Answer:
x = -8
Explanation:
Given the below system of equations;
[tex]\begin{gathered} x=2y-4\ldots\ldots\ldots\ldots\ldots\text{.Equation 1} \\ 7x+5y=-66\ldots\ldots\ldots\ldots\text{Equation 2} \end{gathered}[/tex]The solve the above, let's go ahead and put equation 1 into equation 2 and solve for y;
[tex]\begin{gathered} 7(2y-4)+5y=-66 \\ 14y-28+5y=-66 \\ 19y=-66+28 \\ 19y=-38 \\ y=-\frac{38}{19} \\ y=-2 \end{gathered}[/tex]To find x, we have to substitute the value of y into equation 1 and solve for x;
[tex]\begin{gathered} x=2(-2)-4=-4-4=-8 \\ x=-8 \end{gathered}[/tex]Write each fraction in terms of the LCD.x2x + 12x - 1x + 13x22x – 111X + 1X + 13Need Help?Watch ItAdditional Materials
The given fractions are,
[tex]\frac{x^2}{2x-1},\text{ }\frac{x+1}{x+13}[/tex]The LCD of fractions is the least common multiple of the denominators.
So, the LCD of the above fractions is,
[tex](2x-1)(x+13)[/tex]Multiplying the numerator and the denominator of the fraction by a common term does not change the fraction.
So, the first fraction can be expressed in terms of the LCD as,
[tex]\frac{x^2}{2x-1}=\frac{x^2(x+13)}{(2x-1)(x+13)}[/tex]The second fraction can be expressed in terms of the LCD as,
[tex]\frac{x+1_{}^{}}{x+13}=\frac{(x+1)(2x-1)}{(2x-1)(x+13)}[/tex]The table shows the weights of bananas at a grocery store. Complete the table so that there is a proportional relationship between the number of bananas and their weight.Number Of Bananas. Weight In Kilograms. 2 ? 0.72 15 ?
Let u make the first box x and the second box y.
If there is a proportional relationship between the number of bananas and their weights, it means that:
[tex]\frac{2}{x}=\frac{6}{0.72}=\frac{15}{y}[/tex]We can take the first pair and solve for x as follows:
[tex]\begin{gathered} \frac{2}{x}=\frac{6}{0.72} \\ 6x=2\times0.72=1.44 \\ x=\frac{1.44}{6} \\ x=0.24 \end{gathered}[/tex]We can solve for y in the same manner:
[tex]\begin{gathered} \frac{6}{0.72}=\frac{15}{y} \\ 6y=15\times0.72=10.8 \\ y=\frac{10.8}{6} \\ y=1.8 \end{gathered}[/tex]Therefore, the boxes are filled as shown below:
Estimate the product by adjusting the larger factor to the compatible number 25 and then multiply. 27 x 8 = Think about counting by 25s.
You have the following product:
27 x 8
To estimate the product by rounding 27 to 25, you consider that 25 x 8 is the same as adding 25 eight times.
Then, you have:
25 x 8 = 25 + 25 + 25 + 25 + 25 +25 + 25 +25
25 x 8 = 50 + 50 + 50 + 50 each pair of 25's add up 50
25 x 8 = 100 + 100 each pair of 50's add up 100
25 x 8 = 200
Hence, an estimation of the given product is 200, by considering 27 rounded to 25.
The entire graph of the function h is shown in the figure below.Write the domain and range of h using interval notion.(a) domain=(b) range=
The graph of the function is defined for x greater than or equal to -2 and less than 3. So domain of the function is,
[tex]\lbrack-2,3)[/tex]The value of the function lies between -2 and 3. The function value is greater than or equal to -2 and less than 3. So range of function is,
[tex](-2,3\rbrack[/tex]The 7th grade took a field trip to the zoo. 50 students rode in cars and the rest of the students were split equally onto 4 buses. There are 142 total 7th graders. How many students were on each bus?
traveledGiven:
The total number of students is N = 142.
