The relationships between the amount spent on books and the cost of
each book is a proportional relationship.
The correct responses are;
[tex](a) \ \displaystyle \mathrm{The \ number \ of \ books \ Gaya \ buys \ is } \ \underline{\frac{48}{x} \ books}[/tex][tex]\mathrm{(b) \displaystyle \underline{ \left(\frac{48}{x} -4 \right) \cdot \left(x + 2 \right) - 60 = x^2 - 5 \cdot x - 24 = 0}}[/tex]Reasons:
The amount Gaya spends on books = $48
The cost of each book = $ x
(a) The expression in terms of x for the number of books Gaya buys is therefore;
Number of books Gaya buys × $ x = $48
Therefore;
[tex]\displaystyle Number \ of \ books \ Gaya \ buys = \frac{\$48}{\$ x}[/tex](b) The amount Myra spends to buy books = $60
The cost of each book = $·(x + 2)
The number of books Myra buys = The number of books Gaya buys - 4
We have;
[tex]\displaystyle Number \ of \ books \ Myra \ buys = \frac{48}{x} - 4[/tex]
Which gives;
[tex]\displaystyle \mathbf{\left(\frac{48}{x} - 4 \right) \cdot \left(x + 2 \right)} = 60[/tex]
Using a graphing calculator, we get;
[tex]\displaystyle \frac{4 \cdot x^2 - 20 \cdot x - 96}{x} = 60[/tex]
4·x² - 20·x - 96 = 60·x
Which gives;
4·x² + 40·x - 60·x - 96 = 0
4·x² - 20·x - 96 = 0
x² - 5·x - 24 = 0
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Put the following numbers in order:
3.28, -4/5, -7.1, 0, 11/12, π, .889753, -4 1/3 help please!
In order of smallest to largest.
1) -7.1
2) -4 1/3
3) -4/5
4) .889753
5) 11/12
6) 0
7) π
8) 3.28
Which expression is equivalent to 4(6 - 2x) ?
Answer:
Option A
Step-by-step explanation:
[tex]4(6-2x)\\\rule{150}{0.5}\\\rightarrow ((6 * 4) ( -2x*4)) \leftarrow \text{Distribute the '4' into the content in the parenthesis.}\\\\\\\\\rightarrow 6 * 4 = 24\\\\\rightarrow -2x * 4 = -8x\\\\\\\\\rightarrow 4(6-2x) = \boxed{24 - 8x}[/tex]
Hope this helps.
kayla ran 10 miles it took her 60 minutes how many minutes did it take her to run each mile?
Answer: 4 hours 30 minutes
Step-by-step explanation: 36/8 = 4.5 hours
hours = 4, minutes = 0.5*60 = 30
Please help ASAP!! I am in desperate need and please don’t just do this for points
Answer:
[tex]106 yd^2[/tex]
Step-by-step explanation:
Answer is attached. Let me know if you would like another explanation that would yield the same solution.
Which of the following is(are) the solution(s) to |11x +3 = 6 ?
Hey there!
11x + 3 = 6
SUBTRACT 3 to BOTH SIDES
11x + 3 - 3 = 6 - 3
CANCEL out: 3 - 3 because it gives you 0
KEEP: 6 - 3 because it helps you solve for your x-value
11x = 6 - 3
11x = 3
DIVIDE 11 to BOTH SIDES
11x/11 = 3/11
CANCEL out: 11/11 because that gives you 1
KEEP: 3/11 because it simplifies for the x-value
SOLVE
x = 3/11
Therefore, your answer should bed x = 3/11
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A watch company estimates that the profit (in peso)
for selling a particular model is given by
P(x)=4x^3-31x^3-10058x+158040 for 0 < x < 50
where x is the advertising expense (in tens of thousands of pesos).
What kind of polynomial is described by the equation?
A.quadratic
B.constant
C.cubic
D.quintic
I need an answer right now thank you.
