Answer:
4(x + [tex]\frac{1}{2}[/tex] )²
Step-by-step explanation:
Given
h(x) = 4x² + 4x + 1
To complete the square the coefficient of the x² term must be 1
Factor out 4 from 4x² + 4x
h(x) = 4(x² + x) + 1
add/subtract ( half the coefficient of the x- term )² to x² + x
h(x) = 4(x² + 2([tex]\frac{1}{2}[/tex] )x + [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{4}[/tex] ) + 1
= 4(x + [tex]\frac{1}{2}[/tex] )² - 1 + 1
= 4(x + [tex]\frac{1}{2}[/tex] )²
Answer:
Step-by-step explanation:
4(x+1/2)^2+0
The first box is 4
The second box is 1/2
the third box is 0
One gallon of water weighs 8.34 pounds. How much does 6 gallons of water weigh? Show your work, including labeling your answer with the appropriate units of measure
Answer:
50.04 pounds
Step-by-step explanation:
If 1 gallon weighs 8.34 pounds,
all you have to do is multiply 8.34 by 6
to get what 6 gallons would weigh.
To determine the weight of 6 gallons of water, multiply the weight of one gallon (8.34 pounds) by 6. Thus, 6 gallons of water weigh 50.04 pounds.
To find out how much 6 gallons of water weigh, you simply need to multiply the weight of one gallon by the number of gallons.
Since we know that one gallon of water weighs 8.34 pounds, the calculation is as follows:
6 gallons × 8.34 pounds/gallon = 50.04 pounds.
Therefore, 6 gallons of water weigh 50.04 pounds.
A 12-foot ladder leans against the wall; the base of the ladder is 2 feet away from the wall.To the nearest tenth of a foot, how far up the wall does the ladder reach?
Solution:
The ladder, wall and base of the ladder from wall forms a right angled triangle
Length of ladder forms the hypotenuse
Length of ladder = 12 foot
base of the ladder from wall = 2 feet
To find: height of wall
By pythagoras theorem.
[tex]c^2 = a^2+b^2[/tex]
Where,
"c" is the Length of ladder
"a" is the base of the ladder from wall
"b" is the height of wall
Substituting the values,
[tex]12^2 = 2^2+b^2\\\\144 = 4 + b^2\\\\b^2 = 140\\\\b = \pm 11.832 \\\\Ignore\ negative\ value\\\\b \approx 11.8[/tex]
Thus, the ladder will reach a height of 11.8 feet on wall
There are 60 students in a class. The number of girls is three times the number of boys. How many girls are in
the class?
B = number of boys
G = number of girls
G = 3*B since there are 3 times as many girls compared to boys
B+G = 60
B+3B = 60 ... replace G with 3B, solve for B
4B = 60
4B/4 = 60/4
B = 15, so there are 15 boys
G = 3*B
G = 3*15 ... plug in value of B
G = 45, and 45 girls
as a check
B+G = 15+45 = 60, so that works out
which is more 2 miles or 3,522 yards
Answer:
3,500 yards is more.
Step-by-step explanation:
convert the yards to miles using the formula M = Y/1760
which gives you 2.001 miles so it is slightly longer than 2 miles.
Answer :3,526 yards is 6 yards greater than 2 miles
Step-by-step explanation: 1,760 . 2= 3,520
Which dimensions can create only one unique triangle?
three angles measuring 25 degrees, 65 degrees, and 90 degrees
three angles measuring 50 degrees, 50 degrees, and 50 degrees
three sides measuring 5 in., 12 in., and 14 in.
three sides measuring 4 ft, 8 ft, and 14 ft
Three sides measuring 5 in., 12 in., and 14 in.
Explanation:First of all, you need to know some facts about every triangle:
FIRST FACT:
If two sides of a triangle are [tex]a \ and \ b[/tex], then the third side must be less than [tex]a+b[/tex]. Why? because if its length is exactly [tex]a+b[/tex], then you can't build up a triangle, but you'll have a line segment. In other words:
[tex]a<b+c \\ \\ b<a+c \\ \\ c<a+b[/tex]
SECOND FACT:
The internal angles of any triangle add up to 180°. So if ∠A, ∠B and ∠C are the internal angles of a triangle, then:
[tex]\angle A +\angle B+ \angle C=180^{\circ}[/tex]
__________________________
So let's analyze each case:
Case 1. Three angles measuring 25 degrees, 65 degrees, and 90 degrees :
[tex]\angle A=25^{\circ} \\ \\ \angle B=65^{\circ} \\ \\ \angle C=90^{\circ} \\ \\ \\ \angle A +\angle B+ \angle C=25^{\circ}+65^{\circ}+90^{\circ}=185^{\circ} \neq 180^{\circ}[/tex]
The sum is greater than 180 degrees, so these angles can't form a triangle
Case 2. Three angles measuring 50 degrees, 50 degrees, and 50 degrees [tex]\angle A=50^{\circ} \\ \\ \angle B=50^{\circ} \\ \\ \angle C=50^{\circ} \\ \\ \\ \angle A +\angle B+ \angle C=50^{\circ}+50^{\circ}+50^{\circ}=150^{\circ} \neq 180^{\circ}[/tex]The sum is less than 180 degrees, so these angles can't form a triangle
Case 3. Three sides measuring 5 in., 12 in., and 14 in. [tex]a=5 \\ \\ b=12 \\ \\ c=14 \\ \\ \\ 5<12+14\rightarrow 5<26 \\ \\ 12<5+14 \rightarrow 12<19 \\ \\ 14<5+12 \rightarrow 14<17[/tex]The inequalities are true, so these sides form a triangle.
Case 4: Three sides measuring 4 ft, 8 ft, and 14 ft
[tex]a=4 \\ \\ b=8 \\ \\ c=14 \\ \\ \\ 4<8+14\rightarrow 4<22 \\ \\ 8<4+14 \rightarrow 8<18 \\ \\ 14<4+8 \rightarrow 14<12 \ NOT \ TRUE![/tex]
Since the third inequality is not true, then we can't form a triangle with these sides.
Find the area of a circle with the circumference of 50.27 ft
Answer:
201.1ft²
Step-by-step explanation:
The area of the circle is 200.96 ft².
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
Circumference of a circle = 2πr
This means,
2πr = 50.27 ft
π = 3.14
r = 50.27 / 2 x 3.14
r = 50.27 / 6.28
r = 8.005 ft
r = 8 ft
Now,
The area of the circle.
= πr²
= 3.14 x 8²
= 3.14 x 8 x 8
= 3.14 x 64
= 200.96 ft²
Thus,
The area of the circle is 200.96 ft².
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i need help with this
plz anwswer right away ill mark you brainiest if done.
Answer:
4 x 2 x 3
Step-by-step explanation:
[tex]l = 4\\\\w = 2\\h = 3\\[/tex]
Answer:
you can solve this by finding the volume of the block
Step-by-step explanation
V= lxwxh
= 3x4x2
= 24
therefore there are 24 blocks in this figure
Have a great day
The area of a triangle is 40 square centimeters. The height is 10 centimeters. What is the length of the base of the triangle?
Answer:
20cm.
Step-by-step explanation:
so the answer is 8cm
Hope this will help u...
Which graph shows the function y=(1/3)3x?
Answer: y=0
Step-by-step explanation
Use the formula for the area to find the area of each light 7 inches . Use 3.14 for pi
Answer:
21.990 in circumference area 38.480 area in the square inches
Step-by-step explanation:
Answer: the area formula is A = πr2. Substitute the values of r (3.5 inches) and π (3.14) in the formula to find A:
A = 3.14 × (3.5)2 square inches
A = 38.465 square inches.
The area of each light is about 38.465 square inches.
Convert to scientific notation 0.0000089
Answer:
8.9 x 10^-6
Step-by-step explanation:
move decimal to the right so it makes a negative
8.9 x 10^-6
Answer:
8.9 x 10`6
Step-by-step explanation:
message me if you need a explanation
What is 5/15+3\5=? For the sum
Answer:
14/15
Step-by-step explanation:
make both bases the same number
5/15 + 9/5
add like normally
14/15
Answer:
14/15 is your answer
Step-by-step explanation:
A car wheel as a diameter of 20.8 inches. About how far does the car wheel travel in:
a. 1 rotation?
b. 5 rotations?
c. 30 rotations?
