Okay, here we have this:
Considering the provided equation, we are going to solve it to find the value of y, so we obtain the following:
5/6= v-5 /4
v-5 /4+ 5 /4=5/6 + 5/4
v= 5/6 + 5/4
v=(20+30)/24
v=50/24
v=25/12
Finally we obtain that v is equal to 25/12.
995
× 55 ?? What’s the partial product of this?
Find the sum of (3x2 + 18x – 7) and (-13x2 + 7x – 11)A –13x3 + 3x2 + 25x – 18B –13x3 + 10x2 + 7x – 7C-13x3 + 10x2 + 18x – 18D -10x2 + 25x – 18
Answer:
The correct option is D, the sum of the given polynomials is
[tex]-10x^2+25x-18[/tex]Explanation:
To find the sum of:
[tex]3x^2+18x-7[/tex]and
[tex]-13x^2+7x-11[/tex]We write:
[tex]\begin{gathered} (3x^2+18x-7)+(-13x^2+7x-11) \\ =3x^2+18x-7-13x^2+7x-11 \end{gathered}[/tex]Collect like terms:
[tex]\begin{gathered} 3x^2-13x^2+18x+7x-7-11 \\ =-10x^2+25x-18 \end{gathered}[/tex]Solve: 6 · x=42What dose x=?
We have to solve this expression.
We can solve it dividing both sides by 6:
[tex]\begin{gathered} 6x=42 \\ \frac{6x}{6}=\frac{42}{6} \\ x=7 \end{gathered}[/tex]Answer: x = 7
graph the system of linear inequalities.x + 2y ≥ 2-x + y ≤ 0
INFORMATION:
We have the next system of equations
[tex]\begin{gathered} x+2y\ge2 \\ -x+y\leq0 \end{gathered}[/tex]And we must graph it
STEP BY STEP EXPLANATION:
To graph the system, we need to graph first the two inequalities as equations. So, we would have
[tex]\begin{gathered} x+2y=2 \\ -x+y=0 \end{gathered}[/tex]- x + 2y = 2:
To graph it, we can find the x and y intercepts.
x intercept:
To find it, we need to replace y = 0, and solve for x
[tex]\begin{gathered} x+2(0)=2 \\ x=2 \end{gathered}[/tex]y intercept:
To find it, we need to replace x = 0, and solve for y
[tex]\begin{gathered} 0+2y=2 \\ y=1 \end{gathered}[/tex]So, the graph would be a line that passes through the points (2, 0) and (0, 1).
Since the symbol of this inequality is ≥, the graph would be the values that are on the line and above it.
- -x + y = 0:
To graph it, we can rewrite the equation as
[tex]y=x[/tex]And this is the identity line.
So, since the symbol of this inequality is ≤, the graph would be the identity line and the values below it.
Finally, the graph of the system would be the common part of the graph of each inequality
So, the graph of the system is the part colored in red and blue at the same time
ANSWER:
if the measure of the angles of a triangle are represented by 2x, 3x - 15 , and 7x + 15, the triangle is
Answer:
D An isosceles triangle
Explanation:
Given that the angles of a triangle are represented by;
[tex]\begin{gathered} 2x \\ 3x-15 \\ 7x+15 \end{gathered}[/tex]Recall that the sum of angles in a triangles is equal to 180 degrees.
Summing up the given angles we have;
[tex]\begin{gathered} (2x+3x-15+7x+15)^{\circ}=180^{\circ} \\ 2x+3x+7x-15+15=180 \\ 12x=180 \\ x=\frac{180}{12} \\ x=15 \end{gathered}[/tex]We have calculated the value of x.
We now need to calculate the value of each angle;
[tex]\begin{gathered} 2x=2(15)=30^{\circ} \\ 3x-15=3(15)-15=30^{\circ} \\ 7x+15=7(15)+15=120^{\circ} \end{gathered}[/tex]Therefore, the angles of the triangle are;
[tex]30^{\circ},30^{\circ},120^{\circ}[/tex]From the derived angles, we can notice that the triangle has two equal angles.
So it is an Isosceles triangle.
The plot below represents the function f ( x ) : 1 2 3 4 5 -1 -2 -3 -4 -5 1 2 3 4 5 -1 -2 -3 -4 -5 Evaluate f ( 3 ) : f ( 3 ) =
Solution
The function represented by the graph is
The root of the equation are -0.5 , 1.5
[tex]\begin{gathered} x=-0.5,x=2.5 \\ (x+0.5)(x-2.5) \\ x^2-2.5x+0.5x-1.25 \\ x^2-2x-1.25 \end{gathered}[/tex]Therefore the function of x =
[tex]\begin{gathered} f(x)=x^2-2x-1.25 \\ f(3)=3^2-2(3)-1.25 \\ f(3)=9-6-1.25 \\ f(3)=1.75 \end{gathered}[/tex]Hence the correct value of f(3) = 1.75
Round the number. Write the result as a product of a single digit and a power of 10 0.00063718
EXPLANATION
Given the number 0.00063718, rounding and writting as a product of a single digit and a power of 10 give us:
6x10^-4
At the Dollar Spot, Carl bought pencils for $3.75, sharpies for $5 69, and glue sticks for ? 1. In the box below type which operation you would use: Division Addition Subtraction Multiplication 2. Why did you pick this operation?
Given that Carl bought pencils for $3.75, sharpies for $5 69, and glue sticks for
Although the question didn't give the value for glue sticks, the operation you would use here is Addition.
Addition symbol: +
2. I picked addition because to find the total amount Carl spent at the Dollar spot, you will need to add the amount he spent on pencils, sharpies and glue together.
how much money will be in Devon's retirement account if she continues to make the same monthly investment for 40 years
Annuities
It refers to a special form to accumulate interest over a regular payment or cash flow (C) per period.
Devon decides to save money for her retirement by depositing C=$524 each month in an account that is expected to earn interest with an APR of r=5.25% compounded monthly.
We will calculate the future value (FV) of her investment over a period of n=40 years.
The future value can be calculated with the formula:
[tex]FV=C\cdot\frac{(1+i)^n-1}{i}[/tex]Where i is the interest rate adjusted for the compounding period. Since there are 12 months in one year:
[tex]i=\frac{r}{12}=\frac{0.0525}{12}=0.004375[/tex]The number of periods is also adjusted for monthly compounding:
n = 40*12 = 480
Now apply the formula:
[tex]FV=524\cdot\frac{(1+0.004375)^{480}-1}{0.004375}[/tex]Calculating:
[tex]\begin{gathered} FV=524\cdot1,629.45 \\ FV=853,832.69 \end{gathered}[/tex]There will be $853,832.69 in Devon's retirement account in 40 years
what would be a good upper bound for the number of jelly beans?
From the picture:
• height of 1 bean: 1 unit
,• radius of 1 bean: 0.25 unit (assumed)
,• height of the jar: 11 units
,• radius of the jar 4 units
we assume that the jar and the bean are cylinders.
Volume of a cylinder = π*r²*h
where r is the radius and h is the height. Then:
Volume of 1 bean = π*0.25²*1 = 0.2 cubic units
Volume of the jar = = π*4²*11 = 553 cubic units
Therefore, an upper bound for the number of jelly beans is 553/0.2 = 2765
In the expansion of (3a + 4b)^8, which of the following are possible variable terms?
