Answer:
1
Step-by-step explanation:
The constant term in a perfect square trinomial with leading coefficient 1 is the square of half the coefficient of the linear term.
(2/2)² = 1
The missing constant term is 1.
Answer: The correct answer is: " 1 " .
_____________________________________________________
→ " x² + 2x + 1 = (x + 1)² " .
_____________________________________________________
_____________________________________________________
Step-by-step explanation:
_____________________________________________________
Let us assume that the question asks us to solve for the "missing constant term in the following equation:
→ " x² + 2x + b = 0 " ;
→ in which: " b " is the "missing constant term" for which we shall solve.
_____________________________________________________
The form of an equation in the perfect square would be:
→ (x + b) ² = x² + 2bx + b² ;
→ In our case, "b" ; refer to the "missing constant term" for which we shall solve.
_____________________________________________________
→ " x² + 2x + b = 0 " ;
Note that the term in the equation with the highest degree (highest exponent) is:
→ " x² " ; with an "implied coefficient" of: " 1 " (one) ;
→ {since "any value" , multiplied by " 1 " , results in that same initial value.}.
→ Since the term with the highest degree has a "co-efficient" of " 1 " ;
we can solve the problem; i.e. "Solve for "b" ; accordingly:
_____________________________________________________
→ " x² + 2x + b = 0 " ;
Subtract "b" from each side of the equation:
→ " x² + 2x + b - b = 0 - b " ;
→ to get:
→ x² + 2x = - b
Now we want to complete x² + 2x into a perfect square.
To do so, we take the: "2" (from the: "+2x" );
→ and we divide that value {in our case, "2"}; by "2" ;
to get: "[2/2]" ; and then we "square" that value;
→ to get: " [2/2]² " .
_____________________________________________________
Now, we add this "squared value" to: " x² + 2x " ; as follows:
→ " x² + 2x + [2/2]² " ; and simply: " [2/2]² = [1]² = 1 ."
_____________________________________________________
x² + 2x + (2/2)² = x² + 2x + 1 ;
= (x + 1)² ;
_____________________________________________________
Now: " x² + 2x = - b " ;
We add "(2/2)² " ; to each side of the equation;
→ In our case, " [2/2]² = [1]² = 1 " ;
→ As such, we add: " 1 " ; to each side of the equation:
→ x² + 2x + (2/2)² = - b + (2/2)² ;
→ Rewrite; substituting " 1 " [for: " (2/2)² "] :
→ x² + 2x + 1 = 1 - b ;
→ x² + 2x + 1 = 1 - b ;
_____________________________________________________
And assume "b" would equal "1" ;
since assuming the question refers to the equation:
"x² + 2x ± b = 0 " ; solve for "b" ;
And: "b = 1 " ;
Then: " x² + 2x + 1 = ? 1 - b ??
→ then: " 1 - b = 0 " ; Solve for "b" ;
→ Add "b" to each side of the equation:
" 1 - b + b = 0 + b " ;
→ to get: " 1 = b " ; ↔ " b = 1 " ; Yes!
___________________________________________________
Also, to check our work:
_____________________________________________________
Remember, from above:
_____________________________________________________
" The form of an equation in the perfect square would be:
→ (x + b)² = x² + 2bx + b² " ; _____________________________________________________
→ Let us substitute "1" for all values of "b" :
→ " (x + 1) ² = x² + 2*(b)*(1) + 1² " ;
→ " (x + 1)² = x² + (2*1*1) + (1*1) " ;
→ " (x + 1)² = ? x² + 2 + 1 " ?? ; Yes!
→ However, let us check for sure!
_____________________________________________________
→ Expand: " (x + 1)² " ;
→ " (x + 1)² = (x + 1)(x + 1) " ;
_____________________________________________________
→ " (x + 1)(x + 1) " ;
_____________________________________________________
Note the following property of multiplication:
_____________________________________________________
→ " (a + b)(c + d) = ac + ad + bc + bd " ;
_____________________________________________________
As such:
_____________________________________________________
→ " (x + 1)(x + 1) " ;
= (x*x) + (1x) + (1x) + (1*1) ;
= x² + 1x + 1x + 1 ;
→ Combine the "like terms" :
+ 1x + 1x = + 2x ;
And rewrite:
= x² + 2x + 1 .
