Answer:
V = 33.5 cm^3
Step-by-step explanation:
The volume of a sphere is given by
V=4/3 pi r^3
The diameter is 4
r= d/2
r =4/2 =2
V = 4/3 pi (2)^3
V = 4/3 pi 8
V = 32/3 pi
Assuming pi is approximated by 3.14
V = 32/3 (3.14)
= 33.493333333 cm^3
To the nearest tenth
V = 33.5 cm^3
Which triangle is a 30° -60° -90° triangle?
Answer:
Acute isosceles triangle
Step-by-step explanation:
because an acute angle is more than 45 but less then 90.
that's all i know sorry!
Which of the following nonlinear inequalities is graphed below
Answer:
(x²/4) + (y²/16) ≤ 1
Step-by-step explanation:
The general form of the ellipse in the graph is
x²/4 + y²/16 = 1
we want to find the inequality which represents the shaded area this will determine whether which of the following 2 choices are correct
Choice 1: x²/4 + y²/16 ≥ 1
Choice 2: x²/4 + y²/16 ≤ 1
we note that point (0,0) lies inside the shaded area. Which means if we substitute (0,0), it should create an equality that is valid.
try choice 1: 0²/4 + 0²/16 = 0 ≥ 1 (not valid because obviously zero is smaller than 1)
try choice 1: 0²/4 + 0²/16 = 0 ≤ 1 (this is valid, hence choice 2 is the answer)
35 points?with explanation
Answer:
m∠7 = 142°
Step-by-step explanation:
Note that a straight line's degree measurement = 180°
Note that the angle directly next to (to the left of) m∠7 has a measurement of 38°. Subtract 38 from 180:
180 - 38 = 142
m∠7 = 142°
~
Answer:
m∠7 = 142°
straight line's degree measurement = 180°
Then get the adjacent angle of 38. Subtract 38 from 180:
180 - 38 = 142
m∠7 = 142°
Hope this helped
How many significant figures are in the number 123.9?
Translate “the sum of 6 and the product of 8 and x” into a mathematical expression
Answer:
8x+ 6 is the translated mathematical expression.
Step-by-step explanation:
We are given the following English expression which are to translate into a mathematical expression:
'The sum of 6 and the product of 8 and x” into a mathematical expression'
Translating it in small chunks:
1. the sum of 6 ---> +6
2. product of 8 and x ---> 8x
Therefore, combining these we get the mathematical expression 8x + 6
For this case we must rewrite the given expression mathematically.
The sum of 6 and something else is written as:
[tex]6+[/tex]
The product of 8 and x is written as:
[tex]8x[/tex]
Finally, the expression is given by:
[tex]6 + 8x[/tex]
Answer:
The expression is given by:
[tex]6 + 8x[/tex]
A diagonal of a parallelogram is 10 inches long and makes angles of 25° and 43° with the sides. How long is the longest side? PLEASE ANSWER FAST! NEED HELP ASAP
Answer:
16 inches
Step-by-step explanation:
We are given that the diagonal of a parallelogram is 10 inches long and makes angles of 25° and 43° with the sides.
So the angles of the parallelogram are:
α = 25° + 43° = 68°
β = 180° - 68° = 112°
Using the sine law assuming x to be the longest side of the parallelogram:
[tex]\frac{x}{sin43} =\frac{10}{sin 25}[/tex]
[tex] x = 1 6 . 1 4 [/tex]
Therefore, the longest side is 16 inches.
Suppose an investor builds a stock portfolio with a variety of shares in various high tech companies. The value of the stock portfolio is modeled by the function y = 2x^2 - 20x + 100, where y is the value of the portfolio in hundreds of dollars, and x is the time in months.
a) Find the x-coordinate of the vertex. Show all work leading to your answer and write the answer in simplest form.
b) Find the y-coordinate of the vertex. Show all work leading to your answer and write the answer in simplest form.
c) What does the vertex represent for this situation? Write 1 - 2 sentences to explain your answer.
