Answer:
x=−2 and y=−1
Step-by-step explanation:
Problem:
Solve y=x2;y=−x−3
Steps:
I will solve your system by substitution.
y=1/2x;y=−x−3
Step: Solve y= 1/2x for y:
Step: Substitute 1/2 x for y in y=−x−3:
y=−x−3
1/2x= =−x−3
1/2x+x=−x−3+x(Add x to both sides)
3/2x = -3
3/2x/3/2 = -3/3/2 (Divide both sides by 3/2)
x=−2
Step: Substitute −2 for x in y=1/2x:
y=1/2x
y=1/2(-2)
y=−1(Simplify both sides of the equation)
Answer:
x=−2 and y=−1
1-tan^2(x)/sec^2 = cos(2x)
By applying the formula of trigonometric function the right hand side will
be equal to right hand side which is 1-[tex]tan^{2} x[/tex]/[tex]sec^{2}x[/tex]=cos2x.
Given: 1-[tex]tan^{2} x[/tex]/[tex]sec^{2}x[/tex]=cos2x.
Taking right hand side first which is cos2x.
We know that cos2x=[tex]1-tan^{2}x/1+tan^{2}x[/tex]
Now we will solve the left hand side of the equation give which is
1-[tex]tan^{2} x[/tex]/[tex]sec^{2}x[/tex]
=1-[tex]tan^{2}x[/tex]/1+[tex]tan^{2}x[/tex]
[secant square x minus tangent square x is equal to 1]
By putting both values left hand side and right hand side we will find our solution which is :
1-tan^{2}x/1+tan^{2}x=1-[tex]tan^{2}x[/tex]/1+[tex]tan^{2}x[/tex].
Hence proved
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Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene 97degree
Answer:
Obtuse and the rest of the question is incomplete.
Step-by-step explanation:
For a population with μ = 60 , X=81, and σ = 12. Find the z-score for 81.
The z-score for 81 is 1.75
How to determine the z-score for 81?The given parameters are:
μ = 60 , X=81, and σ = 12
The z scores is calculated using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Substitute the given values
[tex]z = \frac{81 - 60}{12}[/tex]
Evaluate the difference
[tex]z = \frac{21}{12}[/tex]
Simplify
z = 1.75
Hence, the z-score for 81 is 1.75
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what is the Smallest numbers :
p = x^2 + 2x +2 / x+1 (x>-1)
t= 1/x + 4/1-x (0
Answer:
I exactly don't know the answer
Tacoma's population in 2000 was about 200 thousand, and has been growing by about 9% each year. If this continues, what will Tacoma's population be in 2019?
The population of Tacoma in 2019 would be 1,028,332.
What will be the population in 2019?The population can be represented with an exponential equation that has the form:
FV = P (1 + r)^n
FV = Future populationP = Present population R = rate of growth N = number of years200,000 (1.09)^19 = 1,028,332.
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find the first 4 terms and the 10th term from 3n+4
Answer:
16 and 34
Step-by-step explanation:
The general form = 3n+4
The 4th term = 3(4)+4 = 12+4 = 16
The 10th term = 3(10)+4= 30+4= 34
The cost of renting a car is $47 /week plus $0.25 /mile traveled during that week. An equation to represent the cost would be y=47+0.25x , where x is the number of miles traveled.
Answer:
a. 61.25
b. 70
c. 212
Step-by-step explanation:
a. What is your cost if you travel 57 miles?
The cost is $ .
y=47+0.25x
y=47+0.25(57)
y=47+14.25
answer: 61.25
b. If your cost was $64.50, how many miles were you charged for traveling?
You were charged for traveling miles.
64.50-47=0.25x
17.50=1/4x
17.50*4
answer 70=x
c. Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?
The maximum number of miles you could travel is miles.
100-47
53=1/4x
answer : x= 212
What is the scale factor from AABC to ADEF?
B
48
AA
6
A4 CE
48
6
O A.
C
B. 8
32
D
Answer: 8
Step-by-step explanation:
We are going from a smaller triangle to a larger triangle, so the scale factor is greater than 1.
Eliminate A and D.We know scale factor = (image)/(preimage), so the scale factor is 32/4 = 8
The scale factor of dilation of the triangle is k = 8
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔDEF
where the measures of sides of ΔABC are
AB = 6 , BC = 6 and AC = 4
The measure of sides of triangle ΔDEF are
DE = 48 , EF = 48 and DF = 32
The scale factor of dilation k = measure of side DE / measure of side AB
k = 48 / 6
k = 8
Hence , the dilation factor is k =8
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lim(lnx-ln4/x-4) as x approaches 4
Answer:
1/4 = 0.25
Step-by-step explanation:
I assume you mean
lim((ln(x) - ln(4)) / (x - 4))
ln(x) - ln(4) = ln(x/4)
rule of l'hopital
lim f(x)/g(x) = lim f'(x)/g'(x)
if g'(x) <> 0
f(x) = ln(x/4)
g(x) = x - 4
ln(x)' = 1/x
ln(x/4)' = 1/x/4 × 1/4 = 1/x
(x - 4)' = 1
so,
lim f'(x)/g'(x) = 1/x / 1 = 1/x
which is for x approaching 4 : 1/4 = 0.25
How to solve this one
Please step by step
Answer: 1/2
Step-by-step explanation:
Dividing the numerator and denominator by x, we get the limit is equal to:
[tex]\lim_{x \to -\infty} \frac{-\sqrt{1+\frac{5}{x}+\frac{1}{x^2}}+3}{4+\frac{7}{x}}\\\\=\frac{\lim_{x \to -\infty} \left(-\sqrt{1+\frac{5}{x}+\frac{1}{x^2}}+3 \right)}{\lim_{x \to -\infty} \left(4+\frac{7}{x} \right)}\\\\=\frac{2}{4}=\boxed{1/2}[/tex]
Line AB and line BC form a right angle at point B with points A(2,5) and B(8,3) . What is the equation of line BC ?
Answer: y = 3x - 21
Step-by-step explanation:
If the lines form a right angle, this means that they are perpendicular. Therefore, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other (in other words, their slopes multiply to -1).
The slope of AB is [tex]\frac{3-5}{8-2}=\frac{-2}{6}=-\frac{1}{3}[/tex]. This means that the slope of BC is 3.
Substituting into point-slope form,
[tex]y-3=3(x-8)\\\\y-3=3x-24\\\\\boxed{y=3x-21}[/tex]
What is the greatest common factor of 20 and 36?
2
4
5
6
Answer:
GFC = 4
Step-by-step explanation:
Factors of 20 1 2 4 5 10 20
Factors of 36 1 2 3 4 6 9 12 18 36
Answer:4
Step-by-step explanation:nice and simple
Select the point that is a solution to the system of inequalities.
y≤2x-2
y≤ x²-3x
Both statements are true. Therefore (4,2) is a solution and option D is correct.
The given inequalities are [tex]y\leq 2x-2[/tex] and [tex]y\leq x^{2} -3x[/tex].
We need to select the point that is a solution to the system of inequalities (-2,-1), (1,3), (2,1) and (4,2).
What is an example of a system of inequalities in real life?Inequalities can be seen in the speed limits on roads, the minimum age for seeing certain movies, and the distance you have to walk to go to the park. Inequalities represent a limit of what is permitted or achievable rather than a precise quantity.
Any point is a solution to this system of inequality if it satisfies both inequalities.
Check the inequalities by each option.
For (-2, -1), [tex]-1\leq 2(-2)-2 \implies -1\leq -6[/tex].
This statement is false because -1 is greater than -6. Therefore (-2,-1) is not a solution and option A is incorrect.
For (1, 3), [tex]3\leq 2(1)-2 \implies 3\leq 0[/tex]
This statement is false because 3 is greater than 0. Therefore (1,3) is not a solution and option B is incorrect.
For (2,1), [tex]1\leq 2(2)-2 \implies 1\leq 2[/tex].
[tex]1\leq 2^{2} -3(2) \implies 1\leq -2[/tex]
This statement is false because 1 is greater than -2. Therefore (2,1) is not a solution and option C is incorrect.
For (4,2), [tex]2\leq 2(4)-2 \implies 2\leq 6[/tex]
[tex]2\leq 4^{2} -3(4) \implies 2\leq 4[/tex]
Both statements are true. Therefore (4,2) is a solution and option D is correct.
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What is the inequality for this verbal description?
Kyle has d dollars to spend at the garden store. He wants to buy one small
tree for $9.00 and s pounds of soil that cost $5.00 per pound. Which
inequality represents this situation?
OA. d≥ 5s +9
OB. d> 5s +9
OC. d<9s +5
O D. d≥ 9s +5
Answer:
A) d [tex]\geq[/tex] 5s + 9
Answer:
A. d ≥ 5s + 9
Step-by-step explanation:
9.00 is fixed cost5.00 is cost per pound of soilHence, equation will be :
d ≥ 5s + 9 (As d must be greater than/equal to this value for Kyle to afford it)Please answer all four of the questions I would really appreciate it <3
Answer:
1)A because 3 < 3.9 < 4
2)C because 8.2<8.23<8.3
3) D because 6.1>5.9
4)B because 3.6<3.625<3.7
Hope it helps!
Help me with this I’m stuck!!:)
The cardinality of the set indicated in the task content is; 11.
What is the cardinality of the set?It follows from the task content that the cardinality of the intersection set of set A compliment and set B compliment is to be determined.
Hence, it follows that the elements in the described set include the elements in set C only and the elements in the compliment of set A, B and C union.
On this note, it follows that the cardinality of the set is; 4 +7 = 11.
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Chad has a rope that is 24 yards long. How many pieces of rope measuring of a yard can he divide his rope into1/4
The pieces of rope measuring a yard can he divide his rope into1/4 would be 96.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Chad has a rope that is 24 yards long. He wants to divide the rope so each piece will be 1/4 yards
= 24÷1/4
= 24× 4
= 96
Hence he can divide the rope into 96 pieces.
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What is the domain of the function shown on the graph?
The asnwer is C
for finding domain look at just x-axis from left to right , because there are arrows , so domain is all real numbers or from negative infinity to positive infinity
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A wagon is being pulled by a handle making a 40° angle with a force of 35 pounds. What amount of force is moving the wagon along level ground? Round to the nearest tenth.
The amount of force is moving the wagon along ground level will be 26.8 pound
A force in physics is an effect that has the power to alter an object's motion. A mass-containing object's velocity can vary, or accelerate, as a result of a force. Intuitively, a push or a pull can also be used to describe force. Being a vector quantity, a force has both magnitude and direction.
Given a wagon is being pulled by a handle making a 40° angle with a force of 35 pounds
We have to find amount of force is moving the wagon along level ground
The angle with force is given 40 degree
So the formula to find amount of force is moving the wagon along level ground will be as follow:
Fₓ = F cosθ
Fₓ = 35 * cos40
Fₓ = 26.8 pound
Hence amount of force is moving the wagon along ground level will be 26.8 pound
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Which expression is equivalent to this polynomial?
x2+12
OA. (X +2v3i)(c – 2v3i)
OB. (x+6i)(x - 6i)
OC. (x + 2√3)²
OD. (x + 2√3)(x − 2√3)
x² + 12 is equivalent to the polynomial (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i).
What are Polynomials?Polynomials are defined as algebraic expressions consisting of constants, variables and exponents combined using operations like addition, multiplication, subtraction and division.
The given expression is x² + 12.
We have the identity (a + b) (a - b) = a² - b²
(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (2[tex]\sqrt{3}[/tex]i)²
= x² - (2² × √3² × i²)
We know that i² = -1, where i is the imaginary number in complex numbers
(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (4 × 3 × -1)
= x² + 12
Hence we get that (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) is equivalent to x² + 12.
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&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} S = square numbers E = even numbers Complete the Venn diagram. E, S 4 2,6 8, 10, 12 E & = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } S = square numbers E = even numbers Complete the Venn diagram . E , S 4 2,6 8 , 10 , 12 E
The remaining elements if Venn diagram is S= { 4, 9}
What is Venn diagram?A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.
Given:
E = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }
S = square numbers
E = even numbers
Element in set S= { 4, 9}
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For the graph y = 12 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explaln your
answer with two or more sentences.
The line y = 12 has a slope of 0 because it is a horizontal line, meaning that for any change in x, there is no change in y. Ths means the slope of a line parallel to it would be 0 (since parallel lines have the same slope), and the slope of a line perpendicular to it would be undefined (since perpendicular lines have slopes that are negative reciprocals of each other, and when you divide by 0, you get an undefined result).
The domain of the piecewise function is (-infinity,infinity).
a. Graph the function.
b. Use your graph to determine the function's range.
f(x) =
3x if x≤0
3 if x>0
Answer:
The condantrnirte will be 3x if x is 0 (underfined)
Step-by-step explanation:
Need help with this geometric question
Answer: A
Step-by-step explanation:
[tex]V=\frac{1}{2}(6)(4)(2)=\boxed{24}[/tex]
What is the distance from P to Q?
OA. 1 unit
OB. 7 units
OC. 5 units
D. 25 units
Answer:
C) 5 units
Step-by-step explanation:
In order to find the distance between points P and Q, we will be using the Distance Formula.
[tex]\sf \textsf{\underline{Distance Formula:}}\ \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given:
P (3, -1) Q (-1, -4)where:
⇒ x₁ = 3, y₁ = -1
⇒ x₂ = -1, y₂ = -4
Substitute these values into the formula:
[tex]\sf\\\implies d=\sqrt{(-1-3)^2+(-4-(-1))^2}\\\\\implies d=\sqrt{(-1-3)^2+(-4+1)^2}\\\\\implies d=\sqrt{(-4)^2+(-3)^2}\\\\\implies d=\sqrt{16+9}\\\\\implies d=\sqrt{25}\\\\\implies d=5[/tex]
The distance from P to Q is 5 units.
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114
4. Line p contains point (6,-5) and is perpendicular to line q. The equation for line gis y = 3x + 5.
Write an equation for line p.
Part I: Find the slope of line q. (1 point)
Part II: Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.) (1 point)
that
Part III: Use the point given for line p and the slope you found in Part II to write an equation for line pin
point-slope form: y - y₁ = m(x-x₁). (1 point)
Line q has slope 3, as you've found.
Any line perpendicular to q will then have slope -1/3, as you've found.
Line p thus has slope -1/3 and we know it passes through (6, -5), so from the point-slope formula we get the equation
[tex]y - (-5) = -\dfrac13 (x - 6) \implies \boxed{y + 5 = -\dfrac13 (x - 6)}[/tex]
What is the slope of the line (14,0), (2, -6)
Answer:
1/2 is the answers
Step-by-step explanation:
please mark me as brainlest
The slope of the line is = 0.5
Given that:-one point is =(14,0)
other is =(2,-6)
Solution:-We can easily solve the question by the formula of a straight line.
The slope is = 0-(-6)/(14-2)
= 1/2
4x + 2y=4 and 3x -y= -7
Answer:
y = 4
x = -1
Step-by-step explanation:
4x + 2y = 4 Eq. 1
3x - y = -7 Eq. 2
from the Eq. 2
3x = y - 7
3x + 7 = y Eq. 3
Replacing the value of the Eq. 3 in the Eq. 1
4x + 2(3x+7) = 4
4x + (2*3x + 2*7) = 4
4x + (6x + 14) = 4
10x + 14 = 4
10x = 4 - 14
10x = - 10
x = -10/10
x = -1
from the Eq. 3
3x + 7 = y
3*-1 + 7 = y
-3 + 7 = y
4 = y
Check:
from the Eq. 1
4x + 2y = 4
4*-1 + 2*4 = 4
-4 + 8 = 4
a
b
c
or d
question is in picture
A, -9 ≤ -3X -6 ≤ 6
What is inequality?Inequality is an algebraic statement that shows that two quantities are unequal.
Analysis:
From the above, only A, is the correct inequality represented above.
solving for x in A, we have,
-9 ≤ -3x - 6 ≤ 6
splitting,
-9 ≤ -3x -6
-3 ≤ -3x
1 ≥ x
x ≤ 1
-3x-6 ≤ 6
-3x ≤ 12
x ≥ 12/-3 ≥ -4
-4 ≤x ≤1, A
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Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible region. Click to set the corner points. 2 x + 4 y ≤ 36 7 x + 5 y ≤ 63 x ≥ 0 y ≥ 0 { 2x+4y ≤ 36 7x+5y ≤ 63 x ≥ 0 y ≥ 0
Feasible region for the given inequalities is shaded via black color in graph.
What is Inequalities?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Here, given Inequalities are;
2 x + 4 y ≤ 36
7 x + 5 y ≤ 63
x ≥ 0 y ≥ 0
The graph of given inequalities are given below and the feasible region is shaded with the black color.
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