as they are in the same line, the measures of angles AOD and angle DOC they measure 180°
Which of the following is equal to ? 1/5^-2
25
1) Let's evaluate this expression making use of one exponent property:
[tex](\frac{1}{5})^{-2}=(\frac{5}{1})^2=(5)^2=25[/tex]2) Note that negative exponents reciprocate the base.
3) Hence, the answer is 25
Devin owes $26,000 in students loans for college. The interest rate is 8.75% and the loan will be paid off over 15 years. How much will Devin pay altogether?$60,125$72,123$3,412,500$8,125
Answer:
$60,125
Explanation:
We'll use the below formula to determine how much Devin will pay altogether;
[tex]A=P(1+rt)[/tex]where A = final amount = ?
P = principal amount = $2600
r = interest rate in decimal = 8.75/100 = 0.0875
t = time in years = 15 years
Substituting the given values into our formula and solving for A, we'll have;
[tex]\begin{gathered} A=26000(1+0.0875\times15) \\ =26000(2.3125) \\ =60,125 \end{gathered}[/tex]Therefore, Devin will pay $60,125 altogether.
Dave started at the black dot and traveled the distance shown on the map on his bike. The length of the section in red is not known.
About how far did Dave travel on his bike?
Answer: 9,00
Step-by-step explanation:
I am right.
Answer:
1,402
Step-by-step explanation
the red line is further than the 1,396
Which of the following is the graph of f(x)= x² +3x-4?
Given the function
[tex]f(x)=x^2+3x-4[/tex]To determine which graph corresponds to this function you have to determine the coordinates of the vertex and the roots of the function.
Vertex
To determine the coordinates of the vertex you have to calculate the x-coordinate using the formula:
[tex]x=-\frac{b}{2a}[/tex]a is the coefficient of the quadratic term
b is the coefficient of the x-term
The term of the quadratic term, in this case, is a=1 and the term of the x-term is b=3
[tex]\begin{gathered} x=-\frac{3}{2\cdot1} \\ x=-\frac{3}{2}=-1.5 \end{gathered}[/tex]Replace the x-coordinate in the function to calculate the corresponding value of f(x):
[tex]\begin{gathered} f(x)=x^2+6x-4 \\ f(-3)=(-\frac{3}{2})^2+3\cdot(-\frac{3}{2})-4 \\ f(-3)=\frac{9}{4}-\frac{9}{2}-4 \\ f(-3)=-\frac{25}{4}=-6.25 \end{gathered}[/tex]The coordinates of the vertex are (-1.5,-6.25)
Roots of the function
To determine the roots of the function you have to use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]a is the coefficient of the quadratic term
b is the coefficient of the x-term
c is the constant of the function
For a=1, b=3, and c=-4
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2-4\cdot1\cdot(-4)}}{2\cdot1} \\ x=\frac{-3\pm\sqrt[]{9+16}}{2} \\ x=\frac{-3\pm\sqrt[]{25}}{2} \\ x=\frac{-3\pm5}{2} \end{gathered}[/tex]Solve the addition and the subtraction separately
Addition
[tex]\begin{gathered} x=\frac{-3+5}{2} \\ x=\frac{2}{2} \\ x=1 \end{gathered}[/tex]Subtraction
[tex]\begin{gathered} x=\frac{-3-5}{2} \\ x=\frac{-8}{2} \\ x=-4 \end{gathered}[/tex]The roots of the function are (1,0) and (-4,0)
The graph that corresponds to this function is
MAH ~ WCF what is the value of x?picture will be sent in messages
Since both triangles are congruent, the proportion between their sides is the same, so we can write:
[tex]\frac{MA}{MH}=\frac{WC}{WF}\Longrightarrow\frac{62}{92}=\frac{15.5}{x}\Longrightarrow62x\text{ = 92 }\cdot\text{ 15.5 = }1426\Longrightarrow\text{ x = 1426/62 =}23[/tex]x = 23
Answer:
x = 23
6 At a 33-foot depth underwater, the pressure is 29.55 pounds per square inch (psi). At a depth of 66 feet, the pressure reaches 44.4 psi. At what rate is the pressure increasing? ur answer on ouatlon for the
To solve the exercise you can apply the following formula:
[tex]rate=\frac{\text{difference in pressure}}{\text{difference in depth}}[/tex]In this case, based on the information given in the exercise, you can identify that:
[tex]\begin{gathered} \text{difference in pressure= (44.4.}-29.55)psi=14.85\text{ psi} \\ \text{difference in dept}=(66-33)ft=33\text{ ft} \end{gathered}[/tex]Substituting values, you get:
[tex]rate=\frac{14.85\text{ ps i}}{33\text{ ft}}=0.45\text{ }\frac{ps\text{ i}}{ft}[/tex]Therefore, The pressure is increasing at 0.45 psi per foot.
Convert 15 gal to quarts
The conversion rate for a gallon to quart is given as
[tex]1\text{ ga }\to4\text{ quart}[/tex]This means that to get the number of quarts in a given measure in gallons, we multiply the number by 4.
The question asks us to convert 15 gallons to quarts.
This can be calculated as
[tex]\begin{gathered} 15\times4 \\ =60\text{ quarts} \end{gathered}[/tex]Therefore,
[tex]15\text{ gal }\to60\text{ quarts}[/tex]find the first five terms of the recursive sequence. aₙ = -6aₙ₋₁ where a₁ = 45
The first terms is
[tex]undefined[/tex]Substitute 2, 3, 4, and 5 for n in the equation to find first four next terms.
suppose s and t are mutually exclusive events. find p (s or t) if p(s)=29% and p(t)=49%
Given:
P(s) = 29%
P(t) = 49%
For us to be able to determine P(S or T), we will be using the following formula:
[tex]\text{ P\lparen S or T\rparen = P\lparen S\rparen + P\lparen T\rparen}[/tex]We get,
[tex]\text{ P\lparen S or T\rparen = 29\% + 49\% = 78\%}[/tex]Therefore, the answer is CHOICE A: 78%
Evaluate: sin(30 degrees)cos(60 degrees)=(See attached image to assist with these 2 problems)
According to the figure we need to evaluate the sin(30°) and the cos(60°). Remember the trigonometric relations defined over the rectangle triangles as follows, suppose we have an angle called "alpha"
[tex]\begin{gathered} \sin(\alpha)=\frac{oc}{h}, \\ \\ cos(\alpha)=\frac{ac}{h}, \\ \\ tan(\alpha)=\frac{co}{ca} \\ \\ where\text{ }h:Hypotenuse,\text{ }ac:Adjacent\text{ }cathetus\text{ and }oc:Opposite\text{ }cathetus \end{gathered}[/tex]Now, according to the figure, we have that for the angle of 60 degrees:
[tex]\begin{gathered} h=2x,ac=x,oc=\sqrt{3}x \\ \\ \sin(60°)=\frac{oc}{h}=\frac{\sqrt{3}x}{2x}=\frac{\sqrt{3}}{2} \\ \\ \cos(60^{\circ})=\frac{ac}{h}=\frac{x}{2x}=\frac{1}{2} \end{gathered}[/tex]And for the angle of 30 degrees we get the following
[tex]\begin{gathered} h=2x,oc=x,ac=\sqrt{3}x \\ \\ \sin(30°)=\frac{oc}{h}=\frac{x}{2x}=\frac{1}{2}=\cos(60°) \\ \\ \cos(30^{\circ})=\frac{ac}{h}=\frac{\sqrt{3}x}{2x}=\frac{\sqrt{3}}{2}=\cos(60^{\circ}) \end{gathered}[/tex]So, your answer is: sin(30°)=1/2=cos(60°).
Question 4 please . Using a graphing utility (geogebra) to graph the function
Problem N 4
we have the function
[tex]f\mleft(x\mright)=x^4-3x^2+2x-1[/tex]Interval (-2,2)
using a graphing tool
Local minimum value at (1,-1)
Local maximum value at (0.37,-0.65)
Increasing functionIntervals (-1.37,0.37) U (1, infinite)
Decreasing functionIntervals (-infinite, -1.37) U (0.37,1)
Write the equation of the parabola in vertex form given the vertex (–2, 3) and point (0, 1).
the equation is
[tex]y=-\frac{1}{2}(x+2)^2+3[/tex]What are the coordinates of point w? 5 Z 3 2 Y 3 0 2 2. 4 -1 -2 W -3 -5 Х
the point W is positioned 3 units to the right (the x-coordinate is 3) and 2 units down (the y-coordinate is -2), thus the coordinates of W are (3,-2)
Evaluate the determinant.7 3 28 2 76 8 5A) 212B) -464© -212D860
| 7 3 2|
8 2 7
6 8 5
7(10 - 56) - 3(40 - 42) + 2(64 - 12)
7(-46) - 3(-2) + 2( 52)
-322 + 6 + 104
= -212
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer: A 143 degrees because angle 5 is a congruent to angle one
Step-by-step explanation:
Express the following as an algebraic function of x.sin(sin-'(x) – cos-'(x))
Hello there. To solve this question, we'll have to remember some properties about inverse trigonometric functions.
Given the expression:
[tex]\sin (\sin ^{-1}(x)-\cos ^{-1}(x))[/tex]We want to express it as an algebraic function of x.
For this, imagine the following triangle:
Now, we find the missing leg of the triangle applying Pythagoras theorem:
[tex]\begin{gathered} 1^2=x^2+?^2 \\ 1-x^2=?^2 \\ ?^{}=\sqrt[]{1-x^2} \end{gathered}[/tex]Now, finding the sine and cosine of the angles alpha and beta, we get:
First, remember the sine of an angle is equal to the ratio between the opposite side to the angle and the hypotenuse of the triangle. The cosine of the same angle is equal to the ratio between the adjacent side to the angle and the hypotenuse of the triangle.
Therefore, we have:
[tex]\begin{gathered} \sin (\alpha)=\frac{x}{1}=x \\ \cos (\beta)=\frac{x}{1}=x \\ \sin (\beta)=\frac{\sqrt[]{1-x^2}}{1}=\sqrt[]{1-x^2} \\ \cos (\alpha)=\frac{\sqrt[]{1-x^2}}{1}=\sqrt[]{1-x^2} \end{gathered}[/tex]This means that:
[tex]\begin{gathered} \alpha=\sin ^{-1}(x) \\ \beta=\cos ^{-1}(x) \end{gathered}[/tex]Now, the expression we had earlier turns into:
[tex]\sin (\alpha-\beta)[/tex]For this, we'll use the angle sum formula:
[tex]\sin (u-v)=\sin (u)\cos (v)-\sin (v)\cos (u)[/tex]Which gives us:
[tex]\sin (\alpha)\cos (\beta)-\sin (\beta)\cos (\alpha)_{}[/tex]Plugging the results we got earlier, this is simply:
[tex]x\cdot x-\sqrt[]{1-x^2}\cdot\sqrt[]{1-x^2}[/tex]As x > 0, because we're using it as a triangle side (but it could be negative considering inverse sine and cosine as functions), we get:
[tex]\begin{gathered} x^2-(1-x^2) \\ x^2-1+x^2 \\ 2x^2-1 \end{gathered}[/tex]Determine the area of the base of a cone with a volume of 36 cubic inches and a height of 9 inches?
the are of a base cone, while we have the volume and the height
V= pi*r^2*(h/3)
36=pi*r^2*3
we can find out now the r, radius
r=sqrt(3*36/pi*9)=1.95
Area, A= pi*r^2=
we can look at the Volume formula
36=pi*r^2*3
and if we divide both sides by 3 we get
12=pi*r^2, which is area
A= 12
fill in the table using the function rule y=3x+5
Fill in the table using the function rule y= 3x + 5
________________________________________
Replace each value of x in the expression
____________________________________
x= -4
y = 3* (-4)+5
= -12 +5
= -7
_______________
x= -2
y = 3* (-2)+5
= -6 +5
= -1
_____________
x= 0
y = 3* (0)+5
= 0 +5
= 5
_____________
x= 2
y = 3* (2)+5
= 6 +5
= 11
______________________________
Answer
_________________________
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The number 392,000 is divided by 10.
What is the value of the digit 2 in the quotient?
The value of 2 in the quotient is 200.
What is division?
One of the four fundamental operations of arithmetic, or how to mix numbers to create new ones, is division. Addition, subtraction, and multiplication are the other operations.
The opposite of multiplication is division. When you multiply three groups of four to produce twelve, you get four in each group when you split twelve into three equal groups.
Let, the number 392,000 is divided by 10.
That means, [tex]\frac{392000}{10}[/tex]
Here, 392000 is the numerator and 10 is the base.
Simplifying the fraction, we get 39200.
39200 is the quotient.
Here 2 is on the hundredth place.
Therefore, the value of 2 in the quotient is 200.
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The vertices of ABCDE are A(-6,0), B(-3,0), C(0, -3), D(-3,-6), and E(-6, -3). Find the vertices of the image after a translation using the rule (x,y) - (x + 9, y-6) and a dilation with a scale factor of 4s centered at the origin.
Vertices of new image: A' = (12, -24)
B' = (24, -24)
C' = (36, -36)
D' = (24, -48)
E = (12, -36)
Explanation:A(-6,0), B(-3,0), C(0, -3), D(-3,-6), and E(-6, -3)
A translation of (x + 9, y-6)
A becomes A'
A' = (-6 + 9, 0 - 6) = (3, -6)
B(-3,0)
B becomes B'
B' = (-3+9, 0 - 6) = B' (6, -6)
C(0, -3)
C becomes C'
C' = (0+9, -3-6) = C' (9, -9)
D(-3,-6)
D becomes D'
D' = (-3+9, -6-6) = (6, -12)
E(-6, -3)
E becomes E'
E' = (-6+9, -3-6) = (3, -9)
A dilation with scale factor of 4, we multiply the cooordinates of the alphabeths with prime with 4.
Vertices of new image:
A' = 4(3, -6) = (12, -24)
B' = 4(6, -6) = (24, -24)
C' = 4(9, -9) = (36, -36)
D' = 4(6, -12) = (24, -48)
E = 4(3, -9) = (12, -36)
What is the Y intercept of 8X plus 4Y equals -48
the given equation is,
[tex]8x+4y=-48[/tex]Now, we will solve it further,
[tex]\begin{gathered} 8x+4y=-48 \\ 4y=-8x-48 \end{gathered}[/tex][tex]\begin{gathered} y=\frac{-8x-48}{4} \\ y=-2x-12 \end{gathered}[/tex]Now, we will put x=0 to get the intercept of the line on the Y axis,
[tex]\begin{gathered} y=-2x-12 \\ y=-2\times0-12 \\ y=-12 \end{gathered}[/tex]So, the Y-intercept of the given line equation is -12.
There are a total of 50 questions worth 130 points on Chenille's history exam. Someof the questions are worth five points each, and the other questions are worth twopoints each. Which of the following systems of equations could be used todetermine F, the correct number of five point questions, and t, the correct numberof two point questions answered correctly?
Since F represents the number of five point questions and t represents the number of two point questions, and the total amount of questions is 50, then:
[tex]F+t=50[/tex]F correct answers would give us 5F points, and t correct answers would give us 2t points, for a total of 130 points. Then:
[tex]undefined[/tex]In AFGHFH.GF +40, HF 3x - 20, and GH find the value of 21 20
You have the next triangle:
As the triangle has two angles that are congruent, then it is a isisceles triangle. The opposite sides of the equal angles have the same measure.
Sides FG and GH have the same measure:
[tex]FG\cong GH[/tex][tex]x+40=2x+20[/tex]Use this equation to find the value of x:
- Substract in both sides of the equation 2x:
[tex]\begin{gathered} x-2x+40=2x-2x+20 \\ -x+40=20 \end{gathered}[/tex]- Substract in both sides of the equation 40:
[tex]\begin{gathered} -x+40-40=20-40 \\ -x=-20 \end{gathered}[/tex]- Multiply both sides of the equation by -1:
[tex]\begin{gathered} (-1)(-x)=(-1)(-20) \\ \\ x=20 \end{gathered}[/tex]Answer x=20Identify the units you would expect for the given quantity.The price of a bottle of French perfume, found by multiplyingthe unit price of the perfume in euros per milliliter by thevolume of the bottle in milliliters.
Given:
The price of a bottle of French perfume, found by multiplying
the unit price of the perfume in euros per milliliter by the volume of the bottle in milliliters.
the unit of the unit price is: euros per milliliter
And the unit of the volume is: milliliters
By multiplying the two units: the unit of the result will be euros
25. Ally is making a replica of a building that is at ascale of 4 m. to 3 in.The model is 84 in tall. How tallis the building?
We know that in our model 3 inches represent 4 m, to determine how tall the building is with the knowledge that the model is 84 in we can use a rule of three:
[tex]\begin{gathered} 4\text{ m}\rightarrow3\text{ in} \\ x\rightarrow84\text{ in} \end{gathered}[/tex]then:
[tex]x=\frac{84\cdot4}{3}=112[/tex]Therefore, the building is 112 meters tall.
PO Triangle ABC is similar to triangular DEF. What is the value of x?
If triangle ABC is similar to DEF then the ratio between the sides will be a constant so we can get the expression:
[tex]\frac{15}{30}=\frac{x}{36}[/tex]and we solve for x so:
[tex]\begin{gathered} x=\frac{36\cdot15}{30} \\ x=18 \end{gathered}[/tex]You bought a magazine for $7 and some notepads for $5 each. You spend a total of $27 how many notepads did you buy.
From the information available, some magazines (m) and some notepads (n) were bought.
If you bought a magazine for $7, then mathematically that would be;
[tex]\begin{gathered} 1\times m=7 \\ m=7 \end{gathered}[/tex]Also, if you bought some notepads for $5 each, that would be expressed as;
[tex]5\times n=5n[/tex]This represents 5 dollars times every given number of notepads, hence we would have;
[tex]\begin{gathered} m+5n=27 \\ \end{gathered}[/tex]Note that one magazine was bought which is why we have m = 7. We shall now substitute for thw value of m;
[tex]\begin{gathered} m+5n=27 \\ 7+5n=27 \\ \text{Subtract 7 from both sides;} \\ 7-7+5n=27-7 \\ 5n=20 \\ \text{Divide both sides by 5;} \\ \frac{5n}{5}=\frac{20}{5} \\ n=4 \end{gathered}[/tex]The value of n = 4
ANSWER:
This means you bought 4 notepads
write an inequality for the graph using x for the variable.
Given:
There are given that the inequality graph.
Explanation:
In the given question, there are given number line graphs, in which the arrow has been shown in a negative direction.
Also,
There are given that the number 2 has not been included in the given graph.
So,
The inequality will be:
[tex]x<2[/tex]Final answer:
Hence, the inequality is shown below:
[tex]x\lt2[/tex]
If we chose a theater and movie to attend at random, what probability would we have of seeing anything other than a romantic or sci-fi movie ?
we have that
The probability of seeing a romantic or sci-fi movie is
P=0.203+0.12=0.323
therefore
the probability of seeing anything other than a romantic or sci-fi movie is
P=1-0.323
P=0.677
the answer is option B4p-9=2p+21solve the equation
The given equation is,
[tex]4p-9=2p+21[/tex]The equation can be solved as,
[tex]\begin{gathered} 4p-9=2p+21 \\ 4p-2p=21+9 \\ 2p=30 \\ p=\frac{30}{2} \\ p=15 \end{gathered}[/tex]Thus, the requried value of p is 15.N