Remember the Binomial Theorem:
[tex](a+b)^n\text{ =}\sum_{i\mathop{=}0}^n\begin{bmatrix}{n} & \\ {i} & {}\end{bmatrix}a^{(n\text{ - i})}b^i[/tex]Now, consider the following polynomial:
[tex]\left(3a+4b\right)^8[/tex]Applying the Binomial Theorem, where:
a = 3a
b= 4b
we get:
[tex](3a+4b)^8\text{ =}\sum_{i\mathop{=}0}^8\begin{bmatrix}{8} & \\ {i} & {}\end{bmatrix}3a^{(8\text{ - i})}4b^i[/tex]thus, expanding the sum, we get:
[tex]\begin{gathered} \frac{8!}{0!(8\text{ -0})!}(3a)^8(4b)^0+\frac{8!}{1!(8\text{ -1})!}(3a)^7(4b)^1+\frac{8!}{2!(8\text{-2})!}(3a)^6(4b)^2 \\ +\frac{8!}{3!(8\text{ - 3})!}(3a)^5(4b)^3\text{ + ........+}\frac{8!}{8!(8\text{ -8})!}(3a)^0(4b)^8 \end{gathered}[/tex]Now, simplifying we get:
[tex]\begin{gathered} 6561a^8\text{ + 6998a}^7b\text{ + 326592a}^6b^2+870912a^5b^3+1451520a^4b^4 \\ +1548288a^3b^5+1032192a^2b^6+393216ab^7+65536b^8 \end{gathered}[/tex]then, we can conclude that the correct answer is:
Answer:The variable terms are:
[tex]\begin{gathered} a^8\text{ ,a}^7b\text{ , a}^6b^2,\text{ }a^5b^3,\text{ }a^4b^4 \\ ,\text{ }a^3b^5,\text{ }a^2b^6,\text{ }ab^7\text{ and }b^8 \end{gathered}[/tex]Quiz 1 Write an addition equation or a subtraction equation (your choice!) to describe the diagram. _15 10 -5 0 5 Report a prob
Each arrow represents a subtraction. The beginning of the arrow is the number where the subtraction should start and the point of the arrow is the point where the subtraction should end. The first arrow begins in "0" and ends in "-4", while the second arrow begins on the point of the second one and ends in "-13".
We should first represent the arrow number 1, which is shown below:
[tex]0\text{ -4}[/tex]Because the arrow starts at 0 and go "4" units to the left, therefore we need to subtract 4.
The second arrow starts from the first and goes 9 units to the left, so we have:
[tex](0\text{ - 4) - 9}[/tex]find the value of the investment at the end of 5 years
Given: Following details for an amount compounded annually-
[tex]\begin{gathered} P=34900 \\ R=8\% \\ t=5\text{ years} \end{gathered}[/tex]Required: To determine the amount after 5 years.
Explanation: The formula for compound interest is as follows-
[tex]A=P(1+\frac{r}{n})^{\frac{t}{n}}[/tex]Here, A is the amount accrued.
P is the principal amount.
r is the annual rate as a decimal.
t is the time.
n is the number of times interest is compounded in a year.
In this case, the value of n=1 as we are calculating for annual compounding if the interest is compounded semiannually, n=2. For monthly, n=12. Finally, for daily n=365.
Now substituting the values in the formula as-
[tex]\begin{gathered} A=34900(1+0.08)^5 \\ =34900(1.08)^5 \\ =\text{\$}51279.55 \end{gathered}[/tex]Final Answer: Investment after 5 years compounded annually is $51279.55
Chuck's age is five years less than twice Larry's age. If Chuck's age is 150% of Larry's age, then what is Larry's age, in years?A. 6B. 8C. 10D. 15
Answer:
Larry's age is 10 years
Explanation:
Let Chuck's age be c
Let Larry's age be L
Chuck's age is five years less than twice Larry's age
Mathematically:
[tex]c\text{ = 2l-5}[/tex]Chuck's age is 150% of Larry's age
What this mean is that Chuck's age is 1.5 times multiplied by Larry's age
Mathematically, we have this as:
[tex]c\text{ = 1.5l}[/tex]Now, we can proceed to equate the two equations as follows:
[tex]\begin{gathered} 2l-5\text{ = 1.5l} \\ 2l-1.5l\text{ = 5} \\ 0.5l\text{ = 5} \\ l\text{ = }\frac{5}{0.5} \\ l\text{ = 10 } \end{gathered}[/tex]Hi, can you help me answer this question please, thank you!
The t-statistic of the hypothesis is -2.1075 and the P value is 0.04 .
