Answer:
b. 4x^2 -7x +5
Step-by-step explanation:
When you know a sum and one of its contributors, you can find the other by subtraction. The other trinomial is ...
(7x^2 -5x +4) - (3x^2 +2x -1)
= (7 -3)x^2 +(-5 -2)x +(4 -(-1))
= 4x^2 -7x +5 . . . . . matches B
The vertical axis in a coordinate plane is the y-axis. true of false
Answer:True
Step-by-step explanation:The y-axis is vertical and the x is horizontal
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]
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.
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.
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
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.
1. Find the unknown length of the side labeled X.
Answer:
Step-by-step explanation:
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:
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
Mathematics
20. A teacher drew an area model to find the value of 6,986 +8.
Teacher's Model for 6,986 +8
R
Р
N
800
Q
8
560
M
UNIZ
not to scale
• Determine the number that each letter in the model represents and explain
each of your answers.
• Write the quotient and remainder for 6,986 + 8.
Explain how to use multiplication to check that the quotient is correct. You
may show your work in your explanation.
Enter your answers and your explanations in the space provided.
.
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
The hypotenuse of a right triangle measures 6cm and one of its legs measures 3cm.Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
5.2
Step-by-step explanation:
a^2+b^2=c^2
Where c is the length of hypotenuse
and a, b are lengths of the legs.
Put in 6 for c,
Put in 3 for a and you get 9+b^2=36
Subtract 9 from both sides and get b^2= 27
Then find the square root of both sides to get b, so the answer is the square root of 27.
The cloest square root is 5, then apporixmate the tenths value and see if they work.
Answer: 5.2
Answer:
square root of 27, 5.2
Step-by-step explanation:
(I know I'm late but-)
3^2+b^2=6^2
9+b^2=36
b^2=27
Convert 1 gallon to fluid ounces. 1 gal = ______ fl oz (Just put the number answer.) *
Answer:
153.722 fl oz
Match the correct angle measurement with its letter from the diagram.
42
48
90 are the options
Answer:
<C=48 because 90-42=42 as in the other side of the triangle.
<B=42 because vertical angles are always congruent.
<B+<D=90 because <D is 48 because it is vertical to <C
solve the system of equations shown below. 2x-6=-12 x=2y=14
Answer:
please the question is not clear
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
There are 4 consecutive integers that have a sum of 54. What is the greatest of the 4 integers?
Answer:
x + x-1 + x-2 + x-3 =54.
x-1
Answer:
15
Step-by-step explanation:
Let the consecutive numbers be x, x + 1, x + 2, x + 3
==========
x + x + 1 + x + 2 + x + 3 = 544(x) + 6 = 544(x) = 54 - 64(x) = 48x = 12Greatest of the 4 integers:
x + 312 + 315find the missing number?
IF
3+4 = 19
4+5 = 29
5+ 6=41
1+9 = 19
then 1+3= ?
please help me if you know the answer
Mathew finds the deepest part of the pond to be 185 meters
Which measurement describes the depth of the pond?
[tex]\sqrt{196} = 14[/tex], and since [tex]\sqrt{185[/tex] is less than [tex]\sqrt{196}[/tex], the deepest part of the pond is less than 14.
-> The depth of the pond is between 13 and 14 meters.
Or, you can just calculate [tex]\sqrt{185}[/tex] = 13.6014... (between 13 and 14)
The measurement describes the depth of the pond is Between 13 and 14 meters.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Since one side measure 14, and the height (depth) could not be higher than 14 meters .
The length of the pond can be calculated using the Pythagorean theorem as;
length^2 = 36^2 + 14^2
length^2 = 1296 + 196
length^2 = 1492
length = 38.6 m
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Researchers are studying two different designs of computer keyboards, J and K, to investigate the effectiveness of the design on the speed of data entry. The researchers believe there is a tendency for people entering data with keyboard J to have faster entry times compared with people entering data with keyboard K. Using the same set of data for entry, the researchers randomly assigned 5 people to keyboard J and 6 people to keyboard K and recorded the number of seconds each person took to enter the data.
The following dotplots show the observed entry times for the two keyboards.
Keyboard J - 160 180 280 300 200 220 240 260 Entry Time (seconds)
Keyboard K + 160 + 180 280 300 200 220 240 260 Entry Time (seconds)
Explain why it is not appropriate to conduct a two-sample t-test for the difference in population means.
It is not appropriate to conduct a two-sample t-test because there exists an outlier in both variables.
What is a two-sample t-test?
The two-sample t-test is used to determine if two population means are equal. The purpose of the test is to determine whether the difference between these two populations is statistically significant.
In this case, it is not appropriate to conduct a two-sample t-test because there exists an outlier in both variables. Therefore, it might be more appropriate to compare population medians instead of population means.
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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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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
Please use the picture I provided to help me answer the questions:)
Answer:
Let x = time in minutes
Let y = water in ounces
Part A
If the water drips at a constant rate of 2 ounces per 5 minutes, then
x = 0, y = 0
x = 10, y = 4
x = 20, y = 8
Part B
Graph is attached.
Please note that the scales on the y and x axes are different.
Part C
[tex]\sf y=\dfrac25x[/tex]
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.
Donnie ran 6.24 kilometers in a race last weekend. How many meters did he run?
he ran 10meters last weekend
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
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HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
An=A(n-1)-4 where A=7
Step-by-step explanation:
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!
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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