Write an expression to show how much Gretchen paid for drama,action, and comedy videos if she paid $4 for each at a sale. Evaluate the expression
Answers
explanation
To determine how much Gretchen paid, we will have to list out the number of Video purchases made for drama, action, and comedy videos.
Let the Action videos be represented by A
Let the Comedy videos be represented by C
Let the Drama videos be represented by D
Also,
A has 3 purchases
C has 5 purchases
D has 2 purchases
Therefore, we will have the expression
[tex]3A+5C+2D[/tex]If she paid $4 for each, then
The total videos purchased = 3+5+2=10
Thus, the total amount paid will be
[tex]\begin{gathered} 10p \\ \text{where p is the price she paid for each video} \\ \text{Thus, } \\ \text{she paid} \\ 10(4)=\text{ \$40} \end{gathered}[/tex]Thus, Gretchen paid $40
Related Questions
Pls help with the question in the picture. 20 Points and brainliest.
Answers
Answer:
∠ UTV = 66°
Step-by-step explanation:
the central angle USV is twice the angle on the circle ∠ UTV , subtended on the same arc UV , that is
10x + 82 = 2(10x + 16) ← divide both sides by 2
5x + 41 = 10x + 16 ( subtract 5x from both sides )
41 = 5x + 16 ( subtract 16 from both sides )
25 = 5x ( divide both sides by 5 )
5 = x
Then
∠ UTV = 10x + 16 = 10(5) + 16 = 50 + 16 = 66°
Simplify (sqrt)98m^12Using factor tree. Please draw. Quick answer = amazing review. Not a graded or timed assessment. Please use factor tree or split up using perfect squares
Answers
The simplified expression is 7m⁶ √2
STEP - BY - STEP EXPLANATION
What to find?
Simplify the given expression.
Given:
[tex]\sqrt[]{98m^{12}}[/tex]To simplify the above, we will follow the steps below:
Step 1
Apply radical rule:
[tex]\sqrt[]{ab}=\sqrt[]{a}\text{ . }\sqrt[]{b}[/tex]That is;
[tex]\sqrt[]{98m^{12}}=\sqrt[]{98}\times\sqrt[]{m^{12}}[/tex]Step 2
Simplify each value under the square root.
[tex]\sqrt[]{98}=\sqrt[]{49\times2}=\sqrt[]{49}\times\sqrt[]{2}=7\sqrt[]{2}[/tex][tex]\sqrt[]{m^{12}}=(m^{12})^{\frac{1}{2}}=m^{\frac{12}{2}}=m^6[/tex]Therefore, the simplified expression is:
[tex]\sqrt[]{98m^{12}}=7m^6\text{ }\sqrt[]{2}[/tex]Tori is writing an essay for her English class. She already has 235 words, andon average writes 175 words every hour. The essay needs to be at least 1,600words. How many more hours should she plan to work on it? Write and solvean inequality for the situation.
Answers
Let be "h" the number of hours Tori should plan to work on it.
You know that she writes an average of 175 per hour. This can be represented with this expresion:
[tex]175h[/tex]You also know that there must be at least 1,600 words in the essay for her English class. Since she has 235 words written, you can set up the following inequality:
[tex]235+175h\ge1,600[/tex]The symbol used in the inequality means "Greater than or equal to".
In order to solve it, you can follow these steps:
1. Subtract 235 from both sides of the inequality:
[tex]\begin{gathered} 235+175h-(235)\ge1,600-(235) \\ 175h\ge1,365 \end{gathered}[/tex]2. Divide both sides of the inequality by 175:
[tex]\begin{gathered} \frac{175h}{175}\ge\frac{1,365}{175} \\ \\ h\ge7.8 \end{gathered}[/tex]The answer is:
[tex]7.8\text{ }hours[/tex]I will provide another picture with the questions to this problemBefore beginning: please note that this is lengthy, pre calculus practice problem
Answers
Evaluate the indicated function for f(x)=x^2-1 & g(x)=x-2 algebraically .
Answers
Given:
[tex]f(x)=x^2-1\text{ ; g(x)=x-2 }[/tex][tex](\frac{f}{g})(t+2)=\frac{f(t+2)}{g(t+2)}[/tex][tex](\frac{f}{g})(t+2)=\frac{(t+2)^2-1}{(t+2)^{}-2}[/tex][tex](\frac{f}{g})(t+2)=\frac{t^2+4t+4-1}{t+2-2}[/tex][tex](\frac{f}{g})(t+2)=\frac{t^2+4t+3}{t}[/tex][tex](\frac{f}{g})(t+2)=\frac{(t+1)(t+3)}{t}[/tex]Linda's mean speed on her drive home from Cincinnati is 54 mph. If the total trip is 378 miles, how long should she expect the drive to take? Round your answer totwo decimal places, if necessary,
Answers
We have that Linda's mean speed is 54 miles per hour. Since the total trip is 378 miles, we have the following rule of three:
[tex]\begin{gathered} 54\text{miles}\rightarrow1h \\ 378\text{miles}\rightarrow x \end{gathered}[/tex]therefore, we have:
[tex]\begin{gathered} x=\frac{378\cdot1}{54}=7 \\ x=7 \end{gathered}[/tex]Finally, we have that Linda should expect to drive 7 hours.
Drag the tiles to the correct boxes. Not all tiles will be used.
Match each equation with a value of x that satisfies it.
18
1
9
2
5
(x - 2) = 2
√²+7=4
V1-x
= -1
-3
Answers
For a given exponential expression, the determined value is x=3,0,6.
What are exponential expressions?A component of an exponential expression is an exponent. Powers can be expressed succinctly using exponential expressions. The exponent represents the number of times the base has been multiplied.Powers can be expressed succinctly using exponential expressions. The exponent represents the number of times the base has been multiplied. Exponential expressions or the representation of multiplication with exponents can be streamlined to produce the most efficient notation possible.Each exponential expression's x value is evaluated.
Therefore,
1. [tex]$ \sqrt{x^2+7}=4 \\[/tex]
[tex]&\left(x^2+7\right)=4^2 \\[/tex]
[tex]&\left(x^2+7\right)=16 \\[/tex]
simplifying the above equation, then we get
x² = 16 - 7 = 9
x = 3
2. [tex]$\sqrt[2]{1-x}=-1$[/tex]
(1 -x) = (-1)²
1 - x = 1
x = 0
3. [tex](x-2)^{\frac{1}{2}}=2 \\[/tex]
(x - 2) = 2²
x - 2 = 4
x = 6
The determined value is x=3,0,6 for a given exponential expression.
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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 10 people took the trip. She was able to purchase coach tickets for $240 and first class tickets for $1040. She used her total budget for airfare for the trip, which was $4000
. How many first class tickets did she buy? How many coach tickets did she buy?
Answers
Sarah bought 8 first class tickets and she buy 2 coach ticket .
In the question ,
it is given that
total number of people including Sarah = 10 people .
let the number of first class ticket = f
let the number of coach tickets = c
So , the equation is f + c = 10
f = 10 - c
the cost for first class tickets = $240
the cost for "f" first class tickets = 240f
the cost for coach tickets = $1040
the cost for "c" coach tickets = 1040c
total budget is $4000 .
So , the equation is 240f + 1040c = 4000
On substituting f = 10 - c , we get
240(10 - c) + 1040c = 4000
2400 - 240c + 1040c = 4000
1040c - 240c = 4000 - 2400
800c = 1600
c = 1600/800
c = 2
and f = 10 - 2 = 8 .
Therefore , Sarah but 8 first class tickets and she buy 2 coach ticket .
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The circle graph shows the results of a survey by a bakery on which of their new products 105 customerspreferred most. How many customers preferred cake? Round your answer to the nearest whole number.
Answers
If 105 customers were the total, and 35% prefers cake, we must calculate 35% of 105, then we must do 105 multiplied by 35%, we can doit transforming the 35% in the fraction notation:
[tex]35\%=\frac{35}{100}[/tex]And the multiplication
[tex]105\cdot\frac{35}{100}=36.75[/tex]Therefore, if we round it to the nearest whole number, the number of customers that prefer cake is 37.