Answer:
Step-by-step explanation:
We can find the vertex either by completing the square or taking advantage of the simple formula x = -b / (2a), which provides the x-coordinate of the vertex.
Here a = 2, b = -20 and c = 100. Then the x-coordinate of the vertex is at
x = -(-20) / (2*2), or x = 5.
Next, evaluate y = 2x^2 - 20x + 100 to find the y-coordinate of the vertex. It is y(5) = 2(5^2) - 20(5) + 100, or y(5) = 50 - 100 + 100, or 50. y = 50.
The vertex is at (5, 50). This states that the stock reaches its minimum value, $50 per share), after 5 months. From that time on, the stock appreciates (increases) in value.
Directions: Select ALL the correct answers.
Three football players from the Mustang junior football team each spent 20 minutes loading boxes of
food onto a truck for a local charity. The number of boxes, b, that each player loaded onto the truck is
proportional to the number of minutes. m. spent loading boxes.
- Alonzo loaded 14 boxes.
Bennett loaded one fourth as many boxes as Cory.
• Cory loaded twice as many boxes as Alonzo.
Select all of the true statements.
The equation that represents the number of boxes Alonzo loaded is
b= 0.71m.
The equation that represents the number of boxes Cory loaded is
b = 2m.
The proportional relationship b = " can be used to determine the
rate. r. at which the players loaded the boxes.
on that represents the number of boxes Bennett loaded is
b= 0.35m.
For each player. the proportional relationship b = mm can be used to
determine the rate. r. at which each player loaded the boxes.
Based on the rates of loading boxes onto the truck. Alonzo and
Bennett loaded boxes at the same rate.
The equations representating the number of boxes Alonzo, Cory, and Bennett loaded are b = 0.7m, b = 1.4m, and b = 0.35m respectively. This is calculated based on the fact that Alonzo loaded 14 boxes in 20 minutes, and Cory and Bennett loaded twice and a quarter as much as Alonzo respectively.
Explanation:On the basis given, Alonzo loaded 14 boxes in 20 minutes. So, the number of boxes loaded per minute, m , can be calculated as b = 14 boxes ÷ 20 minutes = 0.7 m.
Cory loaded twice as many boxes as Alonzo, so his equation is b = 2 * 0.7m = 1.4m.
Bennett loaded one fourth as many boxes as Cory, which means Bennett's equation can be determined as b = 1/4 * 1.4m = 0.35m.
Based on this, the true statements are:
The equation that represents the number of boxes Alonzo loaded is b = 0.7m.The equation that represents the number of boxes Cory loaded is b = 1.4m. The equation that represents the number of boxes Bennett loaded is b = 0.35m.
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The number of boxes loaded by each player can be represented by different equations. Alonzo and Bennett loaded boxes at the same rate.
Explanation:
The proportional relationship between the number of boxes, b, that each player loaded onto the truck and the number of minutes, m, spent loading boxes can be represented by the equations:
Alonzo: b = 0.71m
Bennett: b = 0.25c (where c is the number of boxes Cory loaded)
Cory: b = 2a (where a is the number of boxes Alonzo loaded)
Based on the given rates, Alonzo and Bennett loaded boxes at the same rate.
Rectangle ABCD has vertex coordinates A(1, -2), B(4, -2), C(4,-4), and D(1,
-4). It is translated 1 unit to the left and 3 units up. What are the coordinates
of B?
Answer:
C
Step-by-step explanation:
first you subtract 1 from 4 to get 3 and then you add 3 to -2 to get 1 so the coordinates are (3, 1)
The coordinate of B' is,
B' = (3, 1)
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;'
Rectangle ABCD has vertex coordinates A(1, -2), B(4, -2), C(4,-4), and
D(1, -4).
Since, It is translated 1 unit to the left and 3 units up.
Now, The rule for translated 1 unit to the left and 3 units up is,
(x, y) = (x - 1, y + 3)
So, The coordinate of B' is,
B' = (4 - 1, - 2 + 3)
B' = (3, 1)
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A teacher calculates the class average on an exam for each of his four classes and finds that the means are equal. Which statement below would lead you to believe that this teacher was most pleased with the exam scores in his period 1 class?
The scores for period 1 had the lowest median.
The scores for period 1 had the highest median.
The scores for period 1 had the lowest standard deviation.
The scores for period 1 had the lowest IQR.
Answer:
The scores for period 1 had the highest median.
Step-by-step explanation:
The median is the middle score.
Thus if the class had the highest median, it would mean that more scores are higher, that there are more high scores, than the other classes.
320miles on 34 gallons in simplest form
Answer:
9 and 2/5 gallons
Step-by-step explanation:
34 x 9 gallons = 306 miles
14 / 34 = 4/10 of the gallons
4/10 simplified = 2/5
Answer: 9 2/5
Answer:
9 and 2/5 gallons
Step-by-step explanation:
320 miles on 34 gallons in simplest form is 9 and 2/5 gallons.
Give the other person brainliest
Which function has a range of y < 3?
y=3(2)x
y=2(3)x
y=-(2)x +3
y = (2)x - 3
Answer:
[tex]\large\boxed{y=-(2)^x+3}[/tex]
Step-by-step explanation:
[tex]\text{A function y = a(b)}^x\ \text{has a range:}\\\\y<0\ \text{for}\ a<0\\\\y>0\ \text{for}\ a>0\\\\f(x)+n-\text{shift a graph}\ n\ \text{units up}\\f(x)-n-\text{shift a graph}\ n\ \text{units down}\\f(x+n)-\text{shift a graph}\ n\ \text{units to the left}\\f(x-n)-\text{shift a graph}\ n\ \text{units to the right}\\\\\text{We have the range}\ y<3.\ \text{Therefore}\ a<0\ \text{and}\ n=3.[/tex]
The function with a range of y < 3 among the given options is y=-(2)x +3, because it decreases by 2 for each increase in x, starting from y=3.
Explanation:The function which has a range of y < 3 is y=-(2)x +3. This is an example of a linear function where the slope is negative and the y-intercept is 3. This means that the y-values (the range) will always be less than 3. This is because the value of y will decrease by 2 for every increase in x, starting from y=3. For the other functions, the range of y-values is not consistently less than 3.
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a triangular pyramid has a triangular base with a height of 1.5 inches and base length of 4 inches, and height of 9 inches. What is the volume ?
Step-by-step explanation:
Volume of a pyramid is:
V = ⅓ AH
where A is the area of the base and H is the height of the pyramid.
The base is a triangle. Area of a triangle is:
A = ½ bh
where b is the base length and h is the height.
A = ½ (4)(1.5)
A = 3
V = ⅓ (3)(9)
V = 9
The volume is 9 in³.
The volume of the triangular pyramid with a triangular base is 9 cubic inches.
What is the volume of a triangular pyramid?The volume of the triangular pyramid with a height h and base area B is
Volume = 1/3 × B × h cubic units
What is the area of a triangle?The area of a triangle is 1/2 × b × h sq. units
where b - base and h - height the triangle.
Calculating the volume:It is given that a triangular pyramid has a triangular base with
base length b = 4 inches
height of the triangle h = 1.5 inches and
height of the pyramid = 9 inches
So, the volume of the pyramid = 1/3 × B × h
Where base area B = 1/2 × b × h
⇒ B = 1/2 × 4 × 1.5
= 3.0 sq. inches
And the volume = 1/3 × 3.0 × 9
= 9 cubic inches.
Therefore, the volume of the given triangular pyramid is 9 cubic inches.
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Use the graph of f(x) to evaluate the following:
The average rate of change of f from x= 0 to x=4 is _______.
Give your answer as an integer or reduced fraction.
