A rectangle with a diagonal of length x is twice as long as it is wide, the area of the rectangle is (B) 2x²/5..
How to find the area of the rectangle?Given that we have a rectangle with a diagonal of length x is twice as long as it is wide.
Let
L = length of rectangle,
W = width of rectangle and
D = length of diagonal = x
Given that the length of diagonal, x is twice as long as it is wide, we have that
L = 2W
Also, since it is rectangle, we have that
D² = L² + W²
D² = (2W)² + W²
D² = 4W² + W²
x² = 5W²
W² = x²/5
W = x/√5
W = x√5/5
since the length of the rectangle, L = 2W, we have that
L = 2W
= 2x√5/5
The area of the rectangle
The area of the rectangle is given by A = LW where
L = length of rectangle and
W = width of rectangle
So, A = LW
= 2x√5/5 × x√5/5
= 2x² × 5/25
= 2x²/5
So, the area of the rectangle is (B) 2x²/5
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kumiko decides to buy the same number of apps and games, and she decides to spend as much of the $50 as possible. how many apps and games does she buy? how much money does she have left on her gift card?
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "."
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
What is Inequality?Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "." These values might be either numerical, algebraic, or both.
The number of apps Kumiko buy is a and the number of games she can buy is g.
The gift card has 50$.
Total amount of apps = 1.25a
Total amount of games = 2.5g
So, the linear equality will be [tex]1.25a+2.5g\leq50[/tex].
She can can only games and apps for amount less than and equal to $50.
Therefore, The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
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The given question is Incomplete. Here is the complete question:
Kumiko has a $50 gift card for a Web site that sells apps and games. Games cost $2.50 each, and apps cost $1.25 each. Write an inequality that represents the number of apps a and the number of games g that Kumiko can buy and describe any constraints.
after sampling a column of water from the surface to a depth of 3000 meters (nearly 10,000 feet), a colleague abroad an oceanographic research vessel tells you that the water column is isopycnal. what does this mean? what conditions create such a situation? what would have to happen in order to create a pycnocline?
Salinity and density decrease as temperature rises. Salinity and density, therefore, have a negative relationship with temperature. The density rises as salinity rises. As the temperature drops, ocean water becomes denser. Therefore, water becomes denser as it becomes colder. The density of seawater also rises as salinity does.
Water that is less dense floats above water that is denser. The warmer water will float on top of the colder water if there are two layers of water with the same salinity. However, there is a catch! Salinity has less of an impact on water density than temperature does. Therefore, if the layer with higher salinity is considerably warmer than the layer with lower salinity, the layer with higher salinity can actually float on top of the layer with lower salinity.
As you descend to the ocean's bottom, the temperature of the water continues to drop. So, as you descend to the ocean's bottom, the density of the water keeps rising. The deep ocean is divided into layers, with the lightest water at the top and the densest water at the bottom. The ocean's depths have horizontal circulation. In other words, water flows in strata of equal density.
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which of the following beverages contains the most alcohol? 12-ounce can of beer 1.5 ounces of 80-proof liquor 5-ounce glass of wine all of these contain the same amount of alcohol
A 12-ounce can of beer contains the same amount of alcohol as a five-ounce glass of wine.
In a five-ounce glass of wine, the percentage of alcohol is 12%, which is the same in the 12-ounce can or bottle of beer, and 1.5 ounces of 86-proof liquor. Although a person under the influence of alcohol will have impaired judgment and therefore must avoid driving, doesn't matter what kind of alcoholic beverage they drink. Digestion of alcohol doesn't take place as soon as you drink it, it is absorbed in your bloodstream which reaches the brain and thus creates impaired judgment.
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angelina drove at an average rate of 80 kmh and then stopped 20 minutes for gas. after the stop, she drove at an average rate of 100 kmh. altogether she drove 250 km in a total trip time of 3 hours including the stop. which equation could be used to solve for the time t in hours that she drove before her stop?
The equation that could be used to solve for the time t in hours that she drove before her stop is 80t + 100(8/3 - t) = 250.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let t = time she drove before her stop
If the total trip time is 3 hours including the stop, which took 20 minutes, then the time she drove after the stop is 3 - t - 1/3 or 8/3 - t.
If altogether she drove a distance of 250 km, then the sum of the products of the rate of speed and time each drive is equal to 250.
(80 km/h)(t) + (100 km/h)(8/3 - t) = 250
Simplify the equation.
80t + 100(8/3 - t) = 250
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The time taken by the rocket to reach its maximum height is 1.25 seconds and the maximum height is 32 feet.
Given equation:
h(t) = -16t^2+40t+7 and initial velocity is 40 feet per second and launching pad is 7 feet tall.
a = 1
t = -b/2a
= -40/2*-16
= -40/-32
= 40/32
= 1.25 seconds
h(2.5) = -16(1.25)^2+40*1.25+7
= -1.5625*16+50+7
= -25+57
= 32 feet.
Therefore The time taken by the rocket to reach its maximum height is 1.25 seconds and the maximum height is 32 feet.
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Angel typically orders a 12-ounce Frappuccino that has 430 calories. If she orders the 20 ounce version, how many calories does it
have? Round to the nearest whole number.
Answer: ___ calories
Answer:717 calories
Step-by-step explanation:
first you need to find what one ounce would be:
430/12=35.83...
then you multiply the answer by 20
35.83*20=716.6...=717
This one too please ! I’m stressing over here guys !
The expression that is equivalent is y(x + 2) and xy + 2y and x(x + y + 2) and x² + xy + 2x
How to find equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.
Now, let's check if the expression are equivalent by simplifying it.
y(x + 2) and xy + 2y
xy + 2y and xy + 2y
Therefore, the expressions are equivalent.
x(x + y + 2) and x² + xy + 2x
x² + xy + 2x and x² + xy + 2x
They are equivalent expression.
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Choose the
system of inequalities that best matches the graph below.
The system of inequalities that best matches the graph is Option C
Step-by-step explanation:
To find the system of inequalities, we simply need to find the equation of each line.
Thus, let's find the inequality that is represented by each line.
Red Line:
First, let’s determine the slope. To do so, we can use the slope formula:
m = (y₂-y₁) / (x₂-x₁)
We can use any two points that's on the Red Line. Using (3, -2) and (6, -4) and substituting them into the slope formula yields:
m = (-4+2) / (6-3) = -2/3
Therefore, the slope of the red line is 2.
To write the equation of the red line, we can use the slope-intercept form:
y = mx + c
Notice that our y-intercept of our red line is (0, 3). Therefore, b = 3 and we already determined that m = -2/3:
y = ((-2/3)x) + (-3)
y = (-2/3)x -3
Now, we need to determine our sign. Notice that the shaded region is below the red line. Therefore, y is less than our equation.
And since our line is shaded, our sign will be less than or equal to. Therefore:
y ≤ (-2/3)x - 3
Blue line:
Again, let’s first find the slope. We can use the two points (3,0) and (0, -3). Hence:
m = (-3-0) / (3-0) = -3/3 = -1
So, the slope is -1.
We can now use the slope-intercept form. Notice that our y-intercept is (0, 0). Thus, we will substitute -1 for m and 0 for b. This yields:
y = -1x + 0
y = -x
Finally, we will determine our sign. Since the shaded region is above the blue line, our y is lesser than our equation. Therefore, our equation is:
y < -x
Thus, all together, our inequalities are:
y ≤ (-2/3)x - 3
y < -x
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I need help like asap !!!
only numbers and decimal points
Answer:
c = 11.46 yd
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ c² = (8.1)² + (8.1)²
→ c² = 65.61 + 65.61
→ c² = 131.22
→ c = √131.22
→ [ c = 11.46 yd ]
Hence, value of c is 11.46 yd.
what is y=6x+20? Stemscopes
The solution of the given equation [tex]y=6x+20[/tex] is [tex]x = \frac{y + 20}{6}[/tex]
What is linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
We have,
[tex]y = 6x + 20[/tex]
Arrange the equation both sides so that all variable terms are on the left hand side.
[tex]6x - 20 = y[/tex]
Add 20 to both sides of the equation.
[tex](6x - 20) + 20 = y + 20[/tex]
[tex]6x = y + 20[/tex]
Divide both sides by 6 we get,
[tex]\frac{6x}{6} = \frac{y + 20}{6}[/tex]
∴ [tex]x = \frac{y + 20}{6}[/tex]
Hence, final solution is [tex]x = \frac{y + 20}{6}[/tex] .
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Peter puts $300.00 into an account to use for school expenses. The account earns 8%
interest, compounded annually. How much will be in the account after 10 years?
Select the ordered pair that is NOT marked on the coordinate plane below.
Answer: C. (2, 1)
Step-by-step explanation:
The numbers labeled are
(-5, -8)
(-2, 1)
(4, 0)
(2, 9)
Find coordinates by looking at each line. (x, y)
The x-axis is the horizontal line in the middle.
The y-axis is the vertical line going across.
The x-axis always goes first when plotting down coordinates, and y goes second.
So, the one NOT labeled is C (2, 1)
The expected value for getting heads, on 30 coin tosses, is 15. The
expected value for rolling a 1, after 30 die rolls is 5. What is the
expected value of the sum of these events? Enter your answer in the
box.
The expected value of the sum of these events will be 2 / 3.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that the expected value for getting heads, on 30 coin tosses, is 15. The expected value for rolling a 1, after 30 die rolls is 5.
The probability of the sum will be calculated as,
P = ( 15 / 30 ) + ( 5 / 30 )
P = ( 20 / 30 )
P = 2 / 3
Therefore, the expected value of the sum of these events will be 2 / 3.
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identify the error in the diagram below. what's wrong with it. 70pts
The triangle does not exist, as the property, the sum of two sides of a triangle is greater than the third side length of the triangle does not hold true.
Describe the triangle.Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric forms is represented by the symbol △ and consists of three connected vertices. Triangles may be categorized into a number of different varieties according to their sides and angles.
It is a triangle's property that the sum of any two sides of a triangle is greater than the third side.
Here sides given are 3 m, 5 m, 9 m.
Let us add the sides length 3 m and 5 m
3 m + 5 m = 8 m
Compare this with the third-side length of the triangle
8 m < 9 m
So, the property does not hold true.
So, the triangle does not exist.
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the lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. a baby is premature if it is born three weeks early. what percent of babies are born prematurely?
8.08 percent of babies are born prematurely .
We have following information,
lengths of pregnancy of humans are Normally distributed.
mean of distribution ( μ ) = 268 days
standard deviations of distribution = 15 days
We shall find out the pecent of babies are born. prematurely.
Using the Normal distribution formula ,
Z = ( X - μ ) /σ
where X---> sample mean
μ --> poplution mean
putting the possble values of variables we get,
if a baby born three weaks early then he is considered as premature.
X = 21 , μ = 268 , r =
Z = ( 21-268)/ 15 = - 247/15 = - 16.4
Now, p-value corresponding to Z-value= -16.4 is
8.08..
thus for z= -16.4 , p-value will be 8.08 .. So, 8.08 percent of babies are born prematurely.
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Surface area of a rectangular prism 2cm 8cm 7 cm
The surface area of the rectangular prism is 172cm^2
What is a prism?Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross sections. The faces of the prism are parallelograms or rectangles.
The surface area of prism is 2A+ pH
where A is the base area
P is the perimeter of the base
and h is the height
for a rectangular prism, the base area is 2×8=16cm^2
perimeter of a rectangle= 2(l+b)
= 2(8+2)
= 20cm
surface area =( 2× 16) + 20× 7
= 32+ 140
= 172cm^2
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-9 (9x -6) = 3 (4x+6)
Answer:
[tex]-9 (9x -6) = 3 (4x+6) \\ - 9 \times 9x + 9 \times 6 = 3 \times 4x + 3 \times 6 \\ - 81x + 54 = 12x + 18 \\ -81x - 12x = - 54 + 18 \\ - 93x = - 36 \\ x = \frac{36}{93} \\ x = \frac{18}{46.5} \\ x = 0.3870967742[/tex]
6 groups of what tenths is 4.2
The answer is 6 groups of 0.7 tenths is 4.2. in the decimal form.
What is Decimals?
Decimals are a form of a number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
6 groups of ____ tenths is 4.2
4.2 ÷ 6 = 0.7
Hence, 6 groups of 0.7 tenths is 4.2
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Convert the standard form equation into slope-intercept form. 6x-2y=-20
Trevor and Michael are hosting a banquet. They plan to spend $400, plus or minus $50, at a cost of $25 per guest. Solve |25x-400| = 50 to find the maximum and minimum number of guests. If there can be up to 7 guests at each table, what is the minimum number of tables Trevor and Michael should reserve so that every guest has a seat?
Answer:
to find the max number of guests:
25x-400 = 50
25x = 50 + 400
25x + 450
then divide
x = 450/25
x = 18
to find the min number of guests:
25x = 400 - 50
25x = 350
then divide
x = 350/25
x = 14
Minimum number of tables reserved:
is dividing the max/7 per table
x = 18/7
x = 3
Step-by-step explanation:
find the circumference using the formula calculate your answer to the nearest hundredth
The circumference of the circle to the nearest hundredth is 21.98 inches.
How to find the circumference of a circle?The circumference of a circle is the measure of the boundary or the length of the complete arc of a circle.
The circumference of a circle is the perimeter of the circle. It's the wholes boundary of the circle.
The circumference of the circle can be found as follows:
circumference of a circle = 2πr
where
r = radiusTherefore,
diameter of the circle = 7 inches
radius of the circle = 7 / 2 = 3.5 inches
Hence,
circumference of a circle = 2 × 3.14 × 3.5
circumference of a circle = 21.98 inches
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Write equivalent fractions for 2/3 and 8/11 using the least common denominator.
Type the fractions, using a slash ( / ) to separate the numerator and denominator.
2/3 =
8/11 =
please give me the RIGHT answer immediately for the fractions using the least common denominator
The equivalent fraction for 2/3 and 8/11 is 22/33 and 24/33.
What is least common denominator?
The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.
Given fractions are
2/3 and 8/11
L.C.M of 3 and 11 is 33.
We get,
2/3 ×11/11 = 22/33
and
8/11×3/3 = 24/33
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a high school statistics class wants to estimate the average number of chocolate chips in a generic brand of chocolate chip cookies. they collect a random sample of cookies, count the chips in each cookie, and calculate a 95% confidence interval for the average number of chips per cookie (18.6 to 21.3). which interpretation of the 95% confidence interval is valid?
Answer:
Step-by-step explanation:
−8×{108÷12−(−3×11−15)÷12}
Answer:
[tex] - 8(9 - ( - 33 - 15) \div 12[/tex]
[tex] - 8(9 - ( - 48) \div 12[/tex]
[tex] - 8(9 + 4)[/tex]
[tex] - 8(13)[/tex]
[tex] - 104[/tex]
Answer:
-104
Step-by-step explanation:
Divide 108 by 12
Calculate -3 × 11 - 15 which is 48
Remove the parentheses
Divide 48 by 12 which is 4
9 + 4 is 13
-8 × 13 = -104
Write and graph linear equations
The equation of the line is y = -3/4x + 10, the graph of the equation has been plotted
The slope of the line = -3/4
The slope of the line the change in y coordinate with respect to the change in x coordinate of the function
The line is passing through the point (0,10)
The point slope form is
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute the values in the equation
y-10 = -3/4(x-0)
y - 10 = -3/4x
y = -3/4x + 10
The equation of the line in slope intercept form is
y = -3/4x + 10
Plot the graph using the slope intercept form
Hence, the equation of the line is y = -3/4x + 10, the graph of the equation has been plotted
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At the fast food restaurant, an order of fries costs $1.08 and a drink costs $1.09. How
much would it cost to get 5 orders of fries and 4 drinks? How much would it cost to
get f orders of fries and d drinks?
Total cost, 5 orders of fries and 4 drinks:
Total cost, f orders of fries and d drinks:
Answer: $9.76
Step-by-step explanation: If you multiply f, the order of fries (5) by the cost of it ($1.08) you would get $5.40 & if you multiply d, the order of drinks (4) by the cost of it ($1.09) you would get $4.36. If you add up both the total numbers, you would get a final answer of $9.76.
Answer:
$9.76
Step-by-step explanation:
1.08f + 1.09d= Total
1.08(5)+1.09(4)= Total
5.40+4.36= Total
. Use the distance formula to find the distance between the points (5,6) and (10,12). You
can leave the answer as a square root if it is not a perfect square.
The distance between the two points (5,6) and (10,12) is [tex]\sqrt{61}[/tex]
What is the distance between two points formula?
The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a standard formula to calculate the distance between two points. This equation can calculate the separation between any two locations on an x-y plane.
Solution explained:
First, Write the distance formula:
[tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
Now,
Substitute (5,6) and (10,12) into [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex] :
[tex]\sqrt{(10 - 5)^{2} + (12 - 6)^{2}}[/tex] Calculate
[tex]\sqrt{(5)^{2} + (6)^{2}}[/tex] Calculate
[tex]\sqrt{25 + 36}[/tex] Calculate
Hence. the distance between points (5,6) and (10,12) is [tex]\sqrt{61}[/tex].
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Which expression shows the distance you would travel from the gym to your science class in this hallway?
The expression that shows the distance you would drive from the gym to the office along this road is b.|-6|+|4|
What is a Distance ?Distance is a numerical or qualitative measurement of the distance between two objects or points. Distance is defined as an object's total movement without regard for direction. The distance can be defined as how much ground an object has covered regardless of its starting or ending point.
To find the distance between two points in a number line we do the absolute value of the points subtracted. That is if we need to find the distance between point a and point b in a number line we do |a-b|.
Now, the Gym is at point -6 in the number line and the office is at point 4 in the number line, then the distance from -6 to 4 is |-6-4| = |-10| = 10.
Now, option a is |-6+4| ≠ |-6-4|.
The option b is |-6|+|4| = 6+4 = 10 =|-6-4|. Then, option b is correct.
Option c is -6+4 ≠ |-6-4|.
The option d is -|6|+|4| = -6+4 ≠ |-6-4|.
Then, the correct answer is b.
The complete question is given below.
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Complete question
Which expression shows the distance you would drive from the gym to the office along this road?
a.|-6 + 4|
b.|-6|+|4|
c.-6+4
d.-|6|+|4|
John is in charge of feeding the pigs and cows on the farm. The cow's food costs twice as much as the pig's food. There are 46 cows and 22 pigs on the farm. John has a $860 budget for food a month. How much can John spend on food for each cow per month?
I tried solving this and got some random answer like $7.5432... per pig. Please Help
The cost of feed for a cow in a month is $15.08
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)
Similarly the ratio of the cost of cow's food to pig is 2:1
represent the cost of feed of a cow by x and the cost of feed for a pig to be y
therefore x= 2y
there are 46 cows, therefore the cost of feed for 46 cows is 46x
there are 22 pigs, therefore the cost of pig is 22y
46x+22y= 860
representing 2y for x
46(2y)+22y= 860
114y= 860
y= 860/114
y=$ 7.54
recall x=2y
x= 7.54×2= $15.08
therefore $15.08 is spent on a cow in a month
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Sara has a box of markers. In the box are 5 red markers, 3 blue markers, 9 purple markers,
and 3 pink markers. If she reaches into the box and randomly pulls out a marker, what is the
probability that Sara will pick a blue marker?
The probability that Sara will pick a blue marker is 3/20.
What is probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Math's to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given,
the box contains red markers = 5
blue marker = 3
purple marker = 9
pink markers = 3
Total number of markers = 20
The probability that she picks blue marker = 3/20
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