Answers
The solution to the equation as it is given in (8) above is -21.
What is subtraction and multiplication properties of equality?According to the subtraction property of equality, If you subtract the same number from both sides of an equation, the equation remains true.
Also by the multiplication property of equality, If you multiply both sides of an equation by the same number (except zero), the equation remains true. These can be used to solve the question in (7) above
Given;
280 = -8(-14 + x)
280 = 112 - 8x
280 - 112 = -8x
x = -21
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The wingspan (in feet) of the actual airplane is equal to 87.5 feet.
A property of equality which you would use to solve the equation -15 = x/3 + 18 is: D. Subtraction property of equality and multiplication of equality.
The solution of the equation 280 = -8(-14 + x) is: B. x = -21.
How to determine the wingspan (in feet) of the actual airplane?Based on the scale model, we can logically deduce that the airplane has a length of 12.2 inches and a wingspan of 12.5 inches. This ultimately implies that, we would convert from inches to feet as follows;
1 inch = 1/12 feet
12.2 inches = 12.2 × 1/12 = 12.2/12 feet.
Therefore, the scaled factor is given by;
Scale factor = (85.4 × 12/12.2)
For the actual length of the wingspan with a scaled length of 12.5 inches, we have:
12.5 inches = 12.5/12 feet
Actual length of wingspan = 12.5/12 × (85.4 × 12/12.2)
Actual length of wingspan = 87.5 feet.
Question 7-15 = x/3 + 18
x/3 = -15 - 18 ⇒ (Subtraction property of equality)
x/3 = -33
x = 3(-33) ⇒ (Multiplication property of equality)
x = -99
Question 8280 = -8(-14 + x)
280 = 112 - 8x
8x = 112 - 280
x = -168/8
x = -21
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Related Questions
Yoshi is driving across the United States. If Yoshi's map is 20 inches across, and the United States is 3,000 miles across, what is the scale of the map?
Answers
scale = map distance / actual distance
In this case, the map distance is 20 inches, and the actual distance is 3,000 miles. We need to convert these units so that they are both in the same units. Let's convert miles to inches:
1 mile = 63,360 inches (approximately)
So, 3,000 miles is equal to:
3,000 miles * 63,360 inches/mile = 190,080,000 inches
Now we can plug in the values into the formula:
scale = 20 inches / 190,080,000 inches
scale = 1 / 9,504,000
Therefore, the scale of the map is 1:9,504,000. This means that 1 inch on the map represents 9,504,000 inches (or 150 miles) in real life.
Need help with this please
Answers
The area of the original figure is 1/9 times the area of the new figure
The perimeter of the original figure is 1/2 times the perimeter of the new figure
Estimating the areas of the figuresFrom the question, we have the following parameters that can be used in our computation:
The figures
The areas of the new figures is calculated as
Area = Old area * scale factor
So, we have
Area Figure 1 = (1 * 3) * 3
Area Figure 1 = 9
The perimeter of the new figures is calculated as
Perimeter = Old Perimeter * scale factor
So, we have
Perimeter Figure 2 = (4 * 4 + 4 * (2 + 3)) * 1/2
Perimeter Figure 2 = 18
See attachment for the dilates figures
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Find all intersection points of the parabola y = x^2 and the circle with a radius √6 and center at (0,4).
Answers
The requried, intersection points are (√5, 5), (-√5, 5), (√2, 2), and (-√2, 2).
To find the intersection points of the parabola y = x² and the circle with radius √6 and center at (0,4), we need to solve the system of equations:
x² + (y - 4)² = 6 (equation of circle)
y = x² (equation of parabola)
We can substitute y = x² into the equation of the circle and obtain a quadratic equation in x:
x² + (x² - 4)² = 6
x⁴ - 7x² + 10 = 0
This equation can be factored as:
(x² - 5)(x² - 2) = 0
Therefore, the solutions for x are x = ±√5 and x = ±√2. To find the corresponding values of y, we can substitute these values of x into the equation of the parabola:
y = x²
For x = √5, we have y = (√5)² = 5, and for x = -√5, we have y = (-√5)² = 5.
