Hi
72 Hours before 2:12 am, Monday is 2:12 am, Friday, because 72 hours before is 3 days in the past.
Does 9,12,15 form a right triangle
Answer:
Yes.
Step-by-step explanation:
Note that 15^2 = 122^ + 9^2 ( 225 = 144 + 81 = 225).
So by the Inverse of Pythagoras Theorem it is a right triangle.
The given values of side makes a proper right angle triangle.
To determine if the three given side lengths, 9, 12, and 15, form a right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's check if this holds true for the given side lengths:
[tex]9^2 + 12^2 = 81 + 144 = 225\\\\15^2 = 225[/tex]
The sum of the squares of the two shorter sides, 9 and 12, is equal to the square of the longest side, 15. This satisfies the Pythagorean theorem.
Therefore, the side lengths 9, 12, and 15 do form a right triangle.
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Which of the following statements are true of the parabola shown?
1. It has a directrix of x = -4.
2. It opens to the left.
3. It has a vertex at the origin.
4. The axis of symmetry is the y-axis.
5. It has a focus at (4, 0).
True statements are:
It has a directrix of x = - 4.It has a focus at (4, 0).Step-by-step explanation:
We have the following statements to check on whether it's right or wrong:
1. It has a directrix of x = -4:
According to figure , parabola directrix is at -4 i.e. at x = -4 , Therefore this statement is true!
2. It opens to the left:
In figure, Parabola opens to right not left , Therefore this statement is wrong!
3. It has a vertex at the origin:
Vertex of Parabola is at what points not shown in figure. Therefore this statement cannot be confirmed as true.
4. The axis of symmetry is the y-axis:
Axis of symmetry for above parabola is x-axis as it cuts parabola into two equal halves , y-axis doesn't do this ! Therefore this statement is wrong!
5. It has a focus at (4, 0):
Parabola focus is at [tex]F(4,0)[/tex] on x-axis . And so, Therefore this statement is true!
1. True it has a directrix of x = -4; 2. False it opens to the left; 3. False it has a vertex at the origin; 4. True the axis of symmetry is the y-axis; 5. True it has a focus at (4, 0).
In this parabola, the given statements can be evaluated as follows:
1. Directrix : The given directrix is x = -4. The directrix of a parabola is a vertical line that is equidistant from all points on the parabola. In this case, the directrix is to the left of the origin, so it's possible that the parabola opens to the right.
2. Direction of Opening : The parabola cannot open to the left because the given directrix is to the left of the origin. Parabolas open towards their focus or away from their directrix. Since the directrix is to the left, the parabola opens to the right.
3. Vertex : The vertex is the point where the parabola changes direction. The origin (0, 0) is not the vertex in this case, as the parabola opens to the right.
4. Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two equal halves. Since the parabola opens to the right, its axis of symmetry is the y-axis.
5. Focus : The focus is a point inside the parabola that is equidistant to the vertex and the directrix. The focus should indeed be to the right of the vertex, and at a distance of 4 units, based on the given directrix
x = -4.
Mathematically, the equation of a parabola that opens to the right, with its vertex at the origin, is of the form:
[tex]\[x^2 = 4py\][/tex]
Given that the directrix is x = -4, the distance from the origin to the directrix is 4 units. So, the equation becomes:
[tex]\[x^2 = 16y\][/tex]
The focus is at a distance of p units from the vertex, where [tex]\(p = 4\)[/tex], so the focus is at (4, 0).
In summary, the given parabola opens to the right, has a vertex at the origin, its axis of symmetry is the y-axis, and its focus is at (4, 0), with a directrix of x = -4.
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Eliza bought a meal that cost $12.00. She tipped the waiter 25%of that amount . How much was the tip ?
The question is about calculating a tip which is 25% of a meal cost of $12.00. The tip is calculated by multiplying the total cost of the meal by the tip percentage, converted into decimal form. The answer is $3.00.
Percentage is a mathematical concept used to express a portion of a whole as a fraction of 100. It is a versatile tool in various fields, including finance, statistics, and everyday calculations. To calculate a percentage, you divide a part by the whole and then multiply by 100. Percentages are commonly used to represent proportions, express changes, and compare values, making them vital for analyzing data, understanding discounts, and determining growth rates. In essence, percentages simplify the representation of relative quantities and are fundamental in both practical and academic mathematics.
The subject of the question is Mathematics, specifically Percentage. The student is being asked to calculate 25% of $12.00, which is the cost of Eliza's meal. To calculate the tip, multiply the total meal cost by the percentage of the tip. Here's how we can do it:
Convert the percentage into a decimal: 25% is equal to 0.25 in decimal form.Multiply the total cost of the meal by the decimal: $12.00 * 0.25 = $3.00So the tip Eliza left for the waiter was $3.00.
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what fraction is equivalent to 3/4
Answer:
6/8
Step-by-step explanation:
3/4 = 6/8 = 9/12 and so on
Answer:
9/12
Step-by-step e
9. D is 20 + h
But help :)
Answer:
8. D 269.6
9. A 20 +10h
Step-by-step explanation:
8. The large rectangle is 4+6.4+4+6.4 = 20.8 width and 10.5 length. The area is
A = l*w = 20.8* 10.5 =218.4
The top rectangle is 6.4 width and length is 4
A = l*w =6.4*4 =25.6
The same is true for the rectangle on the bottom.
Add the three rectangles together to get the total surface area
218.4+25.6+25.6 =269.6
9. The plant is 20 inches tall
It grows 2h inches a week for 4 weeks
20 +2h*4
20 +8h
It grows h inches a week after 4 weeks
At 6 weeks, that is 2 weeks of growth
The growth is h *2
Add that to the previous total
20 +8h +2h
20 +10h
An engineer scale model shows a building that is 3 inches tall. If the scale is 1 inch = 600 feet, how tall is the actual building in feet ?
Answer:
1800ft tall
Step-by-step explanation:
$9.60 for 4 pounds i need help
hey bro, what do you mean by this question?
do you want to convert 9.60 dollars into pounds? if so then right now the exchange rate for dollars to pounds is 0.80. So you will do this (0.80)(9.60)=7.68
If you mean pounds like how much something weighs then all you need to do is just divide 9.60 by 4 = 2.4 which means $2.4 per pound.
What is the surface area of this triangular prism rounded to the nearest tenth? A) 48.6km2 B) 63.4 km2 C) 72.6 km2 D) 84.4 km2
Correct option B)[tex]63.4km^2[/tex] .
Step-by-step explanation:
We have the following figure attached as shown below.
Now, this triangular prism have 2 similar right angled surfaces and 3 rectangular surfaces , Let's calculate area for all of them:
2 similar right angled surfaces
We know that area of triangle = [tex]\frac{1}{2} b(h)[/tex]
⇒ [tex]area = \frac{1}{2} b(h)[/tex]
⇒ [tex]area = \frac{1}{2} (3.6)(7.7)[/tex]
⇒ [tex]area = 13.86km^{2}[/tex]
But there 2 such surfaces so , [tex]area = 2(13.86) = 27.72km^2[/tex]
3 rectangular surfaces
Area of rectangle = [tex]length(breadth)[/tex]
⇒ [tex]area_1 = 3.6(1.8)[/tex]
⇒ [tex]area_1 = 6.48km^2[/tex]
⇒ [tex]area_2= 7.7(1.8)[/tex]
⇒ [tex]area_2 = 13.86km^2[/tex]
⇒ [tex]area_3 = 8.5(1.8)[/tex]
⇒ [tex]area_2 = 15.3km^2[/tex]
Total area =[tex]6.48 + 13.86 + 15.3 = 35.64km^2[/tex]
Adding area of 2 similar right angled surfaces & 3 rectangular surfaces:
[tex]Area = 27.72+35.64 = 63.36km^2[/tex] = [tex]63.4km^2[/tex]
Correct option B)[tex]63.4km^2[/tex] .
Answer:
It is B.
Step-by-step explanation:
Trust me it's B
Find the area of the following geometric figure
area of a triangle with
ase of 15 m and altitude of 12 m.
The area of the triangle is 90 m²
Explanation:
Given that the base of the triangle is 15 m
The altitude of the triangle is 12 m
Area of the triangle:
The area of the triangle can be determined using the formula,
[tex]Area=\frac{1}{2}bh[/tex]
where b is the base and h is the altitude
Thus, we have,
[tex]b=15[/tex] and [tex]h=12[/tex]
Substituting the values in the above formula, we get,
[tex]Area=\frac{1}{2}(15)(12)[/tex]
Multiplying the terms, we get,
[tex]Area=\frac{180}{2}[/tex]
Dividing, we get,
[tex]Area=90 \ m^2[/tex]
Therefore, the area of the triangle is 90 m²
An electrician cut 36 feet of wire into sections that were each 8 1/2 feet long. After cutting, how many pieces of wire did the contractor have?
I need help with problem 27
Answer:
0+7-4=3
Step-by-step explanation:
They started with none, hence the 0. "Gained" typically means addition, so you add seven. "Lost" is a signal word for subtraction, so subtract zero. It comes out to 4.
Larry had $480 he used to thirds of it to buy an electric band he also bought tea set for 60 how much money did he have left
Answer:
Here's our equation:
480 * 1/3 - 60 = []
The 1/3 comes from 1 - 2/3 = 1/3 for note, as that's how much of her money is left after the fan's purchased. (if you're unsure, you can multiply 480 and 2/3 together, and then subtract that amount from 480, and you'll see you end up with the same answer as below)
The order of operations means we deal with the 480 * 1/3 first.
480 * 1/3 → 480/3 = 160
Next is subtraction:
160 - 60 = 100
So Mrs. Ricci has $100 left.
Step-by-step explanation:
A family buys 6 tickets to a show. They also pay $3 parking fee. They spend $27 to see the show.
Answer:
They paid $4.00 per ticket
Step-by-step explanation:
Step 1: Convert words into an inequality
A family buys 6 tickets to a show. They also pay $3 parking fee. They spend $27 to see the show.
6t + 3 = 27
Step 2: Solve for t/tickets
6t + 3 = 27
6t + 3 - 3 = 27 - 3
6t / 6 = 24 / 6
t = 4
Answer: They paid $4.00 per ticket
Answer:
4
Step-by-step explanation:
3 - 27 = 24
24 ÷ 6 = 4
4 · 6 = 24
3 + 24 = 27
A = $27
Help please !!!!!!!!!!!!!!!!!!!!!
Answer:
The last one
Step-by-step explanation:
volume is v= [tex]\pi r^{2} h[/tex] . this means volume is mathematical number pi, times the (radius squared), times the height. the radius is marked at the yellow line, and the height on the side. this means you would have v = [tex]\pi[/tex][tex](x+2)^{2}[/tex][tex](3x+8)[/tex]
first, lets work out [tex](x+2)^{2}[/tex]. we can rewrite this as (x+2)(x+2). we are going to use a system called FOIL. this stands for First Outside Inside Last. This means we are going to take the first number from both and multiply them together, then the outside, inside, and last. so, for first, we will multiply x and x and then we have [tex]x^{2}[/tex], for outside we multiply x and 2 and we get [tex]2x[/tex], for inside we multiply 2 and x and we get [tex]2x[/tex], and for last we multiply 2 and 2 and we get [tex]4[/tex]. then we add all these together. [tex]x^{2} + 2x + 2x + 4[/tex]. then simplify like terms to get
[tex]x^{2} + 4x + 4[/tex]. now, we can't forget about our times [tex]\pi[/tex] and (3x+8)
this means we have to multiply [tex]x^{2} + 4x + 4[/tex] by those two.
it would look like this: ([tex]x^{2} + 4x + 4[/tex])(3x+8)[tex]\pi[/tex]
so now we are going to multiply the other two sets of parentheses
we multiply each number from the first set to each number in the second set.
