Answer:
(-0.84, 0) and (-5.16, 0).
Step-by-step explanation:
What is the measure of AC?
Answer:
5 blocks
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to solve for AC
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
AC² = AB² + BC² ← substitute values
AC² = 3² + 4² = 9 + 16 = 25 ( take the square root of both sides )
AC = [tex]\sqrt{25}[/tex] = 5
vertical angles must check all that apply
Vertical Angles have to be congruent and have the same vertex.
The correct options are:
B. Have the same vertex.
C. be congruent.
Step-by-step explanation:Vertical Angles--
These are formed by the intersection of two lines.When two lines intersect then four angles are formed such that each pair of the opposite angles are called vertical angles.The vertical angles have a common vertex.Since, one vertex is obtained when the lines intersect.They could never be adjacent angles.Also, they may be obtuse, acute or right angles.The measure of each of the vertical angles are always equal i.e. the angles are congruent.Which points could be on the line that is parallel to
and passes through point J? Check all that apply.
(-3,5)
(1,5)
(3,-2)
(3, 2)
(5,1)
Answer:
(-3, 5), (3, 2), (5, 1)Step-by-step explanation:
Parallel lines have the same slope.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the coordinates of the given points G(-4, 1) and H(2, -2):
[tex]m=\dfrac{-2-1}{2-(-4)}=\dfrac{-3}{6}=-\dfrac{1}{2}[/tex]
J(1, 3). Let other point (x, y).
Substitute to the slope:
[tex]\dfrac{y-3}{x-1}=\dfrac{-1}{2}[/tex] cross multiply
[tex]2(y-3)=-1(x-1)[/tex] use the distributive property
[tex]2y+(2)(-3)=-x+(-1)(-1)[/tex]
[tex]2y-6=-x+1[/tex] add 6 to both sides
[tex]2y=-x+7[/tex] divide both sides by 2
[tex]y=-\dfrac{1}{2}x+\dfrac{7}{2}[/tex]
Check the equality for coordinates of each point:
[tex](-3, 5)\\\\5=-\dfrac{1}{2}(-3)+\dfrac{7}{2}\\\\5=\dfrac{3}{2}+\dfrac{7}{2}\\\\5=\dfrac{10}{2}\\\\5=5\qquad\bold{CORRECT}[/tex]
[tex](1,\ 5)\\\\5=-\dfrac{1}{2}(1)+\dfrac{7}{2}\\\\5=-\dfrac{1}{2}+\dfrac{7}{2}\\\\5=\dfrac{6}{2}\\\\5=3\qquad\bold{FALSE}[/tex]
[tex](3,\ -2)\\\\-2=-\dfrac{1}{2}(3)+\dfrac{7}{2}\\\\-2=-\dfrac{3}{2}+\dfrac{7}{2}\\\\-2=\dfrac{4}{2}\\\\-2=2\qquad\bold{FALSE}[/tex]
[tex](3,\ 2)\\\\2=-\dfrac{1}{2}(3)+\dfrac{7}{2}\\\\2=-\dfrac{3}{2}+\dfrac{7}{2}\\\\2=\dfrac{4}{2}\\\\2=2\qquad\bold{CORRECT}[/tex]
[tex](5,\ 1)\\\\1=-\dfrac{1}{2}(5)+\dfrac{7}{2}\\\\1=-\dfrac{5}{2}+\dfrac{7}{2}\\\\1=\dfrac{2}{2}\\\\1=1\qquad\bold{CORRECT}[/tex]
To identify which points could be on a line that is parallel to another and passes through a specific point, we need to know the slope of the original line or the coordinates of the given point. Without this information, it is impossible to accurately determine which points from the list might be on the parallel line.
Explanation:The question asks, Which points could be on the line that is parallel to and passes through point J? This problem is a part of geometry in mathematics where we study about points, lines, and planes.
The location of point J was not specified, but the line that is parallel to another would have the same slope, regardless of its y-intercept. As such, to find the points that can lie on a line that is parallel, we must know the slope of the primary line. If we are given the slope 'm', any points that fall on the line would satisfy the equation of a line, y = mx + b, where 'b' is the y-intercept. The points whose 'y' value remains constant in the given x-y pairs would lie on the line parallel to the original line.
Without the proper information about the slope of the line or the position of point J, it is impossible to accurately determine which points from the given list can lie on the line that is parallel and passes through point J.
Learn more about Lines and Points here:https://brainly.com/question/23986567
#SPJ2
If f(x) = 2x2 - 5 and g(x) = x2 - 4x - 8, find (f - g)(x).
Answer:
= x^2 +4x +3
Step-by-step explanation:
f(x) = 2x^2 - 5
g(x) = x^2 - 4x - 8
(f - g)(x)=2x^2 -5 - (x^2 -4x-8)
Distribute the minus sign
= 2x^2 -5 -x^2 +4x+8
Combine like terms
= x^2 +4x +3
Two garden plots are to have the same
area. One is square and one is
rectangular. The rectangular plot is 4
meters wide and 9 meters long.
Answer:
6m
Step-by-step explanation:
The area of the rectangular plot is
A = l*w
= 4*9
= 36 m^2
To find the area of the square plot
A = s^2
36 = s^2
Take the square root of each side
sqrt(36) = sqrt(s^2)
6 = s
The length of the side of the square plot is 6 m
Find the rate of change for the line that passes through the point (-2, 6) and (-5, 9).
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{9}) \\\\\\ \stackrel{\textit{average rate of change}~\hfill }{slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}}\implies \cfrac{9-6}{-5-(-2)}\implies \cfrac{9-6}{-5+2}\implies \cfrac{3}{-3}\implies -1[/tex]
find the value of 2x-10 given that -5x-9=6
Help me with this question thanks
Answer:
arrow going from 9 to -infinity (open circle)
Step-by-step explanation:
equalize equation by multiplying both sides by 3 to obtain the equation 9>t
then simply plug in numbers to see if they check out, ie: 3> 4/3 makes sense, but 3> 10/3 doesn't.
Draw the arrow to accommodate for the answers that DO fit.
open circle, because it doesn't work for t=9
Answer:
see below
Step-by-step explanation:
3 > t/3
Multiply each side by 3
3*3 > t/3 *3
9 > t
t < 9
There is an open circle at 9, since the symbol is less than
The line goes to the left.
What’s the mode of data set 23,95,100,23,100,100
Answer:100
Step-by-step explanation:
That is the most common number
Hello There!
Mode: The number that occurs most often in a set of numbers
in this case, the number 100 occurs more than any other number in the set. This means that the mode for this set of data is 100.
A factory has to transport raw materials to a project site. The total weight of the raw material will not be less than 1,500 tons. The factory manager plans to use two different trucking firms. Big Red has heavy-duty trucks that can transport 200 tons at a cost of $50 per truckload. Common Joe is a more economical firm, costing only $20 per load, but its trucks can transport only 90 tons. The factory manager does not wish to spend more than $450 on transportation. The availability of trucks is the same for both firms.
Answer:
common Joe is cheaper
Step-by-step explanation:
1500/200 =7.5 truckloads
7.5×50=$375
1500/90=16.666 truckloads
16.666×20=$333.
I really didn't know for sure what u we're looking for
Answer:Common Joe
Step-by-step explanation:
Given
Total weight of Raw material is 1500 tons
Big Red can transport 200 tons at a cost of $50 per truckload
so Big Red need to do 8 rounds to completely transport the raw material
In first 7 round round it carries 200 tons and in last round it carry 100 tons
i.e. [tex]200\times 7+100[/tex]
so cost for Red bus=[tex]50\times 8=$400[/tex]
For Common Joe truck requires 17 round of loading to completely transport 1500 tons
In first 16 round it carries 90 tons and in last round it carries 60 tons
So cost for Common Joe is [tex]17\times 20=$340[/tex]
So Factory should choose Common Joe while considering Economy.
If Allison wants to find 80% of 630 which table should she use?
Answer:
optain A or the first one
Step-by-step explanation:
hop this helps
Finding 80% of 630 doesn't require using a table and can be calculated by simply multiplying 0.80 by 630 which gives 504.
Explanation:To determine 80% of 630, Allison doesn't necessarily need a table. However, we can illustrate the solution using a simple self-created table. The calculation is rather straightforward. If Allison wants to find 80% of 630, she can simply multiply 0.80 (which is the decimal equivalent of 80%) by 630.
Step-by-step process:
Convert 80% to decimal form by dividing 80 by 100, which gives 0.80. Multiply 0.80 by 630 which gives 504.
Therefore, 80% of 630 is 504.
Learn more about Percentage Calculation here:https://brainly.com/question/329987
#SPJ11
A high-interest savings account pays 5.5% interest compounded annually. If $300 is deposited initially and again at the first of
each year, which summation represents the money in the account 10 years after the initial deposit?
Answer:
[tex]\sum_{n=1}^{10} 316.5 (1.055)^{n-1} [/tex]
Step-by-step explanation:
The amount (A) in a deposit after 1 year is calculated as follows:
A = P*(1 + r)
where:
P is the present value
r is the annual rate (decimal)
After the first year:
A = 300*(1 + 0.055) = $316.5
After the second year, the account will have a new amount of $316.5 due to the new $300 and the interest gained with the previous $316.5:
A = 316.5 + 316.5*(1 + 0.055)
After the third year:
A = 316.5 + [316.5 + 316.5*(1 + 0.055)]*(1 + 0.55)
A = 316.5 + 316.5*(1 + 0.055) + 316.5*(1 + 0.055)^2
After 10 years:
[tex]\sum_{n=1}^{10} 316.5 (1.055)^{n-1} [/tex]
Sin(-x)= -cos x for all values of x. True or false
Answer:
That's incorrect. The simplest way to show this is by evaluating the functions at a given point. Let's say x=0, then:
Sin(-x) = Sin(0) = 0
-cos x = -cos (0) = -1
Therefore, Sin(-x)≠-cos x.
The given expression :
[tex]\sin (-x)=-\cos x[/tex] is a false expression i.e. it is not true for all the values of x.
Step-by-step explanation:We are asked to check whether the trignometric expression is true for all the values of x or not.
The expression is given by:
[tex]\sin (-x)=-\cos (x)[/tex]
We consider x=0
Then on taking left hand side of the expression we have:
[tex]\sin (-0)\\\\i.e.\\\\\sin (0)\\\\=0[/tex]
and the right hand side of the expression is:
[tex]-\cos x\\\\i.e.\\\\-\cos 0\\\\i.e.\\\\-1[/tex]
i.e. we have:
[tex]0=-1[/tex]
which is false.
Hence the statement is not true for all the values of x.
What is the yintercept of the line given by the equation below?
y=-10x+ 14
Answer: 14
Step-by-step explanation:
Answer:
The y-intercept is: (0,14).
Help Please..............................................
Answer:
0 and 1 have the same y values for the x values.
computing the probability of rolling two dice in succession face value of two rolls are added together is the sum greater than 7
Answer:
5/12 ≈ 0.41667
Step-by-step explanation:
If the first die rolls a 1 and the second die rolls a 1, then the sum is 2.
If the first die rolls a 1 and the second die rolls a 2, then the sum is 3.
Repeating this, we can build a table showing all the possible outcomes:
[tex]\left[\begin{array}{ccccccc}&1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right][/tex]
As we can see, of the 36 possible outcomes, 15 are greater than seven. So the probability is 15/36, which reduces to 5/12.
Giovanna used the calculations below to determine the height of a stack of 7 books that are each 2 5/8
inches thick what
was her error?
C. There should be a subtract step not an addition step
D. Two should have been multiplied by 5/8
Answer:
Option C. Seven was not multiplied by 5/8
Step-by-step explanation:
we know that
To determine the height of a stack of 7 books that are each 2 5/8 inches thick. multiply 7 by 2 5/8
so
[tex]7(2\frac{5}{8})\\ \\7(2+\frac{5}{8})\\ \\7*2+7*\frac{5}{8}\\ \\14+\frac{35}{8}\\ \\14+4+\frac{3}{8}\\ \\18\frac{3}{8}\ in[/tex]
therefore
Seven was not multiplied by 5/8
Answer:
Option B.
Step-by-step explanation:
Giovanna did the calculations to determine the height of a stacks of 7 books having [tex]2\frac{5}{8}[/tex] inches thickness of each book.
[tex]7(2\frac{5}{8})[/tex]
[tex]=7(2+\frac{5}{8})[/tex]
[tex]=(7\times 2)+7(\frac{5}{8})[/tex]
[tex]=14+\frac{35}{8}[/tex]
[tex]=14+4+\frac{3}{8}[/tex]
=18+[tex]\frac{3}{8}[/tex]
[tex]=18\frac{3}{8}[/tex]
Now when compare this solution with Giovanna's solution we find error in 3rd step, in which she hasn't mutiplied the fraction [tex]\frac{5}{8}[/tex] by 7.
Therefore, option B is the correct one.
The magnitude of m is 29.2 meters, and the magnitude of n is 35.2 meters. If m and n are perpendicular, what is the magnitude of their sum?
Answer:
45.73 m
Step-by-step explanation:
Which expression is equivalent to (125^2 / 125^4/3)
algebra II engenuity
Answer: Last option.
Step-by-step explanation:
To find which expression in equivalent to the expression [tex]\frac{125^2}{125^\frac{4}{3} }[/tex], you need to remember :
The Power of a power property:
[tex](a^m)^n=a^{(mn)}[/tex]
The Quotient of powers property:
[tex]\frac{a^m}{a^n} =a^{(m-n)}[/tex]
And the Product of powers property:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Knowing that:
[tex]125=5*5*5=5^3[/tex]
Then, you get:
[tex]\frac{125^2}{125^\frac{4}{3} }=\frac{(5^3)^2}{(5^3)^\frac{4}{3} }=\frac{5^6}{5^4}=5^{(6-4)}=5^2=25[/tex]
A rectangle on a coordinate plane has vertices Q(-1, 1),R(6, 1), S(6,-8), and T(-1,-8)What are the dimensions of the rectangle? The base is 6 and the height is 9. The base is 9 and the height is 6. The base is 7 and the height is 9. The base is 9 and the height is 7.
ANSWER
The base is 7 and the height is 9.
EXPLANATION
If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.
Consider, Q(-1, 1) and R(6, 1)
The y-values are the same.
The base of the rectangle is the absolute value of difference in the x-values.
[tex]Base = |6 - - 1| = |7| = 7[/tex]
We could have also used S(6,-8), and T(-1,-8) to obtain the same result.
For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.
[tex]Height= |1 - - 8| = |9| = 9[/tex]
Therefore, the base is 7 and the height is 9.
Answer:
Base is 7, and Height is 9.
Step-by-step - If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.
Consider, Q(-1, 1) and R(6, 1)
The y-values are the same.
The base of the rectangle is the absolute value of difference in the x-values.
We could have also used S(6,-8), and T(-1,-8) to obtain the same result.
For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.
Therefore, the base is 7 and the height is 9.
given that (-2,-8) is on the graph of f(x), found the corresponding point for the function f (x)-1
Answer:
(- 8, - 2)
Step-by-step explanation:
Assuming you mean the inverse function
Then any coordinate point (x, y ) in f(x) → (y, x) in the inverse
Given
(- 2, - 8 ) is on the graph of f(x), then
(- 8, - 2) is on the graph of [tex]f^{-1}[/tex](x)
The corresponding point on the graph of function f(x)-1 for a given point (-2,-8) from the graph of function f(x) is (-2, -9). All corresponding x-values remain the same, while the y-values are decreased by 1.
Explanation:The given point (-2,-8) is on the graph of the function f(x). Now, you're asked to find the corresponding point for the function f(x)-1. When we modify a function like this, it affects the y-values (output) of the function. The x-values (input) remains constant.
In this case, for any x-value in the function f(x), the corresponding y-value in the function f(x)-1 is simply the y-value of f(x) minus one. So the corresponding point on the graph of f(x)-1 for the given point (-2,-8) from the graph of f(x) would be (-2, -9), because -8 (the y-value from f(x)) minus 1 equals -9 (the y-value for f(x)-1). Hence, the point (-2, -9) is on the graph of the function f(x)-1.
Learn more about Function here:https://brainly.com/question/26896273
#SPJ12
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of
hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)"
f(x) = 1500(115)
f(x) = 1500(2.15)
f(x) = 1500(215)
Answer:
Step-by-step explanation:
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
The answer to this problem is a f(x) = 1500(2.15)x
Answer:
[tex]f(x) = 1500(2.15)^x[/tex]
Step-by-step explanation:
Let the function that represents the population of bacteria after x hours is,
[tex]f(x)=ab^x[/tex]
For x = 0, f(x) = 1500,
[tex]1500=a(1+r)^0[/tex]
[tex]1500=a[/tex]
Now, the population increases at a rate of 115% each hour,
So, the population after 1 hour = (100+115)% of 1500 = 215% of 1500 = 3225,
That is, for x = 1, f(x) = 3225,
[tex]3225 =ab[/tex]
[tex]3225=1500(b)[/tex]
[tex]\implies b =2.15[/tex]
Hence, the function that represents the given scenario is,
[tex]f(x)=1500(2.15)^x[/tex]
Mac is 5 feet tall and casts a 4 foot 6 inch shadow. At the same time, a nearby tree casts a 20
foot shadow
Which is the closest to the height of the tree?
I will convert feet to inches.
4 feet, 6 inches = 54 inches
20 feet = 240 inches
5/x = 54/240
Let x = closest height of tree
54x = 5(240)
54x = 1,200
x = 1200/54
x = 22.2222222222
The tree is about 22 feet tall.
Answer:
22 inches
Step-by-step explanation:
Height of Mac = 5 feet
Height of shadow of Mac = 4 foot 6 inches = [tex]4+\frac{6}{12}= 4.5[/tex] inches .
We are given that At the same time, a nearby tree casts a 20 foot shadow .
Let the height of the tree be x
ATQ
[tex]\frac{5}{4.5}=\frac{x}{20}[/tex]
[tex]\frac{5}{4.5} \times 20=x[/tex]
[tex]22.22=x[/tex]
Hence the height of the tree is approximately 22 inches .
Which equation is a linear equation?
Question 4 options:
a)
23xy − 34y = 0
b)
3a + 5b = 3
c)
x2+y2 = 0
d)
4m2 = 6
Answer:
b) 3a + 5b = 3
Step-by-step explanation:
It is an exact replica of the Standard Formula [Ax + By = C]. The Standard Formula is an example of a linear equation.
Answer:
3a + 5b = 1 is a linear equation
Step-by-step explanation:
Required?
To state which equation is linear...
An equation is said to be linear if it obeys the following.
1. For Single variables: y = b
An example is y = 4
2. For 2 Variables; it can take any of the following form: Ax + By = C.
An example 3x + 5y = 4
.from option A through D, only option B fits the description.
Note that the arithmetic sign could take the negative form and the position of x and y or any other constraints can take an interchanged forms.
The key thing to watch out when naming a linear equation is that the highest power is 1.
Hence, the 3a + 5b = 1 is a linear equation
what is the slope of the line containg (-2,5) and (4,-4)
Answer:
-3/2
Step-by-step explanation:
(Y2-Y1)/(X2-X1)
(-4 - 5) / (4 - (-2))
-9 / 6
Simplified: -3/2
Answer:
-3/2
Step-by-step explanation:
What is the solution to this system of equations?
4x + 5y = 7
3x – 2y = –12
Answer:
x = -2 and y = 3
Step-by-step explanation:
It is given that,
4x + 5y = 7 -----(1)
3x – 2y = –12 ----(2)
To find the value of x and y
eq(1) * 3 ⇒
12x + 15y = 21 ----(3)
eq(2) * 4 ⇒
12x - 8y = -48 ---(4)
eq(3) - eq(4) ⇒
12x + 15y = 21 ----(3)
12x - 8y = -48 ---(4)
0 + 23y = 69
y = 69/23 = 3
Substitute the value of y in eq(1)
4x + 5y = 7 ----(1)
4x + 5*3 = 7
4x = 7 - 15 = -8
x = -8/4 = -2
Therefore x = -2 and y = 3
Answer:
x = -2 and y = 3
Step-by-step explanation:
If 8y-8=24 find the value of 2y
Answer:
8
Step-by-step explanation:
8y-8=24
+8 +8
8y=32
32/8 = 4
y=4
4*2=8
Answer:
8
Step-by-step explanation:
8 y - 8 = 24
( + 8 )
8 y = 32
( ÷ 4 )
y = 4
Find the value of 2 y
y = 4 so 2 y = 8
Mike is making a scale model of his favorite car. The actual car is 8 feet long and 4 feet wide. Mike wants his model to be 12 inches in length. Which could be used to find the width of his model if he uses the same ratio?
Mike can determine the width of his scale model car by setting up and solving a proportion. Using the ratio of the actual car's dimensions, calculate an equivalent ratio for the model. The width of the model car should be 6 inches.
Explanation:To solve this problem, you can set up a proportion based on the known dimensions of the actual car and Mike's model. Given the actual car's length and width are 8 feet and 4 feet, and Mike's model length is 12 inches, we can set up the proportion like this:
8 feet : 4 feet = 12 inches : X
First, we need to convert all measurements to the same unit. Let's use inches since Mike's model is in inches (remember that 1 foot equals to 12 inches). So, the car's length is 96 inches and its width is 48 inches. Now, the proportion would be:
96 inches : 48 inches = 12 inches : X
To find the value of X (the width of the model), we can cross-multiply:
(96 * X) = (48 * 12)
Solve for X by dividing each side by 96, we get:
X = 6 inches
So, Mike's model car should be 6 inches wide to maintain the same ratio as the actual car.
Learn more about Proportions here:https://brainly.com/question/34018947
#SPJ3
Write 4.3125 as a fraction in simplest form and explain
Answer: [tex]\bold{\dfrac{69}{16}}[/tex]
Step-by-step explanation:
[tex]4.3125=\dfrac{43125}{10000}\\\\\\\dfrac{43125}{10000}\div\dfrac{625}{625}=\large\boxed{\dfrac{69}{16}}[/tex]
what is missing sequence number?
5 6 9 - 25 40
Answer:
15
Step-by-step explanation:
term 1 is equal to 5.
term 2 is equal to 5 + (1) = 5 + 1 = 6
term 3 is equal to 6 + (1 + 2) = 6 + 3 = 9
term 4 is equal to 9 + (1 + 2 + 3) = 9 + 6 = 15
term 5 is equal to 15 + (1 + 2 + 3 + 4) = 15 + 10 = 25
term 6 is equal to 25 + (1 + 2 + 3 + 4 + 5) = 25 + 15 = 40