The numbers represented by the word problems are 33 and 6
How to determine the solution to the word problem?The statements in the question are:
Two numbers add to 39. One number is 9 less than 7 times the other.Let the numbers in the expressions be x and y
So, we have
x + y = 39
x = 7y - 9
Substitute x = 7y - 9 in the equation x + y = 39
So, we have
7y - 9 + y = 39
Evaluate the like terms
8y = 48
Divide both sides by y
y = 6
Substitute y = 6 in x + y = 39
x + 6 = 39
Evaluate the like terms
So, we have
x = 33
Hence, the numbers are 33 and 6
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how much money will be in a bank after three years if nine dollars is deposited adding interest rate of 5% compounded annually? Round to the nearest cent.
ANSWER
[tex]10.45[/tex]EXPLANATION
Given;
[tex]\begin{gathered} p=9 \\ I=5 \\ t=3 \end{gathered}[/tex]Recall, the compound interest formula;
[tex]A=P\cdot \left(1+\frac{r}{n}\right)^{nt}[/tex]Substituting the values into the formula;
[tex]\begin{gathered} A=P\cdot \left(1+\frac{r}{n}\right)^{nt} \\ =9\left(1+\frac{5\%\:}{12}\right)^{12\cdot\:3} \\ =9\left(1+\frac{0.05}{12}\right)^{12\cdot\:3} \\ =9(1+0.00416)^{36} \\ =9\times1.16147 \\ =10.45325 \\ \cong10.45 \end{gathered}[/tex]Therefore, the amount in the bank account after 3 years will be $10.45
need help for answer:10n=1/4+3/20n
Answer:
5/197
Step-by-step explanation:
Please look at the image below!
Answer: n=5/197
Step-by-step explanation:
31.What is the surface area of the cylinder?
Hello there. To solve this question, we'll have to remember some properties about cylinders.
We want to determine the surface area of the following cylinder:
In this case, the surface area comprehends the bottom, the top and the lateral area of the cylinder.
For a cylinder with height h and radius R, it is easy to show that
By redrawing the cylinder as the following figures:
Notice the 2pi * R came from the measure of the circumference of the top and bottom circles.
The area of the circles are given as
[tex]\pi\cdot R^2[/tex]And the area of the rectangle is
[tex]2\pi Rh[/tex]So the surface area of this cylinder is given as
[tex]2\pi R^2+2\pi Rh[/tex]Plugging the values R = h = 1.5 m, we'll get
[tex]2\pi\cdot1.5\cdot(1.5+1.5)=9\pi\approx28.27\text{ m}^2[/tex]In this case, the answer is 9pi and it is contained in the 4th option.
9 1 point Jonah has 20 nickels and dimes. In total, he has $1.75. Use question 7 to find out how many dimes Jo Type your answer... Previous
Answer:
Jonah has 15 dimes.
Step by step explanation:
Since question 7, tells us that we have to use the following equations to solve the system:
Let x be the nickels
Let y be the dimes
[tex]\begin{gathered} x+y=20\text{ (1)} \\ .05x+.10y=1.75\text{ (2)} \end{gathered}[/tex]We can use the substitution method to solve the system, isolate y in equation (1), and then plug it into equation (2)
[tex]y=20-x\text{ (1)}[/tex][tex]\begin{gathered} .05x+.10(20-x)=1.75 \\ \end{gathered}[/tex]Now, solve for x.
[tex]\begin{gathered} .05x+2-.10x=1.75. \\ -.05x=1.75-2 \\ -.05x=-0.25 \\ x=\frac{-0.25}{-0.05} \\ x=5 \end{gathered}[/tex]That means Jonah has 5 Nickels. Now to solve for y(dimes), substitute x=5 into equation (1)
[tex]\begin{gathered} y=20-x \\ y=20-5 \\ y=15 \end{gathered}[/tex]Jonah has 15 dimes.
Find the zeros of the function ƒ(x) = x2 + 2x – 3.
In order to determine the zeros of this function, the steps are:
1. Assume f(x) = 0. Hence, the equation becomes:
[tex]0=x^2+2x-3[/tex]2. Factor the quadratic function by finding some factors of -3 that sums to the middle term 2.
a. -3 and 1 → -2
b. -1 and 3 → 2
So, the factors of -3 that sums to 2 are -1 and 3.
So, the quadratic equation can be factored into:
[tex]0=(x-1)(x+3)[/tex]3. Equate each factor to zero and solve for x.
[tex]\begin{gathered} x-1=0\Rightarrow x=1 \\ x+3=0\Rightarrow x=-3 \end{gathered}[/tex]Therefore, the zeroes of the function are at (-3, 0) and (1, 0). (Option C)
5/9 + 3/9 in decimals
Answer:
0.8 *repeating
Step-by-step explanation:
5/9 + 3/9 = 8/9!
8/9 as a decimal is 0.888888888 (repeating forever)
A triangle has sides with lengths of 10 miles, 12 miles, and 17 miles. Is it a right triangle? yes no
you can solve a triangle if you have the 3 sides
using these formulas
[tex]\begin{gathered} \cos A=\frac{b^2+c^2-a^2}{2bc} \\ \\ \cos B=\frac{a^2+c^2-b^2}{2ac} \end{gathered}[/tex]So
[tex]\begin{gathered} \cos A=\frac{10^2+12^2-17^2}{2(10)(12)} \\ \cos A=\frac{-45}{240} \\ A=\cos ^{-1}(\frac{-45}{240}) \\ A=100.8 \end{gathered}[/tex][tex]undefined[/tex]the sum of all the angles must equal 180
[tex]\begin{gathered} A+B+C=180 \\ 100.8+35.29+C=180 \\ C=180-35.29-100.8 \\ C=43.41 \end{gathered}[/tex]a rigth triangle have an angle of 90°, so this triangle isn't rigth
Write a verbal expression for each algebraic expression.
a. 6
b. – 12m
The verbal expression for the algebraic expression
(a) 6 is " number six "
(b) -12m is " negative twelve times a number m " .
An Algebraic Expression can be defined as an expression that is made up of constants and variables linked with mathematical operators.
For Example : 2x+3y is an algebraic expression.
In the question ,
the algebraic expression are given as ,
Part(a)
6 ,
the verbal expression ,of the algebraic expression 6 is " number six " .
Part(b)
-12m
On Analyzing , we can say "12m" in simple language is "twelve times a number m ",
the sign "-" , means negative
Altogether , we can say that "-12m" means negative twelve times a number m .
Therefore , the verbal expression for the algebraic expression
(a) 6 is " number six "
(b) -12m is " negative twelve times a number m " .
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find the lateral area, surface area, and volume of the following figure. leave answer in simplest radical form or in terms of pi. round to the nearest tenth. Solve for the lateral surface area
Given:
The dimensions of the rectangular prism :
length(l)= 5 in
width (w) = 2 in
height (h) = 3 in
The formula for the lateral surface area L.A of a rectangular prism is:
[tex]L.A\text{ = 2\lparen l + w\rparen h}[/tex]Substituting the given values into the formula:
[tex]\begin{gathered} L.A\text{ = 2}\times\text{ \lparen5 + 2\rparen }\times\text{ 3} \\ =\text{ 42 in}^2 \end{gathered}[/tex]Answer: 42 square inch
ive done this question so many times and I just cant seem to get it can you please help me figure this out
Explanation
to figure out this, we need to check every option
[tex]\begin{gathered} V=\frac{1}{3}Bh \\ \end{gathered}[/tex]Step 1
[tex]\begin{gathered} B=50 \\ h=10 \end{gathered}[/tex]replace.
