Answer:
Step-by-step explanation:
We can set up two equations: one for each sister:
Let C and D be the prices for a Candy bag and and Drink.
Sister 1: 3C + 1D = 3.20 [The total spent by sister 1 is the sum of 3 candy bags(C) and 1 drink (D), which comes to $3.20.]
Sister 2: 2C + 4D = 6.30 [The total spent by sister 2 is the sum of 2 candy bags(C) and 4 drinks (D), which comes to $6.30.]
We have two unknowns, C and D, BUT we have 2 equations. Therefore, we're likely going to be able to solve for C and D if we rearrange one of the equations to isolate one of the unknowns, and then use that expression in the other equation. Seems unlikely, but it always works.
I'll pick Sister 1's equation and solve for D, the price of a drink:
3C + 1D = 3.20
1D = 3.20 - 3C [This tells us the price of a drink is 3.20 - 3C]
Use this definition of 1D in Sister 2's equation:
2C + 4D = 6.30
2C + 4(3.20 - 3C) = 6.30
2C + 12.80 - 12C = 6.30
-10C = - 6.5
C = $0.65
One candy bag, C, is $0.65.
Use this value of C in any equation to find D, the cost of 1 drink. I'll pick The expression we derived above:
1D = 3.20 - 3C
1D = 3.20 - 3(0.65)
1D = 3.20 - 1.95
1D = $1.25
One drink, D, is $1.25.
===================
Check the values:
Candy Bags = $0.65 each Drinks = $1.25 each
Reported
Sister 1 2 1 2
Candy bags 3 2 $1.95 $1.30
Drinks 1 4 $1.25 $5.00
$3.20 $6.30 Calculated
$3.20 $6.30 Reported
T
Find x.
A composite figure consisting of two right angled triangles lying next to each other. Two sides of the triangle on the left are labeled as 13 millimeters and 5 millimeters. Two sides of the triangle on the right are labeled as x and 35 millimeters.
The value of x is 28 millimeters in the composite figure of two right-angled triangles lying next to each other
What is a composite figure?A composite figure is a figure that is produced from the combination of two geometric shapes together.
The diagrammatic expression of a composite figure consists of two right-angled triangles lying next to each other can be seen in the image attached below.
For the left-side right-angled triangle, we have:
13² = h² + 5²
h² = 13² - 5²
h = √(169-25)
h = 12
Recall from the diagram that:
h² = pq
If p = 5 and q = x∴
12² = 5x
x = 144/5
x ≅ 28 millimeters
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What is the inequality shown?
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
Step-by-step explanation:
well it could be -10 < x < 10
or -9 ≤ x < 10
or -10 < x ≤ 9
or -9 ≤ x ≤ 9
What is the equivalent to a dash?
Answer:
a dash is 1/8 tsp.
Step-by-step explanation:
a dash is 1/8 tsp or called 0.13
find this expression in square form with process pls help me !!!!
Answer:
(p -3q )(p -3q )
Step-by-step explanation:
p'2 - 6pq + 9q'2
(p -3q )(p -3q )
find two values that add to give 6 and multiply to 9
p x p =p'2
-3q x p = -3pq -3 x pq = -3pq ...... -3pq - 3pq = -6pq
-3q x - 3q = 9q'2
Find the value of 8power of five
Answer:
the answer is 32,768 hopes this helps
Step-by-step explanation:
8^5 = 8x8x8x8x8 = 64x8x8x8= 64x64x8 = 4096x8= 32,768
In 8 years Jamie will be three times as old as she is now. How old is Jamie?
Answer:
x=4
Step-by-step explanation:
Based on the given conditions, formulate:
x+8=3×x
Rearrange unknown terms to the left side of the equation:
x-3x=-8
Combine like terms:-2x=-8
Divide both sides of the equation by the coefficient of variable:x=-8/-2
Rewrite the fraction:8/2
Cross out the common factor:x=4
get the result:x=4
Answer: 4
Which fraction is equal to 0.38?
A. 3/8
B. 3/11
C. 19/5
D. 19/50
Answer:
D. 19/50
Explanation:
Write 0.38 as
0.38/1
Multiply both numerator and denominator by 10 for every number after the decimal point
0.38 × 100
1 × 100
=
38/100
Reducing the fraction gives
19/50
For the complex number z = (5sqrt(3))/4 - 5/4 * i what is the polar form
The complex number in rectangular form z = (5√3 / 4) - i 5/4 is equivalent to the complex number in polar form z = 5/2 · (cos 11π/6 + i sin 11π/6). (Correct choice: C)
How to transform a complex number in rectangular form into polar formComplex numbers are elements of the form z = a + i b, where [tex]a, b \in \mathbb{R}[/tex]. In other words, represents a generalization from real numbers. The polar form of a complex number is shown below:
[tex]z = r\cdot (\cos \theta + i \,\sin \theta)[/tex] (1)
Where:
r - Normθ - Direction, in radians.The norm is determined by Pythagorean theorem and the direction by inverse trigonometric reason. If we know that z = (5√3 / 4) - i 5/4, then its polar form is shown below:
Norm
[tex]r = \sqrt{\left(\frac{5\sqrt{3}}{4} \right)^{2}+\left(-\frac{5}{4} \right)^{2}}[/tex]
r = 5/2
Direction
[tex]\theta = \tan^{-1} \left[\frac{\left(-\frac{5}{4} \right)}{\left(\frac{5\sqrt{3}}{4} \right)} \right][/tex]
θ = 11π/6 rad
Thus, the complex number in rectangular form z = (5√3 / 4) - i 5/4 is equivalent to the complex number in polar form z = 5/2 · (cos 11π/6 + i sin 11π/6).
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the multiplication law of exponents says that for any numbers b, n, and m,
b^n.b^m=b^n+m
a. true
b. false
Since the exponents were added based on the product rule, hence the multiplication law of exponents is TRUE
Law of indicesIndices are written in term of exponents. Some of the laws of indices;
[tex]a^m\times a^n=a^{m+n}[/tex] (product law of indices)
For the quotient law of indices
[tex]\dfrac{a^m}{a^n} =a^{m-n}[/tex]
According to the given expression, we are to determine if it is true or false
Check:
[tex]b^n.b^m=b^{n+m[/tex]
Since the exponents were added based on the product rule, hence the multiplication law of exponents is TRUE
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Which matrix multiplication is possible?
Answer:
second 0ne
Step-by-step explanation:
3×-1+-2 ×0
3×0+-2×3
simplify fully a+1/3a +7/6a
Answer:
5/2a
Step-by-step explanation:
Factor out common term a: a ( 1 + 1/3 + 7/6)
= a( 1+ 1/3 + 7/6)
1+ 1/3 + 7/6 = 5/2
= a5/2
= 5/2a
2/5 + 1/4= enter answer as a fraction in simplest form.
Answer:
13/20
Step-by-step explanation:
2/5*4=8/20
1/4*5=5/20
8+5=13
13/20
A boat is heading towards a lighthouse, whose beacon-light is 139 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 11 degrees
∘
. What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.
Using the slope concept, it is found that the ship’s horizontal distance from the lighthouse (and the shore) is of 715.09 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem, we have that:
The vertical change is of 139 feet.The horizontal change is of d feet.The angle is of 11º.Hence:
tan(11º) = 139/d
d = 139/tan(11º)
d = 715.09.
The ship’s horizontal distance from the lighthouse (and the shore) is of 715.09 feet.
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Given h of x equals negative 2 times the square root of x minus 3 end root, which of the following statements describes h(x)?
The function h(x) is increasing on the interval (–∞, 3).
The function h(x) is increasing on the interval (–3, ∞).
The function h(x) is decreasing on the interval (–∞, 3).
The function h(x) is decreasing on the interval (3, ∞).
Using translation concepts, it is found that the correct option regarding the function is:
The function h(x) is decreasing on the interval (3, ∞).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is given by:
[tex]f(x) = \sqrt{x}[/tex]
Which increases on (0, ∞).
The translated function is given by:
[tex]g(x) = -2\sqrt{x - 3}[/tex]
With the translation, the domain is now (-3, ∞), and the function is decreasing, hence the correct option is given by:
The function h(x) is decreasing on the interval (3, ∞).
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Find the derivative using the first principles.
[tex]~~~~\dfrac{d}{dx} \left( \sqrt[5]{1+x} \right)\\\\\\=\dfrac{d}{dx} (1+x)^{\tfrac 15}\\\\\\=\dfrac 15 \left(1 + x\right)^{\tfrac 15 -1} \cdot \dfrac{d}{dx}(1+x)\\\\\\=\dfrac 15 (1+x)^{-\tfrac 45} \cdot(0+1)\\\\\\=\dfrac{1}{5(1+x)^{\tfrac 45}}[/tex]
Question in the Picture
Step-by-step explanation:
the picture is not representing the real angle sizes. so, don't let yourself get confused by that.
the right neighbor angle of 90° at E is also 90°.
it has to be, because it is the supplementary angle to the left 90° (that means together they are 180°).
remember, all angles around a single point on one side of a line have to sum up to 180° (because the line can be seen as the diameter of a circle, with the point being the center of the circle, and so one side of the line is representing a half-circle and therefore 180°).
for the same reason angle 1 (the lower neighbor of the 90° angle at A) is also 90°.
for the same reason the lower neighbor angle of the 60° angle at E is 180 - 60 = 120°.
for the same reason the angle ABC is 180 - 40 = 140°.
for the angle BCD we need to remember :
the sum of interior angles of a polygon with n sides is
(n − 2) × 180°.
in our case ABCDE has 5 sides, so the sum of all interior angles is
(5 - 2) × 180 = 3×180 = 540°
we know 4 of the interior angles already, so
angle BCD = 540 - 90 - 90 - 120 - 140 = 100°
x is now the supplementary angle to the angle BCD.
so,
x = 180 - 100 = 80°
4 cups is equivalent to ____ quart
Answer:
1 quart is equal to 4 cups
Step-by-step explanation:
4 cups is equivalent to __1__ quart
Pls help I will give brainliest!!
Answer:
A. (-8, 0)
Step-by-step explanation:
The side of the line that is shaded contains the solutions to the inequality. (-8, 0) is in the shaded part of both graphs.
Also, 0 > -15 and 0 [tex]\geq[/tex] -9
I hope this helps :)
Ethan is looking to take out a mortgage for $620,000 from a bank offering an annual interest rate of 4.5%, compounded monthly. Using the formula below, determine his monthly payment, to the nearest dollar, if the loan is taken over 25 years.
His monthly payment to the nearest dollar of the loan taken over 25 years = $4,391.67
Calculation of monthly paymentThe mortgage capital = $620,000
The rate of payment of interest= 4.5%
The period for the payment = 25 years.
Simple interest
= p×T×R/100
= $620,000 × 25 × 4.5/100
= 69750000/100
= $697,500
Therefore the total amount of money that will be generated = $620,000 + $697,500 = $1,317,500
Therefore the monthly payment,
= $1,317,500/12×25
= $4,391.67
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What is 4 times 4(5+7)
Answer:
192
Step-by-step explanation:
so you basically make an equation like this:
4*4(5+7)
4*4(12)
4*48
=192
C Explain why it is not possible to fill out the frequency distribution table below without additional information.
please someone with a good heart help me ;-;
Answer:
87.5 ft^3
Step-by-step explanation:
Formula:
Volume = length x width x height.
Dimensions:
Length = 3 1/2 ft = 7/2 ft
Width = 5 ft
Height = 2 1/2 ft = 5/2 ft
Substitute and Find Volume:
Volume = (7/2 ft) x (5 ft) x (5/2) ft
Volume = 87.5 ft^3
Which point best represents √10?
0
1
R
P
+2
P Q R
11111
3
Q
S45
4
S
Done ->
Answer:
Point Q best represents the square root of 10.
PLEASE HELP I’LL MAKE YOU THE BRAINIEST
find the area of the trapezoid to the nearest tenth
Answer:
2.7m
Step-by-step explanation:
1.0m
0.5m
+1.2m
2.7m - answer
The radius of a circle is 2 centimeters. What is the length of a 45° arc?
Answer:
1.57 cmStep-by-step explanation:
the circle has a radius of 2.
Then
The circumference of the circle = 2πr = 2π(2) = 4π
…………………………………
Since , 45/360 = 1/8
Then, the arc is 1/8 of the entire circle.
…………………
Therefore,
the length of a 45° arc = 4π/8 = π/2 cm ≈ 1.57 cm
please help me thank you :)
The function on the table is decreasing on the interval [-2, 0).
Over what interval is the function shown in the table decreasing?
A function is decreasing if, as x increases, f(x) decreases.
We can see that at x = -2, f(-2) = 12.
Then at x = 0, f(0) = 0.
And for the value after that:
x = 1, f(1) = 3
So now the function increases. Then we conclude that the function is decreasing on the interval [-2, 0), and after that the function increases.
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I have a bag with 6 marbles numbered from 1 to 6. mathew has a bag with 12 marbles numbered from 1 to 12. matthew chooses one marble from his bag and i choose two from mine. in how many ways can we choose the marbles (where the order of my choices does matter) such that the sum of the numbers on my marbles equals the number on his?
Answer:
It would be 30.
Step-by-step explanation:
If we make a list of all the sums that we can get, we have:
1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6
These 15 sums can be chosen in two ways, since order matters, and we could do 2+1 instead of 1+2.
That gets us to 15x2 which is 30.
The number of ways that we can choose the marbles such that the sum of the numbers on my marbles equals the number on his would be 30.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
I have a bag with 6 marbles numbered from 1 to 6.
Mathew has a bag with 12 marbles numbered from 1 to 12.
1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6
These 15 sums can be chosen in two ways,
Since order matters, and we could do 2+1 instead of 1+2.
15 x 2 which is 30.
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The graph of h(x) is a translation of f (x) = RootIndex 3 StartRoot x EndRoot.
On a coordinate plane, a cube root function goes through (negative 3, negative 1), has an inflection point at (negative 2, 0), and goes through (negative 1, 1).
Which equation represents h(x)?
h (x) = RootIndex 3 StartRoot x minus 2 EndRoot
h (x) = RootIndex 3 StartRoot x + 2 EndRoot
h (x) = RootIndex 3 StartRoot x EndRoot minus 2
h (x) = RootIndex 3 StartRoot x EndRoot + 2
Transformation involves changing the form of a function. The function that represents is C; [tex]g(x) =- \sqrt[3]{x+1}[/tex]
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Function f(x) is given byy;
[tex]g(x) = \sqrt[3]{x}[/tex]
f(x) is reflected across the x-axis.
The rule of this transformation (i.e. reflection) is:
(x, y) ⇒ (x, - y)
So,
[tex]f'(x) = -f(x)[/tex]
This gives
[tex]f'(x) = - \sqrt[3]{x}[/tex]
Now, f'(x) is translated 1 unit left
The rule of this transformation (i.e. translation) is:
(x, y) ⇒ (x+ 1, y)
So,
g(x) = f'(x+ 1)
This gives
[tex]g(x) = -\sqrt[3]{x+1}[/tex]
Hence, the function that represents g(x) is (c)
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Answer:
Step-by-step explanation:
its B on Edge just did it
rodea la fracción que sigue y escribe el patrón que corresponde en cada sucesion
Find the area of a trapezoid shown:
The area of this trapezoid is A = 55
We know that the application formula for calculating the area of a trapezoid is given by:
[tex] \boxed{ \large \sf A = \dfrac{(b + b) \times h}{2} } \\ \\ [/tex]
⚘ Then, the resolution will be:
[tex]{ \large \sf A = \dfrac{(7 + 15) \times 5}{2} } [/tex]
[tex]{ \large \sf A= \dfrac {22 \times 5}{2} } [/tex]
[tex]{ \large \sf A= \dfrac {110}{2} } [/tex]
[tex]\pink{ \boxed{ \purple{ \boxed{ \large \sf A= 55 }}}} \\ \\ [/tex]
Therefore, the area of this trapezoid will be, A = 55