Answer:
[tex]\large\boxed{-\dfrac{5}{4}}[/tex]
Step-by-step explanation:
[tex]\text{The average rate of change of function}\ f(x)\\\text{over the interval}\ a\leq x\leq b\ \text{is given by this expression:}\\\dfrac{f(b)-f(a)}{b-a}.\\\\\text{Read from graph the values of function for}\ x=0\ \text{and}\ x=4.\\(look\ at\ the\ picture)\\\\f(0)=5,\ f(4)=0\\\\\text{Substitute:}\\\\\dfrac{f(4)-f(0)}{4-0}=\dfrac{0-5}{4}=-\dfrac{5}{4}[/tex]
To find the average rate of change of the function from x = 0 to x = 4, subtract the y-coordinate at x = 0 from the y-coordinate at x = 4, then divide by 4. The exact answer depends on the specific values provided by the graph of the function.
Explanation:The average rate of change of a function f(x) on the interval [a, b] is given by the formula: (f(b) - f(a)) / (b - a). For the given problem, we are asked to find the average rate of change from x = 0 to x = 4. However, the specific values of f(0) and f(4) on the graph are not provided. Generally, to find the average rate of change in this case, you will need to subtract the y-coordinate at x = 0 (f(0)) from the y-coordinate at x = 4 (f(4)), then divide by the difference in x-values (4 - 0). Without the exact values from the graph, a specific numerical answer can't be provided.
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How many inches are in 12 feet
WILL MARK BRAINLIEST
Answer:
66 cm
Step-by-step explanation:
Let's define the circumference first.
It is the boundary of any curved geometric figure specially circle.
We are given the diameter of the circle in the diagram
The diameter is:
d = 21 cm
to find the circumference, we have to find the radius of the circle first.
As radius is half of diameter
d = r/2
= 21/2
= 10.5 cm
The formula for circumference is:
[tex]C = 2\pi r\\Putting\ the\ values\\C = 2 * \frac{22}{7}*10.5\\ C = \frac{462}{7}\\ C= 66\ cm[/tex]
The circumference is 66 cm ..
Answer:
The circumference of the circle is 66 cm
Which of the following is the measure of an acute angle?
There is no image, but I can help you by telling you what an acute angle is:
An acute angle is any angle that has a measure LESS then 90 degrees
Hope this helped!
~Just a girl in love with Shawn Mendes
A measure of an acute angle is equal to 86°.
What is an acute angle?An acute angle can be defined as an angle that is formed by a right-angle triangle. Also, the measure of the angle of an acute angle is generally less than ninety (90) degrees.
In geometry, any angle that is lesser than ninety (90) degrees is generally referred to an acute angle such as:
86°45°60°70°Read more on acute angle here: https://brainly.com/question/10651142
Solve the multi-step equation by combining like terms and using inverse operations and the properties of equality.
Equation: –4x – 5 + 2x = –11
Answer:
Step-by-step explanation:
X=3
1. simplify both sides of the equation by combining like terms
2. add 5 to both sides
3.divide both sides by -2
For this case we have the following equation:
[tex]-4x-5 + 2x = -11[/tex]
To solve, we add similar terms to the left side of the equation:
[tex]-2x-5 = -11[/tex]
We add 5 to both sides of the equation:
[tex]-2x = -11 + 5\\-2x = -6[/tex]
We divide between -2 on both sides of the equation:
[tex]x = \frac {-6} {- 2}\\x = 3[/tex]
Thus, the solution of the equation is 3.
Answer:
[tex]x=3[/tex]
Complete the missing parts of the paragraph proof.
A parabola passes through the points (-3,0), (-2,3), and (-1,4). What function does it represent? Use the graphing tool to determine the function.