Given that
Sample Size п, = 80 proportion of mean P₁ = 45%
P₁ = 0·45
Sample size п₂ = 40
proportion of mean P₂ = 55%
P₂=0·55
q₁ = 1- P₁=1-0·45 = 0.55
q₂= 1 - P₂ =1-0.55 = 0.45
V₁ = 0.65
Mean= P₁- P₂ = 0.35 -0.55 =-0.20
standard deviation
SE (P₁ P₂) = 0.0949
Test statistic = 0.0949 = P₁- P₂ / SE( P₁- P₂) = -2.1075
t = -2-1075
DF = (N-1)+(N2-1)
Significance level=0.05
CS = 79+39
df = 118
This is a two tailed test for this hypothesis
P = 0.037236
P = 0.037
Hence the t-statistic of the hypothesis is -2.1075 and the P value is 0.037
To learn more about t-statistic visit:
https://brainly.com/question/15236063
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2. The water level in a reservoir is now 52 meters. Which equation can be used to find the initial depth, d, if this is the water level after a 23% increase? * O 0.23. d = 52 O d = 52 · 0.23 O 1.23. d = 52 O d = 52. 1.23
Answer:
1.23d = 52
Explanation:
If 52 meters is the water level after a 23% increase, then we can say that the initial depth d added to the 23% of d is equal to 52 meters. So:
d + 23%d = 52 meters
Since 23% is equivalent to 0.23, we get:
d + 0.23d = 52
Finally, adding the like terms, we get:
(1 + 0.23)d = 52
1.23d = 52
So, the equation is:
1.23d = 52
For a certain kind of plaster work, 1.5 cu yd of sand are needed for every 100 sq yd of surface. How much sand will be needed for 350 sq yd of surface?
We are told that we need 1.5 cu yd of sand for every 100 sq yd of surface, then we can express the ratio of sand to surface like this:
[tex]\text{ratio}=\frac{1.5}{100}[/tex]In order to find how much sand we need for 350 sq yd of surface, we just have to multiply 350 by this ratio, then we get:
[tex]350\times\frac{1.5}{100}=5.25[/tex]Then, we need 5.25 cubic yards of sand.
The floor of a square closet measures 7 feet on each side, as sho 7 feet What is the area of the floor of the closet?
The formula to find the area of a square is:
[tex]\begin{gathered} A=s^2 \\ \text{ Where A is area and} \\ s\text{ is a side of the square} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} s=7ft \\ A=s^2 \\ A=(7ft)^2 \\ A=49ft^2 \end{gathered}[/tex]Therefore, the area of the floor of the closet is 49 square feet.
Write a cosine function that Has a midline of 2 an amplitude of 3 and a period of 7pi/4
Given:
Amplitude of cosine function, A=3.
Period, T=7π/4.
Midline, D=2.
The time period can be expressed as:
[tex]T=\frac{2\pi}{B}[/tex]Put T=7π/4 to find the value of B.
[tex]\begin{gathered} \frac{7\pi}{4}=\frac{2\pi}{B} \\ B=\frac{4\times2}{7} \\ =\frac{8}{7} \end{gathered}[/tex]The general cosine function can be expressed as,
[tex]f(x)=A\cos (Bx)+D[/tex]Substitute B=8/7, A=3 and D=2 in above equation.
[tex]f(x)=3\cos (\frac{8}{7}x)+2[/tex]Therefore, the cosine function is,
[tex]f(x)=3\cos (\frac{8}{7}x)+2[/tex]Paisley is going to invest in an account paying an interestrate of 34% compounded daily. How much would Paisleyneed to invest, to the nearest dollar, for the value of theaccount to reach $400 in 16 years?
