Answer:
[tex]x=\frac{\sqrt{13}-7 }{18} ,x=\frac{-\sqrt{13}-7 }{18}[/tex]
Step-by-step explanation:
I'm not too good with the quadratic formula so I'm going to complete the square.
First divide everything by 9 and move the 1 to the other side.
[tex]x^2-\frac{7}{9}=-\frac{1}{9}[/tex]
Then take half of [tex]\frac{7}{9}[/tex] and square it and add it to both sides.
[tex]x^2-\frac{7}{9} +\frac{49}{324}=\frac{13}{324}[/tex]
Now you can factor it.
[tex](x-\frac{7}{18})^2=\frac{13}{324}[/tex]
Square root:
[tex]x-\frac{7}{18}=\frac{\sqrt{13} }{18}[/tex]
[tex]x=\frac{\sqrt{13}-7 }{18} ,x=\frac{-\sqrt{13}-7 }{18}[/tex]
One number is 9 more than another number. The sum of the numbers is 25. What is one of the numbers?
Answer:
16? maybe
Step-by-step explanation:
i justed counted from 9 to 25,l
Answer:
8 or 17
Step-by-step explanation:
The system of equations for this is:
x = 9 + y
x + y = 25
Find the value of y by plugging the first equation into the second.
9 + y + y = 25
9 + 2y = 25
2y = 16
y = 8
One of the numbers is 8.
OR
Find the value of x by plugging the value of y into one o the equations.
x = 9 + 8
x = 17
or
x + 8 = 25
x = 17
One of the numbers is 17.
Prove that (2n+1)^2 - (2n+1)^2 is a multiple of 8 for all positive integer values of n
Answer:
(2n + 1)[(2n + 1) � 1]
(2n + 1)(2n + 1 � 1)
(2n + 1)(2n), or 2n(2n + 1)
2n is an EVEN NUMBER, and adding 1 to an even number creates an ODD number
Therefore, 2n(2n+1)=EVEN NUMBER ODD NUMBER=EVEN NUMBER
Step-by-step explanation:
Which equation represents the line that passes through (-8.11) and
(4,7/2)?
Answer:
[tex]y=-5/8x+6[/tex]
Step-by-step explanation:
[tex]m=\frac{7/2 - 11}{4--8}[/tex]
[tex]m=\frac{-15/2}{12}[/tex]
[tex]m=-5/8[/tex]
[tex]y=-5/8x+b[/tex]
[tex](-8,11)[/tex]
[tex]11=-5/8 \times -8+b[/tex]
[tex]b=11-(-5/8)(-8)[/tex]
[tex]b=6[/tex]
A beverage manufacturer performs a taste-test and discovers that people like their fizzy beverages best when the redius of the bubbles is about 0.7 mm. According to the formula below, what would be the volume of one of these bubbles?
Answer:
0.267[tex]mm^3[/tex]
Step-by-step explanation:
Radius of the Bubble = 0.7 mm
Volume of the bubble is given by the formula :
[tex]r=\sqrt[3]{\frac{3V}{4\pi } }[/tex]
Taking cube on both sides
[tex]V=\frac{4\pi\times r^3 }{3}\\\\ V=\frac{4\times3.14\times(0.7)^3}{3}\\\\V=\frac{12.56\times 0.064}{3}\\\\ V=\frac{0.804}{3}\\\\V=0.267mm^3[/tex]
What is the product of ( x + 3) ( x - 4)?
I'm sure its x^2 - x - 12, but I wanted to double-check :D
Answer: x² - x - 12
Step-by-step explanation: When multiplying two binomials together, we can use the F.O.I.L. method.
First, Outer, Inner, Last.
We take the product of the first terms which is x² plus the product of the outer terms which is -4x plus the product of the inner terms which is 3x plus the product of the last terms which is -12.
So we have x² - 4x + 3x - 12.
Simplifying from here by combing the middle terms, we have x² - x - 12.
Pay very close attention to your positives and negatives as you F.O.I.L. because this is the area where most mistakes occur.
if f(x)=1/2x-2 what is f(14)
Answer:
Hi there!
The correct answer is: 5
Step-by-step explanation:
Essentially they replace x with 14, so all you have to do is plug 14 into the equation. 14 multiplied by 1/2 is 7, because it's the same thing as 14 divided by 2. Then you minus 2 from 7, and you get 5.
18 POINTS! At the AoPS office, mice vary inversely with cats, that is, mice=k/cats, for some value of k. When there are 3r-19 cats, there are 2r+1 mice, and when there are 6r-27 mice, there are r-5 cats. Find k. Please help, and do not answer with an "I don't know" or "Sorry, this is too hard." Thank you all!
Answer:
k=30
Step-by-step explanation:
The number of mice vary inversely with cats. This is written as:
[tex]Mice \propto \dfrac{1}{Cat} \\Mice = \dfrac{k}{Cat}[/tex]
When there are 3r-19 cats, there are 2r+1 mice
[tex]2r+1 = \dfrac{k}{3r-19}\\$Cross multiply$\\k=(3r-19)(2r+1)[/tex]
When there are 6r-27 mice, there are r-5 cats.
[tex]6r-27 = \dfrac{k}{r-5}\\$Cross multiply$\\k=(6r-27)(r-5)[/tex]
Taking the values of k above, we have:
[tex]k=(3r-19)(2r+1) =(6r-27)(r-5)\\(3r-19)(2r+1) =(6r-27)(r-5)\\6r^2+3r-38r-19=6r^2-30r-27r+135\\$Collect like terms\\6r^2-6r^2+3r+30r-38r+27r-19-135=0\\22r-154=0\\22r=154\\$Divide both sides by 22\\r=7[/tex]
Therefore:
[tex]k=(3r-19)(2r+1) \\=(3*7-19)(2*7+1)\\=(21-19)(14+1)\\=2*15\\k=30[/tex]
slove for g : 9+3.5g=11-0.5g
Answer:
g= 1/2
Step-by-step explanation:
9+3.5g=11-0.5g
Add .5 g to each side
9+3.5g+.5g=11-0.5g+.5g
9+4g = 11
Subtract 9 from each side
9+4g-9 = 11-9
4g = 2
Divide by 4
4g/4 = 2/4
g= 1/2
Help please !!!!!!!!!!!!!!!!!!!!!!!
Answer:
∠J and ∠K form a linear pair.
Step-by-step explanation:
If angles J and K are supplementary and adjacent, then they form what is known as a linear pair.
"Definition: Two angles that are adjacent (share a leg) and supplementary (add up to 180°)" -mathopenref
Help me please will mark brainliest
Answer:
-2 1/6
Step-by-step explanation:
Please HELP!!!!!!! PLEASE
Answer:
Step-by-step explanation:
Twins born call A
single child born called B
twins in family history 1
twins not in family history 2
my new table
1. 2
A 8/34=0.23 (23.52%) 26/34=0.7647 (76.47%)
B. 125/966=0.1293 (12.93%) 841/966=0.8706(87.06%)
I hope u understand my table
What are the ordered pairs of the
solutions for this system of equations?
f(x) = x2 – 2x + 3; f(x) = -2x + 7
Hey there! :)
Answer:
(2, 3) and (-2, 11).
Step-by-step explanation:
To solve this system of equations, we can set both equations equal to each other:
x² -2x + 3 = -2x + 7
Combine like terms:
x² -4 = 0
Factor using difference of squares:
(x - 2)(x + 2) = 0
Therefore, x = 2 and -2. Plug both of these into an equation to solve for the 'y' value:
f(x) = -2(2) + 7
f(x) = -4 + 7
f(x) = 3
------------------
f(x) = -2(-2) + 7
f(x) = 4 + 7
f(x) = 11
Therefore, the two ordered pairs are (2, 3) and (-2, 11).
Simplify the following expressions by using distributive property. 3x^2(4x-3)
Answer:
12x^3-9x^2
Step-by-step explanation:
[tex]3x^2(4x-3)= \\\\3x^2(4x)+3x^2(-3)= \\\\12x^3-9x^2[/tex]
Hope this helps!
El que responda bien 5 estrellas y un gracias 7u7
Answer: AB=12
Los triangulos BCD y ADE son iguales por tener dos lados y el angulo comprendido respectivamente iguales. por tanto AE=DC=4
Luego AB = AE+EB = 4+8 = 12
factored form of 2x*2+13x+20
Answer:
(2x+5)(x+4)
Step-by-step explanation:
After factoring we can find that it equals
(2x+5)(x+4)
Answer:
(2x +5) (x+4)
Step-by-step explanation:
2x*2+13x+20
(2x + )(x+ )
Factoring 20 into 4 and 5 so we can get 13 in the middle
(2x +5) (x+4)
2*4 +5 = 13 for the middle term
The largest of the great pyramids in Egypt was built with a square base having edges measured 754 feet and a height of 418 feet. To the nearest cubic foot, what was the volume of the original structure
Answer:
[tex]79213229.3 ft^3[/tex]
Step-by-step explanation:
The great pyramids pf Egypt are square based pyramids.
The volume of a square based pyramid is:
[tex]V = a^2h/3[/tex]
where a = length of square base
h = height of pyramid
The pyramid has a square base measured as 754 feet and a height of 418 feet. Its volume is:
[tex]V = 754^2 * 418 / 3\\\\V = 79213229.3 ft^3[/tex]
. The new saleswoman at Clocks Unlimited was very good. During her first day on the job she sold at least two of each of the three models that other salespeople found the most difficult to sell: the kitchen clock that sells for $17, the cuckoo clock that sells for $3 1, and the two-foot high grandfather clock that sells for $61. In all, she collected $300 from selling these models alone. How many $17 clocks did she sell? Justify your answer
Answer:
5
Step-by-step explanation:
Let the number of the kitchen clock sold =a
Let the number of the cuckoo clock sold =b
Let the number of the two-foot high grandfather clocks sold =c
The new saleswoman sold at least two of each of the three models.
Therefore:
[tex]a\geq 2\\b \geq 2\\c \geq 2[/tex]
In all, she collected $300 from selling these models alone
17a+31b+61c=300
17(2)+31(2)+61(2)=218
300-218=82
Next, we try to express the remainder (82) in terms of 17, 31 and 61
82=17(3)+31
Therefore, she sold:
5 kitchen clocks3 cuckoo clocks 2 two-foot high grandfather clocksShe sold 5 $17 clocks.
CHECK:
17(5)+31(3)+2(61)=$300
A sector with a central angle measure of 4pi/5
(in radians) has a radius of 5 cm.
What is the area of the sector?
Answer:
10 pi
Step-by-step explanation:
25 pi
20 pi
10 pi
5 pi
C is the answer
The area of the shaded sector of the circle will be 10π units².
What is the Area of a Sector?Area of a sector of a circle = θ/360 × πr², where r is the radius of the circle and θ is the central angle.
As per the question, QR = 5 and m∠RQS = 4π/5 = 144°.
As per the given question given data:
θ = 4π/5
r = QR = 5
Substitute the values in the formula to get:
Area of sector of a circle = 144/360 × π(5)²
Area of sector of a circle = 1/4 × π(25)
Apply the multiplication operation, and we get
Area of a sector of a circle = 10π units²
Thus, the area of the shaded sector of the circle is 10π units².
Learn more about the area of a sector here:
brainly.com/question/22972014
#SPJ2
The question seems to be incomplete the correct question would be:
In circle Q, QR = 5 and m∠RQS = 4π/5. Find the area of the shaded sector.
Express your answer as a fraction times pi.
Find the length of the third side to the nearest tenth.
5
1
Answer:
square root of 26 (sorry couldn't get the symbol)
Step-by-step explanation:
C^2 = A^2 + B^2 (Pythagoras Theorem)
C^2 = 5^2 + 1^2
C^2 = 26
take square root of both sides
C =
[tex] \sqrt{26} [/tex]
Un cazador se encuentra en la parte mas alta de un arbol. Para averiguar a que altura se encuentra, deja caer una bola, observando que demora 4 segundos. Encuentra el alto del arbol (g=10m/s2)
Answer:
80 m
Step-by-step explanation:
La velocidad inicial de la pelota es 0 m/s.
La altura del árbol es s.
El tiempo necesario es de 4 segundos.
Podemos aplicar una de las ecuaciones de movimiento de Newton:
[tex]s = ut + \frac{1}{2}gt^2[/tex]
donde u = velocidad inicial
t = tiempo empleado
g = aceleración debido a la gravedad
Por lo tanto:
[tex]s = 0 * 4 + (1/2 * 10 * 4^2)\\\\s = 0 + 80 \\\\s = 80 m[/tex]
El árbol tiene 80 metros de altura.
Which word describes a triangle with three angles, if each angle measures less than 90°? Please help
Answer:
acute triangle
Step-by-step explanation:
If an angle measures less than 90 degrees it is an acute angle
A triangle with all acute angles is an acute triangle
Help please picture attached !!! Factoring expression
Answer:
(x+y)^3
Step-by-step explanation:
125 is the third power of five and 216 is the third power of 6
so we can rewrite the expression as (x+y)^3
what is the rule for the reflection?
Answer:
(x,y)→(x,−y)
Step-by-step explanation:
I did it before
Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph. Can we say that this cheetah’s average rate was 55 mph? The average rate for the trip is equal to the total distance traveled divided by the total time traveled. The following equations represent the distance traveled on each leg of the trip. First leg of trip: d=r_1 t_1 Second leg of trip: d=r_2 t_2 Write an equation for the average rate for the trip. Remember, the cheetah runs from point A to point B and back to point A.
Answer:
No.
[tex]\text{Average rate} = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{r_{1}t_{1} + r_{2}t_{2}}{t_{1} + t_{2}}\\\\= \text{50.91 mi/h}[/tex]
Step-by-step explanation:
First leg: d = r₁t₁
Second leg: d = r₂t₂
r₁t₁ = r₂t₂
Total distance: 2d = r₁t₁ + r₂t₂
Total time: t = t₁ + t₂
1. Equation for average rate
[tex]\text{Average rate} = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{r_{1}t_{1} + r_{2}t_{2}}{t_{1} + t_{2}}[/tex]
2. Average rate
Since r₁t₁ = r₂t₂,
[tex]t_{1} = \dfrac{r_{2}t_{2}}{r_{1}} = \frac{40}{70}t_{2} = \frac{4}{7}t_{2}\\\\\text{Average rate} = \dfrac{2r_{2}t_{2}}{\frac{4}{7}t_{2} + t_{2}} = \dfrac{2 \times 40t_{2}}{\frac{4t_{2}+ 7t_{2}}{7}}= 80t_{2} \times\frac{7}{11t_{2}} = \dfrac{560}{11}\\\\= \textbf{50.91 mi/h}[/tex]
We cannot say truthfully that the average rate is 55 mi/h.
The average rate of a body is the total distance travelled divided by the total time.
The cheetah runs at an average rate of 50.91mph, not 55mph
Let
[tex]d \to[/tex] distance
[tex]r \to[/tex] average rate
[tex]t \to[/tex] time
Given that:
[tex]d = r_1t_1 = r_2t_2[/tex]
So, we have:
[tex]r_1 = 70[/tex]
[tex]r_2 = 40[/tex]
The average rate (r) is calculated as follows:
[tex]r = \frac{Total\ Distance (D)}{Total\ Time (T)}[/tex]
Where:
[tex]D=d + d[/tex]
[tex]D = r_1t_1 + r_2t_2[/tex]
and
[tex]T =t_1 + t_2[/tex]
So, the average rate is:
[tex]r =\frac{r_1t_1 + r_2t_2}{t_1 + t_2}[/tex]
Recall that:
[tex]D = r_1t_1 + r_2t_2[/tex]
[tex]r_1t_1 = r_2t_2[/tex]
Make [tex]t_2[/tex] the subject
[tex]t_2 = \frac{r_1t_1}{r_2}[/tex]
Substitute values for [tex]r_1[/tex] and [tex]r_2[/tex]
[tex]t_2 = \frac{70t_1}{40}[/tex]
So, we have:
[tex]r =\frac{r_1t_1 + r_2t_2}{t_1 + t_2}[/tex]
[tex]r = \frac{70t_1 + 40 \times \frac{70t_1}{40}}{t_1 + \frac{70t_1}{40}}[/tex]
[tex]r = \frac{70t_1 + 70t_1}{t_1 + \frac{70t_1}{40}}[/tex]
[tex]r = \frac{140t_1}{t_1 + \frac{70t_1}{40}}[/tex]
Factor out t1
[tex]r= \frac{140t_1}{t_1(1 + \frac{70}{40})}[/tex]
[tex]r = \frac{140}{(1 + \frac{70}{40})}[/tex]
[tex]r = \frac{140}{\frac{40+70}{40}}[/tex]
[tex]r= \frac{140}{\frac{110}{40}}[/tex]
Rewrite as:
[tex]r = \frac{140 \times 40}{110}[/tex]
[tex]r = 50.91mph[/tex]
Hence, the cheetah's average rate is 50.91mph, not 55mph
Read more about distance, average rates and time at:
https://brainly.com/question/22457482
The interior angles of a triangle are 60,45and 75.the shortest side is 10cm less than the longest side, determine the perimeter of the triangle to the nearest cm.include a diagram please and thank you!!
Answer:
20 cm.Step-by-step explanation:
We know that the permiter is defined as
[tex]P=L+S+M[/tex]
Where [tex]L[/tex] is the longest side, [tex]S[/tex] is the smallest and [tex]M[/tex] is the middle side.
If [tex]L=x[/tex] then, [tex]S=x-20[/tex], where we need to find an expression for [tex]M[/tex] using the law of cosines.
[tex]M^{2} =L^{2}+S^{2}-2 \times L \times S \times cos(60\°)\\M=\sqrt{x^{2}+(x-20)^{2}-x(x-20)}\\M=\sqrt{x^{2} +x^{2}-40x+400-x^{2}+20x}=\sqrt{x^{2}-20x+400}[/tex]
Replacing all expression, the perimeter is
[tex]P=x+x-20+\sqrt{x^{2}-20x+400}\\P=2x-20+\sqrt{x^{2}-20x+400}[/tex]
Using a calculator, the perimeter is 20 units centimeters.
Solve the proportion. What number is 20% of 40?
Answer:
What is 20 percent (calculated percentage %) of number 40? Answer: 8.
Step-by-step explanation:
happy to help ya:)
find the 7th term of the geometric progression which begins:
2, -6, 18...
Answer:
a7=1458
Step-by-step explanation:
2; -6; 18... a geometric progression
a1=2; a2=-6; a3=18
r=a2/a1=-6/2
r= -3
a7=a1*r⁶
a7=2*(-3)⁶=2*729
a7=1458
1/6book
2/3hour
as a unit rate.
Answer:
4 hours per book
Step-by-step explanation:
The unit rate per book can be found when the number of books read is 1.
To make 1/6 into 1, you need to multiply by 6, meaning that you have to multiply the time taken by 6 as well.
2/3*6=4 hours per book
Hope this helps!
Rahul was given 32 problems for home work. He has worked out . $ of them on Monday and . % of them on Tuesday . Find the number of problems left unsolved.
Answer: **Incomplete question**
Step-by-step explanation: Your question is incomplete, and missing very important details. However I would attempt to use assumed values in place of the omitted ones so that after explaining, it would be pretty much easy to figure out the solution.
If Rahul was given a total of 32 questions and he has worked out for example 25% of them on Monday and then 50% of them on Tuesday, to find the number of problems left, we would need to find the number of questions represented by the percentage indicated.
If he has worked out 25% of them on Monday, then that means he had done the following
Percentage done = 25% (or 25/100 which equals 0.25)
Number of problems solved = 32 * 25%
Number of problems solved = 32 * 0.25
Number of problems solved = 8
Further he solved 50% of them on Tuesday
Percentage done = 50% (or 50/100 which equals 0.50)
Number of problems solved = 32 * 50%
Number of problems solved = 32 * 0.5
Number of problems solved = 16
This means he has now solved a total of
8 + 16 = 24
If therefore he has solved 24 problems, then the number of problems left is derived simply as
Unsolved problems = 32 - 24
Unsolved problems = 8
Please remember that the use of 25% and 50% are simply assumptions in order to make explaining the solution easier. Please insert the correct values of the percentage as appropriate.
Santiago wants to walk at least 500 miles before the end of this year. He has already walked 437 miles, and there are 36 days left in the year. Which inequality can be used to find , the number of miles he should walk each day to meet his goal?
Answer:
437+36x>=500
Step-by-step explanation:
This basically shows that 437 plus the x miles he will walk per day for 36 will total to more than or equal to 500
Answer:
C 437 + 36x >_ 500
Step-by-step explanation: its because the total amount is 500 miles so its alone on one side of the equation. Then we have 437 miles + 36 days with x as a amount of how many miles per day. so first subtract 437 out off 500 then divide it by 36 which gives u X which is the answer.