A.
f(x) = -x2 + x + 3
B.
f(x) = -2x2 − x + 3
C.
f(x) = -x2 − 2x + 3
D.
f(x) = 2x2 − x − 3
Answer: C
Step-by-step explanation:
(-1,4) is the vertex. reflect (-2,3) and (-3,0) onto the other side of the y-axis. you may use desmos to plug in the functions and the answer will be C, since it goes through the points given and reflected.
Final answer:
The function represented by the given set of points is f(x) = -x^2 - 2x + 3.
Explanation:
To determine the function represented by the given set of points, we can use the general form of a quadratic equation, y = ax^2 + bx + c. Substituting the points (-3,0), (-2,3), and (-1,4) into the equation, we can set up a system of equations and solve for the values of a, b, and c. The resulting function is f(x) = -x^2 - 2x + 3, which corresponds to option C.
Evaluate the step function for the given input values. g(x) = g(2) = g(–2) = g(5) =
Answer:
Step-by-step explanation:
Answer: 3,-4,5
Step-by-step explanation:
A life insurance policy costs $13.58 for every $1,000 of insurance. At this rate, what is the cost of $80,000 of insurance?
Answer:
80 times 13.58 =1086400
Step-by-step explanation:
A 20 foot ladder is resting against the side of the house the base of the latter is 4 feet away from the house approximately how high above the ground is the latter touch the house
The ladder resting against the house forms a triangle similar to the one in the image below
To answer this question you must use Pythagorean theorem
[tex]a^{2} +b^{2}=c^{2}[/tex]
a and b are the legs (the sides that form a perpendicular/right angle)
c is the hypotenuse (the side opposite the right angle)
In this case...
a = x
b = 4
c = 20
^^^Plug these numbers into the theorem
[tex]x^{2} +4^{2} =20^{2}[/tex]
solve for x
[tex]x^{2}[/tex] + 16 = 400
[tex]x^{2}[/tex] = 384
x = 8√6
or
x ≈ 19.5959....
Hope this helped!
~Just a girl in love with Shawn Mendes
Lisle building supplies sold 291 rolls of damaged insulation at a $3 loss per roll. What was the total loss?
Answer:
$873
Step-by-step explanation:
Each roll results in a loss of $3.
There are 291 rolls in all.
Multiply 291 with 3: 291 x 3 = 873
The total loss is $873 for the 291 rolls.
~
Answer:
$873
Step-by-step explanation:
3$ per roll.
291 rolls in total.
291 x 3 = 873
Solve the equation 3x^2+24x=0 for x
Answer:
{0,-8}
Step-by-step explanation:
Factor!
3x(x+8)=0
3x=0 or x+8=0
x=0 or x=-8
Answer:
x=0 x =-8
Step-by-step explanation:
3x^2+24x=0
Factour out a 3x
3x(x+8) =0
Using the zero product property
3x =0 x+8 =0
x=0 x+8-8 =0-8
x=0 x =-8
-5=6m-1 solve for m
Answer:
m= -2/3 or -0.6
Step-by-step explanation:
6m-1= -5+1
6m= -4/-6
m= - 2/3 or -0.6
Answer:
m = -2/3
Step-by-step explanation:
-5 = 6m-1
Rewrite
6m - 1 = -5
Add 1 to both sides
6m = -4
Divide both sides by 6
m = -4/6
Simplifying
m = -2/3
In the diagram, AB = 10 and AC = 2V10. What is the
perimeter of AABC?
