Answer: 4
Step-by-step explanation:
Melinda: y = 10x + 22
George: y = 13x + 10
13x + 10 = 10x + 22
-10x -10x
3x + 10 = 22
-10 -10
3x = 12
÷3 ÷3
x = 4
Lets say Y is the amount they will save.
So Melinda's savings could be described by the equation Y=22+10X, where X is the number of weeks. The same goes to George, but his equation would be Y=10+13X.
To save the same amount, their equations must match:
22+10X = 10+13X
Solving this, one gets
12 = 3x
=> 4=x
So the answer is 4 weeks.
The perimeter of the rectangle below is 76
units. Find the length of side BC.
.
Write your answer without variables.
Answer:
The length of side BC is 18 units
Step-by-step explanation:
Perimeter of the rectangle: P=76 units
AB=4z
BC=3z+3=?
We need to determine z
The formula to calculate the perimeter of a rectangle is:
P=2(w+l)
Width: w=AB=4z
Length: l=BC=3z+3
Replacing in the formula:
76 = 2 [4z+(3z+3)]
Eliminating the parentheses:
76 = 2 [4z+3z+3]
Adding like terms:
76 = 2 (7z+3)
Solving for z: Dividing both sides of the equation by 2:
76 / 2 = 2 (7z+3) / 2
38 = 7z+3
Subtracting 3 both sides of the equation:
38-3 = 7z+3-3
Subtracting:
35 = 7z
Dividing both sides of the equation by 7:
35 / 7 = 7z / 7
Dividing:
5 = z
z = 5
Then:
BC=3z+3
Replacing z by 5 in the formula above:
BC = 3(5)+3
Multiplying:
BC = 15 + 3
Adding:
BC = 18 units
9000 dollars is placed in an account with an annual interest rate of 7.75%. How much will be in the account after 18 years, to the nearest cent?
In one year, $ 9,000 with a profit of 7.75%, is $ 697.5
697.5 × 18 = 12555
After 18 years old, it is $ 15,222
Answer:
The answer is 34494.79
Step-by-step explanation:
Y=ab^x
A= starting value= 9000
r=rate = 7.75% = 0.0775
Exponential growth
Y= 9000(1.0775)^x
Plug in time for x
Y= 9000(1.0775)^18
Y=34494.7918323
ROUND the number and your answer will be Y= 34494.78
The formula for the area of a trapezoid is A = 1 2 h ( b 1 + b 2 ) , A= 2 1 h(b 1 +b 2 ), where h h is the height and b 1 b 1 and b 2 b 2 are the two bases. Rewrite the formula to solve for h h in terms of A , A, b 1 b 1 and b 2 . b 2 .
Answer:
h = 2A / (b1 + b2)
Step-by-step explanation:
A = 1/2h (b1 + b2)
Divide both sides by 1/2 (b1 + b2)
h = A / 1/2 (b1 + b2)
h = 2A / (b1 + b2)
Answer:
2A / (b1+b2) = h
Step-by-step explanation:
The formula for the area of a trapezoid is
A = 1/2 (b1+b2) *h
We want to solve for h
Multiply each side by 2
2A = 2*1/2 (b1+b2) *h
2A = (b1+b2) *h
Divide each side by (b1+b2)
2A / (b1+b2) = (b1+b2) / (b1+b2) *h
2A / (b1+b2) = h
AZUL HAS 4 GREEN PICKS AND NO ORANGE PICKS. YOU ADD ORANGE PICKS SO THAT THERE ARE 2 ORANGE PICKS FOR EVERY 1 GREEN PICK. HOW MANY PICKS ARE THERE NOW?
Answer:
12 total
Step-by-step explanation:
green : orange
4 0
We add in a ratio of
1 2
So we need to multiply by 4
green : orange
4*1 4*2
4 8
We have 4 green and we need to add 8 orange to get the right ratio
4 green + 8 orange = 12 total
Can someone match all of these for me. 1. Molecules with the same molecular formula, but different structures. A. Dehydration Synthesis. 2. A general term for single unit that is repeated in a larger macromolecule. Example: an amino acid is repeated in a polypeptide chain. B. Enzyme. 3. A general term for a chain of units. C. Hydrolysis. 4. A chemical reaction that involves the addition of water to break down a larger molecule. D. Isomer. 5. A chemical reaction that involves two smaller molecules losing water to join together. E. Molecular Formula 6. The type of covalent bond that holds two amino acids together. F. Monomer 7. The way to write out a chemical that shows the ratio of atoms within it, Example: H20. G. Organic 8. The way to write out a chemical that shows the atoms are arranged. Example: H-O-H H. Peptide. 9. The type of chemistry that involves carbon. I. Polymer A protein that helps break down or make macromolecules. J. Structural Formula.
Final answer:
Each term is matched with its correct concept, revealing the fundamental concepts of biological macromolecules and their formation and breakdown through dehydration synthesis and hydrolysis.
Explanation:
Let's match each concept with its correct term:
Molecules with the same molecular formula, but different structures. - D. Isomer.A general term for a single unit that is repeated in a larger macromolecule. Example: an amino acid is repeated in a polypeptide chain. - F. Monomer.A general term for a chain of units. - I. Polymer.A chemical reaction that involves the addition of water to break down a larger molecule. - C. Hydrolysis.A chemical reaction that involves two smaller molecules losing water to join together. - A. Dehydration Synthesis.The type of covalent bond that holds two amino acids together. - H. Peptide.The way to write out a chemical that shows the ratio of atoms within it, Example: H20 - E. Molecular Formula.The way to write out a chemical that shows the atoms are arranged. Example: H-O-H - J. Structural Formula.The type of chemistry that involves carbon. - G. OrganicA protein that helps break down or make macromolecules. - B. Enzyme.Macromolecules such as proteins, carbohydrates, and nucleic acids are essential for life and are composed of smaller organic molecules called monomers. When these monomers join together through dehydration synthesis, they release a water molecule and form covalent bonds to create larger structures known as polymers. The opposite process, hydrolysis, involves adding water to break down polymers into monomers.
Need help with this problem please ASAP
[tex]x=y-2\\4x+y=2[/tex]
i have to use substitution
Answer:
x=0 , y=2
Step-by-step explanation:
x=y-2
4x+y =2
We can substitute the first equation in for x into the second equation
4*(y-2) +y =2
Distribute the 4
4y-8 +y =2
Combine like terms
5y-8 =2
Add 8 to each side
5y-8+8 = 2+8
5y= 10
Divide each side by 5
5y/5 =10/5
y=2
But we still need to find x
x = y-2
x = 2-2
x=0
a bag contains 8 red ribbon, 7 green ribbons, and 3 yellow ribbons. if you randomly remove 3 of the ribbons from the bag without replacement, what is the probability that the first 2 are yellow?
The probability that the first 2 ribbons removed from the bag are yellow is [tex]\(\frac{1}{51}\)[/tex].
First, let's calculate the probability of drawing the first yellow ribbon. There are 3 yellow ribbons and a total of 8 red, 7 green, and 3 yellow ribbons, which sums up to 18 ribbons in total. So, the probability of drawing the first yellow ribbon is:
[tex]\[ P(\text{first yellow}) = \frac{\text{Number of yellow ribbons}}{\text{Total number of ribbons}} = \frac{3}{18} = \frac{1}{6} \][/tex]
After drawing the first yellow ribbon, there are now 17 ribbons left in the bag, with 2 yellow ribbons remaining. The probability of drawing the second yellow ribbon is:
[tex]\[ P(\text{second yellow | first yellow}) = \frac{\text{Number of remaining yellow ribbons}}{\text{Total number of remaining ribbons}} = \frac{2}{17} \][/tex]
Now, we multiply the two probabilities to find the probability that the first two ribbons drawn are yellow:
[tex]\[ P(\text{first two yellow}) = P(\text{first yellow}) \times P(\text{second yellow | first yellow}) = \frac{1}{6} \times \frac{2}{17} \]\[ P(\text{first two yellow}) = \frac{1 \times 2}{6 \times 17} = \frac{2}{102} = \frac{1}{51} \][/tex]
can someone please help me? 20 Pts!!!
