Answer:
C. (0, 14)
Step-by-step explanation:
g(x) = f(x) + 9
g(x) = -3x + 5 + 9
g(x) = -3x + 14
y = mx + b
b = 14
The value of y - intercept of the function are,
⇒ (0, 14)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
the two functions given below.
⇒ f(x) = -3x+5
And, g(x) = f(x)+9
Hence, We get;
g(x) = f(x) + 9
g(x) = -3x + 5 + 9
g(x) = -3x + 14
So, The value of y - intercept of the function are,
⇒ y = 14
⇒ (0, 14)
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Given the sequence -3, 9, -27, 81, -243, ..., find the recursive formula.
Answer:
[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex]
Step-by-step explanation:
There is a common ratio between consecutive terms of the sequence, that is
r = 9 ÷ - 3 = - 27 ÷ 9 = 81 ÷ - 27 = - 243 ÷ 81 = - 3
The recursive formula is of the form
[tex]a_{n}[/tex] = r[tex]a_{n-1}[/tex] = - 3[tex]a_{n-1}[/tex]
graph the circle x2 + y2 - 12x + 6y +36 =0
x^2+y^2-12x+6y+36=0
Top Point: (6,0)
Left Point: (3,-3)
Right Point: (9,-3)
Bottom Point: (6,-6)
Answer:
[tex] x^2 +y^2 -12x +6y +36 =0[/tex]
And we can complete the squares like this:
[tex] (x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2[/tex]
And we got:
[tex] (x-6)^2 + (y+3)^2 = 9[/tex]
And we have a circle with radius r =3 and the vertex would be;
[tex] V= (6,-3) [/tex]
The graph is on the figure attached.
Step-by-step explanation:
For this case we have the following expression:
[tex] x^2 +y^2 -12x +6y +36 =0[/tex]
And we can complete the squares like this:
[tex] (x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2[/tex]
And we got:
[tex] (x-6)^2 + (y+3)^2 = 9[/tex]
And we have a circle with radius r =3 and the vertex would be;
[tex] V= (6,-3) [/tex]
The graph is on the figure attached.
What is the result of subtracting the second equation from the first? \begin{aligned} -2x+7y &= 10 \\\\ 3x+7y &= 2 \end{aligned} −2x+7y=10 3x+7y=2
Answer:
-5x = 8
Step-by-step explanation:
The result is shown here. The y-terms cancel.
[tex]\begin{array}{rccc}& -2x+7y &= &10 \\-&(\ \,3x+7y &= &2)\\\cline{1-4}&-5x+0y&=&8 \end{array}[/tex]
The simplified result is ...
-5x = 8
Answer:
The result is that 5x = -8
Step-by-step explanation:
Here, we want to subtract 3x + 7y = 2 from -2x + 7y = 10
Mathematically that would be;
(-2x+7y)-(3x+7y) = 10-2
-2x + 7y -3x -7y = 8
-2x -3x + 0 = 8
-5x = 8 or 5x = -8
Which statements are true regarding undefinable terms in geometry?
C. A line has one dimension, length.
E. A plane consists of an infinite set of lines.
An oblique prism has trapezoidal bases and a vertical height of 10 units. An oblique trapezoidal prism is shown. The trapezoid has base lengths of x and 2 x, and a height of x. The distance between the 2 trapezoid bases is 20. The vertical height of the prism is 10. Which expression represents the volume of the prism? 10x3 cubic units 15x2 cubic units 20x3 cubic units 30x2 cubic units
Answer:
volume of trapezoidal prism = 15x^2 cubic units
Step-by-step explanation:
First, area of the trapezoidal bases.
Parallel sides measure x and 2x, for an average of 1.5x.
Height = x
Area of trapezoidal base = 1.5x*x = 1.5x^2
Volume of prism = area base * height
(length does not matter, height does)
= 1.5x^2 * 10 = 15x^2
The volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
An oblique prism has trapezoidal bases and a vertical height of 10 units.
As we know, the area of the trapezoidal bases:
From the figure:
Height = x
Area of trapezoidal base = (1.5x)(x) = 1.5x²
The volume of prism = area base×height
= 1.5x²×10 = 15x² cubic units
Thus, the volume of the prism is 15x² cubic units if the oblique prism has trapezoidal bases and a vertical height of 10 units option (B) 15x² cubic units is correct.
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Explain why f(x) = x^2-x-6/x^2-9 is not continuous at x = 3.
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]
Required
Why is the function not continuous at x = 3
First substitute 3 for x at the denominator
[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]
Factorize the numerator and the denominator
[tex]f(x) = \frac{x^2 - 3x+2x -6}{x^2 - 3^2}[/tex]
[tex]f(x) = \frac{x(x - 3)+2(x -3)}{(x - 3)(x+3)}[/tex]
[tex]f(x) = \frac{(x+2)(x - 3)}{(x - 3)(x+3)}[/tex]
Divide the numerator and denominator by (x - 3)
[tex]f(x) = \frac{x+2}{x+3}[/tex]
Substitute 3 for x
[tex]f(3) = \frac{3+2}{3+3}[/tex]
[tex]f(3) = \frac{5}{6}[/tex]
Because [tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex] is defined when x = 3;
Then the function is continuous
Answer:
A: f is not defined at x = -3
Step-by-step explanation: EDGE 2020
i need help plzzzzz
Answer:
A
Step-by-step explanation:
Given
f(x) = [tex]\frac{3+x}{x-3}[/tex]
To evaluate f(a + 2), substitute x = a + 2 into f(x)
f(a + 2) = [tex]\frac{3+a+2}{a+2-3}[/tex] = [tex]\frac{5+a}{a-1}[/tex] → A
What is the standard deviation of the data set given below?
4, 7, 8, 9, 12
O A. -2.5
O B. 18.5
O c. 6.8
O D. 76.8
E. 2.5
O F. 8.5
Answer:
The answer is 2.6 but that's not listed as an option so try 2.5?
(a) use the pythagorean theorem to determine the length of the unknown side of the triangle, (b) determine the perimeter of the triangle, and (c) determine the area of the triangle. the figure is not drawn to scale.
a. the length of the unknown side is ___
b. the perimeter of the triangle is ___
c. the area of the triangle is ___
Answer:
(A) 40 km
(B) 90 km
(C) 180 km²
Step-by-step explanation:
To find the missing side of this triangle, let's use the Pythagorean theorem.
[tex]a^2+b^2=c^2[/tex], assuming that a and b are legs, and c is the hypotenuse.
Assuming the 9km side is a, we need to find the value of b, so we can substitute into the equation.
[tex]9^2+b^2=41^2\\81+b^2=1681\\b^2=1681-81\\b^2=1600\\\\b = \sqrt{1600} \\b=40[/tex]
So, the length of the missing side is 40. Now that we know this piece of information, we can find the perimeter and area of the triangle.
The perimeter is all the sides added together, so [tex]41+9+40 = 90[/tex] km is the perimeter.
The area are the two legs multiplied divided by 2.
So,
[tex]\frac{9\cdot40}{2} \\\\\frac{360}{2}\\\\180[/tex]
So the area of this triangle is 180 cm²
I hope this helped!
HELP ASAP MONEY AND WAGES
Answer: $57,700.00
Step-by-step explanation:
Total Gross Annual income = $70,000
a) Pension at 5% = $70,000(0.05) = $3,500
b) Employee Insurance at 2.4% = $70,000(0.024) = $1,680
c) Income Tax at 0% for $0-$11,000 = $11,000(0) = $0
Income Tax at 8% for $11,000-$25,000 = $14,000(0.08) = $1,120
Income Tax at 12% for $25,000-$50,000 = $25,000(0.12) = $3,000
Income Tax at 15% for $50,000-$100,000 = $20,000(0.15) =$3,000
Total Income Tax = $7,120
Annual Net Income = Gross - Pension - Employee Insurance - Income Tax:
$70,000 - $3,500 - $1,680 - $7,120 = $57,700
Please answer it in two minutes
Answer:
2√3
Step-by-step explanation:
Since this is a 30-60-90 triangle, we can find s by finding the short leg (bottom), then the hypotenuse (s).
To find the short leg, we can divide the long leg (which is 3mm) by sqrt 3 (also √3, as any of them are fine), and we will have 3/√3. Since we don't want the square root on the bottom, we can multiply √3 on both sides, giving us 3√3/3, which is technically √3 because of simplifying.
Since you have the short leg now, you can find s. By finding s, you can multiply the short leg by 2, which will be √3 * 2 which is 2√3.
The Department of Health in the United Kingdom wants to know whether the healthcare system is achieving its goals in Scotland. Much information about healthcare comes from patient records, but that source doesn't allow us to compare people who use health services with those who don't. Therefore, the Department of Health conducted the Scotland Health Survey, which was used to interview a random sample of 34,572 people who live in Scotland.
Part A: What is the population for this sample survey? What is the sample? (4 points)
Part B: The survey found that 70% of males and 87% of females in the sample had visited a general practitioner at least once during the past year. Do you think these estimates are close to the truth about the entire population? Explain. (6 points)
Answer:
A. the population for this sample survey is 34,572 people, and the sample is the people who live in Scotland.
B. The estimates are close to the truth about the entire population.
Step-by-step explanation:
A. According to the given data we have that it was used to interview a random sample of 34,572 people who live in Scotland, therefore, the population for this sample survey is 34,572 people, and the sample is the people who live in Scotland.
B. The estimates are close to the truth about the entire population becuase a large sample was conducted, hence we can make an aproximation that represents the population parameter.
WILL MARK BRAINLIEST!!!!!!!! :))))))))))))))))
Answer:
(A) No solution
(B) One solution
(C) One solution
(D) One solution
(E) No solution
Please tell me if this is incorrect. I hope this helps!
44. The length of a road is 380 m, correct to the nearest 10 m. Maria runs along this road at an average speed of 3.9 m/s. This speed is correct to 1 decimal place. Calculate the greatest possible time taken by Maria.
Answer:
The greatest possible time taken by Maria is 97.4 seconds.
Step-by-step explanation:
The greatest possible time taken by Maria occurs when she moves at constant rate and is equal to the length of the road divided by the length of the road. That is to say:
[tex]t = \frac{\Delta s}{v}[/tex]
Where:
[tex]\Delta s[/tex] - Length of the road, measured in meters.
[tex]v[/tex] - Average speed, measured in meters per second.
Given that [tex]\Delta s = 380\,m[/tex] and [tex]v = 3.9\,\frac{m}{s}[/tex], the greatest possible time is:
[tex]t = \frac{380\,m}{3.9\,\frac{m}{s} }[/tex]
[tex]t = 97.4\,s[/tex]
The greatest possible time taken by Maria is 97.4 seconds.
if an article is sold with 20% discount,there will be a profit of 15%.If it is sold at 10% discount, there will be a profit of Rs.200.Calculate the market price of an article
Answer:
The market price of the article is Rs. 978.72
Step-by-step explanation:
Let x represents the market price.
Let y represents the selling price.
Let z represents the cost price.
if an article is sold with 20% discount then there will be a profit of 15%.
SP = CP+Profit =z+0.15z=1.15z
ATQ
[tex]0.80x = 1.15z\\0.80x- 1.15z = 0[/tex]
If it is sold at 10% discount then there will be a profit of Rs.200
ATQ
[tex]0.9x - z = 200[/tex]
Now we are supposed to find the market price of an article.
[tex]0.9x - z= 200[/tex]
Multiplying 1.15 both sides
[tex]0.9x \times 1.15 - 1.15z = 200 \times 1.15\\1.035x - 1.15z = 230[/tex]
We know that[tex]1.15z = 0.80x[/tex]
[tex]1.035x - 0.80z = 230\\0.235x = 230\\x = \frac{230}{0.235}\\x= Rs. 978.72[/tex]
Hence The market price of the article is Rs. 978.72
I need help i will mark brainliest please
Answer:
1) true
2) false
hope it worked
and pls mark me as BRAINLIEST
Latesha’s mother puts $85 in Latesha’s lunch account at school. Each day Latesha uses $3 from her account for lunch. The table below represents this situation. Latesha’s Lunch Account Day Amount Left in Account ($) 0 $85 1 2 3 4 5 How much is left in Latesha’s lunch account after she has had lunch for 5 days? $15 $67 $70 $82
Answer: it 70
Step-by-step explanation:
Latesha’s mother puts $85 in Latesha’s lunch account at school. Each day Latesha uses $3 from her account for lunch. The table below represents this situation.
How much is left in Latesha’s lunch account after she has had lunch for 5 days?
$15
$67
$70 is correct$82
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Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased
Answer:
[tex]\large \boxed{87.5 \, \%}[/tex]
Step-by-step explanation:
Let x = the original number of books
Then 0.375x = the total number of biographies
and 0.20 x = the original number of biographies
[tex]\text{Percent increase} = \dfrac{\text{ New number - Old number }}{\text{Old number }} \times 100\, \%\\\\= \dfrac{0.375x - 0.20x}{0.20x} \times 100\, \% = \dfrac{0.175x}{0.20x} \times 100\, \% = 0.875 \times 100\, \% = \mathbf{87.5 \, \%}\\\\\text{The number of biographies has increased by $\large \boxed{\mathbf{87.5 \, \%}}$}[/tex]
Which expression is equivalent to 10 to the 4 power? A.) 10 times 10 times 10 times 10 B.) 40 C.) 4 times 4 times 4 times 4 times 4 times 4 times 4 times 4 times 4 times 4 D.) 4,444,444,444
Answer:
A
Step-by-step explanation:
Here in this question, we want to select which of the options particularly represents what was given in the question.
Mathematically 10^4 means that we are raising 10 into a continued exponential raising up to 4 times.
So 10^4 is pronounced as the first option in the question.
10 raised to power 10 , raised to power 10 etc
the volume v (in cubic inches) of a rectangular cardboard box is modeled by the function v(x)= (18-2x)(3-2x)x, where x is the width (in inches) of the box. Determine the values of x for which the model makes sense. Explain your reasoning. (WILL GIVE BRAINLY FOR BEST ANSWER!!!)
Answer:
0 < x < 3/2
Step-by-step explanation:
The dimensions are positive when ...
18 -2x > 0 ⇒ x < 9
3 -2x > 0 ⇒ x < 3/2
x > 0
So, the values of x where the model makes sense are ...
0 < x < 3/2
For what value of x does 5^x-2 not equal zero?
a. all except 2
b. all except 0
c. all except -4
d. all except -2
e. all real numbers
Answer:
E: all real numbers
Step-by-step explanation:
The inequality x > y is satisfied by point (5,5).
true false
Answer:
There is not enough information.
Step-by-step explanation:
Can someone help me solve this :): ?
( brainliest to the correct answer/explanation)
Answer:
1and1/2yrs ago
Step-by-step explanation:
price dis year= 56545
reduction per year= 11309
...number of years ago = 73810-56545=17265
and is about 20% of annual deductions
so if 56545 +20% + 1/2 20% = 1nd1/2 yrs
State if the two triangles are congruent. If they are, state how you know.
Answer:
yes, by AAS there are two sides of corresponding angles
Step-by-step explanation:
HOPE this helps...
Answer:
Last option..
Yes by AAS
Step-by-step explanation:
the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal
Therefore by this statement we understand that these two are the sides of the corresponding angles!
Hope it helps!
Item 25 The linear function m=45−7.5b represents the amount m (in dollars) of money that you have after buying b books. Select all of the values that are in the domain of the function. 0 1 2 3 4 5 6 7 8 9 10
Answer:
[tex]Domain: \{0,1,2,3,4,5,6\}[/tex]
Step-by-step explanation:
Given
[tex]m = 45 - 7.5b[/tex]
[tex]Values: \{0,1,2,3,4,5,6,7,8,9,10\}[/tex]
Required
Select all values that belongs to the domain of the given function
Analyzing the question;
The question says that the function, m represent the amount left after buying b number of books
This means that, after purchasing b books, I'm expected to have a certain m amount of dollars left with me;
This implies that the value of m can never be negative;
So, the domain of m are values of b such that [tex]m \geq 0[/tex]
When b = 0
[tex]m = 45 - 7.5(0)[/tex]
[tex]m = 45 - 0[/tex]
[tex]m = 45[/tex]
When b = 1
[tex]m = 45 - 7.5(1)[/tex]
[tex]m = 45 - 7.5[/tex]
[tex]m = 37.5[/tex]
When b = 2
[tex]m = 45 - 7.5(2)[/tex]
[tex]m = 45 - 15[/tex]
[tex]m = 30[/tex]
When b = 3
[tex]m = 45 - 7.5(3)[/tex]
[tex]m = 45 - 22.5[/tex]
[tex]m = 22.5[/tex]
When b = 4
[tex]m = 45 - 7.5(4)[/tex]
[tex]m = 45 - 30[/tex]
[tex]m = 15[/tex]
When b = 5
[tex]m = 45 - 7.5(5)[/tex]
[tex]m = 45 - 37.5[/tex]
[tex]m = 7.5[/tex]
When b = 6
[tex]m = 45 - 7.5(6)[/tex]
[tex]m = 45 - 45[/tex]
[tex]m = 0[/tex]
When b = 7
[tex]m = 45 - 7.5(7)[/tex]
[tex]m = 45 - 52.5[/tex]
[tex]m = -7.5[/tex]
There's no need to check for other values, as they will result in negative values of m;
Hence, the domain of m are:
[tex]Domain: \{0,1,2,3,4,5,6\}[/tex]
The values that are in the domain of the function are 7, 8, 9 and 10
Linear functionsGiven the linear function m=45−7.5b
where:
b represents the amount m (in dollars) of moneyFor th domain to exist, then;
45 - 7.5b< 0
7.5 b > 45
b > 45/7.5
b > 6
Hence the values that are in the domain of the function are 7, 8, 9 and 10
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Consider a regular pyramid A with a square base and a right circular cone B.
It is given that the length of a side of the square base of pyramid A is the same as the base radius of cone B.
If the two solids have the same volume, which solid will have a greater height? Explain your answer.
Please help me solve this question with steps!orz
Answer:
Pyramid
Step-by-step explanation:
[tex]\text{Volume of a Square Pyramid }=\frac{1}{3} \times l^2 \times Height\\\\ \text{Volume of a Cone }=\frac{1}{3} \pi r^2 \times Height[/tex]
Given that the two solids have the same volume
[tex]\frac{1}{3} \times l^2 \times Height=\frac{1}{3} \pi r^2 \times Height[/tex]
If the length of a side of the square base of pyramid A is the same as the base radius of cone B. i.e l=r
[tex]\frac{1}{3} \times l^2 \times $Height of Pyramid=$\frac{1}{3} \pi l^2 \times $Height of cone$\\\\$Cancel out $ \frac{1}{3} \times l^2$ on both sides\\\\Height of Pyramid= \pi \times $ Height of cone$[/tex]
If the height of the cone is 1
[tex]H$eight of Pyramid= \pi \times 1 \approx 3.14$ units[/tex]
Therefore, the pyramid has a greater height.
Romain knows the following information about the 323232 classes he took in high school: He studied for but did not pass 333 classes. He passed 272727 classes in total. He studied for 262626 classes in total. Can you help Romain organize the results into a two-way frequency table?
Answer:
Classes studied for, Classes he did not study for Total
Classes Passed, 23 4 27
Classes Failed, 3 2 5
Total, 26, 6 32
Please find attached the two way frequency table formatted on Excel spreadsheet
Step-by-step explanation:
The given information are;
The total number of classes Romain took in high school = 32
The number of classes he studied for but did not pass = 3
The total number of classes Romain passed = 27
The number of classes Romain studied for = 26
Therefore;
The number of classes Romain studied for and passed = 26 - 3 = 23
The total number of classes Romain failed = 32 - 27 = 5
The total number of classes Romain passed but did not study for = 27 - (26 - 3) = 4
The number of classes Romain did not study for and failed = 5 - 3 = 2
The total number of classes Romain did not study for = 4 + 2 = 6
Adding Rational Numbers Using Properties of Operations we can
add integers in any order using the
and
properties of addition.
Consider the integers a, b, c, and -d. We can add this group of
integers in several different ways:
a + (-b) + C+ (-0)
a+c+ (-6) + (-d)
(a + c) + [(-b) + (-d)]
The sum of the integers remains the
regardless of
their arrangement. We can use the commutative and associative
properties to break up numbers by
to find the sum of two or more rational numbers.
Answer:
First blank: Commutative
Second blank: Associative
Third blank: Same
Fourth blank and fifth blank: Rearranging them? (Not entirely sure)
Hope this helps :)
The co ordinates of the point where lines ax = by and ay=6x intersects are
Answer: (0, 0)
Step-by-step explanation:
ax = by ay = 6x
[tex]\dfrac{ax}{b}=y\qquad \quad y=\dfrac{6x}{a}[/tex]
Use substitution:
[tex]\dfrac{ax}{b}=\dfrac{6x}{a}\\\\\\\text{Cross Multiply:}\\a^2x=6bx\\\\\\\text{Solve for x:}\\a^2x-6bx=0\\x(a^2-6b)=0\\x=\dfrac{0}{a^2-6b}\\\large\boxed{x=0}[/tex]
Substitute x = 0 to solve for y:
[tex]\dfrac{ax}{b}=y \\\\\dfrac{a(0)}{b}=y\\\\\large\boxed{0=y}[/tex]
Please help me with this problem! If anybody answers first in this, i will give brainliest to you! Be the first one to answer this then i will give out a brainliest award to you!
Are you sure your that person?
Answer:
32 remainder 2
Step-by-step explanation:
To divide 162 by 5, we simply do the following:
5 goes into 16 => 3
Multiply 5 by 3 => 3 × 5 = 15
Subtract 15 from 16 => 16 – 15 = 1
Put the 1 before 2 => 12
5 goes into 12 => 2
Multiply 5 by 2 => 5 × 2 = 10
Subtract 10 from 12 => 12 – 10 => 2
In summary,
162 divided by 5 => 32 remainder 2
Please see attached photo for further details.