We are going to find the simple interest of $8000, for 2.5 years, at 4.25%. We remember that the formula for the simple interest is given by:
[tex]I=Prt[/tex]Where P represents the principal value, r the interest rate, and t the time in years. For finding the simple interest, we will replace the values given onto the formula:
[tex]I=(8000)\cdot(0.0425)\cdot(2.5)[/tex]Given that 4.25% is equivalent to the value 0.0425, and we obtain:
[tex]\begin{gathered} I=340\cdot2.5 \\ =850 \end{gathered}[/tex]This means that the simple interest is $850.
Use the imaginary number I to rewrite the expression below as a complex number simplify all radicals
Here, we want to use the imaginary number to rewrite the given expression as a complex number
Mathematically, the complex number can be written as;
[tex]i\text{ = }\sqrt[]{-1}[/tex]Thus, we have;
[tex]\begin{gathered} -\sqrt[]{-4\text{ }}\text{ = -1 }\times\text{ }\sqrt[]{-4} \\ \\ =\text{ -1 }\times\text{ }\sqrt[]{-1\text{ }}\text{ }\times\text{ }\sqrt[]{4} \\ \\ =\text{ -1 }\times\text{ i }\times\text{ }\sqrt[]{4} \\ =\text{ -1 }\times\text{ i }\times\text{ }\pm2 \\ \\ =\text{ -2i or 2i} \end{gathered}[/tex]translate each Graph as specified below(a)the graph of y=(x)+4 is shown. Translate it to get the graph of y=f(x)+4(b) The graph of y=g(x) is shown. Translate it to get the graph of y=g(x-2).
Solution:
Given the graphs (a) and (b)
a) The function of graph (a) is
[tex]f(x)=-4\sqrt{x+3}+1[/tex]The graph of the function is shown below
Translating it to get the graph of
[tex]y=f(x)+4[/tex]The translated function becomes
[tex]\begin{gathered} y=f(x)+4 \\ y=(-4\sqrt{x+3}+1)+4 \\ y=-4\sqrt{x+3}+1+4 \\ y=-4\sqrt{x+3}+5 \end{gathered}[/tex]The translated graph is
b) The function of graph (a) is
[tex]g(x)=-|x|[/tex]The graph of the function is shown below
Translating it to get the graph of
[tex]y=g(x-2)[/tex]The translated function becomes
[tex]\begin{gathered} y=g(x-2) \\ y=-|x-2| \end{gathered}[/tex]The translated graph is
what is the coordinates of midpoint of EF write your answer as an integer or a decimal or mixed number in simplest form
To calculate the midpoint between 2 points we must add both points and divide them by 2
[tex]\frac{P_1+P_2}{2}=P_M[/tex][tex]\begin{gathered} P_1=0 \\ P_2=-4 \end{gathered}[/tex][tex]\begin{gathered} P_M=\frac{-4+0}{2} \\ P_M=-2 \end{gathered}[/tex]how much interest earned on 124 ar 4% for one year
The principal amount is 124
The interest rate is 4% [in decimal, 4% is 4/100 = 0.04]
To get the interest amount, we mutiply the principal with the interest rate (in decimal).
The answer is:
[tex]124\cdot0.04=4.96[/tex]In ASTU, the measure of ZU=90°, US = 5.9 feet, and TU = 2.6 feet. Find the measureof ZT to the nearest tenth of a degree.
In ASTU, the measure of ZU=90°, US = 5.9 feet, and TU = 2.6 feet. Find the measure
of ZT to the nearest tenth of a degree.
step 1
In the right triangle STU
we have
tan(T)=SU/TU -------> by opposite side divided by the adjacent side
substitute given values
tan(T)=5.9/2.6
using a calculator
Someone please help me with this
Answer:
x = 30°, y = 80°
x = 40°, y = 50°
Step-by-step explanation:
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Therefore, as the two horizontal lines are parallel:
⇒ x = 30°
Exterior Angle Theorem
The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
⇒ y = 50° + x°
⇒ y = 50° + 30°
⇒ y = 80°
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Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Therefore, the angles marked red on the attached diagram are equal.
This means that the two triangles outlined in green are similar.
If two triangles are similar, their corresponding angles are congruent.
⇒ x = 40°.
Interior Angles of a Triangle
The interior angles of a triangle sum to 180°.
Therefore:
⇒ 90° + x + y = 180°
⇒ 90° + 40° + y = 180°
⇒ 130° + y = 180°
⇒ y = 50°
can someone please help me solve the "evaluate Ramon's equation" with the given from the above .so, based on that information. the equation that would correctly show the relationship between the number of seconds and the number of minutes would be 60 × s = m?
In the first table, we can see that 1 minute is equal to 60 seconds, thats why 2 minutes has 120 seconds and 3 minutes has 180 seconds.
Therefore, the second table must be
If we suppose that Ramon is correct, then the number of seconds would be less than the number of minutes. However, we saw that its no correct, then Ramon equation will not let him the correct number of minutes.
The correct equation must be
[tex]60xm(number\text{ of minutes = s (number of seconds)}[/tex]The radius of a circle is 4 feet. What is the area of a sector bounded by a 180° arc?Give the exact answer in simplest form. ____ square feet.
The area of asemicircle is:
[tex]A=\frac{\pi\cdot r^2}{2}[/tex][tex]A=\frac{\pi\cdot4^2}{2}=\frac{\pi\cdot16}{2}=\pi\cdot\frac{8}{1}=8\cdot\pi\text{ ft}^2[/tex]Therefore, the area of the semicircle in 8*pi ft^2
27.(08.04 MC)The volume of a fish tank is 50 cubic feet. If the density is 0.5fish/feet cubed, how many fish are in the tank?
ANSWER:
25 fish
STEP-BY-STEP EXPLANATION:
We have been given that the volume of a fish tank is 50 ft^3 and the density is 0.5 fish/ft^3. To find the number of fish in the tank, we need to multiply the volume of the tank by the density. Just like this:
[tex]\begin{gathered} n=50ft^3\cdot0.5\frac{fish}{ft^3} \\ n=25\text{ fish} \end{gathered}[/tex]Therefore, there are 25 fish in the tank.
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation.
First we have to find the values in which each factor equals zero.
In the first factor is going to be 5
In the second factor is going to be 7
Then we divide the number line by three parts
First part: Numbers less than 5
Second part: Numbers between 5 and 7
Third part: Numbers greater than 7
We choose any number belonging to each interval
First part: zero (0) because is less than 5
Second part: 6 because is a number between 5 and 7
Third part: 8 because it is a number greater than 7
Then we replace the numbers in the factors and operate
First part: (0-5)*(0-7) = (-5)*(-7)= 35 ( positive)
second part: (6-5)*(6-7) = (1)*(-1)= -1 ( negative)
third part: (8-5)*(8-7) = (3)*(1)= 3 ( positive)
Since we are searching for numbers that replaced in the equation give us negative results the intervals for the inequality must be
[5,7] which is represented in option C
Write an equation and slope intercept form for the line with the slope 2 and the Y intercept 5(Please use 2 points for the graph) (THIS IS ONE QUESTION, I do an online program where this is considered ONE question)equation =
The slope - intercept form of a line is given by the equation:
In this case, we know that m=2 and y=5. So, the equation of this line will be:
To graph it, we need to plot two points and then join them both. These points could be:
Graphing:
A tortilla measures 8 inches in diameter, shown below. What is the tortilla'sarea?8 inches0 0 40x square inches20 0 641 square inches0 0 41 square inchesc) O 321 square inches0 0 161 square inches
A tortilla has a circular shape. The area of the circle can be given by the following expression:
[tex]A=r^2\cdot\pi[/tex]We were given the diameter of the tortilla, the radius is half the diameter, therefore:
[tex]undefined[/tex]Simplify
4b² x 2b³/8b
Answer:
b^4
Step-by-step explanation:
4b^2 (2b^3)/8b = b^4
It's easy and complicated
which of the following expression has the same value select all that apply
Translate figure A 8 units to the left to form figure A'. Then reflect figure A' across the x-axis to form figure A". Draw figures A' and A”. Is figure A congruent to figure A"? How do you know?
Initial points
(-7, 2) (-7, 4) (-4, 2) (-4, 4) (-2, 7)
translate 8 units to the left
(-6, -7) (-4, -7) (-6, -4) (-4, -4) (-1, -2)
reflexion
Reflexion
Translate: "ten more than the product of 8 and a number is less than 26"in numbers
ten more than the product of 8 and a number is less than 26 :
Let the number is x :
product of 8 and a number = 8x
ten more than the product of 8 and a number = 10 more than 8x
ten more than the product of 8 and a number = 10 + 8x
ten more than the product of 8 and a number is less than 26
ten more than the product of 8 and a number < 26
10 + 8x < 26
Answer : 8x + 10 < 26
what is the following is a solution for x / 4 >10
Given the inequality;
[tex]\frac{x}{4}>10[/tex]Multiplying both sides by 4, we have;
[tex]\begin{gathered} \frac{x}{4}\times4=10\times4 \\ x>40 \end{gathered}[/tex]so, the range of solutions of x are numbers that are greater than 40 (40 is not included).
From the options the only possible solution is;
[tex]x=47[/tex]Because 47 is greater t
-2/2 in simplest form is -1, right?
Answer:
Yes
Step-by-step explanation:
Yes, dividing a negative number by a positive number will equate to another negative number.
Applying this logic, -2 divide by 2 is simply -1
Arie's pet shop is selling geckos at 12 and a half percent off! if geckos were originally $20 each, what is the sale price?
DIscount = 121/2 % 0ff
[tex]\begin{gathered} \text{Sales price = 12}\frac{1}{2}\text{ }\times\text{ 20} \\ \text{ =}\frac{\frac{25}{2}}{100}\text{ }\times20\text{ } \\ \text{ } \\ \text{ =}\frac{25}{200}\text{ }\times20\text{ = }\frac{500}{200}\text{ = \$2.5} \end{gathered}[/tex]Find the range of allowable values based on the given information. Round to the nearest tenth. 24; can vary by 3.5%
Round to nearest tenth is 0.9 in percentage .
What does the % mean?
A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Per 100 is what the word percent means. The letter "%" stands for it.By dividing the value by the sum of the values, and then multiplying the outcome by 100, one can get the percentage. The formula for calculating percentage is (value/total value)100%.Percent is derived from the Latin word per centum, which means "by the hundred."24×3.5% = 0.84
so round to nearest tenth is 0.9.
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Evaluatesin^-1 (sin3pi/4)Show your reasoning.
Given the expression:
[tex]\sin ^{-1}(\sin \frac{3\pi}{4})[/tex]The exact value of:
[tex]\sin (\frac{3\pi}{4})=\frac{1}{\sqrt[]{2}}[/tex]Then:
[tex]\sin ^{-1}(\sin \frac{3\pi}{4})=\sin ^{-1}(\frac{1}{\sqrt[]{2}})[/tex]Evaluating, we have:
[tex]\frac{\pi}{4}[/tex]Refer to the figure below to answer the following questions: (a) What is the value of "X"? (b) How Given: t|| v many degrees does angle 4 measure? 9x +41\3 4 13r - 15
Since the angles given by the equation are alternate interior angles the are the same, that is
9x + 41 = 13x - 15
Using this equation, we can find x value
Step 1Rearraging the equation so the terms with the unkown variable x are on the right side and the other ones on the left side:
9x + 41 = 13x - 15
↓ substracting 9x both sides
41 = -9x + 13x - 15
41 = 4x - 15
↓ adding 15 both sides
41 + 15= 4x
56 = 4x
Step 2Solving the equation for x
56 = 4x
↓ dividing by 4 both sides
56/4 = x
14 = x
Answer A: x = 14
Now we want to find angle 4. Since it makes a straight line with the angle given by the expression 13x - 15, then their addition should be equal to 180°:
∡4 + 13x - 15 = 180
We want to find ∡4, and we do know the value for x, so, using the expression we can find it.
Replacing x by 14:
∡4 + 13x - 15 = 180
↓replacing x = 14
∡4 + 13 · 14 - 15 = 180
∡4 + 182 - 15 = 180
∡4 + 167 = 180
We follow the same previous steps to find ∡4
Step 1Rearraging the equation so the terms with the unkown variable ∡4 are on the left side and the other ones on the right side:
∡4 + 167 = 180
↓ substracting 167 both sides
∡4 = - 167 + 180
∡4 = 13°
Step 2:We already found it using step 1 so step 2 is not neccesary to be followed
Answer B: ∡4 = 13°
Instructions: Match the linear equation with its graph. Label the slope and -intercept.
Given the following question:
[tex]y=-3x+1[/tex]Graph 3 is the same as y = -3x + 1
For part B:
[tex]\begin{gathered} y=-3x+1 \\ y=mx+b \\ m=slope \\ b=y-intercept \\ m=-3 \\ b=1 \end{gathered}[/tex]What is the solution to 6(1+3) < 3(21+6)?
[tex]6(1+3) < 3(21+6)[/tex]
[tex]6(1+3)\\6(4)\\=24[/tex]
_______
[tex]3(21+6)\\3(27)\\=81[/tex]
[tex]24 < 81[/tex]
[tex]\fbox{True}[/tex]
Hope this helps!
A solution to a linear system" means which of the following? The y-intercepts are the same A) The rates of change for both functions are the same B) The x value equals the y value The x and y values make both equations true
the x and y values makes both equations true
Explanation
a linear system is the set of 2 linear equations.
Step 1
the solution to a linear system is the coordiante where the line intersect, this coordiante satisfies both equations, then
the x and y values makes both equations true
If x and 2x-15 represent the measure of the acute angles of a right triangle, find the value of x.
In a right triangle, the measure of acute angles is represented by x and 2x -15 then the value of x is equal to 35.
As given in the question,
In a right triangle,
One of the angle is of measure 90°.
Other two angles are acute angles.
Measure of two acute angles are given as x and 2x -15.
Sum of the three angles in a triangle is 180°.
x + 2x -15 + 90° = 180°
⇒3x +75° = 180°
⇒ 3x = 105°
⇒ x = 35°
Therefore, in a right triangle, the measure of acute angles is represented by x and 2x -15 then the value of x is equal to 35.
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6.Which of the following represents a graph with a rate of change of ?
Solution:
The rate of change of a graph is the same as the slope of the graph.
The graph that has a rate of change of 1/2 is the graph with a slope of 1/2.
To calculate the slope of a graph,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Considering two clear points from graph C, picking the points (2,-1) and (4,0)
[tex]\begin{gathered} \text{where} \\ x_1=2 \\ y_1=-1 \\ x_2=4 \\ y_2=0 \\ \\ \text{Substituting these values in the formula to get slope,} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0-(-1)}{4-2} \\ m=\frac{0+1}{4-2} \\ m=\frac{1}{2} \end{gathered}[/tex]Therefore, the graph that represents a rate of change of 1/2 is the graph of option C.
21. The length, width, and height of a rectangular prism can be represented by the expressions (x + 3),
(x + 7) and (x-1). Write an expression to represent the Volume of the prism.
⇒The formula to calculate the Volume of a rectangular prism is V=[tex]L*W*H[/tex]
where L is the length, W is the width and H is the height.
To find the expression of the volume plug in the values given in the equation I provided above and simplify.
⇒It is given that
L=(x+3)
W=(x+7)
H=(x-1)
[tex]V=(x+3)(x+7)(x-1)\\V=(x^{2} +7x+3x+21)(x-1)\\\\V=(x^{2} +10x+21)(x-1)\\V=-1(x^{3} +10x^{2} +21x)\\V= - x^{3} -10x^{2} -21x[/tex]
Consider parallelogram ABCD below.Use the information given in the figure to find x, m ZADB, and m ZA.350Х2x160M ZADB = 0m 2A =1130D© 2021 McGraw-Hill Education.Search for anythingoBI
The diagram is a parallelogram.
from the properties of a parallelogram, opposide are equal. Hence
|AD|=|BC|,
Where |AD|=2x and |BC|=6
[tex]\begin{gathered} 2x=6 \\ \text{dividing both side by 2} \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]find the zeros of the function.f(x) = 3x^2 + 6
f(x) = 3x^2 + 6
0 = 3x^2 + 6 (Replacing f(x) by 0)
-6 = 3x^2 (Subtracting 6 from both sides of the equation)
-6/3 = x^2 (Dividing by 3 on both sides of the equation)
-2 = x^2 (Dividing)
[tex]\begin{gathered} \sqrt[]{-2}\text{ = x (Taking the square root on both sides of the equation)} \\ \sqrt[]{-1}\text{ }\cdot\sqrt[]{2}\text{= x (Separating terms)} \\ \sqrt[]{2}i=x\text{ (Changing }\sqrt[]{-1}\text{ for i)} \end{gathered}[/tex]There are no real solutions. The complex solutions are:
[tex]\pm\sqrt[]{2}i[/tex]