Answer:
a. a = 1, b = -5, c = -14
b. a = 1, b = -6, c = 9
c. a = -1, b = -1, c = -3
d. a = 1, b = 0, c = -1
e. a = 1, b = 0, c = -3
Step-by-step explanation:
a. x-ints at 7 and -2
this means that our quadratic equation must factor to:
[tex](x-7)(x+2) = 0[/tex]
FOIL:
[tex]x^2 + 2x - 7x - 14 = 0[/tex]
Simplify:
[tex]x^2 - 5x - 14 = 0[/tex]
a = 1, b = -5, c = -14
b. one x-int at 3
this means that the equation will factor to:
[tex](x-3)^2=0[/tex]
FOIL:
[tex]x^2 - 3x - 3x +9 = 0[/tex]
Simplify:
[tex]x^2 - 6x + 9 = 0[/tex]
a = 1, b = -6, c = 9
c. no x-int and negative y must be less than 0
This means that our vertex must be below the x-axis and our parabola must point down
There are many equations for this, but one could be:
[tex]-x^2-x-3=0[/tex]
a = -1, b = -1, c = -3
d. one positive x-int, one negative x-int
We can use any x-intercepts, so let's just use -1 and 1
The equation will factor to:
[tex](x+1)(x-1)=0[/tex]
This is a perfect square
FOIL:
[tex]x^2-1=0[/tex]
a = 1, b = 0, c = -1
e. x-int at [tex]\sqrt{3} , -\sqrt{3}[/tex]
our equation will factor to:
[tex](x+\sqrt{3} )(x-\sqrt{3)} =0[/tex]
This is also a perfect square
FOIL and you will get:
[tex]x^2 - 3 = 0[/tex]
a = 1, b = 0, c = -3
The mean of four numbers is 59, The numbers are 52, 58, 57, and x. Find the value of x.
Answer:
X=69
Step-by-step explanation:
52, 58, 57, X =59
52+58+57+X/4=59
167+X/4=59
Multiply both sides by 4
4(167+X) /4 = 59x4
Simplify
167 + X= 236
Subtract 167 from both sides
167 + X- 167 = 236 – 167
Simplify
X= 69
to check
52+ 58+57+69/4 =59
There are 22 fourth-grade students and 26 fifth-grade students who became
cheerleaders. Each cheerleading group will have 8 members. Which equation
can be used to find out how many groups can be made?
(22 + 26) / 8 = x
(/ this means division)
Multiple Choice Find AD and ED for parallelogram ABCD.
A) AD = 13
B) ED = 13
C) ED=9
D) ED = 16
E) AD = 9
F) AD = 16
Answer: A, C
Step-by-step explanation:
Diagonals of a parallelogram bisect each other, so [tex]4x-7=2x+1 \longrightarrow x=4[/tex]. So [tex]ED=4(4)-7=\boxed{9}[/tex].
Opposite sides of a parallelogram are congruent, so [tex]8y-3=3y+7 \longrightarrow y=2[/tex], so [tex]AD=8(2)-3=\boxed{13}[/tex]
Find the greatest common factor.
7x³a +7x²a²
Enter the correct answer.
Answer:
7x²a(x + a)
Step-by-step explanation:
7x³a = 7 * x * x * x * a
7x²a² = 7 *x * x * a *a
Common factor = 7x²a
So we have to take the common factor from the two terms
7x³a + 7x²a² = 7x²a ( x + a)
. If you sampled 2000 people, how many would you expect to have BP> 160? Give your answer to the nearest person. Note: I had a bit of an issue encoding rounded answers, so try rounding both up and down if there's an issue!
Using the normal distribution, it is found that 84 people would be expected to have BP > 160.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Researching the problem on the internet, the mean and the standard deviation for the BPs are given, respectively, by:
[tex]\mu = 122, \sigma = 22[/tex].
The proportion of adults with BP > 160 is given by one subtracted by the p-value of Z when X = 160, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{160 - 122}{22}[/tex]
Z = 1.73
Z = 1.73 has a p-value of 0.9582.
1 - 0.9582 = 0.0418.
Out of 2000 people:
0.0418 x 2000 = 83.6.
Rounding to the nearest integer, 84 people would be expected to have BP > 160.
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Factor completely.
5x² + 25x + 20 =
Answer: 5(x + 1)(x + 4)
Step-by-step explanation Tell me if it is wrong
Two arithmetic means between 3 and 24 are -
The value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.
What is arithmetic mean?Arithmetic mean is the mean or average which is equal to the ratio of sum of all the group numbers to the total numbers.
The two arithmetic means between 3 and 24 are has to be inserted.
3, A₂, A₃, 24
All the four numbers are in arithmetic progression. The nth terms of AM can be found using the following formula:
t(n)=a(n-1)d
Here, d is the common difference a is the first terms and n is the total term. The first term, a=3 and t₄=24. Thus, the common difference is;
[tex]t(n)=a(n-1)d\\t(4)=3(4-1)d\\24=3(3)d\\24=9d\\d=\dfrac{24}{9}[/tex]
The second and 3rd term are:
[tex]A₂=3+\dfrac{24}{9}=\dfrac{51}{9}\\ A₃=\dfrac{51}{9}+\dfrac{24}{9}=\dfrac{75}{9}[/tex]
Thus, the value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.
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If RS= 5 , RT = 12 , ST = 7 , and points R, S, and T are collinear, what is the relationship between points R , S , and T ?
The relationship between points R , S , and T is that the sum of the RS and RT will be equal to RT that is RT=RS+ST
What are collinear points?Collinear points are defined as the points which lie on the same line. Here we have three points R, S and T that are collinear.
We have the length equal to:
RS=5, RT=12 ST=7
So we can set the relationship as the sum of the RS and RT will be equal to RT.
So the relation will be given as:-
RT=RS+ST
hence the relationship between points R , S , and T is that the sum of the RS and RT will be equal to RT that is RT=RS+ST
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Answer:
R, S, and T
Step-by-step explanation:
collinear, is the relationship between all the points
What is the distance between (-5, 2) and (-1, 6). Round to the nearest tenths if necessary. You can either graph it or use the distance formula below.
Answer:
Hope the picture will help you........
PLEASE HELP 15 POINTS!!!
Sequence: 24 + 12 + 6 + 3 +...
Explanation:
This is infinite geometric series converges.
[tex]\sf S \infty \ =a_1 \ x \ \dfrac{1}{1-r}[/tex]
Identify the following
a1 = 24r = 12 ÷ 24 = 1/2Solve:
[tex]\rightarrow \sf S \infty \ =24\ x \ \dfrac{1}{1-\frac{1}{2} }[/tex]
[tex]\rightarrow \sf S \infty \ =48[/tex]
This is series has a sum of 48.
Which three side lengths best describe the triangle in the diagram?
Answer:
Option C . 6 cm , 8 cm and 10 cm
Step-by-step explanation:
Question : Which three side lengths best describe the triangle in the diagram?
Solution :As we can clearly see measurement of the scale [ refer to attachment ]
In Triangle ABC
AC = 6 cm CB = 10 cmAB = 8 cmTherefore option C is Correct.
When the common ratio of an
infinite geometric sequence is
less than 1, its sum can be
found by the formula
a
where s is the sum, a is the first
term, and r is the common
ratio, What is the sum of the
geometric sequence below?
16,8,4,2.
The sum of the infinite geometric sequence 16, 8, 4, 2 is 32
How to find the sum of a geometric sequence?The sum can be represented as follows:
s∞ = a / 1 - r
where
r = common ratio
a = first term
Therefore,
r = 8 / 16 = 1 / 2
a = 16
hence,
s = 16 / 1 - 1 / 2
s = 16 / 1 / 2
s = 16 × 2 / 1
s = 32
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16 out of 80 baseball players are left handed.
What percent of the players are left handed?
Answer:
20% of players are left-handed
Step-by-step explanation:
First, find how much each player is worth percent-wise
100 / 80 = 1.25
Then find out how much percent of players that makes up
1.25 x 16 = 20
The answer is 20% of players are left-handed, to check it you could do
80 * 0.2 = 16
(80 = total players, 0.2 = 20%, 16 = total left handed players)
Please solve (17 points)
Answer:
50.6
Step-by-step explanation:
In a recent survey of gun control laws, a random sample of 1000 women showed that 65% were in favor of stricter gun control laws. In a random sample of 1000 men, 60% favored stricter gun control laws. Construct a 95% confidence interval for p1 − p2.
Answer:
[tex]CI\approx\{0.0076,0.0924\}[/tex]
Step-by-step explanation:
The formula for a z-confidence interval for a difference of proportions is [tex]\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z^*\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}[/tex]:
Let [tex]\hat{p}_1=0.65[/tex] to represent the sample proportion of [tex]n_1=1000[/tex] women who are in favor of stricter gun control laws and let [tex]\hat{p}_2=0.60[/tex] to represent the sample proportion of [tex]n_2=1000[/tex] men who are in favor of stricter gun control laws.
A 95% confidence level corresponds to a critical value of [tex]z^*=1.96[/tex], so now we perform the necessary calculations assuming conditions are met:
[tex]\displaystyle CI=(0.65-0.60)\pm 1.96\sqrt{\frac{0.65(1-0.65)}{1000}+\frac{0.60(1-0.60)}{1000}}\approx\{0.0076,0.0924\}[/tex]
Hence, we are 95% confident that the true difference in the proportion of women and men who favor stricter gun control laws is between 0.0076 and 0.0924
Since the interval does not contain "0" and only contain values greater than "0", it is more likely that the proportion of women who were in favor of stricter gun control laws is higher than the proportion of men who were in favor of stricter gun control laws.
2. Which theorem would show that x = 5 in the diagram?
Answer:
Midsegment theorem for Traoezoids
Step-by-step explanation:
I hope it helps you
Please help me my friends
What is the perimeter of this rectangle?
The length and width of the rectangle will be √68 and √17. Then the perimeter of the rectangle will be 2 (√17 + √68).
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
The graph is shown below.
Then the perimeter of the rectangle will be
P = 2 (length + width)
The length of the rectangle will be
L² = 2² + 8²
L² = 4 + 64
L² = 68
L = √68
The width of the rectangle will be
W² = 1² + 4²
W² = 1 + 16
W² = 17
W = √17
Then the perimeter will be
P = 2 (√17 + √68)
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10.4 sides polygon with 2 sides of parallel sides. What type of polygon is it?
Answer:
Here is the answer:
Step-by-step explanation:
An isosceles trapezoid is a trapezoid whose non-parallel sides are congruent. A kite is a quadrilateral with exactly two pairs of adjacent congruent sides.
Enter the coordinates of the point on the unit circle at the given angle. 120°
The coordinate is (-1/2, √3/2) and the missing values will be 2 and 3 if the angle is 120 degree.
What is the polar equation?A polar coordinate system is a two-dimensional coordinate system in which a distance from a reference point and an angle from a reference direction identify each point on a plane.
We have an angle of 120 degree
θ = 120 degree
r = 1 unit
As we know, the coordinate in the polar form from the rectangular form is:
x = rcosθ = cos120 = -1/2
y = rsinθ = sin120 = √3/2
Thus, the coordinate is (-1/2, √3/2) and the missing values will be 2 and 3 if the angle is 120 degree.
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rewrite the equation in Ax+By=C form. use intergers for A,B,C
y=1/5-1
Answer:
[tex]5y=-4[/tex]
Sure hope this helps you :D
Given a triangle ABC at points A=(-4,-3) B=(4, 5) C=(2,-4), and if the triangle is
dilated with a scale factor of 3, centered at the origin, find the new point C'.
Answer: (6,-12)
Step-by-step explanation:
For dilations centered at the origin, we can multiply each of the coordinates by the scale factor. This means that [tex]C'=(2 \times 3, -4 \times 3)=\boxed{(6, -12)}[/tex]
Identify the intercepts of the graph.
Answer: X-ints = (-1,0) and Y-ints = (1,0)
Step-by-step explanation:
This is quite simple. The way to solve this problem is by visualization, if you have learned how coordinates are created, this is how you would do it.
In a 2D plane, you have an X and Y axis and coordinates are created in the form of (X,Y).
by simply looking at the graph, I can see how the line crosses the positive 1 in the Y-axis, and -1 in the X-axis.
Part A) asks to find the X-intercept(s) which as stated above, it croses -1 on the X-axis and 0 on the Y-axis. Therefore the intercept is:
(-1,0)
part B) asks the same but for the Y-intercepts. We look at the graph and see the line crosses positive 1 in the Y-axis, and 0 in the X-axis. So:
(0,1)
done :)
11. What is the equation of the median-median line for the dataset in the table?
X Y
2 6
4 22
6 30
8 24
10 40
12 46
14 52
16 72
18 60
20 64
The equation of the median-median line for given data will be y = 3x + 10. Then the correct option is A.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The data set in the table is given below.
X Y
2 6
4 22
6 30
8 24
10 40
12 46
14 52
16 72
18 60
20 64
For the above after dividing the above data into 3 parts of the set (3,4,3)
Then the equation of the median-median line for given data will be
y = 3x + 10
Then the correct option is A.
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PLEASEEEEE HELPPP MEEEEEE
Answer:
(4:-4)
Step-by-step explanation:
the graphs y- axis starts at 4 and ends at -4
3f–4g=1
6f–6g=5
use the elimination method
Does (84,-7) has one, two or no solution?
Answer:
No sollution
Step-by-step explanation:
It simple
o is the centre of the circle find the size of each angle
Answer:
In the figure,
AC is the diameter of circle with centre O
∠DAC=37
o
AD || BC
∠ACB=∠DAC (Alternate angles)
Hence,
x=37
o
In Δ ABC,
∠B=90
o
(angle in semicircle)
By angle sum property of triangle, we get,
∠x+∠y+∠B=180
o
37
o
+∠y+90
o
=180
o
∠y=180
o
−127
o
We get,
∠y=53
o
Step-by-step explanation:
solve quadratic 2x^2 -7 +6 =0
Answer:
Assuming you meant 2x^2-7x+6=0,
the answer is x=2, x=1.5
Use the quadratic formula. (-b (+ or -) sqrt(b^2 - 4ac) )/ (2a)
It costs $3.00 to rent a boat on the lake for hour. Select ALL the statements that correctly match this ratio.
4
3
- of a hour costs $9.00
4
2 hours costs $18.00
1 hour costs $12.00
1
2
hour costs $6.00
2 hours costs 6 dollars is the only statements that is true
--
simply add 3.00 to 3.00 because its 2 hours
or if it was half an hour simply add 1.50 because half of 3.00 is 1.50
How can you tell whether two graph functions
represent inverse functions or not?
Answer:
If is not one to one is not inverse (no inverse)
Step-by-step explanation: