Answer:
6x^2 -2x -6
Step-by-step explanation:
f(x) = 6x^2 -4
g(x) = 2x+2
f(x) - g(x) = 6x^2 -4 - (2x+2)
Distribute the minus sign
6x^2 -4 - 2x-2
Combine like terms
6x^2 -2x -6
Answer:
b
Step-by-step explanation:
6x^2
2x
-4+2=-2
Find the area of each shaded region. Show your reasoning.
maybe we could answer if there waas a pic=]
fill in the blank (there's no word bank)
Step-by-step explanation:
Blank
1. Adjacent
2. Linear pair
3. linear
4. complementary
hope this answer helps you dear....may u have a great day ahead!
Amelia and Jamal share pizza in the ratio 3:5. Jamal eats 4 more slices than Amelia. How many slices does Jamal eat
The number of slices that Jamal eats will be 10 slices.
How to calculate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Let Amelia's share be x.
Jamal's share will be x + 4.
Therefore, the equation will be Illustrated as:
3/5 = x/(x + 4)
Cross multiply
5x = 3x + 12
5x - 3x = 12
2x = 12
Divide
x = 12 / 2
x = 6
Jamal's share will be
= 6 + 4.
= 10
Learn more about ratio on:
brainly.com/question/2328454
#SPJ1
Determine if the following sequences are geometric or arithmetic sequences?
Answer:
Step-by-step explanation:
The NY Knicks won 35 games out of 65 games. What is the probability that they win the next game?
Find the experimental probability of a player on the New York Liberty being over 73 inches.
The value of probability that they win the next game is,
⇒ 6/13
We have to given that;
The NY Knicks won 35 games out of 65 games.
Now, We can simplify as;
The possible value of to win next game is,
⇒ 65 - 35
⇒ 30
Thus, The value of probability that they win the next game is,
⇒ 30 / 65
⇒ 6/13
So, The value of probability that they win the next game is,
⇒ 6/13
Learn more about the probability visit:
https://brainly.com/question/13604758
#SPJ1
Answer this with explanation please
The measure of angle MTU m∠MTU is 114 degree.
What is the measure of angle MTU?From the figure in the diagram:
Measure of angle STU is 145 degrees and measure of angle STM is 31 degree.
m∠STU = 145°m∠STM = 31°m∠MTU = ?Since, angle STU composes or is the sum of angle STM and angle MTU.
To find angle MTU, simply subract angle STM from angle STU.
m∠STU = m∠STM + m∠MTU
Hence:
m∠MTU = m∠STU - m∠STM
Plug in the given values and simplify
m∠MTU = 145° - 31°
Subtract 31 from 145
m∠MTU = 114°
Therefore, angle MTU measure 114°.
Learn about complementary angles here: https://brainly.com/question/4410854
#SPJ1
(v-7)(v+5)(v-3)=0 solve the quadraticequation
A quadratic equation, or second-order polynomial equation with a single variable, has the form ax^2 + bx + c = 0. The solution to the given equation is v = 7, -5 and 3
Solving quadratic equations?The form ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given the quadratic expression below:
(v-7)(v+5)(v-3)=0
Required
The solution to the system of equation
Equate each expression to zero calculate the value of 'v' as shown:
v - 7 = 0
v = 0 + 7
v = 7
Also, v + 5 = 0
v = 0 - 5
v = -5
Similarly, v - 3 = 0
v = 0 + 3
v = 3
Hence the solution to the given equation is v = 7, -5 and 3
Learn more on quadratic equation here; https://brainly.com/question/1214333
#SPJ1
A personnel director interviewing 12 senior engineers for five job openings has scheduled seven interviews for the first day and five for the second day of interviewing. Assume that the candidates are interviewed in a random order.
(a) What is the probability that x of the top four candidates are interviewed on the first day?
h(N; 5, 5, 12)
h(x; 5, 12, 5)
h(N; 7, 12, 5)
h(x; 7, 5, 12)
(b) How many of the top four candidates can be expected to be interviewed on the first day? (Round your answer to two decimal places.)
Answer:
a) h(x; 7, 5, 12) = (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)
b) 2.92
Step-by-step explanation:
a)
Here
Number of interviewees = N = 12
Number of job openings = M = 5
Interviews schedules for the first day = n = 7
N − M = 12 - 5 = 7
Using hypergeometric distribution:
Let X be the no. top four candidates interviewed on first day.
The probability mass function of X:
P(X = x) = \((^{M} C_{x})\) \((^{N-M} C_{n-x})\) / \((^{N} C_{n})\)
It can be written as:
h(x; n, M, N) = \((^{M} C_{x})\) \((^{N-M} C_{n-x})\) / \((^{N} C_{n})\)
= (5Cx) (7C7-x) / (12C7)
= (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)
h(x; 7, 5, 12) = (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)
b)
The expectation is: E(X) = np
E(X) = n * M/N
= 7 * 5/12
= 7 * 0.41667
= 2.9167
A GROUP OF 6 ADULTS PAY A TOTAL OF $105 FOR THEIR ADMISSION TO A MUSEUM. EACH PERSON HAS A COUPON FOR $5 OFF THE REGULAR ADMISSION PRICE. THEY WANT TO KNOW WHAT THE REGULAR ADMISSION PRICE IS FOR ONE ADULT.
LET A EQUAL THE REGULAR ADMISSION PRICE. WRITE AN EQUATION THAT REPRESENTS THE SITUATION
The regular admission price for one adult is $17.50.
We have,
Let's first determine the total cost of admission after the coupons have been applied.
Since each person has a coupon for $5 off, the total discount for the group is $5 x 6 = $30.
The total cost of admission after the discount.
$105 - $30
= $75.
Let A be the regular admission price.
Since each person paid the same price after the discount, we can set up the following equation:
6(A - $5) = $75
We subtract $5 from the regular price A because that is the amount of the coupon discount.
We can simplify the equation as follows:
6A - $30 = $75
6A = $105
A = $17.50
Therefore,
The regular admission price for one adult is $17.50.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
99 6th graders took a test the median score was 72 how many students scored greater than 72
For the given median, there are 50 students who scored greater than 72.
What is median?
The median is a measure of central tendency in a set of numerical data. It is the value that separates the higher half of the data from the lower half when the data is arranged in order from least to greatest or greatest to least.
We are given that 99 6th graders took a test and the median score was 72. We want to find out how many students scored greater than 72.
Let the scores be denoted by S1, S2, ..., S99. We can sort these scores in order from least to greatest:
S1 ≤ S2 ≤ ... ≤ S99
Since the median score is 72, exactly half of the scores are above 72 and half are below 72. Thus, the 50th score in the sorted list is 72.
Since there are 99 scores in total, we can approximate the number of students who scored above 72 by dividing the total number of students by 2:
\($\frac{99}{2} = 49.5$$\)
This means that approximately 49.5 students scored above 72.
Since 0.5 rounds up to 1, we round 49.5 up to 50. Therefore, approximately 50 students scored greater than 72.
To learn more about median visit:
https://brainly.com/question/26177250
#SPJ1
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of x in the given right triangle HJK include the following: C. 10.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Hypotenuse, x = 5 × 2
Hypotenuse, x = 10.
Read more on 30-60-90 triangle here: brainly.com/question/30283450
#SPJ1
The measure of an angle is three times the measure of its supplementary angle. What is the measure of each angle?
Answer:
135 degree
Step-by-step explanation:
180 - 45 = 135 degrees for the larger angle.
Beth can swim 2 laps in 7 minutes.What id beths rate in minutes per lap
A.1/2 of a minute per lap.
B.7/1 minutes per lap
C.7/2 minutes per lap
D. 2/7 of a minute per lap
Answer:
C) 7/2 minutes per lap
Step-by-step explanation:
7 laps/ 2minutes. To find how many minutes it takes Beth to swim one lap, which is her in minutes per lap, you have to divide 7/2 to get 3.5 min/1 lap, or 7/2 min/1 lap.
Determine the intercepts of the graph please be sure
Answer:
X= (_7, 0)
Y= (0, 2
Step-by-step explanation:
We meet again
What is the interval of increase of the graphed function?
Answer:
b.
Step-by-step explanation:
The function stops increasing when it reaches its peak at x = -1. The appropriate interval is the one shown in the attachment.
For x-values more positive than -1, the function is decreasing (has negative slope).
please help me solve this problem
The features related to vectors are listed below:
Case A: u' = (- 4√41 / 41, - 5√41/ 41)
Case B: Tip coordinantes of vector v: (x, y) = (10, 10)
Case C: r = 11.402
How to determine vectors
In this question we must determine three features related to vectors: (a) unit vector, (b) the definition of a vector based on the coordinates of its base and its tip, (c) The magnitude of a resulting vector.
Case A - Unit vector
Unit vectors are vectors with magnitude 1, for the case of vector u we have the following definition:
u' = u / ||u||
Where:
u' - Unit vector.u - Vectoru - ||u|| - Magnitude of the vector.Please notice that the magnitude of the vector is determined by Pythagorean theorem:
r = √[(Δx)² + (Δy)²]
Where:
r - MagnitudeΔx - Change in the x-direction.Δy - Change in the y-direction.Thus, the unit vector of u is:
u' = (- 4, - 5) / √[(- 4)² + (- 5)²]
u' = (- 4, - 5) / √41
u' = (- 4 / √41, - 5 / √41)
u' = (- 4√41 / 41, - 5√41/ 41)
Case B - Definition of a vector
This can be found easily by vector subtraction:
v = Tip coordinates - Base coordinates
(3, 4) = (x, y) - (7, 6)
(x, y) = (3, 4) + (7, 6)
(x, y) = (10, 10)
Case C - Magnitude of a vector
The magnitude is found by means of Pyhtagorean theorem:
r = √[(- 4 - 3)² + (- 5 - 4)²]
r = √[(- 7)² + (- 9)²]
r = 11.402
To learn more on unit vectors: https://brainly.com/question/28028700
#SPJ1
The length of the longer leg of a 30 60 90 triangle is 6. The hyp is 9.
State the solution in Simple Root Form:
State the solution to the nearest tenth:
Step-by-step explanation:
there is something severely wrong with the problem definition.
when the Hypotenuse = 9, there is no 30-60-90 triangle with a leg = 6.
and when we are just focusing that this is a right-angled triangle with the Hypotenuse = 9, then 6 cannot be the longer leg.
it is also not clear what the solution is supposed to be. the 2nd leg ? the area ? the perimeter ? the height(s) ? ...
what ?
so, all I can do here is to show you why I said what I said :
30-60-90 triangle with Hypotenuse = 9
then the longer leg is opposite of the 60° angle and therefore sin(60)×9 = 7.794228634...
the shorter leg is opposite of the 30° angle and therefore sin(30)×9 = 0.5×9 = 4.5
a right-angled triangle with Hypotenuse = 9, one leg = 6 gives us per Pythagoras for the other leg
9² = 6² + leg²
81 = 36 + leg²
45 = leg²
leg = sqrt(45) = 6.708203932...
so, you see, as stated above, there is no leg with the length 6 in such a 30-60-90 triangle.
and in a more general right-angled triangle, if one leg = 6, then the other leg is actually longer.
therefore, there is everything wrong with the problem definition.
Ed bought some
t-shirts at a yard sale.
He gave 3 to his sister
and had 6 left. How
many t-shirts did Ed
buy at the yard sale?
Answer:
9. he bought 9.
which ordered pair is not graphed below???
A. 3,2
B. 2.5
C. 5,2
D. 2,3
Answer:
5,2
Step-by-step explanation:
if you look for the point 5,2 its not there
hope this helps <3
Answer:
C. 5,2
Step-by-step explanation:
We can find out the ordered pairs that are marked in the picture first before finding the correct answer.
To write an ordered pair, we follow the format: (x, y).
Thus, the ordered pairs in the picture are:
(2, 5)
(2, 3)
(3, 2)
If we check from the options, the only ordered pair not in the picture is (5, 2) so that is the answer.
the area of a rectangular place mat is 98 inches its length is seven inches longer than the width. find the length and width of the place mat
A
Answer:
width is 7, length is 14
Step-by-step explanation:
x(x+7) = 98
x^2 + 7x = 98
x^2 + 7x - 98 = 0
( x + 14 )( x - 7 ) = 0
x+14=0 results in negative measures
x-7=0 ---> x= 7
width is 7, length is 14
Find a • b. a = <5, 2>, b = <4, 5> (2 points) a <20, 10> b <9, 7> c -10 d 30
The dot product of vectors a and b is option D. 30.
How did we get the value?To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.
Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:
a • b = (5 x 4) + (2 x 5)
= 20 + 10
= 30
Therefore, the dot product of vectors a and b is 30.
learn more about product of vectors: https://brainly.com/question/30394406
#SPJ1
Which measurement is most accurate to describe the distance from Los Angeles to New York City?
4,000 km
6,000 m
8,000 mm
50 km
Answer:
4,000km
Step-by-step explanation:
If John solved the equation x? - 10x + 8 = 0 by completing the
square, one of the steps in his process would be
(1) (x-5)^2 = -8
(2) (x-5)^2 = 17
(3) (x+ 4)^2 = 10x
(4) (x + 4)^2 = 10x + 16
Answer:
\((x - 5)^{2} =17\)
Step-by-step explanation:
\(x^{2} -10x = -8 \ add \ and \ subtract \ 25;\\x^2-10x+25-25= -8\\(x-5)^2 - 25 = -8\\(x-5)^2 = 17\\x-5=+\ \sqrt{17} \\\x_{1,} _{2} =5+\sqrt{17}\)
The expression 2362 x 1= 2362 is true because of what property
Answer:
The multiplication property of 1
Step-by-step explanation:
Any number that multiplied by one gives the number
Find the length of side AB. Round to the nearest hundredth inch.
The value of length of side AB is,
⇒ AB = 5 units
We have to given that;
The figure is shown a trapezoid.
Hence, By using Pythagoras theorem we get;
⇒ AB² = 4² + (5.25 - 2.25)²
⇒ AB² = 16 + 3²
⇒ AB² = 16 + 9
⇒ AB² = 25
⇒ AB = √25
⇒ AB = 5 units
Therefore, The value of length of AB is,
⇒ AB = 5 units
Learn more about the Pythagoras theorem visit:
https://brainly.com/question/343682
#SPJ1
Statistics indicate that the world population sinceworld war II has been growing exponentially. If weassume exponential growth, the world population canbe modeled by P (t) = 6(1.025)^t where P(t) isthe world population in billions and t is the time inyears since 1995.When (which year) will the population reach 12 billion?{your final answer just number without decimal}
P(t) = 6 ( 1.025 ) ^t
Let p(t) = 12 since the equation is given in billions
12 = 6 ( 1.025 ) ^t
Divide each side by 6
12/6 = 6/6 ( 1.025 ) ^t
2 = ( 1.025 ) ^t
Now take the natural log of each side
ln(2) = ln( ( 1.025 ) ^t)
Using the exponent rule ln( a^b) = b ln a
ln (2) = t ln ( 1.025)
Divide each side by ln(1.025)
ln (2) / ln(1.025) = t
28.01703= t
Rounding to the nearest year
28 years from the start
The start was 1995
1995+28 = 2023
The year would be 2023
Krystal categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The percentages she spent in each category are pictured below.Rent26%Food20%Fun15%Other39% If Krystal spent a total of $2500 this month, how much did she spend on Fun?
Observe the given data carefully.
Krystal's total expenditure is $2500,
\(T=2500\)Given that the percentage expenditure on Fun is,
\(15\text{ percent}\)Obtain the 15% of total expenditure,
\(\begin{gathered} =15\text{ percent of }2500 \\ =\frac{15}{100}\cdot2500 \\ =15\cdot25 \\ =375 \end{gathered}\)Thus, it can be concluded that Krystal spent $375 on Fun.
Which inequality represents the situation described below?
The distance, d, is less than 200 miles.
A. d ≥ 200
B. d > 200
C. d ≤ 200
D. d < 200
Hello!
The distance, d, is less than 200 miles.
B. d > 200
Which number from the set {1, 2, 3,4} makes the inequality 5x² > 12x + 9 true for x?
Is it 1 or 2 or 3 or 4?
Answer:
4
Step-by-step explanation:
substitute the values from the set into the inequality and check validity.
x = 1
5(1)² > 12(1) + 9
5(1) > 12 + 9
5 > 21 ← False
x = 2
5(2)² > 12(2) + 9
5(4) > 24 + 9
20 > 33 ← False
x = 3
5(3)² > 12(3) + 9
5(9) > 36 + 9
45 > 45 ← False
x = 4
5(4)² > 12(4) + 9
5(16) > 48 + 9
80 > 57 ← True
thus the value 4 from the set makes the inequality true
Find the height of the tower using the information given in the illustration.
using SOH CAH TOA
Tan 85.144 =h/130
h=tan 85.144*130
h=1530.19 fr