37 customers prefer cake.
Find the equation of a line that is parallel to the line x = 10 and contains the point (-8,1)the equation of the line is =
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The given line is x = 10, which is a vertical line. All vertical lines have the form x = k, where k is a real number.
So, a parallel line passing through (-8,1) would be x = -8.
Hence, the answer is x = -8.Write an equivalent expression to the following expression: (5^2)7
Answers
Here, we want to write an equivalent expression
To do this, we use one of the laws of indices
The law is as follows;
Which equation is true when the value of x is - 12 ?F: 1/2x+ 22 = 20G: 15 - 1/2x = 21H: 11 - 2x = 17 J: 3x - 19 = -17
Answers
Substitute x = - 12 in each of the given equation, if the equation satisfy then tha x = -1 2
F) 1/2x + 22 = 20
1/2 ( -12) + 22 = 20
(-6) + 22 = 20
16 is not equal to 22
G) 15 -1/2x = 21
Substitute x = -12 in the expression :
15 - 1/2( -12) = 21
15 + 1/2(12) =21
15 + ( 6) = 21
21 = 21
Thus, The equation 15 - 1/2x = 21 is true for x = -12
H) 11 - 2x = 17
Susbstitute x = ( -12) in the equation :
11 - 2x = 17
11 - 2( -12) = 17
11 + 24 = 17
35 = 17
Since, 35 is not equal to 17
D) 3x - 19 = -17
SUsbtitute x = ( -12)
3( -12) - 19 = -17
-36 - 19 = -17
-36 = -17 + 19
-36 = 2
Since - 36 is not equal 2
Answer : G) 15 - 1/2x = 21
given the tableau, circle the pivot and explain how you found it
Answers
The equations are
[tex]2x_1+3x_2+6x_3+S_2=22[/tex][tex]3x_1+5x_2+3x_3+S_1=20_{}[/tex][tex]-3x_2-1x_3+S_1+Z\text{ = 24}[/tex]The smallest negative number is the pivot column
so the smallest negative number is -3 and hence the pivot column is
3
5
-3
The row pivot hence = 5
so pivot will be (x= -3 and S = 5)
distributive property 3x(7x+6)
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By distributive property, we distribute 3x, and multiply it to each term inside the binomial (7x+6) accounting for the sign.
[tex]\begin{gathered} 3x(7x+6) \\ \Rightarrow3x(7x)+3x(6) \\ \Rightarrow21x^2+18x \\ \\ \text{Therefore, }3x(7x+6)=21x^2+18x \end{gathered}[/tex]How many roots does x^2-6x+9 have ? It may help to graph the equation.
Answers
The roots are those values that make a function or polynomial take a zero value. The roots are also the intersection points with the x-axis. In the case of a quadratic equation you can use the quadratic formula to find its roots:
[tex]\begin{gathered} ax^2+bx+c=y\Rightarrow\text{ Quadratic equation in standard form} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\Rightarrow\text{ Quadratic formula} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} y=x^2-6x+9 \\ a=1 \\ b=-6 \\ c=9 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(1)(9)}}{2(1)} \\ x=\frac{6\pm\sqrt[]{36-36}}{2} \\ x=\frac{6\pm0}{2} \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]As you can see, this function only has one root, at x = 3.
You can see this in the graph of the function:
What are the solutions to the equation (x − 21)2 = 25?x= x=
Answers
SOLUTION:
Case: Quadratics equation
Method:
[tex]\begin{gathered} (x-21)^2=25 \\ TakeSquarerootsOfBothSides \\ x-21=\sqrt{25} \\ x-21=\pm5 \\ x=21\pm5 \\ x=21+5\text{ }or\text{ }x=21-5 \\ x=26\text{ }or\text{ }x=16 \end{gathered}[/tex]Final answer:
x= 16
x= 26
An item is regularly priced at $85. Yolanda bought it at a discount of 65% off the regular price?