10 units
10 + 2/10 units
20 units
20+ 2/10 units
For this case we have that by definition, the distance between two points is given by:
[tex]d = \sqrt {(y2-y1) ^ 2 + (x2-x1) ^ 2}[/tex]
We find the distance AB:
[tex]A: (3,4)\\B: (- 5, -2)[/tex]
[tex]AB = \sqrt {(x2-x1) ^ 2 + (y2-y1) ^ 2}\\AB = \sqrt {(- 5-3) ^ 2 + (- 2-4) ^ 2}\\AB = \sqrt {(- 8) ^ 2 + (- 6) ^ 2}\\AB = \sqrt {64 + 36}\\AB = \sqrt {100}\\AB = 10[/tex]
We have the BC distance:
[tex]B: (- 5, -2)\\C: (5, -2)[/tex]
[tex]BC = \sqrt {(5 - (- 5)) ^ 2 + (- 2 - (- 2)) ^ 2}\\BC = \sqrt {(5 + 5) ^ 2 + (- 2 + 2) ^ 2}\\BC = \sqrt {(10) ^ 2 + (0) ^ 2}\\BC = \sqrt {100}\\BC = 10[/tex]
We find the CA distance:
[tex]C: (5, -2)\\A: (3,4)[/tex]
[tex]CA = \sqrt {(3-5) ^ 2 + (4 - (- 2)) ^ 2}CA = \sqrt {(- 2) ^ 2 + (4 + 2) ^ 2}\\CA = \sqrt {4 + 36}\\CA = \sqrt {40}\\CA = \sqrt {4 * 10}\\CA = 2 \sqrt {10}[/tex]
Thus, the perimeter is given by:
[tex]10 + 10 + 2 \sqrt {10} = 20 + 2 \sqrt {10}[/tex]
ANswer:
[tex]20 + 2 \sqrt {10}[/tex]
Circle O has a circumference of 276.32 cm.
What is the length of the radius of the circle?
cm
Answer:
43.98 cm
Step-by-step explanation:
Circumference is π x diameter
Diameter is 2 x radius
276.32/π = 87.955 (3dp)
87.955/2 = 43.978 (3dp)
43.98cm = radius
Find the x-intercepts of the parabola with
vertex (4,75) and y-intercept (0,27).
Write your answer in this form: (X1,Y1), (X2,72).
If necessary, round to the nearest hundredth.
Answer:
(- 1, 0), (9, 0)
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (4, 75), so
y = a(x - 4)² + 75
To find a substitute (0, 27) into the equation
27 = a(- 4)² + 75 , that is
27 = 16a + 75 ( subtract 75 from both sides )
16a = - 48 ( divide both sides by 16 )
a = - 3, thus
y = - 3(x - 4)² + 75 ← equation in vertex form
To obtain the x- intercepts let y = 0
- 3(x - 4)² + 75 = 0 ( subtract 75 from both sides )
- 3(x - 4)² = - 75 ( divide both sides by - 3 )
(x - 4)² = 25 ( take the square root of both sides )
x - 4 = ± [tex]\sqrt{25}[/tex] = ± 5
Add 4 to both sides
x = 4 ± 5, hence
x = 4 - 5 = - 1 or x = 4 + 5 = 9
Substitute these values into the equation for corresponding values of y
x = - 1 : y = - 3(- 5)² + 75 = - 75 + 75 = 0 → (- 1, 0)
x = 9 : y = - 3(5)² + 75 = = 75 + 75 = 0 → (9, 0)
The x- intercepts are (- 1, 0), (9, 0)
Answer:
The x intercepts are (-1, 0) and (9, 0).
Step-by-step explanation:
We can write the equation in vertex form:
y = a(x - b)^2 + c
Here b = 4 and c = 75 so we have
y = a(x - 4)^2 + 75 where a is a constant to be found.
The y-intercept is (0,27) so
27 = a(0 - 4)^2 + 75
16a = 27 - 75
a = -48/16 = -3
So to find the x-intercepts we solve the equation:
-3(x - 4)^2 + 75 = 0
(x - 4)^2 = -75 / -3 = 25
x - 4 = +/- √25
x = 5+ 4 = 9 , -5 + 4 = -1.
Mr hassan opened an account with Rs 45,687. He deposits Rs 5800 in the first month and withdraws Rs6981 in the second month .How much money is left in his account ? If he withdraws Rs 250 again ,how much is left now?
Answer:
44506
Step-by-step explanation:
458687+5800=51487
51487-6981=44506