The number of students riding in a car is n(C) = 50.
The total number of buses is b = 4.
The objective is to find the number of students traveling on each bus.
Explanation:
Consider the number of students travelled in each bus as s.
Then, the total number of students traveling in 4 buses will be 4s.
The algebraic expression for the total number of students N can be represented as,
[tex]N=n(C)+b(s)\text{ . . . . .(1)}[/tex]On plugging the given values in equation (1),
[tex]142=50+4s[/tex]On further solving the above equation,
[tex]\begin{gathered} 142-50=4s \\ 4s=92 \\ s=\frac{92}{4} \\ s=23 \end{gathered}[/tex]Hence, the number of students traveling on each bus is 23.
Please help me!A bag holds 5 pounds of pet food. If Paul uses the 5 pounds of food to fill 6 plastic containers equally, how much pet food will each container hold?0.830.80.8030.83
We must divide the 5 pound bag in 6 different containers, therefore:
[tex]\frac{5}{6}=0.83[/tex]Each container will hold 0.83 pet food
4. Write the equation of the line in SLOPE-INTERCEPT FORM that passes through the given points(4,2) and (0,6)
The slope intercept form equation is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for determining slope is expressed as
slope, m = (y2 - y1)/(x2 - x1)
From the information given,
y2 = 6, y1 = 2
x2 = 0, x1 = 4
Slope, m = (6 - 2)/(0 - 4) = 4/- 4
m = - 1
We would determine the y intercept, c by substituting m = - 1, y = 6 and x = 0 into the slope intercept equation. It becomes
6 = - 1 * 0 + c
6 = c
c = 6
The equation would be
y = - x + 6
3. By elimination 2x - 3y =- 55x + 2y =16
By elimination, it means that we should apply algebraic operations so we find the value of one variable. So first, lets multiply the first equation by 5. We get
[tex]5\cdot(2x-3y)=5\cdot-5\text{ = 10x-15y = -25}[/tex]Now, lets multiply by 2 the second equation
[tex]2\cdot(5x+2y)\text{ = 16}\cdot2\text{ = 10x+4y=32}[/tex]With this two equations, lets subtract the second equation from the first equation
[tex]10x+4y-(10x-15y)\text{ = 32-(-25)}[/tex]We get
[tex]19y\text{ = 57}[/tex]If we divide y by 19 we get
[tex]y=\frac{57}{19}=3[/tex]Now, using this value in the second equation we get
[tex]5x+2\cdot3\text{ = 16 }=5x+6[/tex]If we subtract 6 on both sides, we get
[tex]16-6\text{ = 5x = 10}[/tex]Finally, we divide by 5 on both sides and we get
[tex]x=\frac{10}{5}=2[/tex]Hello may you please check me work for number 5
Surface area of a rectangular prism:
[tex]SA=2(wl+hl+hw)[/tex]Substitute 1.2 for all of the variables in the formula:
[tex]SA=2[(1.2)(1.2)+(1.2)(1.2)+(1.2)(1.2)][/tex]Using a calculator, you should get an answer of:
[tex]SA=8.64\text{ }yd[/tex]The answer is that the surface area of this shape is 8.64 yards.
Answer this question
Okay, in this case the statement talks about the sum, according with this we need to find the sum of the number blue bikes (b) and 9 red bikes.
So, in this case the correct option is A. b+9 because it says sum
Simplify.4n + 12 + 7n4 n + 1923 n16 n +711 n+ 12
11 n+ 12
In this expression, to simplify means to reduce it to the simpler expression. Hence:
1) Grouping similar terms
4n + 12 + 7n =
2) Adding them up:
4n+7n+12=
11n +12
Pleaee help me draw this. Construct a tangent to the circle from point R.
solution
For this case the tangent line to the circle and the point should be:
The reason is because the tangent line and the point needs to touch the circle just one time
indicate whether (2, 7) is a solution of the given system.y is greater than or = -x+1Y is less than 4x+2
In order to determine if the point (2, 7) is a solution to the given system of inequalities we just have to replace 7 for y and 2 for x and see if the two inequalities are met, like this:
For y ≥ -x + 17 ≥ -2 + 1
7 ≥ -1
As you can see, 7 is greater than -1 then the first inequality is met.
For y < 4x + 27 < 4(2) + 2
7 < 8 + 2
7 < 10
As you can see, the second inequality is also met, then (2, 7) is a solution for the system of inequalities.
prove that 1+3+5+......2n-1=n²
As given by the question
There are given that the series
[tex]1+3+5+\cdots+(2n-1)=n^2[/tex]Now,
For step 1:
Put n=1
Then LHS =1
And
[tex]\begin{gathered} R\mathrm{}H\mathrm{}S=(n)^2 \\ =(1)^2 \\ =1 \end{gathered}[/tex]So,
[tex]\therefore L.H.S=R.H.S[/tex]P(n) is true for n=1.
Now,
Step 2:
Assume that P(n) istrue for n=k
Then,
[tex]1+3+5+\cdots+(2n-1)=k^2[/tex]Adding 2k+1 on both sides
So, we get:
[tex]1+3+5\ldots+(2k-1)+(2k+1)=k^2+(2k+1)=(k+1)^2[/tex]P(n) is true for n=k+1
By the principle of mathematical induction P(n) is true for all natural numbers n.
Hence,
[tex]1+3+5+\cdots+(2n-1)=n^2[/tex]For all n.
Hence proved.
Given quadrilateral MNPQ which of the following set of conditons would not be enough to know that MNPQ is a parrelogram?
For a shape to be considered a parallelogram it has to meet the following conditions:
0. The opposite sides must be equal
,1. The opposite sides are equal
,2. Adjacent sides are supplementary
,3. The diagonals bisect each other
,4. The opposite sides are parallel
For the quadrilateral to be considered a parallelogram then, the conditions that should be met are:
MN=QP and MQ=NP
MN || QP and MQ || NP
The diagonals MP and NQ bisect each other.
∠M=∠P and ∠N=∠Q
From the given options, the second one and the third one are not enough to determine MNPQ as a parallelogram
Find the cardinal number of the setWhere N denotes the set of all natural numbers
And x is divisible by 6 . The natural number of x will be
[tex]x=\mleft\lbrace36,42,48,54\mright\rbrace[/tex]The current student population of Kansas City is 2700. If the population increases at a rate of 5.2% each year. What will the student population be in 4 years?Write an exponential growth model for the future population P(x) where x is in years:p(x)=What will the population be in 4 years? (Round to nearest student)
ANSWER
P(x) = 2700(1.052)^t
P(4) = 3307. (Rounded to nearest student)
EXPLANATION
Given:
1. The current student population to be 2700
2. The growth rate = 5.2% = 0.052
Desired Outcome
1. The exponential growth model
2. Population of the students in 4 years
The Exponential Growth Model
[tex]\begin{gathered} P(x)\text{ = 2700\lparen1 + 0.052\rparen}^t \\ P(x)\text{ = 2700\lparen1.052\rparen}^t \end{gathered}[/tex]Population in 4 years
[tex]\begin{gathered} P(4)\text{ = 2700\lparen1.052\rparen}^4 \\ P(4)\text{ = 2700}\times1.2248 \\ P(4)\text{ = 3306.96} \end{gathered}[/tex]Hence, the Exponential Growth Model P(x) = 2700(1.052)^t and the Population of the students in 4 years P(4) = 3307. (Rounded to nearest student)
on a map, the scale is 5 cm = 2km what is the missing distance?town A distance to 5.6km is the actual distance
The distance on the map is 14 cm
Explanation:Parameters:
Map scale: 5 cm = 2 km
Given actual distance = 5.6km
Let x be the distance on map, then
x = 5.6 km
2x = 5 * 5.6
2x = 28
x = 28/2
= 14 cm
A rectangular prism is shown below.A formula for the volume of a rectangular prism V = Bh. The volume, V, of this prism is 600 cm³. Which expression can be used to find x, the width of the prism in centimeters? A: 600/15B: 600/8C: 600/(8)(15)D: (8)(8)(15)(15)/600
Volume of a rectangular prism = base length x width x heigth
Where;
Volume = 600 cm3
base length = 15
width = x
height = 8
Replacing:
600 = (15) (x) (8)
Isolate x
600/ (15)(8) = x
x = 600/ (8)(15)
option C
the odds against (E) are 23:77 Find the probability of (not E) :
We can rewrite the question as the probability of getting the event E is 23:77. Find the probability of getting the event not E.
The number 23:77 is a ratio and is it equivalent to:
[tex]\frac{23}{77}[/tex]To get the probability of the event not-E, we can proceed as follows:
[tex]1-\frac{23}{77}=\frac{77}{77}-\frac{23}{77}=\frac{53}{77}\approx0.7013[/tex]So the probability for the event not-E is about 53/77 or 0.7013 (or a little more than 70%).
find the value of f (4)
we know that
f(4) is the value of the function f(x) when the value of x is equal to 4
so
For x=4
Look at the graph
The value of the function f(x) is equal to 3
therefore
f(4)=3Question 5 of 15, Step 1 of 14/15CorrectIfy is inversely proportional to x and y = -71 when x = 16, find yifx = 7. (Round off your answer to the nearest hundredth.)
Answer:
[tex]y=-31.06[/tex]Step-by-step explanation:
Since y and x are inversely proportional, we'll have that:
[tex]y=\beta x[/tex]For a given betha value. Since we have a pair of x and y values, we can plug them in the formula and find our particular value of betha, as following:
[tex]\begin{gathered} y=\beta x\rightarrow-71=\beta\times16\rightarrow\beta=-\frac{71}{16} \\ \end{gathered}[/tex]This way, our formula would be:
[tex]y=-\frac{71}{16}x[/tex]Plugging in x = 7,
[tex]\begin{gathered} y=-\frac{71}{16}x\rightarrow y=-\frac{71}{16}(7)\rightarrow y=-\frac{497}{16} \\ \\ \Rightarrow y=-31.06 \end{gathered}[/tex]The edge of a cube measures 11 m. Find the surface area.
In order to determine the surface area of the cube, use the following formula:
[tex]S=6a^2[/tex]where a is the length of the side of a cube a = 11 m.
Replace the value of a into the formula for S:
[tex]S=6(11m)^2=726m^2[/tex]Hence, the surface area of the given cube is 726m^2
Solve on the interval [0,27): RCŨsx+c05X +1 = ] T O 3 A. X= 27,x = x=57 4. 4 O B. X = 27,X = O c. X= 7T,X = 1 47T 3 T D. X= ET 6 6 NAMAN
ANSWER:
C.
[tex]x=\pi,x=\frac{2\pi}{3},x=\frac{4\pi}{3}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]2cos^2x+3cosx\: +1\: =\: 0[/tex]Using the substitution method, we can calculate the value of x, like this:
[tex]\begin{gathered} u=\cos x \\ \text{ therefore:} \\ 2u^2+3u+1=0 \\ 3u=2u+u \\ 2u^2+2u+u+1=0 \\ 2u(u+1)+u+1=0 \\ (u+1)(2u+1)=0 \\ u+1=0\rightarrow u=-1 \\ 2u+1=0\rightarrow2u=-1\rightarrow u=-\frac{1}{2} \\ \text{ replacing:} \\ \cos x=-1\rightarrow x=\cos ^{-1}(-1)\rightarrow x=\pi \\ \cos x=-\frac{1}{2}\rightarrow x=\cos ^{-1}(-\frac{1}{2})\rightarrow x=\frac{2\pi}{3},\frac{4\pi}{3} \end{gathered}[/tex]what is 12/8 × 18/16
First of all, simplify the given fractions
Question 1 of 14, Step 1 of 10/19CorrectDetermine if the following expression is a polynomial.4 – 8x + x²AnswerKeyboaO Yes O No
Solution
Given
[tex]4-8x+x^2[/tex]We want to determine if it's a Polynomial
A polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Hence 4 - 8x + x^2 is a Polynomial
describe and correct the error solution error a student made when graphing a linear equation y equals -3 / 4 x - 6
we have two points (0, 6) and (4, 3)
this can be represented as (x, y)
the equation of a straight line is
y = mx + c
slope = m = y2 - y1/ x2 - x1
x1 = 0, y1 = 6, x2 = 4 and y2 = 3
slope = 3 - 6 / 4 - 0
slope = -3/4
slope = -3/4
from the equation of a straight line
(y - y1) = m(x - x1)
y1 = 6 and x1 = 0
y - 6= -3/4(x - 0)
y - 6 = -3/4x + 0
y = -3/4x + 6
the error he made was that he used - 6 instead of +6 in the final answer
Which is the graph of the solution set of -2x + 5y > 15?10 1310 138896421OT810x2468 10622-4Ox681010 138642X246810
To graph the solution set, first, we know that the border of the shaded area will be delimited by the dashed line:
[tex]-2x+5y=15.[/tex]Now, to know if the shaded area will be on top or below the line, we evaluate the point (0,0):
[tex]-2(0)+5(0)=0<15,[/tex]therefore, the origin is not a point of the solution set.
Answer:Use the expressions from the previous questions to determine Mary’s age.
The age of Mary is 15 years old.
To solve this, we have three expressions:
[tex]\begin{gathered} M=J+5 \\ J=T-28 \\ T=3H-1 \end{gathered}[/tex]Where M is the age of Mary, J is the age of Jacob, T is the age of Uncle Tim and H is the age of Henry
Also teh problem give us an additional info, the age of Henry is 13. With this, we can replace the value of H in the thrid equation:
[tex]\begin{gathered} \begin{cases}H=13 \\ T=3H-1\end{cases} \\ \text{Then:} \\ T=3\cdot13-1=39-1=38 \\ T=38 \end{gathered}[/tex]Now we can replace T in the second equation:
[tex]\begin{gathered} \begin{cases}T=38 \\ J=T-28\end{cases} \\ \text{Then:} \\ J=38-28=10 \\ J=10 \end{gathered}[/tex]Finally, we can replace J in the first equation to get the age of Mary:
[tex]\begin{gathered} \begin{cases}J=10 \\ M=J+5\end{cases} \\ \text{Then:} \\ M=10+5=15 \end{gathered}[/tex]Thus, the age of Mary is 15 years old.
A support cable runs from the top of a telephone pole to a point on the ground 42.7 feet from its base. Suppose the cable makes an angle of 29.6 with the ground (as shown in the following figure).(a) Find the height of the pole. (Round the answer to the nearest tenth.) feet (b) Find the length of the cable. (Round the answer to the nearest tenth.) feet
We will draw a sketch to see the position of the cable
From the figure, we can use the tangent ratio to find the height
[tex]\frac{h}{42.7}=tan(29.6)[/tex]By using the cross-multiplication
[tex]\begin{gathered} h=42.7tan(29.6) \\ \\ h=24.3\text{ feet} \end{gathered}[/tex]a) The height of the pole is 24.3 feet to the nearest tenth
To find the length of the cable we will use the cosine ratio
[tex]cos(29.6)=\frac{42.7}{L}[/tex]Switch L and cos(29.6)
[tex]\begin{gathered} L=\frac{42.7}{cos(29.6)} \\ \\ L=49.1\text{ feet} \end{gathered}[/tex]b) The length of the cable is 49.1 feet to the nearest tenth