Answer:
0 represents the ground level
L 1.9.3 Test (CST): Foundations of Geometry
Question 19 of 25
Which of the diagrams below represents the statement "If it is a tree, then it
has leaves"?
has leaves
tree
Figure A
O A. Figure A
OB. Figure B
tree
has leaves
Figure B
Figure A is a diagram which represents the statement "If it is a tree, then it has leaves."
How to analyze and interpret the diagram?In figure A, we can observe that the subset representing "trees" lie inside another subset which represents "has leaves." Thus, we can logically deduce that the statement "All trees have leaves" and "if it is a tree, it has leaves" is represented by figure A.
On the other hand, we can observe that the subset representing "has leaves" lie inside another subset which represents "trees," which contradicts the given statement "If it is a tree, then it has leaves."
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find the domain of the function of the graph.
Answer:
[-3, 5)
Step-by-step explanation:
At x = -3, the circle is filled in, so -3 is part of the domain. At x = 5, the circle is not filled in, so 5 is not part of the domain. So the domain is [-3, 5).
N
32
NEXT QUESTION
C
Patty had four times as many quarters as nickels. She had $12.60 in all. How many nickels and how many quarters did
she have?
G
Which of the following equations could be used to solve the problem?
Answer:
See below
Step-by-step explanation:
q = quarters value = .25 q
n = nickels = 4q value = .05 (4q)
summed = 12.60
.25q + .05(4q) = 12.60 <====== can be used to solve the problem
.45q = 12.60
q = 28 quarters then nickels = 4q = 112
graph y = − 3/2 x − 3
Answer:
Step-by-step explanation:
THIS WILL BE A STRAIGHT LINE rising to the left as the coefficient of x is negative ( -3/2),
When x = 0 y = -3 so mark the point (0, -3) on your graph paper.
When x = 6, y = -3/2 * 6 - 3 = -9 - 3 = -12
So mark the point (6, -12)
The graph will be the straight line passing through the above 2 points.
When planning road development, the road commission estimates the future population using the function represented in the table, where x is the time in years and f(x) is the total population.
What is the significance of 160,000 in the function?
the maximum population of the city
the expected population in 5 years
the initial population at the time of the estimation
the amount of increase in the popu
Considering that 160,000 is the y-intercept of the function, it's significance is given by:
the initial population at the time of the estimation.
What is the y-intercept of a function f(x)?The y-intercept is f(0), that is, the value of y when x = 0, which is interpreted as the initial value of the function.
Researching this problem on the internet, it is found that f(0) = 160,000, hence the significance of 160,000 in the function is given by:
the initial population at the time of the estimation.
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which shows the correct substitution of the values a, b, and c Dr the equation 0=-3x^2-2x+6 into the quadratic formula? Quadratic formula: x= -b±√b^2-4ac/2a
Answer: Option 1
Step-by-step explanation:
Here, a = -3, b = -2, c = 6.
What is the inverse of this function?
8v, for x > 0
Answer:
f(x) = (x/8)^2 for x ≥ 0
Step-by-step explanation:
y = 8 sqrt x switch x and y
x = 8 sqrt y now solve for y
(x/8)^2 = y
f(x)=x^2. which of these is g(x) ?
a. g(x)=(1/5x)^2
b. g(x)=5x^2
c.g(x)=(1/4x)^2
d.g(x)=1/5x^2
Answer:
a
Step-by-step explanation:
we know that g(x) means y therefore in this case let's suppose we have the coordinate (5;y) so we must find the corresponding y value
*DO THE TRIAL AND ERROR METHOD*
take any equation above and substitute the value of x of which is 5 and the corresponding value should be 1.
[tex]g(x) = (\frac{1}{5} x) {}^{2} [/tex]
Harry placed blue and green marbles in a bag. Three-quarters
of the marbles are blue. Which of the following could be the
number of blue marbles in the bag?
It would be 5 because three quarters of 20 would be 15, and 5 would be the remainder.
Step-by-step explanation:
Sorry if its wrong I cant see the answer choices
its math help me out?
Answer:
D IS THE BEST IS WHAT MY TEACHER TOLD ME
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
To determine the correct table of input/outputs, take each input, substitute it into the function for "x", evaluate, and see if it equals the output. If it works for ALL of the pairs, then it is the correct table. Since functions only have one output for any input, there can't be two correct answers.
[tex]f(x)=\frac{3}{x}+4[/tex]
Check x = -3
[tex]f(-3)=\frac{3}{(-3)}+4\\=-1+4\\=3\\f(-3)\overset{\checkmark}{=}3[/tex]
Check x = -2
[tex]f(-2)=\frac{3}{(-2)}+4\\=-1.5+4\\=2.5\\f(-2)\overset{\checkmark}{=}2.5[/tex]
Check x = 1
[tex]f(1)=\frac{3}{(1)}+4\\=3+4\\=7\\f(1)\overset{\checkmark}{=}7[/tex]
Check x = 2
[tex]f(2)=\frac{3}{(2)}+4\\=1.5+4\\=5.5\\f(2)\overset{\checkmark}{=}5.5[/tex]
Check x = 3
[tex]f(3)=\frac{3}{(3)}+4\\=1+4\\=5\\f(3)\overset{\checkmark}{=}5[/tex]
Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces.
The equation will be given as y = 6x for the given information in the question.
The complete question is as below:-
Mr Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Here we are given that the weight of each book is 6 ounces. If there are x number of books, the weight of x books will be 6 times x.
And if y represents the total weight, we can form an equation describing the relation between a number of books and their net weight. The equation can be
y = 6x
Hence all the ordered pairs satisfying the above equation will represent the number of books and the total weight.
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What is the transformation of C(9, 3) when dilated with a scale factor of 1/3,
using the point (3, 6) as the center of dilation
The transformation of C(9, 3) when dilated with a scale factor of 1/3, using the point (3, 6) as the center of dilation would be an option B: C'(3,1).
What is Dilation transformation?A dilation transformation is a transformation that changes the size of the original figure but the shape remains unchanged.
If any figure is dilated by a scale factor k with the center of dilation as the origin.
Then the change of transformation in each of the vertices of the figure is given:
(x,y) → (kx, ky)
It is given a point C which is located at C(9,3).
Hence, here k=3
We get:
C(9,3) → C'(9×3,3×3)
C(9,3) → C'(27,9) = C'(3,1)
Hence, the transformation of C(9, 3) when dilated with a scale factor of 1/3, using the point (3, 6) as the center of dilation would be an option B: C'(3,1).
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Answer:
(5,5)
Step-by-step explanation:
count from the center
Answer each question below.
14. In angle LMN, the exterior angle adjacent to angle L has a measure of 5x+12. If the measure of angle M= 3x-2 and the measure of angle N= 50. Find the measure of angle L.
Answer:
[tex]\huge\boxed{\sf L = 78\°}[/tex]
Step-by-step explanation:
Given that:Exterior angle of L = 5x + 12
M = 3x - 2
N = 50
Statement:Exterior angle is equal to the sum of non-adjacent interior angles.So, the exterior angle that is adjacent to L is equal to the sum of non-adjacent sides (M and N) of the triangle.
Here,
Exterior angle of L = M + N
5x + 12 = 3x - 2 + 50
5x + 12 = 3x + 48
Subtract 12 to both sides
5x = 3x + 48 - 12
5x - 3x = 36
2x = 36
Divide 2 to both sides
x = 18
So,
Measure of angle M:= 3x - 2
= 3 (18) - 2
= 54 - 2
= 52°
Now,
Measure of angle L:We know that,
Sum of all the interior angles of triangle is 180 degrees.L + M + N = 180°
L + 52 + 50 = 180
L + 102 = 180
Subtract 102 to both sides
L = 180 - 102
L = 78°
[tex]\rule[225]{225}{2}[/tex]
What is the approximate length of the radius, r? use 3.14 for . round to the nearest inch. 12 inches 24 inches 38 inches 46 inches
Answer:
2×3.14×r=75
6.28 r=75
r=75/6.28=11.943=12 inch (nearly)
what is the square root of 10,000,000
Answer:
1000√10or 3162.2776601683795
Step-by-step explanation:
what is the square root of 10,000,000?
√10000000
= √2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5
= √26 x 2 x 56 x 5
= 1000√10
or 3162.2776601683795
helpppp! i need to find general form and standard form, pleaseee HELP MEEE!)!#*(_
The general form and the standard form of the graph equation are 13x - 8y = 17 and 13x - 8y - 17 = 0 respectively
How to determine the equations?From the graph, we have the following points
(x,y) = (5,6) and (-3,-7)
Start by calculating the slope:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
This gives
[tex]m = \frac{-7 - 6}{-3 - 5}[/tex]
Evaluate the differences
[tex]m = \frac{-13}{-8}[/tex]
Evaluate the quotient
[tex]m = \frac{13}{8}[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
This gives
[tex]y = \frac{13}8(x - 5) + 6[/tex]
Multiply through by 8
8y = 13(x - 5) + 48
Open the bracket
8y = 13x - 65 + 48
Evaluate the like terms
8y = 13x - 17
Subtract 13x from both sides
-13x + 8y = -17
Multiply through by -1
13x - 8y = 17 ---- this represents the standard form
Subtract 17 from both sides
13x - 8y - 17 = 0 --- this represents the general form
Hence, the general form and the standard form of the graph equation are 13x - 8y = 17 and 13x - 8y - 17 = 0 respectively
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Determine the most precise name for ABCD (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer. You must support your answer using length or slope. A(3, 5), B(7, 6), C(6, 2), D(2, 1)
In the imaged attached, the most precise name for ABCD is known to be rhombus.
What is the shape about?Looking at the shape attached, one can see that the diagonals of a parallelogram are said to be bisecting one other and if it cross at right angles, it is said to be a rhombus.
Using the Diagonal midpoints of AC and BD, the equation will be:
(A+C)/2
(B+D)/2
To find if the midpoints are similar, then:
A +C = (3, 5) +(6, 2) = (9, 7)
B +D = (7, 6) +(2, 1) = (9, 7)
Therefore, from the solution above, the midpoints of the diagonals are the same, making the shape to be a parallelogram.
In terms of Diagonal vectors, the shape will be perpendicular when the figure is a rhombus. So:
AC = C -A = (6, 2) -(3, 5) = (3, -3)
BD = D -B = (2, 1) -(7, 6) = (-5, -5)
So the lengths will be (3√2 vs 5√2).
Note also that the dot-product of these values need to be zero if they are perpendicular and as such:
AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0
Therefore, one can say that the diagonals are known to different length and are perpendicular bisectors, so the shape above is regarded as rhombus.
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what expression is equivalent to 1/3y
1. 1/3(y+12)-12
2. 1/6y+1/3(y+3)
3. 1/6y+1/6(y+12)-2
4. 1/3y+1/3(6-y)
The expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
How to determine the equivalent expression?The expression is given as:
1/3y
Express 1/3y as 1/6y + 1/6y
So, we have:
1/6y + 1/6y
Factor out y
1/6y + 1/6(y)
Add 0 to the above equation
1/6y + 1/6(y + 0)
Express 0 as 12 - 12
1/6y + 1/6(y + 12 - 12)
Expand
1/6y + 1/6(y + 12) - 1/6 * 12
Evaluate the product
1/6y + 1/6(y + 12) - 2
Hence, the expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
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The expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
How to determine the equivalent expression?The expression is given as:
1/3y
Express 1/3y as 1/6y + 1/6y
So, we have:
1/6y + 1/6y
Factor out y
1/6y + 1/6(y)
Add 0 to the above equation
1/6y + 1/6(y + 0)
Express 0 as 12 - 12
1/6y + 1/6(y + 12 - 12)
Expand
1/6y + 1/6(y + 12) - 1/6 * 12
Evaluate the product
1/6y + 1/6(y + 12) - 2
Therefore, the expression that is equivalent to 1/3y is 1/6y + 1/6(y + 12) - 1/6 * 12
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A surveyor is measuring the distance across a canyon. He sets up two similar right triangles and finds that the length of CD = 12 feet and the length of DE = 16 feet.
If △ABC ~ △EDC, what is the length side AB?
The length side AB is 64 ft , Option D is the correct answer.
What is a Right triangle ?A triangle that has one angle 90 degree is called Right angled Triangle.
From the figure it can be seen that
The triangle CDE is a right Triangle
Applying Pythagoras theorem to find the length of CE
CE² = 12² + 16²
CE = 20 ft
As both the triangles are similar therefore the ratio of the sides will be equal
BC : CD = AC : CE
48 / 12 = AC / 20
AC = 80ft
As Triangle ABC is also a right angled triangle
Applying Pythagoras theorem to find the length of AB
AC² = BC² +AB²
6400 = 48² +AB²
AB² = 4096
AB = 64 ft
Therefore Option D is the correct answer.
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Answer:
64 ft.
Step-by-step explanation:
Keep it simple, just givin' the answer :)
Solve 2( 32x-5) -4 =11
The basic equation for calculating compound interest is A = P(1 + nt.
If $1,200 is invested at an interest rate of 8% per year, compounded quarterly, how much will the
investment be worth at the end of 10 years?
Show your work!
The amount of the investment at the end of the 10 years period if compounded quarterly is $2,649.6.
Compound interestPrincipal, P = $1200Interest rate, r = 8% = 0.08Time, t = 10Number of period, n = 4A = P(1 + r/n)^nt
= 1200(1 + 0.08/4)^(4×10)
= 1200(1 + 0.02)^40
= 1200(1.02)^40
= 1200(2.208)
= $2,649.6
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Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of 74000 miles and a standard deviation of miles. these tires come with a -mile warranty. the manufacturer of the tires can adjust during the production process, but the adjustment of is quite costly. the manufacturer wants to set once and for all so that only of the tires will fail before warranty expires. find the standard deviation to be set. carry your intermediate computations to at least four decimal places. round your answer to at least one decimal place.
The standard deviation will be 6816.9645.
How to compute the standard deviation?From the information given, the mean is 74000 and X is given as 60000.
P[(Z < (-60000 - 74000)/SD] = 0.02
Note that 0.02 will be -2.0537 under the normal distribution table.
-14000/SD = -2.0537
SD = -14000/-2.0537
SD = 6816.9645
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Find the equation of the parabola that has zeros of x = - 6 and x = 6 and a y-intercept of (0, 4)
The equation of the parabola that has zeros of x = - 6 and x = 6 and a y-intercept of (0, 4) would be Y=-1/9(x^2-36).
What is the equation of the parabola that has zeros?Since the zeros are symmetrical to the y axis, the equation can be written as;
y = a(x-b)(x+b),
where a is a scale factor and b is x-intercept.
From the given zeroes
y = A(x-6)(x+6).
Now we can plug in the y-intercept (0,4)
4 = A(0-6)(0+6)
4 = A(-36)
-36A=4
A = -1/9
Therefore the equation would be
Y = -1/9(x-6)(x+6),
or Y=-1/9(x^2-36)
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What quadrant is the point (2, -5) in?
Answer:
quadrant 4
Step-by-step explanation:
(2,-5) would be in the 4th quadrant
The Pine Scrub Rail Trail is 126 miles long. If the Willy-Nilly Bike Club rides 18 miles per day, how many days will it take them to ride from one end of the trail to the other?
A. 6 days
B. 9 days
C. 7 days
D. 8 days
Is the following relation a function?
Answer: Yes.
Step-by-step explanation: No number in the map is paired to two different, distinct numbers.
What type of triangle is this triangle?
acute scalene
right isosceles
right scalene
acute isosceles
A triangle with two acute angles and one angle that has a small square. Two sides each have one tick mark.
О A. 24
B. 12
О с. 92
D. 46
A
12
46°
46°
C
Answer:
I think A or C.
Step-by-step explanation:
need help with work would give more points but poor
Answer:
Step-by-step explanation:
2.5
4 quarts per gallon
8 quarts per 2 gallons
2 quarts is half a gallon since 4 quarts is a full gallon
answer: 2.5
which value of a and b make the equation true?
(2xy)4
An equation is formed of two equal expressions. The correct option is B.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The complete option is:
Which values of a and b make the equation true?
[tex]\dfrac{(2xy)^4}{4xy}=4x^ay^b[/tex]
A)a = 0, b = 0
B)a = 3, b = 3
C)a = 4, b = 4
D)a = 5, b = 5
The given equation can be simplified as shown below,
[tex]\dfrac{(2xy)^4}{4xy}=4x^ay^b\\\\\dfrac{2^4 \times x^4 \times y^4}{4xy}=4x^ay^b\\\\\dfrac{16x^4y^4}{4xy} = 4x^ay^b\\\\4x^{(4-1)}y^{(4-1)} = 4x^ay^b\\\\4x^3y^3 = 4x^ay^b[/tex]
Now, comparing the two sides of the equation, the value of a and b should 3 for the equation to be satisfied.
Hence, the correct option is B.
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