Answer:
a = 4.52 km
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (7.2)² = a² + (5.6)²
→ 51.84 = a² + 31.36
→ a² = 51.84 - 31.36
→ a = √20.48
→ [ a = 4.52 km ]
Hence, value of a is 4.52 km.
determine if line AB and line CD are parallel, perpendicular or neither
Answer:
Line 1 is considered perpendicular
Line 2 is considered parallel
Line 3 is also parallel
Step-by-step explanation:
This should be right if this is the rest to your problem:
1. Line AB formed by A(-1,3) and B(1,5); Line CD formed by C(2,3) and D(-2,7)
2. Line AB formed by A(3,8) and B(-6,5); Line CD formed by C(-6,7) and D(-3,8)
3. Line AB formed by A(2,-7) and B(2,3); Line CD formed by C(-4,0) and D(-4,-5)
A furniture company is ordering screws. The company uses 37 screws to make each table and 16 screws to make each chair. The company needs to order screws for 12 tables and 48 chairs.
Which answer is the most reasonable estimate of the total number of screws they need to order?
the company uses 37 screws to make each table and 14 screws to make each chair. The company needs to order screws for 12 tables and 48
What is a,b,c and day
[tex]a=-5(-3)-2=13\\\\b=-5(-1)-2=3\\\\c=-5(1)-2=-7\\\\d=-5(2)-2=-12[/tex]
Answer:
A = 13 B = 3 C = -7 D = -12
Step-by-step explanation:
Just insert the x values for a, b, c, and d. for example if we were to find a.
The x value for a is -3 so we would put -3 in place of x in the equation.
-5(-3) - 2
Remember: Two negative numbers multiplied with each other equal a positive.
15 - 2 = 13
Decide whether each equation is true for all, one, or no values of x.
Answer:
For the first equation, it is "True for one value of x."
For the second equation, it is "True for no value of x."
For the third equation, it is "True for all values of x."
Step-by-step explanation:
Just solve the equation and check the numbers:
If both numbers are the same, it is "true for all values of x"
If there is a variable and a number, it is "true for one value of x"
If there are two numbers and they are different, it is "true for no values of x"
Hope this helps!
Please give brainliest
We need to check whether the given equations are true for all values of [tex]x[/tex] , one value of [tex]x[/tex] , or no values of [tex]x[/tex] .
The equations are ,
[tex]3x +9 = -4.5x +20[/tex]solve this equation for x ,
[tex]\longrightarrow 3x +9=-4.5x+20\\[/tex]
[tex]\longrightarrow 3x+4.5x =20-9\\[/tex]
[tex]\longrightarrow 7.5x =11\\[/tex]
[tex]\longrightarrow \underline{\underline{x =\dfrac{11}{7.5}}}[/tex]
Hence the equation is true for one value of x .
[tex] 9(x+3)=9x+12[/tex]solve out for x ,
[tex]\longrightarrow 9x +27=9x-12\\ [/tex]
[tex]\longrightarrow 9x -9x =-27-12\\ [/tex]
[tex]\longrightarrow 0 = -39[/tex]
This can never to true , so the equation is true for no values of x .
[tex]4(2x+3)=12+8x[/tex]solve out for x ,
[tex]\longrightarrow 8x+12=12+8x \\[/tex]
[tex]\longrightarrow 12-12=8x-8x\\[/tex]
[tex]\longrightarrow 0=0 [/tex]
Hence this equation is true for all values of x .
And we are done!
45 point reward if you help !! Find the volume of each shape and then compare do not reduce your fractions.
Answer:
150/512 < 64/125
Step-by-step explanation:
5/8 * 6/8 * 5/8 = 150/512 = 0.295
4/5 *4/5 * 4/5 = 64/125 = 0.512
Therefore: 0.295 < 0.512 or 150/512 < 64/125
Find the measures of each numbered angle:
Find x
80°
x+51
X =
OK
60°
ALGEBRA
For the given triangle and the measures of the given angle the value of x is equal to -11° .
As given in the question,
For the given triangle,
Let us consider the triangle name ABC,
Where, m ∠A = x + 51° ,
m ∠ABC = 80° ( vertically opposite angle of given 80° angle.)
m ∠ACB = 60° ( vertically opposite angle of given 60° angle.)
To get the value of x we have,
Sum of all the interior angles of a triangle is equal to 180°
m ∠A + m ∠B + m ∠C = 180°
⇒ x + 51° + 80° + 60° = 180°
⇒ x + 191° = 180°
⇒ x = 180° - 191°
⇒ x = - 11°
Therefore, for the given triangle and the measures of the given angle the value of x is equal to -11° .
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Dina pours 16-ounce containers of juice into a dispenser with a capacity of 960 ounces. The function y = 16x models this situation. What is the range of the function?
The range of the function is [0, 960]
How to determine the range of the function?From the question, we have the equation of the function to be
f(x) = 16x
Where
The size of the container is 16 ouncesThe capacity of the dispenser is 960 ouncesWhen the dispenser is empty, it means that f(x) = 0
When the dispenser is full, it means that f(x) = 960
When these values are combined, they represent the range
In other words, the range is 0 to 960
This can be rewritten as [0, 960]
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Answer:
big black men
Step-by-step explanation:
(i have your search history)
A merchant offers a large group of items at 18% off. later, the merchant takes 10% off these price sales and claims that the final price of these items is 86 off the original price. what is the total percent discount?
26.2% is the total percent of discount offered by the merchant.
Let us assume that each item is $100.
As it is given that 18% is off, we have an amount after off is:
Amount after 18% off = 100 × (100 - 18)/ 100
= 100 × 0.82
= 82
Next, there is 10% off
So the amount become = 82 ×( 100 - 10) / 100
= 82 ×0.9
= 73.8
So the final price of an item is $73.8
The discount = (100 - 73.8) / 100
= 26.2%
Therefore the total percent of discount is 26.2%.
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Find the solution to the following equation: 2(2x - 7) = 14
x = 14
x = 7
x = 1
x = 0
Answer:
x=7
Step-by-step explanation:
2(2x - 7) = 14
Solve for x
Divide each side by 2
2/2(2x - 7) = 14/2
2x-7 = 7
Add 7 to each side
2x-7+7 = 7+7
2x = 14
Divide each side by 2
2x/2 = 14/2
x = 7
Answer:
b) x = 7
Step-by-step explanation:
Given equation,
→ 2(2x - 7) = 14
Now the value of x will be,
→ 2(2x - 7) = 14
→ 4x - 14 = 14
→ 4x = 14 + 14
→ x = 28/4
→ [ x = 7 ]
Hence, the value of x is 7.
Write a linear function f with the values f(0) =10 and f(6) =34.
Answer:
f(x) = 4x + 10
Step-by-step explanation:
The given information is in the form f(x) = y.
f(0) = 10 means if x is 0, y is 10. This is the point (0,10)
Likewise, f(6) = 34
means when x is 6, y is 34. That is the point (6,34).
Slope is y-y / x-x
34-10 / 6-0
is 24/6.
The slope is 4.
The y-intercept is where x is 0, that is 10.
y=mx+b is slope-intercept form. Fill in the slope, 4 for m and the y-intercept, 10, for b.
y = 4x + 10
but they also asked to call it f, so for function notation, use f(x) instead of y.
f(x) = 4x + 10
Data were recorded for a car’s fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Given the least-squares regression line, , what is the predicted fuel efficiency for a speed of 30 mph?
17. 67 mpg
26. 50 mpg
30. 00 mpg
37. 74 mpg
The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.
What is the least-squares regression line?If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.
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Find the equation of the line shown in the pic (please help)
Answer:
-1/4 * x + 2
Step-by-step explanation:
first figure out the slope. You can easily read the point where the graph is crossing the y axis. From there, more right and read how much the graph goes up wor down. You see the graph goes down, so you know the slope must be a negative value. To get the full value of the slope, you need to work out how much the graph goes down if you go 1 right. So when you move 1 right from the point 2 on the y axis, you can't easily read how much it went down. But you can see that the graph passes the pont of x = 4 and y = 1. So it went 4 right and 1 down. To only got 1 down you divide y/x -> 1/4
So the slope is -1/4
and because the graph hits the y axis at 2 and not at 0, you need to add +2 to the equation.
(car sales) of the cars sold during the month of july, 90 had air conditioning, 102 had automatic transmission, and 72 had power steering. 7 cars had all three of these extras. 22 cars had none of these extras. 25 cars had only air conditioning, 61 cars had only automatic transmissions, and 33 cars had only power steering. 11 cars had both automatic transmission and power steering. how many cars had exactly two of the given options?
There were 58 cars sold with exactly two of the given options.
1. There were 90 cars sold with air conditioning.
2. There were 102 cars sold with automatic transmission.
3. There were 72 cars sold with power steering.
4. There were 7 cars sold with all three options.
5. There were 22 cars sold with none of the options.
6. There were 25 cars sold with only air conditioning.
7. There were 61 cars sold with only automatic transmission.
8. There were 33 cars sold with only power steering.
9. There were 11 cars sold with both automatic transmission and power steering.
Let's just count the number of cars that have exactly two of the given options:
Air Conditioning & Automatic Transmission: 25
Air Conditioning & Power Steering: 22
Automatic Transmission & Power Steering: 11
So there are 25 + 22 + 11 = 58 cars that have exactly two of the given options.
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Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral.
The dimension of the rectangle of the largest area in an equilateral triangle is √3/4L.
Here we have to find the dimension of the rectangle of the largest area.
Let the distance from the tip of the base of the triangle to the point that the top of the rectangle meets the triangle be x.
The width of the rectangle is √3/2 x.
By this, we can find the area of the rectangle
Area = √3/2x ( L -x) = √3/2 xL - √3/2x²
To find the maximum area we have:
dA/ dx = 0
dA / dx = √3/2L - √3x = 0
From we have to find the value of x,
√3 x = √3/2L
x = L/2
The dimension of rectangle is √3/2x = √3/2(L/2)
= √3/4 L
Therefore the dimension of the rectangle is √3/4 L.
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Can write the equation to this problem?
The equation, in vertex form, of the graph in the diagram is determined as: y = 1|x - 3| + 5.
What is the Equation of a Graph that Represents an Absolute Value Function?The formula that represents the equation in vertex form of an absolute value function is y = a|x - h| + k, where:
Vertex = (h, k).
Therefore, we will need to determine what the values of a, h, and k is using the information derived from the graph.
Thus:
(h, k) = (3, 5)
a = 1 (this is because the graph opens upward)
To write the equation of the graph, substitute a = 1, h = 3, and k = 5 into:
y = 1|x - 3| + 5
The equation is, y = 1|x - 3| + 5.
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Evaluate the problem
5/8 - 1/4.
Answer:
5/8 - 1/4 = 3/8
Step-by-step explanation:
Convert to equivalent fractions by multiplying the top and bottom of 1/4 by 2, in order to match 5/8's denominator.1 x 2 = 2, 4 x 2 = 8, so we're left with 2/8
subtract as normal, top by top.5 - 2 = 3.therefore 5/8 - 1/4 = 3/8Answer:
3/8
Step-by-step explanation:
5/8 - 1/4
to be able to compare fractions or add/subtract them directly, we need to bring them all to the same denominator (the bottom part of the fractions).
it is usually easier to bring the smaller to a larger number than the other way around, because of the existing numerators (the top part of a fraction).
since we are dealing with fractions (divisions !), the best way to manipulate them is by multiplying or dividing them by a factor.
so, what do we need to multiply with 4 to get 8 (the other denominator) ?
2, as 4×2 = 8.
aha.
but now careful, we cannot just multiply the denominator by 2. that would change the value of the whole original fraction.
we have to multiply denominator AND numerator by the same factor. that way the original value of the fraction remains the same, because we are essentially multiplying the whole fraction just by 1.
so,
1/4 × 2/2 = 2/8
and now we can easily use it in a calculation with other 8ths :
5/8 - 2/8 = 3/8
Write the coordinates of the vertices after a translation 3 units right and 12 units down
Step-by-step explanation:
3 units right = x + 3
12 units down = y - 12
E = (-5, 4) -> E' (-2, -8)
F = (-5, 9) -> F' (-2, -3)
G = (1, 9) -> G' (4, -3)
H = (1, 4) -> G' (4, -8)
In the image below, the measure of angle 3 is equal to the sum of the measures of angle 6 and what other angle?
For the given figure, angle 3 will be equal to angle 2.
According to the question,
We have the following information:
We have a figure where some angles are marked in form of numbers and the measure of angle 3 is equal to the sum of the measures of angle 6.
Now, we know that vertically opposite angles are equal and angle 1 and angle 4 are vertically opposite angles like angle 2 and angle 3.
(More to know: the sum of three angles of a triangle is equal to 180°.)
Hence, for the given figure, angle 3 will be equal to angle 2.
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Directions: Write an equation passing through the point and PARALLEL to the given line.
1. (4, 7); y = 3x+6
Answer: y=3x-5
Step-by-step explanation:
This was the answer i got after solving
Hope that helped :)
Screenshot is the proof of the answer btw :)
Can anyone state the vertex of the graph?
There is no vertex in the graph and the transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?The graph represents the given parameter
As a general rule, the maximum or the minimum of a graph is the vertex
In this case, there is no maximum or minimum in the graph
This means that that there is no vertex in the graph
The transformationHere, we have:
We can see that:
The graph is 4 units to the left of the origin and 2 units below the origin
This means that the function has been shifted down and shifted to the left
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Which number should be on the bottom left stamp?
Explain what the answer is and how you got it!
The number that should be on the bottom left stamp is 1. It was gotten by dividing 2 by 2.
What will the number be?From the first picture, we have 82 and the number below it is 4. This was gotten as:
= 8 ÷ 2
= 4
The second picture has 93 and the number below it is 3. This was calculated as:
= 9 ÷ 3
= 3
The third picture has 61 and the number below it is 6. This was calculated as:
= 6 ÷ 1
= 6
The fourth picture will be:
= 2 ÷ 2
= 1
Therefore the value is 1.
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Alonso went to the store to buy some almonds. The price per pound of
the almonds is $7.25 per pound and he has a coupon for $3.50 off the
final amount. With the coupon, how much would Alonso have to pay to
buy 5 pounds of almonds? Also, write an expression for the cost to buy
p pounds of almonds, assuming at least one pound is purchased.
The required price of almond and expression are $32.75 and c= $7.25P - $3.5 respectively.
What is pound?Pound is unit used to measure weight of quantity. It is used by the English speaking peoples.It equal to the 16 ounces and 0.454 kilogram.
According to given information:Alonso has a coupon of $3.5, let us consider P pound of almond. And price per pound of almond is $7.25
So, equation for the cost,
Cost(c) = $7.25P - $3.5
Then, the price of 5 pound of almond = $7.25×5 - $3.5
⇒ $36.25 - $3.5 = $32.75
Thus, the price of 5 pounds of almond is $32.75.
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Ken can walk 40 dogs in 8 hours. How many dogs can Ken walk in 1 hours?
Answer:
5
Step-by-step explanation:
divide.
determine if l=these points have a right angle
2,3 6,3 2,7
The points (2, 3) (6, 3), and (2, 7) sides corresponds to length of 4 : 4 : 5 and do not form Pythagorean triple hence they do not form a right angle
How to determine if the points (2, 3) (6, 3), and (2, 7) form a right angleThe distance between the points is calculated and Pythagoras theorem is used to determine if the triple forms a right angle
let the points be
A (2, 3) B (6, 3), and C (2, 7)
using the equation
d = √{(x₁ - x₂)² + (y₁ - y₂)²}
AB = √{(2 - 6)² + (3 - 3)²} = 4
BC = √{(6 - 2)² + (3 - 7)²} = 5
CA = √{(2 - 2)² + (3 - 7)²} = 4
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Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
-4, (-2 , 1)
0, (-1, 21)
The equation of straight line having
(a) gradient -4 and coordinates (-2,1) is 4x + y [tex]=[/tex] -7
(b) gradient 0 and coordinates (-1,21) is y = 21 .
In the question ,
the gradient and coordinates of the point on the line is given .
we have to find the equation of the straight line .
Part(a)
the gradient of the line [tex]=[/tex] -4 ,
the coordinates of a point on the line = (-2,1)
So , the equation of the line is
(y - 1) = (-4)*(x -(-2))
y - 1 = -4(x + 2)
y - 1 = -4x - 8
4x + y = -8 + 1
4x + y = -7
the equation is 4x + y = -7 .
Part(b)
the gradient of the line = 0 ,
the coordinates of a point on the line = (-1 , 21)
So , the equation of the line is
(y - 21) = 0(x-(-1))
y - 21 = 0
y = 21
the equation of the line is y = 21 .
Therefore , The equation of straight line having (a) gradient -4 and coordinates (-2,1) is 4x + y [tex]=[/tex] -7 and (b) gradient 0 and coordinates (-1,21) is y = 21 .
The given question is incomplete , the complete question is
Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
(a) -4, (-2 , 1)
(b) 0, (-1, 21)
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survey of 397 children given at a local elementary school showed that 175 like chocolate ice cream 225 like pistachio ice cream, and 97 do not like chocolate or pistachio ice cream. how many children like at most one kind of ice cream mentioned in the survey?
297 children like at most one kind of ice cream.
Total number of children = 397
Let C and P be the number of children like chocolate and pistachio ice cream respectively.
n(C) = 175
n(P) = 225
The number of student do not like chocolate or pistachio ice cream is,
n(P' and C') = 97
n(P or C)' = 97, by De Moivre's theorem
n(P or C) = 397-97 = 300
n(P) + n(C) - n(P and C) = 300
175 + 225 - n(P and C) = 300
400 - n(P and C) = 300
n(P and C) = 100
So the required number of children like at most one kind of ice cream = 397-n(P and C) = 397-100 = 297
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Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line x + 2y = 6?
write each choice into the boxes to correctly complete the table. *picture below *
Step-by-step explanation:
in order to be able to decide each case we need the slopes of all involved lines.
and that means we need to bring all of the equating into a "y = ..." form, because then the slope is always the factor of x.
parallel lines have the same slope.
the slopes of perpendicular lines (intercept at a right angle) have the y/x ratio turned upside-down and a flipped sign : -x/y.
"neither" is everything else.
our reference line
x + 2y = 6
2y = -x + 6
y = -1/2 x + 3
so, the reference slope is -1/2.
y = -1/2 x - 5 is parallel (same slope).
-2x + y = -4
y = 2x - 4 perpendicular (2/1 vs. -1/2)
-x + 2y = 2
2y = x + 2
y = 1/2 x + 1 neither
x + 2y = -2 parallel (as the structure except for the constant part is the same as our reference line).
2y = -x - 2
y = -1/2 x - 1
eight times the quotient of x and 2
Answer:
4x
Step-by-step explanation:
the quotient of x and 2 is [tex]\frac{x}{2}[/tex] , then
8 × [tex]\frac{x}{2}[/tex] ( cancel 8 and 2 by 2 )
= 4 × x
= 4x
what is the total surface area of an equilateral triangular pyramid with base side lengths of 6 feet and a height of 10 feet? the total surface area is about square feet.
Using the concepts of equilateral triangle, we got that 107 square feet is the total surface area of an equilateral triangular pyramid with base side lengths of 6 feet and a height of 10 feet.
We have :
Base (b) = 6 feet
Slant height (l) = 10 feet
The lateral surface area is calculated using:
L = (3/2)× Length × Breadth
So, we have:
L = (3/2) ×6 × 10
=>L=(3×3×10)
=>L=90 square feet.
The total surface area is calculated using:
T=Lateral surface area of the wall + area of equilateral triangle
=>T=L+ (√3/4)b²
So, we have:
T = 90 + (√3/4)×(6×6)
=>T=90+(3×3×√3)
=>T=90+9√3
=>T=107 square feet (approx)
Hence, the total surface area of an equilateral triangular pyramid with base side lengths of 6 feet and a height of 10 feet is 107 square feet.
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