The cost of a t shirt at a department store is 7.50 Darnell bought x tshirts as well as a pair of jeans that cost 24 write a function to model the amount of the money Darnell spent
Answer:7.50(x) + 24 is the answer
Step-by-step explanation:
Andy buys x cakes. Betty buys 4 times as many cakes as Andy. Colin buys 3 more cakes than Andy. Each cake costs 65p. The total cost of the cakes is ?52.65. How many cakes did each person buy?
Answer:
Andy bought = 13 cakes.
Betty bought = 52 cakes.
Colin bought = 16 cakes.
Step-by-step explanation:
We are told that Andy buys x cakes. Betty buys 4 times as many cakes as Andy. So number of cakes bought by Betty will be 4*x.
We are also told that Colin buys 3 more cakes than Andy. So number of cakes bought by Colin will be x+3 cakes.
Each cake costs 65 p. The total cost of the cakes is $52.65. We can represent this information as:
[tex]0.65(x+4*x+x+3)=52.65[/tex]
[tex]0.65(2x+4*x+3)=52.65[/tex]
[tex]1.3x+2.6x+1.95=52.65[/tex]
Let us combine like terms.
[tex](1.3+2.6)x+1.95=52.65[/tex]
[tex]3.9x+1.95=52.65[/tex]
[tex]3.9x=52.65-1.95[/tex]
[tex]3.9x=50.7[/tex]
[tex]x=13[/tex]
Therefore, Andy bought 13 cakes.
Let us find number of cakes bought by Betty by substituting x=13 in expression 4*x.
[tex]\text{Cakes bought by Betty}=4*13[/tex]
[tex]\text{Cakes bought by Betty}=52[/tex]
Therefore, Betty bought 52 cakes.
Now we will find number of cakes bought by Colin by substituting x=13 in expression x+3.
[tex]\text{Cakes bought by Colin}=13+3[/tex]
[tex]\text{Cakes bought by Colin}=16[/tex]
Therefore, Colin bought 16 cakes.
Andy bought 13 cakes, Betty bought 52 cakes, and Colin bought 16 cakes.
Explanation:Let's break down the given information and solve the problem step by step:
Let the number of cakes bought by Andy be x.
Betty buys 4 times as many cakes as Andy, so she buys 4x cakes.
Colin buys 3 more cakes than Andy, so he buys (x+3) cakes.
The total cost of the cakes is €52.65, and each cake costs 65p.
Now, we can create the equation to find the value of x:
x*(65p) + 4x*(65p) + (x+3)*(65p) = £52.65
Simplifying the equation:
65x + 260x + 65x + 195 = 5265
390x + 195 = 5265
390x = 5070
x = 13
So, Andy bought 13 cakes, Betty bought 4x13 = 52 cakes, and Colin bought (13+3) = 16 cakes.
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Which lines have slope -4/5 and contain point (0,1)?
Identify the perimeter and area of a square with diagonal length 11in. Give your answer in simplest radical form. HELP PLEASE!!
Answer:
Perimeter = 22*sqrt(2)Area = 60.5 inchesDStep-by-step explanation:
Remark
You need 2 facts.
A square has 4 equal sides. It contains (by definition) 1 right angle but since we are not including and statement about parallel sides, it needs 4 right angles.That means you can use the Pythagorean Theorem.
If one side of a square is a then the 1 after it is a as well.
Formula
a^2 + a^2 = c^22a^2 = c^2Givens
c = 11Solution
2a^2 = 11^22a^2 = 121 Divide by 2a^2 = 121/2 Take the square root of both sidessqrt(a^2) = sqr(121/2) a = 11/sqrt(2) Rationalize the denominatora = 11 * sqrt(2)/[sqrt(2) * sqrt(2)]a = 11 * sqrt(2) / 2Perimeter
P = 4s
P = 4*11*sqrt(2)/2P = 44*sqrt(2)/2P = 22*sqrt(2)You don't need the area. The answer is D
Area
Area = s^2Area = (11*sqrt(2)/2 ) ^2Area = 121 * 2 / 4Area = 60.5For a square with a diagonal length of 11in, the side length is 11√2/2. The area of the square is then 60.5 square inches and the perimeter is 22√2 inches.
Explanation:To find the perimeter and area of a square with a given diagonal length, we need to firstly understand the relation between the diagonal and sides of the square. A square's diagonal divides it into two equal right triangles, and according to Pythagoras' theorem, the diagonal, being the hypotenuse in these right triangles, is equal to the square root of the sum of the squares of the sides. But since all sides of a square are equal, let's say the side length is 'a', then the diagonal would be 'a√2'.