For x = √2, we have y = (√2)² = 2, and for x = -√2, we have y = (-√2)² = 2.
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Find the area of the shaded region.
80°
5 cm
A≈ [?] cm²
Enter a decimal rounded to the nearest tenth.
Answers
[tex]\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) ~~ \begin{cases} r=radius\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=5\\ \theta =80 \end{cases} \\\\\\ A=\cfrac{5^2}{2}\left( ~~ \cfrac{\pi (80) }{180}-\sin(80^o ) ~~ \right)\implies A=\cfrac{25}{2}\left(\cfrac{4\pi }{9}- \sin(80^o) \right) \\\\\\ A=\cfrac{50\pi }{9}-\cfrac{25\sin(80^o)}{2}\implies A\approx 5.1~cm^2[/tex]
Find each angle and arc measure.
⌢
mDGF= degrees
(50 POINTs will give BRAINIEST FOR EFFORT)
Answers
Answer: 226
Step-by-step explanation:
The angle is half of the arc angle
so mDGF is 2 times as big as the angle
mDGF=113*2
mDGF=226
Applying the Right Triangle Altitude Theorem. Which similarity statement is true?
Answers
The true similarity statement are using Right Triangle Altitude Theorem :
ΔABD similar to ΔBCD
ΔABC similar to ΔADB
ΔABC similar to ΔBDC
Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.
By the Right Triangle Altitude Theorem,
If the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then the triangles formed by the division are similar to each other and both are similar to the original triangle.
Using this,
ΔABD similar to ΔBCD
ΔABC similar to ΔADB
ΔABC similar to ΔBDC
Hence the true statements are ΔABD similar to ΔBCD, ΔABC similar to ΔADB, ΔABC similar to ΔBDC.
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The complete question is given below.
What is the range of |x|-7?
Answers
Answer:
3 2/5 +(3/2+3/5)×6/5÷3/2-10 1/2× 2/2
can someone help me with number 2 and 3
Answers
The segments AB and CD are, parallel, perpendicular or neither, depending on the slopes obtained from the coordinates on the segments as follows;
PerpendicularParallelNeitherPerpendicularParallelNeitherWhat are parallel lines?Parallel lines or line segments are line segments that have the same slope.
1. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 13)/(0 - (-2)) = -10/2 = -5
The slope of the segment [tex]\overline{CD}[/tex] is; (3 - 0)/(10 - (-5)) = 3/15 = 1/5
The slope of [tex]\overline{AB}[/tex] is the negative inverse of the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] ⊥ [tex]\overline{CD}[/tex], [tex]\overline{AB}[/tex] is perpendicular to [tex]\overline{CD}[/tex]
2. The slope of the segment [tex]\overline{AB}[/tex] is; (1 - 7)/(-6 - 3) = -6/-9 = 2/3
The slope of the segment [tex]\overline{CD}[/tex] is; (-1 - (-5))/(0 - (-6)) = 4/6 = 2/3
The slope of [tex]\overline{AB}[/tex] is the same as the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex], [tex]\overline{AB}[/tex] is parallel to [tex]\overline{CD}[/tex]
3. The slope of the segment [tex]\overline{AB}[/tex] is; (4 - 2)/(-2 - (-6)) = 2/4 = 1/2
The slope of the segment [tex]\overline{CD}[/tex] is; (-7 - 11))/(5 - (-1)) = -18/6 = -3
The slope of [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular
4. The slope of the segment [tex]\overline{AB}[/tex] is; (3 - 8)/(2 - (-3)) = -5/5 = -1
The slope of the segment [tex]\overline{CD}[/tex] is; (2 - 6)/(-8 - (-4)) = -4/(-4) = 1
The slope of [tex]\overline{AB}[/tex] is the negative inverse of the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] ⊥ [tex]\overline{CD}[/tex]
5. The slope of the segment [tex]\overline{AB}[/tex] is; (2 - (-1))/(-4 - (-8)) = 3/4
The slope of the segment [tex]\overline{CD}[/tex] is; (6 - (-3))/(12 - 0) = 9/12 = 3/4
The slope of [tex]\overline{AB}[/tex] is the same as the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] ║ [tex]\overline{CD}[/tex]
6. The slope of the segment [tex]\overline{AB}[/tex] is; (-1 - 5)/(3 - 6) = -6/-3 = 2
The slope of the segment [tex]\overline{CD}[/tex] is; (7 - (-5))/(-4 - 2)) = 12/(-6) = -2
The slope of [tex]\overline{AB}[/tex] is different from and not the negative inverse of the slope of [tex]\overline{CD}[/tex] therefore;
[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel nor perpendicular.
