Answer:
5b: 3c = 25 : 16
Step-by-step explanation:
[tex] \frac{a}{b} = \frac{4}{5} \: and \: \frac{a}{c} = \frac{3}{4}[/tex]
dividing both to get a : c
[tex] \frac{a}{b} \times \frac{c}{a} = \frac{4}{5} \times \frac{4}{3} \\ \frac{c}{b} = \frac{16}{15} \\ [/tex]
inverting the fractions
[tex] \frac{b}{c} = \frac{15}{16} [/tex]
multiplying the numerator by 5 and denominator by 3
[tex] \frac{5b}{3c} = \frac{5 \times 15}{3 \times 16} \\ = \frac{75}{48} \\ = \frac{25}{16} [/tex]
therefore,
5b: 3c = 25 : 16
Plane X contains point C. Plane Y contains points A and
B.
How many planes exist that pass through points A, B,
and C?
In the equation 17x2 = 12x, the value of c is:
O 0
O 12
O 17
The value of c is 0.
By question,
17x² = 12x
or,(17x-12):x=0
or,17x - 12 = 0#
For some tips,
In the equation 17x2 = 12x,Rewrite in factored formMove terms to the left sideCreate separate equationsHENCE PROVED ##
Atlanta's population is growing at a rate of 2.9% per year while Detroit's population is declining at 1.1% per year. Describe what this means.
PLSSS HELPPP!!!!!
Answer:
Every year, the population is increasing by a certain amount. This type of continuous growth is increasing at an increasing rate. Exponential growth.
Step-by-step explanation:
Let's say the population of Atlanta was 100,000 in year 0. At the end of year 1, it would have grown 3%. 100,000 * 103% = 103,000.
103% because if it were 3%, the population would be shrinking.
at the end of year 2, you take the ending amount of year 1, 103,000*103%=106,090.
Exponential growth is everywhere in the world, population sizes, production, intelligence. The formula f(x)=a(1+r)^x :
f(x): the amount in x years.
a: The starting population.
r: The yearly growth rate.
x: How many years.
If you are given months, convert from years to months.
For example: Detroit is expected to grow 1.1% each year until the year 2029. This means that 8 years would have passed, 2029-2021. You take the starting population, which is roughly 675,000 as of now and input into the exponential formula equation.
f(8)=675,000(1+.011)^8 = 736,738 (Population of Detroit in the year 2029).
.011 because 1.1% is converted to decimal form.
Suppose f (x) = x². Find the graph of
f(x - 2).
Click on the correct answer
2
3
Click on each graph to enlarge it.
graph 1
graph 2
graph 3
graph 4
Answer: Graph 2
Explanation:
The graph of f(x) = x^2 is a parabola with the vertex at the origin. If we replace every x with x-2, then we shift the xy axis 2 units to the left, giving the illusion the parabola shifts 2 units to the right.
In short, going from y = x^2 to y = (x-2)^2 means we shift the curve 2 units to the right. This is shown in the second graph.
Tommy's birthday party costs $2.94 for every guest the invites. If there are 4 guests, how much will Tommy's birthday party cost?
Answer:
$11.76
Step-by-step explanation:
2.94×4=$11.76
Help fast
Luke and Owen have \$100$100dollar sign, 100 each. Their friend offered to invest their money, promising to return a sum rrr times as great as what they invested. Luke was suspicious, so he invested \$10$10dollar sign, 10 only, but Owen invested his entire \$100$100dollar sign, 100. Fortunately, the friend did indeed return a sum rrr times as great to each.
They decided to make another investment. This time, Owen invested all of the money returned to him, and Luke invested the money returned to him and the remaining \$90$90dollar sign, 90. Again, they got a sum rrr times as great as what they invested. In the end, Owen had \$337.50$337.50dollar sign, 337, point, 50 more than Luke.
Write an equation in terms of rrr that models the situation.
An equation in terms of r which models the situation described is : 100r² = 10r² + 90r - 337.50
First investment :
Luke:
Total amount had = $100
Amount invested = $10
Amount left = $100 - $10 = $90
Return = r times the amount invested = (10 × r) = 10r
Owen:
Total amount had = $100
Amount invested = $100
Return = r times the amount invested = (100 × r) = 100r
Second investment :
Luke :
Amount invested = Return on first + amount left = 10r + 90
Return is r times the amount invested :
Return on second investment = (10r + 90) × r = (10r² + 90r)
Total amount earned after both investment = 10r² + 90r
Owen :
Amount invested = Return on first = 100r
Return is r times the amount invested :
Return on second investment = (100r × r) = 100r²
Total amount earned after both investment = 100r²
Owen made 337.50 more than Luke ; This means that :
Total earned by Owen = Total earned by Luke + 337.50
100r² = 10r² + 90r + 337.50
Hence, the equation in terms of r is : 100r² = 10r² + 90r - 337.50
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find the point(s) in which f(x)=e^5-2x and y=6 intercept
Answer:
(1.6, 6)
Step-by-step explanation:
[tex] ln({e}^{5 - 2x} = 6)[/tex]
[tex]5 - 2x = ln(6) [/tex]
[tex]2x = 5 - ln(6) [/tex]
[tex]x = \frac{5 - ln(6) }{2} [/tex]
y = 6
Help me with this question and do not answer unless you know the answer pls and thank you >:(
Answer:
1.5 * 1.5 = 2.25 sq miles
Step-by-step explanation:
1.5 * 1.5 = 2.25 sq miles
Olivia bought 525 Euros at an exchange rate of $1.76/Euro. How many Canadian dollars did she pay for the Euros she bought?
the total amount of money for the price of one euro is equal to 1.76 [tex]\displaystyle\bf 525\cdot1.76=\underbrace{0,44\cdot 4}_{1.76}\cdot 525=2100\cdot0,44=21\cdot 44=924$\\\\Answer:She can exchange \underline{924\$ }for 525 euros[/tex]
What is the vertex form of the quadratic function that has a vertex at (5, 4)
and goes through the point (6, 1)?
O A. y= (x - 5)2 + 4
B. y=-3(x - 5)2 + 4
C. y = 3(x - 5)2 + 4
O D. y = 5(x - 5)2 - 3
Deepak wrote out the steps to his solution of the equation StartFraction 5 Over 2 minus 3 x minus 5 plus 4 x equals negative StartFraction 7 Over 4 EndFraction – 3x – 5 + 4x = –. Which step has an incorrect instruction? Step 1 Step 2 Step 3 Step 4
Answer:
Step 1 is incorrect.
Step-by-step explanation:
The given expression is :
[tex]\dfrac{5}{2}-3x-5+4x=\dfrac{-7}{4}[/tex]
In step 1, Deepak rearranged the terms in order to simplify like terms together that is followed in step 2.
o, rearranging of the terms of an expression is commutative property and not distributive property. The distributive property is generally applicable to multiplication and is given as:
[tex]x(y+z)=xy+yz[/tex]
The commutative property is given as:
x+y = y +a
Therefore, adding terms by changing their order is commutative property of addition and not distributive property. Step 1 instruction is wrong.
Answer:
step1
Step-by-step explanation: yes sirr
Triangle D E F is shown. Use ΔDEF to complete the statements. Angle E is the included angle between sides . The included angle between sides FE and DF is angle
Answer:
Angle E is the included angle between sides DE and EF.
The included angle between sides FE and DF is angle F
Step-by-step explanation:
Given
[tex]\triangle D EF[/tex]
Required
Complete the blanks
To solve this, I will attach an illustration of [tex]\triangle D EF[/tex]
From the attached image of [tex]\triangle D EF[/tex], we can see that"
[tex]\angle E[/tex] is between DE and EF
[tex]\angle F[/tex] is between FE and DF
Answer:
see picture
Step-by-step explanation:
Irene made a mistake when she solved this inequality:
Step 1: -6(x + 3) + 10 < -2
Step 2: -6x − 18 + 10 < -2
Step 3: -6x − 8 < -2
Step 4: -6x < 6
Step 5: x < -1
Between which two consecutive steps did Irene make a mistake?
Answer:
she messed up on step two because she has to subtract 10 from both sides
Step-by-step explanation:
step 1: -6(x+3)+10<-2
step2:-6(x+3)+10-10<-2-10
step3: -6(x+3)<-12
step4: (-6)(x+3)(-1)≥(-12)(-1)
step5:6(x+3)>12
step6:divide both sides by 6
step7:simplify and subtract 3 from both sides and then simplify again
hshsjshshsjsksjjsbsbbs bc hd
Answer:
its b b b
Step-by-step explanation:
Using appropriate properties find 2/3 x (– 3/5) + 1/5 x 4/3 + 2/3 x ( – 3/2)=
Answer:
- [tex]\frac{17}{15}[/tex] -1 [tex]\frac{2}{15}[/tex] , 1.13
Step-by-step explanation:
which point is a solution to y>2x-1?
Answer:
B) (0,2)
Step-by-step explanation:
We substitute the values of x and y into this inequality:
2 ≥ 2(0)-1
2 ≥ 0-1
2 ≥ -1
This is true, so this is the correct point
hope this helps have a good day
Answer:
there it is
Step-by-step explanation:
In a group of 26 pupils, 3 play the flute only.
5 play the piano only.
7 play neither instrument.
How many pupils play both instruments?
Here is a Venn diagram:
Determine the equations of the straight lines
passing through the following pairs of points.
1)(2,-2) and (3, 4)
2)(-3, -2) and (1,2)
3)(4,6) and (5,2)
4)(5,8) and (7, 1)
Answer:
1). 6x - 14 2). y = 1x + 1 3). y = -4x + 22 4).y = -7/2x + 51/2
Step-by-step explanation:
1). y2 - y1 / x2 - x1 4 - (-2) / 3-2 = 6
y = 6x + b 4 = 6(3) + b 4 = 18 + b -14 = b
y = 6x - 14
2). 2 - (-2) / 1 - (-3) = 1
y = 1x + b 2 = 1(1) + b 2 = 1 + b 1 = b
y = 1x + 1
3). 2 - 6 / 5 - 4 = -4
y = -4x + b 6 = -4(4) + b 6 = -16 + b 22 = b
y = -4x + 22
4). 1 - 8 / 7 - 5 = -7/2
y = -7/2x + 51/2
for a project in her geometry class, amira uses a mirror on the ground to measure the height of her school’s football goalpost. she walks a distance of 14.45 meters from her school, then places a mirror on flat on the ground, marked with an x at the center. she then steps 3.65 meters to the other side of the mirror, until she can see the top of the goalpost clearly marked in the x. her partner measures the distance from her eyes to the ground to be 1.55 meters. how tall is the goalpost? round your answer to the nearest hundredth of a meter
Answer:
6.14 m
Step-by-step explanation:
If she moves 3.65 metres to the other side of the mirror. Her spouse calculates that there are 1.55 metres between her eyes and the earth. The height of the tail post is 6.14 m.
What is elevation?The distance up or down a specified point of comparison, most often a reference spherical geometry, a mathematical model of the Earth's sea level as an equipotential gravitational surface, determines a physical location's elevation.
Given that, after travelling 14.45 metres from her school, she lays a flat mirror on the ground in the centre, with an x drawn on it. When she can clearly see the top of the goalpost depicted in the x.
She moves 3.65 metres to the other side of the mirror. Her spouse calculates that there are 1.55 metres between her eyes and the earth.
Suppose the height of the tail post is x,
The geometric relation is,
1.55/3.65 = x/14.45
x=(14.45×1.55)/3.65
x=6.14 m
Thus, if she moves 3.65 metres to the other side of the mirror. Her spouse calculates that there are 1.55 metres between her eyes and the earth. The height of the tail post is 6.14 m.
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If f(x) = 3x + 10 and g(x) = 2x - 4, find (f+g)(x).
O A. (f+g)(x) = -34 - 2x - 14
B. (f+ g)(x) = 3x - 2x + 14
O C. (f+ g)(x) = 5x + 6
D. (f+ g)(x) = 3x + 2x + 6
Help! I’m getting really confused which one it is
Answer:
O D
Step-by-step explanation:
f+g(x)
3x+10+2x-4
3x +2x+6
10. Evaluate the function rule for the given value.
y = 12x3^for x =-2
Answer:
-96
Step-by-step explanation:
by replacing -2 on the place of x we get 12x-8= -96
Which descriptions from the list below accurately describe the relationship between QRS and TUV? check all the apply.
Answer:
The triangles are similar.
Step-by-step explanation:
They are similar because they have the same angles. They may be the same size, but it would be best to refer to whatever definition you were given.
The correct descriptions from the list accurately describe the relationship between QRS and TUV is,
⇒ Similar
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
Two triangles are shown in figure.
Here, All the corresponding angles are same in both triangles.
And, The ratio of their corresponding sides are,
In triangle TUV;
⇒ 90 / 108 = 30 / 36
In triangle QRS;
⇒ 30 / 36
Hence, The correct descriptions from the list accurately describe the relationship between QRS and TUV is,
⇒ Similar
Learn more about the triangle visit;
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The measure of an angle formed by _blank_ is half the sum of the measures of the intercepted arcs
Answer:
The measure of an angle formed by Intersecting chords is half the sum of the measures of the intercepted arcs.
-----------------------------
HOPE IT HELPS
HAVE A GREAT DAY!!
Answer:
Intersecting Chords
Step-by-step explanation:
plz help me with this math and also explain
Step-by-step explanation:
[1]SI = $250Rate (R) = 12[tex] \sf \dfrac{1}{2}[/tex] %Time (t) = 4 years[tex]\longrightarrow \tt { SI = \dfrac{PRT}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 12\cfrac{1}{2} \times 4}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times \cfrac{25}{2} \times 4}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 25 \times 2}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 50}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 \times 100 = P \times 50} \\ [/tex]
[tex]\longrightarrow \tt { 25000 = P \times 50} \\ [/tex]
[tex]\longrightarrow \tt { \dfrac{25000}{50} = P } \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \green{ \tt { \$ \; 500 = P }}}} \\ [/tex]
Therefore principal is $500.
__________________[2]2/7 of the balls are red.3/5 of the balls are blue.Rest are yellow.Number of yellow balls = 36Let the total number of balls be x.
→ Red balls + Blue balls + Yellow balls = Total number of balls
[tex]\longrightarrow \tt{ \dfrac{2}{7}x + \dfrac{3}{5}x + 36 = x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{10x + 21x + 1260}{35} = x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{31x + 1260}{35} = x} \\ [/tex]
[tex]\longrightarrow \tt{ 31x + 1260= 35x} \\ [/tex]
[tex]\longrightarrow \tt{ 1260= 35x-31x} \\ [/tex]
[tex]\longrightarrow \tt{ 1260= 4x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{1260 }{4}= x} \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \tt { 315 = x }}} \\ [/tex]
Total number of balls is 315.
A/Q,
3/5 of the balls are blue.
[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}x} \\ [/tex]
[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}(315)} \\ [/tex]
[tex]\longrightarrow \tt{ Balls_{(Blue)} = 3(63)} \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \green {\tt { Balls_{(Blue)} = 189 }}}} \\ [/tex]
The side length of the chessboard is 7 inches. Find the area of the chessboard.
Answer:
I'm assuming the chessboard is square so 49cm square.
Step-by-step explanation:
Area of a square= side × side
7×7=49
Have a nice day.
The area of the chessboard is 49 square inches, and which side length is 7 inches.
To find the area of the chessboard, we need to calculate the product of its length and width.
In this case, since the chessboard is a square, the length, and width are equal.
Given that the side length of the chessboard is 7 inches, we can calculate the area as follows:
Area of the chessboard = side length x side length
Area of the chessboard = 7 inches x 7 inches
Area of the chessboard = 49 square inches
Therefore, the area of the chessboard is 49 square inches.
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Complete the following proof by dragging and dropping the correct reason in the spaces below
Answer:
2
Step-by-step explanation:
1+1 = 2
So the answer is 2
hope this helps
What is the scale factor from abc to def?
Answer:
the answer is 8 because DEF is 8 times larger than ABC.
Step-by-step explanation:
hope that helps>3
Answer:
3
Step-by-step explanation:
To find scale factor, you need to divide two of the given sides. Meaning you can do any corresponding sides. So, for now, I will do 12 from DEF and 4 from ABC.
12 ÷ 4 = 3
To check if it is accurately 3, you will do it again (optional). You can use 15 from DEF and 5 from ABC
15 ÷ 5 = 3
Since both are 3, that will be the scale factor.
The answer is 3.
On Monday, a local hamburger shop sold a combined total of 456 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Monday?
Answer:
114 hamburger
Step-by-step explanation:
456:4=114
the cheeseburger sold 3 times than the hamburger so 3+1=4
456:4 =114
what is the maximum value of y=-x^2-x+6 ?
Answer:
[tex]{ \tt{y = - {x}^{2} - x + 6 }} \\ { \tt{ \frac{dy}{dx} = - 2x - 1}} \\ f {}^{'} (x) = - 2x - 1 \\ f {}^{'}(1) = - 2 - 1 \\ = - 3 [/tex]
Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 4
Answer:
The length and width that maximize the area are:
W = 2*√8
L = 2*√8
Step-by-step explanation:
We want to find the largest area of a rectangle inscribed in a semicircle of radius 4.
Remember that the area of a rectangle of length L and width W, is:
A = L*W
You can see the image below to see how i will define the length and the width:
L = 2*x'
W = 2*y'
Where we have the relation:
4 = √(x'^2 + y'^2)
16 = x'^2 + y'^2
Now we can isolate one of the variables, for example, x'
16 - y'^2 = x^'2
√(16 - y'^2) = x'
Then we can write:
W = 2*y'
L = 2*√(16 - y'^2)
Then the area equation is:
A = 2*y'*2*√(16 - y'^2)
A = 4*y'*√(16 - y'^2)
If A > 1, like in our case, maximizing A is the same as maximizing A^2
Then if que square both sides:
A^2 = (4*y'*√(16 - y'^2))^2
= 16*(y'^2)*(16 - y'^2)
= 16*(y'^2)*16 - 16*y'^4
= 256*(y'^2) - 16*y'^4
Now we can define:
u = y'^2
then the equation that we want to maximize is:
f(u) = 256*u - 16*u^2
to find the maximum, we need to evaluate in the zero of the derivative:
f'(u) = 256 - 2*16*u = 0
u = -256/(-2*16) = 8
Then we have:
u = y'^2 = 8
solving for y'
y' = √8
And we know that:
x' = √(16 - y'^2) = √(16 - (√8)^2) = √8
And the dimensions was:
W = 2*y' = 2*√8
L = 2*y' = 2*√8
These are the dimensions that maximize the area.