Given that the diagonal length is 11in, we then have:
11 = a√2 or a = 11/√2
It's common to rationalize the denominator which gives: a = 11√2/2
Area of a square is a², therefore, Area = (11√2/2)² = 121/2 = 60.5 square inches.
The Perimeter of a square is 4a, therefore, Perimeter = 4 * (11√2/2) = 22√2 inches.
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Ludovica creates flash cards for her vocabulary words.She creates 3 more cards per noun.
Answer: what is the whole question angel?
Step-by-step explanation:
Caitlin went to the store to buy school clothes .She had a store credit from from a previous return in the amount of $39.58 if she bought 4 of the same style shirt in different colors and spent atotal of $52.22 after the store credit was taken off her total, what was the price of each shirt she bought?
Answer:
Each shirt costs $22.95
Step-by-step explanation:
39.58 + 52.22 = 91.80
91.80/4 = 22.95
Help me please!!Algebra Two!!
Answer:
a) -4 mult. 2
b) [tex](x+4)^2[/tex]
c) 2, quadratic
Step-by-Step Explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity.Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial.The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.In this graph, there is one real zero: -4
We can write them in intercept or factored form as (x+4) since x+4=0 gives x=-4.
Because the graph never crosses the x-axis it has an even multiplicity of at least 2.
The graph is facing up and is a U shape. This can only be a quadratic of degree 2. It is positive.
This means the function has a degree of 2.
A parking garage has 6 levels.Each level has 15 rows.Each row has the same number as parking spaces.There are 2,250 parking spaces in all.How many parking spaces are in each row?
Answer:25 spaces in a row
Step-by-step explanation: Multiply 6 levels by 15 rows. Answer is 90.
Divide 90 into 2,250 parking spaces.
Answer is 25 spaces in each row.
Solve.
{5x+y=2
{4x+y=4
Use the linear combination method.
(1, −8)
(0, 2)
(−2, 12)
(−3, 17)
Given these two equations:
1) 5x + y = 2
2) 4x + y = 4
Let's solve for x and y step by step.
Step 1: We start by subtracting equation (2) from equation (1) to eliminate y:
This gives us:
5x - 4x = 2 - 4
Which simplifies to:
x = -2
Step 2: Now, we substitute x = -2 into the equation (1) to find the value of y:
5*(-2) + y = 2
Which simplifies to:
-10 + y = 2
And therefore:
y = 12
So, the solution to the system of equations is x = -2 and y = 12.
Does anyone know this
A. 5.831 m
B. 16.552 m
C. 2.828 m
D. 13.267 m
Answer:
D. 13.267 m
Step-by-step explanation:
We can use the Pythagorean theorem to solve this problem
a^2 + b^2 = c^2
where a and b are the legs and c is the hypotenuse
7^2 + b^2 = 15^2
49 + b^2 = 225
Subtract 49 from each side
b^2 = 225-49
b^2 =176
Take the square root of each side
sqrt(b^2) = sqrt(176)
b = sqrt(176)
b = 13.266
Two angles are supplementary. The measure of one angle is 4 times the measure of the other angle. What is the measure of the smaller angle
The measure of the smaller angle, when it is one-fourth the measure of the other supplementary angle, is 36 degrees.
The student is asking about the measures of two supplementary angles where one angle is four times the measure of the other angle. In Mathematics, supplementary angles are two angles whose sum is 180 degrees. Let's call the smaller angle 'x' and the larger angle '4x'. The equation we need to solve is:
x + 4x = 180
This equation simplifies to '5x = 180', meaning that 'x', the smaller angle, is equal to '180 / 5', which calculates to be 36 degrees. Therefore, the measure of the smaller angle is 36 degrees.
The number of orange fish is 1 1/4 times the number of blue fish. How many blue fish for every five orange fish
Janice bought juice packets for the 15 players on the soccer team The juice packets come in boxes of 6 How many boxes did Janice buy?
Answer:
3 boxes.
Step-by-step explanation:
We are told that Janice bought juice packets for the 15 players on the soccer team. The juice packets come in boxes of 6.
To find the number of boxes that Janice need to buy for 25 players, we will divide 15 by 6.
[tex]\text{Number of boxes that Janice needs to buy}=\frac{15}{6}[/tex]
[tex]\text{Number of boxes that Janice needs to buy}=2.5[/tex]
Since the juice packets come in boxes of 6, so we will round our answer to nearest whole number.
[tex]\text{Number of boxes that Janice needs to buy}=2.5\approx 3[/tex]
Therefore, Janice will buy 3 boxes of juice packets for 15 players.
The question entails a simple division operation of 15 players divided by 6 juice packets per box which gives 2.5. However, since Janice can't buy half a box, she ends up buying 3 boxes of juice packets.
Explanation:To answer your question, we need to perform a simple division arithmetic operation. This involves taking the total number of players which is 15 and dividing that by the number of juice packets in one box, which is 6 . The calculation is as follows: 15 ÷ 6 = 2.5. However, Janice cannot purchase half of a box so she would need to round up to the nearest whole number. Hence, Janice bought 3 boxes of juice packets for the soccer team.
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**BRAINLIEST AVAILABLE****
PLEASE HELP ME WITH THIS!!!
Answer:
E.
Step-by-step explanation:
Even though we have a sample of 40 units, we cannot determine that the units that are not in the sample will have the same or similar quality as the units that are in the sample. Thus none of the conclusions can be true.
Answer: Choice B) 100 pieces must be defective
Assuming the sample selected is representative of the population, we have two copies of "25" in that list (row 4; row 8) out of 40 total. So 2/40 = 1/20 = 0.05 = 5% of the items should be defective out of the entire population. Again this is assuming the sample is representative.
So we take 5% of 2000 and we end up with 0.05*2000 = 100 items we expect to be defective from a sample of 2000 items. Keep in mind that the true count will probably not be 100 items but some value close around it (eg: 98 or 101). This value is an estimate and not always perfect.
If choice B said "around 100" or "about 100" or "approximately 100" then I think it would be more technically correct. I think this is what your teacher is after.
Plz help on 36, with work if any
Answer:
A. (10,1)
Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
What is the remainder when you divide 4x^3 - 5x^2 + 3x - 1 by x - 2?
Answer: D
Step-by-step explanation:
x - 2 = 0 --> x = 2
Using synthetic division:
2 | 4 -5 3 -1
| ↓ 8 6 18
4 3 9 17 ← this is the remainder!
Using remainder theorem:
f(x) = 4x³ - 5x² + 3x - 1
f(2) = 4(2)³ - 5(2)² + 3(2) - 1
= 32 - 20 + 6 - 1
= 17
Exponential functions exhibit exponential growth (or decay). What does this mean to the graphs of these functions?
Answer:
Option a is correct.
Exponential functions exhibit exponential growth (or decay) which mean the graph will rise or fall more dramatically than a polynomial graph
Step-by-step explanation:
An exponential function is in the form of [tex]y =ab^x[/tex] where a≠0 is a y-intercepts and b is a positive number other than 1, multiplier this base is constant , x is the independent variable and y is the dependent variable.
Exponential growth:
If b > 1 when x increases, y increases at a increasing rate .Exponential decay:
if b is between 0 and 1 i.e, 0 <b< 1 when x increases, y decreases at a increasing rate .therefore, the graph will rise or fall more dramatically than a polynomial graph
630 baseball cards he sorts the cards into stacks of 30 how many stacks can he makes
Answer:21
Step-by-step explanation:
Answer:
21 stacks of 30
Step-by-step explanation:
630 divided into 30 stacks:
630/30= 21
If sin theta = -3/5 and q terminates in the fourth quadrant, find the exact value of tan2q.
A: -7/24
B:-24/7
C:-9/25
D:-25/9
[tex]\sin^2q+\cos^2q=1\to \cos^2q=1-\sin^2q\to\cos q=\pm\sqrt{1-\sin^2q}\\\\q\ \text{terminates in the fourth quadrant, therefore}\ \cos q > 0.\\\\\sin q=-\dfrac{3}{5}\to\cos q=\sqrt{1-\left(-\dfrac{3}{5}\right)^2}\\\\\cos q=\sqrt{1-\dfrac{9}{25}}\\\\\cos q=\sqrt{\dfrac{25}{25}-\dfrac{9}{25}}\\\\\cos q=\sqrt{\dfrac{16}{25}}\\\\\cos q=\dfrac{4}{5}[/tex]
[tex]\tan q=\dfrac{\sin q}{\cos q}\\\\\sin2q=2\sin q\cos q\\\\\cos2q=\cos^2q-\sin^2q\\\\\text{therefore}\\\\\tan2q=\dfrac{\sin2q}{\cos2q}=\dfrac{2\sin q\cos q}{\cos^2q-\sin^2q}\\\\\text{substitute}\\\\\tan2q=\dfrac{2\left(-\dfrac{3}{5}\right)\left(\dfrac{4}{5}\right)}{\left(\dfrac{4}{5}\right)^2-\left(-\dfrac{3}{5}\right)^2}=\dfrac{-\dfrac{24}{25}}{\dfrac{16}{25}-\dfrac{9}{25}}=\dfrac{-\dfrac{24}{25}}{\dfrac{7}{25}}=-\dfrac{24}{25}\cdot\dfrac{25}{7}=-\dfrac{24}{7}[/tex]
[tex]Answer:\ \boxed{B:\ -\dfrac{24}{7}}[/tex]
The exact value of tan 2θ will be –24/7. Then the correct option is B.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
If sin θ = -3/5.
Then the value of cos θ will be
cos² θ = 1 – sin² θ
cos² θ = 1 – (-3/5)²
cos² θ = 1 – 9/25
cos² θ = 16/25
cos θ = 4/5
Then the value of tan 2θ will be
[tex]\tan 2\theta = \dfrac{\sin 2\theta }{ \cos 2\theta}\\\\\\\tan 2\theta = \dfrac{2 \sin \theta \cos \theta }{ \cos^2 \theta - \sin ^2 \theta}\\\\\\\tan 2\theta = \dfrac{2 * \frac{-3}{5} * \frac{4}{5} }{( \frac{4}{5})^2 - ( \frac{-3}{5}) ^2 }[/tex]
Simplify the equation, we have
tan 2θ = (–24/25) / (7/25)
tan 2θ = –24/7
Then the correct option is B.
More about the trigonometry link is given below.
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Translate the phrase into a variable expression. Use the letter b to name the variable. If necessary, use the asterisk ( * ) for multiplication and the slash ( / ) for division. ... The number of books in the library minus the 60 checked out
Answer:
b - 60
Step-by-step explanation:
Let the number of books in the library be b.
The number of books in the library minus the 60 checked out is translated into a variable expression as b - 60
Answer:
[tex]b-60[/tex]
Step-by-step explanation:
We are given that the number of books in the library minus the 60
We have to translate the phrase into a variable expression.
We are given that a letter ''b'' is used for the number of books in the library.
Number of books in the library=b
According to question
[tex]b-60[/tex]
Hence, the required expression is given by
[tex]b-60[/tex]
check my answer? am i correct?
simplify the expression.
(16y^5/4y^3)^1/2
i think it is 2y
For the expression (16y^5/4y^3)^12, you need to simplify the fraction inside the parentheses and then apply the square root to the simplified fraction. The final result is 2y.
The simplification of the expression (16y^5/4y^3)^12 into steps.
Simplify the fraction inside the parentheses:
16y5/4y3
=4y2
Apply the square root to the simplified fraction:
(4y2)12
=2y
By taking the square root, we reduce the exponent by half.
Therefore, the simplified expression is 2y.
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students a. Find the standard error of the mean b. What is the probability that the sample mean exceeds the population mean by more than 2 hours? c. What is the probability that the sample mean is more than 3 hours below the population mean? d. What is the probability that the sample mean differs from the population mean (on either side) by more than 4 hours? e. Suppose that a second (independent) random sample of ten students was taken. Without doing the calculations, state whether the probabilities in b, c, and d would be higher, lower, or the same for the second sample.
The sample mean X¯
X
¯
has normal distribution, mean the population mean μ
μ
, and standard deviation τ=84√
τ
=
8
4
. We want Pr(X¯−μ>2)
Pr
(
X
¯
−
μ
>
2
)
, which is Pr(Z>2τ)
Pr
(
Z
>
2
τ
)
, where Z
Z
is standard normal.
A certain corporation listed their sales in 100s as 20700. What was their actual volume in millions?
Answer: Their actual volume in millions is 207×10⁹.
Step-by-step explanation:
Since we have given that
A certain corporation listed their sales in 100s as 20700
We need to find their actual volume in millions,
According to question,
In 100s, their volume = 2070000
In 100000, their volume is given by
[tex]207\times 10^5\\\\=2070000\times 10^5=207\times 10^9[/tex]
Hence, their actual volume in millions is 207×10⁹.
Factor completely. 3x^2-3x-18 HINT: Factor out the greatest common factor first.
Answer:
3(x - 3)(x + 2)
Step-by-step explanation:
take out a common factor of 3 from each term
= 3(x² - x - 6)
to factor the quadratic consider the factors of - 6 which sum to - 1
These are - 3 and + 2, hence
3x² - 3x - 18 = 3(x - 3)(x + 2) ← in factored form
At the newest animated movie, for every 99 9 children, there are 44 4 adults. There are a total of 3939 39 children and adults at the movie. How many children are at the movie?
