The values of the following numbers, using the symbols > (greater than), < (less than), and = (equal to) 7.826 < 7.8
To compare the values of the given numbers 7.826 and 7.8, we can use the symbols > (greater than), < (less than), and = (equal to).
We need to determine which symbol we should use to compare the numbers. Here's how we can do it: 7.826 ______ 7.8 We need to compare the digits in the tenths place.
The digit in the tenths place for 7.826 is 2, while the digit in the tenths place for 7.8 is 8. Since 2 is less than 8, we can say that 7.826 is less than 7.8.
Therefore, we can use the symbol < (less than) to compare the values of the two numbers. Thus, the answer is:7.826 < 7.8
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The square represents a scale model that was created by using a factor of 4.
8 ft
8 ft
[Not drawn to scale]
Which is true of the measures of the sides of the original square?
Each side of the original square is the length of each side of the scale model.
Each side of the original square is 4 times the length of each side of the scale model.
Each side of the original square is the same length as each side of the scale model.
Each side of the original square is 4 feet less than the scale model.
Mark this and return
Save and Exit
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Submit
None of the provided options accurately describe the relationship between the sides of the original square and the scale model.
Based on the information given, the scale model was created using a factor of 4. This means that each dimension of the scale model is 1/4 of the corresponding dimension of the original square.
The original square has sides measuring 8 feet.
To determine the length of each side of the scale model, we divide the length of the corresponding side of the original square by the scale factor:
Length of each side of the scale model = 8 feet / 4 = 2 feet.
Now, let's evaluate the given options:
a) Each side of the original square is the length of each side of the scale model.
This option is incorrect because the length of each side of the original square is 8 feet, whereas the length of each side of the scale model is 2 feet.
b) Each side of the original square is 4 times the length of each side of the scale model.
This option is incorrect because the length of each side of the original square is not 4 times the length of each side of the scale model. In fact, it is 4 times larger.
c) Each side of the original square is the same length as each side of the scale model.
This option is incorrect because, as mentioned earlier, the length of each side of the original square is 8 feet, whereas the length of each side of the scale model is 2 feet.
d) Each side of the original square is 4 feet less than the scale model.
This option is incorrect because the length of each side of the original square is not 4 feet less than the scale model. In fact, it is 6 feet larger.
Based on the evaluation, none of the provided options accurately describe the relationship between the sides of the original square and the scale model.
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In our new car, we were able to drive 30 miles in a half an hour. From this information, we can determine the car's
acceleration
velocity
speed
direction
Answer:
Step-by-step explanation:
Direction or acceleration
a) Complete the table of values for y = x² - 2x - 3
-2 -1 0 1 2 3
4
0
-3
X
5
-3
-4
y
b) i) Which of the three curves drawn
matches y = x² - 2x - 3?
ii) Estimate the value of y
when x = 2.5
0
iii) Find the values of x
when y = 1
5
-5 -4
-3 -2
-4
نها
3-
O
B
--4-
2 3
A B
C
+x
5
a) Completing the table of values for y = x² - 2x - 3:
x | y
-2 | 11
-1 | 2
0 | -3
1 | -4
2 | -3
3 | 2
b) i) Comparing the values in the table to the equation y = x² - 2x - 3, we can see that the corresponding curve is Curve A.
ii) To estimate the value of y when x = 2.5, we can interpolate using the nearby points in the table. Looking at the table, we see that when x is between 2 and 3, the corresponding y values are -3 and 2. Since x = 2.5 lie halfway between these two values, we can estimate the value of y to be approximately halfway between -3 and 2, which is -0.5.
iii) To find the values of x when y = 1, we need to solve the equation x² - 2x - 3 = 1. Rearranging the equation, we get x² - 2x - 4 = 0. This is a quadratic equation, which can be factored as (x - 4)(x + 1) = 0. Setting each factor to zero, we find x = 4 and x = -1.
In summary:
a) Completing the table, we have:
x | y
-2 | 11
-1 | 2
0 | -3
1 | -4
2 | -3
3 | 2
b) i) Curve A matches the equation y = x² - 2x - 3.
ii) The estimated value of y when x = 2.5 is approximately -0.5.
iii) The values of x when y = 1 are x = 4 and x = -1.
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Does the graph represent a function? Why or why not ?
Answer:
A.
Step-by-step explanation:
The vertical line test is a way of finding out if a relation is a function.
Graph the relation.
Then imagine a vertical line moving from left to right over the graph of the relation.
If the vertical line intersects at most one point of the graph in any position you place the vertical line, then the relation is a function.
This function passes the vertical test since it never intersects more than one point on the vertical line at a time.
Answer: A.
Josué tiene 2 años más que su hermano Miguel, y María, que es madre de los dos, tiene el triple que el mayor de ellos. Si la suma de la edad de los tres es de 48 años, ¿cuántos años tiene Miguel?
The correct answer is Miguel is 8 years old.
We are given that Josué is 2 years older than his brother Miguel. So, if we let Miguel's age be "x," Josué's age would be "x + 2".
María, who is the mother of both Josué and Miguel, has three times the age of the older sibling. Therefore, María's age would be "3(x + 2)".
The sum of the ages of the three individuals is 48 years. Setting up the equation:
x + (x + 2) + 3(x + 2) = 48
Simplifying the equation:
x + x + 2 + 3x + 6 = 48
5x + 8 = 48
Solving for x:
5x = 40
x = 8
Therefore, Miguel is 8 years old.Llamemos "x" a la edad de Miguel. Según la información dada, Josué tiene 2 años más que Miguel, lo que significa que su edad es "x + 2". María, por otro lado, tiene el triple de la edad del mayor de ellos, es decir, "3(x + 2)".
La suma de las edades de los tres es de 48 años, por lo tanto, podemos establecer la ecuación:
x + (x + 2) + 3(x + 2) = 48
Resolviendo la ecuación, encontramos:
x + x + 2 + 3x + 6 = 48
5x + 8 = 48
5x = 40
x = 8
Por lo tanto, Miguel tiene 8 años.
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An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that average refers to the mean, which of the
following claims must be true based on this information?
Note: More than one statement could be true. If none of the statements is true, mark the appropriate box.
O
0
Check
Last year fewer than half of their clients made a profit of
10% or less.
Last year all of their clients made a profit of 10% or more.
Last year some of their clients made a profit of exactly
10%.
This year at least one of their clients will make a profit of at
least 10%.
Last year at least one of their clients made a profit of
less than 15%.
None of the above statements are true.
©2023 McGra
Save For Later
Assuming that average refers to the mean, the following claims must be true based on this information:
Last year some of their clients made a profit of exactly 10%.
This year at least one of their clients will make a profit of at least 10%.
Last year at least one of their clients made a profit of less than 15%.
How to determine the true claim based on the informationBased on the information given, the following claims must be true:
1. Last year some of their clients made a profit of exactly 10%.
2. This year at least one of their clients will make a profit of at least 10%.
3. Last year at least one of their clients made a profit of less than 15%.
These statements are true because the average profit of 10% implies that some clients made a profit of exactly 10% (statement 1), and since the average includes all clients, it is guaranteed that at least one client will make a profit of at least 10% this year (statement 2). Additionally, since the average is 10%, it is possible for some clients to have made a profit of less than 15% (statement 3).
Therefore, the correct answer is:
Last year some of their clients made a profit of exactly 10%.
This year at least one of their clients will make a profit of at least 10%.
Last year at least one of their clients made a profit of less than 15%.
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Which of the following represents the series? –13 + (–7) + (–1) + 5 + 11
Answer:
Adding +6 in turn
Step-by-step explanation:
-13+6=(-7)
(-7)+6=(-1)
(-1)+6=5
5+6=11
11+6=17
17+6=23
23+6=29
29+6=35
........... And so on
if it helped uh please mark me a brainliest :))A shelf has books with different-colored covers; 5 are blue, 6 are red, 1 is orange, 3 are white, and 1 is blue and white.
What is the probability of choosing a book with blue on its cover and replacing it before choosing a book with white on its cover?
(can you please explain how you got your anwer?)
The probability of choosing a book with blue on its cover and replacing it before choosing a book with white on its cover is 15/256, or approximately 0.059.
To find the probability of choosing a blue book and then a white book, we need to consider the total number of books and the number of blue and white books in the given scenario.
The total number of books on the shelf is:
5 blue + 6 red + 1 orange + 3 white + 1 blue and white = 16 books
The probability of choosing a blue book and replacing it before choosing a white book can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
The number of favorable outcomes is the number of blue books, which is 5. After choosing a blue book and replacing it, the probability of choosing a white book is 3, as there are 3 white books left.
Therefore, the probability of choosing a blue book and then a white book can be calculated as:
[tex](5/16) \times (3/16) = 15/256[/tex]
The probability calculation is based on the assumption that each book is equally likely to be chosen and that the events of choosing each book are independent of each other.
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Factor as the product of two binomials.
�
2
−
10
�
+
21
=
x
2
−10x+21=x, squared, minus, 10, x, plus, 21, equals
The answer is $(x-7)(x-3)$.
Given expression is $x^2-10x+21=-10x+21$We can factor this expression by splitting the middle term. That means we have to find two numbers which, when multiplied, will give us $21$ and when added will give us $-10$.That means we have to find two numbers $a$ and $b$ such that $ab=21$ and $a+b=-10$.The numbers are $-3$ and $-7$.Now, let's write $-10x$ as $-3x-7x$.$$x^2-3x-7x+21$$$$x(x-3)-7(x-3)$$$$(x-7)(x-3)$$Thus, the given expression can be factorised as $$(x-7)(x-3)$$
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The population of a species in a preserve is 800. The population is expected to decrease at a rate of 2% each year.
What function equation represents the population of the species after t years?
Enter your answer by filling in the boxes.
Answer:
P(t) = 800 * 0.98^t
Step-by-step explanation:
If the population of a species in a preserve is 800, and it is expected to decrease at a rate of 2% each year, we can use the exponential decay model to represent the population after t years:
P(t) = P (1 - r)^t
P = initial population (800 in this case)
r = decay rate (2% or 0.02 as a decimal)
t = time
Substituting the given values into the formula, we get:
P(t) = 800 * (1 - 0.02)^t
P(t) = 800 * 0.98^t
So, the equation is P(t) = 800 * 0.98^t
The equation for exponential decay is given by:
[tex]y = a(1-r)^t[/tex]where:
y = the population after t yearsa = the initial population ([tex]800[/tex])r = the rate of decrease ([tex]2\%[/tex] or [tex]0.02[/tex])t = the number of yearsSubstituting the given values, we get:
[tex]y = 800(1-0.02)^t[/tex]Simplifying this equation, we get:
[tex]\boxed{y=800(0.98)^t}[/tex][tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]
Find a quarter of the difference of N8450 and N1290
To find a quarter of the difference between N8450 and N1290, we first need to calculate the difference between the two values, and then divide that difference by 4.
The difference between N8450 and N1290 can be calculated by subtracting N1290 from N8450:
N8450 - N1290 = N7160
Now, we have the difference of N7160. To find a quarter of this difference, we divide it by 4:
N7160 / 4 = N1790
Therefore, a quarter of the difference between N8450 and N1290 is N1790.
In other words, if we take N8450 and subtract N1290 from it, the result is N7160. And if we divide this difference by 4, we get N1790.
It's important to note that the "N" in the values N8450, N1290, N7160, and N1790 likely refers to some currency or numerical unit. Without further context, we cannot determine the exact nature of this unit, but the calculations presented demonstrate how to find a quarter of the difference between two given values.
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JetBlue sells a non-refundable ticket to John Rogowski. John can, for a change fee of $250, rebook his flights should he be unable to use the ticket purchased. If he does not change their tickets before the flight, the cost of the ticket is forfeited completely (this is called breakage). If a ticket is sold on May 1st, 2019 for a flight on July 1st, 2019, when can JetBlue recognize revenue for tickets if the customer postpones the flight until August 15th, and pays an additional $300 (change fee and increased travel costs)?
JetBlue can recognize the change fee revenue of $250 immediately and the additional travel costs revenue of $50 on August 15th when the customer flies.
How to determine when JetBlue rcan ecognize revenue for tickets if the customer postpones the flight until August 15th,JetBlue can recognize revenue for the ticket sold on May 1st, 2019, when the customer postpones the flight until August 15th and pays an additional $300, under the following conditions:
1. The change fee of $250 is recognized as revenue immediately when the change is made. This is because the change fee represents the consideration received by JetBlue for modifying the ticket.
2. The increased travel costs of $50 ($300 - $250) should be allocated to the new flight date, which is August 15th. JetBlue can recognize this portion of the revenue on August 15th when the customer actually flies.
The initial ticket cost ($0 if forfeited completely) is not recognized as revenue since it represents breakage, and revenue is recognized when the service is provided (i.e., when the customer flies).
Therefore, JetBlue can recognize the change fee revenue of $250 immediately and the additional travel costs revenue of $50 on August 15th when the customer flies.
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Which step is included in the construction of perpendicular lines using a point on the line? (5 points)
Answer:
it is
exactly 15 points
that will be included in the construction
To construct a perpendicular line using a point on the line, the following steps need to be followed:
1. Draw a line that passes through the given point and is perpendicular to the given line.
2. This perpendicular line should intersect the given line at a 90-degree angle.
3. Use a protractor to measure the angle between the given line and the perpendicular line.
4. Divide this angle in half to determine the angle that the perpendicular line should make with the given line.
5. Draw a line at this angle from the given point, and this line will be perpendicular to the given line.
Solve for length of segment c.
11 cm
10 cm
8.8 cm
c = [?] cm
If two segments intersect inside
or outside a circle: ab = cd
Answer:
c = 8
Step-by-step explanation:
Using the Intersecting Chords Theorem, we can form the following equation and solve for c:
[tex]ab=cd\\(10)(8.8)=11c\\88=11c\\c=8[/tex]
How can you divide one rectangle with equal parts 1/2 and 1/3?
Step-by-step explanation:
Let us take the length of the rectangle as 1 m.
Now, if we want to divide the rectangle by 1/2, then the answer would be 1*1/2= 0.5m
Now, if we want to divide the rectangle by 1/3, then the answer would be
1*1/3=0.333....m
what is (1/2 + isqrt3/2)^5?
Answer:
[tex](\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i[/tex]
Step-by-step explanation:
Convert 1/2 + i√3/2 to rectangular form
[tex]\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}[/tex]
Use DeMoivre's Theorem
[tex]\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i[/tex]
A counterclockwise quarter-turn Q about the origin is applied to the point (x, y). What
are the coordinates of the image point? Answer in the form Q(x, y) = (ax + by, cx + dy).
Answer: The aim of this question is to find the first-order partial derivatives of an implicit function made up of two independent variables.
Step-by-step explanation:
Someone please help me solve this question. Im not good with graphs nor solving equations like this at all.
The graph of the translated funciton is on the image at the end.
How to find the graph of the translated function?We start with the absolute value funciton:
f(x) = -|x|
And we want to graph the translated function:
g(x) = -|x - 4| - 3
So we can write:
g(x) = f(x - 4) - 3
That is a translation of 4 units to the right and 3 units down, so the graph of the function is the one you can see below.
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Center (9, 8); touching the x-axis
The equation of the circle with center (9,8) and touching the x-axis is given as follows:
(x - 9)² + (y - 8)² = 64.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The coordinates of the center for this problem are given as follows:
(9,8).
Hence:
(x - 9)² + (y - 8)² = r².
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, and since it touches the x-axis(y = 0), the measure is given as follows:
r = 8 - 0
r = 8 units.
Thus the equation is given as follows:
(x - 9)² + (y - 8)² = 8²
(x - 9)² + (y - 8)² = 64.
Missing InformationThe problem asks for the equation of the circle with the given features.
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You or your parents earned $53,698 a year and you have deductions of FICA 7.65% Federal tax withholding 11.5% and state tax withholding 9%. How much is the allowed housing expense for the year? How is did you arrive at $10,802.96?
Thank you so much!
Based on an annual income of $53,698 and deductions for FICA, federal tax withholding, and state tax withholding, the calculated allowed housing expense is approximately $11,572.84.
To calculate the allowed housing expense for the year, we need to determine the net income after deducting FICA (7.65%), federal tax withholding (11.5%), and state tax withholding (9%) from the annual income of $53,698.
First, let's calculate the deductions:
FICA deduction: 7.65% of $53,698 = $4,111.97
Federal tax withholding: 11.5% of $53,698 = $6,177.07
State tax withholding: 9% of $53,698 = $4,832.82
Next, subtract the deductions from the annual income:
Net income = $53,698 - $4,111.97 - $6,177.07 - $4,832.82 = $38,576.14
The allowed housing expense is generally recommended to be around 30% of the net income. To calculate this, we multiply the net income by 0.3:
Allowed housing expense = 0.3 * $38,576.14 = $11,572.84
However, it appears there is a discrepancy between the provided answer of $10,802.96 and the calculated value of $11,572.84. The difference could be due to rounding or other factors not accounted for in the given information. To reconcile this difference, we would need additional details or clarification.
