.
Answer:
110 degrees
Step-by-step explanation:
Since completing the known angle is 70 degrees, angle 1 must be 70 degrees. It is also adjacent to 110, which means it equals the same.
please fill in the blanks of the question i sent a pic of
Answers
The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.
What is the center and the radius of the circle?
In this question we must determine the location of the center and the measure of the radius of a circle. According to Euclidean geometry, diameters are the longest possible chords of a circle. First, we determine the location of the center by definition of midpoint:
(h, k) = (1/2) · (4, 5.5) + (1/2) · (4, 10.5)
(h, k) = (4, 8)
And the radius is found by Pythagorean theorem:
\(d = \sqrt{(4 - 4)^{2}+(10.5-5.5)^{2}}\)
d = 5
r = 0.5 · 5
r = 2.5
The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.
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As you wake up to get your day started, you decide to make muffins for breakfast. The recipe you are
using makes 2 dozen muffins and calls for 3 cups of flour and 1 cup of sugar. You decide to only make
18 muffins. How many cups of flour and sugar will you need for your recipe?
The above problem can easily be solved using a proportion. Show your work
Answers
Answer:
4 cups of flour is needed and 4/3 cups of sugar
Step-by-step explanation:
Given
2 dozen Muffins; 3 cups of flour and 1 cup of sugar
Required
Determine the cups of flour if 18 muffins is used
First, we have to determine the proportion of the number of muffins used previously and now;
Represent this with p;
\(p = \frac{2\ dozen}{18}\)
\(p = \frac{2 * 12}{18}\)
\(p = \frac{24}{18}\)
\(p = \frac{4}{3}\)
Multiply this to the previous cups of flours and sugars;
Cups of flour = p * previous cups of flour
\(Cups\ of\ flour = \frac{4}{3} * 3\)
\(Cups\ of\ flour = 4\)
Cups of Sugar = p * previous cups of sugar
\(Cups\ of\ sugar= \frac{4}{3} * 1\)
\(Cups\ of\ sugar= \frac{4}{3}\)
Hence, 4 cups of flour is needed and 4/3 cups of sugar
50 POINTS HELP PLS
what is the equation in point slope form of the line passing through (-3, -4) and (0,2)
Answers
Answer:
this the answery=x/3+2
pls do this for me pls I need it for my homework do it in a PowerPoint and show me it
Answers
Answer:
i might need more info unless this is the only questions
Step-by-step explanation:
I'm not sure what it means by "define the types of linear" (maybe theres a given function?), but to find the x intercept you need to make y 0. For example:
if we have a function
f(x) = 2x + 1
and we want to find the x intercept we substitute 0 to y
0 = 2x + 1
not
f(0) = ......
Answer:
To find the x-intercept of a given linear equation, plug in 0 for ‘y’ and solve for ‘x’. To find the y-intercept, plug 0 in for ‘x’ and solve for ‘y’. How do you find the Y intercept in a word problem? When a word problem involves a constant rate or speed and a beginning amount, it can be written in slope-intercept form: y=mx+b.
Step-by-step explanation:
Solve the inequality 5(x + 2) – 3x > 7 -4(x - 3).X> 3x < -2.5x < -1.5X > 1.5
Answers
The given expression is
5(x + 2) – 3x > 7 -4(x - 3)
We would multiply the terms inside the parenthese with the term outside it on both sides of the inequality. Thus, we have
5x + 10 - 3x > 7 - 4x + 12
Collecting like terms, we have
5x - 3x + 4x > 7 + 12 - 10
6x > 9
Dividing both sides of the inequality by 6, we have
6x/6 > 9/6
x > 1.5
the last option is correct
Which are the best statistics to use to compare the teams' scores?
A.
Mean and standard deviation
B.
Median and IQR
C.
Median and standard deviation
D.
Mean and IQR
Answers
Step-by-step explanation:
In the image, we are presented a box plot, which has the minimum, lower quartile, the median, the upper quartile and the maximum. In order to find the median, we would need to add all of the scores (which are dots in the graph) and then divide it by the number of it. However, a box plot does not show to exact scores that all team members of the two teams got. Therefore, we are unable to find the mean with this. Standard deviation is where a set of dot data leans, which is not displayed in the image too. So, the answer is B.
finding values of products and quotient functions
\(( \frac{r}{s} )(3) = \)
(3) = [/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/fo6qtw13QDITrL0XHWTkFEFXENPGcfQd.jpeg)
Answers
The product and the quotient of the functions are as follows:
(rs)(4) =8
(r / s)(3) = 2
How to solve function?A function relates input and output. It relates an independent variable with a dependent variable.
Therefore, let's solve the function as follows:
r(x) = 2√x
s(x) = √x
Therefore, let's find
(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8
Let's find
(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2
Therefore,
(rs)(4) =8
(r / s)(3) = 2
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How do you skip videos on edunuity?
Answers
Answer: let the video play for a while, pause, disconnect from wifi, reconnect, then refresh the page.
Step-by-step explanation:
You may have to press next activity again and it might not work the first time but I promise it works.
Answer:
you skip when it comes to the very end
Step-by-step explanation:
Please Give BrainleastEdward runs 30 miles in 5 days. Martha runs 28 miles in 4 days. Who runs more miles per day?
Answers
PLEASE WHAT IS THIS?!!? WHATS THE ANSWER?
Answers
Answer: bottom right
Let S be the universal set, where:
S= {1, 2, 3,..., 18, 19, 20}
Let sets A and B be subsets of S, where:
Answers
Answer:
Step-by-step explanation:
Therefore, the height of the tower is approximately 121.4 meters.
I need help with math
Answers
Answer:
6:3
Step-by-step explanation:
Number System - Evaluate the integer
5- (-3) =
Answers
Answer:
-8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
When you try to subtract a negative its the same thing as adding, so the equation becomes:
5 + 3
And 5 + 3 = 8
I REALLY NEED HELP? :,)
Answers
Answer:
3/7
Step-by-step explanation:
Find all points on the x-axis that are 16 units from the point (5,-8)
Answers
To find all points on the x-axis that are 16 units away from the point (5, -8), we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the y-coordinate of the point (5, -8) is -8, which lies on the x-axis. So, any point on the x-axis will have a y-coordinate of 0. Let's substitute the given values and solve for the x-coordinate.
d = √((x - 5)² + (0 - (-8))²)
Simplifying:
d = √((x - 5)² + 64)
Now, we want the distance d to be equal to 16 units. So, we set up the equation:
16 = √((x - 5)² + 64)
Squaring both sides of the equation to eliminate the square root:
16² = (x - 5)² + 64
256 = (x - 5)² + 64
Subtracting 64 from both sides:
192 = (x - 5)²
Taking the square root of both sides
√192 = x - 5
±√192 = x - 5
x = 5 ± √192
Therefore, the two points on the x-axis that are 16 units away from the point (5, -8) are:
Point 1: (5 + √192, 0)
Point 2: (5 - √192, 0)
In summary, the points on the x-axis that are 16 units away from the point (5, -8) are (5 + √192, 0) and (5 - √192, 0).
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x-8/6 = 1/3 what is X
Answers
Answer:
x = 10
Step-by-step explanation:
Answer:
i got the answer 10
x-8/6 =1/3
or, x-8 = 6/3
or, x=8+2 =10
When an object is weighed on a scale, the number displayed may vary from the object’s actual weight by at most 0.4 pounds. The scale says the object weighs 125.8 pounds. Part A: Write an absolute value inequality that describes the range of the actual weight of the object. Use the variable w to represent the actual weight of the object. Part B: Solve the absolute value inequality for w. Express your answer as a compound inequality.
Answers
The compound inequality that represents the range of the actual weight of the object is 125.4 ≤ w ≤ 126.2.
Part A: The absolute value inequality that describes the range of the actual weight of the object is:
|w - 125.8| ≤ 0.4
Part B: To solve the absolute value inequality, we can break it down into two separate inequalities:
w - 125.8 ≤ 0.4 and - (w - 125.8) ≤ 0.4
Solving the first inequality:
w - 125.8 ≤ 0.4
Add 125.8 to both sides:
w ≤ 126.2
Solving the second inequality:
-(w - 125.8) ≤ 0.4
Multiply by -1 and distribute the negative sign:
-w + 125.8 ≤ 0.4
Subtract 125.8 from both sides:
-w ≤ -125.4
Divide by -1 (note that the inequality direction flips):
w ≥ 125.4
Combining the solutions, we have:
125.4 ≤ w ≤ 126.2
The object is 125.4 ≤ w ≤ 126.2.
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write the slope form of the equation of the line through the given points.
Answers
3)
Given that the line passes through (-5, -5) and (-5, 3).
We have to find the slope form of the equation.
The equation passes through (x1, y1) and (x2, y2) is given by:
\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)So, the required equation is:
\(\begin{gathered} y-(-5)=\frac{3-(-5)}{-5-(-5)}(x-(-5)) \\ y+5=\frac{8}{0}(x+5) \\ 0=8(x+5) \\ 0=x+5 \\ x=-5 \end{gathered}\)Thus, the equation of the line passes through (-5, -5) and (-5, 3) is x = -5.
Find the numbers of faces, edges, and vertices of the solid.
Answers
Answer:
7 faces15 edges10 verticesStep-by-step explanation:
This is a counting problem. As with many counting problems, it is helpful to adopt a strategy that helps ensure you count everything only once.
__
FacesThere are two pentagonal faces and 5 rectangular faces for a total of ...
7 faces
__
EdgesThere are 5 edges around each of the pentagonal faces, and 5 edges connecting the top face to the bottom faces, for a total of ...
15 edges
__
VerticesThere are 5 vertices on the top face, and 5 on the bottom face, for a total of ...
10 vertices