Answer:
-11
Step-by-step explanation:
f(x)=-2x-5
Let x = 3
f(3) = -2 *3 -5
= -6 -5
= -11
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
Need help ASAP thank you
Answer:
A. Volume = 462 cm³; Surface Area = 458 cm²
B. Volume
C. Surface area
Step-by-step explanation:
A. Given a rectangular box:
[tex] Width (w) = 3 cm [/tex]
[tex] Height (h) = 14 cm [/tex]
[tex] length (l) = 11 cm [/tex]
=>Volume of the juice box
[tex] Volume (V) = whl [/tex]
[tex] Volume (V) = 3*14*11 [/tex]
[tex] = 3*14*11 = 462 [/tex]
Volume of juice box = 462 cm³
=>Surface area (S.A) of juice box:
[tex] S.A = 2(wl + hl + hw) [/tex]
[tex] S.A = 2(3*11 + 14*11 + 14*3) [/tex]
[tex] S.A = 2(33 + 154 + 42) [/tex]
[tex] S.A = 2(229) [/tex]
[tex] S.A = 458 cm^2 [/tex]
Surface area of juice box = 458 cm²
B. Volume would be used to find the amount of juice the box can hold
C. Surface area would be used to know how much wax to buy to use in coating the box.
Three candidates were running for president of a student council. Altogether, 1524 students cast a vote in the election. The second place candidate had 140 votes less than the winner, but 395 votes more than the last place candidate. What percentage of all the votes cast were received by the winner? (Round your answer to the nearest percent).
Answer:
48%
Step-by-step explanation:
The total number of votes casted = 1524 votes = 100%
Let a = votes of first place candidate
b = votes of second place candidate
c = votes of third place candidate
The second place candidate had 140 votes less than the winner
b = a - 140 votes...... Equation 1
Hence,
a = b + 140.......... Equation 2
Second place candidate has 395 votes more than the last place candidate
b = c + 395.......Equation 3
Hence,
c = b - 395......Equation 4
a + b + c = 1524 votes....... Equation 5
If a = b + 140 and c = b - 395
The number of votes by b(second place candidate ) =
b + 140 + b + b - 395 = 1524 votes
3b = 1524 + 395 - 140
3b = 1779
b = 1779/3
b = 593 votes.
Therefore, the second place candidate had 593 votes.
Now we can calculate how many votes, the other candidates had.
The second place candidate had 140 votes less than the winner
Votes for the winner( first place candidate)
b = a - 140 votes...... Equation 1
Hence,
a = b + 140.......... Equation 2
Since b = 593
a = 593 + 140
a = 733 votes
Votes for the last place candidate
Since, Second place candidate has 395 votes more than the last place candidate
b = c + 395.......Equation 3
Hence,
c = b - 395......Equation 4
b = 593
c = 593 - 395
c = 198
From the above calculation,
a = votes of first place (winner) candidate = 733
b = votes of second place candidate = 593
c = votes of third(last) place candidate = 198
In the above question, we were asked to calculate the percentage of all the votes cast were received by the winner.
This is calculated as
= Voted received by winner/ Total number of votes casted × 100
= 733/1524 × 100
= 48.09711286%
Approximately to the nearest percent = 48%
Therefore, the percentage of all the votes cast were received by the winner = 48%
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]
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:
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)
Jordan and his bro got 100 dollar to divied up. If 1/3 of the money jordon got was the same as 1/2 the money his bro got how much money did his bro get
Answer:
Jordon's brother got $40
Step-by-step explanation:
We can set up a system of equations to solve this.
Let's say that Jordon got x dollars.
His brother got y dollars.
x+y=100 since they are dividing the 100 dollars
1/3x=1/2y (the same indicates that they are equal)
Multiply the entire second equation by 3.
x=1.5y
Now we can substitute 1.5y in for x in the first equation.
x+y=100
1.5y+y=100
2.5y=100
Divide both sides by 2.5
y=40
Jordon's brother got $40.
Plug that in to find how much Jordon got.
x+y=100
x+40=100
Subtract 40 from both sides
x=60
Jordon got 60.
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
The x-coordinate of the intersection point of Line B D and Line C E is StartFraction 2 (a + c) Over 3 EndFraction. y = (StartFraction b Over a minus c EndFraction)x − (StartFraction 2 b c Over a minus 2 c EndFraction) y = (StartFraction b Over a minus 2 c EndFraction) (StartFraction 2 (a + c) Over 3 EndFraction) minus (StartFraction 2 b c Over a minus 2 c EndFraction) y = (StartFraction b Over a minus 2 c EndFraction) (StartFraction 2 (a + c) Over 3 EndFraction) minus (StartFraction 6 b c Over 3(a minus 2 c) EndFraction) y = StartFraction 2 b (a + c) minus 6 b c Over 3 (a minus 2 c) EndFraction y = StartFraction 2 a b + 2 b c minus 6 b c Over 3 (a minus 2 c) EndFraction What is the y-coordinate? StartFraction b c Over 3 EndFraction StartFraction 2 b Over 3 EndFraction StartFraction 2 b c Over 3 EndFraction StartFraction a b c Over 3 EndFraction
Answer:
y = 2b/3
Step-by-step explanation:
The x-coordinate of the intersection point of Line B D and Line C E is at [tex]\frac{2(a+c)}{3}[/tex]. Given that:
[tex]y=\frac{b}{a-2c}x -\frac{2bc}{a-2c} \\\\The\ y\ coordinate\ can\ be \ gotten\ by\ substituting\ the \ value\ of\ x\ and\ simplifying.\\ Substituting\ x:\\\\y=\frac{b}{a-2c}(\frac{2(a+c)}{3} ) -\frac{2bc}{a-2c}[/tex]
[tex]Simplyfing\ the\ parenthesis\\y=\frac{2b(a+c)}{3(a-2c)} -\frac{2bc}{a-2c}\\\\y=\frac{2ab+2bc}{3(a-2c)} -\frac{2bc}{a-2c}\\\\Simplyfying\ using\ LCF\\y=\frac{2ab+2bc-6bc}{3(a-2c)}\\\\y=\frac{2ab-4bc}{3(a-2c)}\\\\Factorizing:\\\\y=\frac{2b(a-2c)}{3(a-2c)}\\\\y=\frac{2b}{3}[/tex]
The y-coordinate of the intersection point of Line B D and Line C E is at [tex]\frac{2b}{3}[/tex].
Answer:
b
Step-by-step explanation:
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
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...
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
.. ..
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!
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°
I need help with the image below ASAP
Answer:
a
Step-by-step explanation:
The standard form of the equation of a circle is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (0, 0), thus
(x - 0)² + (y - 0)² = r², that is
x² + y² = r² → a
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°.
NEED HELP AND PLEASE ANSWER IT RIGHT!! I AM GIVING OUT A LOT OF POINTS TO WHOEVER DOES THIS RIGHT
Answer:
452.39
Step-by-step explanation:
A=4πr^2
=4·π·6^2
≈452.38934
find sin(a) in the triangle
Answer:
sin (a) = 12/37Step-by-step explanation:
sin ∅ = opposite / hypotenuse
From the question
the hypotenuse is 37
the opposite is 12
So we have
sin (a) = 12/37
Hope this helps you
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!
Factor 16a+72 to identify the equivalent expressions. choose 2 answers a.4(4a+18) b.8(2a+9) c.2(8+36a) d.2(8a+72)
help ASAP
Answer:
[tex] \boxed{\sf b. \ 8(2a + 9)} [/tex]
Step-by-step explanation:
[tex] \sf Factor \: the \: following: \\ \sf \implies 16a + 72 \\ \\ \sf Factor \: 8 \: out \: of \: 16a + 72: \\ \sf \implies 8 \times 2a + 8 \times 9 \\ \\ \sf \implies 8(2a + 9)[/tex]
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 :)
Determine the intercepts of the line.
9x-7y=149x−7y=14
Answer:
see below
Step-by-step explanation:
9x−7y=14
To find the x intercept set y = 0 and solve for x
9x = 14
Divide by 9
9x/9 = 14/9
x = 14/9
(14/9 ,0)
To find the y intercept set x = 0 and solve for y
-7y = 14
Divide by -7
-7y/-7 = 14/-7
y = -2
(0,-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!!
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
Una estudiante gráfica muestras de mayolicas que desea comprar su papa para poner en el piso de la ducha. Las representaciones gráficas de 3/4 corresponde a la parte coloreada en cada una de las mayolicas ¿Son equivalentes las fracciones que representan la parte coloreada de cada muestra? ¿Cómo verifico que 2 fracciones son equivale?
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)
Karen has $600. She spent $240 on clothes. What percentage of money did she have left?
Answer: She had 60% of the money left
Step-by-step explanation:
240/600=0.4
0.4 = 40%
100%-40%=60%
Answer:
60%
Step-by-step explanation:
LETS MAKE IT INTO A FRACTION
FIRST LETS CALCULATE HOW MUCH SHE SPENT
=240/600
WE CAN SIMPLIFY BY DIVIDING THE EQUATION BY 10
=24/60
LETS DIVIDE BY 6
=4/10
DIVIDE BY 2
=2/5
NOW LETS CALCULATE HOW MUCH SHE HAS LEFT
THE EASIEST WAY IS TO SUBTRACT
5/5-2/5=3/5
3/5 IS ALSO EQUAL TO 60/100
SO KAREN HAS 60% OF HER MONEY LEFT
HOPE I HELPED
PLS MARK BRAINLIST
(DESPERATELY TRYING TO LEVEL UP)
✌
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
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
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