Answer:
d. people began buying more than they had the cash to pay for because they
could access loans and buy things on credit.
Step-by-step explanation:
In the 1920's, it was a period of prosperity and people in the middle class began to have more income available to purchase products. Also, there were more products available because of the assembly line production and the credits expanded which resulted in people being able to buy things that they couldn't purchase paying the full price. According to this, the answer is that the statement that best decribes the demand for consumer goods in the 1920's is that people began buying more than they had the cash to pay for because they could access loans and buy things on credit.
Which of the following is a type of data that is likely to be normally
distributed?
Answer: The answer is A
Step-by-step explanation:
Its the only one that has the least amount of options and the highest probability chance
Solve 3x+5y=30 for y
Answer:
y = [tex]\frac{30-3x}{5}[/tex]
Step-by-step explanation:
Given
3x + 5y = 30
Isolate the term in y by subtracting 3x from both sides
5y = 30 - 3x ( divide both sides by 5 )
y = [tex]\frac{30-3x}{5}[/tex]
Answer:
[tex]y=\frac{-3}{5}x+6[/tex]
Step-by-step explanation:
3x+5y=30 is the given equation.
We are asked to isolate y.
The term that contains y is 5y. I'm going to first isolate 5y.
To isolate 5y we see that we have +3x with it. To undo addition of 3x we will need to subtract 3x on both sides.
3x+5y=30
-3x -3x
5y=-3x+30
We now have 5y by itself. There is actually one step left to get the y by itself.
The last step is undo this multiplication between 5 and y.
To undo multiplication you divide.
So we will be dividing 5 on both sides. This gives us:
3x+5y=30
-3x -3x
5y=-3x+30
-- ---------
5 5
So the whole reason we did that is because 5y/5 is just y. I'm going to separate that fraction on the right hand side. This gives me:
y=-3/5 x + 30/5
I'm going to simplify the 30/5 to 6.
y=-3/5 x +6
Which of the following best describes a parabola?
O
A. The set of all points in a plane that are equidistant from a single
point and a single line
O
B. The set of all points in a plane that are equidistant from two points
O
C. The set of all points in a plane at a given distance from a given
point
O
D. The set of all points in a plane that are equidistant from two points
and a single line
Answer:
A
Step-by-step explanation:
The definition of a parabola.
Any point on the parabola (x, y) is equidistant from a point ( the focus ) and a line ( the directrix ).
Parabola is best describe by:
The set of all points in a plane that are equidistant from a single point and a single line What is parabola?"Parabola is defined as the set of all the points in a plane that are equidistant from a fixed point known as focus and a fixed line called directrix."
According to the question,
A. The set of all points in a plane that are equidistant from a single
point and a single line.
Equidistant from a single point called focus.Equidistant from a single line known as directrix.It represents the parabola.
Option(A) is the correct answer.
B. The set of all points in a plane that are equidistant from two points.
It represents the line.
Option (B) is not the correct answer.
C. The set of all points in a plane at a given distance from a given
point.
Given point is center of the circle.It represents the circle.
Option (C) is not the correct answer.
D. The set of all points in a plane that are equidistant from two points
and a single line.
It represents the perpendicular bisector.
Option (D) is not the correct answer.
Hence, Option(A) is the correct answer.
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A system of equations is shown:
2x = -y + 6
- 4x + 3y = 8
What is the solution to this system of equations?
(-1,-4)
(1,4)
(4,1)
(-4,-1)
Answer:
(1, 4)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x=-y+6&(1)\\-4x+3y=8&(2)\end{array}\right\\\\(1)\\-y+6=2x\qquad\text{subtract 6 from both sides}\\-y=2x-6\qquad\text{change the signs}\\y=6-2x\\\\\text{substitute it to (2):}\\\\(2)\\-4x+3(6-2x)=8\qquad\text{use the distributive property}\\-4x+(3)(6)+(3)(-2x)=8\\-4x+18-6x=8\qquad\text{subtract 18 from both sides}\\-10x=-10\qquad\text{divide both sides by (-10)}\\x=1\\\\\text{put the value of x to (1):}\\\\y=6-2(1)\\y=6-2\\y=4[/tex]
Answer:
(1,4)
Step-by-step explanation:
i just did the quiz and it was correct
If the distance between point R(a,a,a) and point J(6,-2,0) is 10, then the value of a could be?
Answer:
Step-by-step explanation:
√(6-a)^2+(-2-a)^2+(0-a)^2 = 10
36-12a+a^2+4+4a+a^2+a^2 =100
3a^2 -8a -60=0
(3a+10)(a-6)=0
a= -3/10 or 6
A square has an area is 49yd^2 what is the side length of each side
Answer:
The side length is 7 yds
Step-by-step explanation:
We know the formula for area of a square is
A = s^2 where s is the side length
49 = s^2
Take the square root of each side
sqrt(49) = sqrt(s^2)
7 =s
The side length is 7 yds
Final answer:
To find the side length of a square given its area, calculate the square root of the area. In this case, the side length of the square is 7 yards.
Explanation:
A square has an area of 49yd². To find the side length of each side, you need to take the square root of the area. In this case, the side length of each side would be 7 yards.
Which expression is equivalent to (-9x^-1 y^-9)/(-15x^5 y^-3)? assume x =/ 0 y =/ 0
Answer:
The answer is 3/5x^6y^6
Step-by-step explanation:
The given expression is:
-9x^-1 y^-9/-15x^5 y^-3
It can be written as:
= -9/-15 * x^-1/x^5 * y^-9/y^-3
As we know that [x^m/x^n = x^m-n]
= 3/5 * x^-1-5 * y^-9+3
= 3/5 * x^-6 * y^-6
= 3/5 * 1/x^6 * 1/y^6
= 3/5x^6y^6
The answer is 3/5x^6y^6....
The expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]
Evaluating an expressionFrom the question, we are to determine the expression that is equivalent to the given expression
The given expression is
(-9x^-1 y^-9)/(-15x^5 y^-3)
This can be written as
[tex](-9x^{-1}y^{-9} )\div (-15x^{5}y^{-3})[/tex]
[tex](-9\times \frac{1}{x} \times \frac{1}{y^{9} } )\div (-15 \times x^{5} \times \frac{1}{y^{3} } )[/tex]
[tex](\frac{-9}{xy^{9} } )\div (\frac{-15x^{5} }{y^{3} } )[/tex]
This becomes
[tex](\frac{-9}{xy^{9} } )\times (\frac{y^{3} }{-15x^{5} } )[/tex]
[tex]\frac{-9}{-15 } \times \frac{y^{3} }{xy^{9}\times x^{5} }[/tex]
[tex]\frac{3}{5 } \times \frac{1 }{y^{6}\times x^{6} }[/tex]
= [tex]\frac{3}{5x^{6}y^{6} }[/tex]
= [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]
Hence, the expression that is equivalent to the given expression is [tex]\frac{3}{5}x^{-6}y^{-6}[/tex]
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When you multiply a function by -1 what is the effect on its graph
Answer:
Please see attached image.
Step-by-step explanation:
When you multiply a function by -1 you are basically reflecting the values of the function over the x-axis.
The values that were negative become positive and the positive values become negative.
Please, take a look at the attached graph below, where there are examples with two functions.
Which equation represents a line that passes through (-2,4) and has a slope of 2/5?
Answer:
[tex]\large\boxed{y=\dfrac{2}{5}x+\dfrac{24}{5}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the slope [tex]m=\dfrac{2}{5}[/tex] and the point (-2, 4).
Put them in the equation of a line:
[tex]4=\dfrac{2}{5}(-2)+b[/tex]
[tex]4=-\dfrac{4}{5}+b[/tex] add 4/5 to both sides
[tex]4\dfrac{4}{5}=b\to b=\dfrac{24}{5}[/tex]
Answer:
I think that the answer is C
Find the y -axis intercept for the functions f(x) = -{3/2} -x-1 +2
Answer:
-1/2
Step-by-step explanation:
The equation given is
[tex]f(x)=-\frac{3}{2} -x-1+2[/tex]
Write it in form of y=mx+c where m is the gradient and c is the y-intercept
[tex]f(x)=-\frac{3}{2} -x-1+2\\\\\\y=-\frac{3}{2} -x+1\\\\\\y=-x-\frac{3}{2} +1\\\\\\y=-x-\frac{1}{2}[/tex]
y-intercept is -1/2
What additional information is needed to prove that the triangles are congruent using the ASA congruence theorem?
NL ≅ MP
NK ≅ MQ
N ≅ M
L ≅ P
Answer:
L ≅ P
Step-by-step explanation:
To prove congruence through ASA, we need the measures of two angles that are adjacent to a given side. If we are given that two angles are congruent to other angles in another triangle respectively and both of those angles are adjacent to one side (in which each side of each triangle is congruent) then the triangles are congruent through ASA.
To prove congruence using the ASA congruence theorem, we need to show that the angle measures of the triangles are equal. The additional information needed is that angle NM is congruent.
Explanation:To prove that the triangles are congruent using the ASA congruence theorem, we need to show that the angle measures of the triangles are equal.
Given that NL ≅ MP and NK ≅ MQ, we can conclude that the corresponding sides are congruent.Since N ≅ M and L ≅ P, we know that the corresponding angles are congruent.However, to fully prove congruence using ASA, we need to show that the included angle, angle NM, is congruent.Therefore, the additional information needed is that angle NM is congruent.Learn more about ASA congruence theorem here:https://brainly.com/question/13671709
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what dose 24/15 equals to?
Answer: 1.6 or 8/5
Step-by-step explanation: If you want to simplify it, the answer would be 8/5 because each number can be divided by 3. If you need the decimal, it would be 1.6.
Step-by-step explanation:
[tex]\dfrac{24}{15}=\dfrac{24:3}{15:3}=\dfrac{8}{5}\\\\\\\dfrac{8}{5}=\dfrac{5+3}{5}=1\dfrac{3}{5}\\\\\\1\dfrac{3}{5}=1\dfrac{3\cdot2}{5\cdot2}=1\dfrac{6}{10}=1.6[/tex]
You need to find the distance across a river, so you make a triangle. BC is 943 feet, m∠B=102.9° and m∠C=18.6°. Find AB.
Answer:
352.8 feet
Step-by-step explanation:
The given triangle is drawn in the image attached with. Note that the image is not drawn to scale.
We can find the length of AB using the law of sines. According to which:
[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]
Since sum of angles in a triangle is 180, we can write:
A + B + C = 180
A + 102.9 + 18.6 = 180
A = 58.5
Using the values, in the law of sines, we get:
[tex]\frac{943}{sin(58.5)} = \frac{c}{sin(18.6)}\\\\ c = \frac{943 \times sin(18.6)}{sin(58.5)}\\\\ c = 352.8[/tex]
Thus, the measure of side AB would be 352.8 feet
Answer:
The length of AB is 352.8 feet
Step-by-step explanation:
* Lets revise some facts to solve the problem
- The sine rule: [tex]\frac{sinA}{BC}=\frac{sinB}{AC}=\frac{sinC}{AB}[/tex]
- The sum of the measures of the interior angles of a triangle is 180°
* Lets solve the problem
- In Δ ABC
∵ m∠ B = 102.9°
∵ m∠ C = 18.6°
∵ m ∠A + m∠ B + m∠ C = 180° ⇒ interior angles of a Δ
∴ m ∠A + 102.9 + 18.6 = 180
∴ m ∠A + 121.5 = 180 ⇒ subtract 121.5 from both sides
∴ m∠A = 58.5°
* Lets use the sine rule to find AB
∵ BC = 943
∵ m∠A = 58.5°
∵ m∠ C = 18.6°
∴ [tex]\frac{sin(58.5)}{943}=\frac{sin(18.6)}{AB}[/tex]
- By using cross multiplication
∴ AB × sin(58.5) = 943 × sin(18.6)
- Divide both sides by sin(58.5)
∴ AB = [943 × sin(18.6)] ÷ sin(58.5) = 352.76 ≅ 352.8
* The length of AB is 352.8 feet
y = 3/5x + 1, 5y = 3x - 2, 10x - 6y = -4
is it perpendicular, parallel, neither
Answer:
[tex]y=\frac{3}{5} x+1[/tex] and [tex]5y=3x-2[/tex] are parallel.
[tex]10x-6y=-4[/tex] is neither parallel nor perpendicular.
Step-by-step explanation:
First, you have to simplify each equation in terms of y.
[tex]y=\frac{3}{5} x+1\\5y=3x-2\\10x-6y=-4[/tex]
Your first equation is already in terms of x, so simplify your second equation.
[tex]5y=3x-2\\y=\frac{3}{5} x-\frac{2}{5}[/tex]
Now you can simplify your third equation.
[tex]10x-6y=-4\\-6y=-10x-4\\y=\frac{5}{3} x+\frac{2}{3}[/tex]
These are your three equations in terms of y:
[tex]y=\frac{3}{5} x+1\\\\y=\frac{3}{5} x-\frac{2}{5} \\\\y=\frac{5}{3} x+\frac{2}{3}[/tex]
Now, all you have to know is how to tell using your slope if a line is parallel or perpendicular to another.
Two parallel lines will have the exact same slope.
Two perpendicular lines will have slopes which are opposite reciprocals. For example, a line with a slope of 2 is perpendicular to a line with a slope of [tex]-\frac{1}{2}[/tex], as they have opposite signs and are reciprocal (2/1 versus 1/2) to each other.
Your first two equations have the same slope and are therefore parallel.
Your third equation is a reciprocal, but it is not opposite, and is therefore not parallel nor perpendicular.
The first and the second lines are parallel as they both have a slope of 3/5. None of the lines is perpendicular to the others.
Explanation:In geometry and algebra, lines can be either parallel, perpendicular, or neither. To determine this, we need to look at the slope of each line. The slope of a line is the value of 'm' in the equation of the line, y = mx + c.
The equations you have provided are:
y = (3/5)x + 1, slope = 3/55y = 3x - 2, rearrange to y = (3/5)x - 2/5, slope = 3/510x - 6y = -4, rearrange to y = (5/3)x + 2/3, slope = 5/3When two lines have the same slope, they are parallel. When two lines have slopes that are negative reciprocals of each other (meaning their product is -1), they are perpendicular. In this case, the first and the second line are parallel (both have a slope of 3/5), and none of these lines is perpendicular to the others.
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A number is divided by 4, and then the quotient is added to 17. The result is 25. Find the number.
[tex]\bf \stackrel{\textit{number divided by 4}}{(x\div 4)}\qquad \stackrel{\textit{then added to 17}}{+17}\qquad \stackrel{\textit{the result is}}{=}\qquad 25\implies \cfrac{x}{4}+17=25 \\\\\\ \cfrac{x}{4}=25-17\implies \cfrac{x}{4}=8\implies x=(4)8\implies x=32[/tex]
Daquan and Juan are twins but their sister phillipa is 3 years older than them if the sum of their three ages is 36 how old are the twins
Step-by-step explanation:
Daquan's age = x
Juan's age = x
Phillipa's age = x + 3
x + x + x + 3 = 36
3x + 3 = 36
3x = 36 - 3
3x = 33
x = 33 ÷ 3
x = 11
the twins are 11 years old
One package of blueberries costs $3. How
many packages of blueberries can you buy
for $9?
Answer:
3 packages
Step-by-step explanation:
To find how many packages you can buy for $9, you have to divide 9 by 3.
Since each package costs $3.
So, 9/3 = 3
So you can buy 3 packages of blueberries.
Answer:
3 packages
Step-by-step explanation:
Since you can buy a package for $3, and you only have $9, how many $3 can you fit? Only 3. In conclusion, you can only buy 3 packages.
In the figure below, triangle ABC is similar to triangle PQR, as shown below:
what is the length of side PQ?
A) 18
B) 4
C) 32
D) 6
Answer:
So, Option A is correct.
Step-by-step explanation:
If the triangles are similar, then the sides are proportional
If triangle ABC is similar to triangle PQR
then sides
AB/PQ = BC/QR = AC/PR
We need to find PQ
We are given AB = 6, BC =8 and QR=24
AB/PQ = BC/QR
Putting values:
6/PQ = 8/24
Cross multiplying:
6*24 = 8*PQ
144/8 = PQ
=> PQ = 18
So, Option A is correct.
Answer: Option A
[tex]PQ=18[/tex]
Step-by-step explanation:
Two triangles are similar if the length of their sides is proportional.
In this case we have the triangle ∆ABC and ∆PQR so for the sides of the triangles they are proportional it must be fulfilled that:
[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}[/tex]
In this case we know that:
[tex]BC=8[/tex]
[tex]QR=24[/tex]
[tex]AB=6[/tex]
Therefore
[tex]\frac{BC}{QR}=\frac{AB}{PQ}[/tex]
[tex]\frac{8}{24}=\frac{6}{PQ}[/tex]
[tex]PQ=6*\frac{24}{8}[/tex]
[tex]PQ=18[/tex]
The Rangers won 5 of their first
8 games. At this rate, how many
games should the Rangers win out
of 56 games?
Answer:
35 games.
Step-by-step explanation:
5 out of 8 is 5/8 of their games which they have won.
So they should win (5/8) * 56
= 5*56 / 8
= 5*7
= 35 games.
Given the Rangers' current win rate of 5 wins out of 8 games, we can predict they would win about 35 games out of 56 if they continue at this rate.
Explanation:The question you've asked is related to
ratios
and
proportions
. You're given that the Rangers won 5 out of 8 games. If we extend this winning rate to 56 games, we need to find a proportion that equals the same win rate. The setup is: 5/8 = x/56, where 'x' is the number of games we expect the Rangers to win. To solve for x, we multiply across the diagonal (5*56) and divide by 8. That results in a value of
35
, so the Rangers should win 35 games out of 56 if they continue their current winning rate.
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Evaluate the function at the indicated values if possible. If an indicated value is not in the domain, say so.
f left parenthesis x right parenthesis equals StartFraction x plus 7 Over x squared minus 9 EndFraction
; f left parenthesis negative 7 right parenthesis, f left parenthesis 2 right parenthesis, f left parenthesis 3 right parenthesis
Answer:
f(-7)=0.
f(2)=-9/5.
f(3) doesn't exist because 3 isn't in the domain of the function.
Step-by-step explanation:
[tex]f(x)=\frac{x+7}{x^2-9}[/tex] is the given function.
We are asked to find:
[tex]f(-7)[/tex]
[tex]f(2)[/tex]
[tex]f(3)[/tex].
f(-7) means to replace x in the expression called f with -7:
Evaluate [tex]\frac{x+7}{x^2-9}[/tex] at [tex]x=-7[/tex]
[tex]\frac{(-7)+7}{(-7)^2-9}[/tex]
[tex]\frac{0}{49-9}[/tex]
[tex]\frac{0}{40}[/tex]
[tex]0[/tex]
So f(-7)=0.
f(2) means to replace x in the expression called f with 2:
Evaluate [tex]\frac{x+7}{x^2-9}[/tex] at [tex]x=2[/tex]
[tex]\frac{2+7}{2^2-9}[/tex]
[tex]\frac{9}{4-9}[/tex]
[tex]\frac{9}{-5}[/tex]
[tex]\frac{-9}{5}[/tex]
So f(2)=-9/5
f(3) means to replace x in the expression called f with 3:
Evaluate [tex]\frac{x+7}{x^2-9}[/tex] at [tex]x=3[/tex]
[tex]\frac{3+7}{3^2-9}[/tex]
[tex]\frac{10}{9-9}[/tex]
[tex]\frac{10}{0}[/tex]
Division by 0 is not allowed so 3 is not in the domain of our function.
plz solve my problem.any how
This was too long for me to write on the computer.
So I wrote it and took a picture.
If you have any questions, please don't hesitate to ask in the comments.
if the coefficient of determination for a data set containing 9 points is 1, how many of the data points must lie on the regression line for the data set.
Answer: 9 points
Step-by-step explanation:
The coefficient of determination is a number between 0 and 1 used to measure the level of precision with which the regression model created fits the data. A measure of [tex]R ^ 2 = 1[/tex] means that the model explains the entire variation between the two variables without error.
Therefore, in this case if [tex]R ^ 2 =1[/tex] means that the 9 points are on the line
Answer:
9 points
Step-by-step explanation:
A quadrilateral PQRS is inscribed in a circle, A quadrilateral PQRS is inscribed in a circle. The measure of angle PQR is 85 degrees. What is the measure of arc PQR?
Answer:
Measure of arc PQR is 190°
Step-by-step explanation:
First have a sketch of the quadrilateral PQRS inside a circle
You should notice that the intercepted angle is ∠PSR
You should remember that the intercepted arc PQR is twice the intercepted angle ∠PSR
Find the intercepted angle ∠PSR
Remember that in a quadrilateral opposite angles add up to 180°
Hence;
∠PQR+∠PSR=180°
85 + ∠PSR=180°
∠PSR=180°-85°=95°
Find arc PQR
Arc PQR =2×∠PSR
Arc PQR=2×95°
=190°
Price of a jeep dropped from 27000 to 22900. What was the percent decrease in price nearest hundredth percent?
Answer:
(27,000 - 22,900)/27,000 = 0.1519 or 15.19% decrease in price.
Step-by-step explanation:
For this case, we propose a rule for three:
27,000 -----------> 100%
22,900 -----------> x
Where "x" represents the percentage associated with 22,900.
[tex]x = \frac {22,900 * 100} {27,000}\\x = 84.8148148148[/tex]
Now we look for the percentage of decrease:
100% -84.8148148148% = 15.1851851852%
Rounding off we have:
15.19%
Answer:
15.19%
What are the zeros of f(x) = x2 + x - 20?
Answer:
x = - 5, x = 4
Step-by-step explanation:
Given
f(x) = x² + x - 20
To find the zeros equate f(x) to zero, that is
x² + x - 20 = 0
Consider the factors of the constant term ( - 20) which sum to give the coefficient of the x- term ( + 1)
The factors are + 5 and - 4, since
5 × - 4 = - 20 and + 5 - 4 = + 1, hence
(x + 5)x - 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 4 = 0 ⇒ x = 4
Answer:
The zeroes are {-5, 4}.
Step-by-step explanation:
f(x) = x^2 + x - 20 = 0
To factor this function we need 2 numbers whose sum is + 1 ( x = 1x) and whose product is -20. They are 5 and - 4 so we have:
(x + 5)(x - 4) = 0
x + 5 = 0 gives x = -5
and x - 4 = 0 gives x = 4.
The speed of sound is about 3.4 × 102 meters per second. Mark is performing a science experiment and he needs to know how far sound travels in 3 × 1010 seconds. If Mark uses a calculator to solve this problem, how will the calculator show the answer?
Answer:
[tex]1.02 \times 10^{13}[/tex]
Step-by-step explanation:
Speed of the sound = [tex]3.4 \times 10^{2}[/tex] meters per second
Time to calculate the distance traveled = [tex]3 \times 10^{10}[/tex] seconds
Since,
Distance = Speed x Time
Using the values we get:
[tex]Distance=3.4 \times 10^{2} \times 3 \times 10^{10}\\\\ = 3.4 \times 3 \times 10^{(2+10)}\\\\ = 10.2 \times 10^{12}[/tex]
Since the calculators show the final answer is scientific notation, the above answer in scientific notation would be:
Distance = [tex]1.02 \times 10^{13}[/tex]
Answer:
1.02 E 13
Step-by-step explanation:
The Answer is 1.02 E 13 because E means "time 10 to the power of". So 1.02 E 13 is basically just 1.02 time 10 to the power of 13.
You need to purchase centerpieces for no more than 12 tables at Prom. There is a
budget of no more than $100 and you have choices of flowers, f, that cost $4 each
and candles, c, that cost $7 each. Write a system of linear inequalities that would
represent the choices you have of selecting candles and/or flowers.
Answer:
{f + c < 12
{7c + 4f < 100
-5⅓ < f
7⅓ > c
Step-by-step explanation:
The keyphrase is no more than, which tells you that the inequality symbol has to be less than.
I am joyous to assist you anytime.
1. If the surface area of a square pyramid is 2225 yards squared. The base of the pyramid has a length of 25 yards. What is the height of the slant on one of the lateral faces?
2. The surface area of the cone below is about 151.58 inches squared. The radius of the base is 4 inches. What is the slant height? Use 3.14 for Pi. Round your answer to the nearest whole number.
Answer:
1) 32
2) 8 yards
Step-by-step explanation:
1. We must first subtract the base area of the pyramid from the total surface area to get the lateral surface area:
[tex]LA=2225-25^2=1600[/tex]
The lateral surface area is 4 times the area of one the congruent triangles.
[tex]LA=4\cdot \frac{1}{2}\cdot 25\cdot x[/tex]
[tex]\implies 1600=50x[/tex]
[tex]\implies \frac{1600}{50}=\frac{50x}{50}[/tex]
[tex]32=x[/tex]
Therefore the height of the slant surface is 32 yards
2) The surface area of a cone is [tex]S.A =\pi r^2+\pi r l[/tex], where l is the slant height.
We substitute the surface area S.A=151.58 and [tex]\pi=3.14,r=4[/tex] to obtain:
[tex]151.58=3.14\cdot 4^2+3.14\cdot 4 l[/tex]
[tex]151.58=50.24+12.56l[/tex]
[tex]101.34=12.56l[/tex]
[tex]\frac{101.34}{12.56}=l[/tex]
l=8.06
To the nearest whole number, the slant height is 8 yards
Select the graph of the solution. Click until the correct graph appears. {x | x < 4} ∩ {x | x > -2
Answer:
So the solution is -2<x<4 with it's graph is
O~~~~~~O
------(-2)--------(4)-----------
Step-by-step explanation:
The intersection symbol means it has to be included in both sets.
We have that x<4 and x>-2.
If we graph this, where do we see both shadings:
~~~~~~~~~~~~~~~0 x<4
O~~~~~~~~~~~~~~~~~ x>-2
-------(-2)-------------(4)------------
Both shadings happen between -2 and 4 (and not outside that area).
So the solution is -2<x<4
It's graph is
O~~~~~~O
------(-2)--------(4)-----------
Disclaimer:
I didn't see any equal signs in your problem.
You know the [tex]\ge[/tex] or the [tex]\le[/tex] so we didn't have any closed dots.
The graph is, °←--------------------→°
-2____0_________4
What is intersection?
The intersection of two sets is the set of all those elements which are common to both of the sets.
Here, given that, {x | x < 4} ∩ {x | x > -2}
It indicates that, x is less than 4, i.e. x= 3,2,1,0,-1,-2,-3,......
Again, x is greater than -2, i.e. x = -1,0,1,2,3,4,....................
Now, as it is intersection of this two sets
So, we have, x= -1,0,1,2,3.
Hence, the required graph is,
°←------------------------------------→°
_(-2)__________0____________4_____
To learn more on intersection click:
https://brainly.com/question/12089275
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What is a requirement of supplementary angles?
Supplementary angles are 2 angles that have the sum of 180 degrees. Therefore, the requirement of supplementary angles is to have the 2 angles to equal 180 degrees.
Hope this helps!
Answer:
the sum of angles must be 180 degrees
Step-by-step explanation:
The definition of supplementary angles is
"Two angles are supplementary angles if their sum is 180 degrees".
For example, if x and y are supplementary angles then
x + y = 180
Therefore, we can conclude that the requirement of supplementary angles is " the sum of angles must be 180 degrees".