Answer:
distance travelled in one rotation is the circumference of the tyre.
so
a. 1 rotation=pi×20.8
=22×20.8/7
=65.37 approx
b.5 rotations is 65.37×5
=325.86 aprox
c. 30 rotations is 30×65.37
=1961.14 inches aprox
Answer: a ≈ 65in. b ≈ 325in. c ≈ 1950in.
Step-by-step explanation:
Diameter = 20.8
Circumference = d or 2r
= 3.14
Radius = d/2
This question requires us to find the circumference as the circumference is one full rotation around the circle (car wheel in this case)
Put it all together:
C = 3.14 x 20.8
= 65.31200
R = 10.4
The question says ABOUT hence we will round it to a whole number
C ≈ 65
D ≈ 10
As the circumference is one full rotation around the circle, the circumference itself is the answer for a.
If one full rotation is equal to 65, we would have 65 x 5 for 5 and so on
65 x 5 = 325
65 x 30 = 1950
Hope this helped, have a great day/night!
Jennifer has the scatterplot shown for her data set, where water is measured in ounces, and is trying to describe the line of best fit. Which choice correctly describes the line of best fit? A) As the temperature increases, her water intake decreases. B) As the temperature increases, her water intake increases. C) As the temperature decreases, her water intake increases. D) There is no relationship between temperature and water intake.
Answer: B. As the temperature increases, the water take increases.
Step-by-step explanation: I just took the test
Express 0.003259 in standard form correct to two significant figures
explain please
Answer:
5.9 x 10^-5
Step-by-step explanation:
Move the point to the right . The power of the exponent becomes negative because we’re moving the point from left to right. The opposite is the case if we move the point to the left .
To two significant figures, move the point until you have just two figures left. So
5.9 x 10^-5 is the answer
Answer: 3.3×10^-3
Step-by-step explanation:
0.003259 in standard form
When you see a standard form questions like this,you have to be patient
You will have to count the zeros backward
How many zeros are in front of the 3,that's two right
That means you take the decimal to the back of 3,that means the decimal is jumping three numbers
Since you are counting backward, that will be negative
So we have,
3.259×10^-3
Now to two significant figures
You will round up the 5 behind the 2 to 1 and add to the 2
Making 3,
So we have
3.3×10^-3
(x-20) (2x+10) (x+40) find the value of x
Answer:
2 • (x - 20) • (x + 5) • (x + 40)
Step-by-step explanation:
Final answer:
To solve the equation (x-20) (2x+10) (x+40)=0, we set each factor equal to zero and solve for x, resulting in three solutions: x = 20, x = -5, and x = -40.
Explanation:
To find the value of x in the equation (x-20) (2x+10) (x+40) = 0, we need to use the property that if a product of factors equals zero, at least one of the factors must be zero. This gives us three separate equations to solve: x - 20 = 0, 2x + 10 = 0, and x + 40 = 0.
Step-by-Step Solution:
Solve x - 20 = 0: Add 20 to both sides, which gives x = 20.
Solve 2x + 10 = 0: Subtract 10 from both sides and then divide by 2, giving x = -5.
Solve x + 40 = 0: Subtract 40 from both sides, which gives x = -40.
Therefore, the solutions to the equation are x = 20, x = -5, and x = -40.
The answer is 11 can someone tell me why?
Answer:
The sum of interior angles is found by using the following equation:
∑ of interior angles = (S - 2)180
S = sides.
Note that the sum is given to you, or 1620. Plug in 1620 for the sum:
1620 = (S - 2)180
Next, isolate the variable, s. Note the equal sign, what you do to one side, you do to the other. Divide 180 from both sides:
(1620)/180 = ((S - 2)180)/180
S - 2 = 1620/180
S - 2 = 9
Next, isolate the variable, s. Add 2 to both sides:
S - 2 (+2) = 9 (+2)
S = 9 + 2
S = 11
~
Step-by-step explanation:
to find the interior angles of a polygon, you must figure out 2 things: the number of angles, and what each measures
since there is 1620 for the angles and (n-2)180 = sum of int. angles, we can solve using this (n = the number of sides)
(n-2)180 = 1620
180n - 360 = 1620
180n = 1620 + 360
180n = 1980
1980/180 = n
n = 11 sides
A cylinder has a diameter of 5 centimeters and a height of 50 millimeters. Which of the following steps should be done first in order to find the surface area of the cylinder?
convert the diameter and the height to the same unit
determine the radius and multiply by 2
calculate the circumference of the circle
multiply the circumference of the circle by the height of the cylinder
Answer:
B determine the radius and multiply by 2pi
Step-by-step explanation:
Answer:
The first guy is rite. ♥☻
2x+3(5x−7)=47
Solve for x
Answer:
x=580
Step-by-step explanation:
The required value of x in the given equation 2x + 3(5x - 7) = 47 is 4.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
We have to find the value of x in the equation 2x + 3(5x - 7)
Distribute the 3 across the parentheses on the left-hand side of the equation:
2x + 15x - 21 = 47
Combine like terms on the left-hand side of the equation:
17x - 21 = 47
Add 21 to both sides of the equation to isolate the variable term on the left-hand side:
17x = 68
Divide both sides of the equation by 17 to solve for x:
x = 4
Therefore, the value of x in the equation 2x + 3(5x - 7) = 47 is 4.
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The complete question would be as:
Find the value of x for the below equation. explain
2x + 3(5x − 7) = 47
what fraction multiplied by itself is equal to 4/25
Answer:
2/5 times 2/5 equals 4/25
Step-by-step explanation:
An angle measures 156° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
12° and 168°
Step-by-step explanation:
If x is the angle, and y is the supplementary angle, then:
x + y = 180
x = y − 156
Solve the system of equations using substitution:
y − 156 + y = 180
2y = 336
y = 168
Plug back into either equation to find x:
x = 12
Final answer:
The measure of angle A is 12° and the measure of its supplementary angle B is 168°. This is determined by setting up the equation based on the property that the sum of supplementary angles is 180°.
Explanation:
The question asks to find the measures of two supplementary angles when one angle is 156° less than the other. Supplementary angles sum up to 180°. Let's designate angle A as the unknown angle and angle B as its supplementary angle. According to the given information, angle B is 156° more than angle A. Therefore, we can set up the equation A + B = 180°, where B = A + 156°.
Solving the equation A + (A + 156°) = 180° gives us 2A + 156° = 180°, and when we subtract 156° from both sides, we get 2A = 24°. Dividing both sides by 2 will give us A = 12°. To find angle B, we add 156° to angle A, resulting in B = 12° + 156°, which equals 168°.
Therefore, angle A is 12° and angle B is 168°. These are the measures of the two supplementary angles.
5. SURVEYS Out of
300 students surveyed,
68% said that pizza
was their favorite lunch.
How many students
surveyed said that pizza
was their favorite lunch?
Answer:
204 students said that pizza
was their favorite lunch
Step-by-step explanation:
300 · 0.68= 204
too find the percent of a number, you turn the percent into a decimal and multiply it by the original number.
PLEASE MARK BRAINLIEST!
Answer:
68% of 300 [problem we must solve]
68% ⇒ 0.68 [convert percent into decimal by dividing by 100]
0.68(300) [multiply decimal by the total amount, 300]
204 [your answer]
Your answer is 204 studentsI hope this helps!
- sincerelynini
In the cylinder below, the radius, r, is 5 m, and the volume is 200 m3. What is the altitude of the cylinder?
A.
4 m
B.
13 m
C.
16 m
D.
8 m
what’s the missing angle
Answer:
125 degrees.
Step-by-step explanation:
The 3 angles in a triangle add up to 180 degrees.
So the missing angle is 180 - (40 + 15)
= 125 degrees.
WORTH 100 POINTS!!
Based on the diagram, what is tanA ?
Right triangle A B C. Angle A C B measures 90 degrees. Side length a is across from angle A. Side length b is across from angle B. Side length c is across from angle C.
Answer:
a/b
Step-by-step explanation:
The value of tan A is a / b.
What is Trigonometry?In a right triangle ABC, where angle ACB measures 90 degrees, we can use the trigonometric function tangent (tan) to relate the sides of the triangle.
TanA is defined as the ratio of the length of the side opposite angle A (side a) to the length of the side adjacent to angle A (side b).
So, tanA = a / b.
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What is another name for Angle 2?
Lines EH and DF intersect at point G. Angle 2 is formed by line segments DG and GE and angle 1 is formed by line segments EG and GF.
a. Angle DGE
b. Angle GED
c. Angle EGF
d. Angle GEF
Answer:
a is the answer
Step-by-step explanation:
In the given scenario, angle 2 is formed by line segments DG and GE. Another name for angle 2 is Angle DGE (Option a).