The leading degree of the polynomial is 3. This shows that the polynomial described by the equation is a cubic polynomial
The standard form of a polynomial expression is written as:
[tex]a_nx^n+ a_{n-1}x^{n-1}+ a_{n-2}x^{n-2}+...[/tex]
A polynomial function has a leading degree that is greater than 2;
Given the polynomial function
[tex]P(x)=4x^3-31x^3-10058x+158040[/tex]
From the given polynomial, the leading degree of the polynomial is 3. This shows that the polynomial described by the equation is a cubic polynomial
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whats 2 + 2 ??!?!?!?!?!?!?!?
Answer:
4 duhh... Ur kidding me??
Answer:
22 because 2+2
Step-by-step explanation:
if we put 2 near 2 it will be 22 so the answer is 22
math question please help meeee
Answer: what the math question is
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
7 plus 5 (painters plus photographers) equals 12. The remaining (4) adds to 16. 12/16 can be simplified to 3/4
Hope it helps
Would appreciate a brainliest
SOLVE FOR f
3/5 · f = 1 5/7
Answer:
f = 2 6/7
Step-by-step explanation:
[tex]\dfrac 35 \cdot f = 1 \dfrac 57 \\\\\\\implies \dfrac{3f}5 = 1 + \dfrac 57 = \dfrac{12}7\\\\\\\implies 21f = 60\\\\\implies f = \dfrac{60}{21} = \dfrac{20}7 = 2 \dfrac 67[/tex]
the greatest common factor of 12x^2y^3 and 24xy^2 is
Answer: (12xy^2)
Step-by-step explanation:
12x^2y^3
(12xy^2)*(xy)
24xy^2
(12xy^2)*(2)
The greatest common factor of the expressions 12x²y³ and 24xy² will be 12xy².
What is the greatest common factor?Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).
The expressions are given below.
12x²y³ and 24xy²
The factor of the expression 12x²y³ is given as,
12x²y³ = 12 × x × x × y² × y
The factor of the expression 24xy² is given as,
24xy² = 2 × 12 × x × y²
The common factors in both expressions are 12, x, and y². Then the greatest common factor will be given as,
⇒ 12 × x × y²
⇒ 12xy²
The best normal component of the articulations 12x²y³ and 24xy² will be 12xy².
More about the greatest common factor link is given below.
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please help me in questions 19, 21, 24 and i’ll mark u as brainliest i promise
Answer:
19. m = -3; f(x) = -3x +5
21. m = 0; f(x) = 9
24. m = -3/2; f(x) = -3/2x +18 1/2
Step-by-step explanation:
The slope of the function is given by the slope formula ...
m = (y2 -y1)/(x2 -x1)
The y-intercept (b) can be found from the table when it includes a point (x, y) = (0, b). If the table doesn't have the y-intercept, it can be found from ...
b = y -mx
When m and b are known, the slope-intercept equation is ...
f(x) = mx +b
__
19.m = (11 -14)/(-2 -(-3)) = -3/1 = -3
The slope is -3. The function is f(x) = -3x +5.
__
21.m = (9 -9)/(2 -3) = 0/-1 = 0
The slope is 0. The function is f(x) = 9.
__
24.m = (14 -17)/(3 -1) = -3/2
b = 17 -(-3/2)(1) = 18 1/2
The slope is -3/2. The function is f(x) = -3/2x + 18 1/2.
From a point on the ground 12 ft. from the base of a flagpole, the angle of elevation of the top of the pole measures 53°. How tall is the flagpole
Answer:
4.75 feet
Step-by-step explanation:
Let the height of the flagpole be x
Sin 53 = x/12
x = 12 × Sin 53
x = 12 × 0.3959
x = 4.75 feet
Answer:
15.9
Step-by-step explanation:
The 12 ft is the adjacent side and you are trying to find the opposite side or the height of the flagpole. You use Tan. Lowercase x means multiply.
Tan 53 = X
--------
12
To get rid of the 12 multiply both sides of the equation by 12. so
Tan 53 x 12 = X/12 x 12
Tan 53 x 12= X
X= 15.9
Can someone help? This is so hard.
y equals 50° since there is a 90° and a 30°
Answer:
cos^-1 (9/15)
Step-by-step explanation:
answer this question!.
Answer:
∠A = 44°
Step-by-step explanation:
Let b represent the measure of the exterior angle at B. Let c represent the measure of the exterior angle at C. The sum of angles in the lower triangle is ...
b/2 +c/2 +68° = 180°
b +c = 360° -136° . . . . . multiply by 2, subtract 136°
b +c = 224°
__
The exterior angle b is the supplement of the interior angle there, so the interior angle B is ...
B = 180° -b
The exterior angle c is the sum of the remote interior angles, so we have ...
c = B +A
c = (180° -b) +A
A = (b +c) -180° . . . . . . . . add b-180° to both sides
A = 224° -180° = 44° . . . . substitute for (b+c)
The measure of angle A is 44°.
_____
Additional comment
The angle naming is perhaps a little unconventional, but we wanted to use names that made the answer less cumbersome to write. We consider the angle A, B, C to be the interior angles of ΔABC, and we have named the exterior angles at B and C as 'b' and 'c'.
Conventionally, 'b' and 'c' would name the sides opposite angles B and C, respectively. We're not concerned with side lengths here, so we used those letters for an unconventional purpose.
Joshua gave away 1/3 of his marbles to Kale.If Kale got 25 marbles,how many marbles did Joshua have at first?
Answer:
75
Step-by-step explanation:
joshua - x
kale - 1/3x
1/3x = 25
x = 25(3)
x = 75
If you treat 2 friends to lunch, the 1st lunch is $12. 35, the 2nd lunch is $14. 22, and your lunch is $11. 47. You want to add a 20% tip. How much will you pay in total?.
The solution is
The total amount for the lunch is given by the equation A = $ 45.648
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount for the lunch be represented as A
Now , the equation will be
The amount for the first lunch = $ 12.35
The amount for the second lunch = $ 14.22
The amount for the third lunch = $ 11.47
The percentage of tip = 20 %
So , the total amount for the lunch without tip = $ 12.35 + $ 11.47 + $ 11.47
On simplifying the equation , we get
The total amount for the lunch without tip = $ 38.04
The amount of tip = total amount for the lunch without tip x percentage of tip
Substituting the values in the equation , we get
The amount of tip = 38.04 x ( 20/100 )
The amount of tip = 38.04 x 0.20
The amount of tip = $ 7.608
So ,
The total amount for the lunch A = total amount for the lunch without tip + amount of tip
Substituting the values in the equation , we get
The total amount for the lunch A = $ 38.04 + $ 7.608
The total amount for the lunch A = $ 45.648
Therefore , the value of A is $ 45.648
Hence , the total amount is $ 45.648
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PLEASE HELP AD EXPLAIN WELL!
Answer:
y intercept is (0, -4)
equation is y = x - 4
Step-by-step explanation:
The slope is rise/run which you can find by choosing "any" two points on the line. For instance (0,-4) and (4,0)
The rise is the difference in y direction: 0 - - 4 = 4, the graph "rises" by 4.
The run is the difference in x direction: 4 - 0 = 4, the graph "runs" by 4.
So the slope is 4/4 = 1.
The y intercept is the point on the y axis where the line passes through. This is (0,-4). The intercept value is y= - 4.
The equation is slope times x plus y intercept value.
So putting this all together gives you an equation of
y = 1·x + -4
a.k.a.
y = x-4
answer this please ty
Answer:
Answer will be 1/53 as a fraction, and 0.02 as a decimal.
Step-by-step explanation:
In order to solve this equation, we will first plug in -8 into every x term.
So now we will have:
[tex]f( - 8) = \frac{1}{ - 8 {}^{2} - 11 } [/tex]
{Don't mind the f (-8), just think of it as a sort of place holder.}
Anyways, now we will do -8 × -8, since that's what -8^2 implies:
-8 × -8 = 64
Next do 64 - 11, to get 53.
Now we have 1/53
(You can also divide the numerator by the denominator, to get the answer in decimal form.)
Hope this helps you :)
Sorry if it doesn't.
Can-25 be expressed as a ratio in the form?
Yes
No
Answer:
-25 can be expressed as a ratio of -50/2, -75/3, etc
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
1. There are 216 employees in a store. The ratio of men to women is 5:7. How many men and how many women work at the store? 2. A car traveled 180 miles in 3 hours. Assuming the car's speed was constant, at what unit rate did the car travel, in miles per hour?