[tex]\begin{gathered} V=\frac{1}{3}Bh \\ V=\frac{1}{3}\cdot50\cdot10 \\ V=166.66 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} B=50 \\ h=30 \end{gathered}[/tex]
replace
[tex]\begin{gathered} V=\frac{1}{3}Bh \\ V=\frac{1}{3}\cdot50\cdot30 \\ V=500 \end{gathered}[/tex]Step 3
[tex]\begin{gathered} B=100 \\ h=10 \end{gathered}[/tex]
replace
[tex]\begin{gathered} V=\frac{1}{3}Bh \\ V=\frac{1}{3}\cdot100\cdot10 \\ V=\frac{1000}{3}=\frac{999}{3}+\frac{1}{3}=333\text{ }\frac{1}{3} \\ V=333\text{ }\frac{1}{3} \end{gathered}[/tex]so, the answer is
[tex]B=100cm^2\text{ h=10 cm}[/tex]I hope this helps you
A) 104 units^2 B) 2184 units^2 C) 248 units^2 D) 250 units^2
First find the perimeter of the rectangle
P = 2(l+w) where l is the length and w is the width
P = 2( 5x-1+x)
Combine like terms
P = 2( 6x-1)
P = 12x -2
Find the perimeter of the triangle
P = s1 + s2 +s3 where s is the side length
P = 5x+12+ 6x+7
Combine like terms
P = 11x+19
We are told the perimeters are equal
12x-2 = 11x+19
Subtract 11x from each side
12x-2 -11x = 11x+19-11x
x-2 = 19
Add 2 to each side
x-2+2 = 19+2
x = 21
The side lengths of the rectangle are
x=21 and 5x-1 = 5*21 -1 = 105-1 = 104
We can find the area
A = l*w where l is the length and w is the width
A = 21 * 104
A = 2184 units^2
Answer:
B 2184 units^2
Pigeons once used to be welcome at Trafalgar Square and the public were encouraged to feed them. This gave a good opportunity to estimate the pigeon population in London. At one point 84 pigeons were caught and tagged. Two days later, 120 pigeons were caught in Trafalgar Square and it was found that 3 of the pigeons were tagged. Approximately how many pigeons were there in London?
A total of 201 pigeons are there in London as determined by set theory.
What is Set Theory?
The area of mathematical logic known as set theory examines sets, which are essentially collections of objects.Set theory is an area of mathematics that primarily deals with objects that are pertinent to mathematics as a whole, despite the fact that any form of an object can be gathered into a set.The pigeon caught in the first attempt=84
No. of them tagged=84
⇒Set A=84
Pigeon caught in second attempt =120
⇒Set B=120
No. of them found tagged=3
No. of Pigeons in London = Set A∪Set B-3
84+120-3=201
A total of 201 pigeons are there in London as determined by set theory.
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Write the percent as decimal 5.3%
Given:-
[tex]5.3\%[/tex]To convert the given percentage as decimal.
So now we simplify,
[tex]5.3\%=\frac{5.3}{100}=0.053[/tex]So the required decimal number is 0.053
hey, I would like to know how to this problem
Given:
Graph is given.
Insecting point of two lines is (1,2.5)
[tex]\text{Solution : (1,2.5)}[/tex]GEOMETRY IAWhat is the coordinate of the midpoint of RP?
1) Examining the number line, we know that RP is a line segment. And the midpoint is located at half the segment RP.
2) Then on the number line we can write out, the following:
We can take the average of those points -8 and -1
[tex]\frac{-8+(-1)}{2}=\frac{-8-1}{2}=-\frac{9}{2}[/tex]
3) Hence, the midpoint of this line segment RP is -9/2 or -4.5
Triangle A(1, 2), B(3, 2), C(2, 4) is rotated 90
degrees around the origin. What are the
coordinates of A'B'C'?
The coordinates of the transformed figure are: A ’(-1, -2), B ’(-3, -2), C ’(-2, 4)
When a shape is rotated, it must be rotated through a point, here itis rotated around the origin
The coordinates of the triangle is given as:
A(1, 2), B(3, 2), C(2, 4) is rotated 90 degree
The rule of 90 degrees clockwise rotation is:
x, y = -x, -y
So, we have:
A(1, 2) which becomes (-1, -2)
B(3, 2), which becomes (-3, -2)
C(2, 4) which becomes (-2, -4)
Hence, the coordinates of the transformed figure are:
A ’(-1, -2), B ’(-3, -2), C ’(-2, 4)
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Jamie earned 18 more points on her test than Paul earned. Their points add up to 60. How many points did each student earn?
Answer:
Paul earned 21 points and Jamie earned 39 points.
Step-by-step explanation:
So, you start off with 60-18=42. Now, you have how much they earned minus Jamie's bonus 18. So, now that they have earned the same amount, you divide 42/2=21. So, now you know how many points Paul earned, 21, and now you just have to add the points Jamie earned that Paul didn't back to their score. 21+18=39
Find the area of the circle. Use 3.14 or 22/7 fir Pi
ANSWER
132.7 km^2 option B
EXPLANATION
Step 1: Formula for Area of a Circle
[tex]\text{Area of a circle = }\pi r^2[/tex]where radius r = diameter/2
r = 13/2
r = 6.5km
Step 2: Substitute the values of r = 6.5 and pi = 3.14
[tex]\begin{gathered} \text{Area = }\pi r^2 \\ \text{ = 3.14 }\times6.5^2 \\ \text{ = 3.14 }\times\text{ 42.25} \\ \text{ = }132.665\text{ }=\text{ 132.7 }km^2\text{ (to nearest tenth)} \\ \end{gathered}[/tex]Hence, the area of the circle with radius 6.5km is 132.7km^2 (to the nearest tenth).
Solve the inequality />
d > 105
Explanations:The given inequality is:
[tex]\frac{d}{7}>\text{ 15}[/tex]Multiply both sides by 7:
[tex]7\text{ }\times\frac{d}{7}>\text{ 15}\times7[/tex][tex]d\text{ > }105[/tex]An investigation of a number of automobile accidents revealed the following information:15 accidents involved alcohol and excessive speed27 accidents involved alcohol.13 accidents involved excessive speed but not alcohol22 accidents involved neither alcohol nor excessive speedHow many accidents were investigated? ** note: Let the universal set U be the set of all automobile accidents. Use the information provided to create a Venn diagram containing 2 subsets. Let A be the set of accidents involving alcohol and S be the set of accidents involving excessive speed. **
To solve this type of question we should use the Venn diagram
Let me draw it and show you where we will put each number given
Since there are 15 accidents involved alcohol and excessive speed
Then we should put 15 in the common part of the 2 circles
Since there are 27 accidents involved alcohol
That means 27 = alcohol only + alcohol and excessive speed
Then to find alcohol only we should subtract 15 from 27 to get the number of alcohol only
27 - 15 = 12
Since there are 13 accidents involved excessive speed but not alcohol
That means the excessive speed only is 13
Let us put it in the Venn diagram
Since there are 22 accidents involved neither alcohol nor excessive speed
That means we will put this number outside the circles inside the rectangle
To find the total number of accidents we will add all the numbers in the figure
[tex]\begin{gathered} T_{acc}=12+15+13+22 \\ T_{acc}=62 \end{gathered}[/tex]Then there are 62 accidents in this investigated
What is the slope of the line represented by the equation y = 4/5x-3?
A. -3
B. -1/
C. //
D. 3
Hurry!!!!
Raina pays $3.84 for a bag of 16 tangerines. find the unit price in dollars per Tangerine. If necessary, round your answer to the nearest cent.
Which is the approximate percentage change in water constant after maple tree sap became maple syrup?
Looking at the graphs, the maple tree sap has 98% of water, while the maple syrup has 33% of water.
That means the amount of water decreased by:
[tex]98\%-33\%=65\%[/tex]Therefore maple tree sap has 65% more water than maple syrup.
Correct option: first one.
A population has a mean of 128 and a standard deviation of 32. Suppose a sample of 64 is selected. What is the probability that the sample mean will be within +- 5 of the population mean?
The probability that the sample mean will be within +- 5 of the population mean is 0.7888.
What will the probability be?In this case, within 5 will be:
= 128 ± 5 = 123, 133
The probability will be:
P(123 < x < 133)
= P(123 - 128))4 =(133 - 128)/4
= P(-1.25< Z < 1.25 )
= P(Z < 1.25) - P(Z < -1.25 )
Using z table,
= 0.8944 - 0.1056
= 0.7888
The probability is 0.7888.
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Zion has an 80:1 scale-drawing of the floor plan of his grandmother’s house. On the floor plan, the dimensions of his grandmother’s rectangular living room are 1 inches by 2 inches. 8721 What is the area of his grandmother’s real living room in square feet?
1) Gathering the data
80:1 scale
On the floor plan : width: 1 inch x 2 inches
2) Let's find the real area of the living room by setting a proportion:
Since on the fo
Find the area of the triangle belowunits given are cm, cm^2, cm^3
Answer:
[tex]A_T=150cm^2[/tex]Explanation: We need to find the area of the triangle, We know that the area of any right triangle is:
[tex]A_T=\frac{1}{2}(b\times h)[/tex]Therefore in the information given we have the following:
[tex]\begin{gathered} h=20\operatorname{cm} \\ b=15\operatorname{cm} \end{gathered}[/tex]Therefore the Area of this triangle is as follows:
[tex]\begin{gathered} A_T=\frac{1}{2}(b\times h) \\ \therefore\rightarrow \\ A_T=\frac{1}{2}(20cm\times15cm)=\frac{1}{2}(20\times15)cm^2 \\ A_T=\frac{1}{2}(300)cm^2=150cm^2 \\ \therefore\rightarrow \\ A_T=150cm^2 \end{gathered}[/tex]Note! Units are centimeter-squared
A hacker is trying to guess someone’s password. The hacker knows (somehow) that the password is ) digits long, and that each digit could be a number between 0 and 4 assume that the hacker makes random guesses.
What is the probability that the hacker guesses the password on his first try?
Step-by-step explanation:
easy the hacker got the password by hacking maybe he is bot so he gusss it but if he guss it he may got brainlist answer mark me ok so he got 2312
Solve for x.×+8=-6 what's the answer
The equation is
[tex]x+8=-6[/tex]Since we have a "+8" in the left side, we can substract 8 in both sides to get rid of it, which will solve the equation:
[tex]\begin{gathered} x+8=-6 \\ x+8-8=-6-8 \\ x=-14 \end{gathered}[/tex]a number m is no less than -1 or less than or equal to -5 1/3
Answer:
Step-by-step explanation:
y=5 1/3 can be expressed in infinite ways
PREMISES
y=5 1/3 expressed as a fraction
CALCULATIONS
The mixed number 5 1/3 can be written in various ways:
y=5 1/3
y=
(.25/.046875, .5/.09375, 1/.1875, 2/.375, 4/.75, 8/1.5, 16/3 as improper fractions or 5.3333 repeating as a decimal fraction]
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee
thank you
The domain and range for the relation is [-∞, ∞] and [0,-3], and both of them can be described by interval notation .
Since the graph given to us present a relation or a function, The domain and range of a function are the set of all the inputs and yield a function that can grant separately. The domain and range are vital viewpoints of a function. The domain takes all the conceivable input values from the set of real numbers and the range takes all the yield values of the function. In simple words, the domain is the set of all "x" values and the range is the set of all "y" values in a set of ordered sets and the requested sets are composed as in the form (x, y) or [x,y]
for the given the points are : (0,-3),(1,-3),(2,-3),(3,-3),(4,-3),(5,-3),(-1,-3)(-2,-3),(-3,-3),(-4,-3),(-5,-3)
so the domain set is ={-5,-4,-3,-2,-1,0,1,2,3,4,5}
and the range set is ={0,-3,-4,-5,-6,-7,-8}
so the domain and range is [-∞, ∞] and [0,-3]
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