You buy 3 shirts and 1 pair of pants for $32. Your friend buys 2 shirts and 3 pairs of pants for $40. How much did each item cost?
First let’s define a shirt as X and pants as Y!
In the first scenario, the equation will be 3X + Y =$32
In the second scenario, the equation will be 2X + 3Y = $40
Now because we have two different variables (X & Y) let’s solve for one of them (Ex: Y) to simplify the equations!
3X + Y= $32—> subtract 3X on both sides of the equation
-3X. - 3X
Net result: Y= 32- 3X
Now we can insert this into the second equation 2X + 3Y = $40 in order to solve for X variable
2X + 3(32-3X) = $40
2X + 96 - 9X = $40 —> simplify the equation
-7X + 96 = $40 —> substrate 96 from both sides
-7X = -56 —> divide both sides by -7
X= 8
Now reinsert 8= X into 3X + Y = $32
3(8) + Y = $32
24+ Y = $32 —> substract 24 from both sides
y = 8
ANSWER: X= 8, Y= 8
Find the distance between the pair of points given on the graph. Distance = √ (blank)
Answer:
√2.236
Step-by-step explanation:
(2,0) (5,-2). 2 - 5 = -3. 0 - -2 = 2. -3 squared = -9. 2 squared = 4. -9 + 4 = -5. Square root of -5 = 2.236, so the distance would be √2.236
PLEASE HELP FAST!!!
The measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees
Angle of elevation and depressionFrom the question given, we have the following parameters
Base of the building = 7feet
Height of the building = 18 feet
Required
angle of elevation
Using the SOH CAH TOA identity
tanФ = opp/adj
tanФ = 18/7
Ф = 68.73 degrees
Hence the measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees
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Question:
A ladder leans against a building. The top of the ladder reaches a point on the building, which is 18 feet above the ground. The foot of the ladder is 7 feet from the building. Find the measure of the angle of elevation from the ground to the top of the ladder.
Pls help!!!!!!!!!!!!!!!!
Answer:
D: 6.5, 3
C: 23.5, 9
I think
Answer:
C (23.5, 9)
D (6.5, 3)
prove that (1- cos(pi)/(8))(1-cos(3 pi)/(8))(1-cos(5 pi)/(8))(1=cos(7 pi)/(8))=(1)/(8)
Step-by-step explanation:
1&$)&(5$6$5*-_+_7&'+&-^€=%
Triangle rst is dilated by a scale factor of 5 to form triangle r's't'. side r's' measures 40. what is the measure of side rs?
Answer: 8
Step-by-step explanation:
We know that scale factor = (image)/(preimage).
Substituting in what we have,
[tex]5=\frac{R'S'}{RS}\\\\5=\frac{40}{RS}\\\\RS=\boxed{8}[/tex]
Answer:
Step-by-step explanation:
We know that r's't' was formed by a scale factor of 5.
This means rst was multiplied by 5 to create r's't'.
Dividing the sides of r's't' by 5 will give us the sides of the
pre-image. If r's' = 40 - dividing 40 by 5 = 8.
So rs is 8.
1) Which statement is needed to fill in the blank in this syllogism? If two lines are parallel, then ____________________. If the lines never intersect, then the lines have the same slope. Therefore, if two lines are parallel, then the lines have the same slope.
A) the lines have the same slope
B) the lines never intersect
C) the lines have the same equation
D) the lines are continuous
Answer:
B) the lines never intersect
Step-by-step explanation:
okay essentially, syllogism is formatted in a repetitive way
it's something like:
if "a" are "b"
and "b" are "c"
then "a" are "c"
(a = b
b = c
logically, c = a)
(idea, thing related to idea, conclusion relating the two)
hope this helps!!
Answer:
the lines never intersect
Step-by-step explanation:
Syllogisms are connected by a shared statement that connects a hypothesis to a different conclusion.
HELP ASAP/NOW...NO LINKS OR JOKING PLS
Answer:
D. 0 < x < 20
Explanation:
Domain is in the x axis, Range lies in the y axis.
Here it is seen that function's domain lies between 0 to 20.
Open circle's are used for '<' and '>'Closed circle's are used for '≤' and '≥'Here, as the circle's are open. Domain: 0 < x < 20
Additionally,
Range: -10 < f(x) < 06root27+root243 simplify
Answer:
6√27 + √243
6√9 x 3 + √81 x 3
6 x 3 √3 + 9√3
18√3 + 9√3
27√3
Shape R is reflected in
a) What are the coordinates of C'?
Then R' is translated by (-3)
-6
R
=
-5 -4 -3 -2 -1
b) What are the coordinates of C"?
Y
5+
4-
3-
2+
1
- 1 to give R'.
-1-
-2-
--3-
-4-
--5+
1
to give R".
2
3 4
sit
5
X
The new coordinates of C is (-5,2), (-5,5) (-7,3) (-7,5)
The correct question is
Shape R is reflected in x axis and is translated by (-3, 0) , What will be the coordinates of the new figure
The figure is attached with the answer.
What happens when a figure is reflected on an axis ?When a figure is reflected along any axis , the coordinate of the axis on which it is reflected remains the same while the other coordinate vis the additive inverse of the given coordinate
It is given that the coordinate point of R
(-2 ,-2) , (-2,-5) (-4,-3) (-4,-5)
When it is reflected along x axis the new coordinates are
(-2 , 2), (-2,5) (-4,3) (-4,5)
and when translated by -3,0
(-5,2), (-5,5) (-7,3) (-7,5)
Therefore the new coordinates of C is (-5,2), (-5,5) (-7,3) (-7,5)
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The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5cm². calculate correct to 3 Significant figures, the base radius, r ,height h Volume of the cone [take π 22/7]
The volume of the cone is V = 381.15 cu.cm
What is the Curved Surface Area of the cone ?The curved surface area of the cone is given by
A = πrl
The slant height given in the question is
l = 10.5 cm
A = 115.5 sq.cm
radius = ?
Height = ?
Volume = ?
Using the Curved Surface Area Formula
115.5 = π * r * 10.5
taking π = 22/7
r = 3.5 cm
The slant height is given by
[tex]\rm l = \sqrt{ r^2 + h^2}[/tex]
Therefore the height is
[tex]\rm h = \sqrt{ 10.5^2 -3.5^2}[/tex]
h = 9.9 cm
The volume of the cone is
V = π r²h
V = (22/7) * 3.5 * 3.5 * 9.9
V = 381.15 cu.cm
The volume of the cone is V = 381.15 cu.cm
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the equation below describes a circle. what are the coordinates of the circle?
(x+5)^2 + (y+7)^2 = 21^2
Answer:
center = (-5, -7)
radius = 21
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven equation:
[tex](x+5)^2 + (y+7)^2 = 21^2[/tex]
Comparing the given equation with the standard equation of a circle:
center = (-5, -7)radius = 21Hence, the coordinates of centre is (-5,-2).
What is circle ?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.
The given equation of circle,
(x+5)² + (y+7)² = 21²
We know that,
Equation of a circle is:
(x-a)² + (y-b)² = r²
where:
(a, b) is the center
And r is the radius
Comparing with the given equation we have,
center = (-5,-7)
And radius = 21 units
Thus,
Coordinates = (-5,-7).
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
From unit conversion, it is found the following results:
6km ≈ 3.73 mi
2.5 L≈ 0.66 gal
90 lb ≈ 40.82 kg
Unit Conversion
Units of measurement are part of our daily lives. There are different units for area, length, volume, mass, and others. Because of this, it is important to know converting them.
For solving this question you need some information as:
1 km = 0.621371 mi ( unit for length and distance)
1 L = 0.2641722 gallons (unit for volume)
1 lb = 0.453592 kg (unit for mass)
Therefore,
If 1 km = 0.621371 mi, you will have:1 km -------- 0.621371 mi
6 km -------- x mi
x= 6* 0.621371
x=3.73 mi
Thus, 6km ≈ 3.73 mi.
If 1 L = 0.2641722 gallons, you will have: 1 L-------- 0.2647122 gal 2.5L -------- x gal x= 2.5* 0.2647122 x=0.66 galThus, 2.5 L≈ 0.66 gal.If 1 lb = 0.453592 kg, you will have: 1 lb-------- 0.453592 kg 90 lb -------- x kg x= 90* 0.453592 x=40.82 kgThus, 90 lb≈ 40.82 kg.Read more about unit conversion here:
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Find the missing side of each triangle. Leave your answers in simplest radical form.
2√3 m
A) √ 19 m
c) √5 m
O a
a
Ob b
Oc
√7m
C
Od d
B) √17 m
D) √√2 m
Answer:
C [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Use pythagorean theorem.
[tex]x^{2}[/tex] +[tex]\sqrt{7} ^{2}[/tex] = (2[tex]\sqrt{3}) ^{2}[/tex]
[tex]x^{2}[/tex] + 7 = 12 Subtract 7 from both sides
[tex]x^{2}[/tex] = 5 Take the square root of both sides to solve
x = [tex]\sqrt{5}[/tex]
Question 4 (Essay Worth 10 points)
(05.06; 05.07 MC)
A prism and two nets are shown below:
Image of a right triangular prism and 2 nets. The triangle bases have base 4, height 3, and diagonal side 5. The length of the prism from the bases is 8.6. Net A has 3 rectangles in a row. The middle one has sides AC and CD. This middle one has triangle ABC on top and identical triangle below. Net B is the same except that the triangle base ABC is on top of the last rectangle which has sides AC and CD. Units are in inches.
Part A: Which is the correct net for the prism? Explain your answer. (2 points)
Part B: Write the measurements of Sides AB, BC, and CD of the correct net. (4 points)
Part C: What is the surface area of the prism? Show your work. (4 points)
Answer:
115.2 in^2
Step-by-step explanation:
total surface area Stot = 113.2 in2
lateral surface area Slat = 103.2 in2
top surface area Stop = 6 in2
bottom surface area Sbot = 6 in2
For every 10 yards on a football field, there is a boldly marked line labeled with the amount of yards.
There are two parallel sidelines on each side of the field. If the 50 yard line is perpendicular to one of the
sidelines, what is its relationship to the other sideline?
Answer:
Same, because they are parallel.
Step-by-step explanation:
If a(x) = 3x + 1 and (x)= x-4, what is the domain of (boa)(x)?
I am assuming you meant to write b(x) = x-4.
[tex](b \circ a)(x)=b(a(x))=b(3x+1)=(3x+1)-4=\boxed{3x-3}[/tex]
Since this is a linear function, the domain is all real numbers.
If a point is reflected over the y-axis, then the coordinates of (x, y) are changed to ______________.
Answer:
its opposite
Step-by-step explanation:
Which number line represents the solution set for the inequality 3(8-4x) < 6(x - 5)?
[tex]3(8 - 4x) < 6(x - 5) \\ 24 - 12x < 6x - 30 \\ 24 + 30 < 6x + 12x \\ 54 < 18x \\ \frac{54}{18} < \frac{18x}{18} \\ x > 3[/tex]
Solution : ] 3 , + ♾️ [
PLEASE GIVE BRAINLIEST
Which of the following is most likely the next step in the series?
Answer:
I think the answer is B
Step-by-step explanation:
i need help filling in the blanks
Complete the steps to solve the equation above.
2x + 5 = 4x - 1
+ +
After adding on both sides, the equation looks like this:
2x + = 4x
Now it's time to the combine like terms and .
2x + = 4x
- -
After subtracting on both sides, the equation looks like this:
=
Finally, we divide by on both sides, and we have solved the equation!
x is equal to .
The 3 steps to solve the algebra equation have each sub step as explained and written below.
How to solve algebra problems?We are given the algebraic equation;
2x + 5 = 4x - 1
Step 1; After adding 1 to both sides, we have;
2x + 5 + 1 = 4x - 1 + 1
2x + 6 = 4x
Step 2; We subtract 3x from both sides to get;
2x - 2x + 6 = 4x - 2x
2x = 6
Step 3; Divide both sides by 3 to get;
2x/2 = 6/2
x = 3
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Think about the zoo meals in another way. Many different foods are prepped in the commissary for the
animals. Though each animal has a very specific combination of foods, there may be foods repeated in diets
for different animals. For example, cabbage may be used in the morning meals for 20 different animals. If
the food is the input, and the animal is the output, is this relationship a function?
Answer:
89
Step-by-step explanation:
(08.01)
A new video game is expected to sell 120 copies the first hour at a local game store. After that, the sales will follow the function s(x) = 15(=
1) where x is the number of hours. What is the function that shows total sales, including the first hour?
Answer:
f(x)=15x+120
Step-by-step explanation:
trust
A sample of substance x that has a mass of 326.0 g releases 4325.8 cal when it freezes at its freezing point. if substance x has a molar mass of 58.45 g/mol, what is the molar heat of fusion for substance x? use q equals n delta h.. 13.31 cal/mol 74.00 cal/mol 775.6 cal/mol 19054.7 cal/mol
The molar heat of fusion for substance X , given the data is 775.6 cal/mol
How to determine the mole of the substance XMass = 326 gMolar mass = 58.45 g/molMole = ?Mole = mass / molar mass
Mole = (326 / 58.45) moles
How to determine the heat of fussionMole (n) = (326 / 58.45) molesHeat (Q) = 4325.8 calHeat of fusion (ΔHf) = ?
Q = n × ΔHf
4325.8 = (326 / 58.45) × ΔHf
4325.8 = (326 × ΔHf ) / 58.45
Cross multiply
326 × ΔHf = 4325.8 × 58.45
Divide both sides by 326
ΔHf = (4325.8 × 58.45) / 326
ΔHf = 775.6 cal/mol
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it is about Name the property of the rational numbers in each of the following
The property of each given rational number operation are respectively; Commutative Property; Closure Property; Associative Property; Closure Property; Distributive Property
What is the property of the rational number?The main properties of rational numbers are:
Commutative property.Associative Property. Distributive Property.Closure property.a) The property used here is commutative property which says that;
a + b = b + a.
This tallies with the operation used on the rational numbers.
b) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.
c) The property used here is called associative property because it states that; a * (b * c) = (a * b) * c.
d) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.
e) The property used here is called distributive property because it states that; a * (b * c) = (ab * ac)
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which property is illustrated for all expressions a and b if a=b then b=a
Answer:
Symmetric property
Kevin and Randy Muise have a jar containing 65 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $8.65 .How many of each type of coin do they have?
What is the value of x in the triangle?
Answer:
45 degree=√2/2
√2/2=12√2
we use criss-cross method
√2x/√ 2=12√2/√ 2
×=24
Step-by-step explanation:
if it confused you this is (/)is dividing
hope I helped
please mark me as brainlyst
solve X/3 + 5/2 = -3/2 pls pls
Answer:
X=-12
Step-by-step explanation:
Subtract -5/2 on both sides:
X/3+5/2-5/2=-3/2-5/2
X/3=-8/2
X/3=-4
Multiply both sides by 3:
X/3*3=-4*3
X=-12
Answer:
x = -12
Step-by-step explanation:
To solve for x, we always want to isolate x {isolate = getting it by itself}
So, for the equation: X/3 + 5/2 = -3/2
we should first get x on its own side:
[tex]\frac{x}{3}+\frac{5}{2}=-\frac{3}{2}[/tex]
[tex]-\frac{5}{2}[/tex] [tex]-\frac{5}{2}[/tex] {subtract 5/2 from both sides} {-3/2 - 5/2 = -8/2}
[tex]\frac{x}{3} = -4[/tex]
×3 ×3 {multiply both sides by 3 to find "1"x}
x = -12
check:
-12/3 + 5/2 = -3/2
-4 + 5/2 = -3/2
(5/2 = 2 [tex]\frac{1}{2}[/tex] ; 2 [tex]\frac{1}{2}[/tex] - 4 = -1 [tex]\frac{1}{2}[/tex])
-1 [tex]\frac{1}{2}[/tex] = -3/2 {3/2 = 1 [tex]\frac{1}{2}[/tex]}
-1 [tex]\frac{1}{2}[/tex] = -1 [tex]\frac{1}{2}[/tex]
{TRUE}
so, x = -12
hope this helps!!
HELP PLEASE!!!!!!!!!!!!!!!!!!!
Answer:
D.) x - 4
Step-by-step explanation:
This is a graph of an exponential/quadratic function. There general structure looks like this:
ax² + bx + c
Generally, when finding the zeros these functions, you are told to factor the equation. Once you have factored the equation, you can set the factors equal to zero to find the points where the function touches the x-intercept.
That being said, you can determine the factors without having the entire equation by identifying the zeros on the function. On this graph, there is a zero at (4,0). This means that one of the factors must have been "x - 4". You can check your work by setting the factor equal to zero.
x - 4 = 0
x = 4
Charlie is installing new carpet in his rectangular living room, which is 5 feet longer than it is wide. He has received quotes for the total
installation costs from two different contractors for the same style of carpet.
Contractor A charges an installation fee of $125 plus $2 per square foot for the carpet.
Contractor B charges an installation fee of $75 plus $2.50 per square foot for the carpet.
Based on this information, which system of equations could be used to determine the width of the living room, x, in feet, at which the
quote for the installation costs, y, is the same for both companies?
Considering the area of a rectangle, the equation that could be used to determine the width for which the costs are the same is:
125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:
A = lw
In this problem, the dimensions are given as follows:
w = x, l = x + 5.
Hence the area in square feet is:
A = x(x + 5) = x² + 5x.
Then the costs are given as follows:
A(x) = 125 + 2(x² + 5x).B(x) = 75 + 2.5(x² + 5x).The costs will be equal when:
A(x) = B(x)
125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)
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Answer:
see photo
Step-by-step explanation:
Plato/Edmentum
