Answer:
[tex]x^{2}[/tex]+12x+27
Step-by-step explanation:
First, you need to distribute. You multiply x by 9 and x, and then multiply 3 by 9 and x, which results in 9x + [tex]x^{2}[/tex] +27 +3x.
Second, you collect like terms. In this case, there is only one like term, which is x. The results of this should be [tex]x^{2}[/tex] + 27 + 11x.
Lastly, reorder the terms properly, and you're done!
Hope this helps.
Can you do the bottom please which it says lesson 11.9 - 11.10
1.19)
In general, the area of a rectangle is given by the formula
[tex]\begin{gathered} A=lw \\ l\to\text{ length} \\ w\to\text{width} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} A_A=4\cdot4=16 \\ A_B=3\cdot4=12 \\ A_C=6\cdot2=12 \end{gathered}[/tex]The area of figure A is 16 square units, the area of B is 12 square units and the area of shape C is 12 square units.
As for the area of a rectangle, in general,
[tex]P=2l+2w=2(l+w)[/tex]Then, in the case of each rectangle,
[tex]\begin{gathered} P_A=2(4+4)=2\cdot8=16 \\ P_B=2(3+4)=2\cdot7=14 \\ P_C=2(2+6)=2\cdot8=16 \end{gathered}[/tex]11.10)
Therefore, figures A and C have the same perimeter, whereas rectangles B and C have the same area.
Bo rolls a fair 6-sided number cube then chooses one card from a deck of four cards numbered 1through 4. What is the probability that the number cube and the card have the same number?
the probability is 1 whole number 1 over 2
NAMEDATEPERIOD21. Clare has a 1/2 liter bottle full of water. A cone-shaped paper cup has diameter 10 cmand slant height 13 cm as shown. Can she pour all the water into one paper cup, or willit overflow? Explain your reasoning. (3 pts.)(The volume of a cone ismerhand liter = 500 cubic centimeters)10cm13 cm
We have the following:
The first thing is to calculate the volume of the cone
[tex]\begin{gathered} V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h \\ \end{gathered}[/tex]where r is the radius and h is the height
the radius is half the diameter, like this
[tex]r=\frac{d}{2}=\frac{10}{2}=5[/tex]The radius is 5 cm.
Now, for the height, we calculate it by means of the Pythagorean theorem that says the following
[tex]\begin{gathered} c^2=a^2+b^2 \\ c=13 \\ a=5 \\ b=h \\ \text{replacing:} \\ 13^2=5^2+h^2 \\ h^2=13^2-5^2 \\ h=\sqrt[]{169-25} \\ h=\sqrt[]{144}=12 \end{gathered}[/tex]The height is 12 cm
The volume is:
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot5^2\cdot12 \\ V=314 \end{gathered}[/tex]The water bottle has a total of 500 cubic centimeters, while the cone is 314 cubic centimeters, therefore it cannot pour out all the water and it would overflow
Sketch the vectors u and w with angle θ between them and sketch the resultant.
Given:
Two vectors (u) and (w) and the angle between them θ
[tex]\begin{gathered} |u|=50 \\ |w|=12 \\ \theta=35\degree \end{gathered}[/tex]the sketch of the vectors will be as shown in the following figure:
As shown, the resultant vector is the blue line segment
The vector R has a magnitude = 60.22
And the angle between u and R = 5.56°
Z A I + 5 4x - 3 3r-1 2x + 1 What value of x makes ASTW - AXYZ? s 3 + 1 T 4r-5 x = 2 X = 3 X=4 X=1
Here, we have two congruent triangles.
Given:
ST = 3x - 1 XY = 4x - 5
SW = 3x + 1 XZ = 4x - 3
TW = 2x + 1 YZ = x + 5
Since triangle STW and triangle XYZ are congruent, they have exactly the same corresponding sides.
To find the value of x, equate the corresponding sides and evaluate.
ST = XY
SW = XZ
TW = YZ
Take one of the corresponding sides.
We have:
ST = XY
3x - 1 = 4x - 5
Subtract 4x from both sides:
3x - 4x - 1 = 4x - 4x - 5
-x - 1 = -5
Add 1 to both sides:
-x - 1 + 1 = -5 + 1
-x = -4
Divide both sides by -1:
[tex]\begin{gathered} \frac{-x}{-1}=\frac{-4}{-1} \\ \\ x=4 \end{gathered}[/tex]Therefore, the value of x that makes ΔSTW ≅ ΔXYZ is 4
ANSWER:
x = 4
The cost in dollars for removing p percent of pollutants from a river in Smith County is Find the cost of removing 20%Cost for removing 20%, in dollars is = _________Find the cost of removing half of the pollutants. Cost for removing half, in dollars is = __________ Find the cost of removing all but 5% of the pollutants. Cost for removing all but 5%, in dollars, is = _________
Given the cost of removing p percent of pollutant from a river is Smith County in dollars as
[tex]C(p)=\frac{71000p}{100-p}[/tex]To find the cost of removing the pollutant for a particular percentage, we will substitute the value of the pollutant in the cost formula above.
Thus, for p equal to 20%
[tex]\begin{gathered} C(20)=\frac{71000\times20}{100-20}=\frac{1420000}{80} \\ C(20)=\text{ \$}17,750 \end{gathered}[/tex]Hence, the cost of removing 20% of the pollutant is $17,750
The cost of removing half of the pollutants is equivalent to the cost of removing 50%, thus, p in percentage is 50%
[tex]\begin{gathered} C(50)=\frac{71000\times50}{100-50}=\frac{3550000}{50} \\ C(50)=\text{ \$}71,000 \end{gathered}[/tex]Hence, the cost of removing half of the pollutants is $71,000
The cost of removing all but 5% of the pollutant is equivalent to the cost of removing 95% of the pollutants. Hence, p is 95
[tex]\begin{gathered} C(95)=\frac{71000\times95}{100-95}=\frac{6745000}{5} \\ C(95)=\text{ \$}1,349,000 \end{gathered}[/tex]Hence, the cost of removing all but 5% of the pollutants is $1,349,000
In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm and AB = 21 cm, find the value of (x − y).
The value of (x-y) is 9 cm for the given triangle ABC.
According to the question,
We have the following information:
In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm and AB = 21 cm.
So, we have:
x+y = 21 cm
y = (21-x) cm
Using Pythagoras theorem in right-angled triangle ADC and CDB:
[tex]AC^{2} = AD^{2} +CD^{2}[/tex] and [tex]BC^{2} = BD^{2}+CD^{2}[/tex]
Now, we have the equal values of [tex]CD^{2}[/tex]:
[tex]17^{2} -x^{2} = 10^{2} -y^{2}[/tex]
289 -[tex]x^{2}[/tex] = 100 - [tex](21-x)^{2}[/tex]
289 - [tex]x^{2}[/tex] = 100 - (441+[tex]x^{2}[/tex]-42x)
289-[tex]x^{2}[/tex] = 100 - 441-[tex]x^{2}[/tex] + 42x
289 = 100 -441+42x
42x-331 = 289
42x = 289+331
42x = 630
x = 630/42
x = 15 cm
y = 21-x
y = 21-15
y = 6 cm
Now, x-y = 15-6
x-y = 9 cm
Hence, the value of (x-y) is 9 cm.
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The sum of three
numbers is 18. The largest
is 5 times the smallest,
while the sum of the
smallest and twice the
largest is 22. Write a
system of equations to find
the numbers, then solve.
The required system of equation is x+y+z=18, z=5x, x+2z=22 and the required values of x=2, y=6 and z=10 by using the substitution method of solving equations and according to given conditions: The sum of three numbers is 18. The largest is 5 times the smallest, while the sum of the smallest and twice the largest is 22. .
What is system of equation?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the other equation in this method, as the name implies.
x+y+z=18
z=5x
x+2z=22
x+10x=22
x=2
y=6
z=10
The required system of equations is x+y+z=18, z=5x, x+2z=22, with the required values of x=2, y=6, and z=10 when solving equations using the substitution method under the conditions stated: Three numbers added together equal 18. The sum of the smallest and twice-largest numbers is 22, while the largest is five times the smallest.
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jamals lawn is shaped like a square with an area of 224.9ft2 .which measurement is closest to the side length of his lawn in feet
We use the formula for the area "A" of a square with equal sides of length "l":
[tex]A=l^2[/tex]Since we know the value of the area is:
[tex]A=224.9ft^2[/tex]We substitute that value into the formula for the area:
[tex]224.9ft^2=l^2[/tex]Next, we take the square root of both sides of the equation:
[tex]\sqrt[]{224.9ft^2}=\sqrt[]{l^2}[/tex]On the right side, the exponent and the square root will cancel, and we will get "l", and on the left side, we calculate the square root:
[tex]14.99ft=l[/tex]Which can be rounded to the closest value, that is 15 ft.
Answer: 15 feet
Help me please I paid for the tutor Version of this app and it can’t fine me a tutor like I just paid 100 dollars for nothing
The Solution.
The function is increasing on the interval below:
[tex](-2.5,1)[/tex]The function is decreasing on the intervals below:
[tex](-\infty,-2.5)\cup(1,\infty)[/tex]Make a scatter plot of the data. Scale the x-axis by ones and the y-axis by twos.
Answer
Age of Car in years is represented as x
Avg. Miles per Gallon is represented as y
y = 0.97x + 1.214
Correlation Coefficient = 0.673
Explanation
Age of Car in years is represented as x
Avg. Miles per Gallon is represented as y
The datapoints are fed into a calculator and plotted with the datapoints also processed according to some formulas that'll be provided here
The first figure contains the data points and the regression data processed to be used to calaculate the required parameters.
The second attached image shows the plotted data and the line of best fit and the equation that best represents the relationship between the two parameters.
Then the last image shows the parameters used to calculate the equation of correlation and the correlation coefficient.
Hope this Helps!!!
Find the volume of a cone. Round your answer to the nearest wholenumber.7 ft4 ft
Answer:
117 cubic feet
Explanation:
From the diagram:
• The radius of the cone, r = 4 ft
,• The perpendicular height, h = 7 ft
[tex]\text{Volume of a cone=}\frac{1}{3}\pi r^2h[/tex]Substitute the given values:
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times4^2\times7 \\ =117.2ft^3 \\ \approx117\; ft^3 \end{gathered}[/tex]The volume of a cone is 117 cubic feet (to the nearest whole number).
Consider 3x=y. a. Complete the table for the equation. x y 0 1 2
Answer/Step-by-step explanation:
x | 3x | y | (x, y)
----------------------------------------
0 | 3(0) | 0 | (0, 0)
----------------------------------------
1 | 3(1) | 3 | (1, 3)
----------------------------------------
2 | 3(2) | 6 | (2, 6)
----------------------------------------
I hope this helps!
Fill in the gaps to factorise the expression.
2x^2+7x+3
The factorised form of the expression given in the task content is; 2x² + 7x + 3 is; (2x + 1) (x + 1).
Factorisation of quadratic expressions.It follows from the task content that the factorised form of the expression is to be determined.
On this note, the factorised form of the expression is as follows;
2x² + 6x + x + 3.
By grouping terms; we have;
(2x² + 6x) + (x + 3).
Factorise two terms each at as follows;
2x(x + 1) + 1(x+3)
(2x + 1) (x + 1)
Therefore, the factorised form of the expression; 2x² + 7x + 3 is; (2x + 1) (x + 1).
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Compute the derivative of f(x) = x * sin(x) . Use the result to compute f^ prime ( pi 2 )
Solution
Step 1
f(x) = xsinx
Step 2
[tex]\begin{gathered} f(x)=x\sin\left(x\right) \\ \\ f^{\prime}(x)=\sin\left(x\right)+x\cos\left(x\right) \end{gathered}[/tex]Step 3
[tex]\begin{gathered} f^{\prime}(\frac{\pi}{2})=\sin\left(\frac{\pi}{2}\right)+\frac{\pi}{2}\cos\left(\frac{\pi}{2}\right) \\ \\ f^{\prime}(\frac{\pi}{2})=1 \end{gathered}[/tex]Final answer
A. 1
You and a friend are in school and are trying to figure out where to eat. You told her that you would like to go to your favorite pizza place that is 5 miles away from your home. Both of you know that your home is 10 miles away from school. Approximately how far is the pizza place from the school?The pizza place is between approximately 5 to 15 miles away from school.Not enough information to solve the problem.The pizza place is approximately less than 5 miles away from school.
Okay, here we have this:
Considering the provided information, we are going to identify approximately how far is the pizza place from the school, so we obtain the following:
Then from the given information we can identify that the pizzeria can be 5 miles in the same direction from the school or 5 miles in any other direction,
This means that in the best case the distance from the pizzeria to the school is 5 miles (if it is halfway), and in the worst case it is 15 miles (if it is in a completely opposite sense).
