Answer:
Step-by-step explanation:
y = x² + 7x - 5 ............ (1)
2x - y = - 9 ................ (2)
(1) ------> (2)
2x - ( x² + 7x - 5 ) = - 9
- x² - 5x + 14 = 0 ........ (3)
- 1 × (3)
x² + 5x - 14 = 0
( x + 7 )( x - 2 ) = 0
[tex]x_{1}[/tex] = - 7 and [tex]x_{2}[/tex] = 2
2( - 7) - [tex]y_{1}[/tex] = - 9 ⇒ [tex]y_{1}[/tex] = - 5
2(2) - [tex]y_{2}[/tex] = - 9 ⇒ [tex]y_{2}[/tex] = 13
The solutions of system are
( - 7, - 5 ) and ( 2, 13 )
Let the numbers below represent the lengths of the sides of a triangle. Which of the triangles is a right triangle?
I. 4, 5, 6
II. 6, 8, 10
III. 5, 13, 14
IV. 7, 11, 13
A
I
B
II
C
III
D
IV
Answer:
B. II (6, 8, 10)
Step-by-step explanation:
A set of triangle side lengths will form a right triangle if they satisfy the Pythagorean theorem. The sum of squares of the shortest two sides must equal the square of the longest side.
__
Pythagorean triplesSets of integers that satisfy the Pythagorean theorem are called "Pythagorean triples." Some of these for smaller integers are ...
(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17)
If small integer side lengths are not one of these triples, or a multiple of one of these triples, they will not form a right triangle.
I. not a match to any triple
II. matches (3, 4, 5) multiplied by 2 -- a right triangle
III. not a match to any triple
IV. not a match to any triple
_____
Pythagorean equationOf course, you can actually compute the squares to see if they satisfy the Pythagorean theorem:
I. 4² +5² = 41 ≠ 6² (acute triangle)
II. 6² +8² = 100 = 10² -- right triangle
III. 5² +13² = 194 ≠ 14² (obtuse triangle)
IV. 7² +11² = 170 ≠ 13² (acute triangle)
__
form factorThe sum f = a² +b² -c² (where c is the longest side) can be considered to be a "form factor" for the triangle. For ...
f>0, the sides form an acute triangle f=0, the sides form a right trianglef<0, the sides form an obtuse triangleThis "form factor" is related to the largest angle (C) by ...
cos(C) = f/(2ab)
I'm kinda lost in this problem. Can you teach me how to solve these
53) Vertical angles are congruent, so [tex]m\angle IDA=121^{\circ}[/tex]
54) [tex]\angle YDA[/tex] and [tex]\angle YDF[/tex] are supplementary, so [tex]m\angle YDA=180^{\circ}-121^{\circ}=59^{\circ}[/tex]
55) Because vertical angles are congruent, [tex]m\angle FDI=59^{\circ}[/tex]. Now, because DR bisects [tex]\angle FDI[/tex], this means [tex]m\angle RDI=\frac{59}{2}=29.5^{\circ}[/tex]
56) This is a geometric sequence where the next term is obtained by multiplying the previous term by -2, so the next two numbers are 16, -32
Sandhu lights a candle at 6 pm. It is 30 cm high. At 7pm, the candle is 27 cm high. At 8pm, it is 24cm high. a) How many cm does the candle burn down every hour? b) How high is the candle at 11 pm?
I need help explanation if possible
Step-by-step explanation:
tan x = sin x / cos x
[tex]tan \: x \: = \frac{ \frac{7}{15} }{ \frac{4 \sqrt{11} }{15} } = \frac{7}{4 \sqrt{11} } [/tex]
the equation below describes a circle. what are the coordinates of the circle?
(x+5)^2 + (y+7)^2 = 21^2
Answer:
center = (-5, -7)
radius = 21
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven equation:
[tex](x+5)^2 + (y+7)^2 = 21^2[/tex]
Comparing the given equation with the standard equation of a circle:
center = (-5, -7)radius = 21Hence, the coordinates of centre is (-5,-2).
What is circle ?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.
The given equation of circle,
(x+5)² + (y+7)² = 21²
We know that,
Equation of a circle is:
(x-a)² + (y-b)² = r²
where:
(a, b) is the center
And r is the radius
Comparing with the given equation we have,
center = (-5,-7)
And radius = 21 units
Thus,
Coordinates = (-5,-7).
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The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 28, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B
Which describes the spread of the data in the two box plots?
The range of shelter A is 22. The range of shelter B is 18.
What are the measures of spread?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number. The range is the difference between the two numbers.
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find the value of a from the following 1. sin3a=cos3a
✏Answer:
Sin3A=Cos3A
Cos(90-3A)=Cos3A
90-3A=3A
90=3A+3A
90=6A
90/6=A
A=15^•^
The answer is A=15
Find the missing term or terms in each arithmetic sequence.
4) ..., 27,__,__,__, 43, ...
I need help again please!!!!!!
Answer:
I believe the terms would be 31, 35, 39.
Step-by-step explanation:
We know this because 43-27 is 16. since there are 3 terms missing, we divide the answer by 4, and you get 4. The number you get there is how many you add to each term to get the missing ones. For example, 27+4=31. The pattern is adding 4 to each term. Hope I helped!
PLEASE HELP ASAP
thank you :)
Answer:
y = x/2 -3
Step-by-step explanation:
x - 2y = 6
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
We need to solve for y
Subtract x from each side
x-2y-x = -x+6
-2y = -x+6
Divide each side by -2
-2y/-2 = -x/-2 +6/-2
y = x/2 -3
The slope intercept form is
y = x/2 -3
Answer: slope intercept form is
y = x/2 -3
Step-by-step explanation:
hope this helps ; )
if you are examining a triangle with given measurements for one leg and the hypotnuse,how will you determine the measure of the unknown leg?
We will apply the Pythagoras theorem to find the measure of the unknown leg in a triangle when one leg and the hypotenuse are provided dimensions.
What is the definition of a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.
According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.
[tex]\rm h^2 = p^2+ b^2[/tex]
Where,
h is the hypotenuse
p is the perpendicular
b is the base
If any of the two is given the third side will be obtained using the Pythagoras theorem.
In a triangle with given measurements for one leg and the hypotenuse, we will determine the measure of the unknown leg by the Pythagoras theorem.
Hence we willl apply the pythogorous theorem for finding the unknown side.
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the function f(x)=-3 cos(2x+pi/4) has ___
The domain will be ( 0, ∞) and the range of the function F(x) = -3Cos[2x+[tex]\dfrac{\pi}{4}[/tex]] will be [[tex]\dfrac{-\pi}{8}[/tex] , -3 ] and [ [tex]\dfrac{3\pi}{8}[/tex],3].
What are domain and range?Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
The range of the function we can see from the graph of the function will be from [[tex]\dfrac{-\pi}{8}[/tex] , -3 ] and [ [tex]\dfrac{3\pi}{8}[/tex],3]
The domain of the function will be all the values of the real numbers for the function ranges from ( 0, ∞ ).
Therefore the domain will be ( 0, ∞) and the range of the function F(x) = -3Cos[2x+[tex]\dfrac{\pi}{4}[/tex]] will be [[tex]\dfrac{-\pi}{8}[/tex] , -3 ] and [ [tex]\dfrac{3\pi}{8}[/tex],3].
The complete question is given below:-
what is the domain and range of the function
F(x) = -3Cos[2x+[tex]\dfrac{\pi}{4}[/tex]] .
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Two positive integers have a product of 242. One integer iS twice the other. What are the integers?
Answer:
11 and 22
Step-by-step explanation:
let one positive integer be n then the other is 2n , so
n × 2n = 242
2n² = 242 ( divide both sides by 2 )
n² = 121 ( take square root of both sides )
n = [tex]\sqrt{121}[/tex] = 11
2n = 2 × 11 = 22
the 2 integers are 11 and 22
Which equation can be used to solve for x in the following diagram?
!!!HELP!!!
A plane intersects one cone of a double-napped cone such that the plane is parallel to the generating line.
What conic section is formed?
A. hyperbola
B. circle
C. parabola
D. ellipse
Answer: C. Parabola
Definition: a parabola is a conic section in which it is mostly characterised of having a U-shape wherein it is symmetrical and an open plane curve.
Question 3 of 21
Which of the following are the domain and range that represent the inverse of
the function f(x), given the mapping diagram of f(x) below?
Answer: C
Step-by-step explanation:
The inverse of a function maps the domain onto the range.
PLEASE HELP
How many integers are there on the number line between $2\sqrt{10}$ and $10\sqrt{2}$?
Answer:
8
Step-by-step explanation:
To one decimal place:
[tex]2 \sqrt{10} = 6.3[/tex]
[tex]10 \sqrt{2} = 14.1[/tex]
So there are eight integers between 2√10 and 10√2: 7, 8, 9, 10, 11, 12, 13, and 14.
Please can someone help me on this I’m trying to revise for my test and I don’t understand this question
Answer:
∠ EAB = 85°
Step-by-step explanation:
∠ EBC and ∠ BCD are same- side interior angles and sum to 180° , so
∠ BCD = 180° - ∠ EBC = 180° - 148° = 32°
the sum of the 3 angles in Δ ADC = 180° , that is
∠ EDC + ∠ BCD + ∠ EAB = 180°
63° + 32° + ∠ EAB = 180°
95° + ∠ EAB = 180° ( subtract 95° from both sides )
∠ EAB = 85°
Answer:
first of all the line EAB is a triangle and all the angles in a triangle equate to 180° therefore;
[tex]angle \: ebc = 148 \\ angle \: edc = 63 \\ 148 + 63 = 180[/tex]
next I subtract 148 from 63 which gives 85⁰ therefore eab is equals 85⁰
Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard form, given that the point-slope form is y+1=3/3(x-8)
The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.
The given coordinate are (8, -1) and (2, -5).
What is the slope of an equation?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
The slope of the equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].
The standard form of an equation is Ax + By = C.
The given the point-slope form is [tex]y+1=\frac{2}{3} (x-8)[/tex].
Multiply each term by 3 of the equation.
[tex](y+1) \times3=\frac{2}{3} (x-8) \times3[/tex]
⇒3y + 3 = 2x - 16
Subtract 2x from both sides of a equation.
That is, -2x + 3y + 3 = - 16
Subtract 3 from both sides of a equation.
That is, -2x + 3y = - 19
Multiply each term by - 1 from both sides of an equation.
That is, 2x - 3y = 19
Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.
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Amanda think of a number, a. She subtract 4 then multiples the result by 2. Write an expression for her number?
determine whether the given graph is a function or not
Cooper was out at a restaurant for dinner when the bill came. His dinner came to $28. After adding in a tip, before tax, he paid $33.32. Find the percent tip.
Cooper left his dinner server a 19% tip.
To find the percent tip, we need to first subtract the cost of the meal from the total amount paid, which will give us the tip amount:
Tip amount = Total amount paid - Cost of the meal
Tip amount = $33.32 - $28
Tip amount = $5.32
Now we can calculate the percentage of the tip by dividing the tip amount by the cost of the meal and multiplying by 100:
Percent tip = (Tip amount / Cost of the meal) x 100
Percent tip = ($5.32 / $28) x 100
Percent tip = 0.19 x 100
Percent tip = 19%
Therefore, Cooper gave a 19% tip on his dinner.
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2 more questions and 100 points answer asap!
Answer:
-6
Step-by-step explanation:
Well you just plug in the value 3 for x. This will give you the following equation: [tex]\frac{4(3+3)(3+1)}{(3+5)(3-5)}[/tex] which simplifies to [tex]\frac{4(6)(4)}{(8)(-2)}[/tex] which further simplifies to [tex]-\frac{96}{16}[/tex] which can further be simplified by dividing the two numbers and that results in -6
Answer:
A
Step-by-step explanation:
it really only means to replace every x by 3 and then simply calculate.
4(3+3)(3+1) / ((3+5)(3-5)) =
= 4×6×4 / (8×-2) = 96/-16 = -6
Casey picked 6 pounds of strawberries. Karen picked 48 ounces of blueberries. Jude picked 2 pounds of raspberries. They are going to make berry pies. The table shows the amount of berries needed for 1 pie.Select all of the true statements below.
A.
Together, Karen and Jude picked the same weight of fruit as Casey picked.
B.
Casey picked 2 times the weight of fruit that Karen picked.
C.
There are enough berries to make 6 berry pies.
D.
If they make as many pies as they can with the berries they picked, there will be 4 pounds of strawberries left over.
E.
To make 8 berry pies, they will need 1 more pound of blueberries and 2 more pounds of raspberries.
Answer:
Option B is correct
Answer:
B there is enough raspberries to make 4 pie they can 6 pies if they 2 more of raspberries
given, what are the domain and range?
Factor the rational function,
.
.
.
.
Notice that the denominator and numerator both have x-1. This means that we have a removable discontinuity there so set x-1=0.
.
.
So our domain can be all reals except 1.
Range: First factor out the x-1. We will be left with
.
Since 1 isn't in the domain, plug in 1 to find the what won't be in the range
.
So 7 isn't in the range,
End Behavior:
Since the rational function numerator is a quadratic and the denominator is a linear function, the rational function will approach will not have a horizontal asymptotes.
6
E
Right triangle ABC is reflected over AC, then dilated by
a scale factor of to form triangle DEC. Which
statements about the two triangles must be
true? Select three options.
DAABC-ADEC
OZB ZE
3BC= 2EC
3DE = 2AB
3mzA= 2mzD
25:04
2mzA=3m2D
Triangle ABC is similar to triangle DEC, ∠B ≅ ∠E and 3DE = 2BC
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Dilation is the increase or decrease in the size of a figure by a scale factor.
Right triangle ABC is reflected over AC, then dilated by a scale factor of 2/3 to form triangle DEC, hence:
Triangle ABC is similar to triangle DEC, corresponding angles are congruent (∠B ≅ ∠E) and DE = (2/3)BC i.e. 3DE = 2BC
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What is the probabily of the 90th percentile given mean of 262 and a standard deviation of 45
The probability of the 90th percentile given a mean of 262 and a standard deviation of 45 is 319.672
Here,
The formula for the percentile probability is
[tex]P=\mu+z\sigma[/tex]
P=262 + 1.2816(45)
P = 319.672
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please help me its math
Answer:
the answer is $62
Step-by-step explanation:
if you subtract 110 by 98 you get 12 and the same for the rest so if you subtract 74 by 12 you get 62
Hope that help :)
Answer:
62
Step-by-step explanation:
Hi can I have help on this question with a simple explanation as I find things difficult to understand. Thank you :)
Step-by-step explanation:
Line L → 2x - 3y = 6
Where a = 2 and b = -3
• So, we can use this formula to find the gradient of Line L.
m = -a/b
m = -2/-3
m = 2/3 IS THE ANSWER
Answer:
gradient = 2/3
Step-by-step explanation:
Here is another way....manipulate the equation to y = mx+ b form
where m = slope ( gradient)
2x - 3y = 6 add 3 y to both sides
6 + 3y = 2x subtract 6 from both sides
3y = 2x - 6 divide by 3
y = 2/3 x - 2 gradient = 2/3
What is the value of x?
Enter your answer in the box.
...°
Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?
(2, 3)
(–2, 3)
(3, 2)
(3, –2)
The coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a trapezoid GHJK that was rotated 180° about the origin.
The rule for 180-degree rotation about the origin:
(x, y) → (-x , -y)
From the graph:
Coordinate of H' is (-3, -2)
(-3, -2) → (3, 2)
Thus, the coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.
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