Whether this prophecy is ever fulfilled or not, it is nevertheless plain that a very different-looking class of people are springing up at the south, and are now held in slavery, from those originally brought to this country from Africa; and if their increase do no other good, it will do away the force of the argument, that God cursed Ham, and therefore American slavery is right. If the lineal descendants of Ham are alone to be scripturally enslaved, it is certain that slavery at the south must soon become unscriptural; for thousands are ushered into the world, annually, who, like myself, owe their existence to white fathers, and those fathers most frequently their own masters.
What is the allusion in this passage and its interpretation?
A.) "The descendants of Ham"; since some slaves have white fathers who are not the sons of Ham, they should not be enslaved.
B.) "The descendants of Ham"; although some slaves have white fathers, they are still lineal descendants of Ham and should remain slaves.
C.) "Thousands are ushered into the world"; since some slaves have fathers, they should not be enslaved.
D.) "Thousands are ushered into the world"; although some slaves have white fathers, they are still lineal descendants of Ham and should remain slaves.
the length of a recycling cart is 1.5 yards..1 yard is equal to 3 feet...what is the length in feet of the recycling cart
Answer:
4.5 feet
Step-by-step explanation:
Because one yard is 3 feet and half a yard is 1.5 feet and 3 plus 1.5 equals 4.5.
8v+1=7v-20 I need help!
I need help doing the math
How many pints are there in 33 gallons
Answer:
There are 264 pints in 33 gallons.
Step-by-step explanation:
Because there are 8 pints in 1 gallon.
Answer: 264 pints
Step-by-step explanation:
There are 8 pints in a gallon so you multiply that by 33 and you get your answer.
Find the probability of Drawing a blue marble from a bag of 18 marbles, three of which is blue
Answer:
The probability is 3/18 which you can simplify down to 1/6. :) Hope this helps! And if you don't mind please mark as brainliest :)
Step-by-step explanation:
Answer:
3 out of 18 or 3/18
Consider this equation and the steps taken to solve it. –9(a – 5) = –18 (distribute) –9a + 45 = –18 (subtract 45) –9a = –63 (divide by –9) a = 7 What steps might you take to verify the solution? Check all that apply. Substitute 7 for a. Pick any value for a and substitute. Simplify the equation after substituting the value for a. Verify that a = 7 is correct when the result is a true statement. Verify that a = 7 is correct when the result is a false statement.
Answer:
Substitute 7 for a.
Simplify the equation after substituting the value for a.
Verify that a = 7 is correct when the result is a true statement.
Step-by-step explanation:
–9(a – 5) = –18
Distribute
-9a +45 = -18
Subtract 45 from each side
-9a +45-45 = -18-45
-9a = -63
Divide each side by -9
-9a/-9 = -63/-9
a = 7
To check the solution put a =7 back into the original equation
–9(a – 5) = –18
-9(7-5) = -18
Simplify
-9(2) = -18
-18 = 18
This is true so 7 is the solution
Answer:
Substitute 7 for a.
Simplify the equation after substituting the value for a.
Verify that a = 7 is correct when the result is a true statement.
Step-by-step explanation:
Here, the given equation is,,
[tex]-9(a-5)=-18[/tex]
And, after solving it the result is,
a = 7
We can check whether a result is the solution of an equation by substituting the result in the given equation.
If we get a true statement, then the result is the solution of the equation.
Thus, for verifying the solution, steps are as follow,
Step 1 : Substitute 7 ,
-9(7-5) = -18
Step 2 : Simplify the equation after substituting the value of a
-9(2) = -18
Step 3 : Verify that a = 7 is correct when the result is a true statement.
-18 = -18
What triangle congreunce theorem could you use to prove triangle ADE is congruent to triangle CBE?
Answer:
ASA
Step-by-step explanation:
We're already given a pair of congruent angles and sides
∠DEA and ∠BEC are congruent because they are verticle angles
So we can use ASA to prove the triangle ADE and triangle CBE congruent
To prove that triangle ADE is congruent to triangle CBE, you can use the SSS, SAS, or ASA congruence theorems depending on the given information. The Pythagorean theorem or trigonometry can be used if applicable. You must match corresponding sides or angles to decide which theorem to use.
Explanation:There are several congruence theorems for triangles including Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA). To determine which theorem to use in order to prove that triangle ADE is congruent to triangle CBE, you need to determine what information is given in the problem. For example, if you know that corresponding sides and angles are equal, you might use the SSS postulate, the SAS postulate, or the ASA postulate respectively.
If right angles are involved, we could also factor in the Pythagorean theorem to help establish side lengths - this theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), expressed as: a² + b² = c². Solving for c gives us c = √a² + b². Similarly, if vectors and trigonometry are relevant factors in deriving your triangle sides or angles, they can also be used in establishing congruence.
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A sandwich cost $5.70 and a piece of fruit cost $2.15. If you have a $20 bill,how much change will u get (explain plz)
Answer: $12.15
Step-by-step explanation:
5.70 + 2.15 = $7.85
$20 - 7.85 = $12.15
26=-8/5y what is it 30 points!!!!!
Answer:
Alright well solve for y by simplifying both sides of the equation, then isolating the variable
Exact form: y = - 65/4
Decimal form: y = - 16.25 Hope this helps Have a nice day :)
Step-by-step explanation:
How many solutions does the following equation have? 14(z+3)=14z+2114(z+3)=14z+21
Answer:
it has no solution
Step-by-step explanation:
Answer:
No solution
Step-by-step explanation:
Life
The 17 students on the math team want to raise $483.62 to buy practice books. They have already raised $218.25. If each student raises the same amount, how much more money must each student raise?
Answer:
$15.61
Step-by-step explanation:
483.62 - 218.25 = 265.37
265.37/17 = $15.61
If each student raises the same amount, how much more money must each student raise is: $15.61.
Amount raisedUsing this formula
Amount raised=Current amount to raised-Old Amount raised /Number of students
Where:
Current amount to raised=$483.62
Old Amount raised =$218.25
Number of students=17
Let plug in the formula
Amount raised=483.62 - 218.25/17
Amount raised= 265.37/17
Amount raised= $15.61
Thus, if each student raises the same amount, how much more money must each student raise is: $15.61.
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jan quint earns 11.00 an hour at her job and is entitled to time and a half for overtime and double time on holidays last weeks she worked 40 hours of regular time 9 hours of overtime and 12 hrs of holiday time how much did she earns last weeks
Answer:
$852.5
Step-by-step explanation:
$11 * 40 hours = $440 for reg. hours
$16.5 * 9 hours = $148.5 for overtime
$22 * 12 hours = $264 for holiday time
$440 + $148.5 + $264 = $852.5 in total
Please help I will give brainiest :)
A relation is plotted as a linear function function on the coordinate plane starting at point E at (0,27) and ending at point F at (5, -8) what is the rate of change for the linear function and what is its initial value ? Select from the drop down menus to correctly complete the statement.
The rate of change for the linear function is choose -7, 0, 7, 27 and the initial value is, choose, -8 , -5, 0, 27
Thank You!!! :)
Answer:
see explanation
Step-by-step explanation:
the rate of change is the measure of the slope m of the line
To calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (0, 27) and (x₂, y₂ ) = (5, - 8)
m = [tex]\frac{-8-27}{5-0}[/tex] = [tex]\frac{-35}{5}[/tex] = - 7 ← rate of change
the initial value is the y-coordinate of the starting point
That is y = 27 ← starting value
The rate of change for the linear function is -7 and the initial value is 27.
What’s the answer and work?:)
Answer:
The answer is 7.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
9.75 divided by 1.3 equals 7.5
I used a calculator... :)
In parallelogram ABCD point K belongs to diagonal BD so that BK:DK=1:4. If the extension of AK meets BC at point E, what is the ratio of BE:EC?
Answer:
BE : EC = 1 : 3
Step-by-step explanation:
Consider triangles AKD and EKB. In these triangles
∠AKD≅∠EKB as vertical angles;∠ADK≅∠EBK as alternate interior angles;∠KAD≅∠KEB as alternate interior angles.Then ΔAKD is similar to ΔEKB by AAA theorem.
Similar triangles have proportional corresponding sides:
[tex]\dfrac{AD}{EB}=\dfrac{AK}{EK}=\dfrac{DK}{KB}.[/tex]
Since [tex]\dfrac{DK}{KB}=\dfrac{4}{1},[/tex] then [tex]AD=4BE.[/tex]
Opposite sides in parallelogram have the same lengths, then [tex]BC=AD.[/tex]
Now
[tex]BC=BE+EC,\\ \\BC=\dfrac{1}{4}BC+EC,\\ \\EC=BC-\dfrac{1}{4}BC=\dfrac{3}{4}BC.[/tex]
Find the ratio
[tex]\dfrac{BE}{EC}=\dfrac{\frac{1}{4}BC}{\frac{3}{4}BC}=\dfrac{1}{3}.[/tex]
The ratio of BE:EC is 1:2.
How do we calculate?We have Parallelogram ABCD
Point K on diagonal BD such that BK:DK = 1:4
The extension of AK meets BC at point E
Since BK:DK = 1:4,
we know that BK = 1/5 * BD
and DK = 4/5 * BD.
AK extends to meet BC at point E means that AE is parallel to BD and BE is parallel to AK.
pair A,B,C,D,K,E;
A = (0,0);
B = (5,0);
C = (5,5);
D = (0,5);
K = (3.5,0);
E = (3.5,2.5);
Since AE is parallel to BD and BD is a diagonal of parallelogram ABCD, we know that AE bisects BD. This means that AE = BD/2 = 3/5 * BD.
Since BE is parallel to AK and AK is a diagonal of parallelogram ABCD, we know that BE bisects AK. This means that BE = AK/2 = 1/5 * BD.
Therefore, the ratio of BE:EC = 1/5 * BD
: 2/5 * BD
= 1:2.
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A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 16o when staring at the top of the statue. Then the person looks down at an angle of depression of 8o when staring at the base of the statue. How tall is the statue to the nearest tenth of a foot?
Answer:
The height of the statue is 21.4 feet
Step-by-step explanation:
We are given
A person is standing 50 ft from a statue
The person looks up at an angle of elevation of 16 degree when staring at the top of the statue
hen the person looks down at an angle of depression of 8 degree when staring at the base of the statue
Firstly, we will draw diagram
In triangle ABF:
FC=50
we can use trig formula
[tex]tan(16)=\frac{y}{50}[/tex]
[tex]y=50tan(16)[/tex]
[tex]y=14.33727ft[/tex]
now, we can find x
In triangle DEF:
we can use trig formula
[tex]tan(8)=\frac{x}{50}[/tex]
[tex]x=50tan(8)[/tex]
[tex]x=7.0270ft[/tex]
we can see that
height of statue =x+y
so, the height of statue is
[tex]=14.33727+7.0270[/tex]
[tex]=21.4ft[/tex]
The height of the statue to the nearest tenth of a foot is 21.4 ft and this can be determined by using the trigonometric properties
Given :
A person is standing 50 ft from a statue.The person looks up at an angle of elevation [tex]16^\circ[/tex] when staring at the top of the statue.The person looks down at an angle of depression [tex]8^\circ[/tex] when staring at the base of the statue.Refer to the diagram attached below.
From the diagram in triangle ABF:
[tex]\rm tan(16)=\dfrac{a}{50}[/tex]
a = 14.33 ft
From the diagram in triangle DEF:
[tex]\rm tan(8)=\dfrac{b}{50}[/tex]
b = 7.02 ft
Now, the height of the statue is given by:
[tex]\rm Height = a +b[/tex]
Height = 14.33 + 7.02
Height = 21.4 ft
The height of the statue to the nearest tenth of a foot is 21.4 ft.
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Which graph represents the function f(x) =0.75^x
The top-left graph is the correct representation of the function[tex]\( f(x) = 0.75^x \)[/tex]. It shows a decreasing function as [tex]\( x \)[/tex] increases, and the y-intercept is at (0, 1).
The correct option is (A).
To determine which graph represents the function [tex]\( f(x) = 0.75^x \)[/tex], we should consider the key characteristics of an exponential function where the base is between 0 and 1:
1. As [tex]\( x \)[/tex] increases, [tex]\( f(x) \)[/tex] should decrease because 0.75 raised to a higher power becomes smaller.
2. As [tex]\( x \)[/tex] decreases (becomes more negative), [tex]\( f(x) \)[/tex] should increase because 0.75 raised to a negative power becomes larger.
3. The graph will never touch the x-axis, as an exponential function does not cross the axis when the base is positive.
4. The y-intercept should be at [tex]\( f(0) = 0.75^0 = 1 \)[/tex] because any non-zero number to the power of 0 is 1.
Now let's evaluate the provided graphs with respect to these characteristics:
- Top-left graph:This graph shows a decreasing function as [tex]\( x \)[/tex] increases, and the y-intercept is at (0, 1), which matches the behavior of [tex]\( f(x) = 0.75^x \)[/tex].
- Top-right graph:This graph increases as [tex]\( x \)[/tex] increases, which is not correct for [tex]\( f(x) = 0.75^x \)[/tex].
- Bottom-left graph:This graph also increases as [tex]\( x \)[/tex] increases, which does not match the expected behavior.
- Bottom-right graph:This graph shows a decreasing function as [tex]\( x \)[/tex]increases, but the y-intercept is not at (0, 1), so it does not represent [tex]\( f(x) = 0.75^x \)[/tex].
Based on this analysis, the top-left graph is the correct representation of the function[tex]\( f(x) = 0.75^x \)[/tex]. It shows a decreasing function as [tex]\( x \)[/tex] increases, and the y-intercept is at (0, 1).
complete question given below:
Which graph represents the function f(x) =0.75^x
5/9x-3/7 in fraction form
Answer:
-15
63 but in simplified form, it's like this: -5
21
Step-by-step explanation: For multiplication and division, you don't need a common denominator, but for addition and subtraction you have to find the common denominator...
For this problem, since your multiplying, you just multiply straight accross, and if it needs to be simplified, then simplify:
5/9 x -3/7
-15
63
SIMPLIFIED because both -15 & 63 can be divided by 3 and end up like this:
-5
21
A person must be at least 4 feet tall to ride an amusement park ride. Which inequality represents the height, h, of a person who cannot get on the ride
Answer:
4≥x
Step-by-step explanation:
The person has to be at least four feet (=) or he can be higher (>).
Latisha hiked along a trail that is 9.66 miles long she had 4.2 miles every hour. How many hours did it take latisha to finish hiking the troll
Answer:
It took Latisha 2 hours and 18 minutes to finish hiking the trail.
Step-by-step explanation:
Speed = Distance traveled / Time taken
Given:
Distance traveled = 9.66 miles
Speed = 4.2 miles/hour
Time taken = Distance traveled/Speed
= 9.66/4.2 =2.3 hours = 2 hours 18 minutes.
∴ It took Latisha 2 hours and 18 minutes to finish hiking the trail.
The standard deviation for a set of data is 7.5. The mean is 235. What is the margin of error?
The margin of error is 0.97849
we are given
mean=235
so,
[tex]n=235[/tex]
standard deviation =7.5
so,
[tex]\sigma=7.5[/tex]
we know that
ME=2*standard error
and
[tex]SE=\frac{\sigma }{\sqrt{n} }[/tex]
If confidence level is 95%, then we can multiply by 1.96
so, we can multiply by 2 to get ME
now, we can use marginal error formula
[tex]ME=\frac{2\sigma }{\sqrt{n} }[/tex]
now, we can plug values
and we get
[tex]ME=\frac{2\times 7.5 }{\sqrt{235} }[/tex]
[tex]ME=0.97849[/tex]
Answer: 15
Step-by-step explanation: