Answer:
complementary angles 25
In a café, I order a cup of tea and a piece of cake and it costs £1.10. The next time I order 2 cups of tea and one piece of cake and it costs £1.70. Find the cost of a piece of cake.
Answer:
£0.50
Step-by-step explanation:
t = one cup of tea
c = one piece of cake
t + c = £1.10
2t + c = £1.70
the cost increases by £0.60 (£1.70 - £1.10) when you order one more cup of tea which means that one cup of tea costs £0.60
substitute £0.60 into t + c = £1.10
£0.60 + c = £1.10
rearrange to get c = £1.10 - £0.60 = £0.50
so one piece of cake costs £0.50
Help me fast plz plz help
Answer:
5/8
Step-by-step explanation:
Add the two fractions
3/8 + 1/4
Get a common denominator
3/8 + 1/4 *2/2
3/8 + 2/8
5/8
Clifford is paid $4.25 per hour plus time and a half on holidays and makes an average of 21% tips on his food sales as a server at the local seafood restaurant. This is modeled by the expression 4.25(x) + 4.25(1.5)(y) + 0.21(z). What is Clifford's gross pay if he worked 15 regular hours and 7 holiday hours and had $1,345 in food sales? (2 points)
$356.83
$390.83
$422.70
In AABC, mZA = 32°, mZB = 25°, and a = 18. Find c to the nearest tenth.
Answer:
Step-by-step explanation:
Describe the translation y= (x-2) squared +5 -> y = (x+2) squared - 3
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Answer:
A. T<-4, -8>
Step-by-step explanation:
To get the second equation, we had to replace x with x+4 (a translation left 4) and we had to add -8 to the function value (a translation down 8).
Left 4 and down 8 is the translation ...
T<-4, -8>
When Asia was young, her father marked her height on the door frame every month. He noticed that between the ages of one and three, he could predict her height (in inches) by taking her age in months, adding 75 inches, and multiplying the result by one-third.
Create an equation linking her predicted height, h, with her age in months, m.
[tex]The \: text \: tells \: us \: that \: we \: can \\ predict \: her \: height \: by \: taking \\ her \: age \: in \: months, \: adding \: 75, \\ and \: multiplying \: by \: \frac{1}{3} . \: So \: our \\ equation \: is [/tex]
[tex]h = (m + 75). \frac{1}{3} [/tex]
(or)
[tex]h = \frac{1}{3} (m + 75)[/tex]
b) Determine her predicted height on her second birthday
To predict Asia’s height on her second birthday, we substitute m=24
into our equation (because 2 years is 24 months) and solve for h.
[tex]h = \frac{1}{3} (24 + 75)[/tex]
[tex]h = \frac{1}{3} (99)[/tex]
[tex]h = 33[/tex]
Asia’s height on her second birthday was predicted to be 33 inches.
A children's rectangular pool holds 480 cubic feet of water. What is the depth of the pool of its length is 30 feet and it's width is 16 feet
Answer:
1 ft
Step-by-step explanation:
1, 480/30=16
2, 16/16=1
3, 1 ft
Find the radius of a circle with a diameter of 14 cm
Answer:
r = 7 cm
Step-by-step explanation:
The radius is 1/2 of the diameter
r = d/2
r =14/2
r = 7 cm
Which could be a binomial expansion of (4x + y)?
16x2 + xy + y2
16x2 + 4xy + y2
O 64x3 + 16x2y + 5xy2 + y3
64x3 + 48x2y + 12xy2 + y3
+
Answer: D
Step-by-step explanation:
[tex](4x+y)^3\\\\=(4x)^3+3*(4x)^2*y+3*(4x)*y^2+y^3\\\\=64x^3+48x^2y+12xy^2+y^3\\\\Answer\ D[/tex]
Answer:
D
Step-by-step explanation:
Car drove 2hours at a speed of 100km per hour & 3 hour at a speed of 50 km per hour . What was the average speed of the car during the trip?
Answer:
200 kilometers and 150 kilometers
A ball is kicked from the ground. At 1 second it is 3 m off the ground. At 2 seconds it is 12 m off the ground, at 3 seconds it is 27 m off the ground After 3 bounces, how high is the ball
Answer:
the correct answer is 3 m............
Let f(x) = 12/4x+2 Find f(-1). (1 point)
Answer:
-1
Step-by-step explanation:
let,x=-1
f(x)= 12/4x + 2
f(-1)= 12/4x(-1) + 2
=12/(-4) +2
= -3+2
= -1
Find the slope of the line that contains (4, -6) and (4, 4)
Answer:
Undefined
Step-by-step explanation:
Slope formula = [tex]\frac{y_{2}-y_{1}}{y_{2}-y_{1}}[/tex]
[tex]\frac{4-(-6)}{4-4}[/tex]
[tex]\frac{10}{0}[/tex]
A number can not have a denominator of 0, therefore making the slope undefined.
Answer:
Undefined.
Step-by-step explanation:
Use the slope formula: [tex]\frac{y_1-y_2}{x_1-x_2}[/tex]
[tex]m=\frac{-6-4}{4-4}=\frac{-10}{0}=[/tex] Undefined
what is a cell and atom
Step-by-step explanation:
An atom is a chemical unit. It is the smallest particle of a chemical element. A cell is a biological unit. It is the smallest unit of any living beings. A cell is composed of molecules, and molecules are composed of atoms
The scale on a map is
1:25 000
(a) On a map, a distance
measures 5cm. What is this
in real life? Give your
answer in kilometres.
(b) In real life a distance is
2.2km. What would this be in
the map in centimetres?
Answer:
Step-by-step explanation:
a) 5 cm(25000)(1 m/100 cm)(1 km/1000 m) = 1.25 km
b) 2.2 km (1000 m/km)(100 cm/m) / 25000 = 8.8 cm
Which of the following is a valld conclusion for the quadratic equation?
x2 - 6x+8=0
OX-3 = 0 and x+ 5 = 0
Ox+ 4 = 0 and x + 2 = 0
O x-4 = 0 and x + 2 = 0
O x-4 = 0 and x - 2 = 0
Answer:
[tex]x-4=0\: and\: x-2=0[/tex]
Step-by-step explanation:
[tex]x^{2} -6x+8-0[/tex]
[tex]x^{2} -4x-2x+8-0[/tex]
[tex]x(x-4)-2(x-4)=0[/tex]
[tex](x-4)(x-2)=0[/tex]
[tex]x-4=0[/tex] and [tex]x-2=0[/tex]
----------------------
OAmalOHopeO
-----------------------
The valid conclusions for the quadratic equation x² - 6x + 8 = 0 are:
x - 4 = 0 and x - 2 = 0
Option D is the correct answer.
We have,
Quadratic equation x² - 6x + 8 = 0.
Now,
To solve the quadratic equation x² - 6x + 8 = 0, we can use the quadratic formula, which states that:
x = (-b ± √(b² - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation.
In this case,
a = 1, b = -6, and c = 8.
Substituting these values into the quadratic formula, we get:
x = (-(-6) ± √((-6)² - 4(1)(8))) / (2(1))
x = (6 ± √(36 - 32)) / 2
x = (6 ± √(4)) / 2
x = (6 + 2) / 2 or x = (6 - 2) / 2
x = 4 or x = 2
Therefore,
The valid conclusions for the quadratic equation x² - 6x + 8 = 0 are:
x - 4 = 0 and x - 2 = 0
because the roots of the equation are x = 4 and x = 2,
which can be written in factored form as (x - 4)(x - 2) = 0.
Learn more about quadratic equations here:
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Proceed as in Example 4 in Section 6.1 and find a power series solution y = [infinity] n = 0 cnxn of the given linear first-order differential equation. (Give your answer in terms of c0.) y' = xy
Let y be a solution to the given differential equation,
[tex]y' = xy[/tex]
where
[tex]\displaystyle y = \sum_{n=0}^\infty c_n x^n \\\\ y' = \sum_{n=0}^\infty nc_nx^{n-1} = \sum_{n=1}^\infty nc_nx^{n-1} = \sum_{n=0}^\infty (n+1)c_{n+1}x^n[/tex]
Substituting these series into the DE gives
[tex]\displaystyle \sum_{n=0}^\infty (n+1)c_{n+1}x^n = x\sum_{n=0}^\infty c_nx^n \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=0}^\infty c_nx^{n+1} \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty \bigg((n+1)c_{n+1}-c_{n-1}\bigg)x^n = 0[/tex]
Then the coefficients [tex]c_n[/tex] in the series solution are governed by the recurrence,
[tex]\begin{cases}c_0 = c_0 \\ c_1 = 0 \\ (n+1)c_{n+1}-c_{n-1} = 0&\text{for }n\ge1\end{cases}[/tex]
We have
[tex](n+1)c_{n+1}-c_{n-1} = 0 \implies nc_n - c_{n-2} = 0 \implies c_n = \dfrac{c_{n-2}}n[/tex]
so it follows that [tex]c_1=c_3=c_5=\cdots = 0[/tex], while
[tex]c_0 = \dfrac{c_0}1 = \dfrac{c_0}{2^0\times0!} \\\\ c_2 = \dfrac{c_0}2 = \dfrac{c_0}{2^1\times1!}\\\\ c_4 = \dfrac{c_2}4 = \dfrac{c_0}{2\times4} = \dfrac{c_0}{2^2\times2!}\\\\ c_6 = \dfrac{c_4}6 = \dfrac{c_0}{2\times4\times6} = \dfrac{c_0}{2^3\times3!}[/tex]
and so on, with the general n-th coefficient being
[tex]c_n = \begin{cases}0&\text{if }n\text{ is odd} \\ \dfrac{c_0}{2^{n/2}\left(\frac n2\right)!} &\text{if }n\text{ is even}\end{cases}[/tex]
Then the power series solution is
[tex]\displaystyle y(x) = c_0 \sum_{n=0}^\infty \frac{x^n}{2^{n/2}\left(\frac n2\right)!} = c_0 \sum_{n=0}^\infty \frac1{\left(\frac n2\right)!} \left(\frac x{\sqrt2}\right)^n[/tex]
but this doesn't tell the whole story because it doesn't capture the odd-index-is-zero case.
More concisely: let n = 2k for integers k ≥ 0. Then
[tex]\displaystyle y(x) = c_0 \sum_{k=0}^\infty \frac{x^{2k}}{2^k k!} = c_0 \sum_{k=0}^\infty \frac1{k!} \left(\frac{x^2}2\right)^k[/tex]
and as a bonus, it's easier to get an exact solution for this DE,
[tex]y(x) = c_0e^{x^2/2}[/tex]
A radio telescope has a parabolic surface, as shown below. A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 9 meters and its width from left to right is 12 meters. If the telescope is 9 m deep and 12 m wide, how far is the focus from the vertex?
The telescope shape and the characteristic equations of the telescope parameters are the same as parabolic equations
The distance between the focus and the vertex, of the parabola is 3.375 meters
The process for obtain the above values is as follows:
The known parameters of the parabola are;
The location of the vertex of the parabola= The origin = (0, 0)
The height of the parabola = 9 meters
The width of the parabola = 12 meters
The unknown parameter;
The distance between the focus and the vertex
Method:
Finding the coordinate of the focus from the general equations of the the parameters of a parabola
The equation of the parabola in standard form is y = a·(x - h)² + k
From which we have;
(x - h)² = 4·p·(y - k)
The coordinates of the focus, f = (h, k + p)
Where;
(h, k) = The coordinates of the vertex of the parabola = (0, 0)
∴ a = 1/(4·p)
From the question, we have the following two points on the parabola,
given that the parabola is 12 meters wide at 9 meters above the origin and
it is symmetric about the y-axis;
Points on the parabola = (9, 6), and (9, -6)
Plugging in the values of the vertex, (h, k) and the two known points, in the equation, y = a·(x - h)² + k, we get;
6 = a·(9 - 0)² + 0 = 81·a
a = 6/81 = 2/27
p = 1/(4·a)
∴ p = 1/(4 × 2/27) = 27/8
The coordinate of the focus, f = (h, k + p)
∴ f = (0, 0 + 27/8) = (0, 27/8)
The coordinate of the focus f = (0, 27/8)
Given the vertex and the focus of the parabola have the same x-values of 0, we have;
The distance between the focus and the vertex, d = the difference in their y-values;
∴ d = 27/8 - 0 = 27/8 = 3.375
The distance between the focus and the vertex, d = 3.375 meters
Learn more about parabola here;
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HELP
F=3
J=-3
I=2
G=0
H=0
0(0(2(-3(3(1)))))=0
^^i think that is right but I need to show my work and explain
f is a function defined by
{(-3, 1), (-2, 2), (-1, -3), (0, -1), (1, 3), (2, -2), (3, 0)}
so f (1) = 3. Then
h (g (i (j (f (1))))) = h (g (i (j (3))))
j is defined by
{(-3, 0), (-2, 1), (-1, 2), (0, -1), (1, -2), (2, 3), (3, -3)}
so j (3) = -3, and
h (g (i (j (f (1))))) = h (g (i (-3)))
And so on. Next you have i (-3) = 2, then g (2) = 0, and finally, h (0) = 0, so your answer is correct.
Find the length of AB
Answer:
C. 44.98
Step-by-step explanation:
Hi there!
We are given the right triangle ABC, m<B=12°, and CB =44
We want to find the length of AB
We can use trigonometry to do it
Let's find the ratio in reference to angle B, as that angle is given.
In reference to angle B the opposite angle is AC, the adjacent side is CB, and the hypotenuse is AB
Now let's recall the 3 most commonly used functions:
[tex]sine=\frac{opposite}{hypoptenuse}[/tex]
[tex]cosine=\frac{adjacent}{hypotenuse}[/tex]
[tex]tangent=\frac{opposite}{adjacent}[/tex]
Let's find the cosine of angle B, as it uses CB and AB, which are the given side and the side we need to find
In that case,
cos(12)=[tex]\frac{CB}{AB}[/tex]
cos(12)=[tex]\frac{44}{AB}[/tex]
Multiply both sides by AB
[tex]AB[/tex]*cos(12)=44
Divide both sides by cos(12)
AB=[tex]\frac{44}{cos(12)}[/tex]
Now plug [tex]\frac{44}{cos(12)}[/tex] into your calculator. Make sure your calculator is on degree mode
AB≈44.98
So the answer is C
Hope this helps!
Kane's Furniture Store advertised a table at 9% discount. The original selling price was $109, and the sale price was $100. Was the sale price consistent with the ad? Explain.
Answer:
No, the sale price wasn't consistent with the ad
Step-by-step explanation:
The original selling price is 109. 9% of 109 is 9.81. So the sale price should be 99.19.
16.Brendan practiced soccer for 12 hours on Monday, 1 hours on
Tuesday, 14 hours on Wednesday, and hour on Thursday in
preparation for the game on Friday. How many total hours did
Brendan practice soccer in this week
Answer:
27
Step-by-step explanation:
A group of hikers is descending a mountain at a rate of 400 feet per hour. After three hours, what integer represents their total change in elevation?
I am not sure if it's -1200 (because it said descending)
Or if it's just 1200
Answer:
Bro it will be +1200
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
2. What is the solution to the equation 1/2x + 3/2(x+1) - 1/4=5
Answer:
1/2x + 3/2(x+1) - 1/4 = 5
1/2x + 3/2(x) + 3/2 - 1/4 = 5
1/2x + 3/2(x) + 6/4 - 1/4 = 5
4/2(x) + 5/4 = 5
2x + 5/4 = 5
2x = 15/4
x = 15/8
Let me know if this helps!
Answer:
x = 15/8
Step-by-step explanation:
1/2x + 3/2(x+1) - 1/4=5
1/2x + 3/2x + 3/2 - 1/4 = 5
2x + 5/4 = 5
2x = 15/4
x = 15/8
If Q(x) = x2 + 3x + 2, find Q(-4).