In conclusion, based on the given information, the calculated allowed housing expense for the year is $11,572.84.
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what is the length of ac?
Answer:
48
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
*Assuming that OM is a perpendicular bisector*
The correct answer is 24.
A perpendicular bisector splits the line segment, AC, in half directly, making one side 12 and the other side also 12.
So, AC in total is 24 units.
Hope this helps! :)
Juan tiene 3 hijos de 6, 8 y 9 años de edad. Para premiar su desempeño en la escuela, Juan quiere entregarles 667 figuritas del mundial de fútbol. Para que la entrega sea más justa, Juan reparte las figuritas proporcionalmente, de acuerdo a las edades de sus hijos.
Juan's three children, aged 6, 8, and 9, are to receive 667 World Cup figurines as a reward for their school performance.
To distribute the 667 World Cup figurines proportionally among Juan's three children based on their ages, we need to calculate the proportion of figurines each child should receive.
Total figurines: 667
Let's calculate the proportion for each child:
Child 1 (6 years old):
Proportion = (Age of Child 1) / (Sum of Ages of all children)
Proportion = 6 / (6 + 8 + 9) = 6 / 23
Child 2 (8 years old):
Proportion = (Age of Child 2) / (Sum of Ages of all children)
Proportion = 8 / (6 + 8 + 9) = 8 / 23
Child 3 (9 years old):
Proportion = (Age of Child 3) / (Sum of Ages of all children)
Proportion = 9 / (6 + 8 + 9) = 9 / 23
Now, let's calculate the number of figurines each child will receive based on their proportions:
Child 1:
Figurines = Proportion of Child 1 * Total figurines
Figurines = (6 / 23) * 667
Child 2:
Figurines = Proportion of Child 2 * Total figurines
Figurines = (8 / 23) * 667
Child 3:
Figurines = Proportion of Child 3 * Total figurines
Figurines = (9 / 23) * 667
After performing the calculations, we will have the number of figurines each child should receive.
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Note the translated question is Juan has 3 children of 6, 8 and 9 years old. To reward their performance at school, Juan wants to give them 667 World Cup figurines. To make the delivery more fair, Juan distributes the figurines proportionally, according to the ages of his children.
If you bought something in Florida for $59.00, you would be charged $3.54 in state sales tax. What is the state sales tax rate in Florida?
Round your answer to the nearest hundredth of a percent
Answer:
6%
Step-by-step explanation:
Tax rate = sales tax / price
We Take
(3.54 ÷ 59) x 100 = 6%
So, the state sales tax rate in Florida is 6%
You need to move 45 boxes from the
warehouse to the loading dock. It
takes 20 minutes to move 10 boxes.
How long will it take to move all the
boxes? *Required
45 Minutes
1 Hour
1 Hour 30 minutes
2 Hours
A man standing near a radio station antenna observes that the angle of elevation to the top of the antenna is 54. He then walks 70 feet further away and observes that the angle of elevation to the top of the antenna is 31. Find the height of the antenna to the nearest foot.
Answer:
The correct answer for me is 2.5926
What comes next?
1,3,4,8,15,27,?
Find the surface area of this solid
The surface area of the given triangular prism is 164 square feet.
To find the surface area of a solid, we need to calculate the area of each individual face and then sum them up. In the given case, we have a triangular prism with dimensions of 5 ft (height), 8 ft (base length), and 4 ft (base width).
The triangular prism has three rectangular faces and two triangular faces. Let's calculate the area of each face:
The top and bottom faces are rectangles with dimensions of 8 ft by 4 ft. The area of each rectangular face is given by length times width, so the area of one face is [tex]8 ft \times 4 ft = 32[/tex] square feet. Since there are two rectangular faces (top and bottom), their combined area is [tex]2 \times 32 = 64[/tex]square feet.
The front and back faces are also rectangles with dimensions of 5 ft by 8 ft. The area of each rectangular face is [tex]5 ft \times 8 ft = 40[/tex] square feet. Since there are two rectangular faces (front and back), their combined area is [tex]2 \times 40 = 80[/tex] square feet.
The side face is a triangle with a base of 8 ft and a height of 5 ft. The area of a triangle is given by half the base times the height, so the area of the side face is [tex](1/2) \times 8 ft \times 5 ft = 20[/tex] square feet.
To find the total surface area, we add up the areas of all the faces: 64 square feet (rectangular faces) + 80 square feet (front and back faces) + 20 square feet (side face) = 164 square feet.
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Triangles D E F and P Q R are shown.
Given that StartFraction D F Over P R EndFraction = StartFraction F E Over R Q EndFraction = three-halves, what additional information is needed to prove △DEF ~ △PQR using the SSS similarity theorem?
DE ≅ PQ
∠D ≅ ∠P
StartFraction D E Over E F EndFraction = three-halves
StartFraction D E Over P Q EndFraction = three-halves
If we can determine the ratio of corresponding sides between the two triangles, such as StartFraction PQ Over EF EndFraction or StartFraction PR Over EF EndFraction, we would have sufficient information to prove the similarity.
To prove that △DEF is similar to △PQR using the SSS (Side-Side-Side) similarity theorem, we need one additional piece of information.
In this case, we are given that StartFraction DF Over PR EndFraction = StartFraction FE Over RQ EndFraction = three-halves. We also know that DE ≅ PQ and ∠D ≅ ∠P. However, to apply the SSS similarity theorem, we need to establish a ratio of corresponding sides between the two triangles.
To find this additional information, we can examine the ratios involving the remaining sides. We have StartFraction DE Over EF EndFraction = three-halves and StartFraction DE Over PQ EndFraction = three-halves.
Without this additional information, we cannot establish the necessary ratios of corresponding sides, and therefore, we cannot prove that △DEF is similar to △PQR using the SSS similarity theorem.
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Si ƒ (x) = g(x) + h(x), g(x) = x2 + 3y ƒ(x) = x3, calcule h (2)
To calculate the value of h(2), we need to use the given information and equations. Let's break down the problem step by step.
Given:
[tex]ƒ(x) = g(x) + h(x)\\g(x) = x^2 + 3y\\ƒ(x) = x^3[/tex]
We want to find h(2), which means we need to determine the value of h when x = 2.
First, let's substitute the given expressions for g(x) and ƒ(x) into the equation ƒ(x) = g(x) + h(x):
[tex]x^3 = (x^2 + 3y) + h(x)[/tex]
Now, we can isolate h(x) by moving the other terms to the other side of the equation:
[tex]h(x) = x^3 - (x^2 + 3y)[/tex]
Since we want to calculate h(2), we substitute x = 2 into the equation:
[tex]h(2) = 2^3 - (2^2 + 3y)\\ = 8 - (4 + 3y)\\ = 8 - 4 - 3y\\ = 4 - 3y[/tex]
Therefore, h(2) is equal to 4 - 3y.
The value of h(2) depends on the value of y. Without any additional information or an equation relating to y, we cannot determine a specific value for h(2). However, we have expressed it in terms of y as 4 - 3y.
If you have any further information about y or any other equations or constraints related to h(x), please provide them so that we can calculate a specific value for h(2).
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Seven years ago, Grogg's dad was 6 times as old as Grogg, and 3 years ago, his dad was 4 times as old as Grogg. How old is Grogg's dad currently?
Answer:
Grogg's dad is 22
Step-by-step explanation:
Let D = dad's current age
Let g = Grogg's current age
6(d - 7) = g - 7 → 6d - 42 = g - 7 → 6d -35 = g
4(d - 3) = g - 3 → 4d -12 = g - 3 → 4d -9 = g
Set the two equations equal to each other and solve for d
6d - 35 = 4d - 9 Subtract 4d from both sides
2d -35 = -9 Add 35 to both sides
2d = 44 Divide both sides by 2
d = 22
Helping in the name of Jesus.
Answer:
Step-by-step explanation:
d = current dad age
g = current grogg age
d-7 = 6(g-7)
d-3 = 4(g-3)
Let's solve the first equation first:
Add 7 to both sides: d - 7 +7 = 6g - 42 + 7 so d = 6g - 35
Substitude d = 6g - 35 for d in d - 3 = 4g - 12
(6g-35)-3 = 4g-12 = 6g-38 = 4g-12
Subtract 4g from both sides: 2g - 38 = -12
Add 38 to both sides: 2g = 26
Easy: g = 13
And now substitude g in for any equations.
d-3 = 52-12
d = 43