Answer:
27 children.
Step-by-step explanation:
We are told that at the newest animated movie, for every 9 children, there are 4 adults. There are a total of 39 children and adults at the movie.
We can see that number of children is proportional to number of adults. So we will use proportions to solve for number of children at the movie.
[tex]\frac{\text{Number of children}}{\text{Number of children + Adults}}=\frac{9}{4+9}[/tex]
[tex]\frac{\text{Number of children}}{\text{Number of children + Adults}}=\frac{9}{13}[/tex]
Let us substitute number of children and adults in our proportion.
[tex]\frac{\text{Number of children}}{39}=\frac{9}{13}[/tex]
Multiply both side of equation by 39.
[tex]39*\frac{\text{Number of children}}{39}=39*\frac{9}{13}[/tex]
[tex]\text{Number of children}=39*\frac{9}{13}[/tex]
[tex]\text{Number of children}=3*9[/tex]
[tex]\text{Number of children}=27[/tex]
Therefore, 27 children are at the movie.
You are given two triangles. On the first triangle side GH = 3 and side IG = 5. On the second triangle side JK = 3 and side LJ = 5. What side corresponds to side HI and can be used to show that ?GHI ? ?JKL by SSS? (Enter your answer using letters only) (5 points)
Answer:KL
Step-by-step explanation:
Help me with these math questions....
Answer: cotθ
Step-by-step explanation:
tanθ * cos²θ * csc²θ
= [tex]\dfrac{sin\theta}{cos\theta} * \dfrac{cos\theta*cos\theta}{} *\dfrac{1}{sin\theta*sin\theta}[/tex]
= [tex]\dfrac{cos\theta}{sin\theta}[/tex]
= cotθ
Answer: B
Step-by-step explanation:
The parent graph is y = x²
The new graph y = -x² + 3 should have the following:
reflection over the x-axisvertical shift up 3 unitsAnswers:
a. Quadrant IIb. negativec. [tex]\dfrac{\pi}{6}[/tex]d. Ce.[tex]-\dfrac{\sqrt{3}}{3}[/tex]Explanation:
[tex]\dfrac{17\pi}{6} - \dfrac{12\pi}{6} = \dfrac{5\pi}{6}[/tex]
a) Quadrant 2 is: [tex]\dfrac{\pi}{2} < \theta < \pi[/tex]
b) In Quadrant 2, cos is negative and sin is positive, so tan is negative
c) [tex]\pi-\dfrac{5\pi}{6}[/tex] = [tex]\dfrac{\pi}{6}[/tex]
d) the reference line is above the x-axis so it is negative --> [tex]-tan\dfrac{\pi}{6}[/tex]
e) [tex]tan(\dfrac{5\pi}{6})=\dfrac{1}{-\sqrt{3}}=-\dfrac{\sqrt{3}}{3}[/tex]
PLEASE CAN SOMEONE HELP ME WITH THIS QUESTION
Answer:
see below
Step-by-step explanation:
(a) this is in the second quadrant.
(b) The tangent is negative in this quadrant
(c)
17 pi / 6 = 2 5pi/6
= 5pi/6 (this is the reference angle)
(d) this is equivalent to -tan (pi/6)
(e)
tan 17pi/6
= tan 5pi/6
-√3/3
The table show the total distance d, in miles, a car traveled after t hours. Time in hours (h) Distance in miles (d) 0 0 1 50 2 100 3 150 Which equation shows the relationship between d and t? d=t+50 d=50t d=t+150 d=150t
answer is d=50t
am i right
Answer:
yes you are right
Step-by-step explanation:
d=50t
Answer:
Yes. It is :
D=50t
Step-by-step explanation:
What is the linear function equation that is represented in the graph?
Answer: y = (-1/2)*x + 1
Step-by-step explanation:
In the graph we can see a linear equation, the first thing we know is that a linear equation has the shape of:
y = ax + b
first, to find the slope we can use two pairs of the graphed ones, in the notation (x,y) we can select the pairs: (0, 1) and (2, 0)
we have that a = (y2 - y1)/(x2 - x1)
a = (0 - 1)/(2- 0 ) = -1/2
so the slope is -1/2
now, b is the y-intercept, this is the value of y when x = 0, and we can see that this value is 1 (the point where the graph intercepts the y-axis) so b = 1.
then the equation is y = (-1/2)*x + 1