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Garnier's Opera House is a revival of the________style.
Romantic
Gothic
Renaissance
Baroque
Answers
Answer: Garnier's Opera House is a revival of the Baroque style.
An ordinary fair dice is a cube with the numbers 1 through 6 on the sides
Answers
The probability values are P(A) = 0.722 and P(B) = 0.50
Calculating the probability valuesFrom the question, we have the following parameters that can be used in our computation:
A fair die
The sample space of the events are
A = Sum is greater than 5
B = Sum is an even number
From the sample space of the sum of outcomes, we have
n(A) = 26
n(B) = 18
So, we have
P(A) = 26/36 = 0.722
n(B) = 18/36 = 0.50
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(x)<0 over and what other interval?
Answers
The other interval is (-1.1, 0.9)
In a graph of any function, values of f(x) are represented by the values on the y-axis for the different input values on x-axis.
For the given graph, values of f(x) are less than zero.
That means interval in which the values of the function are negative for the different values of x.
Negative values of the given function are in the intervals (-∞, -3), (-1.1, 9).
Therefore, from the given options, Option (4) will be the answer.
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The complete question is
F(x)<0 over (-∞, -3) and what other interval?
O (-2.4, - 1.1)
O (-3, - 1.1)
O (-1.1, 2)
O (-1.1, 0.9)
Which of the following represents the symmetric property of equality?
A) If a = b and b = c, then a = c
B) If a = b, then ac = bc
C) If a = b, then b = a
D) a(b + c) = ab + ac
Answers
Answer:
C) a = b ⇒ b = a
Step-by-step explanation:
You want to identify the statement that represents the symmetric property of equality.
A.If a = b and b = c, then a = c. This is the transitive property of equality.
B.If a = b, then ac = bc. This is the multiplication property of equality.
C.If a = b, then b = a. This is the symmetric property of equality.
D.a(b +c) = ab +ac. This is the distributive property of multiplication over addition.
maria and joan went shopping. maria bought 3 pair of jeans that each cost the same amount and 4 t-shirts that each cost the same amount. joan bought 2 pair of jeans that each cost the same amount, and 1 t-shirts that each cost the same amount. what is the cost of the jeans and shirts
Answers
Result:
The total cost of the jeans and shirts = 5(x + y)
How do we determine the cost?Let's use variables (x and y) to show the total cost of one pair of jeans and one T-shirt, respectively.
Let x = the cost of one pair of jeans.
Let y = e the cost of one T-shirt.
Given:
Maria bought 3 pairs of jeans and 4 T-shirts, all at the same price. That is:
3x = cost of Maria's jeans
4y = cost of Maria's T-shirts
Joan bought 2 pairs of jeans and 1 T-shirt, all at the same price. That is:
2x = cost of Joan's jeans
y = cost of Joan's T-shirt
To find the total cost of all they bought, add up the costs:
Total cost = Maria's cost + Joan's cost
Total cost = 3x + 4y + 2x + y
Total cost = 5x + 5y
So the total cost is 5 times the sum of the cost of one pair of jeans and one T-shirt.
Simplify the expression by factoring out a common factor of 5, and we get:
Therefore, total cost = 5(x + y)
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what is the area of triangle ADC, if A is (-1, 3), D is (-1, 7), and C is (0, 4)?
Answers
Answer:
e
Step-by-step explanation:
g
URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS!!!!
If you know what question this is please answer I couldn’t fit everything in the picture :(
Restaurant
No commute 3
0-1 Hr Commute 10
> 1 Hr Commute 28
Sum 41
Answers
The correct groupings for each probability are given below as follows:
The probability that you have more than a 1 hour commute: Marginal-57/134 = 42.5% chanceThe probability that you make a home-cooked meal and you have more than a 1-hour commute: Joint-7/134 = 5% chanceThe probability that you eat at a restaurant given that you have no commute: Conditional-3/37 = 8% chanceThe probability that you get takeout food: Marginal-50/134 = 37% chanceThe probability that you eat at the restaurant and have no commute: Joint probability 3/134 = 2% chanceThe probability that you commute 0-1 hour given that you get take-out food: Conditional-18/50 = 36% chanceWhat is joint probability?The possibility of two events occurring simultaneously and at the same time is known as joint probability.
Joint probability is the likelihood that event Y will take place at the same time as event X.
An example of a joint probability is the probability that you eat at the restaurant and have no commute
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how many paperclips that weigh 2 grams would balance a scale of 1 pound?
Answers
Answer: 226.795 paperclips
Step-by-step explanation:
First, we need to know how many grams are in a pound.
[tex]\boxed{\text{1 pound = 453.59 grams}}[/tex]
Next, we will divide 453.59 grams by the 2 grams per paper clip to see how many paper clips would balance the scale with one pound.
453.59 / 2 = 226.795 paperclips
Help me solve and show my work please
Answers
The simplified form of trigonometric functions by trigonometric formulas are listed below:
Case 1: 0.5√(2 - √3)
Case 2: (0.5√2) / (1 + 0.5√2)
Case 3: sin 6x
Case 4: sin θ
How to simplify and evaluate trigonometric functions
In this problem we must simplify and evaluate trigonometric functions by means of trigonometric formulas. The first two expressions must be simplified and evaluated by of half angle formulas:
Case 1
sin 15° = √[(1 - cos 30°) / 2]
sin 15° = √[(1 - √3 / 2) / 2]
sin 15° = √[(2 - √3) / 4]
sin 15° = 0.5√(2 - √3)
Case 2
tan 22.5° = sin 45° / (1 + cos 45°)
tan 22.5° = (0.5√2) / (1 + 0.5√2)
The last two expressions are simplified and evaluated by double angle formulas:
Case 3
2 · sin 3x · cos 3x
sin 6x
Case 4
2 · sin 0.5θ · cos 0.5θ
sin θ
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What transformations take the graph of f(x) = e^x to f(x) = -e^x -2?
Answers
The transformations of the given functions is vertical shift 2 units down.
Given that, the function is f(x)=-eˣ to f(x)=-eˣ-2.
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Parent Function: f(x)= −eˣ
Horizontal Shift: None
Vertical Shift: Down 2 Units
Reflection about the x-axis: None
Vertical Compression or Stretch: None
Therefore, the transformations of the given functions is vertical shift 2 units down.
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find the measure of TDC
Answers
The measure of angle TDC in the triangle is 32 degrees.
How to find the angle of a triangle?The tangent CD forms a right angle with the radius CT of the circle. This forms a right angle triangle.
Therefore, the sum of angles in the triangle is 180 degrees.
Hence,
∠C = 90 degrees
Therefore,
3x + 14 + 8x + 10 + 90 = 180
11x + 114 = 180
11x = 180 - 114
11x = 66
divide both sides by 11
x = 66 / 11
x = 6
Therefore,
∠TDC = 3x + 14 = 3(6) + 14 = 18 + 14 = 32 degrees.
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Hawa models a can of ground coffee as a right cylinder. She measures its radius as
3/4 in and its volume as 8 cubic inches. Find the height of the can in inches. Round your answer to the nearest tenth if necessary
Answers
Answer: The height is 4.5 in
Step-by-step explanation:
We can use the given formula for volume, transform it to solve for height (h), and then substitute our given values to solve.
Given formula:
[tex]\displaystyle V=\pi r^2h[/tex]
Transformed to solve for height:
[tex]\displaystyle h=\frac{V}{\pi r^2}[/tex]
Substitute given points:
[tex]\displaystyle h=\frac{(8\; \text{cubic inches})}{\pi (0.75\; \text{inches})^2}[/tex]
Square:
[tex]\displaystyle h=\frac{(8\; \text{cubic inches})}{\pi (0.5625)}[/tex]
Multiply:
[tex]\displaystyle h=\frac{8}{1.767146}[/tex]
Divide:
[tex]\displaystyle h=4.527[/tex]
Round to the nearest tenth:
[tex]\displaystyle h=4.5[/tex]
I don’t understand this problem
Answers
The area of the composite figure is equal to 521.080 square milimeters.
How to determine the area of a composite figure
In this problem we have the representation of a composite figure, whose area should be found. This figure is the consequence of the combination of three figures: a semicircle, a rectangle and a triangle. The area formulas for each case are introduced below:
Semicircle
A = 0.5π · r²
Where r is the radius, in milimeters.
Rectangle
A = b · h
Triangles
A = 0.5 · b · h
Where:
b - Base, in milimeters.h - Height, in milimeters.A - Area, in square milimeters.Now we proceed to compute the area of the composite figure:
A = 0.5π · (10 mm)² + (20 mm) · (14 mm) + 0.5 · (12 mm) · (14 mm)
A = 50π mm² + 280 mm² + 84 mm²
A = 521.080 mm²
RemarkThe statement is absent. Complete statement is introduced below:
Find the area of the figure.
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In Martha's food storage, she has 13 cans of chicken noodle soup, 15 cans of tomato soup, and 17 cans of mushroom soup. If she randomly chooses a can of soup from her food storage, what is the probability it is a can of tomato soup?
Answers
Answer:
1/3
Step-by-step explanation:
p(event) = (number of desired outcomes)/(total number of outcomes)
total number of outcomes = 13 + 15 + 17 = 45
number of desired outcomes = 15
p(can of tomato soup) = 15/45 = 1/3
The Cruiser Bicycle Company makes two styles of bicycles: the Traveler (x), which sells for $300, and the Tourister (y), which sells $600. Each bicycle has the same frame and tires, but the assembly and painting time required for the Traveler is only 1 hour, while it is 3 hours for the Tourister. There are 300 frames and 360 hours of labor available for production.
Write an inequality for each of the constraints (one for frames, one for hours for assembly, and 2 non-negative inequalities describing the products).
Answers
An inequality for each of the constraints (one for frames, one for hours for assembly, and 2 non-negative inequalities describing the products is:
x + y ≤ 300
x1 + y3 ≤ 360
What is an inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.
Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
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Which of the following ratios would form a proportion with Two-thirds?
a.
Three-fourths
c.
StartFraction 12 Over 15 EndFraction
b.
StartFraction 6 Over 9 EndFraction
d.
One-third
Answers
The proportion equivalent with Two-thirds would be 6/9.
Since we know that the proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that the proportion with Two-thirds
If you actually divide it’ll make since , so first we want to divide the 2 , then you want to multiply the third of the two
2/3 x 3/3
6/9
thus, the answer will be 6/9.
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The measure of weights of 15 students is normally distributed with a sample mean of 6 and standard deviation of 5. Find the 95% confidence interval for the mean.
Answers
The 95% confidence interval for the mean is [3.23, 8.76].
What is the confidence of interval?
The confidence of interval of the mean is calculated as follows;
Confidence interval = σ ± (t-value x μ)
where;
σ is the sample meanμ is the standard errorThe standard error is calculated as follows:
μ = std / √n
μ = 5 / √15
μ = 1.29
Based on this value we will check the distrbution table, for the t-value of 95% confidence;
= 2.145.
Confidence interval = σ ± (t-value x μ)
= 6 ± (2.145 x 1.29)
= [3.23, 8.76]
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In the following diagram, triangle EFG is similar to triangle MNP and cos E=4/7. If MP=20 then find the length of MN to the nearest tenth. Show the work that leads to your answer.
Answers
The length of MN to the nearest tenth is 11.4 units
Finding the length of MN to the nearest tenthFrom the question, we have the following parameters that can be used in our computation:
cos E = 4/7
MP = 20
Because the triangles are similar triangles, we have
cos M = cos E = 4/7
So, we have
cos M = MN/MP
This gives
MN/MP = 4/7
So, we have
MN/20 = 4/7
Evaluate
MN = 20 * 4/7
So, we have
MN = 11.4
Hence, the length is 11.4
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1-The tangent line to the curve y = x³ at point A(a, a³) intersects the curve at point B. Let
R be the area of the region bounded by the curve and the tangent line. The tangent line at B
intersects the curve at another point C. Let S be the area of the region bounded by curve and
the second tangent line. How are the areas R and S related?
Answers
Answer:
The areas R and S are equal.
Step-by-step explanation:
Since, the tangent line to the curve y = x³ at point A(a, a³) is given by y = 3a²(x - a) + a³. This line intersects the curve at point B(a, a³), and we can find the x-coordinate of point B by setting y = 3a²(x - a) + a³ equal to x³ to get the equation x³ - 3a²x + 3a³ - a³ = 0. Using the fact that x = a is a root of this equation, we can factor it as (x - a)³ = 0, which implies that the curve and the tangent line are tangent at point B.
The slope of the tangent line at point B is 3a², so the equation of the tangent line at point B is y = 3a²(x - a) + a³. This line intersects the curve at another point C, and we can find the x-coordinate of point C by setting y = 3a²(x - a) + a³ equal to x³ to get the equation x³ - 3a²x + 3a³ - a³ = 0. Using the fact that x = a is a root of this equation, we can factor it as (x - a)³ = 0, which implies that the curve and the tangent line are tangent at point C.
The region bounded by the curve and the tangent line at point A is a triangle with base a - (a - a) = 0 and height a³ - a³ = 0, so its area is 0. The region bounded by the curve and the tangent line at point B is a triangle with base a - a = 0 and height a³ - a³ = 0, so its area is also 0. Therefore, the areas R and S are both equal to 0, which means they are equal to each other.
HELP ME ALSO WITH THIS!!!!!
Answers
Explanation:
Start by multiplying both sides of the second equation by -2. Now line up both equations and add them to each other. Since the 2y and -2y cancel out, you are left with -10x = -60. Thus, you get x = 6 and can plug it back in to either equation to solve for y. After that, you are left with the solution (6,3).
I need help with this question. please help!!
Answers
The value of x in the heptagon is 38.6 degrees.
How to find the angle of an heptagon?An heptagon is a polygon with 7 sides. A regular heptagon is an heptagon with all sides equal to each other.
Therefore, sum of angles in an heptagon is equal to 900 degrees.
Let's find each angle of the heptagon.
each angle in the regular heptagon = 900 / 7
each angle in the regular heptagon = 128.57 degrees
Therefore, each angle of a square is 90 degrees.
Hence,
x = 128.57 - 90
x = 38.5714285714
Finally,
x = 38.6 degrees
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In a standard deck of cards (NOT including jokers), there are:
4 suits (diamonds, hearts, clubs, spades)
13 number and face cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King)
2 colors (red, black)
Face cards are Jack, Queen, King
a) What is the probability of drawing a red or black card?
b) What is the probability of drawing a 7 of spades?
c) What is the probability of NOT drawing a Diamond?
d) What is the probability of drawing a black 2?
Answers
hmm im not sure, but I'm going to try to help you!! but I think it is B or D. Maybe but I'm not too sure. though. :((