Answer:
$2
Explanation:
To solve the given problem, we'll use the below compound interest formula;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A = future amount = $400
P = the initial amount( principal)
r = annual interest rate in decimal form = 34/100 = 0.34
n = number of compounding periods in a year = 365
t = time in years = 16
Let's go ahead and substitute the above values into our formula and solve for P;
[tex]\begin{gathered} 400=P(1+\frac{0.34}{365})^{365\times16} \\ 400=P(1.0009)^{5840} \\ 400=229.86P \\ P=\frac{400}{229.86} \\ \therefore P=2\text{ dollars} \end{gathered}[/tex]Jody invested $4400 less in account paying 4% simple interest than she did in an account paying 3 percent simple interest. At the end of the first year, the total interest from both accounts was $592. find the amount invested in each account
The rule of the simple interest is
[tex]I=P\times R\times T[/tex]P is the initial amount
R is the rate in decimal
T is the time
Assume that she invested $x in the account that paid 3% simple interest
then she invested x - 4400 dollars in the account that paid 4% simple interest
Then let us find each interest, then add them, equate the sum by 592
[tex]\begin{gathered} P1=x-4400 \\ R1=\frac{4}{100}=0.04 \\ T1=1 \\ I1=(x-4400)\times0.04\times1 \end{gathered}[/tex]Let us simplify it
[tex]\begin{gathered} I1=0.04(x)-0.04(4400) \\ I1=0.04x-176 \end{gathered}[/tex][tex]\begin{gathered} P2=x \\ R2=\frac{3}{100}=0.03 \\ T2=1 \\ I2=x\times0.03\times1 \\ I2=0.03x \end{gathered}[/tex]Since the total interest is $592, then
[tex]\begin{gathered} I1+I2=592 \\ 0.04x-176+0.03x=592 \end{gathered}[/tex]Add the like terms on the left side
[tex]\begin{gathered} (0.04x+0.03x)-176=592 \\ 0.07x-176=592 \end{gathered}[/tex]Add 176 to both sides
[tex]\begin{gathered} 0.07x-176+176=592+176 \\ 0.07x=768 \end{gathered}[/tex]Divide both sides by 0.07 to find x
[tex]\begin{gathered} \frac{0.07x}{0.07}=\frac{768}{0.07} \\ x=10971.42857 \end{gathered}[/tex]Then She invested about 10971 dollars in the account of 3%
Since 10971 - 4400 = 6571
Then she invested about
[tex] 4\sqrt{109.6} [/tex]find the quotient
The given division is
[tex]\frac{109.6}{4}[/tex]If we use the long division method, we get the following
As you can see in the image above, the quotient is 27.4.What is the slope in c = 1.05p - 4?
a linear equation is in the form
[tex]y=mx+b[/tex]in which the m is the slope that multiplies the independent variable and b will be the point for the y-intercept
The slope for the equation given is 1.05 since is the value multiplying the independet variable p
A tank has a capacity of 13 gallons. When it is full, it contains 20% alcohol. How many gallons must be replaced with an 70% alcohol solution to give 13 gallons of 30% solution? Round your final answer to 1 decimal place if necessary.
Given:
A tank has a capacity of 13 gallons. When it is full.
The tank contains 20% alcohol.
We will find the number of gallons that must be replaced with a 70% alcohol solution to give 13 gallons of 30% solution
Let the number of gallons that must be replaced = x
so, there are x gallons with a 70% alcohol and (13 -x) with a 20% alcohol.
So, we can write the following equation:
[tex]70x+20(13-x)=30*13[/tex]Solve the equation to find (x):
[tex]\begin{gathered} 70x+20*13-20x=30*13 \\ 50x+260=390 \\ 50x=390-260 \\ 50x=130 \\ x=\frac{130}{50}=2.6\text{ gallons} \end{gathered}[/tex]So, the answer will be 2.6 gallons
Flex Gym charges a membership fee of $150.00 plus $41.00 per month to join the gym. Able gym charges a membership fee of $120.00 plus $46.00 per month. Find the number of months for which you would pay the same total fee to both gyms.
We have to write an equation for each gym of the cost as a function of the months, so:
[tex]\begin{gathered} We\text{ call c=the total cost and m=months.} \\ \text{For Flex Gym:} \\ c_F=41\cdot m+150 \\ \text{For Able Gym}\colon \\ c_A=46\cdot m+120 \end{gathered}[/tex]Now, we want to find the number of months at which the both gym have the same cost, so:
[tex]\begin{gathered} c_F=c_A \\ 41\cdot m+150=46\cdot m+120 \\ 150-120=46\cdot m-41\cdot m \\ 30=5\cdot m \\ m=\frac{30}{5}=6 \end{gathered}[/tex]At 6 months the cost of the both gyms is the same.
We are stuck on this I will need some help trying to figure out which one is the right answer
The general form of represented of a number in scientific notation is,
[tex]a\times10^n[/tex]Here, the required conditions are,
[tex]\begin{gathered} 1\leq a<10 \\ n\in N \end{gathered}[/tex]Note that N represents the set of all possible natural numbers.
Consider the given numbers and match them with the above form.
Clearly, the rightmost number in the given image is in the proper form of the scientific notation,
[tex]8.98\times10^6[/tex]Here, 'a' is 8.98 and 'n' is 6.
Both the values satisfy the required conditions.
Therefore, it can be concluded that out of all the given numbers, the number represented in scientific notation is,
[tex]8.98\times10^6[/tex]Find the solutions to the following quadric equation 2Xsquared -1x-2=0
Given the quadratic equation:
[tex]2x{}^2-1x-2=0[/tex]We can use the general solution for the quadratic equation ax² + bx + c = 0:
[tex]x=\frac{-b\pm\sqrt{b{}^2-4ac}}{2a}[/tex]From the problem, we identify:
[tex]\begin{gathered} a=2 \\ b=-1 \\ c=-2 \end{gathered}[/tex]Finally, using the general solution:
[tex]\begin{gathered} x=\frac{-(-1)\pm\sqrt{(-1)^2-4(2)(-2)}}{2\cdot2}=\frac{1\pm\sqrt{1+16}}{4} \\ \\ \therefore x=\frac{1\pm\sqrt{17}}{4} \end{gathered}[/tex]A coin is tossed 10 times. It lands on heads 7 times and lands on tails 3 times. What is the experimental probability of the coin landing on tails?7/103/101/20
The experimental probability is given by the following formula
[tex]\text{experimental probability=}\frac{successful\text{ tries}}{\text{total number of tries}}[/tex]In our case, the total number of tries is 10 and the successful number of tries is 3 (landing on tails); thus,
[tex]\Rightarrow\text{experimental probability}=\frac{3}{10}[/tex]The answer is 3/10
Which best represents the transformations for the coordinates of the verticals of the given pairs of triangles (1,6), (-1,3), (5,2), and (-1,6), (-3,3), (3,2) Is it a rotation (that my educated guess)Reflection or translation?
No. It's not a rotation. It's translation.
for translation, there is a formula that is
[tex]x^{\prime}=x+a\text{ }[/tex]and
[tex]y^{\prime}=b+y[/tex][tex]y^{\prime}=b+y[/tex]where (x',y') is the new coordinate and (x,y) is the old one and (a,b) is the increasing value of (x,y)
so here we have the new coordinates are (-1,6), (-3,3), (3,2)
and the olds are (1,6), (-1,3), (5,2)
[tex]\begin{gathered} -1=a+1 \\ and\text{ }6=b+6 \\ this\text{ gives } \\ a=(-2)\text{ and b=0} \\ similarly\text{ you take each case you will get the value of a is \lparen-2\rparen and the value of b is 0.} \end{gathered}[/tex]Thus we can say that the triangle is translated by adding the horizontal value (a) =(-2) to the x-coordinate of each vertex and the vertical value (b)=0 to the y-coordinate.
now you can see
[tex]\begin{gathered} 1+(-2)=1\text{ \& 6+\lparen0\rparen=6 ie \lparen1,6\rparen+\lparen-2,0\rparen=\lparen-1,6\rparen} \\ similarly \\ (-1,3)+(-2,0)=(-3,3) \\ (5,2)+(-2,0)=(3,2) \end{gathered}[/tex]so the right answer is translation.
The distance from. Eight to point B is blank units. This is from. Eight to. C is blank units. The decision for point B de point C is blank units. The given points choose/does not form a right triangle?
EXPLANATION
Since we have the given points:
A= (2,1)
B= (10,1)
C= (2,7)
We can represent this in a graphing calculator:
Now, in order to obtain the distance from A to B, we need to subtract both
x-coordinates points:
10-2 = 8 units
Therefore, the distance from A to B is 8 units.
Next, computing the distance from point A to the point C:
y_C - y_A = 7 - 1 = 6 units
Thus, the distance from point A to point C is 6 units.
In order to obtain the distance from the point B to C we need to apply the distance equation as shown as follows:
[tex]\text{distance}=\sqrt[]{(7-1)^2+(10-2)^2}[/tex]Subtracting numbers:
[tex]\text{distance}=\sqrt[]{6^2+8^2}[/tex]Computing the powers:
[tex]\text{distance}=10\text{ units}[/tex]The distance from point B to point C is 10 units.
Finally, we can conclude that the given points do form a right triangle.