To simplify this expression, we can following the next steps:
First, apply the distributive property:
[tex]8x\text{ + 40 - 4x -16}[/tex]Then, sum similar terms:
[tex]8x-4x\text{ + 40 - 16 = 4x + }24[/tex]Therefore, the simplified expression is
[tex]4x+\text{ 24}[/tex]We can even write the previous expression as
[tex]4(x\text{ + 6)}[/tex]Since 4 is a common factor in the expression.
What is the slope of the line that passes through the points (-8, -1) and(-8, -11)? Write youranswer in simplest form.
Answer:
Undefined
Explanation:
Given any two points (x1, y1) and (x2, y2), the slope of the line is calculated using the formula:
[tex]Slope,m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let (x1, y1) = (-8,-1) and (x2, y2)=(-8,-11).
Substitute:
[tex]\begin{gathered} m=\frac{-11-(-1)}{-8-(-8)} \\ =\frac{-11+1}{-8+8} \\ =-\frac{10}{0} \end{gathered}[/tex]Since division by 0 is not possible, the slope of the line that passes through (-8, -1) and (-8, -11) is undefined.
In general, the slope of any vertical line is undefined.
For questions 6 – 10, find the unknown side length. number 7solve number 7
Let us begin by labelling the sides of the triangle
The triangle is a right-angled triangle hence we can use Pythagoras theorem to find s
[tex]Hypothenuse^2\text{ = Opposite}^2\text{ + Adjacent}^2[/tex]Substituting the given sides:
[tex]\begin{gathered} s^2\text{ = 12}^2\text{ + 12}^2 \\ s^2\text{ = 288} \\ s\text{ = }\sqrt{288} \\ s\text{ = 12}\sqrt{2} \\ s\text{ }\approx\text{ 16.97} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} Exact\text{ answer : 12}\sqrt{2} \\ Decimal\text{ approx : 16.97} \end{gathered}[/tex]Horus has 50 girls and35 boys. If two are chosenat random to sing a duet,What is the probability thatboth will be boys?
[tex]\frac{1}{6}[/tex]
1) Let's begin by finding the number of children: 50 girls and 35 boys=85 children.
2) The favorable event is 35 boys
3) So now, let's write out the following probability bearing in mind that one person was chosen right after the another.
[tex]P(boys\:and\:boys)=\frac{35}{85}\times\frac{34}{84}=\frac{1}{6}[/tex]Solve the following equation. If there are multiple answers, enter each answer separated by a comma. Enter none if there are no solutions. |5x+12|=4
We have an absolute value equation
[tex]|5x+12|=4[/tex]In order to solve it we will have two cases
First case
[tex]5x+12=-4[/tex]we solve for x
[tex]5x=-4-12[/tex][tex]5x=-16[/tex][tex]x=-\frac{16}{5}[/tex]For the second case
[tex]5x+12=4[/tex]we solve for x
[tex]5x=4-12[/tex][tex]5x=-8[/tex][tex]x=-\frac{8}{5}[/tex]ANSWER
x=-16/5
x=-8/5
help help help help help help i lost two tutors due to system malfunction
Given:
There are given the piecewise function:
[tex]f(x)=\begin{cases}9x-3\text{ x<0}{} \\ 9x-6\text{ x}\ge0{}\end{cases}[/tex]Explanation:
First, find the value for f(-1).
Then,
To find the value for f ( -1 ), first, we need to check the value of x which is less than 0
Then,
In the given piecewise function, the value of x which is less than o is;
[tex]f(x)=9x-3[/tex]Ten,
Put the value -1 for x into the above function:
So,
[tex]\begin{gathered} f(x)=9x-3 \\ f(-1)=9(-1)-3 \\ f(-1)=-9-3 \\ f(-1)=-12 \end{gathered}[/tex]Now,
For the f(0):
Then,
We need to check the function whose value of x is equal to 0.
Then,
The function is:
[tex]f(x)=9x-6[/tex]Then,
Put the value 0 for x into the above function:
[tex]\begin{gathered} f(x)=9x-6 \\ f(0)=9(0)-6 \\ f(0)=-6 \end{gathered}[/tex]Now,
For the function f(2):
Then,
We need to check the value of x has greater than 0:
Then,
The function is:
[tex]f(x)=9x-6[/tex]Then,
Put the value 6 for x into the above function:;
Then,
[tex]\begin{gathered} f(x)=9x-6 \\ f(2)=9(2)-6 \\ f(2)=18-6 \\ f(2)=12 \end{gathered}[/tex]Final answer:
Hence, the values are shown below:
[tex]\begin{gathered} f(-1)=-12 \\ f(0)=-6 \\ f(2)=12 \end{gathered}[/tex]awnser the question below B) Correctly simplify the exponential expression please show your work as well
Given the expression:
[tex](\frac{a^4b^{-2}c^5}{a^{-6}b^{-7}})^4[/tex]A) 2 errors in the student work are:
1) In the step of removing negative exponents, the student makes a⁴ in the denominator.
2) In the step of distributing exponents the student wrote b⁹ and the correct is b²⁰
B) Correctly simplify the exponential expression please show your work as well
Removing the negative exponents:
[tex](\frac{a^4a^6b^7c^5}{b^2})^4[/tex]Dividing and multiplication of the exponents:
[tex](a^{10}b^5c^5)^4[/tex]Distributing the exponents:
[tex]a^{40}b^{20}c^{20}[/tex]Apply the Distributive Property to rewrite 2(6-x) = 3. Choose the correct answer below. O A. 6(2) + 6x = 3 OB. 6(2) - 6x = 3 OC. 2(6) + 2x = 3 OD. 2(6) - 2x = 3
let's apply the Distributive Property to the formula below:
[tex]2(6-x)=2(6)-2(x)=3[/tex]So the final answer is D
What is the area of the parallelogram shown in the coordinate plane?
The heigt of a parallelogram is the product of the length of its base and its height.
The height of a parallelogram is the distance between the base and the side parallel to the base.
If we take the segment JC as the base of the parallelogram, then the height has a measure of 7 units and the base has a measure of 6 units, as shown:
Calculate the area of the parallelogram by multiplying its height and its base:
[tex]\begin{gathered} A=b\times h \\ =6\times7 \\ =42 \end{gathered}[/tex]Therefore, the area of the parallelogram shown in the coordinate plane is 42.
Find the lateral surface area and volume of the cylinder shown in the picture
Okay, here we have this:
Considering the provided cylinder we are going to find the lateral area and the volumen, so we are going to use the following formula:
LA=2piRH
V=pi(r)²(h)
And, in this case we have the R is 42.2 cm and H is 85.7 cm. Replacing we obtain:
LA=2pi(42.2 cm)(85.7 cm)
LA=22723.39 cm²
V=pi(r)²(h)
V=pi(42.2 cm)²(85.7 cm)
V=479463.55 cm³
Finally we obtain that the lateral surface area is 22723.39 cm² and the volume is 479463.55 cm³ rounded to the nearest hundredth.
Find all real numbers a such that the given point is on the circle x2 + y2 = 1.8gia
Let the coordinate be as follows.
[tex](x,y)=\mleft(-\frac{8}{9},a\mright)[/tex]Substitute the coordinates into the equation.
[tex]\mleft(-\frac{8}{9}\mright)^2+a^2=1[/tex]Simplify the left side of the equation.
[tex]\frac{64}{81}+a^2=1[/tex]Subtract both sides of the equation by 64/81.
[tex]\begin{gathered} a^2=1-\frac{64}{81} \\ =\frac{81}{81}-\frac{64}{81} \\ =\frac{17}{81} \end{gathered}[/tex]To obtain the value of a, use the square root property. Find the square root of both sides of the equation.
[tex]a=\pm\sqrt[]{\frac{17}{81}}=\pm\frac{\sqrt[]{17}}{9}[/tex]Thus, the values of a is as follows.
[tex]a=\frac{\sqrt[]{17}}{9}\text{and -}\frac{\sqrt[]{17}}{9}[/tex]* 100% What is 4,328 rounded to the nearest 100? 4,000
The number 4,328 rounded to the nearest 100 is 4,300.
As we can see, we have two possible options: 4,300 or 4400. The nearest is, therefore, 4300.
A coat has a purchase price of $22. If the sales tax on this purchase is $1.43, find the sales tax rate.
Given:
A coat has a purchase price of $22
The sales tax on this purchase is $1.43
The sales rate will be calculated by dividing the sales tax by the price
So, the sales tax rate =
[tex]\frac{1.43}{22}=0.065[/tex]The sale rate as a percent = 0.065 x 100 = 6.5%
A car rental company offers two plans for renting a car: Plan A: 30 dollars per day and 12 cents per mile Plan B: 50 dollars per day with free unlimited mileage
Given:
• Plan A: 30 dollars per day and 12 cents per mile
,• Plan B: 50 dollars per day with free unlimited mileage.
Let's find the range of miles where plan B will save you money.
Let's create equations representing both equations in slope-intercept form:
Plan A: y = 30 + 0.12x
Plan B: y = 50
Here, x represents the number of miles.
For plan B to save you money, the total cost of plan B will have to be lesser than the total cost of plan A.
Now to find where plan B will save you money set the expression in part B less than that of plan A.
We have:
[tex]50<30+0.12x[/tex]Let's solve for x.
We have:
[tex]\begin{gathered} 50-30<0.12x \\ \\ 20<0.12x \\ \\ \frac{20}{0.12}<\frac{0.12x}{0.12x} \\ \\ 166.67166.67 \end{gathered}[/tex]Therefore, to save money the mileage must be greater than 166.67 miles per day.
ANSWER:
166.67 miles
How do I find acceleration when velocity is 0? also assume t is >= 0 s is meters t is seconds
ANSWER
a(t) = 18 m/s^2
EXPLANATION
We are given that:
[tex]\begin{gathered} v(t)=3t^2\text{ - 27} \\ a(t)\text{ = }6t \end{gathered}[/tex]b) To find the acceleration when velocity is 0, we have to find the time at which the velocity is 0.
After finding that, we then find the value of a(t) at that time.
To find the time when velocity is 0, we make v(t) = 0 and find t.
That is:
[tex]\begin{gathered} 0=3t^2\text{ - 27} \\ \Rightarrow3t^2\text{ = 27} \\ \text{Divide through by 3:} \\ t^2\text{ = }\frac{27}{3} \\ t^2\text{ = 9} \\ t\text{ = }\sqrt[]{9} \\ t\text{ = 3 seconds} \end{gathered}[/tex]Now, we find the value of a(t) when t = 3:
a(t) = 6 * (3)
a(t) = 18 m/s^2
That is the answer.
Simplify each expression using the order of operations 3 + jk + k^2, when j = 2 and k = 6
Answer
Answer = 51
Explanation
We are told to simplify the expression
3 + jk + k²
if j = 2 and k = 6
So, to solve this, we just substitute the known variables
3 + jk + k²
= 3 + (2 × 6) + (6²)
= 3 + 12 + 36
= 51
Hope this Helps!!!
What is the answer to 69x69?
Answer:
Multiplying both numbers will give;
[tex]69\times69=4761[/tex]Explanation:
We want to solve the expression;
[tex]69\times69[/tex]Solving;
[tex]69\times69=69(60+9)=69(60)+69(9)=4140+621=4761[/tex]Multiplying both numbers will give;
[tex]69\times69=4761[/tex]need help asap pleaseSolve -4A+2=-26
Rearranging the terms so the terms with the unkown variable A are on the left side and the other ones on the right side:
- 4A + 2 = -26
↓
- 4A = -26 - 2
- 4A = -28
Step 2Solving the equation for A
- 4A = -28
↓
A = -28/(-4)
A = 7
Answer: A=7Answer:
a = 7
Step-by-step explanation:
The first step of this problem is isolating this variable. This means putting this variable on the side of the equation by itself.
We need to rearrange the equation to isolate the variable to solve the equation.
The unedited equation.
-4a+2=-26
Subtract 2 on both sides to remove it from the left side of the equation.
-4a + 2 - 2 = - 26 - 2
Combine like terms.
-4a = -28
Divide both sides by -4 to solve for a.
[tex]\frac{-4a}{-4} = \frac{-28}{-4}[/tex]
-4a/-4 = 1a = a
-28/-4 = 7
a=7
If DA is a diameter of OZ and m/DZC = (2x)°, find m/CZB.A. 22°B. 58°C. 69°D. 73°
Since DA is the diameter the formed angle equals 180
since DZC=2x
then
[tex]180=DZC+CZB+BZA[/tex][tex]180=(2x)+(7x-4)+85[/tex][tex]180-85+4=9x[/tex][tex]x=\frac{99}{9}[/tex][tex]x=11[/tex]since x= 11
then the measure of the angle CZB is given by
[tex]7(11)-4[/tex][tex]mCZB=73[/tex]measure of the angle CZB is 73°
Correct answer option D
73°
4. Mitch took out a school loan for $24,000. The interest rate on the loan was 8%.Mitch paid off the loan in just 5 years. How much did he pay altogether?24000 0.08.5p24000R=0.08T5 years1920.5u9600+I-
Answer:
Explanation:
Ajar contains 65 coins. 3/5 of the coins are pennies. What fraction of the coins are pennies, using 65 as the denominator? (Write 3/5 as an equivalent fraction with a denominator of 65.)
39 out of 65 are pennies.
Explanation:Given that the jar contains 65 coins, and 3/5 of the coins are pennies.
We have:
3/5 = (3 * 13)/(5 * 13)
= 39/65
Therefore, 39 out of 65 are pennies.
x⁴• x⁷ simplify. write each expression with no negative exponents and show work
x⁴• x⁷
Using the law of indices;
x⁴• x⁷ = x⁴⁺⁷ = x¹¹
Lin has a drawing with an area of 20 in². if she increases all the sides by a scale factor of 4, what will the new area be?
Lin has a drawing with an area of 20 in². if she increases all the sides by a scale factor of 4, what will the new area be?
Remember that
the ratio between similar areas is equal to the scale factor squared
so
that means
scale factor=4
x/20=4^2
where
x is the new area
x/20=16
x=320 in2
the new area is 320 square inchesExplanationassume that the original figure is a squareA=20 in2the area of a square is A=b^2Find out the length b[tex]\begin{gathered} b=\sqrt[]{20} \\ b=2\sqrt[]{5}\text{ in} \end{gathered}[/tex]Increase the original side by a scale factor of 4
[tex]b1=4(2\sqrt[]{5})\text{ in}[/tex]Find the new area
A1=b1^2
substitute the new value of b1
[tex]\begin{gathered} A1=\lbrack8\sqrt[]{5})^2 \\ A1=64\cdot5 \\ A1=320\text{ in2} \end{gathered}[/tex]that is the same that multiply the original area by the scale factor squared
Problem N 2
Remember the problem N 1
the ratio between similar areas is equal to the scale factor squared
in this problem
the scale factor=6
(scale factor )^2=6^2=36
that means
the enlarged area is 36 times the area of the originalThe given line passes through the points (0,3) and (-4,0).what are 4 equations that describes this line?
We have a line that passes through point (0,3) and (-4,0).
Slope-intercept form:
We can calculate the slope of the line as:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{0-3}{-4-0}=\frac{-3}{-4}=\frac{3}{4}[/tex]The y-intercept can now be calculated using the slope and one of the points:
[tex]\begin{gathered} y=mx+b \\ 3=\frac{3}{4}\cdot0+b=0+b=b \\ b=3 \end{gathered}[/tex]Then, we can express the equation as:
[tex]y=\frac{3}{4}x+3[/tex]Direct variation:
We can not express as a direct variation line as the line do not go through the origin.
Point-slope form:
This form is:
[tex]y-y_1=m(x-x_1)[/tex]We have to know the slope and one point in order to be able to write it.
The slope is 3/4 and one of the points is (0,3). We can write it as:
[tex]y-3=\frac{3}{4}(x-0)[/tex]Two intercept form:
This form is:
[tex]ax+by=c[/tex]We can write this for our case as:
When x=0, y=c/b=3, and when y=0, x=c/a=-4.
We can write that c=1, and then b=1/3 and a=-1/4.
Then, our equation becomes:
[tex]\frac{-1}{4}x+\frac{1}{3}y=1[/tex]If we multiply both sides by 12 (the common factor of 3 and 4), we would get:
[tex]-3x+4y=12[/tex]that is equivalent to the previous equation.
One serving of rice is 2/3 of a cup. I ate 1 cup of rice. How many servings of rice did I eat?
We have an equality between the servings and the amount of rice:
1 serving = 2/3 cups
Then, if you have 1 cup, we can calculate the amount of servings as:
[tex]1\text{ cup}\cdot\frac{1\text{ serving}}{\frac{2}{3}\text{ cups}}=\frac{3}{2}\text{ servings}[/tex]You eat 3/2 servings.
Not sure on how to could, this could really use some help.
Solution
The volume of a cylinder = 1044 πcm³
radius of the base cylinder = 6cm
The formula for the volume of a cylinder is V=Bh or V=πr2h
[tex]\begin{gathered} V=\pi r^2h \\ 1044\pi=\pi(6^2)h \\ 1044\pi=36\pi h \\ h=\frac{1044\pi}{36\pi} \\ h=29cm \end{gathered}[/tex]Therefore the height of the cylinder = 29cm
D. Write the equation of the line inslope-intercept form. Check your answerusing the Gizmo.
The equation of the line in slope-point form is
[tex]y-y_1=m(x-x_1)[/tex]The equation of the given line in this form
y + 5 = 0.5(x - 2)
By comparing them
m = 0.5
x1 = 2
y1 = -5
The slope-intercept form is
y = m x + b
Where: m is the slope and b is y-i
Jon scored 80% on a test and 20 problems correct. How many problems are on the test?
Answer: 25 questions on the test
Step-by-step explanation:
First, 80% divided by 100 becomes a decimal, 0.8.
Next, let x be the total number of problems on the test. We can multiply x by 0.8 and set it equal to 20 as our equation to solve.
0.8 * x = 20
Lastly, we will divide both sides of the equation by 0.8 to find the answer to our question.
x = 25 questions on the test
what is the solution for y=2x+2 and y = 3x
we have to equalize both equations. We get that:
[tex]\begin{gathered} 3x=2x+2\rightarrow \\ 3x-2x=2 \\ x=2 \end{gathered}[/tex]so the answer is x=2
A consumer buys a used car for $19300 with monthly payments of $380, an annual interest rate of 3.79%. Find the number of payments. Note: You should use a Graph in an Appropriate Window. List the window settings and draw the graph in your notebooks. Use the Intersect feature on your graphing calculator and write down an answer rounded to 3 decimal places. Give a whole number answer in this box in months for how many payments would be needed.
the total for the car is $19300, with an interest of 3.79%. that means that the total amount the person will end up paying includes that interest:
I = P * r * t
Total Accrued value = P (1+r*t)
Total accrued value = 19300 (1+0.0379*t)
where we have used 0.0379 to represent the 3.79% interest in decimal form.
Notice that the total value paid is going to be $380 (the monthly payment) times 12 (for a full year of payments) times "t" (the number of years the person would be making payments:
380 * 12 * t = 19300 (1 +.0379 * t )
4560 t = 19300 (1 +.0379 * t)
We can try to solve this equation as suggested by your teacher via a graphing calculator. Allowme to plot the two expressions on each side of the equal sign, and find where they intersect. Give me a little time to create the image, please.
Where the line in blue is the expression as a function of time: for the monthly payments: 4580 * t
and the line in orange is the accrued value (total of the car price plus the interest accumulated over "t" number of years: 19300 (1+ 0.0379 t)
We found the crossing of the two lines at a point very close to 5 years: 5.041 years (rounded to three decimals as required).
Now we calculate the number of monthly payments multiplying 5.041 years times 12 (for the 12 months in every year) and get:
total number of payments is: 60.492 . Now this number rounded to the nearest whole number (in math terms) would be 60, but if we consider that the total will not be completely covered in 60 payments, if the 60 answer fails, please try 61.
-3 es un numero racional
Hannah is wrong beacuse any integer number can be written as a rational number. Any integer m can be written as m/1.
Then, for the case of -3, this number can be written as -3/1, that is, -3 is a rational number.