Answer:
7 ftStep-by-step explanation:
[tex]h(x)=-0.5(x^2-4x-21)\\\\\text{The zeros for}\ h(x)=0:\\\\-0.5(x^2-4x-21)=0\qquad\text{divide both sides by}\ -0.5\\\\x^2-4x-21=0\\\\x^2+3x-7x-21=0\\\\x(x+3)-7(x+3)=0\\\\(x+3)(x-7)=0\iff x+3=0\ \vee\ x-7=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3<0\\\\x-7=0\qquad\text{add 7 to both sides}\\x=7[/tex]
The quadratic function h(t)=-16.1t^2+150 models a balls height in feet over time in seconds after it is dropped from a 15 story building
someone please answer
Answer:
A
Step-by-step explanation:
I did the same test
Miss Clark’s farm has chickens and pigs. There are a total of 26 animal feet and 8 animal heads on her farm. If 20 feet belong to the pigs and 6 feet belong to the chickens, the ratio of the number of pigs to the number of chickens is
Answer:
5 : 3
Step-by-step explanation:
Given in the question that,
total number of animal feet = 26
number of pig's feet = 20
number of chicken's feet = 6
As we know that pig have four legs and chicken have 2 legs so,
number of pigs in the farm = 20/4 = 5
number of chickens in the farm = 6/2 = 3
Questions says that there are 8 heads so we can confirm our calculations as
5 + 3 = 8The ratio of the number of pigs to the number of chickens is
5 : 3
Which expression is 5 times as large as the expression 345+23
Answer:
1840
Step-by-step explanation:
345+23=368*5
Answer: 1840
Step-by-step explanation:
you add 345 + 23 and multiply by 5
Find the value of term a14 in the sequence.
6, 5, 4, 3, 2, . . .
Answer:
[tex]a_{14}=-7[/tex]
Step-by-step explanation:
The given sequence is:
6, 5, 4, 3, 2, . . .
The first term of the sequence is:
[tex]a_1=6[/tex]
The common difference is
d=5-6=-1
The nth term of the sequence:
[tex]a_n=a_1+d(n-1)[/tex]
[tex]a_n=6-1(n-1)[/tex]
[tex]a_n=6-n+1[/tex]
[tex]a_n=7-n[/tex]
When n=14
[tex]a_{14}=7-14=-7[/tex]
Find the range of the sample data set.
16,465 17,342 19,835 15,147 15,898 18,324
Lowest number is 15,147 the highest number is 19,835 simple subtract the lowest from the highest you get 4688
Answer:
The answer is 4,688
Hope this helped : )
Step-by-step explanation:
the range is the difference between the largest and smallest numbers in a set of data.
So, for this set of data. To find the range you subtract 19,835 - 15,147 = 4,688
In 18 years time Halley will be five times as old as she was two years ago. Write this information in the form of an equation involving Halley's present age, a years How old is Halley now?
To solve any questions relating to ages, I find it easier to make a table, like in the picture below.
See picture for answer and clear diagram.
-----------------------------------------------------------------
Notes/Explanations + answer in written form
Let's say that Halley's age now is: x
That means that her age in 18 years is: x + 18
It also means that her age 2 years ago is: x - 2
In the question, we are told that when Halley is 18 years older that her current age, she will be 5 times the age she was when she was 2 years younger than her current age
That means:
Halley's current age + 18 years = 5 times (Halley's current age - 2 years)
So we get this equation (which we solve to get the answer) :
x + 18 = 5 * (x -2) ( expand the brackets)
x + 18 = 5x - 10 (subtract x from both sides)
18 = 4x - 10 (add 10 to both sides)
28 = 4x (now divide both sides by 4)
7 = x
Therefore, Halley's current age is 7 years
What is the approximate surface area of a cylinder with a height of 12 meters and a base radius of 2 meters? Use 3.14 for π
The approximate surface area of a cylinder with a height of 12 meters and a base radius of 2 meters is 175.84 square meters, using 3.14 for pi.
Explanation:The question asks for the approximate surface area of a cylinder with specific dimensions, using 3.14 for π. The surface area of a cylinder can be calculated through the formula for surface area which includes the areas of the two bases and the side surface. The area of one base is πr², which is the area of a circle. For our cylinder, with a base radius (r) of 2 meters, the area of one base is 3.14 × (2 m)² = 12.56 m². Since the cylinder has two bases, you double this area. The side surface is a rectangle when rolled out, and its area is the perimeter of the base circle (circumference) times the height (h) of the cylinder. The circumference (C) of the base is 2πr, so for our cylinder C = 2 × 3.14 × 2 m = 12.56 m. The side surface area is therefore C × h = 12.56 m × 12 m = 150.72 m². Add the areas of the two bases and the side surface to find the total surface area: 2 × base area + side surface area = 2 × 12.56 m² + 150.72 m² = 175.84 m².
plss help will give brainliest and thx and 5star
Answer:
12. Heptagon
13. 14 cm
14. 50°
Step-by-step explanation:
12.
A polygon containing
3 sides is a triangle
4 sides is Quadrilateral
5 Sides is a Pentagon
6 sides is a Hexagon
7 sides is a Heptagon
Our polygon contains seven sides, it is hence a Heptagon
13. RST = ?
S is the mid point of RT
Hence RS = ST
ST = 7 given
Hence RS = 7
RT = RST = RS + ST
= 7 + 7
= 14 cms
14.
∠RSQ = ∠QST = 25°
∠RST=∠RSQ + ∠QST = 25°+ 25° = 50°
choose the correct expression to represent the piecewise-defined function?
Answer:
-3 5 2
Step-by-step explanation:
trust
Is the answer is b, also what is the perimeter of the rectangular!
yes B is the correct answer, the perimeter would be 16
Answer:
B and 16
Step-by-step explanation:
It's B because all the other answers would make a rectangular shape. You can find the plots on the lie by figuring out what coordinate each number is. For example, (3,1) the 3 is the x coordinate and 1 is the y coordinate. To find the perimeter you count the the boxes between the dots. 1 side is 4 and since it's the other sides are 4 you add it up to get 16 units squared.
Simplify don’t show your work got it
Answer:
43
Step-by-step explanation:
Answer:
43
Step-by-step explanation:
using pemdas you would first do exponent
so 6*6 is 36
so you have 36-1*3+4/2+8
then you would do mutiplication
so -1 * 3 is -3
then divide 4/2 which is 2
then add and subtract
36-3+2+8
46-3
43
Solving for matrices
Answer:
D
Step-by-step explanation:
The augmented matrix for the system of three equaitons is
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\5&2&-2&|&11\\5&-4&4&|&-7\end{array}\right)[/tex]
Multiply the first row by 5, the second row by -3 and add these two rows:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\5&-4&4&|&-7\end{array}\right)[/tex]
Subtract the third row from the second:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&6&-6&|&18\end{array}\right)[/tex]
Divide the third row by 6:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&1&-1&|&3\end{array}\right)[/tex]
Now multiply the third equation by 26 and add it to the second row:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&0&-45&|&-90\end{array}\right)[/tex]
You get the system of three equations:
[tex]\left\{\begin{array}{r}3x-4y-5z=-27\\-26y-19z=-168\\-45z=-90\end{array}\right.[/tex]
From the third equation
[tex]z=\dfrac{90}{45}=2.[/tex]
Substitute z=2 into the second equation:
[tex]-26y-19\cdot 2=-168\\ \\-26y-38=-168\\ \\-26y=-168+38=-130\\ \\y=\dfrac{130}{26}=5.[/tex]
Now substitute z=2 and y=5 into the first equation:
[tex]3x-4\cdot 5-5\cdot 2=-27\\ \\3x-20-10=-27\\ \\3x-30=-27\\ \\3x=-27+30=3\\ \\x=1.[/tex]
The solution is (1,5,2)
The correct answer is option d (1, 5, 2).
To solve the system of equations, let's write the augmented matrix and perform row operations to get it into reduced row-echelon form (RREF). The system of equations is as follows:
3x−4y+5z (1)
5x+2y−2z (2)
5x−4y+4z (3)
The augmented matrix for this system is:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\5&2&-2&|11\\5&-4&4&|7\end{array}\right][/tex]
Now, let's perform row operations to get the reduced row-echelon form:
Subtract 5 times the first row from the second row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&22&-27&|-134\\5&-4&4&|7\end{array}\right][/tex]
Subtract 5 times the first row from the third row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&22&-27&|-134\\0&16&-21&|-118\end{array}\right][/tex]
Multiply the second row by 8/11:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&-8/11&|-67/11\\0&16&-21&|-118\end{array}\right][/tex]
Subtract 16 times the second row from the third row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&-8/11&|-67/11\\0&0&5/11&|10/11\end{array}\right][/tex]
Multiply the third row by 11/5:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&-8/11&|-67/11\\0&0&1&|2\end{array}\right][/tex]
Add 4/11 times the third row to the second row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&0&|1\\0&0&1&|2\end{array}\right][/tex]
Add 4 times the third row to the first row:
[tex]\left[\begin{array}{ccc}3&-4&0&|35\\0&1&0&|1\\0&0&1&|2\end{array}\right][/tex]
Add 4 times the second row to the first row:
[tex]\left[\begin{array}{ccc}3&0&0&|39\\0&1&0&|1\\0&0&1&|2\end{array}\right][/tex]
Now, we can read off the solutions:
3x=39⇒x=13
y=1
z=2
So, the correct answer is (d) (1,5,2).
Use the drop down menus to complete the statements
Answer:
what are on the tabs
Step-by-step explanation:
The ordered pair given in the first row of the table can be written using Function notation as (x, f(x)), which is (3, -2).
f(3) is -2.
f(x) = -5 when x is 4.
Now, let's complete the statements:
f(3) is -2.
This statement tells us that when the input value (x) is 3, the function f(x) evaluates to -2. In the table, you can see that when x = 3, f(x) is indeed -2.
f(x) = -5 when x is 4.
This statement indicates that when the input value (x) is 4, the function f(x) takes on the value of -5. In the table, you can see that when x = 4, f(x) is -5.
In summary, these statements highlight specific values of the function f(x) for particular input values (x) based on the table of values provided. The function notation f(3) = -2 indicates that when x = 3, the function returns -2, and the statement f(x) = -5 when x is 4 tells us that when x = 4, the function evaluates to -5, as observed in the table.
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Which equation represents the graphed function? (0,3) (1,1)
y=-2x+3 in slope-intercept form
3 is the y-intercept and -2 is the slope
Answer:
2x - y + 3 = 0
Step-by-step explanation:
The formula used to find the equation is:
[tex]y-y_1= \frac{(y_2-y_1)}{(x_2-x_1)} (x-x_1)[/tex]
Here, (x₁, y₁) = (0, 3)
and (x₂, y₂) = (1, 1)
Putting all values in above formula,
[tex]y-3= \frac{(1-3}{(1-0)} (x-0)[/tex]
⇒ [tex]y - 3 =\frac{-2}{1}x[/tex]
⇒ y - 3 = 2x
⇒ 2x - y + 3 = 0
which is the requires equation.
given x+2<-5 choose the solution set.
Answer:
[tex]\large\boxed{\{x|x\in\mathbb{R},\ x<-7\}}[/tex]
Step-by-step explanation:
[tex]x+2<-5\qquad\text{subtract 2 from both sides}\\\\x+2-2<-5-2\\\\x<-7\to\{x|x\in\mathbb{R},\ x<-7\}[/tex]
Answer:
x < -7; the answer is the first choice.
Step-by-step explanation:
x + 2 < -5
Subtract 2 from both sides.
x < -7
The answer is the first choice.
Which of the following statements is true?
15+0=0
15-0=0
15 divided 0=0
0 divided 15=0
0 divided 15=0 is your answer
0 divided by 15 is 0.
Anything multiplied or divided by 0 is 0!
GEOMETRY FIND THE VALUE OF Y Please Help ASAP!!
Answer:
32 degrees
god bless all
plz pray for my dead great grandfather
Mrs Rivas wants to install carpet in her basement and family room. Her basement is 62/square yards and her family room is 18/square yards if carpet costs $13/per square yard ,how much will it cost to carpe these two rooms?
It will cost $1040 in the two rooms
For this case we have that the total cost will be given by:
[tex]C {t} = C {b} + C_ {f}[/tex]
Where:
[tex]C_ {b}:[/tex] Cost of installing carpet in the basement
[tex]C_ {f}:[/tex] Cost of installing carpet in the family room
So:
[tex]C_ {b} = 62 \ yard ^ 2 * 13 \frac {dollars} {yard ^ 2}\\C_ {b} = 806 \ dollars[/tex]
Also:
[tex]C_ {f} = 18 \ yard ^ 2 * 13 \frac {dollars} {yard ^ 2}\\C_ {f} = 234 \ dollars[/tex]
Thus, the total cost will be:
[tex]C_ {t} = 806 + 234\\C_ {t} = 1040[/tex]
ANswer:
The total cost will be 1040 dollars
express 45 minutes as a fraction of 1 hour
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
There are 60 minutes in 1 hour
To express as a fraction
[tex]\frac{45}{60}[/tex]
Divide numerator/denominator by 15
[tex]\frac{45}{60}[/tex] = [tex]\frac{3}{4}[/tex]
What is the approximate measure of this angle?
Answer:
The answer is B.
Step-by-step explanation:
the angle is not even 90 degrees so anything bigger is an automatic no and it's pretty obvious that the answer is not 0. Lol
The approximate measure of an angle can be estimated using nearby or known angles as reference points or by using a protractor.
Explanation:The approximate measure of an angle can be determined using various methods, including estimation or using a protractor. If you are estimating the measure of an angle, you can use nearby angles or known angles as reference points. For example, if you have a right angle measuring 90 degrees, and the given angle appears to be slightly less than a right angle, you can estimate it to be around 85-88 degrees.
Alternatively, you can use a protractor which is a tool specifically designed to measure angles. Place the center of the protractor on the vertex of the angle and line up one of the lines on the protractor with one of the sides of the angle. Read the measurement indicated on the protractor scale to determine the approximate measure of the angle.
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Gigi makes a scale drawing of a patio. The drawing below shows the two scales use she used to plan two patios of different sizes. Which shows the correct dimensions of the rectangle in both scales?
Answer:
Scale 1 35 ft by 25 ft and Scale 2 56 ft by 40 ft
Step-by-step explanation:
step 1
Find the actual dimensions of a patio with the scale 1
The scale 1 is equal to
1 cm/5 ft
Length=7 cm=7*5=35 ft
Width=5 cm=5*5=25 ft
therefore
The dimensions are 35 ft by 25 ft
step 2
Find the actual dimensions of a patio with the scale 2
The scale 2 is equal to
1 cm/8 ft
Length=7 cm=7*8=56 ft
Width=5 cm=5*8=40 ft
therefore
The dimensions are 56 ft by 40 ft
Answer:
C
Step-by-step explanation:
If Scale 1 is 1 cm:5 ft, multiply 5 and 7 by 5 to get the correct dimensions. 7×5=35 and 5×5=25. If Scale 2 is 1 cm: 8 ft, multiply 5 and 7 by 8 to get the correct dimensions. 7×8=56 and 5×8=40. The answer is: Scale 1: 35 ft by 25 ft; Scale 2: 56 ft by 40 ft.
Hope this helps!
What is the equation of a vertical line passing through the point (-4,7)?
Answer:
x = -4
Step-by-step explanation:
a vertical line is the x-coordinate in an ordered pair, while a horizontal line is the y-coordinate in an ordered pair
a useful mnemonic is VUX/HOY which stands for:
VUX:
Vertical line
Undefined slope
X: x coordinate
HOY:
Horizontal line
0 is the slope
Y: y coordinate
Suppose h(t)= -0.2t^2+2t models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds.
After how many seconds does the ball reach its maximum height?
What is the maximum height of the ball?
After how many seconds does the ball reach the ground?
Answer:
Step-by-step explanation:
Height: h(t)= -0.2t^2+2t = 2t(-0.1t + 1)
-0.2t^2+2t is a quadratic expression with a = -0.2 and b = 2.
The ball reaches its max height at t = -b/(2a).
Here, t = -2 / (2·[-0.2] ), or t = 2/0.4 = 5 (sec)
The ball reaches its max height at at 5 sec.
The max ht. of the ball is h(5) = -0.2(5 sec)^2 + 2(5 sec) = (-5 + 10) sec, or 5 ft.
To determine after how many sec the ball reaches the ground, we set h(t) = 0 and solve for t:
h(t)= -0.2t^2+2t = 0 = 2t(-0.1t + 1). Thus, t = 0 sec or t = 10 sec
The ball reaches the ground again after 10 sec.
Help me please and explain, thanks
Answer:
15 degrees
Step-by-step explanation:
3.5 times 10 = 35
50-35=15
Answer:
29 Degrees Fahrenheit
Step-by-step explanation:
So at 4,000 ft. high, it's 50 Degrees Fahrenheit, that means we don't need the first 4,000 because 50 is our starting point. 10,000 - 4,000 = 6,000.
Every 1,000 ft. is down another 3.5 Degrees Fahrenheit, and so first we divide 6,000 by 1,000 to have 6.
Then we multiply 3.5 with 6 to get 21 Degrees Fahrenheit.
50 - 21 = 29 Degrees Fahrenheit.
I say trapezoidal prism. Am I right! Thanks
The correct answer is:
D=Trapezoidal Prism
Yep! You're right!
It is trapezoidal prism.
The volume of a cube is 1953.1 25 cm³ find the length of the side round your answer to the nearest 10th
Answer:
s = ∛( 1953.125 cm³ ) = 12.5 cm
Step-by-step explanation:
The volume of a cube is V = s³, where s represents the length of one edge.
Here, V = s³ = 1953.125 cm³, and we need to solve for s. Do this by taking the cube root of both sides:
s = ∛( 1953.125 cm³ ) = 12.5 cm
Match the expression 7x^2-5x+9
A. Cubic trinomial
B. Constant monomial
C. Quadratic trinomial
D. Not a polynomial
it it c becauee I had already learned this
What is the solution to the equation
[tex] \frac{1}{40} \times = \frac{1}{8} [/tex]
x = 320
x = 5
x = 48
x = 32
Solution:
Given Expression is 1/40* x = 1/8
Step : Define x in the Equation:
Step : Divide the Equation by 8
Step : Do cross multiplication
Step : Arrange it in particular form
____________________________
☞ 1/40x = 1/8
☞ x/40 = 1/8
☞ x = ⅛ × 40
☞ x = 5
.
Therefore, Answer is 5.
x = 5
1/40 of x is the same x divided by 40, so let’s put that into the equation to get x/40 = 1/8.
Now, multiply both sides of the equation by 40 to cancel out the division by 40.
x = 1/8 * 40
x = 40/8
Now, just simplify.
x = 5
what's 20 percent of 376,900
376900x.2= 75380.......
To find 20 percent of 376,900, multiply it by 0.2, which equals 75,380.
Explanation:To find 20 percent of 376,900, you can multiply 376,900 by 0.2.
20 percent, written as a decimal, is 0.2.
Multiplying 376,900 by 0.2 gives you 75,380.
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In the morning, the temperature starts out around 50° F. As the day goes on, the temperature rises first slowly, then more quickly. It stays constant for an hour before dropping slowly. Select the graph that best represents this description
Answer:
Graph A.
Step-by-step explanation:
We will try to understand the graph plotted for the change in temperature for whole day.
In the morning, temperature starts out around 50°F. As the day goes on, the temperature rises first slowly- Slope of the first line will be less.
Then temperature rises more quickly - Slope of the second line will be more than first line.
It stays constant for an hour- third line will be parallel to the x-axis for one hour gap.
Then the temperature dropped down slowly - Last line of the graph will go down.
By the understanding we made for the graph we find graph A is the answer.
Answer:
the top left graph