Answer:
(4x + 5)²
4x² + 20x + 25
Step-by-step explanation:
Step 1: Factor 16x² + 40x + 25
(4x + __)(4x + __)
What multiplies to 25 and adds up to 40 with 4 multiplied as coefficient?
(4x + 5)(4x + 5) or (4x + 5)²
Step 2: Factor perfect square trinomial
36x² - 4x + 16 --> 4(9x² - x + 4) No
16x² - 8x + 36 --> 4(4x² - 2x + 9) No
25x² +9x + 4 --> 25x² + 9x + 4 No
4x² + 20x + 25 --> (2x + 5)(2x + 5) or (2x + 5)² Yes
Answer:
(4x + 5)(4x + 5).
4x^2 + 20x + 25.
Step-by-step explanation:
16x^2 + 40x + 25
= (4x + 5)(4x + 5)
= (4x + 5)^2.
36x^2 − 4x + 16: To be a perfect square trinomial, the factors would have to be (6x + 4) or (6x - 4). Since the value of b is only -4, this is NOT a perfect square trinomial.
16x^2 − 8x + 36: To be a perfect square, factors would have to be (4x + 6) or (4x - 6). Since the value of b is only -4, this is NOT a perfect square.
25x^2 + 9x + 4: To be a perfect square, factors have to be (5x + 2) or (5x - 2). Since b is positive, factors would be (5x + 2)(5x + 2) = 25x^2 + 20x + 4. 20x is not equal to 9x, so this is NOT a perfect square.
4x^2 + 20x + 25: Perfect square would have to have factors (2x + 5) or (2x - 5). b is positive, so factors are (2x + 5)(2x + 5) = 4x^2 + 10x + 10x + 25 = 4x^2 + 20x + 25. This IS a perfect square!
Hope this helps!
Allison is rolling her hula hoop on the playground. The radius of her hula hoop is 35 \text{ cm}35 cm35, start text, space, c, m, end text. What is the distance the hula hoop rolls in 444 full rotations?
Answer: 880 cm
Step-by-step explanation:
Given: Radius of the hula hoop = 35 cm
Hula hoop is circular in shape
Then, Circumference = [tex]2\pi r[/tex] , where r = radius
Now , Circumference of hula hoop = [tex]2\times \dfrac{22}{7}\times35=220\ cm[/tex]
Now , the distance the hula hoop rolls in 4 full rotations = 4 × (Circumference of hula hoop)
[tex]= 4 \times 220=880\ cm[/tex]
Hence, the required distance = 880 cm
Answer:
880
Step-by-step explanation:
Distribute 10 (3x + 8x2).
Answer:
30x+160
simple all you had to do is 10*3x and 8x2=16 and 10*16 and you will get 30x+160
Step-by-step explanation:
Answer:
30x + 80x^2
Step-by-step explanation:
10 (3x + 8x^2)
10 * 3x + 10 * 8x^2
30x + 80x^2
Simplify by combing like terms: -18 + 3(5x - 2) + 8
Answer:
15x-16
Step-by-step explanation:
3(5x-2)+(-18+8)
3(5x-2)-10
15x-6-10
15x+(-6-10)
15x-16
Two shaded identical rectangular decorative tiles are first placed (one each) at the top and at the base of a door frame for a hobbit's house, as shown in Figure 1. The distance from W to H is 45 inches. Then the same two tiles are rearranged at the top and at the base of the door frame, as shown in Figure 2. The distance from Y to Z is 37 inches. What is the height of the door frame, in inches?
Answer:
41 inches
Step-by-step explanation:
Let the point at the top of the door on the left be x
Wx + xH = 45
Let the point at the top of the door on the right be c
Yc + cZ = 37
We know the door is
xH + plus the width of the tile
The width of the tile is Yc
xH + Yc
On the right door
cZ + the height of the tile
cZ + Wx
Add the two doors together
xH + Yc + cZ + Wx = 2 times the height of the door
Rewriting
xH + Wx + Yc + cZ = 2 times the height of the door
45+ 37 = 2 times the door height
82 = 2 times the door height
Divide by 2
41 = door height
WILL MARK BRAINLIEST!!! PLZ HELP! The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. Function 1 Function 2 f(x) = −x2 + 4x + 1 Function 1 has the larger maximum at (4, 1). Function 1 has the larger maximum at (1, 4). Function 2 has the larger maximum at (2, 5). Function 2 has the larger maximum at (3, 2).
Answer:
C: Function 2 has the larger maximum at (2, 5).
Step-by-step explanation:
We are given two functions, with Function 1 being described by the graph and Function 2 given by the function:
[tex]f(x)=-x^2+4x+1[/tex]
Notice that the leading coefficient of Function 2 is negative. The graph of Function 1 is curving downwards. So, both functions will have maximum values.
Recall that for a parobala, the maximum (or minimum) values is the y-value of the vertex point. So, let's find the vertex for each function.
For Function 1, we can see that the vertex is at (4,1). Thus, its maximum value is y = 1.
For Function 2, we will need to work out the vertex. Recall that the vertex is given by:
[tex]\displaystyle \left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)[/tex]
Function 2 is defined by:
[tex]f(x)=-x^2+4x+1[/tex]
Therefore, a = -1, b = 4, and c = 1.
Find the x-coorindate of the vertex:
[tex]\displaystyle x=-\frac{(4)}{2(-1)}=2[/tex]
Substitute this back into the function to find the y-coordinate.
[tex]f(2)=-(2)^2+4(2)+1=5[/tex]
So, the vertex of Function 2 is (2,5). Therefore, the maximum value of Function 2 is y = 5.
Since 5 is greater than 1, the maximum value of Function 2 is greater.
The answer is choice C.
The interest of the sum of money at the end of 10 years is one third of the sum. Find the rate of interest
Answer:
3.33%
Step-by-step explanation:
Intrest = P. A. *Intrest Rate * Time
(1/3)*P. A. = P. A. *Intrest Rate * 10
Intrest Rate = 1/30)=3.33%
In parallelogram ABCD, m∠B = 105°.
What is the value of x. (Round your answer to the nearest tenth, if necessary.)
Answer:
x=52.5
Step-by-step explanation:
Since ABCD is a parallelogram, B= ADC. So angle ADC is 105. Next since ED=AD, angle EAD=angle AED=x and ADE=75. So 2x+75=180, 2x=105, x=105/2
In parallelogram ABCD, m∠B = 105° then the value of x = 52.5
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Since ED ≈ AD,
∆AED is an isosceles triangle where ∠EAD and ∠AED has the same angle measurement
Now, ∠B = 105°, since ABCD is a parallelogram,
∠B = ∠D
∠ADC = 105°
∠ADE = 180°-105° = 75°
Now, ∠EAD + ∠AED+ ∠ADE = 180°
∠AED+∠AED+∠ADE = 180°
x+x+75°=180°
2x=180+75°
2x = 105°
x = 52.5°
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What is the constant term for 4x-2y+3
Answer:
Step-by-step explanation:
3 is the constant term.
Constant term is the term without any variables
Answer:
3
Step-by-step explanation:
The constant number is the number that has no variable and just a number.
Question
0
Which angle between 90 and 270 has the same sine value as 60°?
Which angle between –180° and 0 has the same cosine value as 290°?
degrees
Answer:
(i) 120°
Step-by-step explanation:
(i)
sine 90 = 1
sine 120 = 0.87 (rounded up to two decimal places)
sine 150 = 0.5
sine 180 = 0
sine 210 = -0.5
sine 240 = -0.87 (rounded up to two decimal places)
sine 270 = -1
sine 60 = 0.87 (rounded up to two decimal places)
So the angle x such that 90° < x < 270° that has the same sine value as 60° is 120°
if polynomial ax3 + 3x2 - 3 and 2x3 - 5x + a leaves the same remainder when each is devided by x - 4 find the valuse of a
Answer:
a = 1
Step-by-step explanation:
Given that both ax³ + 3x² - 3 and 2x³ - 5x + a have the same remainder when divided by x - 4.
x - 4 = 0
x = 4
When ax³ + 3x² - 3 is divided by x - 4, the remainder is gotten by substituting x = 4:
a(4)³+3(4)²-3 = 64a + 48 - 3 = 64a + 45
The remainder is 64a³ + 45
For 2x³ - 5x + a we find the remainder by substituting x = 4:
2(4)³ - 5(4) + a = 128 - 20 + a = 108 + a
Since they both have the same remainder, therefore:
64a + 45 = 108 + a
64a - a = 108 - 45
63a = 63
a = 1
Alonso overdrew his bank account and his account balance showed -$50. He spent an
additional $37 going out to the movies with friends. Write an expression and draw a line
number to determine Alfonso's current bank account balance.
Answer:
-$87
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
Helpppp pleaseeeeee!!!
Answer: yes.
Step-by-step explanation:
Answer: Yes
The roll of the dice is a random process that Jon has no control over (this is assuming the dice is fair of course). Whoever is selected first is not selected again, so the probability for the second selection will increase as there is a smaller pool of people to pick from.
Please please please please help
Answer:
[tex]x^2 +4x +3 [/tex]
Step-by-step explanation:
f(x)=x²-1
g(x)= x+2
f(g(x)) =f(x+2)
=(x+2)²-1
=x²+4x+4-1
=x²+4x+3
30 in.
20 in.
36 in.
Find the area of the trapezoid shown above.
[?] square inches
Answer:
660 in^2
Step-by-step explanation:
The formula to calculate area of trapezoid : (a+b)/2*h (a: base, b: base, h: height)
(30+36)/2*20 = 660 in^2
Solve for the value of p.
p =
Answer:
p = 4
Step-by-step explanation:
[tex](8p + 4) \degree + 54 \degree = 90 \degree \\ (complementary \: \angle s)\\ (8p + 4+54) \degree = 90 \degree \\ (8p + 58) \degree = 90 \degree \\ 8p + 58 = 90 \\ 8p = 90 - 58 \\ 8p = 32 \\ p = \frac{32}{8} \\ p = 4[/tex]
Answer:
p = 4
Step-by-step explanation:
8p+4+90+54=180
180-90-54=36
36-4=32
32/8=4
p=4
to check the answer
90+54+(8×4)+4=180⁰
Kia was 200 m north of the Liebrary when he remembered he had to return some books to the library it took him to 200 seconds to do the round-trip which best describes cost round-trip
Answer:
His speed is 2 m/s
His velocity is 0 m/s
Step-by-step explanation:
I'll assume the question is
Kia was 200 m north of the Library when he remembered he had to return some books to the library it took him to 200 seconds to do the round-trip which best describes hist round-trip.
Kia's distance from the Library is 200 m
the round-trip took him 200 s
The total distance for the round trip = 200 x 2 = 400 m
His displacement for the round trip = 0 m (since he returns to his original position)
His speed = distance/time = 400/200 = 2 m/s
His velocity = displacement/time = 0/200 = 0 m/s
The dosage for a certain drug calls for 20mg per kg per day and is divided into two doses(1every 12 hours) if a person weighs 197 pounds how much of the drug should be given each dose
Answer:
893.42
Step-by-step explanation:
1kg=2.205pounds
so 20mg is for 2.205pounds
therefore for 197pounds will be 1784.84mg
but the dose is once every 12hrs meaning twice a day so divide 1784.84/2 to get the pounds
Triangles ABC and XYZ are similar. Find side x.
Answer:
x=6
Step-by-step explanation:
side AB is proportional to side XY
side AC is proportional to side XZ
Since we know side AB and side XY are proportional to each other, if we divide side AB by side XY, we can find the size difference...
12 / 4 = 3
The smaller triangle is 3 times smaller than the bigger triangle so we can find side XZ by dividing side AC by 3...
18 / 3 = 6
x = 6
The measure of the length of x is 9 units.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≈".
Given triangles ABC ≈ XYZ
for similar triangles, corresponding sides are proportionately equal and corresponding angles are congruent,
so AB/XY = AC/XZ = BC/YZ
substitute the values
12/4 = 18/x = 9/YZ
12/4 = 18/x
x= 9 units
Hence the value of x is 9 units.
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A typical television newscast has three cameras. The center camera directly faces the news anchor’s desk. The other two cameras are both angled 45 degrees away from the center camera. Suppose each camera has a filed if 60 degrees. What is the total angle covered by three cameras? Explain your reasoning.
The figure below shows a parallelogram ABCD Side AB parallel to side DC and side AD is parallel to side BC A student wrote the following sentences to prove that parallelogram ABCD has two pairs of opposite sides equal For triangles and COB alternate interior angle ABD is congruent to angle CDB because AB and DC are parallel lines Similarly interior angle equal to angle CBD because AD and are parallel lines equal to DB by the reflexive property Therefore , triangles ABD and COB are congruent by the SAS postulate Therefore AB congruent to and AD congruent BC CPCTC Which statement best describes a flaw in the student's proof ?
Answer:
Second choice
Explanation :
The postulate that is used in order to prove the congruency of the triangles is the ASA which means (Angle – Side – Angle). The property that is applicable for the congruency of DB to itself is the reflexive property. Therefore, the answer to this item is the second choice.
Hope I helped! :)
If yes mark me BRAINLIEST!
Tysm!
Triangles ABD and CDB are congruent to each other by the ASA theorem. The student used SAS which is wrong. The answer is: D.
What is the ASA Theorem?The ASA theorem states that two triangles that have a pair of corresponding included congruent sides and two pairs of corresponding congruent angles are congruent triangles.
Based on the ASA theorem, triangles ABD and CDB are congruent to each other.
Therefore, the use of SAS theorem by the student is wrong.
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darious buys a bottle of chemical solution that contains 70% alcohol. the bottle contains 500 ml of solution. how many ml of alcohol r in the solution
Answer:
350 ml of alcohol
Step-by-step explanation:
70% = 70/100 = 0.7
70% of 500 ml is:
500*0.7 = 350 ml
there are:
350 ml of alcohol
What is the slope of the line that passes through the points (-20, 18) and (30, 14)?
Answer:
-2/25
Step-by-step explanation:
Use the slope formula: rise/run to find the slope
Answer:
slope = - [tex]\frac{2}{25}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 20, 18) and (x₂, y₂ ) = (30, 14)
m = [tex]\frac{14-18}{30-(-20)}[/tex] = [tex]\frac{-4}{30+20}[/tex] = [tex]\frac{-4}{50}[/tex] = - [tex]\frac{2}{25}[/tex]
Does anyone know this?
Answer:
f(-4) = 92
Step-by-step explanation:
f(x) = 3x^2 - 10x + 4
f(-4) = 3(-4)^2 - 10(-4) + 4
= 3(16) + 40 + 4
= 48 + 40 + 4
= 92
Adding the fractions
3/14+2/21+1/6
Answer:
[tex]\frac{10}{21}[/tex]
Step-by-step explanation:
The LCM of 14, 21 and 6 is 42
We require to change the fractions to fractions with a denominator of 42
[tex]\frac{3(3)}{14(3)}[/tex] + [tex]\frac{2(2)}{21(2)}[/tex] + [tex]\frac{1(7)}{6(7)}[/tex]
= [tex]\frac{9}{42}[/tex] + [tex]\frac{4}{42}[/tex] + [tex]\frac{7}{42}[/tex] ← add the numerators, leaving the denominator
= [tex]\frac{9+4+7}{42}[/tex]
= [tex]\frac{20}{42}[/tex] ← divide both values by 2
= [tex]\frac{10}{21}[/tex] ← in simplest form
Which point would be a solution to the system of linear inequalities shown below? {see image for inequalities}
(-10, -2)
(−5,2)
(10,7)
(10,−2)
Answer:
(10, -2)
Step-by-step explanation:
The inequalities are:
y < x - 7 (1)
y < (1/5)x - 2 (2)
To solve this problem, we have to solve both equations simultaneously and then find the value of x and y that makes the inequality true.
To solve the inequality, subtract inequality (2) from inequality (1) which gives:
0 < (4/5) x - 5
-(4/5)x < -5
Dividing both sides of the equation by -4/5 gives:
-(4/5)x / (-4/5) < -5/ (-4/5)
x > 6.25
Put x > 6.2 in inequality 1
y < 6.25 - 7
y < -0.75
The solution of the inequality is x > 6.25 and y < -0.75
From the list of option, the correct answer is (10, -2) since 10 > 6.25 and -2 < -0.75
-32=8n I need help please
Answer:
n = -4
Step-by-step explanation:
-32=8n
Divide each side by 8
-32/8 = 8n/8
-4 = n
- 32 = 8n
Cross multiplying we get
n = -32/8
n = -4
Henceforth, the required solution is -4the product 9f 2 numbers is 16/9 . if one number is 5 /2 find the other number
Answer:
The answer is 32/45Step-by-step explanation:
Let the number be x
The product of two numbers is 16/9
That's
x × y = 16/9
One of the numbers is 5/2
That's
y = 5/2
So we have
[tex] \frac{5}{2} x = \frac{16}{9} [/tex]
Multiply through by the LCM
The LCM of 2 and 9 is 18
That's
[tex]18 \times \frac{5}{2} x = \frac{16}{9} \times 18[/tex]
9 × 5x = 16 × 2
45x = 32
Divide both sides by 45
we have the final answer as
[tex]x = \frac{32}{45} [/tex]
Hope this helps you
4. A prism has an area of cross-section of 89 cm². The volume of the prism is
4895 cm?. Find the height of the prism.
Answer:
55 cm
Step-by-step explanation:
height = 4895/89 = 55 cm
BRAINLIEST, 5 STARS AND THANKS IF ANSWERED CORRECTLY.
A quadratic equation with a negative discriminant has a graph that..
A. touches the x-axis but does not cross it
B. opens downward and crosses the x-axis twice
C. crosses the x-axis twice.
D. never crosses the x-axis.
Answer:
never crosses the x-axis.
Step-by-step explanation:
A quadratic equation with a negative discriminant has a graph that - never crosses the x-axis.
Answer:
The graph of a quadratic equation that has a negative discriminant is the one that never intersect x-axis. The graph of a quadratic equation that has a zero discriminant is the one that intersect x-axis at only one point. To be clearer, it can be seen in the attached image.
Step-by-step explanation:
Answer D
Complete the ordered pairs below so they satisfy the equation.
y = - 7x + 8
Answer:
x=8/7-y/7
Step-by-step explanation: