18x - 7
The terms are 18x and 7
The coeffient of x is 18
The constant is 7
what is the change in Eric‘s total pay for each copy of Mathis fun he sellswhat is eric total pay if he doesn’t sell copy of math is fun
Answer:
1. $120
2. $2200
Explanation:
The linear function representing Eric' s to total pay is
2200 + 120x = y
By rearranging it, it becomes
y = 120x + 2200
where
y represents the total pay
x represents the number of copies sold
Recall, the slope intercept equation is expressed as
y = mx + c
where
m represents slope or rate of change
c represents y intercept or the value of y when x = 0
By comparing both equations,
rate of change = 120
If he doesn't sell any fun book, x = 0. y = 120 * 0 + 2200. Thus
y intercept = 2200
Thus, we have
The change in Eric's total pay for each Math fun book he sells is $120
Eric's total pay if he doesn't sell any math fun book is $2200
Evaluate the logarithmic expression shown below. Round your answer to the nearest hundredth.
ANSWER
log₃ 18 = 2.63
EXPLANATION
To find the value of this logarithm expression, we can apply the change of base rule and then use a calculator - since calculators only have bases 10 and e,
[tex]\log_bx=\frac{\log_cx}{\log_cb}[/tex]In this case, b = 3, x = 18, and we will use the new base 10,
[tex]\log_318=\frac{\log_{10}18}{\log_{10}3}\approx\frac{1.26}{0.48}\approx2.63[/tex]Hence, the value is 2.63, rounded to the nearest hundredth.
I need help with the work question 8Area of Regular PolygonsFind the area of each regular polygon. Leave your answer in simplest form. Ok
The area os any regular polygon is given by:
[tex]A=\frac{1}{2}Pa[/tex]where P is the perimeter and a is the apothem. The perimeter of a regular polygon is given by:
[tex]P=ns[/tex]where n is the number of sides and s is the length of its side. In this case we have a triangle, then n=3; we also know the length of the side, plugging these values we have:
[tex]\begin{gathered} P=(3)(28\sqrt{3}) \\ P=84\sqrt{3} \end{gathered}[/tex]Plugging the value of the perimeter and the apothem on the expression for the area we have:
[tex]\begin{gathered} A=\frac{1}{2}(84\sqrt{3})(14) \\ A=588\sqrt{3} \end{gathered}[/tex]Therefore, the area of the triangle is:
[tex]A=588\sqrt{3}[/tex]This is approximately 1018.4 square units
Jasmin is going to purchase a charm bracelet for her mother that will cost 116 dollars plus 6.0% on sales tax.what is the sales tax of the charm bracelet
Answer:
The sales tax of the charm bracelet is $6.96
Step-by-step explanation:
The sales tax of the bracelet is 6% of the cost. So 6% of 116.
6% of 116 = 0.06*116 = 6.96
The sales tax of the charm bracelet is $6.96
Recommendations Skill plans Math 13 Language arts Eighth grade > T.14 Volume of spheres om What is the volume of this sphere? Use a 3.14 and round your answer to the nearest hundredth. 20 m cubic meters
From the picture, the diameter of the sphere is 20 m, then its radius is 20/2 = 10 m.
The volume of a sphere is computed as follows:
[tex]V=\frac{4}{3}\pi r^3[/tex]Substituting with r = 10 m, we get:
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot10^3 \\ V=\frac{4}{3}\cdot3.14\cdot1000 \\ V=4186.67m^3 \end{gathered}[/tex]11. What is the total surface are of a rectangular prism in square inches? Thedimensions are; height is 10 inches width is 6 inchesfeetlength is 1.5
The total surface area of a rectangular prism can be calculated using the formula shown below:
[tex]TSA=2lw+2lh+2hw[/tex]Where "l" is the length, "w" is the width and "h" is the height of the rectangular prism.
In this case you know that:
[tex]\begin{gathered} l=1.5ft \\ w=6in \\ h=10in \end{gathered}[/tex]As you can notice, you need to make the conversion of the length from feet to inches. Remember that:
[tex]1ft=12in[/tex]Therefore:
[tex](1.5ft)(\frac{12in}{1ft})=18in[/tex]Then, the length in inches is:
[tex]l=18in[/tex]Now you can substitute values into the formula and then evaluate, in order to find the total surface area of the rectangular prism:
[tex]\begin{gathered} TSA=2lw+2lh+2hw \\ TSA=(2)(18in)(6in)+(2)(18in)(10in)+(2)(10in)(6in) \\ TSA=216in^2+360in^2+120in^2 \\ TSA=696in^2 \end{gathered}[/tex]The answer is:
[tex]TSA=696in^2[/tex]Calculate the radius of this shape if the volume is 1017.876m3. Make sure your answer includes the proper units
Given:
Volume of the cone = 1017.876 cubic m
slant height = 15m
height = 12m
To find the radius of the cone, we would have to use the formula of a cone. The formula for the volume of a cone is:
[tex]\text{Volume = }\frac{1}{3}\pi r^2h[/tex]Substituting the given values:
[tex]1017.876\text{ = }\frac{1}{3}\text{ }\times\pi\text{ }\times r^2\times12[/tex]Solving for the radius r:
[tex]\begin{gathered} 12\pi\text{ }\times r^2\text{ = 3 }\times\text{ 1017.876} \\ r^2\text{ = }\frac{3\text{ }\times\text{ 1017.876}}{12\pi} \\ r^2\text{ = 80.9999} \\ r\text{ = }\sqrt[]{80.99999} \\ r\text{ = 8.9} \\ r\text{ }\approx\text{ 9 } \end{gathered}[/tex]Answer:
r = 9m
use the diagram to help answer part A,B and C
Notice that angle B corresponds to one of the interior angles of triangle ADB and triangle CAB, since both triangles are right triangles, then by AA criterion
[tex]\Delta ADB\approx\Delta CAB.[/tex]Now, we are given that the length of segment AC is 8 units and the length of segment AB is 10 units, since the triangles are right triangles, from the Pythagorean theorem we get that:
[tex]BC^2+AC^2=AB^2.[/tex]Solving the above equation for BC, we get:
[tex]BC=\sqrt{AB^2-AC^2}.[/tex]Therefore:
[tex]BC=\sqrt{100u^2-64u^2}=\sqrt{36u^2}=6u.[/tex]( u = units).
To find the length of CD, we will use the trigonometric function cosine:
[tex]\begin{gathered} cos36^{\circ}=\frac{AB}{DB}, \\ DB=\frac{10u}{cos36^{\circ}}\approx12.36u. \end{gathered}[/tex]Finally, we get that:
[tex]CD=DB-BC=12.36u-8u=4.36u.[/tex]Answer:
a)
[tex]\begin{equation*} \Delta ADB\approx\Delta CAB. \end{equation*}[/tex]b)
[tex]\begin{gathered} BC=6\text{ units,} \\ CD\text{ }\approx4.36\text{ units.} \end{gathered}[/tex](These "x/x" are fractions).2/3x+6=1/2x+1/4xA) 6B)72C)14 2/5D) 2
We have to find the value of x in the expression:
[tex]undefined[/tex]how would I get the answer and what would be my answer?
Real zeros
Looking at the graph
x=-1 and x=2
Relative local minima
(-1,0) and (2,0)
Relative local maxima
(0.5,5)
Extreme absolute minimum
(-1,0) and (2,0)
Extreme absolute maximum
(-1.5,6)
Interval(s) of increase
(-1,0.5) and (2, infinite)
Interval(s) of decrease
(-infinite,-1) and (0.5,2)
ght mangles What is m ZB to the nearest tenth? 28.2 c 45.8 B m ZB
We are given a right triangle and we are asked to determine the angle B given the opposite and adjacent sides. To do that we will use the function tangent since this is defined as:
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]Substituting the values we get:
[tex]\tan B=\frac{28.2}{45.8}[/tex]Now, we use the inverse function of the tangent:
[tex]B=\tan ^{-1}(\frac{28.2}{45.8})[/tex]Solving the operations:
[tex]B=31.62[/tex]Therefore, angle B is 31.62°.
Determine whether ACDE is similar to AJKLi Answerby i AnswerNoYesAngles not congruentAA similaritySides not proportionalSSS similaritySAS similarity
Given
Graph
Procedure
[tex]\begin{gathered} \frac{DE}{KL}=\frac{35}{30}=1.166 \\ \end{gathered}[/tex][tex]\frac{DC}{KJ}=\frac{28}{24}=1.166[/tex][tex]\frac{CE}{JL}=\frac{21}{18}=1.166[/tex]
CDE is similar to JKL
SSS similarity
David cast a shadow 42" long at the same place and time in Emma cast a shadow 28" long. David is 66" tall. What is Emma's height?
ANSWER
Emma is 44" tall
EXPLANATION
We have that David cast a shadow 42 inches long and he is 66 inches tall.
At that same place and time, Emma cast a shadow of 28 inches.
Since they are at the same spot and time, we can conclude that the ratio of their height to shadow must be the same.
Let Emma's height be x.
The ratio of David's shadow to height is:
42 : 66 or 42 / 66
For Emma, it is:
28 : x or 28 / x
That means that:
[tex]\begin{gathered} \frac{42}{66}\text{ = }\frac{28}{x} \\ \text{Solve for x by cross-multiplying:} \\ 42\cdot\text{ x = 66 }\cdot\text{ 28} \\ x\text{ = }\frac{66\cdot\text{ 28}}{42} \\ x\text{ = 44 inches} \end{gathered}[/tex]So, Emma is 44" tall.
Need answer fast can talk about explanation later A quadrilateral can have 2 pairs of congruent a sides without being a rectangleTrue or False
EXPLANATION
The kite and dart quadrilaterals have two pairs of congruent sides without being a rectangle.
Therefore, the answer is true.
Suppose your uncle gives you money during the first 15 days of each month. He gives you $100 onthe first day, $50 the next day, then $25 on the day after that, and follows the same pattern until thefifteenth day. How much would your uncle give you in a year?
Okay, here you have a sequence problem. First, you need to find how much money your uncle gives you each month, and then you multiply that result by 12, which are the months in a year. The first term of the sequence is 100 and each day he gives you half of the previous day. The next formula is the one you need to use:
[tex]\sum ^n_{i\mathop=0}100\cdot\frac{1}{2^i}=200-100\cdot2^{-n}=200-100\cdot2^{-15}\cong199.997[/tex][tex]199.997\cdot12=2399.96[/tex]5) Danielle spent half of her weeklyallowance on candy. To earn more moneyher parents let her clean the oven for $9.What is her weekly allowance if she endedwith $16?
Let's use the variable x to represent her allowance.
First, she spent half the total on candy, so now she has x/2.
Then, she earned more $9 from cleaning the oven, so now she has x/2 + 9
This amount is equal $16, so let's write an equation and solve it for x:
[tex]\begin{gathered} \frac{x}{2}+9=16 \\ \frac{x}{2}=16-9 \\ \frac{x}{2}=7 \\ x=7\cdot2 \\ x=14 \end{gathered}[/tex]Therefore her weekly allowance is $14.
iBD bisects ZABC.Find mZABD, mZCBD, and mZABC.(8x +35) DVE/(11x + 23)BहैmZABD =mZCBD =m_ABC =
Answer
Angle ABD = 67°
Angle CBD = 67°
Angle ABC = 134°
Explanation
BD bisecting Angle ABC means that BD divides that angle into two equal parts.
Hence, we can conclude that
Angle CBD = Angle ABD
Angle CBD = (11x + 23)°
Angle ABD = (8x + 35)°
Angle CBD = Angle ABD
11x + 23° = 8x + 35°
11x - 8x = 35° - 23°
3x = 12°
Divide both sides by 3
(3x/3) = (12°/3)
x = 4°
We can then solve for the unknowns now
Angle ABD = (8x + 35)°
= 8(4°) + 35°
= 32° + 35°
= 67°
Angle CBD = (11x + 23)°
= 11(4°) + 23°
= 44° + 23°
= 67°
Angle ABC = Angle ABD + Angle CBD
= 67° + 67°
= 134°
Hope this Helps!!!
Question 101 ptsBrian and Marquise are saving money. Brian has saved $20 and saves $3 per week. Marquisehas saved $10 and saves $5 per week. After how many weeks will Brian and Marquise havesaved the same amount of money?55 weeks50 weeks10 weeks5 weeks
Lets call the amount of weeks till they save the same amount of money x. i.e , it will take them weeks to save the same amount.
Brian would have saved 20+3x
Marquise would have saved 10+5x
Lets equate them because they are the same amount of money, thus
20 + 3x = 10 + 5x
20 -10 = 5x -3x
10 = 2x
x = 5 weeks
Therefore it would take 5 weeks.
Option D
kid has 7 apple he give 1 to
The angles 2x and 36 are vertical angles, which means that they are angles opposite to the same vertex and thus they are equal:
[tex]2x=36[/tex]Now we have to solve this equation to find the value of x.
To solve for x, divide both sides of the equation by 2:
[tex]\frac{2x}{2}=\frac{36}{2}[/tex]On the left-hand side, the 2 on the numerator and the 2 on the denominator cancel each other and we are left only with x:
[tex]x=\frac{36}{2}[/tex]And on the right-hand side 36/2 is equal to 18:
[tex]x=18[/tex]Answer: x=18
Divide(5x³-6x+4) / (x-2)
Given the expression
[tex]\frac{\left(5x³-6x+4\right)}{(x-2)}[/tex][tex]\frac{\left((5x³-10x^2+10x^2)-6x+4\right)}{(x-2)}[/tex][tex]\frac{\left(((5x^2)(x-2)+10x^2)-6x+4\right)}{(x-2)}[/tex][tex]5x^2+\frac{\left(10x^2-6x+4\right)}{(x-2)}[/tex][tex]5x^2+\frac{\left(10x^2-20x+20x-6x+4\right)}{(x-2)}[/tex][tex]5x^2+\frac{\left((10x)(x-2)+20x-6x+4\right)}{(x-2)}[/tex][tex]5x^2+10x+\frac{(14x+4\rparen}{(x-2)}[/tex][tex]5x^2+10x+\frac{(14x-28+28+4\rparen}{(x-2)}[/tex][tex]5x^2+10x+\frac{(14x-28)+32}{(x-2)}[/tex][tex]5x^2+10x+\frac{(14)(x-2)+32}{(x-2)}[/tex][tex]5x^2+10x+14+\frac{32}{(x-2)}[/tex]If the value of X is four what would be the value of Y in the equation 2x+4y=16
Answer: y = 2
Explanation:
The given equation is
2x + 4y = 16
We would substitute x = 4 into the equation and solve for y, We have
2 * 4 + 4y = 16
8 + 4y = 16
Subtracting 8 from both sides, we have
8 - 8 + 4y = 16 - 8 = 8
4y = 8
Dividing both sides by 4,
4y/4 = 8//4
y = 2
Q The value of n is a distance of 1.5 units from -2 on a number line. Click on the number line to show the possible values of n. -5 -4 -3 -2 -1 they 0 1 2 3 4 LO
Input data
n is a distance of 1.5 units from -2
Procedure
n - 1.5 = -2
n = -2 + 1.5
n = -0.5
Also
n + 1.5 = -2
n = -2 - 1.5
n = -3.5
Team A and Team B have entered a chess competition.Team A and Team B have three members each. Each member of Team A must play each member of Team B once. Which of the following network diagrams could represent the chess games to be played?
There are three memners in each of team A and team B. So each player can play with three players of opposite team. This means each vertex of tree diagram has 3 degree.
From the given options, it can be observed that tree diagram in option B represents that each vetex has three degrees.
So answer is option B.
to complete the square for the equation, x² + 12x - 2 = 0, you will have to add ____ to both sides. a) 6b) 12 c) 24 d) 36
We are given the following quadratic equation
[tex]x^{2}+12x-2=0[/tex]To apply the completing the square method,
We have to add the square of half the coefficient of the x -term to both sides of the equation
[tex](\frac{12}{2})^2=(6)^2=36[/tex]Therefore, we need to add 36 to both sides of the equation
Option d is the correct answer.
Karen invested her savings in two investment funds. The amount she invested in fund A. was $2000 less than the amount she invested in fund B. Fund A returned a 8% profit and fund B returned a 6% profit. How much did she invest in fund B, if the total profit from the two funds together was $1940
Step 1:
Let the invested on B = m
Amount invested on A = m - 2000
Step 2
Profit is in percentage of the cost of investment
A profit is 8%
[tex]\begin{gathered} A\text{ profit = 8\% of m - 200}0 \\ =\text{ }\frac{8}{100}\text{ }\times\text{ (m - 2000)} \\ =\text{ 0.08m - 16}0 \end{gathered}[/tex][tex]\begin{gathered} B\text{ profit = 6\% of m} \\ =\text{ 0.06m} \end{gathered}[/tex]Step 3
Total profit = $1940
[tex]\begin{gathered} 0.08m\text{ - 160 + 0.06m = 1940} \\ 0.14m\text{ = 1940 + 16}0 \\ 0.14m\text{ = 2}100 \\ m\text{ = }\frac{2100}{0.14} \\ \text{m = \$15000} \end{gathered}[/tex]Final answer
She invested $15,000 in fund B
Milk Creamery charges $2 for a cup of ice cream and $0.75 for each topping . Justinwants a cup of ice cream with four toppings.How much will the ice cream cost Justin?A $2.75B $3.00C $5.00D $5.75
Explanations:
Price of a cup of Ice cream = $2
Price of one topping = $0.75
Since Justin wants four toppings on the cup of ice cream that he buys:
Price of four toppings = $0.75 * 4
Price of four toppings = $3.00
The total cost of Ice cream bought by Justin = Price of a cup of Ice cream + Price of four toppings
The total cost of Ice cream bought by Justin = $2 + $3.00
The total cost of Ice cream bought by Justin = $5.00
What do you know to be true about the values of p and g?pºgº6030°4545O A. p>gO B. p
Solution:
Given the triangles as shown below:
The sum of interior angles in a triangle equals 180°.
Thus, in ΔABC,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180 \\ \text{where} \\ \angle A=60,\text{ }\angle B=p,\text{ }\angle C=30 \\ 60+p+30=180 \\ \Rightarrow p+90=180 \\ p=180-90 \\ \Rightarrow p=90\degree \end{gathered}[/tex]Similarly, in ΔXYZ,
[tex]\begin{gathered} \angle X+\angle Y+\angle Z=180 \\ \text{where} \\ \angle X=45,\text{ }\angle Y=q,\text{ }\angle Z=45 \\ 45+q+45=180 \\ \Rightarrow90+q=180 \\ q=180-90 \\ \therefore q=90\degree \end{gathered}[/tex]Since the p and q are similarly evaluated to be 90°, we can conclude that the values of p and q are equal.
Hence,
[tex]p=q[/tex]The correct option is C.
the number 6 is plotted on the number line below. Answer the following questions.
Starting point = 6
a.
To obtain a point 2 units to the right add 2.
6 + 2
b.
To obtain a point 2 units to the left, subtract 2.
6 + (-2)
6-2
calculate the next three numbers of each progression1) 15,-14,13,-12...2)243,81,27...3)5,12,26....4)2,5,9,14...
Given data:
The first series is 15,-14,13,-12...
The second term can be written as,
[tex]-14=15\times(-1)+1[/tex]The third term can be written as,
[tex]13=-14\times(-1)-1[/tex]The next term can be written as,
[tex]\begin{gathered} a_5=-12\times(-1)-1 \\ =11 \end{gathered}[/tex]Thus, the next term of the given series is 11.
a radius of a cylindrical construction pipe is 2 ft, and it's length is 23 ft. Answer the parts below. a) find the exact volume of the pipe write your answers in terms of Pi b) approximate the volume of the pipe. To do the approximation use your answer to part A and the pi button on the calculator round your answer to the nearest hundred
a) We know that the volume of a cylinder is:
[tex]V=h\pi r^2[/tex]Now we can replace the values we have so:
[tex]\begin{gathered} V=23\cdot(2^2)\cdot\pi \\ V=92\cdot\pi \end{gathered}[/tex]b) now we can replace pi by 3.1416 and operate so:
[tex]V=289.03[/tex]