Explanation
To find the percentage of the tip we will use the formula below.
[tex]\text{\%Tip}=\frac{\text{Tip(\$)}}{Cost\text{ of meal}}\times100[/tex][tex]\begin{gathered} \text{ \%Tip =}\frac{\text{13.25}}{109}\times100 \\ =13\text{\%} \end{gathered}[/tex]Answer: 13%
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:
Help please and thank you
If f(x) is a linear function and gives f(3) = 3 and f(9) = -2
Part a
The slope of the line = -5/6
Part b
The y-intercept = 11/2
Part c
f(x) = (-5/6)x + 11/2
The values of
f(3) = 3
f(9) = -2
The points are (3,3) and (9,-2)
Part a
The slope of the line is the change in y coordinate with respect to the change in x coordinate.
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{-2-3}{9-3}[/tex]
=-5/6
Part b
The slope intercept form of the line
y = mx+b
b is the y intercept
Substitute the values in the equation
3 = (-5/6)×3 + b
3= -5/2 + b
b = 11/2
Part c
Then the linear function f(x) = (-5/6)x + 11/2
Hence, if f(x) is a linear function and gives f(3) = 3 and f(9) = -2
Part a
The slope of the line = -5/6
Part b
The y-intercept = 11/2
Part c
f(x) = (-5/6)x + 11/2
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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.
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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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
third time asking, please help.
In a triangle one angle is three times the smallest angle and the third angle is 45 more than twice the
smallest angle. Find the measure of all three angles. Hint: The angles of a triangle add up to 180°
Answer:
The 3 angles are 22.5, 67.5 and 90 degrees.
Step-by-step explanation:
Let the smallest angle be x degrees.
Then the other angles = 3x and 2x + 45.
x + 3x + 2x + 45 = 180
6x = 180 - 45
6x = 135
x = 135/6 = 22.5 degrees
3x = 67.5 degrees
2x+45 = 90 degrees.
Identify the domain, vertical asymptotes and horizontal asymptotes of the following rational function: f(x)= \frac{3x-4}{x^3-16x} Domain is all real numbers except x\neq Answer , Answer and AnswerVertical asymptote at x= Answer , Answer and AnswerHorizontal asymptote at y= Answer
Answer
Domain is all real numbers except x ≠ 0, -4, and 4
Vertical asymptote at x = 0, -4, and 4
Explanation
Given function:
[tex]f(x)=\frac{3x-4}{x^3-16x}[/tex]Note: The domain of a function is a set of input or argument values for which the function is real and defined.
For the function to be real; the denominator must not be equal zero, i.e.
[tex]\begin{gathered} x^3-16x\ne0 \\ x(x^2-16)\ne0 \\ x(x-4)(x+4)\ne0 \\ x\ne0,x-4\ne0,\text{ and }x+4\ne0 \\ \therefore x\ne0,x\ne4,\text{ and }x\ne-4 \end{gathered}[/tex]Hence, the domain is all real numbers except x ≠ 0, -4, and 4.
Note: A vertical asymptote with a rational function occurs when there is division by zero.
Hence, the vertical asymptote at x = 0, -4, and 4
32. Recall the pattern that you found in the diamond problems from Ready, Set, Go #2. Use the pattern you discoveredto complete each diamond below.8-121-724ISet
Answer:
Step-by-step explanation:
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).
what is the slope of the line shown graohed belowzero5undefined-5
Answer: undefined
The slope of this graph is undefined because it does not run on the horizontal
Since, slope = y2 - y1 / x2 - x1
Therefore, x2 - x1 = 0
Slope = y2 - y1 / 0 = undefined
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
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
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
identify the equation
SOLUTION
We want to identify the equation that represents the data in the table.
Let's put the first values for x and y from the table, that is x = -2 and y = 11 and see if it works for the first option
[tex]y=x+5[/tex]This becomes
[tex]\begin{gathered} y=x+5 \\ y=-2+5 \\ y=3 \end{gathered}[/tex]Since we didn't get y = 11, but we got y = 3, then the first option is wrong.
Let's try the next one
[tex]y=-3x+5[/tex]This becomes
[tex]\begin{gathered} y=-3x+5 \\ y=-3(-2)+5 \\ y=6+5 \\ y=11 \end{gathered}[/tex]So, we got y = 11, this option should be the correct answer, but let us confirm with the next values of x and y which are (0, 5).
So we will put x = 0, if we get y = 5, then the option is correct, so
[tex]\begin{gathered} y=-3x+5 \\ y=-3(0)+5 \\ y=0+5 \\ y=5 \end{gathered}[/tex]Since we got y = 5, this option is correct.
Hence, the answer is the 2nd option.
[tex]y=-3x+5[/tex]Elsa drove 14 laps on a race track. Each lap was the same length. If she drove atotal of 30.8 mi what was the length of each lap? Write your answer in yards.Use the table of conversion facts as necessary, and do not round your answer.Conversion facts for length12 inches (in) = 1 foot (ft)3 feet (ft) = 1 yard (yd)36 inches (in) = 1 yard (yd)5280 feet (ft) = 1 mile (mi)1760 yards (yd) = 1 mile (mi)|0ydGХ?
Givens.
• The total number of laps is 14.
,• The total distance is 30.8 miles.
First, divide the total distance by the number of laps.
[tex]\frac{30.8mi}{14}=2.2mi[/tex]Each lap length is 2.2 miles.
Let's transform it to yards using the conversion factor 1 mile = 1760 yards.
[tex]2.2mi\cdot\frac{1760yd}{1mi}=3872yd[/tex]Therefore, each lap length is 3872 yards.
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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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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Larry is measuring the volume of a pitcher. He uses a measuring cup that holds 2 cups and fills the measuring cup 7.5 times to fill the entire pitcher. How much does the pitcher hold?
Given,
The amount of liquid hold by measuring cup is 2 cups.
The number of times measuring cup used to fill the pitcher.
Required:
The amount of liquid pitcher hold.
The amount of liquid hold by the pitcher is,
[tex]Amount\text{ of liquid = number of times measuring cups used}\times amount\text{ of liquid hold by measuring cup}[/tex]Substituting the values.
[tex]\begin{gathered} Amount\text{ of liquid =7.5}\times2\text{ cups} \\ =15\text{ cups} \end{gathered}[/tex]Hence, the pitcher can hold 15 cups.
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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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
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!
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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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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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]simplify 3p x 5q x 2
30pq=3p×5q=15pq×2=30pq
Erica paid a self employment tax last year. she calculated the self-employment tax for different amounts of net earnings and recorded them in a table shown . Which function describes the relationship between X ,amount of net earrings and y ,the self- employment.
Answer:
[tex]y=\frac{153}{1,000}x[/tex]Step by step explanation:
Linear functions represent situations that have a constant rate of change, and they are represented by:
[tex]\begin{gathered} y=kx \\ \text{where,} \\ k\text{ is the constant rate of change} \end{gathered}[/tex]We can calculate the constant rate of change with the following formula:
[tex]\begin{gathered} k=\frac{\Delta y}{\Delta x} \\ k=\frac{2,295}{15,000} \\ k=\frac{153}{1,000} \end{gathered}[/tex]Then, the function that describes the relationship between x, the number of net earnings, and y, the self-employment tax would be:
[tex]y=\frac{153}{1,000}x[/tex]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
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.
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]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.)