And in an average case it can be at an angle other than 180 degrees, with which the distance would be between 5 and 15 miles, therefore the correct answer is:
The pizza place is between approximately 5 to 15 miles away from school.
2. Angela is arranging 32 pictures in a photo album. She wants to
have the same number of pictures in each row. How can she
arrange her pictures?
Angela can arrange pictures in 6 different ways; (1 x 32), (2 x 16), (4 x 8), (8 x 4), (16 x 2), (32 x 1).
Given,
Angela have 32 pictures with her.
She wants to arrange it in an album with equal number of pictures in each row.
We have to find the possible arrangements.
Here,
32 pictures.
Lets see the possibilities.
1 row = 32 pictures in a row2 rows = 32/2 = 16 pictures in each row4 rows = 32/4 = 8 pictures in each row8 rows = 32/8 = 4 pictures in each row16 rows = 32/16 = 2 pictures in each row32 rows = 1 picture in each row.That is,
Angela can arrange pictures in 6 different ways; (1 x 32), (2 x 16), (4 x 8), (8 x 4), (16 x 2), (32 x 1).
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I would like to ask for Some help on this equation please?
ABC is a right triangle
AB is perpendicular to BC
If 2 lines are perpendicular, the product of slopes is -1
m1 x m2 = -1
mAB x mBC = -1
mAB = -1 / mBC
mAB = -1 / (1/2)
mAB = -2
A sprinkler rotates back and forth from point A to point B. The water reaches 8 meters from the base of the sprinkler.What is the length of the arc AB, rounded to the nearest tenth of a meter? Use 3.14 for [tex]\pi[/tex]
20.9m
1) Since we want to know the length of that arc, and the angle is written in degrees, let's use a formula to find this out:
[tex]\begin{gathered} l=\frac{\alpha}{360}\cdot2\pi R \\ l=\frac{150}{360}\cdot2(3.14)\cdot8 \\ l=20.93\approx20.9m \end{gathered}[/tex]2) Rounding off to the nearest tenth we have the length of this arc is 20.9, m
Which answer choice gives a correct version of this problem? -35 ÷ -7
A.) - (-35/-7) or B.) -35/7 or C.) 35/7 or D.) 35/-7
(Please note that I'm not looking for the total value rather I'm looking for what (-35 ÷ (-7) is as a fraction.)
Can you please help me find the area of the shaded triangle? Thank you :)
Area of shaded triangle = Area of triangle - area of circle
Area of triangle = 1/2 x base x height
Base= 16 yds
Height= 19 yds
Area of triangle = 1/2 x 16 x 19 = 8 x 19 =152 square yard
[tex]\begin{gathered} \text{Area of circle = }\pi\times r^2 \\ \pi=3.14 \\ r=5\text{yds} \\ \text{Area of circle = 3.14 }\times5^2=78.5yard^2 \end{gathered}[/tex]Area of shaded triangle = 152 - 78.5 =73.5 square yard
HELPPPPAbigail buys 3 gallons of milk a week. How many pints of milk does she buy?
Answer:
She buys 24 pints of milk
Step-by-step explanation:
The conversion rule for a pint to the gallon is represented:
[tex]\text{ 1 pint=0.125 gallons}[/tex]Then, we can make a proportional relationship to determine how many pints of milk she buys:
[tex]\begin{gathered} \frac{1}{0.125}=\frac{x}{3} \\ x=\frac{3}{0.125} \\ x=24\text{ pints} \end{gathered}[/tex]A consumer group feels that the average person spends less than 5 dollars each month on tooth care products. They decide to use hypothesis testing to see if they are right. Which of the following would be the alternative hypothesis?
The alternative hypothesis will be Ha : u < 5
What is an alternative hypothesis?An alternative hypothesis simply means the proposed explanation in the hypothesis test. It is used to demonstrate a particular condition.
In this case, the consumer group feels that the average person spends less than 5 dollars each month on tooth care products.
Therefore, the alternative hypothesis will be that the average is less than 5.
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An accountant finds that the gross income, in thousands of dollars, of a small business can be modeled by the polynomial −0.3t 2 + 8t + 198, where t is the number of years after 2010. The yearly expenses of the business, in thousands of dollars, can be modeled by the polynomial −0.2t 2 + 2t + 131.a. Find a polynomial that predicts the net profit of the business after t years. b. Assuming that the models continue to hold, how much net profit can the business expect to make in the year 2016?I know that the equation is -0.1t^2+6t+67, but i don't know how to find part b.
ANSWER:
STEP-BY-STEP EXPLANATION:
a.
We know that the net profit is equal to the incomes minus the expenses, therefore, the final equation would be:
[tex]\begin{gathered} \text{profit = income - expense} \\ \text{replacing} \\ p=-0.3t^2+8t+198-(-0.2t^2+2t+131) \\ p=-0.3t^2+8t+198+0.2t^2-2t-131 \\ p=-0.1t^2+6t+67 \end{gathered}[/tex]b. t is the number of the years after 2010. Therefore, for the year 2016, x is equal to 6 (2016 - 2010), we replace:
[tex]undefined[/tex]L Pretest: Unit 2Question 5 of 21Which of the following represents the factorization of the polynomial functiongraphed below? (Assume it has no constant factor.)55
1) The best way to tackle questions like this is to locate the x-intercepts. Since according to the options the leading coefficient is 1, we just need to locate the zeroes and plug them into the quadratic equation form, in its factored form.
2) So now, let's write out the factored form and plug the zeroes into them:
[tex]\begin{gathered} y=a(x-x_1)(x-x_2) \\ y=1(x-1)(x-3) \\ y=(x-1)(x-3) \end{gathered}[/tex]in a sale normal prices are reduced by 15%. The sale price of a CD player is £102. work out the normal price of the CD player
The normal price for the CD player is $117.30
How to calculate the value?Since the normal prices are reduced by 15%, the percentage for the normal price will be:
= 100% + 15%
= 115%
Also, the sale price of a CD player is £102.
Therefore, the normal price will be:
= Percentage for normal price × Price
= 115% × $102
= 1.15 × $102
= $117.30
The price is $117.30.
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please help I think I know how to do this it I am not sure it has a time limit and I'm sorry I need to andwer it quick I've been working on it for awhile so it took time off the time limit
we are given the following polynomial:
[tex]x^2+3-7x[/tex]The standard form of a polynomial is of the following form:
[tex]ax^n+bx^{n-1}+cx^{n-2}+\cdots+d[/tex]Rewriting the given polynomial we get:
[tex]x^2-7x+3[/tex]This is a trinomial because it has 3 terms.
Since the maximum exponent of the polynomial is 2, this is a quadratic polynomial.
2. If 25% of 80 is 10% of a number? What is number?
Given that 25% of 80 is 10% of a number.
We have to find the number.
Let the number be x. So, 25% of 80 is equal to 10% of x. Therefore,
[tex]\begin{gathered} \frac{10}{100}\times x=\frac{25}{100}\times80 \\ 10x=2000 \\ x=\frac{2000}{10} \\ x=200 \end{gathered}[/tex]Thus, the number is 200.
3. A square has sides of length 612 inches. Area of length times width.
What is the area of the square in square inches?
The area of the square in square inches is 374544 inches².
How to find the area of a square?A square is a quadrilateral with 4 sides equal to each other. Opposite sides of a square is parallel to each other.
Each angle of a square is 90 degrees.
Therefore,
area of square = l²
where
l = side lengthTherefore,
The square has a side length of 612 inches. The area of the square can be found as follows:
area of square = l²
l = 612 inches
Hence,
area of square = 612²
Therefore,
area of the square = 612 × 612
area of the square = 374544 inches²
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What are the first two steps to graph y=4/5x + 3?
The function y=4/5x + 3 represents a linear equation.
Let's find some points.
Where x=1, then:
[tex]y=\frac{4}{5}x+3[/tex][tex]y=\frac{4}{5}(1)+3[/tex][tex]y=\frac{19}{5}[/tex]We find the point (1,19/5).
Where 19/5 = 3.8
Now, lest find the x-intercept and y-intercept.
To find the x-intercept, set y=0
[tex]0=\frac{4}{5}x+3[/tex]Solve for x:
[tex]-3=\frac{4}{5}x[/tex][tex]5\cdot-3=4x[/tex][tex]-15=4x[/tex]where
[tex]x=-\frac{15}{4}=-3.75[/tex]So, the x-intercept is the point (-15/4, 0)
To find the y-intercept, set x=0. Then:
[tex]y=\frac{4}{5}x+3[/tex][tex]y=\frac{4}{5}(0)+3[/tex][tex]y=3[/tex]So, the y-intercept is the point (0,3)
Use this information to graph the line.
Hence, the graph for y=4/5x + 3 is given by: