Answers
Answer:
Step-by-step explanation:
\(\sqrt{25^2 - 24^2 }\) = \(\sqrt{(25-24)(25+24)}\) = √49 = 7 units
Related Questions
what is the probability of a bag of 12 black chips and 60 red chips
Answers
Answer:
Step-by-step explanation:
12/60
shorten it
it will be 1/5
Angie drove to the beach. She kept track of the number of miles she traveled
and the number of gallons of gas she used. Which method and reasoning can
Angie use to calculate the gas mileage in miles per gallon?
Answers
Answer:
Angie drove to the beach. She kept track of the number of miles she traveled and the number of gallons of gas she used. Which method and reasoning can Angie use to calculate the gas mileage in miles per gallon?
A:435.7 miles • 12.42 gallons,
because multiplying a quantity with units of miles by a quantity with units of gallons gives a quantity with units of miles per gallon.
B:435.7 miles −12.42 gallons,
because subtracting a quantity with units of gallons from a quantity with units of miles gives a quantity with units of miles per gallon.
C:12.42 gallons ÷ 435.7 miles,
because dividing a quantity with units of gallons by a quantity with units of miles gives a quantity with units of miles per gallon.
D:435.7 miles ÷ 12.42 gallons,
because dividing a quantity with units of miles by a quantity with units of gallons gives a quantity with units of miles per gallon.
Step-by-step explanation:
Answer:
435.7 miles divided by 12.42 gallons
because dividing a quantity with units of miles by a quantity with units of gallons gives a quantity with units of miles per gallon.
a. What is the quotient x²+5 x+4 / x²+x-12 / x²-1 / 2 x²-6 x in simplest form? State any restrictions on the variable.
Answers
The quotient (x²+5x+4) / (x²+x-12) / (x²-1) / (2x²-6x) simplifies to (2x+1) / (x-3), with a restriction on x ≠ 1.
To simplify the given quotient, we need to perform the division of the numerator by the denominator, following the order of operations.
First, we factor all the polynomials:
x²+5x+4 factors as (x+4)(x+1),
x²+x-12 factors as (x+4)(x-3),
x²-1 factors as (x+1)(x-1),
and 2x²-6x factors as 2x(x-3).
We then cancel out the common factors between the numerator and denominator:
[(x+4)(x+1)] / [(x+4)(x-3)] * [(x+1)(x-1)] / [2x(x-3)]
Simplifying further, we get:
[(x+1)(x+1)] / [2x]
Which simplifies to:
(x+1)² / (2x)
Finally, we can rewrite it as:
(2x+1) / (x-3)
Therefore, the quotient in simplest form is (2x+1) / (x-3), with the restriction that x cannot be equal to 1.
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A rocket is launched into the air and is modeled by the equation h(t)=-t^2+3t-5, where t is the amount of time in seconds ], and h(t) is the height (in feet) of the rocket after t seconds.
a. After how many seconds does the rocket reach its maximum height?
b. How high does the rocket go at its maximum height?
Answers
Answer:
a. it reaches its max height at 1.5 seconds
b. it reaches 2.75 feet
0
с
z←
85⁰
D
Work out the three-figure bearing of D from C.
Answers
Answer:
095
Step-by-step explanation:
You want the bearing from C to D, given that the bearing from D to C is 85° west of north.
BearingThe bearing from C to D will be the opposite of the bearing from D to C.
Bearing is measured clockwise from north, so the bearing shown from D to C is -85°. Its opposite is found by adding 180°.
180° +(-85°) = 95°
The 3-digit bearing of D from C is 095.
y=−4x−3 y=−2x+1 solve by graphing
Answers
Answer: (-2,5)
Step-by-step explanation: just graph both equations they are already set up in the form and find the point where they intersect
Hopefully this helps!
Which section of the function is constant?
A graph is shown. Segment A begins at the origin and continues upward. Segment B continues upward at a faster rate. Segment C is a horizontal line. Segment D continues upward
Group of answer choices
C
B
A
D
Answers
Answer:
Segment C
Step-by-step explanation:
constants have no slopes and are therefore straight, horizontal lines
Is the answer A B C or D
Answers
Answer:
I am not sure but i think it is D
Answer:
B
Step-by-step explanation:
Because angle F is equal angle G, 2x+4=3x. Solving for x, we get 4.
Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.
Which choice represents the sample space, S, for this event?
S = {PQR}
S = {PQR, PRQ, QPR, QRP, RPQ, RQP}
S = {PQ, PR, QR}
S = {PQ, QP, PR, RP, QR, RQ}
Answers
The resulting sample space of the given situation is S = {PQ, QP, PR, RP, QR, RQ}
Sample space:
Sample space refers the collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.
Given,
Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.
Here we need to find the sample space for the event.
Let us consider,
P represents Patty
Q represents Quinlan
R represents Rashad
And through the question we have know that, the teacher drawn two card at a time,
So we have consider that the teacher is going to draw out of the hat one first, without replacement, and then draw another one.
The first chosen one will be the president, and that could be P, Q or R, Now, the chosen second one is the Vice president, and already one has already being drawn, that could only be two fellows.
Therefore, the total of likely outcomes is PQ,QP, PR, RP, QR, RQ, one paired up with either of the two remaining in the hat.
So, the resulting sample space is
S = {PQ, QP, PR, RP, QR, RQ}
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Expand and simplify
(x + 1)(x + 7)
Answers
Answer: 10x + 7
Step-by-step explanation:
multiply everything
2x + 7x + x + 7
combine like terms
10x + 7
Tom bought
a shirt at safe price of $80.00.This is 20% of the cost price what is the original price?
Help I really really need it.
Answers
Answer:
$400.00
Step-by-step explanation: The shirt was bought at 20% of its original value, or 1/5th. To calculate it's original value, we multiply it by it's inverse 5/1, which is 5 times it's sale price. 80 * 5 = 400.
Can someone help me again please ?!
Answers
Actually, if you notice that two of the lines are parallel, the answer is x=53!
Answer: Answer is 53
Step-by-step explanation:
Please help!
Suppose that the cross section of a piece of pipe looks like the diagram shown. Find the total outer diameter.
Answers
Answer:
-8
Step-by-step explanation:
Prove the induction principle from the well-ordering principle (see Example 11.2.2(c)). [Prove the induction principle in the form of Axiom 7.5.1 by contradic- tion.)
Answers
The induction principle can be proven from the well-ordering principle through a contradiction.
How can the well-ordering principle prove the induction principle?The well-ordering principle states that every non-empty set of positive integers has a least element. We can prove the induction principle by assuming its negation and arriving at a contradiction.
Assume that there exists a set A of positive integers for which the induction principle does not hold. This means there must be a smallest positive integer, n, for which the statement is false. Let B be the set of positive integers for which the statement is true.
Since n is the smallest positive integer for which the statement fails, we know that n-1 must be in B. If it were not, then the statement would hold for n-1, contradicting the assumption that n is the smallest counterexample.
However, if n-1 is in B, then by the induction principle, the statement must also hold for n. This contradicts our assumption that n is a counterexample, leading to a contradiction.
Therefore, our assumption that a counterexample exists is false, proving the induction principle.
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. Suppose you plan to make a box that will hold exactly 40 one-inch cubes. Give the dimensions (ex: 1in x 1in x 40in) of 3 possible boxes you can create to hold all cubes.
Answers
Answer:
The dimensions of the three possible boxes are;
Box 1: 2 inches length by 4 inches width by 5 inches height
Box 2: 2 inches length by 2 inches width by 10 inches height
Box 3: 8 inches length by 1 inch width by 5 inches height
Step-by-step explanation:
The dimensions of the required box = 40 in³
Therefore, a box that will hold all the cubes will have a dimension given as follows;
Length, l × Width, w × Height, h = 40 in.³
We therefore, look for possible dimensions of l, w, h, however to make is faster, we note that l × w = base area, BA, hence we look for the factors 40 thus;
BA × h ≡ l × w × h
8 × 5 = 40 ≡ 2 × 4 × 5 = 40
4 × 10 = 40 ≡ 2 × 2 × 10 = 40
8 × 5 = 40 ≡ 8 × 1 × 5 = 40
Hence we have our three possible boxes as follows;
Box 1: Length = 2 inches, width = 4 inches and height = 5 inches
Box 2: Length = 2 inches, width = 2 inches and height = 10 inches
Box 3: Length = 8 inches, width = 1 inches and height = 5 inches.
Exercise #1: We would like to find the distance between points A and B if they have coordinates A(2,3) and B(14, 12).
Answers
This triangle is isosceles if:
\(AB=BC\)Using the distance formula:
\(\begin{gathered} AB=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ (x1,y1)=(-3,8) \\ (x2,y2)=(-9,0) \\ AB=\sqrt[]{(-9-(-3))^2+(0-8)^2} \\ AB=\sqrt[]{60} \\ \end{gathered}\)\(\begin{gathered} BC=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ (x1,y1)=(-9,0) \\ (x2,y2)=(5,2) \\ BC=\sqrt[]{(5-(-9))^2+(2-0)^2} \\ BC=\sqrt[]{200} \end{gathered}\)Since:
\(AB\ne BC\)We can conclude that:
\(\Delta ABC\)Is not an isosceles triangle
One week a student exercised 2 hours at school and another of an hour at 1/4 home. If of the student's total exercise came from playing soccer, how 1/6 much time did the student spend playing soccer that week? Enter your answer in hoursdo not include units in your answer .
Answers
Answer: 3/8
Step-by-step explanation:
PLEASE ANSWER QUICKLY
Answers
Answer:
3
Step-by-step explanation:
f(x) = 3x² - 2x + 1
f(x) = ax² + bx + c
a = 3
Find the value of LK
Answers
Answer:
LK = 7
Step-by-step explanation:
NK = NM + ML + LK ( substitute values )
23 = x - 6 + 9 + 2x - 19
23 = 3x - 16 ( add 16 to both sides )
39 = 3x ( divide both sides by 3 )
13 = x
Then
LK = 2x - 19 = 2(13) - 19 = 26 - 19 = 7
The diagram shows a square ABCD
M is the midpoint of AB
N is the midpoint of AD
The area of the shaded triangle AMN is 8cm^2
Work out the area of triangle MCN
Answers
The area of the triangle, Δ AMN is 8 cm², so the area of the triangle, ΔMCN is 24 cm².
A triangle is one of the most basic geometric figures with 3 sides, 3 angles, and 3 vertices.
The area of a triangle is half of the product of the base and height.
Given that
ABCD is square and M and N are mid-points of lines AB and AD respectively.
Area of triangle, ΔAMN = 8 cm²
\(\dfrac{1}{2} \times AN \times AM = 8\\AN \times AM = 8 \times 2\\AN \times AM = 16\) ...(i)
Since ABCD is square, therefore AB = AD.
Also, as M and N are mid-points of lines AB and AD, so
AN = AM.
Substitute AN = AM in equation (i),
\(AN \times AN = 16\\AN^2 = 16\\AN = \sqrt{16}\\AN = 4\ cm\)
So,
AD = 2 × AN
= 2 × 4
= 8 cm
As ABCD is square,
AB = BC = CD = AD = 8 cm.
Area of the square ABCD = 8² = 64.
Since CD = BC, ND = MB, ∠D = ∠B.
Therefore by SAS property of similarity,
ΔCDN ≅ ΔCBM
Area of the triangle, ΔCDN = Area of the triangle, ΔCBM.
\(= \dfrac{1}{2} \times CB \times BM\\= \dfrac{1}{2} \times 8 \times 4\\\\= 16\ cm^2\)
Area of the triangle, ΔCMN = Area of ABCD - Area of ΔAMN - Area of ΔCDN - Area of ΔCBM
Area of the triangle, ΔCMN = 64 - 8 - 16 - 16
= 24 cm²
Therefore, the area of ΔCMN is 24 cm².
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There are two other ways to write this fraction.
−15/29
List them in the space below.
Answers
Answer:
-30/58 & -45/87
Step-by-step explanation:
The first answer is just multiplying the original by 2.
The second one is being multiplied by 3.
The multiplicated moves DO NOT CHANGE THE VALUE OF THE ORIGINAL FRACTION, meaning that they are equivalent. :))
A piece of paper is to display ~150~ 150 space, 150, space square inches of text. If there are to be one-inch margins on the sides and the top and a two-inch margin at the bottom, what are the dimensions of the smallest piece of paper that can be used?.
Answers
The paper's smallest dimensions are height=8.660in and width=17.321in.
What are dimensions?In physics and mathematics, the dimension of space is the smallest set of coordinates needed to specify any point within a mathematical space.
A line has a dimension of one because only one coordinate is needed to specify a point on a line, such as a point at 5 on a number.
So, we have:
Area = 150in²
Side margin = 1 in
Top and Bottom Margin = 2 in
To obtain the smallest dimensions, calculate as follows:
The printed material's area is:
Area = l*w
A1 = h*w
A1 should be changed to 150:
150 = h*w
h = 150/w
The complete paper's topic is:
Area = l*w
A2 = (w+2+2)*(H+1+1)
A2 = (w+4)*(H+2)
For H, substitute 150/W:
A2 = (w+4)*(150/w+2)
A2 = w(150/w+2) + 4(150/w+2)
A2 = 150 + 2w + 600w + 8
A2 = 2w = 600/w + 8 + 150
A2 = 2w = 600/w + 158
Calculate a difference with regard to w and set the outcome to 0:
A'2 = 2-600/w²+0
A'2 = 2-600/w²
0 = 2 - 600/w²
2 = 600/w²
2*w² = 600
w² = 600/2
w² = 300
w = 17.321
Remember that:
h = 150/w
h = 150/17.321
h = 8.660
Therefore, the paper's smallest dimensions are height=8.660in and width=17.321in.
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Help me with this pls 10 points
Answers
Answer:
48
Step-by-step explanation:
Add 84+48 to get 132. subtract 180 the total to the 132 to get 48.
Answer:
its not 10 points its says 8
Step-by-step explanation:
Input Output
6
0
3
6
2
12
Oy
Answers
Answer:
The second option. y = 3x +3
Step-by-step explanation:
※ x = -4
y = 3(-4) + 3
= -12 + 3
= -9
※ x = 3
y = 3(3) +3
= 9 + 3
= 12
Find the equation of the parabola with focus at f(0 -4) and directrix x=4
Answers
The equation of the parabola with focus at f(0 -4) and directrix x = 4 is
y² = 16x.
Define parabola.A parabola is a quadratic function graph. A parabola, according to Pascal, is a circle's projection. Galileo demonstrated that projectiles falling under the influence of uniform gravity have a path known as a parabolic path. Many bodily motions follow a curvilinear route that is shaped like a parabola. In mathematics, a parabola is any mirror-symmetrical planar curve that has an approximate U shape. The goal of this section is to comprehend the derivation of a parabola's standard formula, the several standard forms of a parabola, and the properties of a parabola.
Given
Focus at f(0, -4)
Directrix x = 4
As we know, the equation of a parabola with focus (a, 0) and directrix x = a
y² = 4ax.
y² = 4(4)x
y² = 16x
The equation of the parabola with focus at f(0 -4) and directrix x = 4 is
y² = 16x.
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For
f(x)= −3x5+1, f(–10)=7
7 is the answer but i dont have the work
Answers
Answer:
f(-10) = -299999
Step-by-step explanation:
Equation
f(x)= −3x^55+1
Given
x = - 10
Solution
You have to understand what f(x) means. When you put a value in for x, every x on the right is supplied with that value.
In this case I take the equation to mean what ever we are given in the brackets (in this case 10) is what goes into the x on the right. So the new equation is
f(-10) = -3*(-10)^5 + 1
(- 10) ^5 = - 100000
f(-10) = -300000 + 1
f(-10) = -299999
the variables r and s are inversely proportional, and r=7 when s=6. determine s when r=10.
Answers
If the variables "r" and "s" are inversely proportional and r=7 when s=6 , then when r = 10 , value of "s" will be 4.2 .
When the two variables are inversely proportional, their product is constant. That means, for two variables "r" and "s" , the it is represented in equation as :
⇒ r × s = k, where k is a constant ;
the value of variable "r" = 7 when s = 6,
First , we have to find the value of k:
⇒ k = r × s = 7 × 6 = 42 ;
So, for any value of r and s, the product "rs" will always be equal to 42.
When r = 10, we can use the equation to find s:
⇒ s = k/r = 42/10 = 4.2
Therefore , when r = 10 , the variable "s" is 4.2.
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Please help how do I do this because I don’t know
Graph the equation y = 2
Answers
Answer:
Horizontal line on the "2" line of the y axis.
Step-by-step explanation:
y=2 means y is constantly at 2, so it would be a horizontal line there.
Help me please ASAP
10) In 1950, the population of the United States
was 152 million people. In 1990, it was 250
million. Use a linear model to estimate the
population of the United States in 2030.
A) 326 million
B) 337 million
C) 348 million
D) 359 million
E) 360 million
Answers
Answer:
ok so it is e because
Step-by-step explanation: n 1950, the population of the United States
was 152 million people. In 1990, it was 250
million. Use a linear model to estimate the
population of the United States in 2030.
find the sum of the arithmetic series shown below 10+9+8… +(-255)
Answers
Answer:
−228
Step-by-step explanation:
10+9+8+−255
Add 10 and 9 to get 19.
19+8−255
Add 19 and 8 to get 27.
27−255
Subtract 255 from 27 to get −228.
−228