An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation ℎ()=−2+10+9.5 h ( x ) = − x 2 + 10 x + 9.5 , where x is the number of feet away from the sprinkler head (along the ground) the spray is.
Since the height (feet) of the spray of water is given by this equation h(x) = -x² + 10x + 9.5, we can logically deduce that the irrigation system is positioned 9.5 feet above the ground to start.
How to determine the maximum height?For any quadratic equation with a parabolic curve, the axis of symmetry is given by:
Xmax = -b/2a
Xmax = -10/2(-1)
Xmax = 5.
Thus, the maximum height on the vertical axis is given by:
h(x) = -x² + 10x + 9.5
h(5) = -(5)² + 10(5) + 9.5
h(5) = -25 + 50 + 9.5
h(5) = 34.5 feet.
Therefore, the spray reaches a maximum height of 84.5 feet at a horizontal distance of 5 feet away from the sprinkler head.
Also, the spray reaches all the way to the ground at about:
Maximum distance = √34.5 + 5
Maximum distance = 10.87 feet.
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Complete Question:
An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x² + 10x + 9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.
1. The irrigation system is positioned____ feet above the ground to start.
2. The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.
3. The spray reaches all the way to the ground at about_____ feet away
Find the smallest number by which the following numbers should be multiplied to obtain a perfect cube. (a) 3087 (b) 2560
Check each number's prime factorization, then add any factors necessary to make each one a cube.
(a) 3
[tex]3087 = 3^2 \times 7^3 \implies \boxed{3}\times3087 = (3\times7)^3 \implies 9261=21^3[/tex]
(b) 25
[tex]2560 = 2^9\times5^1 \implies \boxed{5^2}\times2560 = \left(2^3\times5\right)^3 \implies 64000 = 40^3[/tex]
I dont know how to do this
Answer:
Option C = 78,125Step-by-step explanation:
First prime factorize 135,
135 = 5×3×3×3
Now prime factorize 128,
128=2×2×2×2×2×2×2 = 2^7
the highest prime factor of 135 is 5,
Let 5 be x
the highest power of the lowest prime factor of 128 which is the power 2 is 7
Let 7 be y
According to the question x^y = 5^7
= 78,125Find the side length of the equilateral triangle whose area is the square root of 3 cm2
Here, Given
Area of Equilateral triangle = 3cm2
therefore, we know;
Area of Equilateral triangle =( [tex]\sqrt{3}[/tex]÷4)×[tex]a^{2}[/tex]
so,
3 =( [tex]\sqrt{3}[/tex]÷4)×[tex]a^{2}[/tex]
3÷( [tex]\sqrt{3}[/tex]÷4) = [tex]a^{2}[/tex]
2.63 cm = a .
The area of an equilateral triangle is the area covered by an equilateral triangle on a two-dimensional plane. An equilateral triangle is a triangle with all sides equal and all angles at 60 degrees. The area of the shape is the number of unit squares that fit inside.
Here, "unit" refers to 1, and a unit square is a square with one side. Alternatively, the area of an equilateral triangle is the total amount of space it surrounds in a two-dimensional plane.
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Check all that apply
X^2+7x-8
Answer:
x = -8, 1.
Step-by-step explanation:
x^2 + 7x - 8 = 0
(x + 8)(x - 1) = 0
x = -8, 1.
Answer:
-8 and 1
Step-by-step explanation:
Quadratic expression.
A quadratic expression is an expression with 2 as the highest power of the unknown.
Solving the question:
[tex]x {}^{2} + 7x - 8 \\ x {}^{2} + 8x - x - 8 \\ x(x + 8) - 1(x + 8) \\ (x - 1)(x + 8) \\ x = 1 \: or \: x = - 8[/tex]
I’ve tried everything and yet don’t understand this
Snow reaches at a 15 inches after 16 hours. and 8 inches melt in next 6 hours.
According to the statement
we have a given that there was 1 inch snow on the ground before the snowstorm starts.
then snow fell at constant rate of 3 inches every 2 hours until the snow level reaches at 12 inch had fallen
It means after that there was 13 inch snow on the ground.
and in 1 hour only 1.5 inches snow increases
and if snow takes 2 hours to increase at 3 inches then
it takes 10 hours to reach at 12 inches.
So, snow falls for 10 hours to increase at 12 inches.
And then the snow falls at constant rate of 1 inch per hour for 2 hours.
It means now snow reaches at a 15 inches after 16 hours.
Then sun melt the snow at a 4 inches per 3 hours and sun came for 6 hours then
it means now the level of snow reduced and came at the 7 inches.
because sun reduced 8 inches snow in 6 hours.
So, this is the data collected by a person.
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If a is an obtuse angle in a triangle and sin a = , calculate the exact value of sin 2a.
Answer:
Step-by-step explanation:
cos A = √( 1 - (5/13)²) = √( 1 - 25/169) = √(144/169) = - 12 /13
in 2 A = 2 sin A cos A
sin 2 A = 2 *5/13 ( - 12/13 ) = - 120 / 169
the answer is -120/169
What elements in domain has the image 5 under function f(x)= 3x+ 2?
plssssssss heeeeeellllllp me
tomorrow is my test T^T
Answer:
Step-by-step explanation:
hello
calculate x : 3x+2 =5
means : 3x+2-2 =5-2
3x = 3
so : x = 3/3 =1
1 is the element in domain has the image 5 under function f(x)= 3x+ 2
Which is the graph of the function f() = x2 + 2x - 6?
The x-intercepts from the graph are -3.646 and 1.646 with the parabolic curve facing upwards
Quadratic graphQuadratic functions are functions that has a leading coefficient of 2.
According to the question, we are to graph the quadratic function f(x) = x^2 + 2x - 6. The curve will be parabolic in nature and facing upwards since it is a quadratic function.
The x-intercepts from the graph are -3.646 and 1.646 as shown in the attached graph.
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WILL MAKE BRAINLIEST!! Solve for x
Answer:
x=17
Step-by-step explanation:
Since they are intersecting lines, 3x=51
x=17
Answer:
x = 17
Step-by-step explanation:
When two lines intersect each other, the opposite angles are identical. Therefore, you can set both angles equal to each other to find the value of "x".
3x = 51
x = 17
Solve the system of equations 4x+5y=-14 and -5x-8y=10 by combining the equations.
The solution of the system is:
x = 62/7
y = 30/7
How to solve the system of equations?
Here we have the system:
4x + 5y = -14
-5x - 8y = 10
To solve it by combining the equations, we need to try to remove one of the variables.
If we take the sum of 5 times the first equation and 4 times the second equation we get:
5*(4x + 5y) + 4*(-5x - 8y) = 5*(-14) + 4*10
If we simplify that we get:
20x + 25y - 20x - 32y = -30
-7y = -30
Now we can solve that for y:
y = -30/-7 = 30/7
Now to get the value of x, we can replace the value of y in any of the given equations:
Using the first one:
4x + 5y = -14
x = (-14 - 5y)/4
x = (-14 - 5*30/7)/4 = (-98/7 - 150/7)/4 = 248/28 = 124/14 = 62/7
The solution of the system is:
x = 62/7
y = 30/7
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A weather balloon is 529 meters above the ground. Two weather stations, A and B, monitor the balloon’s progress.
A weather balloon is 529 meters above the ground. Weather stations A and B are on the ground to form a triangle. A horizontal line is drawn at the top of the triangle to form angle v on the left and angle w on the right. The angle formed with A is x and the angle formed with B is y. A vertical line is drawn from the weather balloon to the ground to form a right angle and split the distance between A and B into 2 parts. The distance from A to the vertical line is 229 meters, and the distance between the vertical line and point B is 347 meters.
Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true? Check all that apply.
x > y
v > x
w = y
y < v
v = w
x < w
A, C, D are correct. In this question the options that are correct are
x > yw = y y < vHow to solve for the correct statements in the questionWe have first with legs height to be =529 m and 229 m;
second with legs height =529 m and 347 m.
Then tan x = 529/229
tan y = 529/347
We can see that tanx > tany
Hence x> y
We have alternate angles in the question. This makes x=v, y=w
For D
x > y while x = v
This tells us that v>y
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Answer:
acd
Step-by-step explanation:
When researching for a business report, you should find reliable sources whose information is accurate, unbiased, and .
Answer:
Creditable
Step-by-step explanation:
Could also be:
up-to-date
m
A math teacher gives a quiz. Each question on the quiz is
worth 8 points. A score of 75 is a passing grade.
Which number of correct answers will result in a passing
grade?
From statement equation, the number of correct answers will result in a passing grade is 9.3
What number of questions is required for passing grade ?Given that each question on the quiz is worth 8 points.
Also given a score of 75 is a passing grade.
Let the number of correct answered questions be x
Thus the total score of the correct answers is 8x
The statement equation is -
⇒ 8x = 75
⇒ x = 75/8 = 9.3
∴ x ≈ 9
Therefore, from statement equation, the number of correct answers will result in a passing grade is 9.3
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Help me please fast
Given (x² − x + 2)(x − 1) = Ax³ + Bx² + Cx + D what is the value of A + D
Answer:
-1
Step-by-step explanation:
Expanding (x² − x + 2)(x − 1) we get [tex]x^{3} -x^{2} -x^{2} +x+2x-2[/tex]. When we simplify that, we get [tex]x^{3} -2x^{2} +3x-2[/tex] which fits the form Ax³ + Bx² + Cx + D.
We can see that A = 1, B = -2, C = 3, D = -2. Thus A + D = 1 - 2 = -1.
Therefore your answer is -1
Answer:
A + D = -1
Step-by-step explanation:
Given: (x² − x + 2)(x − 1) = Ax³ + Bx² + Cx + D
Step 1: Simplify using the Distributive Property.
[tex]\\\implies (x^2 - x + 2)(x - 1) \\\\\implies x(x^2 - x + 2) + -1(x^2 - x + 2)\\\\\implies x^3 - x^2 + 2x - x^2 + x - 2\\\\\implies \bold{1}x^3 -\bold{2}x^2 + \bold{3}x - \bold{2}[/tex]
Step 2: Determine the value of the coefficients.
[tex]\implies {\sf A} = 1, {\sf B} = -2, {\sf C} = 3, {\sf D} = -2[/tex]
Step 3: Find the value of A + D.
[tex]\implies {\sf A} + {\sf D} \Rightarrow 1 - 2 = \boxed{-1}[/tex]
Green’s Sport Shop offers its salespeople an annual salary of $10,000 plus a 6% commission on all sales above $20,000. Every employee receives a Christmas bonus of $500. What are Mr. Cahn’s total earnings in a year in which his sales amounted to $160,000?
(A) $18,900
(B) $18,400
(C) $19,600
(D) $20,100
Answer:
A
Step-by-step explanation:
His commision was 0.06(160000-20000) = $8400.
His salary was $10,000.
His bonus was $500.
Adding these together, we get $18,900.
Theo earns a base salary plus commission. At the end of September, he was paid $3,835.25 based on his monthly sales of $12,850. At the end of October, he earned $3,641 based on $9,875 in sales. What was Theo’s base salary?
Theo's base salary using a simultaneous equation approach is $2,996.22 .
In order to determine the base salary of Theo, we can express the two earnings and sales amounts using simultaneous equation, that we would solve to arrive at the base salary
Bear in mind that total earnings are determined as base salary plus commission
Let X be the base salary
Let R be the rate of commission
commission =sales*rate of commission
When earnings were $3,835.25 and sales is $12,850, we have the below equation:
X+(12,850*R)=3,835.25
X+12850R=3,835.25 .................... equation (1)
When earnings were $3,641 and sales is $9,875, we have the below equation:
X+(9,875*R)=3641
X+9875R=3641 ......................... equation (2)
subtract equation 2 from 1
2975R=194.25
R=194.25/2975
R=commission rate=6.52941176470588%
substitute for R in equation 1 to arrive at X(base salary)
X+(12850*6.52941176470588%)=3,835.25
X=3,835.25-(12850*6.52941176470588%)
X=base salary=$2,996.22
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PLEASE FIND X
NOTE: Angles not necessarily drawn to scale.
x =x=x, equals
\Large{{}^\circ}
∘
degrees
Check the picture below.
PLEASE HELP FAST!!! Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.
The total surface area of the composite figure is calculated as 444 m².
What is the Surface Area of the Composite Figure?Total surface area = surface area of the bottom rectangular prism + surface area of the top triangular prism - area of the shared surface.
Surface area of the triangular prism = (S1 + S2+ S3)L + bh = (16 + 10 + 10)5 + (6)(16) = 276 m²
Rectangular prism surface area = 2(wl + hl + hw) = 2(5×16 + 4×16 + 4×5) = 328 m²
Area of shared surface = 2(16)(5) = 160 m²
Total surface area = 328 + 276 - 160 = 444 m².
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Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) C = {2, 4}. Fill in the blanks by ⊂ or ⊄ to make the
resulting statements true.
(a) B __ A (b)C __ A (c) B __ C (d) ∅ __ B (e) C __C
Answer:
Answer
Step-by-step explanation:
(a) B ⊄ A (b) C ⊂ A (c) B ⊄ C (d) ∅ ⊂ B (empty set is an element of any set)
(e) C ⊂ C (reflexitivity).
Which side lengths form a right triangle?
Choose all answers that apply
Answer:
A and B
Step-by-step explanation:
A : (a²+b²=c²) 11²+13²=290 (c²); c=√290
B : 7²+24²=625; c=√625=25
C : 2²+5²=29≠7²
According to the Pythagorean triple, the side lengths that will form a right triangle are:
A. 11, 13, √290
B. 7, 24, 25
What is the Pythagorean Triple?The Pythagorean triple are three set of sides that can form a right triangle if the square of the longest side equals the sum of the squares of the other two smaller sides.
11² + 13² = (√290)²
290 = 290 [correct]
7² + 24² = 25²
625 = 625 [correct]
2² + 5² = 7²
29 ≠ 49 [correct]
Therefore, the side lengths that will form a right triangle are:
A. 11, 13, √290
B. 7, 24, 25
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A
B
C
D
LO
-5
Y
A'
В'
O
D'
Which rule describes the translation?
(x, y)
(x-8, y - 3)
(x, y)
(x-3, y + 8)
C
(x, y) → (x + 8, y − 3)
O (x, y) → (x + 3, y + 8)
Answer:
C. (x,y) ⇒ (x + 8, y − 3)
Step-by-step explanation:
See attached image.
Two students created a list of steps for the following construction. Which student has steps in the correct order, and which does not? Explain.
The student with the correct list of steps is student B
How to determine the correct student?The list of steps is to create a line parallel to line AB
Both students are correct in step (1).
However, the step (2) of student A is incorrect.
This is so because, the student did not provide how points C and G are created
Hence, the student with the correct list of steps is student B
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Type the correct answer in each box.
Compete the statement about these similar cylinders.
Using proportions to find the radius of figure 2, we have that:
The circumference of the base of figure 2 is of [tex]4\pi[/tex] inches.The area of the base of figure 2 is of [tex]4\pi[/tex] square inches.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The rule of three to find the radius of figure 2 is given as follows:
[tex]\frac{5}{9} = \frac{r}{4.5}[/tex]
Applying cross multiplication:
9r = 4 x 4.5
r = 4 x 4.5/9
r = 2 in
What is the circumference of a circle?
The circumference of a circle of radius r is given by:
[tex]C = 2\pi r[/tex]
In this problem, we have that r = 2 inches, hence:
[tex]C = 2\pi \times 2 = 4\pi[/tex]
What is the area of a circle?The area of a circle of radius r is given by pi multiplied by the radius squared, as follows:
[tex]A = \pi r^2[/tex]
Hence:
[tex]A = 4\pi[/tex]
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Answer: First one is 5, Second is 6.25
Step-by-step explanation: Correct on Edmentum/Plato
What is the area of the shape?
Answer: 21 units²
Step-by-step explanation:
Since there is a pair of parallel sides, this figures is a trapezoid. The formula for the area of a trapezoid is [tex]\frac{1}{2}(a+b)h[/tex], where a and b are the parallel sides and h is the height.
Here, a and b are 5 and 9, while 3 is the height. Let's put all 3 values into the formula.
[tex]A=\frac{1}{2}(5+9)*3[/tex]
[tex]A=\frac{1}{2}(14)*3[/tex] [Adding in the parentheses]
[tex]A=7*3[/tex] [Multiplying one-half by 14]
[tex]A=21[/tex] [Multiplying 7 and 3]
The area is 21 units².
What is the number of degrees in the measure of the smaller obtuse angle formed by the hands of a standard clock at 2:48pm
Answer: 156 degrees
Step-by-step explanation:
Solve: 5(x + 2) = 3x + 5
Answer:
Exact Form: x = -5/2
Decimal Form: x = -2.5
Mixed Form: x = 2 1/2
Answer:
Step-by-step explanation:
5(x+2)=3x+5
5x+10=3x+5
5x=3x-5
2x=-5
x=-0.4
can someone please help me
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{3\pi }{4}[/tex] is an angle in the second quadrant where sin > 0 and cos < 0
cos([tex]\frac{3\pi }{4}[/tex] )
= cos (π - [tex]\frac{3\pi }{4}[/tex] )
= - cos ([tex]\frac{\pi }{4}[/tex] )
= - [tex]\frac{\sqrt{2} }{2}[/tex]
and similarly
sin ([tex]\frac{3\pi }{4}[/tex] )
= sin ([tex]\frac{\pi }{4}[/tex] )
= [tex]\frac{\sqrt{2} }{2}[/tex]
Which system of equations below has no solution? y = 4x 5 and y = 4x – 5 y = 4x 5 and 2y = 8x 10 y = 4x 5 and y = one-fourthx 5 y = 4x 5 and y = 8x 10
Y=4x+5 and y=4x-5 has no solution
What are Linear Equations in two Variables?
The formula for a two-variable linear equation is Ax + By + C = 0, where A and B are the coefficients, C is a constant term, and x and y are the two variables, each with a degree of 1. A linear equation with two variables, for instance, is 7x + 9y + 4 = 0. These two linear equations are referred to be simultaneous linear equations if we take them into consideration.
Steps
[tex]Y=4x+5\\ Y=4x-5[/tex]
Substitute y=4x+5
[tex][4x+5=4x-5][/tex]
Refine [tex][4x+5=4x-5][/tex]
-10=0
-10=0 is a false ,therefore the system of a equation have no solution
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Determine the missing side of a rectangle with an area
of 144 cm² and a width of 8 cm. Please show your work.
O
Answer:
Length is equal to 18
Step-by-step explanation:
The formula for finding the area(A) of a rectangle in Length(L) times width(W): A=(W)(L). If we plug in the given information into the equation, you will get 144=(8)(L). From there we solve for L.
144 = (8)(L)
144/8 = (8)/8 (L)
18 = L