Answer:
Step-by-step explanation:
Use the distance formula for coordinate geoemetry and the fact that x1 = 3, y1 = 5, x2 = 6 and y2 = 8 to fill in the formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
fills in accordingly:
[tex]d=\sqrt{(6-3)^2+(8-5)^2}[/tex]
which simplifies a bit to
[tex]d=\sqrt{(3)^2+(3)^2}[/tex]
which is
[tex]d=\sqrt{18}[/tex]
The square root of 18 simplifies down to [tex]3\sqrt{2}[/tex], which is 4.2426 in decimal form
Answer:
4.24 units
Step-by-step explanation:
We can use the distance formula to solve this.
Distance formula: d = √((x₁ - x₂)² + (y₁ - y₂)²), where (x₁, y₁) and (x₂, y₂) are the two coordinates.
Plug in: d = √((3 - 6)² + (5 - 8)²)
Subtract: d = √((-3)² + (-3)²))
Square: d = √(9 + 9)
Add: d = √18
Square root: d = 4.24264... ≈ 4.24 units
Solve this absolute value equation and show all work.
1) 9 + |2x - 3| = 7
2) 3 + |2x - 4| = 15
Answer:
For the equation
1) [tex]9 + | 2x - 3 | = 7[/tex]
x=0.5 and x=2.5
For the equation
2) [tex]3 + | 2x - 4 | = 15[/tex]
x=8 and x=-4
Step-by-step explanation:
For the equation
1) [tex]9 + | 2x - 3 | = 7[/tex]
we have 2 cases
Case 1 [tex](2x - 3)> 0[/tex]
[tex]9 + 2x - 3 = 7\\2x = 7 + 3-9\\2x = 1\\x = 0.5[/tex]
Case 2 [tex](2x - 3) <0[/tex]
[tex]9 - (2x - 3) = 7\\-2x + 3 = 7-9\\-2x = 7-9-3\\-2x = -5\\x = 2.5[/tex]
For the equation
2) [tex]3 + | 2x - 4 | = 15[/tex]
we have 2 cases
Case 1 [tex](2x - 4)> 0[/tex]
[tex]3 + 2x - 4 = 15\\2x = 15 + 4-3\\2x = 16\\x = 8[/tex]
Case 2 [tex](2x - 4) <0[/tex]
[tex]3 - (2x - 4) = 15\\-2x +4 = 15-3\\-2x = 15-3-4\\-2x = 8\\x = -4\\[/tex]
Write an equation to solve each problem and then solve it. b A 25-foot long board is to be cut into two parts. The longer part is one foot more than twice the shorter part. How long is each part?
Answer:
shorter part: 12 ftlonger part: 13 ftStep-by-step explanation:
Let s represent the length of the shorter part (in feet). Then the longer part has length (s+1), and the total length of the two parts is ...
s + (s+1) = 25
2s = 24 . . . . . . . subtract 1, simplify
s = 12 . . . . . . . . . divide by 2; the length of the shorter part
s+1 = 13 . . . . . . . the length of the longer part
The shorter part is 12 feet long; the longer part is 13 feet long.
_____
Comment on this problem type
You will note that the smaller number is half the difference of the total length (25) and the difference in lengths (1). This is the generic solution to a "sum and difference" problem. The smaller number is half the difference of the given numbers, and the larger number is half their sum: (25+1)/2 = 13.
Answer:
8 and 17
Step-by-step explanation:
Let's say the smaller number is x. The question says "The longer part is one foot more than twice the shorter part" so we reverse that using x which becomes x+2x+1=25 and x=8 so 8+8*2+1=25 => 8+17=25 so the answer is 8 and 17, please like and 5 star rate
I need help ty ty ty :-)
Answer:
First Answer: y + 4 = -3(x - 3)
Second Answer: y - 5 = (-3/4)(x - 4)
Step-by-step explanation:
That answer was correct :)
Answer:
1. y + 4 = -3(x - 3)
2. Second Answer: y - 5 = (-3/4)(x - 4)
:)))
you are trying to recreate flubber because you are obsessed with that movie and you thought it was the coolest. you take 70% slime solution and some 40% slime solution to obtain 120 gallons of a 50% slime solution. how much of the 40% slime solution do you need to create your mixture?
a. 40
b. 80
c. 50
d. 70
can you help me solve?
Let [tex]x[/tex] be the amount (gal) of the 40% slime solution you end up using. You want to end up with 120 gal of the 50% solution, so that you would use [tex]120-x[/tex] gal of the 70% solution.
You want the final solution to consist of 50% slime, or 60 gal of slime. Each gal of the 40% solution contributes 0.4 gal of slime, while each gal of the 70% solution contributes 0.7 gal of slime. This means
[tex]0.4x+0.7(120-x)=0.5\cdot120=60[/tex]
[tex]\implies0.4x+84-0.7x=60[/tex]
[tex]\implies24=0.3x[/tex]
[tex]\implies x=80[/tex]
so the answer is B.
Please help me?????????
Given an implication of the form [tex]P\implies Q[/tex]
The equivalent implication is [tex]\lnot Q \implies \lnot P[/tex]
So, you have to negate both propositions and invert the order:
If a triangle is not isosceles, then it's not equilateral.
Need help ASAP!! Use the graph to find the solution of the system of equations what is the solution?
A.(0,-4)
B.(0,-1)
C.no solution
D.(4,-3)
The solution is the point where the two lines meet. The answer is D.
Find the Geometric Mean of 8 and 50. Be sure to show your work!
Answer:
20
Step-by-step explanation:
The geometric mean of n numbers is the n-th root of their product. For two numbers, it is the square root of their product:
geometric mean = √(8·50) = √400 = 20
The answer is: 20
My work: √8*50 = √400 = 20
You have to take the square root of 8 multiplied by 50. With that, you would get 400, which is still squared because you have to get the numbers inside of the square root to one number. After that, you can now take the square root of the number that is inside of it, which in this case it is 400. The square root of 400 is 20.
I hope this helps!
Please help with this question!! I am out of points now!! I need this!
Answer:
m∠QRS = 30°
Step-by-step explanation:
An inscribed angle has half the measure of the intercepted arc.
(arc QS)/2 = 60°/2 = 30°
The measure of angle QRS is 30°.
What is the value of term a^4?
Answer:
135Step-by-step explanation:
[tex]\text{We have the recursive formula of a series:}\\\\a_1=5\\a_n=3a_{n-1}\\\\a_2=3a_{2-1}=3a_1\to a_2=3(5)=15\\\\a_3=3a_{3-2}=3a_2\to a_3=3(15)=45\\\\a_4=3a_{4-1}=3a_3\to a_4=3(45)=135[/tex]
George Box, a famous statistician, once said, "All models are wrong, but some are useful." What did George Box mean by this statement?
Answer:
a model is an estimate or approximation of a data set. In the real world, there are too many variables to know exactly what will happen. However, if a model is a good fit, then it can be used to make predictions about what will happen. With a useful model, a predicted value should be a good estimate of an observed value.
Step-by-step explanation:
Took the assignment
George Box's statement "All models are wrong, but some are useful" suggests that while models are imperfect, they still offer valuable insights and utility in understanding complex systems.
George Box's statement "All models are wrong, but some are useful" acknowledges the inherent imperfections of models, emphasizing that they are simplified representations of reality.
Models, by nature, cannot perfectly capture every detail of a complex system.
However, despite their inaccuracies, models still hold utility in providing insights and aiding decision-making processes.
This perspective suggests that while models may not be entirely accurate, they can still offer valuable understanding and predictive power.
Box's statement encourages a balanced approach, where users recognize the limitations of models while leveraging their practical usefulness.
In essence, it underscores the importance of not dismissing models due to their imperfections but rather using them judiciously in specific contexts where they can provide meaningful insights.
The probability of winning a prize at a school raffle is 0.62. What is the probability of not winning a prize
at the raffle?
a. 0.48 c. 3.8
b. 0.38 d. 38
We will see that the probability of not winning the prize is equal to 0.38, so the correct option is b.
How to get the probability of not winning?
In this experiment, we have two possible outcomes.
One outcome is winning the prize, with a probability P and the other outcome is losing, with a probability Q.
Because there are only two outcomes we will have that:
P + Q = 1
We know that P = 0.62, replacing that we get:
0.62 + Q = 1
Q = 1 - 0.62 = 0.38
So we conclude that the probability of not winning the prize is 0.38, then the correct option is b.
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
Juanita and Nina are bowling together. The probability of Juanita getting a strike next game is 24%. The probability of Nina getting a strike next game is 0.17. Which of these events is more likely?
(Choice A)
A
Juanita gets a strike next game.'
(Choice B)
B
Nina gets a strike next game.
(Choice C)
C
Neither. Both events are equally likely.
Answer:
Step-by-step explanation:
0.24 is greater than 0.17, and therefore J's getting a strike next game is more likely.
The event that is more likely is Juanita gets a strike next game.
What is a probability?
Probability is the likelihood that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that Juanita would have a strike is higher than that of Nina. Thus, it is more likely that Juanita gets a strike next game.
To learn more about probability, please check: https://brainly.com/question/13234031
What is the sum of the infinite geometric series represented by
A. 240
B. 135
C. 360
D. 720
Answer:
the answr is a 240
Step-by-step explanation:
beacuse you have to desept the question
Answer:
240 is the answer
How many solutios are there for the following triangle:
A=9 C=4 c=12*
Answer Choices:
a. 0 solutions
b. 1 solution
c. 2 solutions
d. infinite solutions
I would personally go w/ b or c
There is exactly one solution for this triangle, and the correct answer is: b. 1 solution
To determine the number of solutions for the given triangle with angles A, C, and side c, we can use the Law of Sines, which states that in any triangle:
[tex]\[\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}\][/tex]
Given:
- Angle A = 90 degrees (since it is a right angle, we assume A is the right angle for the purpose of this solution)
- Angle C = 4 degrees
- Side c = 12 units (opposite to angle C)
Since angle A is 90 degrees, we know that this triangle is a right-angled triangle. In a right-angled triangle, the other two angles must add up to 90 degrees. We are given one of those angles, C, which is 4 degrees. Therefore, the third angle, B, which is opposite side b, can be calculated as:
[tex]\[B = 90^\circ - C = 90^\circ - 4^\circ = 86^\circ\][/tex]
Now, we have all three angles: A = 90°, B = 86°, and C = 4°. The sum of angles in any triangle is 180 degrees, and in this case:
[tex]\[A + B + C = 90^\circ + 86^\circ + 4^\circ = 180^\circ\][/tex]
This confirms that the angles are consistent with the angles of a triangle.
Next, we can find the length of side b using the Law of Sines:
[tex]\[\frac{\sin(B)}{b} = \frac{\sin(C)}{c}\][/tex]
[tex]\[\frac{\sin(86^\circ)}{b} = \frac{\sin(4^\circ)}{12}\][/tex]
Since 86° and 4° are acute angles and sine of an acute angle is unique, there will be a unique positive value for b. This means there is only one possible length for side b that will satisfy the conditions of the triangle.
Therefore, there is exactly one solution for this triangle, and the correct answer is:
b. 1 solution
Please please help me
Answer:
BF = 30
Step-by-step explanation:
Each midsegment is half the length of the parallel side of the triangle. CE is 60 and is parallel to BF, so BF = 60/2 = 30.
Rewrite sqr-100 +26 in complex number notation
Answer:
26 + 10i is your answer.
For which intervals is the function negative? Select each correct answer.
ANSWER
(1,4)
(-∞,-3)
EXPLANATION
The interval where a portion of the graph is below the x-axis is where the graph is negative.
From the graph , the curve is below the x-axis on the interval (-∞,-3). Hence the graph is negative on this interval.
Also the graph is below the x-axis on the interval (1,4). This is also another interval where the graph is negative.
In the first ten months of the year, people took out 427,113 books from the Brookton Library. The librarian would like to set a new record and have 500,000 books go out in one year. If 38,264 books are taken out in November, how many must go out in December to meet the librarian?s goal?
Answer:
34,623
Step-by-step explanation:
427,113 + 38,264 = 465377
500,000 - 465377 = 34,623 books in December must go out to meet the librarian's goal.
Identify the measure of arc HD◠.
Answer:
The measure of arc HD is 20°
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
In the triangle of the figure , the measure of the third interior angle is equal to
180°-92°-38°= 50°
50°=(1/2)[(102+18)°-arc HD]
100°=[120°-arc HD]
arc HD=120°-100°=20°
Answer:
arc HD = 20°
Step-by-step explanation:
Let point N be the point where secant RL intersect the circle, point M be the point of intersection for chords NL and KH, and point S be the vertex of the triangle formed by secants KH and RD.
It is given that m∠SRM = 38∘ and m∠RMS = 92∘. Use the Triangle Sum Theorem to determine m∠MSR.
m∠MSR = 180° − 92∘ − 38∘ = 50∘
It is also given that mPN = 18∘ and mNK = 102∘. So, mPK = 18∘ + 102∘ = 120∘.
If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs. So,
m∠MSR= 1 /2 (mPK − mHD)
Substitute the known values and solve for mHD.
50∘ = 1/2 (120∘ − mHD)
Multiply by 2.
100 = 120∘ − mHD
Simplify.
mHD = 20
Therefore, the measure of arc HD is 20∘.
Evaluate P(5, 2)
20
60
240
10
P(5,2) = n! /(n-r)!
n = 5, r = 2:
= (5 x 4 x 3 x 2 x 1 ) / 3 x 2 x 1
Cancel out common factors:
= 5 x 4 = 20
The answer is 20.
Answer:
P (5,2) = 20
Step-by-step explanation:
First of all, we must understand two basic concepts:
A permutation is the variation of the order or position of the elements of an ordered set or a tuple.
The factorial function (symbol:!) Means that descending numbers are multiplied.
The formula to solve the permutation is:
[tex]\frac{n!}{(n-r)!}[/tex]
where "n" is the number of things you can choose, and you choose "r" from them (it cannot be repeated, order matters).
In the given case ...
P (n, r) = [tex]\frac{n!}{(n-r)!}[/tex]
Being n = 5, and r = 2
[tex]P(5,2)=\frac{5!}{(5-2)!}=\frac{5!}{3!}=\frac{5*4*3!}{3!}=5*4=20[/tex]
P (5,2) = 20
-------------------------------------------------- ----------------------------
I hope this helps!
PLEASE HELP ASAP 60 POINTS + BRAINLIEST TO RIGHT/BEST ANSWER!
Answer:
see explanation
Step-by-step explanation:
Given
P(x) = x³ + 7x² + 4x, then
P(a) = a³ + 7a² + 4a ← substitute x = a into polynomial
To evaluate P(- 2) substitute a = - 2 into P(a)
P(- 2) = (- 2)³ + 7(- 2)² + 4(- 2) = - 8 + 28 - 8 = 12
Since P(- 2) ≠ 0 then (x + 2) is not a factor of P(x)
Answer:
12
Step-by-step explanation:
(-2)³ + 7(-2)² + 4(-2)
12
Which of these is an example of a final good?
Answer:
The answer on Plato is C as this is a final product
Step-by-step explanation:
These are the choices on Plato
A. wood
B. steel
C. needle
Find the volume and surface area of the composite figure. Give your answer in terms of π. HELP ASAP!!
