Answer:
(−1, –1.25), (5, –2.75)
Step-by-step explanation:
If "slope-intercept form" is mentioned, then we already know that the function rule is that of a straight line with slope m and y-intercept b.
As we go from (−1, –1.25) to (5, –2.75), x increases by 6 and y decreases by 1.50. Thus, the slope, m, is m = rise / run = -1.50 / 6, or m = -0.25 or -1/4.
Choosing one of the given points at random: (8, -3.5), we start with the slope-intercept form y = mx + b and substitute -1/4 for m, 8 for x and -3.5 for y: y = mx + b becomes -3.5 = (-1/4)(8) + b. Then -3.5 + 2 = b, or b = -1.5.
The desired equation is y = (-1/4)x - 3/2, or y = -0.25x - 1.5
To write a function rule in slope-intercept form for the given ordered pairs, we need to calculate the slope and find the y-intercept. The slope can be calculated using the formula (Y2 - Y1) / (X2 - X1), and the y-intercept can be found by using the point-slope form and substituting one of the ordered pairs. The function rule in slope-intercept form for the given ordered pairs is y = -0.25x - 1.5.
Explanation:To write a function rule in slope-intercept form, we need to find the slope (m) and the y-intercept (b). Given the ordered pairs (–12, 1.5), (−1, –1.25), (5, –2.75), (8, −3.5), we can calculate the slope using the formula m = (Y2 - Y1) / (X2 - X1). Let's choose two ordered pairs to calculate the slope:
Using (–12, 1.5) and (−1, –1.25):
m = (-1.25 - 1.5) / (-1 - (-12)) = (-2.75) / (11) = -0.25
Now, we can use the point-slope form y - y1 = m(x - x1), where (x1, y1) is one of the ordered pairs and substitute the slope and one of the points to find the y-intercept:
Using the ordered pair (–12, 1.5):
y - 1.5 = -0.25(x - (-12))
y - 1.5 = -0.25(x + 12)
y - 1.5 = -0.25x - 3
y = -0.25x - 3 + 1.5
y = -0.25x - 1.5
Therefore, the function rule in slope-intercept form (fraction form) is y = -0.25x - 1.5.
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A group of 40 students went on a field trip. Exactly 8 students wore blue shirts. What percent of the students on the field trip wore a blue shirt?
20% of the students wore blue shirts
40 x 0.08 = 3.2
3.2% out of the 40 students wore blue shirts.
Which property of addition is shown below?
If x= a + bi and y=-a-bi, x + y = 0.
O commutative property
identity property
associative property
inverse property
Answer: Last option
inverse property
Step-by-step explanation:
The property of the inverse sum says that if we have a number b and we add it with its negative -b then
[tex]b - b = 0[/tex]
In this case we have that:
[tex]x = a + bi[/tex]
and
[tex]y = -b - bi[/tex]
Note that
[tex]y = -x[/tex]
Therefore:
[tex]x + y = x -x= a + bi - a - bi = 0[/tex]
the answer is the last option
How do I solve (x-8)(2x+5=0
Answer:
x = 8 , x = - 2.5
Step-by-step explanation:
( x - 8 ) ( 2 x + 5 ) = 0
1. x - 8 = 0
2. 2 x + 5 = 0
x - 8 = 0
( + 8 on both sides )
x = 8
2. 2 x + 5 = 0
( - 5 from both sides )
2 x = - 5
( ÷ 5 on both sides )
x = - 2.5
PLEASE HELP!!!
1. What is the exponential form of 3*3*3*3*x*x*x*z*z?
2. What is the expanded form of 73a2b4?
1. 3^4 x^3 z^2
2. 73 aabbbb
A square piece of confetti has an area of 25 square millimeters. How long is each side?
The formula for the area of a rhombus is s^2=A. Plug in and solve:
s^2=25
*Take the square root of both sides*
s=5
Hope this helps!!
Answer:
The side length is 5 mm
Step-by-step explanation:
Since it is square, we know the area of a square is given by
A = s^2 where s is the side length of the square
25 = s^2
Take the square root of each side
sqrt (25) = sqrt(s^2)
5 = s
The side length is 5 mm
A chef wanted to know if people liked the food in his new restaurant. For that purpose, he surveyed all the food critics who went to the restaurant during the first month it was open.
A. Is this sample likely to be biased?
B. Explain
Answer and explanation:
A) Yes, the sample gathered by surveying food critics only is most likely to be biased.
B) If the chef is going to survey only the food critics and not include the regular customers who visit the restaurant then this will result in a biased survey.
The reason being that there will exist a systematic error since the surveyed people will not cover the whole population as it will only be limited to the food critics.
Dahlia is trying to decide which bank she should use for a loan she wants to take out. In either case, the principal of the loan will be $19,450, and Dahlia will make monthly payments. Bank P offers a nine-year loan with an interest rate of 5.8%, compounded monthly, and assesses a service charge of $925.00. Bank Q offers a ten-year loan with an interest rate of 5.5%, compounded monthly, and assesses a service charge of $690.85. Which loan will have the greater total finance charge, and how much greater will it be? Round all dollar values to the nearest cent.
It is computed that loan Q's finance charge will be $83.73 greater than loan P's.
How to compute the loan?From the information, the payment for bank P will be:
= (0.058/12)(19450) / [1 - (1 + 0.058/12)^108
= 231.59
The future value will be:
= 231.59 × 12 × 9
= 25011.72
The finance charge for P will be:
= (25011.72 - 19450) + 925
= 6846.72
The payment for Q is 211.08. The future value will be:
= 211.08 × 12 × 10
= 25329.60
The finance charge for Q will be:
= (25329.60 - 19450) + 690.85
= 6570.45.
The difference will now be:
= 6570.45 - 6846.72
= $83.73
Learn more about loans on:
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Answer:
A
Step-by-step explanation:
Got it right
PLEASE HELP 50 POINTS WILL MARK BRAINLIEST. find the value of x rounded to the nearest tenth.
For this case we must find the value of "x", by trigonometric relations.
The tangent of an angle is given by the leg opposite the angle on the leg adjacent to the same angle.
[tex]tg (25) = \frac {10} {x}\\x = \frac {10} {tg (25)}\\x = \frac {10} {0.46630766}\\x = 21.4450691202[/tex]
Rounding:
[tex]x = 21.4[/tex]
Answer:
21.4
Answer:
x = 21.44506921
Step-by-step explanation:
Trigonometry
We need to find x or the adjacent
We are given the Opposite ( 10 )
We don't need the hypotenuse
So we use our formula triangles
TOA SOH CAH
Since we don't need the hypotenuse, we look for a formula without ' H ' in it and it is TOA so we use it
Tan = Opposite ÷ Adjacent
We need to find the adjacent so we rearrange the formula into
Adjacent = Opposite ÷ Tan
Adjacent = 10 ÷ tan(25)
Adjacent = 21.44506921
The 8 students in Mrs. Alexander's class were asked how many minutes it takes them to get to school in the morning. Here is what they answered: 13, 4, 15, 4, 16, 15, 3, 3 Find the mean and median travel times for these students. If necessary, round your answers to the nearest tenth.
To find the mean just add all of them then divide the result by 8. To find the median put the numbers in order. So 3, 3, 4, 4, 13, 15, 15, 16 then find the middle number, if there is not middle number (which there isn’t) add the two middle numbers (4 and 13) to get 17 then divide 17 by 2 to get 8.5 which is the median
Solve -8a + 3a = -9a + 2x - 4 for a in terms of x.
The answer is X= 2a+2
Answer:
a = 1/2x - 1
Step-by-step explanation:
-8a + 3a = -9a + 2x - 4
-8a + 3a + 9a = 2x - 4
4a = 2x - 4
a = (2x - 4) ÷ 4
a = 1/2x - 1
What is the surface area of a rectangle box that measures 1/4 meter by 0.36 meters by 2.8 meters
Answer:
The surface area is [tex]SA=3.596\ m^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the box is equal to
[tex]SA=2[LW]+2(L+W)H[/tex]
Let
[tex]L=1/4=0.25\ m[/tex]
[tex]W=0.36\ m[/tex]
[tex]H=2.8\ m[/tex]
substitute the values
[tex]SA=2[0.25*0.36]+2(0.25+0.36)(2.8)[/tex]
[tex]SA=0.18+3.416[/tex]
[tex]SA=3.596\ m^{2}[/tex]
The transformation (x,y) -> (x + 4,y – 3) is performed on the line segment AB.
The image is the line segment A' B' where point A' = (3, -3) and point B' = (5,-3).
What are the coordinates of A and B in line segment AB?
A. A=(-1,6), B = (1,-6)
B. A= (-1,0), B = (1,0)
C. A = (7,6), B = (9,–6)
D. A = (7,0), B = (9,0)
It’s either d or A but I’m sure it’s A
Dolores bought 3 tapes that cost $4.95 each. the tax on her purchase was %6. What was her total bill
Answer:15.741
Step-by-step explanation: 4.95*3= 14.85, 14.85* 0.06= 0.891+14.85=15.741
Hope it helped!
Translate the word phrase into a math expression: nine more than the quotient of a number and five
Answer: [tex]\frac{x}{5}+9[/tex]
Step-by-step explanation:
Let be "x" the number mentioned in the given phrase.
"...the quotient of a number and five" indicates a division. In other words, the number "x" is divided by 5. This can represented as:
[tex]\frac{x}{5}[/tex]
Now, "Nine more than the quotient of a number and five" indicates that you need to add 9 to the quotient of a number and five ( [tex]\frac{x}{5}[/tex]).
Knowing this, you can conclude that the translation of "Nine more than the quotient of a number and five" into a math expression is:
[tex]\frac{x}{5}+9[/tex]
Final answer:
The word phrase 'nine more than the quotient of a number and five' translates to the math expression '(x/5) + 9', where 'x' represents the number.
Explanation:
To translate the word phrase 'nine more than the quotient of a number and five' into a math expression, we first identify the quotient of a number and five, which is denoted as ‘x ÷ 5’ or ‘x/5’ where x represents the number. Next, we address the phrase 'nine more than', which indicates that we need to add nine to that quotient. So, the phrase translates to the algebraic expression ‘(x/5) + 9’.
Therefore, as per the above explaination, the correct answer is (x/5) + 9
simplify completely sqrt of 20Y^8
Answer:
Final answer is [tex]2y^4 \sqrt{5}[/tex].
Step-by-step explanation:
Given expression is [tex]\sqrt{20y^8}[/tex].
Now we need to smplify the given expression [tex]\sqrt{20y^8}[/tex].
So begin with factoring 20 into two parts so that one part is perfect square number.
[tex]\sqrt{20y^8}[/tex]
[tex]=\sqrt{4 \times 5y^8}[/tex]
[tex]=\sqrt{4 y^8} \times \sqrt{5}[/tex]
[tex]=2y^4 \times \sqrt{5}[/tex]
Hence final answer is [tex]2y^4 \sqrt{5}[/tex].
(HELP ASAP PLEASE!!)
Two brothers went shopping at a back-to-school sale where all shirts were the same price, and all the shorts too. The younger brother spent $79 on 4 new shirts and 3 pairs of shorts. The older brother purchased 7 new shirts and 8 pairs of shorts and paid a total of $185. How much did each item cost?
Each shirt cost $ ___ and each pair of shorts cost $ ___ .
Answer:
Shirts = $7
Shorts $17
Step-by-step explanation:
Let:
T - shirts
S - shorts
We can make two equations out of this problem:
4T + 3S = $79
7T + 8S = $185
Through substitution we can solve for one of the unknowns. We make one equation to solve for an unknown
[tex]4T+3S=\$79\\\\3S = \$79-4T\\\\S=\dfrac{\$79-4T}{3}[/tex]
We use the formula of S and insert it into the other equation:
[tex]7T+8(\dfrac{\$79-4T}{3}) = \$185\\\\7T + \dfrac{\$632-32T}{3}=\$185\\\\\dfrac{\$632-32T}{3}=\$185-7T\\\\\$632-32T=3(\$185-7T)\\\\$632-32T=\$555 - 21T\\\\-32T+21T=\$555-\$632\\\\-11T=-\$77\\\\\dfrac{-11T}{11}=\dfrac{-\$77}{11}\\\\T = \$7[/tex]
Thus T-shirts are $7 each.
Now that we know T, we can use it to solve for the other unknown. You can use it on any of the formulas.
[tex]4T+3S=\$79\\\\4(\$7) + 3S = \$79\\\\\$28+3S =\$79\\\\3S=\$79-\$28\\\\3S=\$51\\\\S=\dfrac{\$51}{3}\\\\S = \$17[/tex]
We know then that Shorts are $17 each.
Select the correct answer from each drop-down menu.
Answer:
q(x)= 2x+5
r(x)= 6
Step-by-step explanation:
Given:
2x^2+13x+26 /x+4
Re-writing in the form of q(x) + r(x)/d(x)
Let
Polynomial P(x)= 2x^2+13x+26
Polynomial d(x)= x+4
Using remainder theorem, putting -4 in P(x) to find r(x)
P(-4)= 2(-4)^2+13(-4)+26
=6
i.e r(x)= 6
Finding q(x) by long division
q(x)= 2x+5
Hence given expression in the form q(x) + r(x)/d(x)
= (2x+5) + 6/x+4 !
What is the following difference 11 square root 45 -4 square root 5
Your problem looks like this
[tex]11\sqrt{45} - 4\sqrt{5}[/tex]
To make this problem easier, we need to simplify these square roots
[tex]11\sqrt{45}[/tex] can be simplified
Here's how :
The factors of 45 are 9 and 5
9 is a perfect square root, but 5 is not
Think of the problem like this
[tex]\sqrt{9} × \sqrt{5}[/tex]
The square root of 9 is 3, but 5 has no perfect square root
Now [tex]11\sqrt{45}[/tex] is simplified to [tex]33\sqrt{5}[/tex]
Now let's solve the problem, because we have a common square root of 5
[tex]33\sqrt{5}[/tex] - 4\sqrt{5}[/tex]
Our final answer is
[tex]29\sqrt{5}[/tex]
Feel free to ask questions if you are confused! Hope I helped :)
For this case we must simplify the following expression:
[tex]11 \sqrt {45} -4 \sqrt {5}[/tex]
So, we rewrite 45 as [tex]3 ^ 2 * 5[/tex]:
[tex]11 \sqrt {3 ^ 2 * 5} -4 \sqrt {5} =[/tex]
We have by definition of properties of powers and roots that:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]11 * 3 \sqrt {5} -4 \sqrt {5} =\\33 \sqrt {5} -4 \sqrt {5} =\\29 \sqrt {5}[/tex]
Answer:
[tex]29 \sqrt {5}[/tex]
PLEASE HELP RIGHT AWAY
Answer:
Approximately 53
Step-by-step explanation:
This is a geometric progression, because each term is found by multiplying the previous one by a constant factor.
In our case, the first term is know (a1 = 3), and the growth factor is also known (q = 1.333333).
What we are tasked to do is to find the 11th (n=11) term of the series, since it asks for AFTER the 10th roll.. That's easy with the base formula:
[tex]a_{n} = a_{1} q^{n-1}[/tex]
Let's place the values we have in the equation and solve it:
[tex]a_{10} = 3 * (1.333333)^{11-1} = 3 * (17.758) = 53.3[/tex]
So, after the 10th roll, you should need 53 dice, approximately.
i have trouble so cn anybody help me?
Greg walked 610 of a mile and hopped 34100 of a mile.
How far did Greg travel?
Answer:
The correct answer is for sure 100 % =33,490
Step-by-step explanation:
34,100-610= 33,490
610+33,490=34,100
PLLZZZZ MARK ME BRAINLIST PLZZZZ!!!
What is the domain of the function shown in the mapping?
{x | x = –5, –3, 1, 2, 6}
{y | y = –9, –6, 0, 2, 4}
{x | x = –9, –6, –5, –3, 0, 1, 2, 4, 6}
{y | y = –9, –6, –5, –3, 0, 1, 2, 4, 6}
Answer:
x verse y on the map
Step-by-step explanation:
It shows what the x and the y cordinates are
The length of a rectangular floor is 2 feet more than its width. The area of the floor is 168 square feet. Kim wants to use a rug in the middle of the room and leave a 2-foot border of the floor visible on all sides. What should the length (the shorter side) of the rug be
Answer:
8 ft
Step-by-step explanation:
let width = x
then length= x+2
Area = l(w)
=x(x+2)
168 = x^2 + 2x
x^2 + 2x-168=0
Using quadratic formula we get roots :
x= 12, x=-14
x= 12 (as width cannot be in negative)
then length= x+2 = 14
length of rug= length of floor - 4
= 14- 4
= 10
width of rug= width of floor- 4
= 12-4
= 8
Hence the length (the shorter side) of the rug be 8 feet !
Simplify the given expression.
Answer:
C. [tex]\frac{32g^2}{3h^4}[/tex]
Step-by-step explanation:
Answer:
Option C is correct
Step-by-step explanation:
[tex]\frac{\frac{h}{3g^2}}{\frac{h^5}{32g^7}}[/tex]
We need to simplify the above expression.
We can write the above expression as:
[tex]\frac{h}{3g^2}\div\frac{h^5}{32g^7}[/tex]
Changing division sign into multiplication and reciprocating the second term we get,
[tex]\frac{h}{3g^2}*\frac{32g^7}{h^5}[/tex]
Applying the power rule: a^m/a^n = a^{m-n}
Solving:
[tex]\frac{h*32g^7}{3g^2*h^5}\\\\\frac{32g^{7-2}}{3h^{5-1}}\\\frac{32g^5}{3h^4}[/tex]
So, Option C is correct.
Solve the following inequality. Then place the correct number in the box provided. 3x < 18
For this case we must solve the following inequality:
[tex]3x <18[/tex]
Dividing between 3 on both sides of the inequality we have:
[tex]x <\frac {18} {3}\\x <6[/tex]
Thus, the solution of the variable "x" is given by all the numbers smaller than 6.
Answer:
All values of "x" less than 6.
(-∞, 6)
COLOUT OLU
Instructions: Type the correct answer in each box. Use numerals instead of words.
Simplify the following polynomial expression.
(-9x² + 2x + 13) - (-7x2 + 3x + 6).
The simplified form of the given polynomial equation is:
[tex]-2x^2-x+7[/tex]
Step-by-step explanation:We are asked to simplify the given polynomial expression in terms of the variable x.
The algebraic expression is given as:
[tex](-9x^2+2x+13)-(-7x^2+3x+6)[/tex]
On taking out the terms from both the brackets the sign of the terms of the second bracket gets interchanged as there is a negative sign preceding it.
Hence, we get the expression as:
[tex]=-9x^2+2x+13+7x^2-3x-6\\[/tex]
Now on combining the like terms we get:
[tex]=-9x^2+7x^2+2x-3x+13-6\\\\\\=-2x^2-x+7[/tex]
Simplify: a + 2a + 3a + 4a
A)
9a
B)
10a4
C)
9a4
D)
10a
You just need to factor a to get
[tex]a(1+2+3+4) = 10a[/tex]
Need help ASAP please! 60 points! -Does anyone have an idea as to how the function should be drawn? I think that there should be a shift but I don't know to what direction. Your help would be very appreciated
P(x) to P(x+2), you need to graph the same but shift 2 units to the left.
New function :
Max = 4 ,coordinate points (-5, 0) and (5,0)
You are try to dunk a basketball. You need to jump 2.5 feet in the air to dunk the ball. The height that your feet need to be of the ground is given by the function h(t)= _ 16t2+12r. What is the maximum height your feet will be above the ground? Will you be able to dunk the ball?
Answer:
1)he maximum height your feet will be above the ground is 2.25
2)Will you be able to dunk the ball= No
Step-by-step explanation:
Given:
In order to dunk the basket ball, height needed to jump= 2.5 feet
The height that your feet need to be of the ground is given by the function h(t)= -16t^2+12t
1) the maximum height your feet will be above the ground=?
Given function of height,h(x)=-16t^2+12t
finding maximun of the above function
The maximum of any function written in form of ax^2+bx+c is given by
max= c - (b2 / 4a)
Putting values c=0, b=12 and a=16, we get
max= 0-(12^2/4(-16))
= 144/64
=2.25 feet
he maximum height your feet will be above the ground is 2.25 feet.
2) Will you be able to dunk the ball=?
As the height needed to jump in the air to dunk the ball is 2.5 feet which is greater than the maximum height the feet will be above the ground i.e.
2.5>2.25
hence No you will not be able to dunk the ball !
The maximum height your feet will be above the ground is 2.25 feet. No, you will not be able to dunk the ball.
Explanation:To find the maximum height your feet will be above the ground, we need to determine the vertex of the quadratic function h(t) = -16t^2 + 12t.
The vertex of a quadratic function of the form h(t) = at^2 + bt + c is given by the formula t = -b/2a. In this case, a = -16 and b = 12, so the vertex is t = -12/(2*(-16)) = 0.375 seconds.
Substituting this value back into the function h(t), we get h(0.375) = -16(0.375)^2 + 12(0.375) = 2.25 feet. Therefore, the maximum height your feet will be above the ground is 2.25 feet.
Since you need to jump 2.5 feet in the air to dunk the ball and the maximum height your feet will reach is only 2.25 feet, you will not be able to dunk the ball.
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A teacher is told he will have 20 students in his first-period class this year. He wants to predict the birthday month of his students, so he decides to run a simulation where January = 1, February = 2, etc. Use the simulated results to estimate the probability that a randomly picked student will have a September birthday.
9 6 5 8 9 2 4 10 9 7 2 10 12 6 9 2 9 11 1 3
Answer:
[tex]P = 0.25[/tex]
Step-by-step explanation:
The simulation shows a result composed of 20 data.
If January represents month 1 and February represents month 2 then September is represented by number 9.
According to this simulation, the probability of a randomly selected student having birthdays in September is:
[tex]P = \frac{X_9}{20}[/tex]
Where [tex]X_9[/tex] is the frequency of 9. That is, [tex]X_9[/tex] is the number of times the number 9 appears among the 20 data
Therefore:
[tex]P = \frac{5}{20}[/tex]
[tex]P = \frac{1}{4}[/tex]
[tex]P = 0.25[/tex]
Answer:
0.25
Step-by-step explanation:
gradpoint
The graph shows two lines, A and B.
Part A: How many solutions does the pair of equations for lines A and B have?
Part B: What is the solution to the equations of lines A and B?
part a: 1
part b: (3,5)