Answer:
Multiply the second equation by 9.
Step-by-step explanation:
To use the elimination method, you need to be able to add the equations and have one variable add to zero. That way you eliminate that variable.
The first equation has -9y. The second equation has y. If you multiply the second equation by 9, you will have 9y in the second equation. Then when you add equations, you will add -9y and 9y and will eliminate y.
Answer: Multiply the second equation by 9.
Answer:
Step-by-step explanation:
6x - 9y = 21
-6x -2y = -10
-11y = 11
y = -1
3x - 1 = 5
3x = 6
x = 2
(2, -1)
someone please help me, im so confused ack. In the derivation of the formula for the volume of a cone, the volume of the cone is calculated to be StartFraction pi Over 4 EndFraction times the volume of the pyramid that it fits inside. A cone is inside of a pyramid with a square base. The cone has a height of h and a radius r. The pyramid has a base edge length of 2 r. Which statement best describes where the StartFraction pi Over 4 EndFraction comes from in the formula derivation? A. It is the ratio of the area of the square to the area of the circle from a cross section. B. It is the ratio of the area of the circle to the area of the square from a cross section. C. It is the difference of the area of the square and the area of the circle from a cross section. D. It is the sum of the area of the square and the area of the circle from a cross section.
Answer:
The correct option is;
B. It is the ratio of the area of the circle to the area of the square from a cross section.
Step-by-step explanation:
The formula for the volume of a pyramid = 1/3*Area of base*Height
The formula for the volume of a cone = 1/3*Area of base*Height
The area of the base of the square pyramid of side 2r = 2r*2r = 4r²
The area of the base of the cone of base radius r = πr²
The ratio of the volume of the cone to the volume of the square pyramid is given as follows;
[tex]\dfrac{\dfrac{1}{3} \times \pi \times r^2\times h}{\dfrac{1}{3} \times( 2 \times r)^2\times h}[/tex]
Given that the height are equal, h/h = 1, which gives;
[tex]\dfrac{\dfrac{1}{3} \times \pi \times r^2}{\dfrac{1}{3} \times( 2 \times r)^2} = \dfrac{Area \ of \ the \ circle}{Area \ of \ the \ square} =\dfrac{\dfrac{1}{3} \times \pi \times r^2}{\dfrac{1}{3} \times 4 \times r^2} = \dfrac{\pi }{4}[/tex]
Therefore, where the π/4 comes from is that it is the ratio of the area of the circle to the area of the square from a cross section.
Answer:
b
Step-by-step explanation:
The probability of spinning a 4 on a spinner is 0.125.If you spun 150 times approximately how many times would the spinner land on 4?
Answer:
19
Step-by-step explanation:
To calculate this, all we need to do is 150 * 0.125 ≈ 18.75 which rounds to 19. We round to the nearest integer because you can't land on the 4 18.75 times.
Answer: 19
Step-by-step explanation:
.125 is equal to 1/8, so it will be roughly 1/8 of the 150 times so we can multiply
150(.125)=18.75, which rounded up, or normally becomes 19
find the value. 2x-5 when x=5/2
Answer:
0Step-by-step explanation:
Given,
x = [tex] \frac{5}{2} [/tex]
Now, let's find the value of 2x - 5
[tex]2x - 5[/tex]
plug the value of x
[tex] = 2 \times \frac{5}{2} - 5[/tex]
Reduce the number with Greatest Common Factor 2
[tex] = 5 - 5[/tex]
The sum of two opposites equals 0
[tex] = 0[/tex]
Hope this helps..
best regards!!
Answer:
0
Step-by-step explanation:
x=5/2
therefore
2(5/2)-5=10/2-5
=5-5(since 10/2=5)
=0
Can help me pleaseee I need help
Answer:
B since the correlation between the numbers in x raise at a higher rate than any other chart
Raul bought 6 tangerines and ate 2/3 of them. Omar bought 8 tangerines and ate 1/4 of them. Who ate more tangerines?
Rahul ate more tangerines...
Solve the equation using square roots. x2 – 14 = –10
Answer:-12
Step-by-step explanation:
Add 10+14 to get 24 then divide it by a negative 2 to get -12
Answer:
x = ±2
Step-by-step explanation:
x^2 – 14 = –10
Add 14 to each side
x^2 – 14+14 = –10+14
x^2 = 4
Take the square root of each side
sqrt(x^2) = ±sqrt(4)
x = ±2
ax = bx + 1. How is the value of x related to the difference of a and b?
Answer:
x = 1/(a-b)
Step-by-step explanation:
The given equation is ax = bx + 1
Collecting like terms:
ax - bx = 1
Factorizing x out of the equation:
x(a - b) = 1
Dividing both sides by (a - b):
[tex]\frac{x(a - b)}{(a - b)} = \frac{1}{a - b} \\x = \frac{1}{a - b}[/tex]
Therefore, x is related to the difference of a and be by the equation
x = 1/(a-b) where a - b is the difference of a and b
Answer:
x = 1/(a-b)
Step-by-step explanation:
I really need help with this question! Please help me!!!
Answer:
42°
Step-by-step explanation:
AD bisects ∠CAB, which means it splits ∠CAB into two equal parts. ∠CAB equals 84°. 84° ÷ 2 = 42°.
A block measure 22 cm by 11 cm by 7 cm.
How many of these blocks will be needed to
build a wall 5 1/2m long, 22 cm thick and 3 1/2
m high?
Answer: 2,500 blocks
Step-by-step explanation:
Hi, to answer this question we have to calculate both volumes:
Volume of a rectangular prism= length x width x height
Volume of the block = 22 x 11 x 7 = 1,694 cm3
Before calculating the volume of the wall, we have to convert the measures in m to cm:
Since:
1m = 100 cm
5 1/2 m x 100 = 550 cm (length)
3 1/2 m x 100 =350 cm (height)
Volume of the wall = 550 x 22 x 350= 4,235,000 cm3
Finally:
Volume of the wall /Volume of the block = 4,235,000 / 1,694 = 2,500 blocks.
Feel free to ask for more if needed or if you did not understand something.
Determine the sum of the first ten terms of the geometric series -1 + 2 - 4 + 8 + ...
Answer:
-1+2-4+8-10+12-14+16-18+20
=
-47+68
= +21
hope youlike this
stay at home stay safe
keep rocking
There are 28 brown ducks swimming in a pond. Twice as many white ducks flew in and landed in the pond. Then half of the ducks flew away. How many ducks remained in the pond?
Answer:
42 ducks remain in the pond
Step-by-step explanation:
First, find the number of white ducks
28*2=56
Add them to the brown ducks
56+28= 84
Then divide by 2 because half flew away
84/2=42
So 42 ducks remain in the pond. Hope this helps :)
HELP ASAP PLEASE
I JUST NEED WORK SHOWN BUT ASAP
Answer:
s = 25.33m
θ = 60.65°
12.37m
A = 160m^2
Step-by-step explanation:
The pyramid has a side base of 35m and a height of 22m.
side base = b = 35m
height of the pyramid = h = 22m
To calculate the slant edge of the pyramid, you first calculate the diagonal of the squared base of the pyramid.
You use the Pythagoras theorem:
[tex]d=\sqrt{(\frac{35}{2})^2+(\frac{35}{2})^2}=24.74[/tex]
With the half of the diagonal and the height, and by using again the Pythagoras theorem you can calculate the slat edge:
[tex]s=\sqrt{(\frac{24.74}{2})^2+(22)^2}=25.23[/tex]
The slant edge of the pyramid is 25.33m
The angle of the base is given by:
[tex]\theta=sin^{-1}(\frac{h}{s})=sin^{-1}(\frac{22}{25.23})=60.65\°[/tex]
The angle of the base is 60.65°
The distance between the corner of the pyramid and its center of its base is half of the diagonal, which is 24.74/2 = 12.37m
The area of one side of the pyramid is given by the following formula:
[tex]A=\frac{(b/2)l}{2}[/tex] (1)
l: height of the side of pyramid
then, you first calculate l by using the information about the side base and the slant.
[tex]l=\sqrt{s^2-(\frac{b}{2}^2)}=\sqrt{(25.33)^2-(\frac{35}{2})^2}\\\\l=18.31m[/tex]
Next, you replace the values of l and b in the equation (1):
[tex]A=\frac{(35/2)(18.31)}{2}=160m^2[/tex]
The area of one aside of the pyramid is 160m^2
Find the missing side. Round your answer to the nearest tenth.
Answer:
5.4Step-by-step explanation:
ABC is a right angle triangle.
Therefore,
[tex]cos \: (75) = \frac{ab}{ac} [/tex]
Plug the values
[tex]cos \: (75) = \frac{x}{21} [/tex]
Apply cross product property
[tex]x = 21 \times cos(75)[/tex]
Calculate
[tex]x = 5.435[/tex]
After rounding to the nearest tenth, the answer will be:
[tex]x = 5.4[/tex]
Hope this helps...
Best regards!!
PLEASE ANSWER THIS ASPA Which of the following choices is equivalent to -6x > -42? x > 7 x -7 x < -7
Answer:
x < 7
Step-by-step explanation:
-6x > -42
Divide each side by -6, remembering to flip the inequality
-6x/-6 < -42/-6
x < 7
Answer:
[tex]\boxed{x<7}[/tex]
Step-by-step explanation:
[tex]-6x > -42[/tex]
Divide both sides by -6 (flip sign).
[tex]\displaystyle \frac{-6x}{-6} < \frac{-42}{-6}[/tex]
[tex]x<7[/tex]
Pls answer ASAP I need by end of day #1
Answer:
m<A = 90° - m<B
(AB)^2 = (AC)^2 + (BC)^2
sin A = cos B
if <A = <B, then m<A = 45°
Answer:
Step-by-step explanation:
∠A+∠B=90 complementary angles ( the sum equal 90°)
∠A=90 degrees-∠B
tan A=sinA/cos A
AB²= AC² +BC² (Pythagorean theorem)
if angle A=angle B then the angles are 45 degrees
cos A=sin(90-A)
sin (a - b) = sin a.cos b - sin b.cos a
sin(90-A)=sin90.cosA-sinbAcos90 cos 90=0 and sin 90=1
sin(90-A)=1*cosA
sin(90-A)=cosA
the ones are in bold are right
I'll mark you brainlyist, if I know how to do it, if you help me out real quick thx
Answer:
4 in
Step-by-step explanation:
as you see from the first rectangle it has been reduced 3 times of length
so the breadth also should be reduced 3 times
Answer:
x = 4
Step-by-step explanation:
the simplest way to do that is to divide
12 / 18 = 2 / 3
then we move to the another square:
x / 6 = 2 / 3
x = 6 x 2 / 3
x = 4
.. ..
Using the equation y = 2x + 5, what would the input need to be for an output of -15? A : -25 B : -35 C : -10 D : -5
Answer: C: -10
Step-by-step explanation:
An output is another word for y. If we set y to -15, we can solve for x, or the input variable.
[tex]-15=2x+5[/tex]
Subtract 5 from both sides of the equation.
[tex]-20=2x\\[/tex]
Divide both sides of the equation by 2.
[tex]-10=x[/tex]
Therefore, x = -10.
Hope this helps!
Answer:
the answer is -25
Step-by-step explanation:
y = 2x + 5
y = 2x(-15) + 5
2 times -15 = -30
-30 + 5 = -25
Hope this helps! :)
An animal shelter takes in an average of 5 animals per day. The shelter must keep its total occupancy below 300. Currently, the shelter has 165 animals.
If none of the animals get adopted, which inequality represents how many more days, x, the shelter can continue to take in animals without exceeding its occupancy limit?
A.
x < 25
B.
x < 27
C.
x < 33
D.
x < 35
Answer:
B. x<27
Step-by-step explanation:
300-165=135
135/5=27
Answer:
B. x<27
Step-by-step explanation:
The shelter has 165 animals. The shelter must keep its total occupancy below 300. The shelter takes in an average of 5 animals per day. If x is the number of days, then in x days the shelter takes 5x animals. In total there will be 165+5x animals. This number must be less than 300
165+5x<3005x<300-1655x<135< 27X<27
Three-fourths of the employees at a bookstore came to a staff meeting. Less than 24 employees were at the meeting,
The inequality representing this scenario is e<24, where e represents the total number of employees. Which graph
shows the solution to the inequality?
After translating the expression I got:
[tex] \frac{3}{4} x < 24[/tex]
Once you cross multiply you should have the following expression:
[tex]x < 32[/tex]
Then when you graph, remember it should be an open circle on the 32 and the direction of the arrow should be towards 0
Answer:
D
Step-by-step explanation:
just took the test
Write the point-slope form of an equation of the line through the points (6, -1) and (5, -7).
A. Y- 6 = 6(x + 1)
B.y - 5 = 6(x + 7)
C.Y+7= 6(x + 5)
D.y +1 = 6:1-6)
Answer:
D.y + 1 = 6(x - 6)
Step-by-step explanation:
The general form of a straightline equation is given as
y = mx + c
where m is the slope and c is the intercept
m = Δy/Δx
from the given points
m = (-7 - -1)/(5 - 6)
= -6/-1
= 6
Considering the points x₁ and y which are 6 and -1
and using the formular
m = (y - y₁)/(x - x₁)
6 = (y - -1)/(x - 6)
y + 1 = 6(x - 6)
I WILL MARK THE BRAINLIEST! please help me
There are 200 students in 8th grade. There are 3 different elective classes. All 8th grade students must take at least one elective.
- 35 total students are in drama
- 75 total students are in cooking
- 15 students are in both drama and P.E
-10 Students are in drama and cooking
- 5 students are in P.E and cooking
- 8 students are in all three electives
How many students are in P.E?
How many are ONLY in P.E?
Please answer both questions in two sentences.
Answer:
How many students are in P.E? 90
How many are ONLY in P.E? 62
Step-by-step explanation:
How many students are in P.E?
200 students in 8th grade.
35=drama
75=cooking
200-110=90=PE.
How many are ONLY in P.E?
Within 90 students, 15 is also in drama, with 5 is also in cooking, and 8 is in all of 3. =28.
90-28=62
Hope this helps!
Container 1 has 174 lires of oil, Container 2 has 258 litres of oil. Sam pours entire contents of container 1 into smaller jars, so that the oil completely fills the jars and there is no oil left. He also pours the entire contents of container 2 into the same size jars so that there is no oil left. What can the maximum size of the smaller jars be?
Answer:
The maximum size of the smaller jars is 6 liters
Step-by-step explanation:
Container 1=174 liters of oil
Container 2=258 liters of oil
Same pours the entire content of container one and container 2 into the same number of smaller jars
The maximum size of the smaller jar can be found by finding the highest common factor of 174 and 258
Factors of 174=1,2,3,6,29
Factors of 258=1,2,3,6,43
Common factors of 174 and 258=1,2,3 and 6
Highest common factor=6
Therefore,
The maximum size of the smaller jars is 6 liters
La trayectoria de cierto satelitese ajusta ala grafica de la funcionf(x) igual6x al cuadradomenos 12donde x representael tiempo en días y f(x9 el recorrido en kilometroscuantos kilómetros habrá recorridoel sateliteal cabo de diez días desde su lanzamiento
Answer:
588 kilómetros
Step-by-step explanation:
La función con la que estamos trabajando según la pregunta es;
F (x) = 6x ^ 2 -12
Ahora, la pregunta que simplemente nos hace es encontrar el valor de F (x) dado que x = 10
Entonces, lo simple que hacemos aquí es hacer una sustitución de x = 10 Eso sería;
F (10) = 6 (10) ^ 2 - 12 = 600-12 = 588
Sales of a popular toy were about 20 million in 2000 and growing about 5% each year. At this growth rate, the function f(x) = 20(1.05)^x gives the annual number of toys sold in million in the xth year after 2000. Using this model, in about what year will the annual sales surpass 37 million?
===========================
Work Shown:
Plug in f(x) = 37. Solve for x. Use logarithms.
f(x) = 20(1.05)^x
37 = 20(1.05)^x
20(1.05)^x = 37
1.05^x = 37/20
1.05^x = 1.85
log( 1.05^x ) = log( 1.85 )
x*log( 1.05 ) = log( 1.85 )
x = log( 1.85 )/log( 1.05 )
x = 12.6088044498867
Round up to the nearest whole number to get x = 13.
In the year 2013, sales exceed 37 million.
In the equation y = 2x + 6
If x= 2, then what is y equal to?
Answer:
y = 10
Step-by-step explanation:
y = 2x + 6
Let x =2
y = 2*2 +6
y = 4+6
y = 10
Answer:
y= 10Step-by-step explanation:
[tex]y = 2x + 6 \\ x = 2 \\ y = 2(2) + 6 \\ y = 4 + 6[/tex]
[tex]y = 10[/tex]
Given that the quadrilateral QRST is a parallelogram, m∠S = 6x + 6 and m∠R =3x + 24, what is the measurement of ∠S?
Answer:
42°
Step-by-step explanation:
→ Since this quadrilateral is a parallelogram, ∠S is equal to ∠R. Let's represent the situation in terms of equations
6x + 6 = 3x + 24
→ Minus 3x from both sides to collect the 'x' terms
3x + 6 = 24
→ Minus 6 from both sides isolate 3x
3x = 18
→ Divide by 3 on both sides isolate x
x = 6
⇒ The value of x is 6, but this isn't the measurement of ∠S, we need to substitute in x = 6 into the expression 6x + 6
6 (6) + 6 ⇔ 36 + 6 = 42°
m<S= 42°
Step-by-step explanation:
6x + 6 = 3x + 24
-6 -6
6x= 3x + 18
-3x -3x
3x = 18
[tex] \frac{3x}{3x} = \frac{18}{3x} [/tex]
x= 6
m<S= 6x + 6
m<S= 6(6) + 6
m<S= 42°
Find the value of x.
Answer:
8.8Option A is the correct option.
Step-by-step explanation:
As PW is the median.
PW = [tex] \frac{1}{2} [/tex] ( YZ + TM )
Plug the values
x = [tex] = \frac{1}{2} (5.5 + 12.1)[/tex]
Calculate the sum
x = [tex] = \frac{1}{2} \times 17.6[/tex]
Calculate the product
x = [tex] = 8.8[/tex]
Hope this helps...
Best regards!
Answer the problem below
Answer:
D. 4z^3
Step-by-step explanation:
First, you see what cubed is 64, which is 4, so you know it is either A or D, but it can not be A because it is not z to the power 5 but x to the power of 3
Hope this helps, if you want me to explain more, feel free to ask questions.
Have a good day! :)
Answer:
4 z^3
Step-by-step explanation:
( 64 z^9) ^ 1/3
Rewriting 64 as 4^3
( 4^3 z^9) ^ 1/3
We know that ( ab) ^c = a^c * b^c
4^3 ^ 1/3 z^9 ^ 1/3
We know that a^ b^c = a^ ( b*c)
4^(3 * 1/3) z^ (9 * 1/3)
4 ^ ( 1) z^ ( 3)
4 z^3
Factor the equation.
X2-15x+50=0
Answer:
(x - 10)(x - 5)
Step-by-step explanation:
Well to factor X^2-15x+50
we need to find 2 numbers that multiply to get 50 and add to get -15.
-5 * -10 = 50
-5 + -10
x*x = x^2
Factored (x - 10)(x - 5)
Hope this helps :)
Answer:
(x - 10)(x - 5)
Step-by-step explanation:
Step 1- Find 2 numbers that multiply to be 50.
10 × 5
-10 × -5
25 × 2
-25 × -2
All these multiply to get 50.
But the numbers must also add up to be -15.
Step 2- Find the 2 numbers that also add up to be -15.
10 + 5 = 15
-10 + -5 = -15
25 + 2 = 27
-25 + -2 = -27
The correct equation would be - 10 + -5
The 2 number you would use when you factor would be -10 and -5
Step 3- Write the equation
You can write the equation as (x - 10)(x - 5)
Or you can also write it as (x - 5)(x - 10)
In the picture down below
Answer:
Option C. f¯¹(x) = x + 3
Step-by-step explanation:
f(x) = x – 3
To find the inverse, f¯¹(x) of f(x), we simply do the following:
f(x) = x – 3
Replace f(x) with y
y = x – 3
Interchange y and x
x = y – 3
Make y the subject by rearranging
x + 3 = y
y = x + 3
Replace y with f¯¹(x)
f¯¹(x) = x + 3
Therefore, the inverse of f(x) = x – 3 is f¯¹(x) = x + 3