Answer:
2. the car drove at 60 miles per hour
Step-by-step explanation:
:)
PLSSS HELP!!!! I offer 25 points!!
A box has a volume of 1008 cubic inches. Your friend told you that he found the polynomial that represents the volume of the box: 4x³-28x² +144x. If x is the height of the box how tall is the box?
Answer:
7 inches tall
Step-by-step explanation:
A graphing calculator quickly finds the solution to the cubic equation. It is convenient to define ...
f(x) = 4x^3 -28x^2 +144x -1008
so f(x) = 0 gives the value of x that is of interest. That value is x=7.
The box is 7 inches tall.
_____
The equation f(x) = 0 can be divided by 4 to give ...
x^3 -7x^2 +36x -252 = 0
This can be factored by grouping:
(x^3 -7x^2) +(36x -252) = 0
x^2(x -7) +36(x -7) = 0
(x -7)(x^2 +36) = 0
The only real root is x = 7, which makes a factor zero.
_____
Additional comment
For finding solutions to cubic and higher-degree polynomials, I find a graphing calculator to be an extremely helpful tool. Desmos provides an online calculator and apps for various platforms. It may take a little while to learn how to use it effectively, but it can save immense amounts of time and frustration. Of course, your handheld graphing calculator can be just as useful.
Modeling Real Life A principal invites 138 students to a reward breakfast. Nine students sit at each table. How many tables are there?
Answer:
16 tables
Step-by-step explanation:
So there are 138 students, and 9 sit at each table. This means you do 138/9, which leaves you with 15.3333. However you cant have .3 of a table so there must be 16 tables!
can someone help with this question
Answer:
<1= 60
<2=120
<3=60
<4=60
<5=120
<6=120
<7=60
Step-by-step explanation:
12x-15 distributive property
[tex]\\ \sf\longmapsto 12x-15[/tex]
Distributive property
A(B+C)=AB+ACTake 3 common
[tex]\\ \sf\longmapsto 3(4x-5)[/tex]
Done
Write an equation in slope-intercept form for the line with slope 3 and y-intercept "-7." Then graph the line.
Answer:
The equation of a straight line is always [tex]y=mx+b[/tex], where m is a constant which is the slope and b is a constant which is the y-intercept.
Substitute these values in:
[tex]y=3x-7[/tex]
The graph would look like the image attached.
3. One leg of a right triangle measures 10 inches while the other leg measures 21 inches. What is the length of the hypotenuse?
A) c = 9in
B) c = 11in
C) c = 12in
D) c = 7in
4. If the length of the hypotenuse is 10m and its base leg is 6m, what is the length of its remaining leg?
A) a = 8m
B) a = 9m
C) a = 12m
D) a = 10m
5. The altitudes of a right triangle has a length of 32cm. It’s hypotenuse measures 9cm. How long is its base leg?
A) b = 5cm
B) b = 7cm
C) b = 6cm
D) b = 9cm
6. Ben pushes a stick in the ground next to a flag pole so that its measure from the ground is 1 foot. The stick casts a shadow of 4 feet while the flag pole casts a parallel shadow of 60 feet. How tall is the
Step-by-step explanation:
Pythagoras formula for the relation of the side lengths in a right-angled triangle :
c² = a² + b²
c is the Hypotenuse, the side opposite of the 90 degree angle.
a and b are the "legs".
3.
c² = 10² + 21² = 100 + 441 = 541
c = sqrt(541) = 23.2594066...in
so, none of the provided answers. are you sure you put the right numbers ? maybe the second leg is sqrt(21) instead of 21 ? because then it would be
c² = 10² + sqrt(21)² = 100 + 21 = 121
c = 11in
4.
10² = a² + 6²
100 = a² + 36
64 = a²
a = 8 m
5.
again, there must be something wrong. the height of the triangle cannot be longer than the legs of the triangle.
given the answer options of 5 - 9 cm it cannot be 32cm. maybe you mean 3.2 cm ?
also interesting that it says "attitudes" - plural. what do you mean by that ?
because there is something else missing. like how long are the segments of the Hypotenuse where the height (or altitude) is touching the Hypotenuse ?
with just the Hypotenuse length and the height length we cannot calculate the other parts of the triangle, because we can move the height freely along the Hypotenuse and draw fitting right-angled triangles on that "skeleton".
6.
similar triangles. that means the lengths of corresponding lines (like sides or heights) are all in relation with the same scaling factor.
so, the small triangle has its "height" side of 1 ft, and multiplying with the scaling factor would then give us the height of the flag pole.
what is the scaling factor ? we get that from the pair of corresponding sides we already know : the shadows.
going from the small to the large triangle we have to transform 4ft into 60ft.
what do I have to multiply 4 with to get 60 ?
4 × x = 60
x = 60/4 = 15
so, the flag pole is
15×1 = 15ft tall.
Explain why the square root of a number or variable can be either positive or negative.
Answer:
Well, the answer is: it depends on what was printed in the problem. The principal square root symbol never has a negative output, so if the test maker printed that symbol, it’s restrictions have to be respected: all square roots then are positive.
Step-by-step explanation:
a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. For example, 4 and −4 are square roots of 16, because 4² = (−4)² = 16. Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √(x), where the symbol √( ) is called the radical sign or radix.
Answer/Step-by-step explanation:
The square root could be positive or negative because multiplying two negative numbers gives a positive number. The principal square root is the nonnegative number that when multiplied by itself equals a. The square root obtained using a calculator is the principal square root.
Write an equation of the line that passes through the pair of points.
(-5,-4), (5,-3)
Step-by-step explanation:
the most common form of line equation is
y = ax + b
a is the slope of the line. it is expressed as the ratio
y coordinate change / x coordinate change
when going from one point to the other.
b is the y-intercept (the y value when x = 0).
once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and since for b.
for the slope a :
x changes by +10 (from -5 to 5)
y changes by +1 (from -4 to -3)
the slope is +1/+10 = 1/10
the equation looks now like
y = (1/10)x + b
let's use the first point.
-4 = (1/10)×-5 + b = -1/2 + b
-3 1/2 = -7/2 = b
the equation is
y = (1/10)x - 7/2
so, the second answer option is correct.
Of the 120 apartments in a building, 75 have been scheduled to receive new carpet. What fraction of the apartments have not been scheduled to receive new carpet?
1/4
3/8
5/8
3/4
Answer:
3/8
Step-by-step explanation:
Well, let's start out by figuring out how many apartments have not been scheduled to receive new carpet. We know that 75 have been scheduled and that there are 120 total apartments, so the number of apartments that have not been scheduled is 120 - 75 or 45.
Now, we need to find the fraction of apartments that have not been scheduled to receive new carpet. To do this, we divide the number of apartments that have not been scheduled to receive new carpet by the total number of apartments:
[tex]\frac{45}{120}[/tex]
We can divide both sides by a common factor of 15 to find the simplified fraction and determine our answer.
[tex]\frac{45}{120} /\frac{15}{15} =\frac{3}{8}[/tex]
So, 3/8 of the apartments have not been scheduled to receive new carpet.
tell the number of decimal places that will be in the product
1. 6.3×0.75=___
2. 9.7×48.8=____
3. 5.96×62.15=___
4. 37.6×8.3=____
Answer:
3242Step-by-step explanation:
The number of decimal places in the product is the sum of the numbers of decimal places in the factors.
1. the factors have 1 and 2 decimal places, so the product will have 1+2 = 3 decimal places.
2. 1 + 1 = 2 decimal places in the product
3. 2 + 2 = 4 decimal places in the product
4. 1 + 1 = 2 decimal places in the product
_____
Additional comment
If the factor has m decimal places, the place value of its least-significant digit is 10^-m. Similarly, if the factor has n decimal places, the place value of its least-significant digit is 10^-n. When these numbers are multiplied, the place value of the least-significant digit of the product is (10^-m)(10^-n) = 10^-(m+n). That is, there will be m+n decimal places in the product.
Note that the product in problem 3 is 370.4140. That is, the least-significant digit of the product is zero. Many calculators will not show that zero, giving the (false) impression that the product has only 3 decimal places.
Answer:
4.725
2.473.6
3.370.414
5.312.08
Step-by-step explanation: