Answer:
The line intercepts the y-axis and [tex]y = 8[/tex]
Step-by-step explanation:
The intersection on the y-axis of a line is found to be [tex]x = 0[/tex].
That is, the intercept with the y-axis is the value of the function when x is equal to zero.
In this case we know the following points of the function:
x : -2 -1 0 1 2 3
y : 16 12 8 4 0 -4
Note that when [tex]x = 0[/tex] then [tex]y = 8[/tex].
Therefore the line intercepts the y-axis and [tex]y = 8[/tex]
Which statement is always true
Answer:
Step-by-step explanation:
The sine of any acute angle is equal to the cosine of its complement. The cosine of any acute angle is equal to the sine of its complement. of any acute angle equals its cofunction of the angle's complement. Yes, there is a "relationship" regarding the tangent of the two acute angles (A and B) in a right triangle.
hope this helps u
Help!!!!! NEED HELP WITH INTRODUCTION TO INEQUALITIES
need help with Introduction to inequalities its says circle the numbers in the replacement set that make each inequality true. With questions 1,3,5,7
< less than ≤ less than or equal to (line underneath sign)
> greater than ≥ greater than or equal to (line underneath sign)
# is just the number they gave you in the inequality
x < # [you can put any number into "x", but it has to be less than #]
x > # [you can put any number into "x", but it has to be greater than #]
x ≤ # [number has to be less than or equal to #]
x ≥ # [number has to be greater than or equal to #]
1. t < 7 [t is a number less than 7]
So you circle: 4, 6, 8, 0, -6
3. a ≤ -4 [a is a number less than or equal to -4]
circle: -7, -4
5.
k + 5 < 9 You can simplify this by subtracting 5 on both sides
k < 4 [k is a number less than 4]
circle: -1, 3, -2, 3.5
7. u - 5 ≥ -1 Simplify
u ≥ 4 [u is a number greater than or equal to 4]
circle: 4, 5, 4.1
what is the quotient when x^3 -5x^2 + 3x -8 is divided by x-3 ?
For this case we have that the parts of a division are:
Dividend, divisor, quotient and remainder.
To make the division of polynomials, we must build a quotient that when multiplied by the divisor (and when the sign is changed), eliminate the terms of the dividend until reaching the remainder of the division.
It must be fulfilled that:
[tex]Dividend = Quotient * Divider + Remainder[/tex]
Then, if we look at the attached figure, the quotient is:
[tex]x ^ 2-2x-3[/tex]
Answer:
[tex]x ^ 2-2x-3[/tex]
how many points out of 416 do i need to get to get a 60% in class
Right now I have 153.
Answer: 249.6 so 250
Step-by-step explanation: Take 416 times it by 0.6 Have a nice day. Hope it helped!
You currently have a 36%.
You need 249-250% to get a 60% in your class.
Best of luck!
If the graph of y= |x| is translated so that the point (1, 1) is moved to (4,1), what is the equation of the new graph?
Answer:
The new equation is y= (x-3)
Step-by-step explanation: we know that the point (1, 1) is moved to (4,1).
So, the rule of the translation is: [tex](x,y) -----> (x+3, y)[/tex]
that means the translation is 3 units to the right
Answer:
[tex]y=|x-3|[/tex]
Step-by-step explanation:
The parent absolute function is
[tex]y=|x|[/tex]
The graph of y= |x| is translated so that the point (1, 1) is moved to (4,1). It means the rule of translation is
[tex](x,y)\rightarrow (x+3,y)[/tex]
it means the graph of y=|x| translated 3 units right. So, the new vertex of the function is (3,0).
The vertex form of an absolute function is
[tex]y=|x-h|+k[/tex]
The new vertex of the function is (3,0). Substitute h=3 and k=0 in the above equation.
[tex]y=|x-3|+0[/tex]
[tex]y=|x-3|[/tex]
Therefore, the required equation is y=|x-3|.
find the quotient 3/4 ÷ 6/7.=
[tex]\bf \cfrac{3}{4}\div \cfrac{6}{7}\implies \cfrac{3}{4}\cdot \cfrac{7}{6}\implies \cfrac{7}{4}\cdot \cfrac{3}{6}\implies \cfrac{7}{4}\cdot\cfrac{1}{2}\implies \cfrac{7}{8}[/tex]
the numbers of points scored by a football team in 7 different games are
26, 38, 33, 20, 27,3, and 28. For numbers 4a-4c select true or false to
indicate whether the statement is correct.
4a.
The outlier in the data set is 3.
O True
O False
4b. The difference between the
outlier and the median is 24.
O True
O False
4c.
The outlier in this set of data
affects the mean by increasing it.
O True
O False
A. True
B. False
C.true
How do you solve for a side in right triangles?
Answer:
pythagorean theorem
Step-by-step explanation:
a²+b²=c²
Pythagorean theorem
Find the value of this expression if x=-6 x^2-6/x-4
Answer:
x=−0.825789
Step-by-step explanation:
x=(−6x3−4x−6)/x
Step 1: Multiply both sides by x.
x2=−6x3−4x−6
x2−(−6x3−4x−6)=−6x3−4x−6−(−6x3−4x−6)(Subtract -6x^3-4x-6 from both sides)
6x3+x2+4x+6=0
(Use cubic formula)
x=−0.825789
Answer:
- 3
Step-by-step explanation:
Substitute x = - 6 into the expression
[tex]\frac{(-6)^2-6}{-6-4}[/tex]
= [tex]\frac{36-6}{-10}[/tex] = [tex]\frac{30}{-10}[/tex] = - 3
our product is 72. the difference between us is 1. what number are we?
Answer: 8 and 9
Step-by-step explanation:
8 times 9 equals 72
9 minus 8 equals 1.
how many millimeters are in a centimeter
Answer:
1 centimeter = 10 millimeters
Step-by-step explanation:
we have to find about how many millimeters are in a centimeter.
We know that 1 centimeter = 10 millimeters
or 10 millimeters = 1 centimeter
divide both sides by 10
or \frac{10}{10} millimeters = \frac{1}{10} centimeter
or 1 millimeters = 0.1 centimeter
But we need millimeters in centimeters so we should write :
final answer as 1 centimeter = 10 millimeters.
i have 3 questions can you answer them?
what is 73 divided by 8967
what is 91 divided by 8743
and what is 37 divided by 86,322 ?????????????????
73 divided by 8967:
0.0081409613
91 divided by 8743:
0.01040832666
37 divided by 86322:
0.00042862769
Kai is conducting a study about the percentage of students with jobs. His school has 2500 students. He asks everyone in his drama class to participate in a survey. He bases his findings on these results. Is this a valid study? Why or why not?
A) YES, he asked everyone in his class.
B) YES, since drama students tend to have after-school jobs.
C) NO, he should have taken a small sample from the drama class.
D) NO, the drama class does not represent all students in the school.
Answer: D
Step-by-step explanation:
That is a small sample out of the entire school
Which strategies can be used to solve this problem? Marcus bought books for his vacation. He bought a mystery book for $14, a fantasy novel for $25, and 3 biographies that cost $6 each. How much money did Marcus spend on the books altogether? Choose all answers that are correct. A. Translate into an equation. 14 + 25 + 6 = n B. Work backward. Start with $6 and add this amount to $25 and $14. Multiply the sum by 3 to get the amount Marcus spent. C. Use logical reasoning. Think that Marcus bought a total of 5 books. Multiply $6 by 3 to get the cost of the biographies. Add this amount to the cost of the two other books ($14 and $25) to get the total amount Marcus spent. D. Draw a diagram. Draw 5 rectangles to represent the 5 books Marcus bought. Put $14 in one rectangle and $25 in another rectangle. Write $6 in each of the remaining 3 rectangles. Add the 5 amounts together to get the total amount Marcus spent.
Answer: c is your answer
Step-by-step explanation:
Triangle ABC is similar to triangle WYZ. select all angles whose tangent equals 3/4
Answer:
∠B
∠Y
Step-by-step explanation:
we know that
In the right triangle ABC
[tex]tan(B)=\frac{AC}{BC}[/tex] ----> opposite side to angle B divided by the adjacent side to angle B
substitute the values
[tex]tan(B)=\frac{3}{4}[/tex]
Remember that
If two triangles are similar, then the corresponding sides are proportional and the corresponding angles are congruent
so
∠A=∠W
∠B=∠Y
∠C=∠Z
therefore
[tex]tan(B)=tan(Y)[/tex]
Base on the fact that the triangle ABC and WYZ are similar, the angles whose tangent equals 3 / 4 are ∠B and ∠Y
What are similar triangles?Similar triangle are only different in sizes but are of the same shape.
Similar triangles, corresponding sides are always in the same ratio. Corresponding angles of similar triangles are always congruent. Therefore,
∠A = ∠W
∠B = ∠Y
∠C = ∠Z
Therefore, let's find all angles in the similar triangles whose tangent is equal to 3 / 4 .
tan ∅ = opposite / adjacent
Since,
tan B = 3 / 4
Then
tan Y = 3 / 4
Therefore,
The angles whose tangent equals 3 / 4 are ∠B and ∠Y
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The area of a square can be found using the equation A= s2, where A is the area and S is the measure of one side of the square. Match the equation for how to slice for the side length of a square to its description. A square has area of 99 in2
Answer:
the answer is the first option
The correct answer is [tex]\sqrt{99}[/tex] in.
What is a square?
A 2-dimensional figure bounded by 4 sides having 4 corners and hence 4 angles, in which all the sides are equal and opposite sides are parallel and all the angles are 90° is called a square. In a square the diagonals bisects each other at right angles.
How to find the area of a square?Area of square can be found by squaring the length of a side.How find length of each side of the square?In the question, the area of the square is given 99 in²
According to the problem,99 = S², S is the measure of one side of the square.
Length of each side will be [tex]\sqrt{99}[/tex] in.
Option a is correct.
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Can you please help me.
Answer:
7)60
8)1/6
9)9
10)11.5
11)14.4
Step-by-step explanation:
Answer:divide
Step-by-step explanation:
which of the following is true about the expression5*1/4
Answer:
C. It represents the product of two rational numbers and its equivalent to a rational number.
Step-by-step explanation:
5 is a natural number, a real number and a rational number.
[tex]\frac{1}{4}[/tex] is a real number and a rational number.
The product of 5 × [tex]\frac{1}{4}[/tex] = 1.25 which is also a rational number in addition to being a real number.
Answer:
The correct answer is option C.
Step-by-step explanation:
It s given that 5 * 1/4
To find the correct answer
The given expression is 5 * 1/4
Here 5 is a rational number and 1/4 is a rational number
5 * 1/4 = 5/4
The number 5/4 is a rational number.
5/4 represents the product of two rational numbers and is equivalent to a rational number.
Therefore the correct answer is option C
Find the rate of change of the function h(x)=2x^2 in the interval 2<_ x<_4
[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{31em}{0.25pt}\\\\ h(x)= 2x^2\qquad 2\leqslant x \leqslant 4 \qquad \begin{cases} x_1=2\\ x_2=4 \end{cases}\implies \cfrac{h(4)-h(2)}{4-2} \\\\\\ \cfrac{2(4)^2~~-~~2(2)^2}{2}\implies \cfrac{32-8}{2}\implies \cfrac{24}{2}\implies 12[/tex]
What is the x-intercept of the equation y=-5x+1,450?
Substitute the value for y as 450
450=-5x+1
Solve for x
450-1=-5x
449=-5x
89.8=-x
x=-89.8
Answer:
x = 290
Step-by-step explanation:
The x- intercept is the point on the x- axis where the line crosses.
substitute y = 0 into the equation and solve for x
- 5x + 1450 = 0 ( subtract 1450 from both sides )
- 5x = - 1450 ( divide both sides by - 5 )
x = 290 ← x- intercept
line crosses x- axis at (290, 0)
Find all solutions for a triangle with a=26, b=29, and A=58
Answer:
i think its C
Step-by-step explanation:
Final answer:
To solve the triangle with sides a=26, b=29, and angle A=58 degrees, apply the Law of Sines to find another angle, use the sum of angles to find the third angle, and then the Law of Cosines to find the remaining side, ensuring all conditions are satisfied for a valid triangle.
Explanation:
To find all solutions for a triangle given a=26, b=29, and A=58 degrees, we use the Law of Sines, which relates the lengths of sides to the sine of their opposite angles. Since sin A > sin a (opposite side to angle A) would result in no solution and considering the given values, we don't encounter this issue. Instead, we have:
sin B / b = sin A / a
Rearranging for B, we have:
B = sin⁻¹(sin A / a × b)
Plugging in our numbers:
B = sin⁻¹((sin 58°) / 26 × 29)
Once B is calculated, we can find angle C since the interior angles of a triangle sum to 180 degrees. Following that, we can use the Law of Cosines to find the third side, c. The process is:
Calculate B using the Law of Sines.Calculate C by subtracting A and B from 180 degrees.Calculate c using the Law of Cosines: c² = a² + b² - 2ab cos C.After finding all angles and sides, verify the solution by checking if the interior angles sum to 180 degrees and the sides satisfy the Triangle Inequality Theorem.
An equation is written to represent the relationship between the temperature in Alaska during a snow storm, y, as it relates to the time in hours, x, since the storm started. A graph of the equation is created. Which quadrants of a coordinate grid should be used to display this data? Quadrant 1 only
Answer:
1 and 4
Step-by-step explanation:
30 POINTS! x + 1 = 2 ÷ x + 1
In the equation above, which choice is a possible value of x + 1?
A) 1 - √2
B) √2
C) 2
D) 4
For this case we have the following equation:
[tex]x + 1 = \frac {2} {x + 1}[/tex]
We must find the value of [tex]x + 1[/tex]:
Multiplying both sides of the equation by[tex]x + 1:[/tex]
[tex](x + 1) ^ 2 = 2[/tex]
Applying square root on both sides of the equation to eliminate the exponent:
[tex]x + 1 = \sqrt {2}[/tex]
Answer:
Option B
Answer: B
Step-by-step explanation:
A rectangular room is 2 times as long as it is wide, and its perimeter is 30 meters. Find the dimension of the room.
Answer:
5 by 10
Step-by-step explanation:
We know that the equation of a perimeter of a recangle is 2(l)+2(w), l being length and w being width. We know that l=2w. So the perimeter of this room would be:
2(2w)+2(w)=30
4w+2w=30
6w=30
w=5
l=2w
l=10
the dimensions are 5 by ten
The dimensions of the rectangular room with a perimeter of 30 meters and length twice its width are 5 meters wide and 10 meters long.
Explanation:The subject matter of your question falls into the category of Mathematics, specifically dealing with basic geometry and algebra. You want to find the width and length of a rectangular room given that it is twice as long as it is wide, and that its perimeter is 30 meters.
The perimeter P of a rectangle is calculated by the formula 2L + 2W = P, where L is the length and W is the width. Since the length is given as twice the width, we can substitute 2W for L in the formula and get 2(2W) + 2W = 30, which simplifies to 6W = 30. Solving for W, we find that W = 5. Therefore, the width of the room is 5 meters and the length of the room is 2W = 2*5 = 10 meters.
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If f(x) = 1-x which value is equivalent to |f(I)|
Answer:given that
F (x)=1-x
Step-by-step explanation:
Answer:
The value of |f(i)| is √2.
Step-by-step explanation:
The given function is
[tex]f(x)=1-x[/tex]
We need to find the value of |f(i)|.
Substitute x=i in the given function.
[tex]f(i)=1-i[/tex]
Taking modulus on both the sides.
[tex]|f(i)|=|1-i|[/tex]
Using the formula for modulus of a complex number, we get
[tex]|f(i)|=\sqrt{(1)^2+(-1)^2}[/tex] [tex][\because |a+ib|=\sqrt{a^2+b^2}][/tex]
[tex]|f(i)|=\sqrt{1+1}[/tex]
[tex]|f(i)|=\sqrt{2}[/tex]
Therefore the value of |f(i)| is √2.
Which equations have the same value of x as 5/6 x + 2/3 ? Check all that apply.
Answer:
B. [tex]6(\frac{5}{6} x+\dfrac{2}{3}) =-9(6)[/tex]
C. 5x + 4 = -54
F. 5x = -58
Step-by-step explanation:
Solving given equation step to step:
The given equation is a linear form and to solve for x.
[tex] \dfrac{5}{6} x+\dfrac{2}{3}=-9\\\Rightarrow6(\dfrac{5}{6} x+\dfrac{2}{3}) =-9(6)\ \ \ \ \ [\because \text{Multiplying both side by 6}]\\\Rightarrow 6(\dfrac{5x+4}{6}) =-9(6)\ \ \ \ \ [\because text{taking LCM of 6 and 3} ]\\\Rightarrow 5x+4=-9(6)\\\Rightarrow 5x+4 =-54\\\Rightarrow 5x =-54-4\\\Rightarrow 5x =-58 [/tex]
Which statement best explains why the equation X +2=3x-14 can be used to slice for x ?
Answer:c
Diagonals bisect each other
Step-by-step explanation:
This cute the diagonal into two equal parts
Answer: Diagonals of a rhombus bisect each other
Step-by-step explanation:
i got that right
"Complete the square" to convert the equation of each circle to graphing form. Identify the center and the radius.
x² + 6x + y2 – 4y= -9
Answer:
The center is (-3,2) and the radius is r=2
Step-by-step explanation:
The general equation of the given circle is
[tex]x^2+6x+y^2-4y=-9[/tex]
Add the square of half the coefficient of the linear terms to both sides of the equation to obtain;
[tex]x^2+6x+3^2+y^2-4y+(-2)^2=-9+3^2+(-2)^2[/tex]
[tex]x^2+6x+9+y^2-4y+4=-9+9+4[/tex]
[tex]x^2+6x+9+y^2-4y+4=4[/tex]
The quadratic trinomials in x and y on the left side of the equations are perfect squares.
We factor to obtain;
[tex](x+3)^2+(y-2)^2=4[/tex]
[tex](x--3)^2+(y-2)^2=2^2[/tex]
Comparing to:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The center is (-3,2) and the radius is r=2
To complete the square and put the equation into graphing form, group x's and y's, add appropriate constants to each group, and rewrite. The circle's equation becomes (x + 3)² + (y - 2)² = 4, with the center at (-3, 2) and a radius of 2.
Explanation:To complete the square for the equation x² + 6x + y² - 4y = -9 and convert it to graphing form, we need to group the x's and y's together and add the right constants to each group.
First, group the x terms and the y terms: (x² + 6x) + (y² - 4y).Next, for x terms, add and subtract (6/2)², which is 9, inside the parentheses: (x² + 6x + 9) - 9.For y terms, add and subtract (-4/2)², which is 4, inside the parentheses: (y² - 4y + 4) - 4.Combine the constant terms with -9, the constant on the right side of the equation: -9 - 9 - 4.The equation becomes (x + 3)² + (y - 2)² = 4.Now, the equation is in the graphing form of a circle ((x-h)² + (y-k)² = r²), where (h, k) is the center and r is the radius. Hence, the circle's center is at (-3, 2) and its radius is 2.
If you can explain your answer that’d be great!! Thank you!
Answer:
[tex]A(t)=A_{0}e^{\frac{ln(\frac{1}{2})}{22}t}[/tex]
Step-by-step explanation:
This half life exponential decay equation goes by the formula:
[tex]A(t)=A_{0}e^{kt}[/tex]
Where
[tex]k=\frac{ln(\frac{1}{2})}{Half-Life}[/tex]
Since half life is given as 22, we plug that into "Half-Life" in the formula for k and then plug in the formula for k into the exponential decay formula:
So,
[tex]k=\frac{ln(\frac{1}{2})}{Half-Life}\\k=\frac{ln(\frac{1}{2})}{22}[/tex]
Now
[tex]A(t)=A_{0}e^{\frac{ln(\frac{1}{2})}{22}t}[/tex]
third choice is correct.
10. Jaime is running a marathon, which is a 26 2/5 Mile Race. At 6 3/4 miles from the start, she passes Friends cheering on her. After she passes a water stop 9 1/2 miles farther along the route, How Far From The Finish Line is Jaime?
Answer:
A
Step-by-step explanation:
6 3/4 + 9 1/2 = 65/4
26 2/5 - 65/4 = 203/20 or 10 3/20