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
As mentioned in the question, Lines EH and DF intersect at point G. Angle 2 is formed by line segments DG and GE, and angle 1 is formed by line segments EG and GF. So angle 2 is constituted by segments jointly as DGE.
Thus, Another name for angle 2 is Angle DGE (Option a).
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Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
N(t)=⎧⎩⎨⎪⎪⎪⎪f(t)25t+150200+80t2+0.05tfor0≤t<6for6≤t<8fort≥8
The number of fish in a pond at time t years is modeled by the function N defined above, where f is a continuous function such that f(0)=80.
(a) Find limt→∞N(t). Explain the meaning of limt→∞N(t) in the context of the problem.
(b) Is the function N continuous at t=8 ? Justify your answer.
(c) The function N is continuous at t=6 . Is there a time t , for 0≤t≤6 , at which N(t)=250 ? Justify your answer.
Answer:
See Below
Step-by-step explanation:
The function is a piecewise function defined as:
[tex]N(t)=\left \{ {{25t+150} \ 0 \leq t \leq 6 \atop {\frac{200+80t}{2+0.05t} \ t \geq 8}} \right.[/tex]
a)
We need to find the limit of the function as t goes to infinity. This means what is the max value of fish in the pond given times goes to infinity (on an on).
We will take the 2nd part of the equation since t falls into that range, t is infinity, which is definitely greater than 8.
[tex]\lim_{t \to \infty} \frac{200+80t}{2+0.05t} \\\lim_{n \to \infty} \frac{80t}{0.05t}\\ \lim_{n \to \infty} \frac{80}{0.05} =1600[/tex]
This means the maximum number of fish at this pond is 1600, no matter how long it goes on.
b)
A function is continuous at a point if we have the limit and the functional value at that point same.
Functional value at t = 8 is (we use 2nd part of equation):
[tex]\frac{200+80t}{2+0.05t}\\\frac{200+80(8)}{2+0.05(8)}\\=350[/tex]
We do have a value and limit also goes to this as t approaches 8.
So, function is continuous at t = 8
c)
We want to find is there a "time" when the number of fishes in the pond is 250, during t from 0 to 6. We plug in 250 into N(t) and try to find t. Make sure to use the 1st part of the piece-wise function. Shown below:
[tex]N(t)=25t+150\\250=25t+150\\25t=250-150\\25t=100\\t=4[/tex]
The time is 4 years when the number of fishes in the pond is 250
If I like geometry, then I like math.
Choose the equivalent statement
Answer:
C
Step-by-step explanation:
If you don't like math you don't like geometry because geometry is math. Just like if you like geometry you like math because geometry is math
Answer:
C
Step-by-step explanation:
Since geometry is math, then if you don’t like math, you won’t like geometry.
The box plots show the average wind speeds, in miles per hour, for two different islands.
Average Wind Speeds on Island A
2 box plots. The number line goes from 1 to 11. For the average wind speeds of cities on Island A, the whiskers range from 1 to 9.5, and the box ranges from 3 to 7. A line divides the box at 4. For the average wind speeds of cities on Island B, the whiskers range from 1.5 to 11, and the box ranges from 4 to 9. A line divides the box at 6.
Average Wind Speeds on Island B
Which explains, on a given day, which island is more likely to have a wind speed close to its median?
Country A because the median is closer to one end of the box in the box plot.
Country B because the median is closer to the center of the box in the box plot.
Country A because it has a smaller interquartile range.
Country B because it has a larger interquartile range.
Answer:The correct answer would most likely be Country A. (The second one.)
Step-by-step explanation:
The reasoning for that would be because if you have a smaller interquartile range, it would most likely be closer to the median and won't have a chance of falling farther.
If you have questions please ask.
I hope this helps. :)
The island that is more probable to possess a wind speed nearer to its median would be as follows:
C). Country A because it has a smaller interquartile range.
"Median" is described as the middle number that functions to "isolate the higher half of a particular data from its lower half." In the given data, Country A is more probable to possess a wind speed nearer to the median. The reason behind this is that it carries a smaller/lower interquartile range(50% values in the middle ranging from the very lowest to the highest").Thus, option C is the correct answer.
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Can someone help with this
Answer:
50
Step-by-step explanation: