Answer:
d. 15
Step-by-step explanation:
Let A and C be the initial number of marbles Ali and Cho have, respectively.
We are told that:
A = 3C [Ali had 3 times as many marbles as cho does]
We then discover that
C-4 = A-18 [After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does]
How many more marbles does cho have in the beginning?
We have 2 equations and 2 unknowns (A and C). That means we can likely rearrange one of the equations and isolate one unknown on the left, and then use that in the second equation.
The first equation already has one of the unknowns isolated (A) so I'll use that in equation 2.
Eq. 1: A = 3C
Eq. 2: C-4 = A-18
Use the definition of A from Eq. 1 (=3C) to replace A in Eq. 2:
Eq. 2: C-4 = A-18
C-4 = (3C)-18 [Replace A with 3C, as promised in E1q. 1]
-2C = -14
C=7
If C = 7, then from Eq. 1, A = 21
In the beginning, Ali has 21 marbles and Cho has 7.
Cho has 15 more marbles than Ali in the beginning.
a. 5
b. 9
c. 10
d. 15
Write the word phrases into an algebraic expression : 4 less than 5 times a number "p"
The triangle inequality theorem states the sum of the lengths of any two sides of a triangle is _____ the length of the third side.
Answer:
see explanation
Step-by-step explanation:
the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
if the sides are a, b, c , then the following must be true
a + b > c
a + c < b
b + c > a
for the 3 sides to form a triangle
Consider the following graph.
Which statement best describes Cheryl's commute?
A. Cheryl accelerated to 65 mph, made a stop for 5.5 minutes, and then decelerated to 45 mph.
B. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and the decelerated to 45 mph.
C. Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.
D. Cheryl drove at a speed of 65 mph for 1 minute, made a stop for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes
Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.Option C is correct.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
Cheryl traveled at a steady pace for 5.5 minutes, then 45 mph for 2.5 minutes after traveling at 65 mph for a minute.
Statement C best describes Cheryl's commute.
Hence option C is correct.
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culture started with 2,000 bacteria. After 3
ours, it grew to 2,600 bacteria. Predict how
any bacteria will be present after 9 hours.
ound your answer to the nearest whole
umber.
P = Aekt
Step-by-step explanation:
2600 = 2000•e^3k
e^3k = 2600/2000
e^3k = 13/10
3k = ln(13/10)
k ≈ 0.087
P = 2000•e^0.087•9
P = 4376
Help question is in the pic
11 potters can make 143 pots in 8 days. How many potters will be required to make 169 pots in 4 days?
26 potters will be required to make 169 pots in 4 days.
Given: 11 potters can make 143 pots in 8 days.
Step 1:
1 potter makes 143 pots in 8 × 11 days.
1 potter can make 1 pot in
(8 × 11)/143 days.
Step 2:
Let the number of potters required be x, then
x potters can make 1 pot in (8 × 11)/( 143 × x) days
x potters can make 169 pots in (8 × 11 × 169)/(143 × x ) days
Step 3:
The number of days given is 4. Hence equating the above equation to 4.
(8 × 11 × 169)/(143 × x ) = 4
Step 4:
Solve for x
14872/(143x) = 4
572x = 14872
x = 14872/572
x = 26
Thus, 26 potters will be required to make 169 pots in 4 days.
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The height in feet, h, of a model rocket t seconds after launch is given by the equation h (t) = 3 + 70 t minus 16 t squared. The average rate of change in h(t) between t = 1 second and t = 3 second is 6. What does the average rate of change tell you about the rocket?
The rocket is traveling six times as fast when t = 3 than it is when t = 1.
The rocket is at a greater height when t = 3 than it is when t = 1.
The rocket is 6 feet higher above the ground when t = 3 than it is when t = 1.
The rocket is traveling at a constant rate of 6 feet per second between t = 1 and t = 3.
The average rate of change in h(t) is 6.
What is Average Rate of change?It is a measure of how much the function changed per unit, on average, over that interval.
h(t) = 3 + 70t - 16t²
Average rate of change
At t = 1 second
h(1) = 3 + 70(1) - 16(1)^2
h(1) = 57
At t = 3 second
h(3) = 3 + 70(3) - 16(3)^2
h(3) = 69
Average rate of change = Δh / Δt
=[h(3) - h(1)] / (3 - 1)
= (69 - 57) / 2
= 12 / 2
= 6.
Hence, the rate of change is 6.
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Solve the equation 2x + 10 = 30.
Answer:
X=10
Step-by-step explanation:
1. Subtract 10 from both sides
2. Simplify
3. Divide both sides by the same factor
4. Simplify
Find the range for the given domain: {-2, 0, and 1}and the function is y = 3x + 1.
Answer:
It's the first option: -5, 1 and 4
Joe kept track of how much TV she watched each day for two weeks how many hours did she spend watching TV
The total hours joe spent watching TV each day for two weeks is 12 1/2 hours
Total hours spent watching TVTotal hours spent watching TV for two weeks = Number of hours × days
= (0 × 1) + (1/4 × 1) + (1/2 × 1) + (3/4 × 3) + (1 × 3) + (1 1/4 × 4) + (1 1/2 × 1)
= 0 + 1/4 + 1/2 + 9/4 + 3 + 5 + 3/2
= 8 + (1+2+9+6) / 4
= 8 + 18/4
= 8 + 4 2/4
= 8 + 4 1/2
= 12 1/2 hours
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I need this due by tonight what is 45+x=75
Answer:30
Step-by-step explanation: jus subtract total number by 45 to c what u missin
Given: [tex]\textsf{45 + x = 75}[/tex]
Need: [tex]\textsf{The value of the unknown x}[/tex]
Solution: In order to solve for the unknown we must subtract 45 from both sides which would isolate x and given us the value.
Subtract 45 from both sides
[tex]\textsf{45 - 45 + x = 75 - 45}[/tex][tex]\textsf{x = 75 - 45}[/tex][tex]\textsf{x = 30}[/tex]After simplifying the expression we were able to determine that x is equal to 30.
The area of a rectangle is 20 square meters. The length of the rectangle is (x-3) meters and the
width of the rectangle is (x - 2) meters. Find the length and the width of the rectangle.
With steps and explanation please.
Answer:
length = 4 cm
Width = 5 cm
Step-by-step explanation:
Area of rectangle:Area of rectangle = length * width
length = (x - 3) meters
Width = (x - 2) meter
Area = 20 square meters
(x - 3)*(x - 2) = 20
Use FOIL method.
x*x + (x)(-2) + (-3)*x + (-3)*(-2) = 20
x² -2x - 3x + 6 =20
Combine like terms
x² - 5x + 6 = 20
Now subtract 20 from both side
x² - 5x + 6 - 20 = 0
x² - 5x - 14 = 0
Factorize the equation and find the roots
Sum = -5
Product = -14
Factors = (-7) , 2
When we add (-7) + 2 = -5 and when we multiply (-7)*2 = -14
x² + 2x - 7x - 14 = 0
x(x + 2) -7(x + 2) = 0
(x + 2)(x - 7) = 0
x - 7 = 0 {Ignore (x + 2 = 0) as measurements wont't be in negative}
x = 7
length = x - 3
= 7 - 3
[tex]\sf \boxed{\bf length = 4 \ cm}[/tex]
width = x - 2
= 7 - 2
[tex]\sf \boxed{\bf width = 5 \ cm }[/tex]
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
D
Step-by-step explanation:
definitely
Clem's credit score is 733, while ingrid's credit score is 688. according to the
following table for a $150,000 mortgage, how much more would ingrid have
to pay per month than clem?
fico
interest monthly
score
rate
payment
720-850
5.59% $860
700-719
5.71% $872
675-699
6.25% $924
620-674
7.40% $1039
560-619
8.53% $1157
500-559
9.29% $1238
Ingrid would have to pay 64 per month more than clem.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given;
fico interest monthly score rate
720-850 5.59% $860
700-719 5.71% $872
675-699 6.25% $924
620-674 7.40% $1039
560-619 8.53% $1157
500-559 9.29% $1238
Clem's score is 733 which is 924 on the chart.
Ingrid's score is 688 which allows her to pay 860 per month.
924 - 860 = 64
Hence,
Ingrid would have to pay 64 per month more than clem.
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Find the volume of this sphere.
Use 3 for pie.
V≈ [?]cm³
V = πr³
10 cm
Answer:
V ≈ 500 cm³
Step-by-step explanation:
Volume of a sphere: ⁴⁄₃πr³ (where r is the radius)
π (pi) ≈ 3r (radius) = diameter/2 ⇒ 10/2 = 5 cmSubstitute the given values into the formula:
⇒ V = ⁴⁄₃πr³
⇒ V ≈ (⁴⁄₃)(3)(5)³
⇒ V ≈ (⁴⁄₃)(3)(125)
⇒ V ≈ (⁴⁄₃)(375)
⇒ V ≈ 500 cm³
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Given: [tex]\textsf{Diameter = 10 cm, Volume = 4/3} * \pi*r^3[/tex]
Find: [tex]\textsf{Determine the volume}[/tex]
Solution: First we need to determine the radius by dividing the diameter by 2 and after that we can plug in the information into the equation and simplify it until we get the volume.
Determine the radius
[tex]\textsf{Radius = Diameter / 2}[/tex][tex]\textsf{Radius = 10 cm / 2}[/tex][tex]\textsf{Radius = 5 cm}[/tex]Plug in the values
[tex]\textsf{Volume = 4/3 } * \pi*r^3[/tex][tex]\textsf{Volume = 4/3 } * 3 * (5\ cm)^3[/tex]Simplify the expression
[tex]\textsf{Volume = (4 * 3)/3} * (5\ cm)^3[/tex][tex]\textsf{Volume = 4} * (5\ cm)^3[/tex][tex]\textsf{Volume = 4} * 125\ cm^3[/tex][tex]\textsf{Volume = } 500\ cm^3[/tex]After completing the steps we were able to determine that volume of the sphere that was provided is 500 cubed centimeters.
Here are three studies:
a: june asks eight of her friends if they plan on buying a school lunch that day.
b: sam selects a random sample of coins from his coin bank to see how many of them are older than 1982.
c: peyton randomly selects six eggs from a carton. she randomly assigns three of them to be boiled for 10 minutes and the other three are boiled for 15 minutes. after they have cooled she compares how easy they are to peel.
for which of these studies can we draw conclusions of cause and effect?
a
b
c
none of them
Answer:
The answer is C
Step-by-step explanation:
Just got it.
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
The correct answer is option B which is y > 3x + 2.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The given statement says that On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2)
The plot of the inequality is given in the graph attached with the answer the inequality will be y > 3x +2 which passes through the points (-3,-7 ) and ( 0, 2 ).
Therefore the correct answer is option B which is y > 3x + 2.
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Vincent and Aidan buy the same number of pens. Vincent buys packs of 6 pens, and Aidan buys boxes of 20 pens. What is the least number of pens each boy can have brought?
The least number of pens each boy can have brought is 60
How to determine the least number of pen?We have:
Vincent = 6 packs
Aidan = 20 boxes
Factorize 6 and 20
6 = 1 * 2 * 3
20 = 1 * 2 * 2 * 5
Multiply all factors
LCM = 1 * 2 * 2 * 3 * 5
Evaluate the product
LCM = 60
Hence, the least number of pens each boy can have brought is 60
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The length of a rectangle is 3 yd longer than its width. if the perimeter of the rectangle is 58 yd, find its length and width.
Answer:
Length = 16 yds
Width = 13 yds
Step-by-step explanation:
P = 2w + 2l
l = w + 3
58 = (2w + 2(w + 3))
58 = 4w + 6
52 = 4w
w = 13
L = w + 3
= 13 + 3
= 16
The length and width of the rectangle are 16,13yd.
The Length and Width of the rectangle can be found as:
Given:The length of the rectangle is 3yds longer than the width which means length = w+3
and the perimeter is given by 58yd
Let W be the width and L be the length
We know that the perimeter of a rectangle is 2(L+w)
The perimeter of a rectangle is defined as the sum of all the sides of a rectangle
By simplifying we get2(w+w+3)=58
2(2w+3)=58
2w=29-3
w=13
then the length of the rectangle will be w+3
13+3 = 16
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a. What type of triangle is Triangle ABC?
b. Give reasons for your answer
Since two of the angles are equal, hence the triangle ABC is isosceles triangle
What is a triangle?A triangle is a 2D shape that has 3 sides and angles
From the given triangle
<CAB = 50 (alternate angle) and;
<ACB = 180 - (50 + 80)
<ACB = 180 -130
<ACB = 50 degrees
Since two of the angles are equal, hence the triangle ABC is isosceles triangle
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Jamaal is allowed to walk no farther than three blocks in either direction from his house. If his house is located on the 57th block of the town, which absolute value equation can be used to determine the farthest block to which Jamaal is allowed to walk?
|x – 57| = 0
|57 – 3| = x
|3 – 57| = x
|x – 57| = 3
Answer:
|x – 57| = 3
Step-by-step explanation:
let x be the farthest block to which Jamaal is allowed to walk.
the statement “Jamaal is allowed to walk
no farther than three blocks in either direction from his house.”
means
the distance between the 57th block and the farthest block = 3
means
|x – 57| = 3
Answer:
|x – 57| = 3
Step-by-step explanation:
let x be the farthest block to which Jamaal is allowed to walk.
the statement “Jamaal is allowed to walk
no farther than three blocks in either direction from his house.”
means
the distance between the 57th block and the farthest block = 3
means
|x – 57| = 3
find the range of the given function y= 8x +1, where x>2
Answer:
infinite or if where using whole numbers
y≥25
Hope This Helps!!!
Each staple is made from 0.21 g of metal.
How many staples can be made from 1 kg of metal?
Answer:
4762
Step-by-step explanation:
0.21g x 10,000= 2100
0.21 x 5,000= 1050
0.21 x 4,000= 840
0.21 x 4700 = 987
0.21 x 4760 = 999.6
0.21 x 4762= 1000.02
( how much it's made from x the quantity = the grams or kg)
x=y²-1
2x - y = 4
Which of the following equations could be the result of using substitution to solve the system?
2y²-y-5=0
2y2-y-6=0
2y2-2y-5=0
Answer:
B) 2y² - y - 6 = 0
Given following:
x = y² - 1 ___equation 12x - y = 4 ___equation 2Insert equation 1 into 2:
2(y² - 1) - y = 42y² - 2 - y = 42y² - y - 2 - 4 = 02y² - y - 6 = 0Put in second
2x-y=42(y²-1)-y=42y²-2-y=42y²-y-6=0
What is the domain of the function shown in the
mapping?
Ox|x=-5, -3, 1, 2, 6}
O lyly=-9, -6, 0, 2, 4)
O {x|x=-9, -6, -5, -3, 0, 1, 2, 4, 6}
Oyly=-9, -6, -5, -3, 0, 1, 2, 4, 6}
Domain is the set of values for which the given function is defined. The correct option is A.
What is domain and range of a function?Domain is the set of values for which the given function is defined, therefore the are values that the function can take.
Range is the set of all values which the given function can produce an output.
Domain of a function is the range of the inputs which the function can take, therefore, the domain of the function shown in the mapping is,
x|x= -5, -3, 1, 2, 6}
Hence, the correct option is A.
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A school show had ticket sales of $1345 the first night and $935 the second night. 180 student tickets were sold and 110 adult tickets were sold on the first night. 100 student tickets were sold and 90 adult tickets were sold. find the price of a student ticket
Using a system of equations, it is found that the price of a student ticket is of $3.49.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: Price of a student ticket.Variable y: Price of an adult ticket.Considering the revenues and the number of tickets sold, the equations are given as follows:
180x + 110y = 1345.100x + 90y = 935.From the second equation:
90y = 935 - 100x
y = (935 - 100x)/90
y = 10.39 - 1.11x
Replacing in the first equation:
180x + 110y = 1345.
180x + 110(10.39 - 1.11x) = 1345
57.9x = 202.1.
x = 202.1/57.9
x = 3.49.
The price of a student ticket is of $3.49.
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Solve for [x]. The polygons in each
2x-20
16
16
8
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 16 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
If two polygons are similar, their corresponding sides ratios will be equal to each other.
[tex]\qquad \tt \rightarrow \: \cfrac{8}{16} = \cfrac{2x - 20}{24} [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{1}{2} = \cfrac{2x - 20}{24} [/tex]
[tex]\qquad \tt \rightarrow \: 2x - 20 = \cfrac{24}{2} [/tex]
[tex]\qquad \tt \rightarrow \: 2x = 12 + 20[/tex]
[tex]\qquad \tt \rightarrow \: 2x = 32[/tex]
[tex]\qquad \tt \rightarrow \: x = 16[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
What is the value of x?
(See attached image for details.)
Enter your answer in the box.
x =
Answer:
x = 8°
y = 6°
Step-by-step explanation:
Hello!
All 3 sides of the triangle are equal, indicating that it is an equilateral triangle. The rules of this particular triangle say that all angles are equal to 60°.
We can solve for x by setting the equation 7x+4 to 60.
Solve for x7x + 4° = 60°7x° = 56°x = 8°The value of x is 8°.
We can go ahead and solve for y by setting that equation to 60°.
Solve for y8y + 12° = 60°8y = 48°y = 6°The value of y is 6°.
Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a square?
Shape ABCD is shown. Point A is at negative 3, 5. Point B is at 1, 7. Point C is at 3, 3. Point D is at negative 1, 1.
10. A In the adjoining Figure, ab is perpendicular to bc and ed is to cd while bc=cd . prove i) triangle abc is corresponding to triangle edc
ii)ab = cd
Part (i)
1) AB is perpendicular to BC, ED is perpendicular to CD, BC = CD (given)
2) Angles ABC and CDE are right angles (perpendicular lines form right angles)
3) Angles ABC and CDE are equal (all right angles are equal)
4) Angles ACB and DCE are equal (vertical angles are equal)
5) Triangles ABC and EDC are congruent (ASA)
Part (ii)
6) AB = DE (corresponding parts of congruent triangles are equal)