_____________________________________________________
" (x + 1)² = ? x² + 2 + 1 " ?? ; Yes!
_____________________________________________________
→ So: The answer is: " 1 " .
_____________________________________________________
→ " x² + 2x + 1 = (x + 1)² " .
_____________________________________________________
Hope this answer helped!
Best wishes to you in your academic endeavors
— and within the "Brainly" community!
_____________________________________________________
Which statement is true for the equation 4x – 4x – 5 = –5? (5 points) It has no solution. It has one solution. It has two solutions. It has infinitely many solutions. Answer me!!!
Answer:
it has no solution
Step-by-step explanation:
4x-4x will cancel outadd 5 to both sides which make the 5 cancel out0Identify whether the figure has plane symmetry, symmetry about an axis, or neither.
There's no axis of symmetry in a house, no way to rotate it a little bit without changing it. There is plane symmetry, two different ways, the one shown in the last choice, and one through the center of the front and back.
Answer: Plane symmetry only, last choice
Answer: C) plane symmetry and symmetry about an axis
Step-by-step explanation: Please see the image below!
What’s the answer?????
You are given that all three sides of both the triangles are "approximately equal"
This means the answer is D. SSS (Side-Side-Side)
It can't be A. because S-A-S means side-angle-side and these are not the "givens"
It can't be B. because A-S-A means angle-side-angle and these are not the "givens"
It can't be C. because A-A-A means angle-angle-angle and these are not the "givens"
Hope this helped!
~Just a girl in love with Shawn Mendes
Please help?? ASAP!!!???
Answer: 1.9
Step-by-step explanation:
[tex]f(x)=\dfrac{14}{7+2e^{-0.6x}}\\\\\\f(3)=\dfrac{14}{7+2e^{-0.6(3)}}\\\\\\.\qquad =\dfrac{14}{7+2e^{-1.8}}\\\\\\.\qquad =1.9\qquad \quad need\ to\ use\ a\ calculator\ after\ replacing\ x\ with\ 3[/tex]
Two numbers have been added together and There are some is 67 one subtracted the difference is 11 what is the smaller number please help
Answer:
2 no.be x and y
x+y=67
x-y=11
solving both eqx
x=39
y=28
small no=28
Three parts of yellow paint are mixed with 4 parts of red paint to make orange paint Zahid has 75 ml of yellow paint and 120ml of red paint what is the maximum amount of orange paint he can make
Answer:
175ml of orange paint
Step-by-step explanation:
3/4 = 75/x
3 × 25 = 75 so...
4 × 25 = 100 so...
75 + 100 = 175ml of orange paint
Can someone please help me with this math question involving transformation
Answer:
X+ 6
Y+ 1
Step-by-step explanation:
The image of point A after the reflection along the x-axis the is A(-5,-2).
When this point was translated the new point became A(1, -1). The is means the translation from (-5, -2) to (1, -1) can be given by:
for the x-coordinate
-5 + x = 1
x =6
for the y-coordinate;
-2 + y =-1
y = -1 + 2
= 1
Answers are
x + 6 and
y + 1
Answer:
x+6 y+1
Step-by-step explanation:
PLEASE HELP ME ASAP WITH STEPS 27 POINTS AND BRAINLIEST! The area of a rectangle is given by the expression 8x 3 − 2x 2 − 11x + 15. If the width of the rectangle is 2x + 3, what is the expression that represents the length of the rectangle?
To find the length, divide the area by the width.
See the attached picture:
I have a math final tomorrow and I don’t know how to do this. Someone please help!
What is the sum of the areas of circle C and circle D?
7 units
14 units
49 units
98 units
Help Please
Answer:
D
Step-by-step explanation:
Circle C and D both have a radius of 7. So the sum of their areas is:
A = π(7)² + π(7)²
A = 98π
Answer: The correct option is
(D) 98π units².