2. The number of years that Elijah has been on the soccer team is 2 less than 5 times the number of years that Deaundre
has. In total, the boys have been on the soccer team for 10 years. How long has Elijah been on the soccer team?
The Elijah have been on the soccer team for 8 years.
Step-by-step explanation:
Let,
The number of years that Deaundre have been on the soccer team "x".The number of years that Elijah have been on the soccer team = 2 less than 5 times the number of years that Deaundre.The number of years that Elijah have been on the soccer team = 5x - 2.Given that,
The boys have been on the soccer team for 10 years.
Number of years of Deaundre + Number of years of Eliijah = 10 years.
x + (5x-2) = 10
Keep x terms on one side and constants on another side to solve for x value :
6x = 10+2
6x = 12
x = 12/6
x = 2
The Deaundre have been on the soccer team for 2 years.
Substitute x=2 in (5x-2) to find the number of years of Elijah,
5(2)-2 = 8 years.
Therefore, the Elijah have been on the soccer team for 8 years.
Simplify this expression
a) 2a + 5a
Answer:
7a
Step-by-step explanation:
Rotate (-4,8) 90cc. What is the new order pair?
Answer:
(- 8, - 4 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ), thus
(- 4, 8 ) → (- 8, - 4 )
what is the unit price of a 16-ounce box of cereal that sells for $2.48?
Answer:
0.155
Step-by-step explanation:
Answer:
$0.15 per ounce
Step-by-step explanation:
2.48/16 = 0.155
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Which scatterplot suggests no relationship between x and y?
A) II only
Eliminate
B) III only
C) I and III only
D) II and III only
Answer:
B) III only, it doesn't suggests relationship between x and y.
What is the length of line segment QP? Round to the
nearest unit.
O
O
O
o
13 units
17 units
18 units
20 units
Answer:
[tex]QP=20\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
Let
O ---> the center of the circle
we have that
Line segment QP is tangent to the circle
That means
OQ (radius) is perpendicular to segment QP
OQP is a right triangle
Applying Pythagorean Theorem
[tex]OP^2=OQ^2+QP^2[/tex]
we have
The radius is equal to
[tex]r=24/2=12\ units[/tex] ----> the radius is half the diameter
[tex]OP=r+NP=12+11.5=23.5\ units[/tex]
[tex]OQ=r=12\ units[/tex]
substitute
[tex]23.5^2=12^2+QP^2[/tex]
[tex]QP^2=23.5^2-12^2[/tex]
[tex]QP^2=408.25[/tex]
[tex]QP=20\ units[/tex]
Answer:20 units
Step-by-step explanation:
List all the multiples of 8 that are less than or equal to 100. List all the multiples of 12 that are less than or equal to 100. What are the common multiples of 8 and 12 from the two lists?
Answer:
24,48,72,96
Step-by-step explanation:
Multiples of 8
8, 16,24,32,40,48,56,64,72,80,88,96
Multiples of 12
12,24,36,48,60,72,84,96
Common multiples
24,48,72,96
Answer:
See below.
Step-by-step explanation:
"List all the multiples of 8 that are less than or equal to 100."
0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
"List all the multiples of 12 that are less than or equal to 100."
0, 12, 24, 36, 48, 60, 72, 84, 96
Common multiples: 0, 24, 48, 72, 96
Liam's last grocery bill was $105. This week, his bill was $85. Calculate the percent change. Round to the nearest hundredth.
Answer:
.199 or 20% (.20)
Step-by-step explanation:
Percentage change:
p=(85-105)/105=-20/105=-19.047%
Rounded value: -19.05%
The minus sign indicates a decrease in amount spent.
A triangular prism has a volume of 350 cubic meters. If the dimensions are tripled what is the volume of the new
prism?
Answer:
9450 m³
Step-by-step explanation:
(S1/S2)³ = V1/V2
3³ = V1/350
New Volume = 27 × 350
= 9450 m³
can someone please help me with this question What is the minimum value of the quadratic function f(x) = x² - 2x + 7
minimum value of the quadratic function f(x) = x² - 2x + 7 is at x=1 & is (1, 6).
Step-by-step explanation:
Here we have , f(x) = x² - 2x + 7 or [tex]f(x) = x^2 - 2x + 7[/tex] . We need to find the minimum value of f(x) for which we need to differentiate it one time and equate it to zero . Value of x at which first differentiation of f(x) is zero will be the minimum value of function . Let's solve this:
[tex]f(x) = x^2 - 2x + 7[/tex]
⇒ [tex]f(x) = x^2 - 2x + 7[/tex]
⇒ [tex]\frac{df(x)}{dx} = \frac{d(x^2 - 2x + 7)}{dx}[/tex]
⇒ [tex]\frac{df(x)}{dx} = \frac{d(x^2)}{dx} - \frac{d(2x)}{dx} + \frac{d(7)}{dx}[/tex]
⇒ [tex]\frac{df(x)}{dx} = 2x-2 = 0[/tex]
⇒ [tex]2x-2 = 0[/tex]
⇒ [tex]x =1[/tex]
Now, value of function at x=1 is :
[tex]f(x) = x^2 - 2x + 7[/tex]
⇒ [tex]f(x) = x^2 - 2x + 7[/tex]
⇒ [tex]f(1) = 1^2 - 2(1) + 7[/tex]
⇒ [tex]f(1) = 8- 2[/tex]
⇒ [tex]f(1) = 6[/tex]
Therefore, minimum value of the quadratic function f(x) = x² - 2x + 7 is at x=1 & is (1, 6).
The minimum value of the quadratic function f(x) = x² - 2x + 7 is 6, which occurs at x = 1, as determined by finding the vertex of the parabola.
Explanation:The minimum value of the quadratic function f(x) = x² - 2x + 7 can be determined by finding the vertex of the parabola represented by the function. This is because the graph of a quadratic function is a parabola, and if the coefficient of the x² term is positive, the parabola opens upwards and the vertex represents the minimum point.
To find the vertex, use the formula -b/2a to determine the x-coordinate of the vertex. For the function f(x), the value of 'a' is 1 and 'b' is -2. Substituting these values gives us the x-coordinate of the vertex as x = -(-2)/(2*1) = 1. Substituting x = 1 back into the function f(x), we get the y-coordinate of the vertex, which is the minimum value of the function: f(1) = (1)² - 2*(1) + 7 = 6.
Therefore, the minimum value of the quadratic function f(x) is 6, occurring at x = 1.
If ABCD is a parallelogram,which statement would prove that ABCD is a rhombus?
(Picture is the choices to the question)
To prove ABCD is a rhombus, showing that all sides of parallelogram ABCD are equal in length would suffice.
Explanation:If ABCD is a parallelogram, to prove that it is a rhombus, a statement that would suffice is that all four sides of the parallelogram are of equal length.
This is because a rhombus is defined as a parallelogram with four congruent sides. If any one of its diagonals bisects an angle of the parallelogram, or its diagonals are perpendicular, or its diagonals are of the same length, these conditions would not exclusively prove it to be a rhombus, although they are properties of a rhombus. However, the definition of a rhombus centers on the equality of all sides.
Equal adjacent angles would not necessarily mean that all sides are equal, which is a requirement for a rhombus.
The correct option is (B).
To prove that a parallelogram is a rhombus, you need to show that all four sides are of equal length. A parallelogram has opposite sides that are equal and parallel, but for it to be a rhombus, every side must be equal in length to every other side.
The statement options you might have in your image could be something like:
a. Diagonals are perpendicular (AC ⊥ BD)
b. Adjacent angles are equal (∠ABC ≅ ∠CDA)
c. One pair of opposite sides are equal (AB ≅ CD)
d. Diagonals are equal (AC ≅ BD)
From these options:
- Option a: If the diagonals are perpendicular, it's an indication that the parallelogram could be a rhombus, but it's not conclusive proof because a rectangle also has perpendicular diagonals.
- Option b: Equal adjacent angles would not necessarily mean that all sides are equal, which is a requirement for a rhombus.
- Option c: Having one pair of opposite sides that are equal is already a property of a parallelogram and does not prove it's a rhombus.
- Option d: Equal diagonals would be a property of a rectangle, not necessarily a rhombus.
The conclusive proof that a parallelogram is a rhombus would be if you can show that all sides are of equal length (not provided in the typical options above), or if the diagonals are perpendicular and bisect each other into equal segments. This latter property is unique to a rhombus among parallelograms. If this were one of the choices, it would be the correct answer.
Since I can't see the options, please review them and look for the one that indicates all four sides are of equal length or that the diagonals bisect each other into equal segments and are perpendicular. That would be the correct choice to prove the parallelogram is a rhombus.
ted, sam, and jack can do a piece of work in 15, 12 and 20 days respectively. they started the work together, but jack left after 2 days. in how many days will the remaining work be completed by ted and sam?
Answer:
the answer was 24
Step-by-step explanation:
What is the measurement of the unknown fourth interior angle of this quadrilateral? A) 80° B) 95° C) 100° D) 115°
Answer: The Answer is 100, sorry that you got it so late.
Step-by-step explanation:
What I did
1. Find the difference between the numbers
2. Look through answer choices
3. Because the difference of 80 and 75 was 5, 105 would be 100.
Sorry if this doesn't make sense.
Explain how the product 1\2 ×1\3 relates to the model
Final answer:
The product 1/2 x 1/3 equals 1/6, which can be visualized using a two-dimensional model where a rectangle is divided into halves and then thirds, resulting in 1/6 of the total area.
Explanation:
The product 1/2 times 1/3 can be understood through a two-dimensional model. If you take a rectangle and divide it into 2 equal parts, taking 1/2 of the whole, and then divide one of those halves into 3 equal parts, taking 1/3 of that half, you will have 1 out of the 6 equal parts of the original rectangle, which is 1/6, the product of 1/2 and 1/3.
To visualize this process, imagine a bar or a piece of chocolate that is first divided down the middle, and then one of those halves is divided into 3 equal pieces.
Taking one of these smaller pieces represents 1/6 of the original chocolate bar. In mathematical terms, when we multiply fractions, we multiply the numerators ( 1 times 1) to get the numerator of the product, and the denominators (2 times 3) to get the denominator of the product, yielding 1/6 as the answer. This demonstrates the first partial product principle, where in this case the third vector (1/3) is multiplied by the scalar product of 1/2.
How to solve 16 * 12.5
Answer: 200
Step-by-step explanation:
First I would do it like this.
12.5
X. 16
—————-
6 times 5 is 0, carry the 3, 6 times 2 is 12 and add 3 from the other which is 15, put the 1 from the 15 to the one next to the 12. 6 times 1 is 6 plus 1 is 7 which now you have 750. 5 times 1 is 5, 2 times 1 is 2, 1 times 1 is 1. It should look like this now.
12.5
X 16
—————
750
+ 1250
——————-
Which is 8750 but wait. Where is the decimal? Well, there is only one number behind the decimal so it is 875.0 or 875.
What value does the 3 represent in the number 16.344?
Answer:
00.300
Step-by-step explanation:
What value does the 3 represent in the number 16.344
The 3 in the number 16.344 represents 0.003, since it's located on the third decimal place. It contributes three-thousandths to the total value. The position of the number changes the value it represents.
Explanation:The value of 3 in the number 16.344 is represented as 0.003 in decimal place value. This is because it is situated in the third digit after the decimal point, signifying that it contributes the amount equal to three thousandths (0.003) to the total value of the number. For example, in using the concept of Six significant figures, we can say the number 16.344 has five significant figures, that is, the digits that give us precise information about the magnitude of the number - these digits being 1, 6, 3, 4 and 4.
It's also worthwhile to note that the placement of the digit 3 in the number 16.344 is different from a 3 that is located at other decimal places. For instance, if we look at the number 16.3443, the second 3 after the decimal point represents three ten-thousandths (0.0003) contribution to the total value of the number.
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