Answers
Miguel made $17.15 profit from selling 7 custom t-shirts through a website. Miguel knows the total profit he earns is proportional to the number of shirts he sells, and he wants to create an equation which models this relationship so that he can predict the total profit from selling any number of t-shirts.
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Let:
[tex]\begin{gathered} P(x)=\text{profit} \\ k=\text{price of each t-shirt} \\ x=\text{Number of t-shirts sold} \end{gathered}[/tex]Miguel made $17.15 profit from selling 7 custom t-shirts, therefore:
[tex]\begin{gathered} P(7)=17.15=k(7) \\ 17.15=7k \\ \text{Solving for k:} \\ k=\frac{17.15}{7}=2.45 \end{gathered}[/tex]Therefore, the equation that models this relationship is:
[tex]P(x)=2.45x[/tex]In the figure shown, what is mzA? Explain.57°; AABC is an isosceles triangle with base angles A and C. m2A = mc.B. 66; AABC is an isosceles triangle with base angles B and C. m2B = m_C = 57, and m2A + m2B + m2 = 180.C. 57. AABC is an equilateral triangle.
Answers
Since ABC is an isosceles triangle with sides AB=AC, then the angle ABC is the same as ACB, an it's equal to 57º.
Since all three internal angles should add up to 180º, then the angle BAC should have a measure of 180-2(57)=66º.
Calculate Sse for the arithmetic sequence {a,}5sequence {1,3 ={}+}=Ο Α. 1463OB. 91220 C. 8,6716D. 9,26767
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Answer:
[tex]\frac{8,671}{6}[/tex]Explanation:
Here, we want to get the sum of the 58 terms in series
Mathematically, we have the formula to use as:
[tex]S_n\text{ = }\frac{n}{2}(a\text{ + L)}[/tex]where a is the first term and L is the last term
The first term is when n is 1
We have this calculated as:
[tex]\text{ a}_{}\text{ = }\frac{5}{6}+\frac{1}{3}\text{ = }\frac{5+2\text{ }}{6}\text{ = }\frac{7}{6}[/tex]The last term is the 58th term which is:
[tex]\text{ a}_{58}\text{ = }\frac{290}{6}\text{ + }\frac{1}{3}\text{ = }\frac{292}{6}[/tex]We finally substitute these values into the initial equation
Thus, we have it that:
[tex]S_{58}\text{ = }\frac{58}{2}(\frac{292}{6}+\frac{7}{6})\text{ = 29(}\frac{299}{6})\text{ = }\frac{8671}{6}[/tex]
round 6.991 to two decimal places
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Since 6.99 < 6.991 < 7.00, and the number 6.991 is nearer to 6.99 than to 7.00, then 6.991 rounded to two decimal places, is:
[tex]6.99[/tex]multiply decimals 3.76 × 4.8=this is how the problem needs worked
Answers
18.048
Explanation:[tex]\begin{gathered} 3.76\text{ }\times\text{ 4.8} \\ \\ To\text{ make it easy, we remove the decimal points while multiplying:} \\ 376\text{ }\times\text{ 48} \end{gathered}[/tex][tex]\begin{gathered} We\text{ count the numbers of decimal points:} \\ 2\text{ decimal point in 3.46} \\ 1\text{ decimal point in 4.8} \\ \text{Total decimal points = 3} \\ We\text{ count 3 decimal points in our result} \end{gathered}[/tex]The result is 18.048
Use the distance formula, slopes and your knowledge of characteristics of different
types of quadrilaterals to determine the type of quadrilateral formed by the
following four points (-3, 1) , (-2, 3) , (0, 4) , (-1, 2)
Answers
This quadrilateral is square . It have same length of side.
How to Find type of quadrilaterals?In geometry, a quadrilateral is a four-sided polygon with four edges and four corners. The angles stood present at the four vertices or corners of the quadrilateral. If ABCD is a quadrilateral, the angles of the vertices are A, B, C, and D. The sides of a quadrilateral are AB, BC, CD, and DA. The four vertices of the quadrilateral ABCD are A, B, C, and D.The diagonals are formed by connecting the quadrilateral's opposite vertices.Quadrilaterals are typically four-sided shapes such as rectangles, squares, and trapezoids.In a concave quadrilateral, one interior angle is greater than 180°, and one of the two diagonals lies outside the quadrilateral.A convex quadrilateral's interior angles are all less than 180°.Therefore,
From question the coordinates of A,B,C,D are given as ,
A = (-3, 1) B = (-2, 3) C = (0, 4) D = (-1, 2)
We use distance formula :
Distance = √(x2 -x1)²+(y2 - y1)²
AB = √(-2 + 3)²+(3 - 1)² = √(5)
BC = √(0+2)²+(4–3)² = √5
CD = √(-1 –0)²+(2–4)² =√5
DA = √(-1 +3)²+(2–1)² =√5
We get the distance is √5 for all points, so the type of quadrilateral is square.
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Could you solve the table
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The relation is decreasing by a factor of 2 each time, so:
[tex]\begin{gathered} y-9=-2(x-0) \\ y=-2x+9 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} y(100)=-2(100)+9 \\ y(100)=-200+9 \\ y(100)=-191 \end{gathered}[/tex]Answer:
-191
Consider the graph of g(x) shown below. Determine which statements about the graph are true. Select all that apply.
Answers
SOLUTION
From the graph, the root of the equation is the point where the graph touches the x-axis
[tex]x=-4,x=0[/tex]Hence the equation that models the graph becomes
[tex]\begin{gathered} x+4=0,x-0=0 \\ x(x+4)=0 \\ x^2+4x=0 \\ \text{Hence } \\ g(x)=x^2+4x \end{gathered}[/tex]Since the solution to the equation are x=-4 and x=0
Hence the equation has two real zeros
The minimum of g(x) is at the point
[tex]\begin{gathered} (-2,-4) \\ \text{Hence minimum is at x=-2} \end{gathered}[/tex]The minimum of g(x) is at x=-2
The vertex of g(x) is given by
[tex]\begin{gathered} x_v=-\frac{b}{2a} \\ \text{and substistitute into the equation to get } \\ y_v \end{gathered}[/tex][tex]\begin{gathered} a=1,\: b=4,\: c=0 \\ x_v=-\frac{b}{2a}=-\frac{4}{2\times1}=-\frac{4}{2}=-2 \\ y_v=x^2+4x=(-2)^2+4(-2)=4-8=-4 \\ \text{vertex (-2,-4)} \end{gathered}[/tex]Hence the vertex of g(x) is (-2,-4)
The domain of the function g(x) is the set of input values for which the function g(x) is real or define
Since there is no domain constrain for g(x), the domain of g(x) is
[tex](-\infty,\infty)[/tex]hence the domain of g(x) is (-∞,∞)
The decreasing function the y-value decreases as the x-value increases: For a function y=f(x): when x1 < x2 then f(x1) ≥ f(x2)
Hence g(x) decreasing over the interval (-∞,-2)
Therefore for the graph above the following apply
g(x) has two real zeros (option 2)
The minimum of g(x) is at x= - 2(option 3)
the domain of g(x) is (-∞,∞) (option 4)
g(x) decreasing over the interval (-∞,-2)(option 4)
PLEASE GIVE ME THE ANSWER AND HOW YOU GOT IT IM BEGGING YOU I WILL GET KICKED OUT IF I DONT GET A GOOD SCORE ON THIS
Answers
By solving the given equations, the values of x are 7 and -7.
What are equations?A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, |x| -7:
Now, solve for x as follows:
|x| -7Then,
x - 7 = 0 and -x - 7 = 0Which gives, x = 7 and x = -7Therefore, by solving the given equations, the values of x are 7 and -7.
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Answer:
see below
Step-by-step explanation:
All the given equation have mod function in them .We know that, if
[tex]\longrightarrow |x| = y \\[/tex]
then ,
[tex]\longrightarrow x =\pm y \\[/tex]
1) |k| = 8
[tex]\longrightarrow k =\pm 8 \\[/tex]
__________________________
2)|x| = 7
[tex]\longrightarrow x = \pm 7\\[/tex]
__________________________
3) |a+2| = 8
[tex]\longrightarrow a + 2 =\pm \\[/tex]
[tex]\longrightarrow a = 8-2 \ or \ -8-2\\[/tex]
[tex]\longrightarrow a = 6 , -10 \\[/tex]
__________________________
4) |8a|/10 = 2
[tex]\longrightarrow |8a| = 20 \\[/tex]
[tex]\longrightarrow 8a =\pm 20\\[/tex]
[tex]\longrightarrow a =\pm\dfrac{20}{8} \\[/tex]
[tex]\longrightarrow a = \pm\dfrac{5}{2} \\[/tex]
___________________________
5)|-m+9| = 13
[tex]\longrightarrow -m+9 =\pm 13\\[/tex]
[tex]\longrightarrow m -9 =\pm 13\\[/tex]
[tex]\longrightarrow m = 13-9\ or \ -13-9\\[/tex]
[tex]\longrightarrow m = 4 , -22\\[/tex]
____________________________
6)|7-5x|=27
[tex]\longrightarrow 7-5x =\pm 27 \\[/tex]
[tex]\longrightarrow 5x -7 =\pm 27\\[/tex]
[tex]\longrightarrow 5x = 27 +7 \ or \ -27+7 \\[/tex]
[tex]\longrightarrow 5x = 34 \ or -20 \\[/tex]
[tex]\longrightarrow x =\dfrac{34}{5}, -4\\[/tex]
_____________________________
7)|2x+7|/5=5
[tex]\longrightarrow |2x+7|=25\\[/tex]
[tex]\longrightarrow 2x +7 =\pm 25 \\[/tex]
[tex]\longrightarrow 2x = 25-7 \ or \ -25-7\\[/tex]
[tex]\longrightarrow 2x = 18 \ or \ -32\\[/tex]
[tex]\longrightarrow x = 9 , -16 \\[/tex]
And we are done!
Find the volume of the pyramid. Round your answer to the nearest tenth.16 in.5 in.3 in.The volume of the pyramid isin?
Answers
Recalls that the formula for the volume of a pyramid is given by the product of the area of its base times the height, and all of that divided by 3
Then we start by calculating the area of the base:
Since the base is a rectangle of 3in by 5in, then its area is 15 square inches.
Now this area times the pyramid's height and divided by 3 gives:
Volume = AreaBase x Height / 3
Volume = 15 x 16 / 3 = 80 in^3 (eighty cubic inches)
Then, please just type the number 80 in the provided box (notice that the cubic inches unit is already written on the right of it.
Last year, Susan had $20,000 to invest. She invested some of it in an account that paid 10% simple interest per year, and she invested the rest in an account that paid 7% simple interest per year. After one year, she received a total of $1790 in interest. How much did she invest in each account?
Answers
Last year, Susan had $20,000 to invest. She invested some of it in an account that paid 10% simple interest per year, and she invested the rest in an account that paid 7% simple interest per year. After one year, she received a total of $1790 in interest. How much did she invest in each account?
Let
x ------> amount invested in an account that paid 10% simple interest per year
20,000-x ------> amount invested in an account that paid 7% simple interest per year
so
The formula of simple interest is equal to
I=P(rt)
In this problem we have that
10%=0.10
7%=0.07
x*(0.1)+(20,000-x)*(0.07)=1,790
solve for x
0.10x+1,400-0.07x=1,790
0.03x=1,790-1,400
0.03x=390
x=$13,000
therefore
amount invested in an account that paid 10% simple interest per year was $13,000and amount invested in an account that paid 7% simple interest per year was $7,000The function, f. is drawn on the accompanying set of axes. On the same set of axes, sketch the graph of f-?, the inverse of f
Answers
We are given the following graph:
The inverse of the graph is shown below:
Figure 1 and Figure Il are similar figures. Figure I Figure II R S А B F C w T E D V U Which proportion must be true?
Answers
From the diagram,
CD is corresponding to WR
VW is corresponding to BC
RS is corresponding to DE
ST is corresponding to EF
TU is corresponding to FA
Final answer
[tex]\frac{ST}{EF}\text{ = }\frac{WR}{CD}[/tex]