Given that ΔPQR and ΔXYZ are congruent triangles, the measure of XY is: D) 4 units
Recall:
Congruent triangles have pairs of congruent angles and congruent sides.Distance between two vertices can be calculated using the distance formula: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]Given ΔPQR ≅ ΔXYZ, therefore, PQ = XY.
Find the distance between P(0, 0) and Q(-4, 0) using[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]PQ = \sqrt{(-4 - 0)^2 + (0 - 0)^2}\\\\\mathbf{PQ = 4 $ units}[/tex]
Since ΔPQR ≅ ΔXYZ, therefore the measure of XY is: D) 4 unitsLearn roe about congruent triangles on:
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Answer:
4 units
Step-by-step explanation:
Elena is paid a constant rate for each hour she works. The table shows the amounts of money that Elena earned for various amounts of
time that she worked.
Constant rates are used to illustrate linear functions.
The average rate of change is $9.0 per hourThe function that models the table is: [tex]\mathbf{f(x) = 9x }[/tex]The amount earned in 7.5 hours is $67.5(a) The average rate of change
This is calculated using:
[tex]\mathbf{Rate = \frac{y_2 -y_1}{x_2 -x_1}}[/tex]
So, we have:
[tex]\mathbf{Rate = \frac{31.5-22.50}{3.5 - 2.5}}[/tex]
[tex]\mathbf{Rate = \frac{9}{1.0}}[/tex]
[tex]\mathbf{Rate = 9.0}[/tex]
Hence, the average rate of change is $9.0 per hour
(b) A function that models the table of values
Let x represent hours, and y represent the earnings.
So, we have:
[tex]\mathbf{y =m (x - x_1) + y_1}[/tex]
Where:
m =Rate = 9.0
So, we have:
[tex]\mathbf{y = 9(x - 2.5) + 22.5}[/tex]
Expand
[tex]\mathbf{y = 9x - 22.5 + 22.5}[/tex]
[tex]\mathbf{y = 9x }[/tex]
Represent as a function
[tex]\mathbf{f(x) = 9x }[/tex]
Hence, the function that models the table is: [tex]\mathbf{f(x) = 9x }[/tex]
(c) Amount earned for 7.5 hours
This means that x = 7.5
So, we have:
[tex]\mathbf{f(7.5) = 9 \times 7.5 }[/tex]
[tex]\mathbf{f(7.5) = 67.5}[/tex]
Hence, the amount earned in 7.5 hours is $67.5
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Jemina has 4 dogs, 8 cats and 12 fish as pets at her house.
What is the ratio of cats to all of her pets?
Answer:
8:16
Step-by-step explanation:
Which graph has exactly one y-intercept
Answer:
B
Step-by-step explanation:
It touches the y-axis (one y - intercept)
It also touches the x-axis( one x-intercept)
-Chetan K
he directions for Grow Better fertilizer say that the 25-pound bag covers a 1,000-foot row of vegetables Which brand would Cala need more of to fertilize her vegetables? Explain
Using the principle of proportional relationship, the amount in pounds of Grow better Fertilizer exceeds the required amount of Feed all Fertilizer. Hence, more of Grow better Fertilizer would be needed.
Feed - All Fertilizer :
2 pounds = 100 foot row
x pounds = 450 foot row
Cross multiply
100x = 900
Divide both sides by 100
x = 900 / 100
x = 9 pounds
Grow better Fertilizer :
25 pounds = 1000 foot rows
x pounds = 450 foot rows
Cross multiply
1000x = 450 × 25
1000x = 11250
Divide both sides by 1000
x = 11250 / 1000
x = 11.25 pounds
Hence, Cala will need more of Grow better Fertilizer.
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Ms. Suzuki is buying soda for the pizza party her class earned. She estimates that each of her
24 students will drink 250 milliliters of soda on average. How many 2-liter bottles of soda
should she buy?
Answer: 3
Step-by-step explanation:
There are 24 students
1 student = 250 ml
24 students = 250ml x 24
= 6000 ml
To convert from millilitres to litres, divide by 1000
6000ml = 6000/1000l = 6 litres
2litres = 1 bottle
6 litres = 6/2 = 3 bottles
Therefore, she will need 3 2-litre bottles of soda
Answer:
The answer is 3
Step-by-step explanation:
(4 x 100,000) + (6 x 10.000) =
Answer:
answer is 400060
have a good day!!
If it's help pls give me Brainliest
tysm
Answer:
4000,060
answer explanation : when you add 4 times 100,000 ypu get 400,000 and now you get 400,000 and now you are going to muptiple 4,000,6 and 10.000 which is equal to 4,000,060
I need assistance on this question please
X-3y=24
Answer:
x = -24 + 3y
Step-by-step explanation:
PLS SOLVE I WILL GIVE BRAINLIST
Answer:
first one, u can't ride a decimal of a ride
Step-by-step explanation:
y = 7.50 + 2.50x
Harvey is studying the polynomial f(x) = (4x – 3)(x – 3)(x2 +5) and determines that the polynomial has four real roots. Do you agree or disagree with Harvey’s statement? Explain your reasoning.
A.yes because there are 4 roots
B.yes because complex solutions do not matter
C.yes because when I solve he gets 4 x intercepts
D.no because there are two complex solutions
Yes because when I solve he gets 4 x-intercepts. The x-intercept is a point where the y value is zero.
The degree of a polynomial always determines the number of roots such polynomial function will have;
Given the polynomial function studied by Harvey as g(x) = (4x – 3)(x – 3)(x2 +5)
Taking the product of the leading variables
g(x) = (4x – 3)(x – 3)(x2 +5)
g(x) = 4x(x) (x^2)
g(x) = 4x^4
Since the degree of the polynomial is 4, hence the polynomial has four real roots.
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Help needed! Please and thanks
Answer:
8.125 inches
Step-by-step explanation:
Ok so basically what you needed to do was this
Find out what was the value like this 3 1/4 = 3.25 and 2 1/2 = 2.5
Then you will do
3.25 x 2.5 and get your answer
8.125
There you go! Have a Wonderful Day
What is the value of the expression x² + y² given x = 10 and y = 2?
A. 104
B. -98
C. 89
D. -89
Answer:
A. 104Step-by-step explanation:
Use properties to evaluate (-25) HIS O A. – 15 5 O B. 5 C. - OC. 15 O D. 1
Answer:
-15/4
Step-by-step explanation:
Answer: Its - 15/4 or 05/12 but the person above me is correct
Step-by-step explanation:
what is 15/2 into a mixed number
7 1/2.
2 goes into 15 7 times with one left over.
Write a word problem that
could represent the equation
below. Then solve the
equation
7y + 3 = 101
-PLEASE HELP IM FR HALF ASLEEP-
Answer:
y = 14
You have to travel 101 miles. On the first day, you traveled 3 miles. How many miles do you need to travel each day after that to reach your destination in 7 days?
Step-by-step explanation:
You have to travel 101 miles. On the first day, you traveled 3 miles. How many miles do you need to travel each day after that to reach your destination in 7 days?
7y=98
y=14
Answer: 14
Step-by-step explanation:
First you do 3 - 3 which cancels each other out.
2nd step :
you do 101 - 3 which equals 98
3rd step :
Divide 98 by 7 and your final answer is 14 !! <3
y = - 4x + 3 & x - 4y = 8 : parallel or perpendicular or neither
Answer:
perpendicular
Step-by-step explanation:
Parallel lines have equal slopes
The product of the slopes of perpendicular lines = - 1
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 4x + 3 ← is in slope- intercept form
with slope m = - 4
x - 4y = 8 ( subtract x from both sides )
- 4y = - x + 8 ( divide through by - 4 )
y = [tex]\frac{1}{4}[/tex] x + 2 ← in slope- intercept form
with slope m = [tex]\frac{1}{4}[/tex]
Since the slopes are not equal the lines are not parallel
- 4 × [tex]\frac{1}{4}[/tex] = - 1
Then the lines are perpendicular
10. What is the value of c?
Answer:
VALUE OF C = SUCK IT BRO
Step-by-step explanation:
I don’t know how to do this…
Step-by-step explanation:
f^-1 means the inverse function that finds the x responsible for the creation of a given y (functional result) value.
y = 3x - 1
3x = y + 1
x = 1/3(y + 1)
and now we rename x to y and y to x, so that we get a normal function definition :
y = 1/3(x + 1) = (1/3)x + 1/3
now we create the first derivative d/dx of this function :
y' = 1/3
since both f(x) and f^‐1(x) are line functions with a constant slope, it is not surprising that the first derivative (the function of the slope of the base function) is a constant function.
so, for any value of x (incl. the requested x = 11) d/dx f^-1(x) = 1/3.
therefore also d/dx f^-1(11) = 1/3.
y = 2×sqrt(x)
sqrt(x) = y/2
x = y²/4
again we rename the variables, so that we get a normal function definition for the inverse function :
y = x²/4
the first derivative is :
y' = 2x/4 = x/2
so, d/dx f^-1(6) = 6/2 = 3
Use the inverse function theorem: if f(x) is continuously differentiable at x = a, and given f(a) = b, then f is invertible around x = a, and
[tex]\left(f^{-1}\right)'(b) = \dfrac1{f'(a)}[/tex]
Both the given functions f(x) meet the conditions above. Note that you don't need to actually compute the inverse function itself.
If f(x) = 3x - 1, then f(x) = 11 when
3x - 1 = 11 ⇒ 3x = 12 ⇒ x = 4
Now if f(4) = 11, it follows from the inverse function theorem that
[tex]\left(f^{-1}\right)'(11) = \dfrac1{f'(4)} = \boxed{\dfrac13}[/tex]
since f'(x) = 3.
If f(x) = 2√x, then f(x) = 6 when
2√x = 6 ⇒ √x = 3 ⇒ x = ±9
But note that f(x) is defined only for x ≥ 0, so we must take x = 9. Now if f(9) = 6, the inverse function theorem says
[tex]\left(f^{-1}\right)'(6) = \dfrac1{f'(9)} = \dfrac1{\frac1{\sqrt9}} = \boxed{3}[/tex]
since f'(x) = 1/√x.
Would appreciate your help a lot!
Answer:
None of those answers are right. It should be
[tex] - \frac{23}{24} [/tex]
Step-by-step explanation:
You have to find common denominators first. Multiply -5/6 by 4/4 to get -20/24. Multiply 1/8 by 3/3 to get 3/24.
[tex] - \frac{20}{24} = z + \frac{3}{24} [/tex]
Subtract 3/24 from both sides since it is being added.
[tex] - \frac{20}{24} = z + \frac{3}{24} \\ - \frac{3}{24} \: \: \: \: \: \: \: \: \: \: - \frac{3}{24} [/tex]
Since there are two negatives on the left, add the fractions together and keep the negative sign.
[tex] - \frac{23}{24} = z[/tex]
You cannot reduce this fraction.
What is the y-intercept of the graph of the equation 6x + 3y = 18?
What is the discriminant of the quadratic equation 9x^2+5x-9=0
Answer:
Δ = 349
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 ) , then the discriminant is
Δ = b² - 4ac
9x² + 5x - 9 = 0 ← is in standard form
with a = 9, b = 5 , c = - 9 , then
b² - 4ac
= 5² - (4 × 9 × - 9)
= 25 - (- 324)
= 25 + 324
= 349
Which is equivalent to the expression below?
5(x + 5)
Group of answer choices
x + 25
5x + 25
5x + 10
x + 10
Answer:
The answer is 5x + 25
Explanation:
Apply distribution
distribute 5 to the equation inside the parenthesis
5x + 5 × 5
5x + 25
3 feet + 7 inches = ___ inches
Answer:
10
because when you plus 3+7 is 10
what is the pathgoren therem
A cylinder has a base radius of 10m and a height of 18m. What is its volume in cubic m, to the nearest tenths place?
Based on the question, the volume of the cylinder is approximately 56,520 cubic meters.
What is the cylinder volume?The formula for the volume of a cylinder is seen as:
V = πr²h
where
V = volume
r = radius of the base
h = height of the cylinder.
Then by Substituting the given values, we will have:
V = π(10m)²(18m)
= π(100m²)(18m)
= 18000π cubic meters
To be able to find the value to the nearest tenths place, we need to use π ≈ 3.14. hence:
V ≈ 18000 × 3.14
= 56520 cubic meters
Therefore, the volume of the cylinder is about 56,520 cubic meters to the nearest tenths place.
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4/5 x 2/35 I need help pls!
Answer: 8/175
Step-by-step explanation:
Answer: 8/175
Step-by-step explanation: to multiply fractions, multiply both numerators first then the denominators.
4x2=8
35x5=175
Is the equation y + 1 = 5(x + 3) in point-slope form? Justify your answer.
Answer:
The given equation is in point-slope form. The slope is 5 and is seen on the right side before the parentheses. The point is (-3, -1).
Hope this helps! :)
Answer:
Yes
Step-by-step explanation:
The equation y + 1 = 5(x + 3) is in point slope form. Point slope form is y - y1 = m(x - x1). In the given equation the point would be (-3, -1) with a slope of 5.
If Rick buys a remote control car for $33.00, what is his selling price?
Answer:
a
Step-by-step explanation:
HELPPPPPP plsssssssssss
Answer:
270°
Step-by-step explanation:
∠ PQR = 90° ( angle in a semicircle )
PRST is a cyclic quadrilateral
The opposite angles in a cyclic quadrilateral are supplementary, sum to 180°
Then
∠ PRS + ∠ PTS = 180°
∠ PQR + ∠ PRS + ∠ PTS = 90° + 180° = 270°
5. Do you find similarities between the rules of adding & subtracting dissimilar fractions and
adding & subtracting dissimilar rational algebraic expressions?
Answer:
First, we will change dissimilar fractions into similar fractions by finding the least common denominator. Second, add them like similar fractions. And then finally, convert the answer in the lowest term. Example No.6 Subtract 3/4 from 4/5. What will be our least common denominator? The least common multiple of 5 and 4 is 20. That was an Example
Step-by-step explanation:
The ratio of students in Class X to Class Y is 2 : 5. There are 24 more students in Class Y than Class X. How many students must transfer from Class Y to Class X so that both classes have equal number of students?
Answer: 12 students
Step-by-step explanation:
Let X and Y stand for the number of students in each respective class.
We know:
X/Y = 2/5, and
Y = X+24
We want to find the number of students, x, that when transferred from Y to X, will make the classes equal in size. We can express this as:
(Y-x)/(X+x) = 1
---
We can rearrange X/Y = 2/5 to:
X = 2Y/5
The use this value of X in the second equation:
Y = X+24
Y =2Y/5+24
5Y = 2Y + 120
3Y = 120
Y = 40
Since Y = X+24
40 = X + 24
X = 16
--
Now we want x, the number of students transferring from Class Y to Class X, to be a value such that X = Y:
(Y-x)=(X+x)
(40-x)=(16+x)
24 = 2x
x = 12
12 students must transfer to the more difficult, very early morning, class.