Step-by-step explanation: We are given to find the sum of the areas of circle C and circle D.
From the figure, we note that
both the circle s C and D have equal radii given by
r = 7 cm.
Also, we know that the area of a circle with radius r units is given by
[tex]A=\pi r^2.[/tex]
Therefore, the sum of the area of circle C and D is given by
[tex]S=2A=2\pi r^2=2\times \pi\times7^2=2\times49\pi=98\pi~\textup{sq. units}.[/tex]
Thus, the required sum of the areas is 98π units².
Option (D) is CORRECT.
PLS HELP SHOW ALL YOUR WORKING OUT AND BRAINLIEST WILL BE AWARDED
Answer:
5.97 cm to 3 significant figures.
Step-by-step explanation:
The diameter of the circle will be equal to the length of the diagonal of the square.
Area = 56 = πr^2
r^2 = 56 / π
r = √(56 / π) = 4.222 cm
So the diameter = 8.444 cm.
This is = diagonal of the square so, by The Pythagoras Theorem:
x^2 + x^2 = 8.444^2 where x is the side of the square.
x^2 = (8.444)^2 / 2
x^2 = 35.651
x = 5.971 cm
Estimate the average rate of change between x = 0 and x = 2 for the function shown.
Answer:
[tex]m=5[/tex]
Step-by-step explanation:
The average rate of change m of a function is calculated using the following formula
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
In this case we look for the average exchange rate between [tex]x = 0[/tex] and [tex]x = 2[/tex].
Therefore we must find [tex]f(2)[/tex] and [tex]f(0)[/tex]
You can see in the graph that when [tex]x = 2[/tex] then [tex]y = 11[/tex]
therefore [tex]f(2) = 11[/tex]
You can see in the graph that when [tex]x = 0[/tex] then [tex]y = 1[/tex]
therefore [tex]f(0) = 1[/tex]
Finally
[tex]m=\frac{f(2)-f(0)}{2-0}[/tex]
[tex]m=\frac{11-1}{2-0}[/tex]
[tex]m=\frac{10}{2}[/tex]
[tex]m=5[/tex]
The estimate of the average rate of change of the function given in the graph above is calculated as: 5.
What is the average rate of change of a function?The average rate of change of a function is the ratio of the change in the function's output values to the corresponding change in its input values over a specified interval.
The average rate of change = f(b) - f(a) / b - a.
Given the function in the graph above, we see that:
a = 0, then f(a) = 1
b = 2. then f(b) = 11
Plugin the values into the formula:
Average rate of change = 11 - 1 / 2 - 0
= 10/2
= 5
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Which of the following parabolas opens down?
ANSWER
The correct answer is C.
EXPLANATION
The directrix of the parabolas are parallel to the x-axis. This means that, the orientation of the parabola is parallel to the y-axis. We compare the focus and the directrix to determine whether the parabola opens downwards or upwards.If the directrix is above the focus, then the parabola opens downwards.On the other hand if the directrix is below the focus , then the parabola must open upwards.If you look at option C, y=-2 isthe directrix. The focus is (3,-5). Since the the y-value of the focus , -5 is less than y=-2 which is the directrix, this parabola must open down.The correct answer is C.
The average house in a neighborhood measures 55 ft by 35 ft by 20 ft tall. What is the total outside surface area?
[tex]\bf \textit{surface area of a rectangular prism}\\\\ SA=2(Lh+Lw+wh)~~ \begin{cases} L=length\\ w=width\\ h=height\\ \cline{1-1} L=55\\ w=35\\ h=20 \end{cases} \\\\\\ SA=2[(55\cdot 20)+(55\cdot 35)+(35\cdot 20)]\implies SA=2[1100+1925+700] \\\\\\ SA=2(3725)\implies SA=7450[/tex]
What is the quotient of (4x2 − 15x + 9) ÷ (x − 3)?
Answer:
The quotient is 4x- 3.
Step-by-step explanation:
Suppose AB ≅ AE. Can you use the SSS Postulate or the SAS Postulate to prove ABC ≅ AED?
Answer with explanation:
In Δ ABC and ΔA DE
AC=AD----------[Given]
BC=DE----------[Given]
∠BAC=∠DAE-------[Given]
Any of the two criteria which are →[SAS,SSS] can't be used to prove ⇒ΔABC≅ ΔA ED
Because, neither two sides and Included angle of two triangles ,nor three corresponding sides of two triangles, are congruent to each other.
Option A : Neither Apply
1. Angle BAC = angle EAD( given)
2. line BC = line DE ( given)
3. line AC = line AD( given)
4. Triangle ABC is congruent to AED by SAS or SSS postulate of congruency.
The Side-Angle-Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
1. Angle BAC = angle EAD( given)
2. line BC = line DE ( given)
3. line AC = line AD( given)
4. Triangle ABC is congruent to AED by SAS or SSS postulate of congruency.
A toy rocket is launched at an initial velocity of 50 ft/s at an angle of 75° with the horizontal. How long will it take for the rocket to travel 20 feet horizontally?
Answer:
t = 1.55 sec
Step-by-step explanation:
Because we are asked to find the time it will take for the rocket to travel horizontally, we are only concerned with the x-dimension here.
We are told that the initial velocity is 50 ft/s and the angle is 75 degrees.
The equation we are going to need to solve this involves the displacement, the initial velocity, the acceleration, and the time...all in the x dimension:
Δx = V₀t + 1/2at²
We have the displacement, we can solve for the initial velocity, we know acceleration, and time is what we are solving for.
Let's work to fill in these values:
Δx = 20 feet
V₀x = V₀ cos Ф (that's the closest thing I could find to theta)
a = 0 (acceleration is always 0 in the horizontal dimension)
t = ?
From the information we can determine the initial velocity in the x dimension using the formula
[tex]V_{0x}=V_{0}cos(\theta)[/tex]
Solving for the initial velocity in the x-dimension:
[tex]V_{0x}=50cos(75)[/tex], which gives us from our calculators that initial velocity in the x-dimension is 12.941 (I am not paying attention to significant digits here since 50 has only 1).
Now we can fill in our equation with the info:
[tex]20=12.941t+\frac{1}{2}(0)t^2[/tex]
Because a = 0, the whole portion of the equation after the plus sign equals 0, so we can disregard and simply solve:
20 = 12.941t so
t = 1.55 seconds
The time it will take for the rocket to travel 20 feet horizontally is 1.545 seconds.
What is the equation of motion?There are three equations of motion, v= u +at, s = ut +(1/2)at²and v² = u²+2as.
The initial velocity is 50 ft/s
The angle is 75 degrees.
s = ut +(1/2)at²
v= u cos [tex]\rm \theta[/tex]
v = 50 cos 75
v = 12.94 ft/s
a = 0 in horizontal direction
s = 20
20 = 12.94 *t
t = 20/12.94
t = 1.545 seconds.
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Timothy built a base for a circular tabletop. The base can support a tabletop with a radius of at least 6 inches, but not more than 23 inches. What is the smallest possible area of the tabletop that will fit on Timothy’s table base? Round the answer to the nearest whole square inch. What is the largest possible area of the tabletop that will fit on Timothy’s table base? Round the answer to the nearest whole square inch.
Answer:
The smallest possible are of the tabletop is 113 in²The largest possible area of the tabletop is 1,662 in²Explanation:
1) What is the smallest possible area of the tabletop that will fit on Timothy’s table base?
The statement that the base can support a tabletop with a radius of at least 6 inches means that the radius has to be 6 inches or more, i.e. the smallest possible radius is 6 inches.
a) Area of a circle: A = π r²
The smallest area is given by the smallest radius, which we have just stated that is 6 in.
b) Calculations:
With that A = π (6 in)² = 36π in² ≈ 113.10 in².
Round the answer to the nearest whole square inch: 113 in²
2) What is the largest possible area of the tabletop that will fit on Timothy’s table base?
The statement that the base can support a tabletop with a radius no more than 23 inches means that the radius has to be 23 inches or less, i.e. the largest possible radius is 23 inches.
a) Area of a circle: A = π r²
The largest area is given by the largest radius, which we have just stated that is 23 in.
b) Calculations:
With that A = π (23 in)² = 529 π in² ≈ 1,661.9 in².
Round the answer to the nearest whole square inch: 1,662 in².
Answer is 113 for the first then 1662 for the second
Step-by-step explanation:
find the solution of this system of equations -7x+y=-20 9x-3y=36
Final answer:
To find the solution of the system of equations -7x+y=-20 and 9x-3y=36, we can use the method of substitution. The solution is x = 2 and y = 6.
Explanation:
To find the solution of the system of equations -7x+y=-20 and 9x-3y=36, we can use the method of substitution or elimination. Let's use the method of substitution:
Step 1: Solve one equation for one variable in terms of the other variable. From the first equation, we have y = 7x - 20.
Step 2: Substitute this expression for y in the second equation. Substitute the value of y from Step 1 into the second equation: 9x - 3(7x - 20) = 36.
Step 3: Simplify and solve for x. Distribute the -3 to both terms inside the parentheses: 9x - 21x + 60 = 36.
Step 4: Combine like terms: -12x + 60 = 36.
Step 5: Subtract 60 from both sides of the equation: -12x = -24.
Step 6: Divide both sides of the equation by -12: x = 2.
Step 7: Substitute the value of x back into one of the original equations to find y. Using the first equation, we have -7(2) + y = -20. Simplifying, we get y = 6.
Therefore, the solution to the system of equations is x = 2 and y = 6.
Find the number of real number solutions for the equation. x2 + 5x + 7 = 0 0 cannot be determined 1 2
Answer:
0
Step-by-step explanation:
For a quadratic of the form
ax² +bx +c = 0
The "discriminant" is the expression ...
b² -4ac
For this equation, we have a=1, b=5, c=7, so the discriminant is ...
5² -4·1·7 = -3
When the discriminant is negative there will be two distinct complex roots to the equation, and no real roots.
_____
When the discriminant is zero, there will be one real root with multiplicity 2; when it is positive, there will be two distinct real roots.
This graph shows Matt's progress as he walks in the direction of Grandma's house:
Nathan walks at a rate of 4 miles per hour. Who travels at a faster rate, Matt or Nathan? How do you know this?
Please explain the answer
Random answer gets reported.
Nathan is walking faster than Matt.
Step-by-step explanation:The graph shows that for every hour, Matt walks 3 miles, since it goes to the right 1 and up 3 over and over again. This means Matt's speed is 3 miles per hour.
4 miles per hour is greater than 3 miles per hour, so Nathan is walking at a faster speed.
The perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is
Answer:
16 in = 2W + 2L
Step-by-step explanation:
The equation for the perimeter of this rectangle is
P = 16 in = 2W + 2L.
Without knowing the value of either W or L, we can do no more at this point.
Need help with this math question
Answer:
The measure of angle x is [tex]m\angle x=84\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m\angle x=\frac{1}{2}(168\°)=84\°[/tex]
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Solve and type in a different form by using the given theorems of logarithms.
Answer:
log₁₀(M) + log₁₀(N)
Step-by-step explanation:
The rules of logarithms tell you ...
log(ab) = log(a) +log(b) . . . . . base of logarithms the same in each case
When your log is log₁₀ and a=M and b=N, this becomes ...
log₁₀(MN) = log₁₀(M) + log₁₀(N)
_____
Some functions are not always written with their arguments in parentheses. I believe it avoids ambiguity to put function arguments in parentheses, so I have done that here. It appears your answer form may want you to write ...
log₁₀M+log₁₀N . . . . . I don't recommend this form
Andrew paid an agency 10% of his first year's rent for finding him an apartment. His rent is $1,800 per month.
$216
$900
$1,800
$2,160
Answer:
D. $2,160
Step-by-step explanation:
$1800 per month * 12 months = $21,600
10% of $21,600 = 0.1 * $21,600 = $2,160
Answer:
$2,160
Step-by-step explanation:
There are 12 months in a year
1800 *12 = 21600
He pays 21600 per year in rent
He pays the agency 10%
21600 * 10%
21600*.10
2160
He pays the agency 2160
Can someone help me out
Answer: LAST OPTION.
Step-by-step explanation:
The Pythagorean Theorem states the following relationship between the three sides of a triangle that has an angle of 90 degrees, known as "Right triangle":
[tex]a^2=b^2+c^2[/tex]
Where "a"is the hypotenuse and "b" and "c" are the legs of the right triangle.
If the triangle ABC is a right triangle then AB must be equal to [tex]BC^2+AC^2[/tex], then, you need to substitute the values into [tex]a^2=b^2+c^2[/tex] to check this:
[tex]12^2=5^2+10^2\\144\neq 125[/tex]
Then the triangle ABC is not a right triangle.
Therefore, the statement that justifies why this triangle is not a right triangle is:
[tex]5^2+10^2\neq 12^2[/tex]
PLEASE HELP! The students at Jefferson Middle School are raising money for a charity by selling T-shirts and hats. The number of T-shirts sold was 3 times the number of hats. The profit was $5 for each T-shirt sold and $2.50 for each hat sold. The students raised $840 for the charity. They used the system below to analyze their success and found the solution to be (144, 48).
5x+2.50y=840
x=3y
How much did they earn from T-shirt sales?
They earned $128 from the T-shirts.
They earned $144 from the T-shirts.
They earned $360 from the T-shirts.
They earned $720 from the T-shirts.
Answer: They earned $720 from the T-shirts.
Step-by-step explanation:
Given : The number of T-shirts sold was 3 times the number of hats.
The profit was $5 for each T-shirt sold and $2.50 for each hat sold.
The students raised $840 for the charity.
Let x denotes the number of T-shirts sold and y denotes the number of hats sold.
then, we will have the given system :-
[tex]5x+2.50y=840\\x=3y[/tex]
It is also given that they used the system below to analyze their success and found the solution to be (144, 48).
It means x= 144
It means the number of t-shirt sold = 144
The amount they earn from t-shirt = [tex]144\times5=\$720[/tex]
Hence, they earn $720 from the T-shirts.
Answer:
this is just proof of verification if you don't believe the guy above me
Step-by-step explanation:
How do you know that this function is odd or even? { (1,2),(4,7),(-1,2),(0,4),(-4,7)}
Answer:
The function is even.
Step-by-step explanation:
Compare it to the definition of an odd function or an even function.
Odd function: if (x, y) is in the relation, then (-x, -y) is also in the relation. (The function is symmetrical about the origin.)
Even function: if (x, y) is in the relation, then (-x, y) is also in the relation. (The function is symmetrical about the y-axis.)
__
The first point listed is (1, 2). If this function is odd, we expect to find (-1, -2). There is none such.
If this function is even, we expect to find (-1, 2). That is the third point listed, so it is possible this function is even. Comparing the other points to their even-function counterparts shows all of them match the definition of an even function.
C’E’D is a dilation imagine of CED. Which is the correct description of the dilation
Answer:
An enlargement with scale factor 2
Step-by-step explanation:
C’E’D is a dilation imagine of CED
It's enlargement so scale factor must be greater than 1
SF = 4/2 = 2
Answer
An enlargement with scale factor 2
An enlargement with scale factor 2
What is dilation?A dilation in mathematics is a function f from a metric space M into itself that, for any locations x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is some positive real number. Such a dilatation is a resemblance of the space in Euclidean space.
Given
C’E’D is a dilation imagine of CED
It's enlargement so scale factor must be greater than 1
SF = 4/2 = 2
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Given that f(x) = x^2 + 6x – 2, g(x) = x – 7, and h(x) = x + 4
find each function. (f + g)(x)
Answer:
(f+g)(x) = x^2 + 7x -9
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
= (x^2 + 6x – 2) + (x – 7)
= x^2 + 7x -9