For the given function g(x)=xpower of 2-6x-16, the statement which is true, is the zeros are -2 and 8 because the factor of g are (x+2) and (x-8).
What is a quadratic function?A quadratic function is the function in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic function is,
[tex]f(x)=ax^2+bx+c[/tex]
Here,(a,b, c) is the real numbers and (x) is the variable.
The quadratic function given in the problem is,
[tex]g(x)=x^2-6x+16[/tex]
Factorized it with split the middle term method,
[tex]g(x)=x^2-6x-16\\g(x)=x^2-8x+2x-16\\g(x)=x(x-8)+2(x-8)\\g(x)=(x-8)(x+2)[/tex]
Equate the factors of the function, to find the zeros,
[tex]x-8=0;x=8\\x+2=0;x=-2[/tex]
Hence, for the given function g(x)=xpower of 2-6x-16, the statement which is true, is the zeros are -2 and 8 because the factor of g are (x+2) and (x-8).
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There are 15 students on the debate team. Four will attend the debate. How many groups of four can be selected from the 15 students?
Answer: 1365
Step-by-step explanation:
Why do you replace y with 0 when finding the x-intercept of a graph?
Here’s what you need to know about intercepts. The x intercept of a graph has y coordinate zero. The y intercept of a graph has x coordinate zero.
AN EXAMPLE OF THIS IS:
So if you have a function y = 2x + 8 you would set x = 0 to find the y intercept. So we would get y = 8. To find the x intercept we would set y = 0 and get 0 = 2x + 8
or -8 = 2x or x = -4
Now if you have a more difficult like function y = 3x^2 + 10x - 4 we proceed the same way. To find the y intercept we would set x = 0 and get y = -4 so the y intercept is (0,-4)
To find the x intercept we would set y = 0 and get 3x^2 + 10x - 4 = 0. If you know the quadratic formula you could solve this by:
x = [-b +- SR(b^2 - 4*a*c] / 2a
so in our case x = [-10 +- SR(100 - 4*3*(-4))] / (2*3)
x = [-10 +- SR(100 + 48)] / 6
x = [-10 +- SR (148)] / 6
x = [-10 +- 12.2] / 6 approximately
x = [-10 - 12.2] / 6 or [-10 + 12.2 / 6]
x = -22.2/6 or 2.2/6
2. A baby weighs 8 pounds, 1 ounce. How much does she weigh in ounces?
Answer:
97 oz
Step-by-step explanation:
12 oz per pound
8 pounds + 1 oz
(12 · 8)+ 1
97 oz
Hope this helps!
Donnie ran 6.24 kilometers in a race last weekend. How many meters did he run?
he ran 10meters last weekend
selected value of each decimel number when it is rounded to the nearest whole number
Answer:
5665Remember the decimal hundredths rounding ruleset.
If a decimal is below .50, round down.If a decimal is .50, round up.If a decimal is above .50, round up.View this array below to get a better image.
[tex]\left[\begin{array}{ccc}0.49(down)&0.50(up)&0.51(up)\end{array}\right][/tex]
So, for example, if you had 6.51, you would round that up to 7, and if you had 8.47, you would round that to 8
What are the zeros of the following function?
Answer:
-4 and 2
Step-by-step explanation:
the graph intersects the x-axis only at the points (-4,0) and (2,0) so the only zeroes of the graph are going to be -2 and 2
Which expression is equivalent to
Answer:
First option
Step-by-step explanation:
The expression can be simplified to:
[tex]\frac{8g^{15} }{64h^6}[/tex] = [tex]\frac{g^{15} }{8h^{6} }[/tex]
You can't simplify this further since the indices if you think about it is g 15 times or h 6 times so you can't simply them further.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
An=A(n-1)-4 where A=7
Step-by-step explanation:
Please help me????22pts
Answer:
[tex]\mathrm{1 \dfrac{ 1 }{ 6 }\:cups}[/tex]
Step-by-step explanation:
Given from the graph:
There is [tex]\frac{1}{2}[/tex] cups of paint for one jar
There are 3 cups of paint for three jars
There is 1 [tex]\frac{1}{2}[/tex] cups of paint for one jar
There is 2 cups of paint for one jar
total amount of jars = 6
But since we need to find the amount of cups in each jar, we do:
[tex]\dfrac{ 1 }{ 2 } +3+1 \dfrac{ 1 }{ 2 } +2[/tex]
Add [tex]\frac{1}{2}[/tex] and 1 [tex]\frac{1}{2}[/tex]
[tex]2+3+2[/tex]
Add 2 and 3
[tex]5+2[/tex]
Add 5 and 2
[tex]7[/tex]
total cups of paint = 7
Then we need to find how much paint could be splitted equally among the 6 jars, so we do the following:
total amount of jars = 6
total cups of paint = 7
We divide the total amount of jars by the total cups of paint
7 ÷ 6
Divide 7 by 6
[tex]\dfrac{ 7 }{ 6 }[/tex]
[tex]= 1 \dfrac{ 1 }{ 6 }[/tex]
[tex]\mathrm{Answer: 1 \dfrac{ 1 }{ 6 }\:cups}[/tex]
What is the median of the data set represented by the dot plot?
Enter the answer in the box.
A number line with line with two dots above the number 10, one dot above the number 12, one dot above the number 13, one dot above the number 14, one dot above the number 15, one dot above the number 18, and two dots above the number 19.
Answer:
Median is 14Step-by-step explanation:
The median is the middle number (or average of middle two numbers if data set has even number of elements) of the data set.
According to the graph, the data set has 9 elements.
The 5th number in the set is the median, which is 14
14
Step-by-step explanation:Step-1: Prepare a table that represents the number of dots above a specific number:
[tex]\text{Dots above 10}: || \\ \text{Dots above 12}: | \\ \text{Dots above 13}: | \\ \text{Dots above 14}: | \\ \text{Dots above 15}: | \\ \text{Dots above 18}: | \\ \text{Dots above 19}: ||[/tex]
Step-2: Put the values in ascending or descending upon your choice:
[tex]10, 10, 12, 13, 14, 15, 18, 19, 19[/tex]
Step-3: Determine wether the total number of digits in the data is even or odd. This will help us find the median.
[tex]\text{9 digits in total}\\\\\text{The number of digits is \underline{odd}}[/tex]
Since the number of digits is odd, we will use the formula (a + 1)/2
(where a is the number of digits in the data)
Step-4: Substitute the number of digits in the formula.
⇒ (a + 1)/2th
⇒ (9 + 1)/2th
⇒ (10)/2th
⇒ 5th digit is median
Step-5: Look for the 5th digit in the data. That digit is your median.
[tex]10, 10, 12, 13, \underline{\underline{14}}, 15, 18, 19, 19[/tex]
The median of the dot plot is 14.
Examine the following piecewise function.
Which statements are true?
Select all that apply.
1.The function is increasing over the interval 2≤x≤3.
2.The function is increasing over the interval −2≤x≤2.
3.The function is increasing over the interval −8≤x≤−2.
4.The function is decreasing over the interval 3≤x≤7.
5.The function is constant over the interval −2≤x≤2.
A piecewise function is a function that's simply built from pieces of different functions over several intervals.
What is a piecewise function?Your information is incomplete as the function isn't given. Therefore, an overview will be given. It should be noted that a piecewise function simply means a function that's defined by multiple sub functions.
In this case, each sub-function applies to different interval in the domain as it's way of expressing the function.
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I need help with D, i’m confused on it.
Answer:
Step-by-step explanation:
[tex]A=P(1+\frac{r}{n})^{nt[/tex]
A = future value ($)
P = principal (orignal amount - $400)
R = rate (written as a decimal - 3%/100= 0.03)
N = compound (yearly - 1)
T = number of years (0, 5, 10, 15)
Now, substitute each number into the formula and record them in the table.
0 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*0}\\\\A=400(1+\frac{0.03}{1})^0 < ==any\ number\ raised\ to\ zero=1\\\\A=400(1)\\\\A=\$400[/tex]
5 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*5}\\\\A=400(1+\frac{0.03}{1})^{5}\\\\A=400(1+{0.03})^{5}\\\\A=400({2.03})^{5}\\\\A=400({1.1593})\\\\A=\$463.72 < ==round\ to\ the\ nearest\ dollar\\\\A=\$464[/tex]
10 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*10}\\\\A=400(1+\frac{0.03}{1})^{10}\\\\A=400(1+{0.03})^{10}\\\\A=400({1.03})^{10}\\\\A=400({1.3439})\\\\A=\$537.56 < ==round\ to\ the\ nearest\ dollar\\\\A=\$538[/tex]
15 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*15}\\\\A=400(1+\frac{0.03}{1})^{15}\\\\A=400(1+{0.03})^{15}\\\\A=400({1.03})^{15}\\\\A=400({1.5579})\\\\A=623.16 < ==round\ to\ the\ nearest\ dollar\\\\A=\$623[/tex]
20 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*20}\\\\A=400(1+\frac{0.03}{1})^{20}\\\\A=400(1+{0.03})^{20}\\\\A=400({1.03})^{20}\\\\A=400({1.8061})\\\\A=722.44 < ==round\ to\ the\ nearest\ dollar\\\\A=\$722[/tex]
Note that since we are rounding, answers may vary by a dollar or two.
Hope this helps!
PLEASE ANSWER QUICKLY!
The figure shows a right prism.
1. What is the volume of the figure?
2. If the dimensions of the prism are decreased by a factor of 1/4, how will the volume of the new prism compare to the volume of the original prism? (ANSWER IN A SIMPLIFIED FRACTION).
The volume of the prism is decreased by a factor of: ______
Help!! I’m so stuck!
Giving away all of my points in 100 point bursts. I have 1700 points. How people can I give to?
Total times can give:-
1700/10017One question can be answered by 2
Total persons=17(2)=34
Repost bc I forgot something.
You throw a football and it leaves your hand of 5 feet. Its initial velocity is 20 feet per second. What is the maximum height the ball will reach? Also, how long will it take the ball to hit the ground? (Equation used: h(t)= -16t^2 + v0t + h0.)
Please show work
Answer:
The max height is 11.25 feet and the ball will take 1.464 seconds to hit the ground
Step-by-step explanation:
The quickest way to solve this equation is by using the equation that you gave, which is h(t)= -16t^2 + v0t + h0. This equation models the trajectory of the football, which means that at the equation's vertex, we can model what the height of the ball is. Along with that, by finding the positive root of where h(t) = 0, we can find how long it will take for the ball to hit the ground.
First, lets find h0 and v(0)
h0 is the initial height of the ball. So we know that the ball leaves your hand of 5 feet, so h0 = 5. Similarly, the initial velocity is 20 ft/sec, so v0 = 20.
Plugging 5 in for h0 and 20 for v0, we get h(t) = -16t^2 + 20t + 5.
Second, find max height.
To find the vertex of a parabola, use -b/2a to find the time, and plug that into h(t) to get the height.
b=20
a=-16
t = -b/2a = -20/2(-16) = .625 seconds
h(.625) = 11.25 feet
The max height is 11.25 feet
Third, find how long.
To find this, we need to find the t-intercepts of the equation.
set h(t) = 0
-16t^2 + 20t + 5 = 0
Use quadratic formula to find t
t = (- 20 ± [tex]\sqrt{20^{2} - 4(-16)(5)}[/tex])/2(-16)
t = {1.464}, -.214
The ball will take 1.464 seconds to hit the ground.
simplify l(m-n) + m (n-l) + n (m-l)
Step-by-step explanation:
Multiplying :-l(m-n) + m (n-l) + n (m-l)lm - ln + mn - ml + nm - nlSolve the like terms :-lm - ml - ln - nl + mn + nm2mn - 2nlTake common :-2n(m - l)...simplified Hope it helps you !!Answer:
-2ln + 2mn
Step-by-step explanation:
Simplify l(m-n) + m(n-l) + n(m-l)
Step 1 : Distribute and multiply
l(m-n) + m(n-l) + n(m-l)
l(m) + l(-n) + m(n) + m(-l) + n(m) + n(-l)
lm - ln + mn - lm + mn - ln
Step 2: Combine like terms
lm - ln + mn - lm + mn - ln
lm - lm - ln - ln + mn + mn
0 -2ln + 2mn
Solution:
-2ln + 2mn
Hope this helps!
What additional information could be used to prove that the triangles are congruent using AAS?
Select two options
Answer:
Step-by-step explanation:
We have two congruent angles, so we need a pair of congruent sides. This is satisfied by options 2 and 3.
ABC is a right triangle at B such that
AB = 8 cm and AC = 10 cm.
1° Calculate BC
2º Consider a point M of the segment [AB]
The line passing through M and parallel to the
line (AC) cuts the line (BC) in N.
Supposing that AM = x, calculate MB and BN in
5
terms of x. then verify that MN (8 - x).
4
3° Let D be the fourth vertex of rectangle
ABCD.
The parallel to (BD) passing through M.cuts the
line (AD) at P
Calculate AP and MP in terms of x
4° Prove that the perimeter of the polygon
MNCDP is independent from x
Answer:
Question 1
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, or a right triangle)
Given:
a = BCb = AB = 8cmc = AC = 10 cm⇒ BC² + 8² = 10²
⇒ BC² = 36
⇒ BC = 6 cm
Question 2
Given:
AB = 8 cmAM = x⇒ MB = AB - AM = 8 - x
As ΔABC ~ ΔMBN
⇒ AB : AC = MB : MN
⇒ 8 : 10 = (8 - x) : MN
[tex]\sf \implies \dfrac{8}{10}=\dfrac{(8-x)}{MN}[/tex]
[tex]\sf \implies \dfrac45=\dfrac{(8-x)}{MN}[/tex]
[tex]\sf \implies MN=\dfrac54(8-x)[/tex]
Question 3
D = (6, 8)
As ΔBAD ~ ΔMAP
⇒ AB : AD : BD = AM : AP : MP
⇒ 8 : 6 : 10 = x : AP : MP
[tex]\sf \implies \dfrac{8}{6}=\dfrac{x}{AP}[/tex]
[tex]\sf \implies AP=\dfrac34x[/tex]
[tex]\sf \implies \dfrac{8}{10}=\dfrac{x}{MP}[/tex]
[tex]\sf \implies MP=\dfrac54x[/tex]
Question 4
Perimeter of MNCDP = MN + NC + CD + PD + MP
As ΔABC ~ ΔMBN
⇒ AB : BC : AC = MB : BN : MN
⇒ 8 : 6 = (8 - x) : BN
[tex]\sf \implies \dfrac86=\dfrac{(8-x)}{BN}[/tex]
[tex]\sf \implies BN=\dfrac34(8-x)[/tex]
NC = BC - BN
[tex]\sf \implies NC=6-\dfrac34(8-x)[/tex]
PD = 6 - AP
[tex]\sf \implies PD=6-\dfrac34x[/tex]
Perimeter of MNCDP = MN + NC + CD + PD + MP
[tex]\sf \implies perimeter=\dfrac54(8-x)+6-\dfrac34(8-x)+8+6-\dfrac34x+\dfrac54x[/tex]
[tex]\sf \implies perimeter=10-\dfrac54x+6-6+\dfrac34x+8+6-\dfrac34x+\dfrac54x[/tex]
[tex]\sf \implies perimeter=10+8+6=24[/tex]
Which construction uses the compass for only one step in addition to drawing the circle itself?
A) an equilateral triangle inscribed in a circle
B) a square inscribed in a circle
C) a regular hexagon inscribed in a circle
D) a diameter of a circle
Answer: A) an equilateral triangle inscribed in a circle
Step-by-step explanation:
In the mathematical world, a compass is a mathematical tool used for drawing and constructing precise shapes. You have likely seen one of these before, I have attached a visual example of what one might look like.
Out of these given options, the only one that utilizes a compass for one step in addition to drawing the circle itself is A:
A) an equilateral triangle inscribed in a circle
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The sum of two numbers is 30 and their difference is 10. What are the two numbers?
Answer:
20 and 10
These are the only two possible numbers who match those descriptions.
CAN SOMEONE HELP ME PLEASE ASAP!?
Answer:
3:10
Step-by-step explanation:
3:10 is the ratio form of 3/10
solve the system of equations shown below. 2x-6=-12 x=2y=14
Answer:
please the question is not clear
A square pyramid is shown. What is the surface area of the pyramid? Enter your answer in the box. 100 points
Answer:
33 cm²
Step-by-step explanation:
Formula
Surface Area = 4 x Area (triangle) + Area (square)S.A. = 4 x 1/2 x bh + b²Solving
Given that h = 4 cm and b = 3 cmS.A. = 2 x 4 x 3 + 3²S.A. = 24 + 9 = 33 cm²Answer:
33 cm²
Step-by-step explanation:
Since the pyramid has a square base, the area of each of the triangular sides will be the same.
Therefore, to calculate the total surface area, find the area of one triangle, multiply it by 4, then add it to the area of the square base.
Formulae
Area of a square = x³ (where x is the side length)
Area of a triangle = 1/2 × base × height
Calculation
area of the square base = 3² = 3 × 3 = 9 cm²
area of one triangle = 1/2 × 3 × 4 = 6 cm²
Solution
Total area = area of the square base + 4 × area of one triangle
= 9 + (4 × 6)
= 9 + 24
= 33 cm²
Mark chose two cards randomly from a deck. What is the probabity of getting an Ace or King?
Answer:
50/50
Step-by-step explanation:
Answer:
depends on how many there are in a deck. But going from the usual, it would be 2/52
Step-by-step explanation:
(52 is how many cards there are, if theres a different amount then change it to that)
Plot startroot 1.5 endroot and startroot 1.9 endroot on the number line to find which inequalities are true. check all that apply. startroot 1.5 endroot < 1.5 startroot 1.9 endroot < 1.9 startroot 1.5 endroot < startroot 1.9 endroot 1.2 > startroot 1.5 endroot > 1.3 1.3 < startroot 1.9 endroot < 1.4
The expressions √1.5 and √1.9 are radical expressions
The true inequality about √1.5 and √1.9 is √1.5 < √1.9
How to determine the true inequality?The numbers are given as:
√1.5 and √1.9
Evaluate both root expressions
√1.5 = 1.22
√1.9 = 1.38
By comparison, we have:
1.22 <1.38
Rewrite as:
√1.5 < √1.9
Hence, the true inequality about √1.5 and √1.9 is √1.5 < √1.9
Read more about inequalities at:
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The speed of the jet Alyssa flew on from Boston to London was 480 mph. On her return flight, the speed of the jet was 600 mph with a tailwind. What was Alyssa's average speed on the round trip? Round your answer to one decimal place.
P.S: The answer is not 540
Answer:
533.3
Step-by-step explanation:
x/480+x/600
2x/18x
4800/9=533.333333
533.34
A volleyball player has a assists per game during a 6 game match. The volleyball player has 42 assists during the entire match. Which equation can be used to find a?
Please I really need it :(
Answer:
6a=42
Step-by-step explanation:
This equation would be used to find a because we don't know how many assists are for each match. And multiplying the a by the 6 games would be equivalent to 42 assists for the entire match.
Can you guys help me do today.
Answer:
Down Below
Step-by-step explanation:
b=0.5
g=0.8
1. 3b + 5g = ?
3×0.5+5×0.8=?
1.5+4= 5.5 cm
2. 6(3b+5g) = ?
18b + 30g
18×0.5+30×0.8
9+24= 33 cm
3. 2b + 3g
2×0.5+3×0.8
1+2.4=3.4 cm
4. 7(2b+3g)
14b + 21g
14×0.5+21×0.8
7+16.8= 23.8 cm
5. Add number 2 and 4 together
14b+21g+18b+30g= 32b+ 51g
Take numbers and add them from problems 2 and 4
23.8+33=56.8 cm
Determine if the two figures below are congruent. Use the drop-down
menus below to justify why. Which angle on Figure 2 corresponds to
angle M on Figure 1?
Answer: are congruent, rotation
Step-by-step explanation:
Write a two-column proof on a space provided
Answer:
Step-by-step explanation:
