Answers
ANSWER
mFJH = 210º
EXPLANATION
The measure of an arc is twice the measure of the inscribed angle subteded by it:
[tex]\text{mFJH}=2m\angle FGH[/tex]First we have to find x:
[tex]17x-28=2(6x+21)[/tex]Apply distributive property of addition on the right side:
[tex]\begin{gathered} 17x-28=2\cdot6x+2\cdot21 \\ 17x-28=12x+42 \end{gathered}[/tex]Now we have to get the x together on the same side of the equation. To do that we have to subtract 12x from both sides:
[tex]\begin{gathered} 17x-12x-28=12x-12x+42 \\ 5x-28=42 \end{gathered}[/tex]Now, add 28 to both sides:
[tex]\begin{gathered} 5x-28+28=42+28 \\ 5x=70 \end{gathered}[/tex]And finally divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{70}{5} \\ x=14 \end{gathered}[/tex]Now, with x = 14, we just have to replace it into the expression for the measure of arc FJH:
[tex]\begin{gathered} \text{mFJH}=17x-28 \\ \text{mFJH}=17\cdot14-28 \\ \text{mFJH}=238-28 \\ \text{mFJH}=210 \end{gathered}[/tex]The measure of arc FJH is 210º
Related Questions
If a + 3b = 13 and a + b = 5, the value of b is 1) 1 3) 4.5 2) 7 4) 4
Answers
a + 3b =13 ............... (1)
a + b = 5.............. (2)
By substitution from equation (1) a = 13 - 3b
Substituting for a in equation (2) yields
13-3b+b = 5
13-2b = 5
Bringing like terms together
13-5 = 2b
2b = 8
2b/2 = 8/2
b = 4
From Equation (2) a + b=5
a + 4 = 5
a = 5 -4
a = 1
Solve the equation for the specified variable.Y = AB - 9, for A
Answers
According to the given question we have the following equation:
Y = AB - 9
A would be calculated as follows:
Y = AB - 9
Move -9 to the other side
So,
Y+9=AB
Finally move B to the other side and the A would be as follows:
Y+9/B=A
A=(Y+9)/B
Distribute the negative number.-3(5x - 9)
Answers
Ok this is simple. The distribution works like this: when you are multiplying a number with a parenthesis you need to multiply the number with every term inside that parenthesis.
In this case you have two terms inside: 5x and -9. So you have:
(-3)*(5x - 9) = (-3)*5x + (-3)*(-9) = -15x + 3*9 = -15x + 27
It's important to note that a multiplication between two negative numbers results in a positive number.
how do I draw 3/9 on a 5x12 grid
Answers
We draw a 5x12 grid by drawing 5 squares horizontally and 12 squares vertically, like this:
We continue the process until we get to 12 squares vertically. Since there are 5 squares horizontally and 12 vertically, this means that there are in total (5)(12) = 60 squares. That means that each square represents 1/60. Now, if we multiply 1/60 by 20 we get:
[tex](\frac{1}{60})(20)=\frac{20}{60}=\frac{2}{6}=\frac{1}{3}[/tex]Therefore, a group of 20 squares represents 1/3. Since 1/3 can also be represented as 3/9, a group of 20 squares also represent 3/9.
please can you help me find the derivatives for the following equations
Answers
D.
We were given that:
[tex]g(x)=(x^3+2x+1)(2+\frac{1}{x^2})[/tex]We will proceed to expand the bracket as shown below. We have:
[tex]undefined[/tex]City planners want to construct a bike path perpendicular to Ravine Road at point P. An equation for the Ravine Road line is y= -2/7x. Find an equation for the line for the bike path.
Answers
Perpendicular lines have slopes that are negatiive reciprocals.
Ravine has a slope of -2/7
So, perpendicular line would have slope of 7/2
Hence, equation will be:
[tex]y=\frac{7}{2}x+b[/tex]We need a point, it is P, which is (0.0).
We substitute and find b:
[tex]\begin{gathered} y=\frac{7}{2}x+b \\ 0=\frac{7}{2}(0)+b \\ 0=0+b \\ b=0 \end{gathered}[/tex]Hence, final equation:
[tex]y=\frac{7}{2}x[/tex]The Renault Kaper is a popular brand of car in Republica. it has a fuel capacity of 28liters. it has a fuel efficiency of 225 kilometer per lier. with a full tank of fuel, could a Renault Kaper travel the 725 kilometer distance between capital city and costa costa bay without needing a refill tank?
Answers
Renault Kaper has a fuel capacity of 28 liters.
It has a fuel efficiency of 225 kilometers per liter.
With a full tank of fuel, could a Renault Kaper travel the 725-kilometer distance between the capital city and costa bay without needing a refill tank?
We know that the car can travel 225 km per liter and the total capacity of the car tank is 28 liters, so we can easily find out how much distance it can cover.
[tex]\begin{gathered} total\: distance=efficiency\times capacity \\ total\: distance=225\times28 \\ total\: distance=6300\: km \end{gathered}[/tex]As you can see, Renault Kaper can travel up to a distance of 6300 km that is way higher than 725 km.
Therefore, Renault Kaper can travel the 725-kilometer distance between the capital city and costa bay without needing a refill tank.
A certain drug is made from only two ingredients: compound B. There are 4 millimeters of compound A used for every 3 milliliters of compound B. If a chemist wants to make 406 milliliters of the drug, how many milliliters of comped B are needed
Answers
Given:
4 milliliter of compounf A used for every 3 milliliter of compound B.
That mean ratio is:
[tex]4\colon3[/tex]ler "x" the multiplier then:
[tex]\begin{gathered} 4x=\text{ amount of compound A} \\ 3x=\text{ amount of compound B} \end{gathered}[/tex]If chemist wants to make 406 milliliter that mean:
[tex]\begin{gathered} 4x+3x=406 \\ 7x=406 \\ x=\frac{406}{7} \\ x=58 \end{gathered}[/tex]The compound B needed is:
"3x" then the value is:
[tex]\begin{gathered} =3x \\ =3(58) \\ =174 \end{gathered}[/tex]So 174 milliliter used of compound B
Write an equation relating S to N and then graph your equation
Answers
Bill monthly salary is $2100 plus an additional $100 for every copy of history is fun
We set S to represent his total monthly salary and N the total number of copies that he sells
Therefore, 2100 is an independent value and 100 depends on the number of sells
then, the equation is:
[tex]S=2100+100N[/tex]To graph the equation, we need to find the x-intercept and y-intercept:
To find the y-intercept, set x=0:
In this case, x is represented by N, and y is represented by S:
[tex]S(0)=2100+100(0)[/tex][tex]s(0)=2100[/tex]So the graph starts at S=2100, point (S,N) = (2100, 0)
Then,
when he sells one book
N=1
[tex]S=2100+100(1)=2200[/tex]Y = 2200
-When he sells 2 books
N =2
[tex]S=2100+100(2)=2300[/tex]S=2300
- When he sells 3 books
N =3
[tex]S=2100+100(3)=2400[/tex]then, S=2400
- When he sells 4 books
N = 4
[tex]S=2100+100(4)=2500[/tex]Then, S=2500
Therefore, his salary depends on how many books he sells, then change the N value to find all the points of the graps
5. For the given circle, find the value of x and y
Answers
Answer
x = 4 units
y = 30°
Explanation
The secant-secant product theorem explains that If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
In mathematical terms, using the diagram given,
4 × (4 + x) = 2 × (2 + 8)
16 + 4x = 2 × 16
16 + 4x = 32
4x = 32 - 16
4x = 16
Divide both sides by 4
(4x/4) = (16/4)
x = 4 units.
Then the secant angle theorem explains that
25° = (80° - y)/2
Cross multiply
2 × 25° = 80° - y
50° = 80° - y
y = 80° - 50°
y = 30°
Hope this Helps!!!
Determine the slope m and y-intercept (if possible) of the linear equation(Pre-algebra)
Answers
Answer:
[tex]\begin{gathered} a)\text{ slope = -}\frac{8}{9} \\ b)\text{ Intercept \lparen x,y\rparen = \lparen0,}\frac{1}{9}) \\ c)\text{ E} \end{gathered}[/tex]Explanation:
The general equation of a straight line can be represented as:
[tex]y\text{ = mx + b}[/tex]where m is the slope and b is the y-intercept
Now, let us rewrite the given equation in the form above:
[tex]\begin{gathered} 9y\text{ = -8x + 1} \\ y\text{ = -}\frac{8}{9}x\text{ + }\frac{1}{9} \end{gathered}[/tex]Now, from the above:
[tex]\begin{gathered} slope\text{ = -}\frac{8}{9} \\ \\ y-intercept\text{ = }\frac{1}{9} \end{gathered}[/tex]Now, let us describe the graph:
The graph will pass through the y-intercept
The y-intercept is at the point (0,1/9)
Hence, the graph passes through (0,1/9)
Furthermore, we can see that the slope is negative
This indicates a falling graph
This means the graph falls by 8 units vertically for every horizontal increase by 9 units
Write number as a difference of integers in three different ways. +15
Answers
N 1
we have
-5
-3-2=-5
10-15=-5
3-8=-5
N 2
we have
+15
35-20=15
25-10
30-15=15
N 3
we have
0
15-15=0
3-3=0
4-4=0
N 4
-3.5 ----> is not an integer
7. Use the pair of functions to find the value of each of the following combinations of functions
Answers
Given:
[tex]\begin{gathered} f(x)=x^2 \\ \\ g(x)=\frac{9}{-8x+5} \end{gathered}[/tex]Required:
To find (f-g)(-10).
Explanation:
Consider
[tex]\begin{gathered} (f-g)(x)=x^2-\frac{9}{-8x+5} \\ \\ (f-g)(-10)=(-10)^2-\frac{9}{-8(-10)+5} \\ \\ =100-\frac{9}{80+5} \\ \\ =100-\frac{9}{85} \\ \\ =100-0.1058 \\ \\ =99.8941 \end{gathered}[/tex]Final Answer:
[tex](f-g)(-10)=99.8941[/tex]I need this problem answered. It’s asking to drag the matrix dimensions provided to each box to match the product
Answers
Before two(2) matrices, say A and B can be multiplied together,to form AB, the number of the columns in A must be equal to the number of the rows in B.
The order/dimension of the resulting matrix, AB, will the combination of the number of rows in A and the number of columns in B.
For instance, if a matrix A has a dimension of ( p x q ) and a matrix B has a dimension of ( q x r ) to form matrix AB.
We can see that the number of columns in A, which is q, is equal to the number of rows in B, which is q also. Thus, the matrix are conformable i.e can be multiplied.
The order of the resulting matrix AB will have an order ( p x r ), as explained in the second statement above.
Hence, for the given problem, we have:
[tex]\begin{gathered} \text{Matrix B is a (2x2)} \\ \text{Matrix D is a (2x1)} \\ \text{The order of BD will be (2x1)} \end{gathered}[/tex][tex]\begin{gathered} \text{Matrix C is a (2x3)} \\ \text{Matrix A is a (3x1)} \\ \text{The order of CA will be (2x1)} \end{gathered}[/tex][tex]\begin{gathered} \text{Matrix B is a (2x2)} \\ \text{Matrix C is a (2x3)} \\ \text{The order/dimension of BC will be (2x3)} \end{gathered}[/tex]If m/_KNM = (8x - 5)° and m/_MNJ =(4x - 19)° . Find the m/_LNJ.Value of x: m/_LNJ = degrees
Answers
Suppose an angle has a measure of 85 degrees.If a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is  times as long as 1/360th of the circumference of the circle.A circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long. What is the length of the arc subtended by the angle's rays? cm
Answers
We have and angle (85°) and a circle, both disposed as the following figure:
We want to find the measure of the blue segment. We know that a centered angle's ray corresponds to the same angle. Since each angle is 1/360th of the circumference, then the arc is 85 times one of those angles.
Then, we have the answer:
If a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 85 times as long as 1/360th of the circumference of the circle.
Part BHaving the same graphic representation as before, in this case, we know that each 1/360th of the circumference is 0.06 cm long, since the arc is 85 times as long, then its lenght is
85 x 0.06 cm = 5.1 cm
What is the length of the arc subtended by the angle's rays? 5.1 cm
Given the parallelogram TVWY shown above, determine how triangles TUZ and WXV can be shown to be similar.O A. Since ZZTU = VWX and VX = XW, the triangles are similar by angle-side.OB. Since ZTUZ = WXV and ZZTU = VWX, the triangles are similar by angle-angle..C. Since ZTUZ = VWX and ZZTU = WXV, the triangles are similar by angle-angle.OD. Since ZTUZ = WXV and TU = UZ, the triangles are similar by angle-side.dmentum. All rights reserved.
Answers
From the given figure, since TVWY is a parallelogram, opposite angles are congruent. This implies that angle ZTU is equal to angle VWX. Additionally, since angle TUZ is equal to angle WXU, then the answer is option B.. The third angle will be given by the fact that interior angles add up 180 degrees.
A rectangular window has a length of 12 ft and a width of x ft.Which expression represents the area of the window? 6xx + 1212x12/x
Answers
Answer:
The expression that represents the area of the window is;
[tex]12x[/tex]Explanation:
Given that the rectangular window has a length of 12 ft and a width of x ft;
[tex]\begin{gathered} l=12 \\ w=x \end{gathered}[/tex]Recall that the area of a rectangule can be calculated using the formula;
[tex]A=l\times w[/tex]Substituting the given values of l and w;
[tex]\begin{gathered} A=12\times x \\ A=12x \end{gathered}[/tex]Therefore, the expression that represents the area of the window is;
[tex]12x[/tex]what is 3N? A. [-6 09 15]B [1 36 8] C [30 -4 0 9D [-6 03 5]
Answers
WE have the matrix
[tex]N=\begin{bmatrix}{-2} & {0} & {} \\ {3} & {5} & {} \\ {} & & \end{bmatrix}_{}[/tex]Then
[tex]\begin{gathered} 3N=3\begin{bmatrix}{-2} & {0} & \\ {3} & {5} & \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{3(-2)} & {3(0)} & {} \\ {3(3)} & {3(5)} & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{-6} & {0} & {} \\ {9} & {15} & {} \\ {} & {} & \end{bmatrix} \end{gathered}[/tex]Therefore the answer is A.
are they school assembly for out of the first 10 student for wearing spirit wear based on this information if 500 students were at the assembly then how many students could be expected to be wearing spirit wear
Answers
EXPLANATION:
1.We must know the data that the exercise gives us.
if 4 out of 10 wore spiritual clothing for 500 how many?
we can solve it with a rule of three;so
[tex]\begin{gathered} 4\rightarrow10\text{ } \\ x\rightarrow500 \\ \text{then }we\text{ multiply 4 }by\text{ 500 }and\text{ divide by 10;} \\ \frac{4\times500}{10}\text{ }=200 \\ \text{the the answer is }for\text{ 500 people 200 wear spiritual clothing} \end{gathered}[/tex]The value of y varies directly as x. When x= 12, y= 9.6. What is the value of y when x = 20
Answers
y ∝ x
y = kx
where k is the constant of proportionality
we need to find the value of k
substitute x=12 and y=9.6 into the equation above and solve for k
9.6 = k(12)
Divide both-side by 12
k=0.8
This implies that;
y = 0.8x
when x=20, then the value of y is:
y=0.8(20) = 16
Therefore, when x=20 y=16
Enter the equation of the line in slope-intercept form.Slope is -5, and (8,4) is on the line.
Answers
The slope intercept form is:
y = mx + b
Where
m is slope
b is y intercept
Since, slope = -5, we can write:
y = -5x + b
It goes through (8,4), so we plug it in and find the equation (with b):
[tex]\begin{gathered} y=-5x+b \\ 4=-5(8)+b \\ 4=-40+b \\ b=40+4_{}_{} \\ b=44 \\ \text{Hence} \\ y=-5x+44 \end{gathered}[/tex]X squared - x - 2 factor the trinomial
Answers
Given the following trinomial expression:
[tex]x^2-x-2[/tex]We will factor the trinomial as follows:
We need two numbers the product = -2, and the difference = -1
First the factor of 2 = 2 * 1
So,
[tex]x^2-x-2=(x-2)(x+1)[/tex]So, the answer will be: (x-2)(x+1)
Use the x and y intercepts to sketch a graph of each equation, 5. x + 4y = 8 6. 3x - 4y = 247.5x = 20 8.-3y=9
Answers
First, we determine the x and y-intercepts.
x-intercept
[tex]\begin{gathered} \text{When y=0} \\ x+4y=8 \\ x+4(0)=8 \\ x=8 \\ We\text{ have the point: (8,0)} \end{gathered}[/tex]y-intercept
[tex]\begin{gathered} \text{When x=0} \\ x+4y=8 \\ 0+4y=8 \\ 4y=8 \\ y=\frac{8}{4}=2 \\ We\text{ have the point: (0,2)} \end{gathered}[/tex]Next, we sketch the graph of x + 4y = 8.
What numbers are located exactly 2/3 units from point P on the number line?Select all that apply.
Answers
1) Given that point P is located at 1/3, 2/3 to the right is:
[tex]\frac{1}{3}+\frac{2}{3}=\frac{3}{3}=1[/tex]As well as, 2/3 to the left:
[tex]\frac{1}{3}-\frac{2}{3}=-\frac{1}{3}[/tex]2) Thus, the answer is:
This is homework assignment it’s statistics class thank you for your time
Answers
The best fit line given is:
P= -0.79t+20.95
P is the profit or loss
t is the time in years after 1965.
So, 1980-1965 = 15 => t=15
P= -0.79*15 +20.95
P= -11.85 + 20.95
P= 9,1
$9,1 thousands of dollars
Translate the following verbal statement into an algebraic equation and then solve:Use x for your variable.The difference of two times a number and five is eight.
Answers
According to the givn question we have the following verbal statement:
The difference of two times a number and five is eight.
The translation of this verbal statement into an algebraic equation would be the following:
2x - 5 = 8
So, to calculate the equation above, we would have to calculate the x value as follows:
First move the number -5 to the other side:
So,
2x=8+5
2x=13
x=13/2
x=6.5
The value of the x would be 6.5
Standard notation0.9X10^-1
Answers
To write the given scientific notation in standard notation, move the decimal point 1 place to the left since the exponent is negative.
Thus, the standard notation is 0.09.
from x=1 to x=2, the graph is (linear or nonlinear) and (increasing or decreasing)
Answers
We have here a quadratic function. In this kind of function, the rate of change is not constant (as it happens in a linear function). Then, we can say that the graph is nonlinear, that is, it does not have the same behavior as a line does.
To determine if the graph is increasing or decreasing from x = 1 to x =2, we need to calculate the rate of change for this function as follows:
We can see from the graph that:
For x = 1 ---> y = 2.
For x = 2 ---> y = -1.
Then, we have:
x1 = 1, y1 = 2
x2 = 2, y2 = -1
[tex]m=\frac{y_2-y_1}{x_2-x_1}\Rightarrow m=\frac{-1-2}{2-1}\Rightarrow m=-\frac{3}{1}\Rightarrow m=-3[/tex]Then, we can see that the function is decreasing from x = 1 to x = 2 (the rate of change is negative.)
In summary, we can say the function is nonlinear and it is decreasing from x = 1 to x =2.
A 30% solution of fertilizer is to be mixed with a 70% solution of fertilizer in order to get 160 gallons of a 60% solution. How many gallons of the 30% solution and 70% solution should be mixed?
Answers
We will determine the number of gallons of the 30% & 70% solutions as follows:
[tex]0.30x+0.70(160-x)=0.60\cdot100\Rightarrow0.30x+112-0.70x=60[/tex][tex]\Rightarrow-0.4x+112=60\Rightarrow-0.4x=-52[/tex][tex]\Rightarrow x=130[/tex]So, we would need 130 gallons of 30% solution, and:
[tex]160-(130)=30[/tex]And we would also need 30 gallons of 70% solution.