Q(x)=x^2+3x+2
[tex]\\ \sf\longmapsto Q(-4)[/tex]
[tex]\\ \sf\longmapsto (-4)^2+3(-4)+2[/tex]
[tex]\\ \sf\longmapsto 16+(-12)+2[/tex]
[tex]\\ \sf\longmapsto 16-12+2[/tex]
[tex]\\ \sf\longmapsto 4+2[/tex]
[tex]\\ \sf\longmapsto 6[/tex]
The value of the function at x = - 4 will be 6. Then the correct option is D.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The function is given below.
Q(x) = x² + 3x + 2
The value of the function at x = - 4, then we have
Q(-4) = (-4)² + 3(-4) + 2
Simplify the equation, then we have
Q(-4) = (-4)² + 3(-4) + 2
Q(-4) = 16 - 12 + 2
Q(-4) = 18 - 12
Q(-4) = 6
The value of the function at x = - 4 will be 6. Then the correct option is D.
More about the function link is given below.
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If x - A = B, what is X?
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Answer:
(a)
Step-by-step explanation:
Add A to both sides of the equation:
X -A +A = B +A
X = B + A
The sum of the two matrices is the matrix that is the sum of corresponding terms.
x11 = B11 +A11 = -9+2 = 7
x12= B12 +A12 = 5-7 = -2
These calculations are sufficient to match the answer with choice (a).
vector v has a horizontal vector component with magnitude 19 and a vertical vector component with magnitude 35. what is the acute angle theta formed by v and positive x-axis?
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Answer:
61.5°
Step-by-step explanation:
The tangent relation is useful here. The angle is opposite the vertical side and adjacent to the horizontal side of the right triangle.
Tan = Opposite/Adjacent
tan(α) = 35/19
α = arctan(35/19) ≈ 61.5°
The angle made by v and the positive x-axis is 61.5°.
13. Find the smallest number which when divided by 21,28,36 and 44 leaves a
remainder of 3 in each case?
Answer:
2775
Step-by-step explanation:
Well of course since the problem is not restricted, the smallest number is 3. I'm almost sure that's not what you mean. The next smallest number is 2775. I found that using a programing language. I'm sure as well that does not satisfy the question, either.
I think you are intended to do this by finding the lowest common multiple and adding 3.
21: 3 * 7
28: 2 * 2 * 7
36: 2 * 2 * 3 * 3
44: 2 * 2 * 11
LCM = 2 * 2 * 3 * 3 * 7 * 11 = 2772
Now add 3 and the number you want is 2775
In the Brady's Family, each girl has twice as many brothers as she has sisters.
However, each boy has the same number of brothers as sisters. Is this possible; and
if so how many girls are there in the family, and how many boys?
Answer:
3 girls and 4 boys
Step-by-step explanation:
Writing the number of girls in the family as g and the number of boys in the family as b,
we know that each girl has twice as many brothers as sisters. Therefore, the amount of boys in the family (b, or how many brothers each girl has) is twice the number of the amount of girls in the family (g) minus 1 (g-1) (subtract 1 because each girl's number of sisters does not include the girl herself). We can write this as
b = 2(g-1)
Next,
we know that each boy has the same amount of brothers as sisters. Therefore, the amount of boys in the family minus 1 (b-1, subtracting 1 because we don't include the boy that has the brothers) is equal to the amount of girls in the family (g). we can write this as
b-1 = g
Therefore, we have
b = 2(g-1)
b-1 = g
Plugging b-1 = g into the first equation, we get
b = 2 (g-1)
2(g-1) = 2((b-1) - 1) = b
= 2(b-1-1)
= 2(b-2)
= 2b-4
b = 2b-4
subtract 2b from both sides to make it so that only b values and their coefficients are on one side
-b = -4
multiply both sides by -1 to solve for b
b=4
Therefore, there are 4 boys in the family and b-1 = 4-1 = 3 girls in the family.
could anyone help me solve this? I’ve had several questions like this and I don’t understand how to solve it. I’ll give brainliest:)
Answer:
-2, - 1, - 2 and - 3
Step-by-step explanation:
As the graph depicts an odd function, it will follow the rule f(-x) = - f(x)