Answer:
Part 1) The volume of the composite figure is [tex]620.7\pi\cm^{3}[/tex]
Part 2) The surface area of the composite figure is [tex]273\pi\ cm^{2}[/tex]
[tex]V=620.7\pi\cm^{3}, S=273\pi\ cm^{2}[/tex]
Step-by-step explanation:
Part 1) Find the volume of the composite figure
we know that
The volume of the figure is equal to the volume of a cone plus the volume of a hemisphere
Find the volume of the cone
The volume of the cone is equal to
[tex]V=\frac{1}{3} \pi r^{2} h[/tex]
we have
[tex]r=7\ cm[/tex]
Applying Pythagoras Theorem find the value of h
[tex]h^{2}=25^{2} -7^{2} \\ \\h^{2}= 576\\ \\h=24\ cm[/tex]
substitute
[tex]V=\frac{1}{3} \pi (7)^{2} (24)[/tex]
[tex]V=392 \pi\cm^{3}[/tex]
Find the volume of the hemisphere
The volume of the hemisphere is equal to
[tex]V=\frac{4}{6}\pi r^{3}[/tex]
we have
[tex]r=7\ cm[/tex]
substitute
[tex]V=\frac{4}{6}\pi (7)^{3}[/tex]
[tex]V=228.7\pi\cm^{3}[/tex]
therefore
The volume of the composite figure is equal to
[tex]392 \pi\cm^{3}+228.7\pi\cm^{3}=620.7\pi\cm^{3}[/tex]
Part 2) Find the surface area of the composite figure
we know that
The surface area of the composite figure is equal to the lateral area of the cone plus the surface area of the hemisphere
Find the lateral area of the cone
The lateral area of the cone is equal to
[tex]LA=\pi rl[/tex]
we have
[tex]r=7\ cm[/tex]
[tex]l=25\ cm[/tex]
substitute
[tex]LA=\pi(7)(25)[/tex]
[tex]LA=175\pi\ cm^{2}[/tex]
Find the surface area of the hemisphere
The surface area of the hemisphere is equal to
[tex]SA=2\pi r^{2}[/tex]
we have
[tex]r=7\ cm[/tex]
substitute
[tex]SA=2\pi (7)^{2}[/tex]
[tex]SA=98\pi\ cm^{2}[/tex]
Find the surface area of the composite figure
[tex]175\pi\ cm^{2}+98\pi\ cm^{2}=273\pi\ cm^{2}[/tex]
For every pound a company spends on advertising, it spends ?0.75 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.
Answer:
The ratio is equal to [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Let
x----> the amount spent on advertising
y----> the amount spent on its website
The ratio is equal to x/y
Remember that
[tex]0.75=\frac{3}{4}[/tex]
so
[tex]\frac{1}{(3/4)}=\frac{4}{3}[/tex]
PLEASE HELP ME ON THESE 2 QUESTIONS!!!
THANK U!!!
Answer:
Step-by-step explanation:
You might see this a bit easier if you change the 5/4 * pi into degrees.
pi/180 = 5/4*pi / x This is the proportion. Change 5/4 into a decimal
pi/180 = 1.25 *pi / x Cross multiply
x * pi = 1.25 pi * 180 Divide by pi
x = 1.25 * 180
x = 225 degrees.
The fraction of the area of the sector is angle/360
The fraction of the area of the sector is 225/360
The fraction of the area area of the sector is 5/8 Reduced.
225: 3*3*5*5
360 = 2*2*2*5*3 *3
Cancel out the common factors
3 * 3 * 5
which leaves 5/8
Two
-3x^2 + 5x - 2 - 2x^2 + 4x + 2
- 5x^2 + 9x (the 2's cancel)
a = - 5
b = 9
c = 0
A chord of a circular clock is 48 inches long, and its midpoint is 7 inches from the center of the circle. What is the radius of the clock to the nearest whole number?
ANSWER
The radius is 25 inches
EXPLANATION
From the diagram, the radius of the circle is AC.
From the Pythagoras Theorem,
[tex] {r}^{2} = {7}^{2} + {24}^{2} [/tex]
[tex]r^{2} = 49 + 576[/tex]
Simplify
[tex]r^{2} = 625[/tex]
Take positive square root,
[tex]r = \sqrt{625} [/tex]
[tex]r = 25[/tex]
Hence the radius is 25 inches
Adriana's computer code 20% less than jocelyn's computer. Adriana's computer cost $640. Adriana's computer cost 15% more than corbins computer. Write an equation that could be used to find the cost of jocelyn's computer
Answer:
640 = 0.80·j
Step-by-step explanation:
Let j represent the cost of Jocelyn's computer (in dollars). Adriana's computer cost 20% less, so has a cost that is 0.80·j. We are told that amount is $640, so we can write the equation ...
640 = 0.80·j
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Simplify.
Answer: [tex]\bold{B)\quad \dfrac{x-2}{x+1}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x^2+5x-14}{x^2+8x+7}\\\\\\=\dfrac{(x+7)(x-2)}{(x+7)(x+1)}\\\\\\=\dfrac{x-2}{x+1}[/tex]
99 PLZ HELP BRAINLIEST Which strategy would not correctly solve this story problem?
There are 14 bikes for sale at a bicycle store. Four of the bikes are black, 5 are white, and the rest are red. How many bikes are red?
A.
Translate into an equation. 4 + 5 + r = 14
B.
Use logical reasoning. There were 14 bikes to start with. Subtract the number of black bikes (4) and subtract the number of white bikes (5). The remaining bikes must be red.
C.
Work backward. Start with 14 bikes and add 4. Then subtract 5. The number left is the number of red bikes.
D.
Draw a diagram. Draw 14 circles. Cross out 4 of the circles and then cross out 5 more circles. Color the remaining circles red.
Which strategy would not correctly solve this story problem?
Billy put up some balloons for a party. He had 4 times as many green balloons as red ones. There were 3 red balloons. During a game, 2 green balloons popped. Then another 5 green balloons popped. How many green balloons did Billy have left?
A.
Use objects to model the problem. Use toothpicks to represent the green balloons. Count out a total of 4 groups of 3 toothpicks. Remove 2 toothpicks and then 5 more. Count the remaining toothpicks to find the number of green balloons left.
B.
Work backwards. Start by adding the number of green balloons that popped (5 + 2) Then multiply the sum by 4. Subtract the number of red balloons (3) and that gives the number of green balloons that were left.
C.
Use logical reasoning. Step 1. Multiply 3 × 4 to figure out the total number of green balloons. Step 2. Add 2 + 5 to figure out how many green balloons popped. Step 3. Subtract the sum in Step 2 from the product in Step 1 to find out the number of green balloons that were left.
D.
Translate into an equation. (3 × 4) – (2 + 5) = g
Which strategy would not correctly solve this story problem?
Comic books cost $1, paperback books cost $3, and hardcover books cost $5 at the used book store. Sara bought 2 comic books, 5 paperbacks, and 2 hardcover books. How much money did Sara spend?
A.
Use objects to model the problem. Use coins to represent $1. Drop 1 coin into a jar 2 times for the cost of comic books. Drop 3 coins into the jar 5 times for the cost of the paperbacks. Drop 5 coins into the jar 2 times for the cost of the hard cover books. Count the coins in the jar.
B.
Draw a diagram. Draw 2 squares and write $1 inside each. Draw 5 circles and write $3 inside each. Draw 2 triangles and write $5 inside each. Add all the dollar amounts inside the shapes to find the total Sara spent.
C.
Use logical reasoning. Sara bought 2 comic books at $1 each for a total of $2. She bought 5 paperbacks at $3 each for a total of $15. She bought 2 hard cover books at $5 each for a total of $10. So Sara adds $2 + $15 + $10 to find the total amount she spent.
D.
Translate into an equation. (1 + 3 + 5) × (2 + 5 + 2) = n
Answer:
is this all apart of the answers or separate questions??
Step-by-step explanation:
1. B
2.C
3.C
4.A
5.D
lim (-x^2 + 6x-8)
x->-3
[tex]\bf \lim\limits_{x\to 3}~-x^2+6x-8\implies \lim\limits_{x\to 3}~-(3)^2+6(3)-8\implies 1[/tex]
Answer:
2///////////////////////////