Answer: both roots are greater than zero
Step-by-step explanation:
If this is factored, you can find the roots.
(x-3)(x-5)=0
Set each factor equal to zero and solve.
x-3=0
x=3
Find the mean absolute deviation of the following numbers. 10, 8, 5, 12, 20
The varsity girl's basketball team has a ratio of seniors to juniors that is 3 to 2. If each team has 12 juniors, which team has more seniors?
This question is incomplete
Complete Question
A varsity boys' basketball team has a ratio of seniors to juniors that is 7:4.
The varsity girls' basketball team has a ratio of seniors to juniors that is 3 to 2. If each team has 12 juniors, which team has more seniors
Answer:
The boys' team has more seniors
Step-by-step explanation:
If each team has 12 juniors,
Step 1
For the boys' basketball team, lets find the total number of people on the team
A varsity boys' basketball team has a ratio of seniors to juniors that is
7:4 = seniors : juniors
Sum of proportion
= 7 + 4 = 11
Let the total number of people on the team = x
Hence:
4/11 × x = 12
4x/11 = 12
Cross Multiply
4x = 11 × 12
x = 11 × 12/4
x = 33 members
The number of seniors is calculated as
33 members - 12 juniors
= 21 seniors
Step 2
For the girls' basketball team, lets find the total number of people on the team
The varsity girls' basketball team has a ratio of seniors to juniors that is 3 to 2.
= 3:2 = seniors : juniors
Sum of proportion
= 3+2 = 5
Let the total number of people on the team = x
Hence:
2/5 × x = 12
2x/5 = 12
Cross Multiply
2x = 5 × 12
x = 5 × 12/2
x = 30 members
The number of seniors is calculated as
30 members - 12 juniors
= 18 seniors
Therefore, from our above calculations, the boys' team has more seniors
Susan and Katie are running an ultra marathon. Susan averages 5 miles per hour. Katie averages 5.2
miles per hour. If Susan gets a 45 minute head start, then exactly how many hours after Katie begins
running will she catch up to Susan?
Answer:
Katie will catch up to Susan after running 33.4 h.
Step-by-step explanation:
We can find the time that takes Katie to catch up to Susan by using the following equation:
[tex] x_{f_{k}} = x_{0_{k}} + v_{0_{k}}t + \frac{1}{2}at^{2} [/tex]
Where:
[tex] x_{f_{k}} [/tex]: is the final position of Katie
[tex] x_{0_{k}} [/tex]: is the initial position of Katie = 0
[tex] v_{0_{k}}[/tex]: is the initial speed of Katie = 5.2 mi/h
a: is the acceleration = 0 (she is moving at constant speed)
t: is the time
Since Katie will catch up to Susan, the final distance traveled by Katie will be equal to the final distance traveled by Susan.
[tex] x_{f_{s}} = x_{0_{s}} + v_{0_{s}}t + \frac{1}{2}at^{2} [/tex]
[tex] x_{0_{k}} + v_{0_{k}}t = x_{0_{s}} + v_{0_{s}}t [/tex]
Since Susan gets a 45 minutes head start, in that time she traveled the following distance:
[tex] d = \frac{v}{t} = \frac{5 mi/h}{45 min*\frac{1 h}{60 min}} = 6.67 mi [/tex]
So, this will be the initial position of Susan.
[tex] 0 + v_{0_{k}}t = x_{0_{s}} + v_{0_{s}}t [/tex]
Hence, the time will be:
[tex] 5.2t = 6.67 + 5t [/tex]
[tex] t = 33.4 h [/tex]
Therefore, Katie will catch up to Susan after running 33.4 h.
I hope it helps you!
What is the sum of the polynomials below ? 3y^5-2y+8 2y^5 - 4y^3-7
Answer:
[tex](3 {y}^{5} - 2y + 8) + (2 {y}^{5} - {4y}^{3} - 7) \\ = 5 {y}^{5} - 4 {y}^{3} - 2y + 1[/tex]
Simplify using suitable property. Also name the property used:-3/5 x 4/7 + 8/5x 4/7
Answer:
The answer is 4/7 and the property used is the distributive property
Step-by-step explanation:
Recall from the distributive property;
a * (b + c) = ab + ac
Applying same here, we have it that;
4/7 (-3/5 + 8/5)
= 4/7 * ((-3 + 8)/5)
= 4/7 * 5/5
= 4/7 * 1 = 4/7
consider the equation k over x equals 12 where k is any number between 20 and 65 and X is a positive integer what are the possible values for x
I need help with this question w2–23w–50
Answer:
(w - 25)(w + 2)
Step-by-step explanation:
w² - 23w - 50
w² + 2w - 25w - 50
w(w + 2) - 25(w + 2)
(w - 25)(w + 2)
W² – 23 W – 50 =0
(w - 25) ( w+2) =0
As for:
w-25=0
w=25
or :
w+2=0
w=-2
I hope I helped you^_^
Which of the following is the definition of the sine ratio in a right triangle
Answer:
Oppositeleg
adjacenleg
Answer:
option 1
Step-by-step explanation:
Just remember this to get the trigonometric ratio in a right triangle :
Old Henry And His Old Aunt
O for opposite
H for hypotenuse
A for Adjacent
Sin = O/ H
Cos = A /H
Tan = O /A
PLEASE HELP How can you make different triangles with the same angle measures?
Form different triangles with angle measures 90°, 75°, and 15°
How can you make different triangles with the same angle measures?
O A. Make triangles with the same angle measures and the same side lengths
OB. It is not possible to make different triangles with the same angle measures.
OC. Make triangles with the same angle measures but different side lengths
OD. Make triangles with the same side lengths but different angle measures
if cos a>0 and cot a is undefined then where does the terminal side of a located?
A. Quadrant II
B.quadrant III
C.negative x axis
D.negative y axis
E.no such angle a exists
Answer:C
Therefore: In Quadrant I, cos(θ) > 0, sin(θ) > 0 and tan(θ) > 0 (All positive). For an angle in the second quadrant the point P has negative x
Step-by-step explanation:
Oksana wrote the equation below on the whiteboard.
6 b + 6 = 48
What is the value of b?
4
7
8
9
Answer:
b = 7
Step-by-step explanation:
6 b + 6 = 48
Subtract 6 from each side
6b+6-6 = 48 -6
6b = 42
Divide each side by 6
6b/6 = 42/6
b = 7
Answer:
7Step-by-step explanation:
6b +6 = 48
collect terms that is ,
6b =48 - 6
6b = 42
divide both sides by 6
therefore, b = 42/6 =7
Hope this helps !
express 81 as sum of odd numbers.
Step-by-step explanation:
[tex]1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17[/tex]
Solution all the odd no. show sum is 81please help me!!!!!!!!!
Answer:
10 * 5 / 2 = 25 cm
Step-by-step explanation:
Hope this helps
Answer:
25 cm² is the answer ..... my sister
1 3,000 600 2 1,600 40 3 640 32 4 3,048 381
Answer:
What?
Step-by-step explanation:
Is that a question?
PLEASE I REALLY NEED HELP
Plans for a new school call for classrooms directly across the hall from each other to be congruent. This computer printout shows a math classroom. If the vertices of a science classroom are located at (-3x¹,y¹). (-3x²,y²), (-3x³, y³), and (-3x⁴, y⁴), will the science classroom be congruent to the math classroom?
The lengths of the horizontal sides of the science class is larger than the
length of the horizontal side of the math class.
The correct option is; No, the the transformation applied was not a rigid motion.
Reasons:
The given vertices of the science classroom are;
(-3·x₁, y₁), (-3·x₂, y₂), (-3·x₃, y₃), and (-3·x₄, y₄)
The coordinates of the vertices math classroom are;
(x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄)
Whereby x₁ = x₄, we have;
Length of the vertical side of the rectangular math class = y₁ - y₄
Length of the horizontal side, [tex]L_M[/tex] = x₂ - x₁
Similarly;
The length of the horizontal side of the science class is, [tex]L_S[/tex] = -3·x₂ - (-3·x₁)
Therefore;
[tex]L_S[/tex] = 3·(x₁ - x₂) = [tex]\mathbf{3 \cdot L_M}[/tex]
The length of a side of the science is three times the length of the side of
the math class, which gives that the dimensions of the science class are not
the same as the the dimensions of the math class.
Therefore;
The science class and the math class are not congruent
The the correct option is, no the transformation that gives the science class from the math class is not a rigid transformation.Learn more about non-rigid transformation here:
https://brainly.com/question/2396426
whats the value of x? 8(-6 + 6x) = 240
Answer:
x = 6
Step-by-step explanation:
8(-6 + 6x) = 240
Distribute the 8
-48 + 48x = 240
Add 48 to both sides
48x = 288
Divide both sides by 48
x = 6
Right triangle XYZ has right angle Z. If the sin(X)=1213
, what is the cos(X)
Given:
Right triangle XYZ has right angle Z.
[tex]\sin(x)=\dfrac{12}{13}[/tex]
To find:
The value of [tex]\cos x[/tex].
Solution:
We know that,
[tex]\sin^2(x)+\cos^2(x)=1[/tex]
[tex]\cos^2(x)=1-\sin^2(x)[/tex]
[tex]\cos(x)=\pm\sqrt{1-\sin^2x}[/tex]
For a triangle, all trigonometric ratios are positive. So,
[tex]\cos(x)=\sqrt{1-\sin^2x}[/tex]
It is given that [tex]\sin(x)=\dfrac{12}{13}[/tex]. After substituting this value in the above equation, we get
[tex]\cos(x)=\sqrt{1-(\dfrac{12}{13})^2}[/tex]
[tex]\cos(x)=\sqrt{1-\dfrac{144}{169}}[/tex]
[tex]\cos(x)=\sqrt{\dfrac{169-144}{169}}[/tex]
[tex]\cos(x)=\sqrt{\dfrac{25}{169}}[/tex]
On further simplification, we get
[tex]\cos(x)=\dfrac{\sqrt{25}}{\sqrt{169}}[/tex]
[tex]\cos(x)=\dfrac{5}{13}[/tex]
Therefore, the required value is [tex]\cos(x)=\dfrac{5}{13}[/tex].
At the dance shoe store, they sell Tap, Point, and Ballet shoes. A pair of point shoes are double the price of ballet shoes. The tap shoes are $10 more than ballet shoes. If the total price of all the shoes is $648, how much is each shoe
Answer:
a pair of Tap shoes costs $169.50
a pair of Point shoes costs $319.00
a pair of Ballet shoes costs $159.50
Step-by-step explanation:
first tell your teacher, that the problem description is misleading.
as a shoe store has more than one pair per type. so, "all the shoes" would mean all the sites in the store. but that is for sure not meant here.
what your teacher hopefully meant was that the total price of buying one pair of each of the shoe types is $648.
and your teacher was hopefully asking for the price of pairs of shoes, and not actually single shoes.
my solution bases on these assumptions.
so, we got Tap (t), Point (p) and Ballet (b) shoes.
buying one pair each is
t + p + b = 648
now we know some other information.
p = 2×b (Point shoes are double the price of Ballet shoes)
t = b + 10 (Tap $10 more than Ballet)
so, we can replace t and p by expressions of b and get
b + 10 + 2×b + b = 648
4×b + 10 = 648
4×b = 638
b = 159.50
p = 2×159.50 = 319.00
t = 159.50 + 10 = 169.50
Solve the following equation for x.
18 – 4.x = 10 - 2x
A x = -4
B) x = -1
C) x = 1
D) x =4
Answer:
D) x = 4
Step-by-step explanation:
18 - 4x = 10 - 2x
10 - 2x = 18 - 4x
10 - 2x + 4x = 18 - 4x + 4x
10 + 2x = 18
10 - 10 + 2x = 18 - 10
2x = 8
2x ÷ 2 = 8 ÷ 2
x = 4
CORRECTLY ANSWER PLEASE AND THANK YOU
9514 1404 393
Answer:
(-3, 4)
Step-by-step explanation:
The midpoints of the diagonals of a parallelogram are coincident. This means the sums of coordinates at the ends of the diagonals are the same. For missing point P, we must have ...
P +(0, -3) = (-6, -6) +(3, 7)
P = (-6, -6) +(3, 7) -(0, -3)
P = (-6 +3 -0, -6 +7 -(-3))
P = (-3, 4)
Identify the angle between 0 and 360 degrees that is coterminal with the
following angle *
1155°
Answer:
option 2
Step-by-step explanation:
By repeatedly subtracting 360° from the given angle.
1155° - 360° = 795°
795° - 360° = 435°
435° - 360° = 75° ← coterminal angle
The odometer on Ed's car shows 8,946 miles. The odometer on Beth's car shows 5,042 miles driven. Which car has traveled the most miles?
(NO LINKS)
Answer:
since 8946 is more then 5042 we know ed has driven the most miles.
Step-by-step explanation:
A circle P is circumscribed about a regular hexagon ABCDEF
Arc AB =
Select one:
a. 60
b. 120
c. not enough information
d. 90
Answer:
angle degrees is 60
so the answer would be A
Step-by-step explanation:
because there are 6 sides, 360 is divided by 6.
which of the following is the slope of a line perpendicular to the line y = -2/3 x +5
Answer:
-2/3x is the slope
Step-by-step explanation:
y=mx+b is the equation to follow
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli. The correct value of t* to construct a 98% confidence interval for the true mean amount of cheese filling is ________. Group of answer choices 2.797 2.492 2.064 3.467 3.745
Answer:
The correct value is t* = 2.492.
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.492, which is the answer to this question.
A Department of transportation report about air travel that nationwide, 76% of all flights are on time. In a sample of 12 flights, what is the probability that 3 flights will be late?
Answer:
The probability of 3 flights are late is 0.25.
Step-by-step explanation:
Total number of flights = 12
Flights on time = 76 % = 0.76 x 12 = 9.12 = 9
flights which are late = 24 % = 0.24 x 12 = 2.88 = 3
The probability of 3 flights are late is
P = 3/12= 1/4 = 0.25
The president of a small company
made $72,000 last year. She cut her
salary this year to $60,000 because
the company was not doing as well.
What was the percent decrease in
her salary to the nearest percent?
Answer:
17%
Step-by-step explanation:
Percent decrease
[tex] = \frac{72000 - 60000}{72000} \times 100 \\ \\ = \frac{12000}{72000} \times 100\\ \\ = \frac{1200000}{72000} \\ \\ = 16.67 \% \\ \\ \approx \: 17 \%[/tex]
Solve the system of equations below using the elimination method.
Show how you determined your solution.
4x+y=23
3x-y=12
Answer:
The solution is (5, 3)
Step-by-step explanation:
To solve this system of linear equations, let's use elimination by addition and subtraction. This approach is particularly easy because one equation already has +y and the other -y, summing up to zero:
4x+y=23
3x-y=12
---------------
7x = 35
Then x must be 5.
Substituting 5 for x in the first equation, we get
4(5) + y = 23. Then 20 + y = 23, or y = 3.
The solution is (5, 3)
11.) Evaluate the expression.
Answer:
- 116
Step-by-step explanation:
Given
28 - ( [tex]\sqrt{144}[/tex] )²
= 28 - (12)²
= 28 - 144
= - 116
Determine the general rule for the sequence 19;11;3;.....
Answer:
Answer 3.0/528 claudiasai 88-2n + 2927,25,23,21,19- 2 difference- 2n + 29-2 x (1 ) + 29 =27-2 x (3) +29 =23
Step-by-step explanation:
Write a recursive formula for each sequence. 3. 1, 6, 11, 16, ... SOLUTION: ... Check for a common ratio by dividing each term by the term that precedes it. = 3 ;. = 3 ; ... 19. 100, 80, 64, 51.2, ... SOLUTION: Subtract each term from the term that follows it. ... Patrick thinks that the sequence can be written as a recursive formula.
Answer:
[tex]a_{n}[/tex] = 27 - 8n
Step-by-step explanation:
There is a common difference between consecutive terms, that is
11 - 19 = 3 - 11 = - 8
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 19 and d = - 8 , then
[tex]a_{n}[/tex] = 19 - 8(n - 1) = 19 - 8n + 8 = 27 - 8n ← general rule
