4x = 2 + 14
4x = 16
4 is multiplying on the left, then it will divide on the right
x = 16/4
x = 4
Simplify the expression showed question … which is the correct answer
Okay, here we have this:
We need to simplify the following expression:
[tex]\begin{gathered} (5^{-4}(25)^4)^2 \\ =(5^{-4}(5^2)^4)^2 \\ =(5^{-4}\cdot5^8)^2 \\ =(5^{-4+8})^2 \\ =(5^4)^2 \\ =5^8 \end{gathered}[/tex]Finally we obtain that the correct answer is the option B.
Write an equation of the line passes through (-4,4) y=1/2x+1
Answer: y = -2x - 4
The equation of the line given is
[tex]\frac{1}{2}x\text{ + 1}[/tex]The slope - intercept form of equation is written as
y = mx + b
Where m = slope and b = intercept
From the above equation
m = 1/2
For a perpendicular line
[tex]\begin{gathered} For\text{ perpendicular line} \\ m1\text{ x m2 = -1} \\ m1\text{ = }\frac{1}{2} \\ \text{Therefore,} \\ \frac{1}{2}\text{ x m2 = -1} \\ \text{Make m2 the subject of the formula} \\ m2\text{ = }\frac{-1}{\frac{1}{2}} \\ m2\text{ = -1 x }\frac{2}{1} \\ m2\text{ = -2} \end{gathered}[/tex]Since m2 = -2
Hence, the perpendicular equation can be calculated
(y - y1) = m(x - x1)
The given point is ( -4, 4)
x1 = -4 and y1 = 4, and m = -2
(y - 4) = -2(x - (-4)
(y - 4) = -2(x + 4)
Open the parenthesis
y - 4 = -2x - 2*4
y - 4 = -2x - 8
y = -2x -8 + 4
y = -2x - 4
I can’t figure this out. Getting different answer than listed. Please help with attached pic.
Solution
We are required to use synthetic division to rewrite the expression
[tex](x^3+6x^2-5)\div(x+2)[/tex]The synthetic division is shown below
Re-write the result in polynomial form
[tex]=x^2+4x-8+\frac{11}{x+2}[/tex]The answer is
[tex]=x^2+4x-8+\frac{11}{x+2}[/tex]graphing on the coordinate plane how does absolute value help you write a number sentence to help you find the distance
Given:
The points 7 and -7.
Required:
We need to find the distance between 7 and -7 by using absolute values.
Explanation:
1)
We need to subtract the given numbers to find the distance.
Subtract 7 from -7 and take absolutely to find the distance.
[tex]Distance=|-7-7|[/tex]Just add the absolute value of each number together, put a negative sign in front,
[tex]Distance=|-(|-7|+|-7|)|[/tex][tex]Distance=|-(7+7)|[/tex][tex]Distance=|-14|[/tex][tex]Distance=14[/tex][tex]We\text{ know that abosulute values of negative number is postive.}[/tex]The absolute value of a number is never negative.
Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
2)
Subtract 5 from -5 and take absolutely to find the distance.
[tex]Distance=|-5-5|[/tex]Just add the absolute value of each number together, put a negative sign in front,
[tex]Distance=|-(|-5|+|-5|)|[/tex][tex]Distance=|-(5+5)|[/tex][tex]Distance=|-10|[/tex][tex]Distance=10[/tex]Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative
3)
Subtract 2 from -2 and take absolutely to find the distance.
[tex]Distance=|-2-2|[/tex][tex]Distance=|-4|[/tex][tex]Distance=4[/tex]Answer:
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative
Final answer:
1)
The absolute value of the difference between 7 and -7 is 14.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
2)
The absolute value of the difference between 5 and -5 is 10.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
3)
The absolute value of the difference between 2 and -2 is 4.
The distance is non-negative. so absolute values help to avoid the negative values for distance since the absolute value of a number is never negative.
find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores. z= 1 and z= 1.9
The area, to the nearest thousandth, of the standard normal distribution between the z-scores z= 1 and z= 1.9 is 0.130
A guidebook says that one night at a mid-range hotel the capital city, republica cost between $25 an $40 us dollars. The hotel capital city offers a one week rental for 150 rp ( republica pounds) the current exchange rate is 1=0.0147 usd ($us dollars) does the price per night at the hotel capitol suggest that it a mid range hotel?
To determine if the hotel capital suggests is a mid-range hot, we need to do the conversion:
[tex]150rp\cdot\frac{0.0147\text{usd}}{1rp}=2.2\text{ usd}[/tex]By the exchange rate 1rp=0.0147usd, notice the rental week of Hotel Capital city is $2.2
Then, for the night:
[tex]\frac{2.2}{7}=0.31[/tex]Then, a night at Hotel Capital City would be $0.31. It is not a mid-range hotel.
f(x) = 2x + 4 and g(x) = -8f(x). = What equation shows the correct rule for the function g? O g(x) = -4x O g(x) = -4x + 4 = g(x) = -8x - 32 O g(x) = -4x - 32 – -
The given functions are
[tex]\begin{gathered} f(x)=\frac{1}{2}x+4 \\ g(x)=-8f(x) \end{gathered}[/tex]Multiply f by -8 to get g
[tex]\begin{gathered} g(x)=-8(\frac{1}{2}x+4) \\ g(x)=-8(\frac{1}{2}x)+(-8)(4) \\ g(x)=-4x+(-32) \\ g(x)=-4x-32 \end{gathered}[/tex]The correct answer is D
if you receive a 175.84 cents on 314 invested at a rate of 7% for how long did yo invest the principle
Answer:
The number of years you should invest the principal is;
[tex]8\text{ years}[/tex]Explanation:
Given;
[tex]\begin{gathered} \text{Interest i = \$175.84} \\ \text{ Principal P = \$}314 \\ \text{Rate r = 7\% =0.07} \end{gathered}[/tex]Recall that the formula for simple interest is;
[tex]\begin{gathered} i=P\times r\times t \\ t=\frac{i}{Pr} \\ \text{where;} \\ t=\text{time of investment} \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} t=\frac{i}{Pr} \\ t=\frac{175.84}{314\times0.07} \\ t=\frac{175.84}{21.98} \\ t=8 \end{gathered}[/tex]Therefore, the number of years you should invest the principal is;
[tex]8\text{ years}[/tex]We can also solve as;
[tex]\begin{gathered} i=P\times r\times t \\ 175.84=314\times0.07\times t \\ 175.84=21.98t \end{gathered}[/tex]then we can divide both sides by 21.98;
[tex]\begin{gathered} \frac{175.84}{21.97}=\frac{21.98t}{21.98} \\ 8=t \\ t=8\text{ years} \end{gathered}[/tex]the sum of 2 numbers is 30. the sum of the squares of the two numbers is 468 what is the product of the two numbers
Take x and y as the 2 numbers
Define the equation that represents each situation
The sum of 2 numbers is 30
[tex]x+y=30[/tex]The sum of the squares of the numbers is 468
[tex]x^2+y^2=468[/tex]Complete the square in the second equation (don't forget to write
What number is 2% of 35
Answer:
The 2% of 35 is;
[tex]0.7[/tex]
Explanation:
We want to find the 2% of 35
[tex]\begin{gathered} \text{ 2\% of 35 =} \\ \frac{2}{100}\times\text{ 35 = }\frac{70}{100}=0.7 \end{gathered}[/tex]Therefore, the 2% of 35 is;
[tex]0.7[/tex]
Answer:0.7
Step-by-step explanation:
35x2=70
70/100=0.7
The graph of a function is shown on the coordinate plane below. Which relationship represents a function with the same slope as the function graphed?
If (x_1, y_1) and (x_2, y_2) are points of a line, its slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\text{.}[/tex]From the graph of the function, we see that the line passes through the points:
• (x_1, y_1) = (-1, 6),
,• (x_2, y_2) = (0, 1).
The slope of the line is:
[tex]m=\frac{1-6}{0-(-1)}=-5.[/tex]A) Using the points:
• (x_1, y_1) = (-2, 0),
,• (x_2, y_2) = (2, 10).
We find that the slope of this line is:
[tex]m=\frac{10-0}{2-(-2)}=\frac{10}{4}=2.5.[/tex]This function has not the same slope as the line of the graph.
B) The general equation of a line is:
[tex]y=m\cdot x+b\text{.}[/tex]Where m is the slope and b is the y-intercept.
Comparing the general equation with the equation:
[tex]y=-5x+3,[/tex]we see that the slope of the line of this equation is m = -5.
This function has the same slope as the line of the graph.
C) Using the points:
• (x_1, y_1) = (-4, 8),
,• (x_2, y_2) = (0, 5).
We find that the slope of this line is:
[tex]m=\frac{5-8}{0-(-4)}=-\frac{3}{4}=-0.75.[/tex]This function has not the same slope as the line of the graph.
D) Comparing the general equation with the equation:
[tex]y=-\frac{5}{4}x+2.[/tex]we see that the slope of the line of this equation is m = -5/4.
This function has not the same slope as the line of the graph.
Answer
B. y = -5x + 3
W XZWhich statement regarding the diagram is true?O mzWXY = mzYXZO mzWXY
Linear pair of angles are formed when two lines intersect each other at a single point.
The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.
The figure shows the line WZ intersected by lines YX and YZ. At X, two adjacent angles are formed at the point where WZ and YX intersect.
This means angles WXY and YXZ are linear angles.
Linear angles always add up to 180°, thus:
m∠WXY + m∠YXZ = 180°
which statement is true if the graph of the linear function passes through the points (-1, -6)and (5,6) function first if needed
The correct option is C
Explanation:We check through each of the options to see if they are true
Option A is not true
The slope of the graph is as follows:
(6 - (-6))/((5 - (-1))
= (6 + 6)/(5 + 1)
= 12/6
= 2
Option B is not true
The zero of the graph is the point on the x-axis where y = 0, this is x = 2
Option C is true
The x-intercept is the point where the graph crosses the x-axis. This is (2, 0)
Option D is not true
the width of a rectangular rug is 3 1/4 inches longer than twice its length. if the perimeter of the rug is 54 1/2 inches, which equation represents this situation?
The equation represents the relation of perimeter with length and width is 109/4 = 24 l + 13.
What is meant by the perimeter of the rectangle?For the given question;
Let the dimensions of the rectangle be;
Length lWidth wPerimeter PFor the condition, width of a rectangular rug is 3 1/4 inches longer than twice its length.
w = 2×l + 3 1/4
Solve the mixed fraction;
w = 2×l + 13/4
Now, the perimeter is;
P = 2(l + w)
P = l x w
Put the value of w.
P = 2 ( l + 2×l + 13/4) ....eq1
P = 54 1/2 inches = 109/4
Put in eq 1
109/4 = 3 l + 13/4
109/4 = 24 l + 13
Multiplying equation by 4.
109/4 = 24 l + 13
Thus, the equation represents the relation of perimeter with length and width is 109/4 = 24 l + 13.
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I need help with this please If the triangle on the grid is translated three units left and nine units down what are the coordinates of c
Explanation
From the question
we are simply asked to get the new coordinates of point C if the triangle ABC is translated three units to the left and nine units down
To do so, we will make use of the relationship
If a coordinate is translated left or right, it affects the x-coordinate. Left is negative, Right is positive
If a coordinate is translated up or down, it affects the y-coordinates. Down is negative, Up is positive
Therefore
For point C
The initial coordinate is (-1,2)
After the triangle has been translated, we will have
[tex]\begin{gathered} x-value=-1-3=-4 \\ y-value=2-9=-7 \end{gathered}[/tex]Therefore, we have the new coordinate as (-4,-7)
The answer is
Which of the following is equal to 11.4 9? A. (11 x 9) + (0.4 9) B. (11 + 9) + (0.4 +9) C. (11 x 9) * (0.4 * 9) D. (11 + 9) * (0.4 +9)
Answer
Option A is correct.
(11.4 × 9) = (11 × 9) + (0.4 × 9) = 102.6
Step-by-step Explanation
The best way to explain this is to examine the options one at a time to examine the one that is the most correct.
We want to know which of the options is equal to (11.4 × 9).
11.4 × 9 = 102.6
The options are
A. (11 × 9) + (0.4 × 9)
11 × 9 = 99
0.4 × 9 = 3.6
(11 × 9) + (0.4 × 9) = 99 + 3.6 = 102.6
B. (11 + 9) + (0.4 + 9)
11 + 9 = 20
0.4 + 9 = 9.4
(11 + 9) + (0.4 + 9) = 20 + 9.4 = 29.4
C. (11 × 9) × (0.4 × 9)
11 × 9 = 99
0.4 × 9 = 3.6
(11 × 9) × (0.4 × 9) = 99 × 3.6 = 356.4
D. (11 + 9) × (0.4 + 9)
11 + 9 = 20
0.4 + 9 = 3.6
(11 + 9) × (0.4 + 9) = 20 × 3.6 = 72
Since only option A gives the same answer as the expression in the question, option A is the only correct option.
Hope this Helps!!!
In the triangle below, if < C = 62 °, what is the measure of angle B?
In the given triangle ABC
[tex]BA=BC[/tex]Then the triangle is isosceles
In the isosceles triangle, the base angles are equal
Since [tex]m\angle A=m\angle C[/tex]Since m[tex]m\angle A=62^{\circ}[/tex]In any triangle the sum of angles is 180 degrees, then
[tex]m\angle A+m\angle B+m\angle C=180^{\circ}[/tex]Substitute angles A and C by 62
[tex]\begin{gathered} 62+m\angle B+62=180 \\ \\ m\angle B+124=180 \end{gathered}[/tex]Subtract 124 from both sides
[tex]\begin{gathered} m\angle B+124-124=180-124 \\ \\ m\angle B=56^{\circ} \end{gathered}[/tex]The answer is b
Please answer correctly! Giving brainliest!
Describe in words where cube root of 30 would be plotted on a number line.
Between 3 and 4, but closer to 3
Between 3 and 4, but closer to 4
Between 2 and 3, but closer to 2
Between 2 and 3, but closer to 3
Answer:
A) Between 3 and 4, but closer to 3======================
First, find the cubes of 2, 3 and 4 and then compare them with 30.
2³ = 8,3³ = 27,4³ = 64We see that 30 is between 27 and 64 and is closer to 27:
27 < 30 < 64Therefore cube root of these numbers are:
∛27 < ∛30 < ∛643 < ∛30 < 4So the ∛30 is between 3 and 4 and closer to 3.
Correct answer choice is A.
Answer:
A) Between 3 and 4, but closer to 3.
Step-by-step explanation:
A perfect cube is the result of multiplying the same integer three times.
First few perfect cubes: 1, 8, 27, 64, 125, etc.To estimate the value of the cube root of a number, find the perfect cubes above and below the number:
The perfect cubes either side of 30 are:
27 < 30 < 64Therefore, the cube roots are:
[tex]\implies \sf \sqrt[3]{27} < \sqrt[3]{30} < \sqrt[3]{64}[/tex]
[tex]\implies \sf 3 < \sqrt[3]{30} < 4[/tex]
As 30 is closer to 27 than 64, the cube root of 30 is closer to the cube root of 27 than the cube root of 64.
Therefore, the cube root of 30 would be plotted on a number line:
between 3 and 4, but closer to 3.Can anyone help me? I don't know the answer.
Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].
What is the rectangle?
A rectangle is a two-dimensional flat shape. In an [tex]XY[/tex] plane, we can easily represent a rectangle, where the arms of x-axis and y-axis show the length and width of the rectangle, respectively.
Area of rectangle = Length × Width
Here given that,
[tex]L=\frac{7}{8}m[/tex]
[tex]W=\frac{3}{4}m[/tex]
So,
Area of rectangle = [tex](\frac{7}{8}m)*(\frac{3}{4}m)\\[/tex]
[tex]=\frac{21}{32}m^2[/tex]
Hence, the area of the rectangle is [tex]\frac{21}{32}m^2[/tex].
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1 금35Lolo19.Which type of variation is modeled in the table?jointdirectcombinedInverse
The answer to your question is inverse varaiation.
Explanation: Inverse variation is a reciprocal term. Or say a variable is increasing while the other is decreasing.
So it is observed that as when y increases, then x decreases.
And also when y decreases, then x increases.
Thus, It is an inverse variation.
Write an Equation: Gary worked for 20 hours tutoring students at the library. He uses $35 to pay for gas on his way home. If he has $60 left after paying for gas, how much money, x, in dollars, was Gary paid per hour?
Answer:4.75 in us dollars it will be 5.31
Step-by-step explanation:
first you divide 95 by 20 witch will give you 4.75 and if you want to check that answer you do 4.75 times 20 and it will give 95
In ΔIJK, k = 53 cm, j = 66 cm and ∠J=64°. Find all possible values of ∠K, to the nearest 10th of a degree.
The value of ∠K is 46.2° as the definition of angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint".
What is angle?An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. Based on measurement, there are different kinds of angles in geometry. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by joining two rays at their termini. In most cases, an angle is expressed in degrees.
Here,
Side i = 68.91521 cm
Side j = 66 cm
Side k = 53 cm
Angle ∠I = 69.8°
Angle ∠J = 64°
Angle ∠K = 46.2°
∠K= sin⁻¹(k·sin(J)/j)
=sin⁻¹(53.(sin 64°)/66)
=46.2°
Since the definition of an angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint," the value of ∠K is 46.2°.
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Evaluate the expression when x = 32 and y = 2.
x/14 A. 1/16
B.16/21
D.2
C.4
Answer:
I think its 16/21
Step-by-step explanation:
Answer:
2Step-by-step explanation:
Given x = 14, y = 2x/14
Void "y" because it is not in this equation.= x/14
32/14
= 2.2
≈ 2
Please answer and explain the problem. This is due soon, please help!!
In all cases use the following formula for the are of a rectangular shape:
A = lw
Plot A:
The area and height are known, then, solve the formula for the length l:
l = A/w
repace the given values
l = (204 ft²)/(10.2 ft)
I = 20 ft
For the perimeter you have:
P = 2l + 2w = 2(20 ft) + 2(10.2 ft) = 60.4ft
Plot B:
The length and the perimeter are known. For the expression for the perimeter solve for w:
P = 2l + 2w
w = (P - 2l)/2
replace the values of P and l:
w = (57.56 ft - 2(12.78 ft))/2 = 16 ft
Then, replace in the formula for the area:
A = lw = (12.78 ft)(16 ft) = 204.48 ft²
Plot C:
The area and the height are known. Use the formula for A to obtain the length:
l = A/w = 204.49 ft/14.3 ft = 14.3 ft
and for the perimeter:
P = 2w + 2l = 2(14.3 ft) + 2(14.3 ft) = 57.2 ft
Hence, you can conclude:
- The plost with the least amount of fencing is the plot with the lowest perimeter, hence, Plot C requires the least amount of fencing.
- The plot with the greatest area is Plot A.
Dr. Jordan is a veterinarian. The table shows the weights of 5 kittens at her office. What is the mean weight of the kittens? Kitten Weight (ounces) Kitten 1 6 Kitten 2 11 Kitten 3 6 Kitten 4 10 Kitten5 7
Recall that the mean of a given set of values is given as
[tex]\begin{gathered} \text{Mean = }\frac{sum\text{ of all the items or values}}{total\text{ number of item or values}} \\ =\text{ }\frac{6+11+6+10+7}{5} \\ =\frac{40}{5} \\ =8 \end{gathered}[/tex]the volume of a cylinder is 1269 pi cm^3 and its height is 16 cmthe length of the cylinders radius is ___ cm
The volume of cylinder is.
[tex]V=1296\pi[/tex]The height of cylinder is h = 16.
The formula for the volume of the cylinder is,
[tex]V=\pi(r)^2h[/tex]Determine the length of radius of cylinder.
[tex]\begin{gathered} 1296\pi=\pi(r)^216 \\ r^2=\frac{1296\pi}{16\pi} \\ =81 \\ r=\sqrt[]{81} \\ =9 \end{gathered}[/tex]So length of cylinder radius is 9 cm.
What is the m stand for in -3 = m-14
Step 1:
Write the equation
- 3 = m - 14
Step 2: Collect similar terms
- 3 = m - 14
m = -3 + 14
m = 11
Final answer
m = 11
What is the total amount of the monthly payments for a $5,300, 4-year
loan with an APR of 3% ? (Follow Example 2)
Do not use the $ sign in your answer and round to the nearest Cent
(100th):t
The principal amount given out as loan is 239447.08
Monthly PaymentThe monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.
Monthly payment = $5300Time = 4 yearsrate = 3%Principal = ?n = number of times compoundedThe formula is given as
[tex]m = P[\frac{r(1+r)^n}{(1+r)^n^-^1}[/tex]
Substituting the values and solving for the principal amount, this will cost 239,447.08.
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Translate the sentence into an equation.Seven less than the product of 6 and a number is 2.Use the variable x for the unknown number
Seven less than the product of 6 and a number is 2.
→ The product of 6 and a number can be expressed as 6x
→ "Seven less than the product of 6 and a number", indicates that you have to subtract 7 to 6x, so that: 6x-7
→ According to the sentence, the result of this calculation is seven, so the complete expression is:
[tex]6x-7=2[/tex]Preform the indicated Operation g(n)=2n^2-4nh(n)=n-1find g(h(1-b))
GIven:
The expressions are given as,
[tex]\begin{gathered} g(n)=-2n^2-4n \\ h(n)=n-1 \end{gathered}[/tex]The objective is to find g(h(-1-b)).
Explanation:
To find h(-1-b):
The value of h(-1-b) can be calculated by replacing the n with (-1-b) in the expression of h(n).
[tex]\begin{gathered} h(n)=n-1 \\ h(-1-b)=-1-b-1 \\ h(-1-b)=-2-b\text{ . . . . . . (1)} \end{gathered}[/tex]To find g(h(-1-b)):
The value of g(h(-1-b)) can be calculated by replacing the n with h(-1-b) in the expression g(n).
[tex]\begin{gathered} g(n)=-2n^2-4n \\ g(h(-1-b))=-2(-2-b)^2-4(-2-b)\text{ . . . . (2)} \end{gathered}[/tex]On further solving the equation (2),
[tex]undefined[/tex]