Let:
x = Unknown number
Twice the sum of a number and five:
[tex]2(x+5)[/tex]Is equal to 40:
[tex]2(x+5)=40[/tex]Solve for x:
Expand the left hand side using distributive property:
[tex]2x+10=40[/tex]Subtract 10 from both sides:
[tex]2x=30[/tex]Divide both sides by 2:
[tex]x=15[/tex]Tina babysits and cuts lawns to earn money. For one week, she babysits for 5 hours. She earns $8.25 per hour babysitting If Tina earns $92 this week, how much does tina earn cutting lawns? 1) $10.152) $16.753) $41.254( $50.75
Answer:
[tex]\text{ \$50.75}[/tex]Explanation:
Here, we want to calculate how much Tina earns cutting lawns
From the question, she earns $8.25 per hour for 5 hours cutting lawns
What she earned in totality that week would be:
[tex]\text{ 5 }\times\text{ \$8.25 = \$41.25}[/tex]What she earned cutting lawns would be the total earned minus what she earned cutting lawns
Mathematically, we have that as:
[tex]\text{ \$92 - \$41.25 = \$50.75}[/tex]Miss Johnson has a tree in her garden that grows apples in the spring and summer the tree has a diameter of 32 ft from its base what is the circumference of that tree in Miss John's Garden
We know that the circunference of a circle is:
[tex]C=2D[/tex]where D is the diameter so the circunference will be:
[tex]\begin{gathered} C=2\cdot32 \\ C=64 \end{gathered}[/tex]SI unit conversion Could you please help me with exercise number 12 please and explain the process? I copied exercise 11 from the board and trued to solve #13 but not sure if it’s correct
Given:-
[tex]9468mg=\ldots kg[/tex]To find the required solution.
So we use the formula,
[tex]1\operatorname{kg}=1000000mg[/tex]So now we substitute,
[tex]\frac{9468}{1000000}=0.009468[/tex]So the required solution is 0.009468 kg.
how do i do this i need answers help please
SOLUTION:
Step 1:
In Question 8, we have that:
The three vertices of Triangle ABC are located in Quadrant III.
The image of Triangle ABC after a reflection in the x-axis in the x-axis is
[tex]\text{Triangle A}^IB^IC^I[/tex]Then, the triangle
[tex]A^IB^IC^I[/tex]is located in II -- OPTION B
y=-2xy=x-8how do you do this
Separate
y =- 2xy
-2xy = x - 8
Now solve first equation
and then second equation
PART2
y = -2x
y= -4x + 10
Is solved by , substracting both equations
Then
(y - y) = -2x - ( -4x + 10)
0 = -2x + 4x - 10
10 = 2x
10/2= xx
9 divided by 2765 that’s what I’m am asking for
Answer: 307.22222222222 ......
Step-by-step explanation: use the bus stop method to help you
Please please please help me
The lines l, m, and n are parallel to each other and the value of x is 8.34.
What are parallel lines?Parallel lines are lines that are equidistant from each other and do not meet no matter how far they extend in either direction. Parallel lines form angles when crossed by a transversal and show some significant properties.
Angles that correspond are equal.Angles that are vertically opposite or vertically angled are equal.Interior angles that are opposite each other are equal.On the same side of the transversal, a pair of interior angles are supplementary.For the given question, we can see that lines l ║m ║n.
Therefore, (6x - 2)° = 52° [Vertically opposite angles are equal]
6x = 52 - 2
6x = 50
x = 50/6
x = 8.34
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the graph represent 1, and the equation represents function 2: function 2: y=8x + 12how much more is the rate of function 2 then the rate of change of function 1?answer choices:a.3b.4c.5d.8
as the graph represent a constant function, we have that the rate for function 1 is 0. The rate for the second function is 8. So we get that the the answer is D
Wyatt's eraser box is shaped as a rectangular prism. His erasers are cubes with 1-centimeter sides. The
bottom of the box can hold 14 erasers, and the box is 6 centimeters tall. How many erasers can Wyatt fit
in his box?
Each eraser has the shape of a cube with a side length of 1 cm.
The eraser box is a rectangular prism (a rectangular box).
We know the bottom of the box can hold 14 erasers. If we lay 14 more erasers on top of it, we would have used 2 cm of the box's height.
We can do it a total of 6 times until we top up the box, thus the total number of erasers that fit the box is 6*14 = 84 erasers
I require assistance on a troubling problem
Given data:
The given table.
The standard expression for the exponential function is,
[tex]y=a(b)^x[/tex]Substitute o for x and 5 for y in the above expression.
[tex]\begin{gathered} 5=a(b)^0 \\ 5=a \end{gathered}[/tex]Substitute 1 for x, 15 for y, and 5 for a in the standard exponential expression.
[tex]\begin{gathered} 15=5(b)^1 \\ b=3 \end{gathered}[/tex]The exponential expression can be written as,
[tex]y=5(3)^x[/tex]Thus, the expression for the exponential function is y=5(3)^x.
A given circle has an approximate area of 78.5 square units. How long is the circles diameter?
Remember that
The area of a circle is equal to
[tex]A=\pi\cdot r^2[/tex]we have
A=78.5 unit2
I will assume pi=3.14
substitute in the formula
[tex]\begin{gathered} 78.5=3.14\cdot r^2 \\ r^2=\frac{78.5}{3.14} \\ r=5\text{ units} \end{gathered}[/tex]the diameter is two times the radius
so
D=2(5)=10 units
therefore
The diameter is 10 unitsFind the slope of the line shown on the graph to the right.What is the slope of the line? The slop of the line is ___
The formula for determining slope is expressed as
slope = (y2 - y1)/(x2 - x1)
where
y1 and y2 are the y coordinates of initial and final points on the line
x1 and x2 are the x coordinates of initial and final points on the line
From the graph,
when x1 = - 4, y1 = 0
when x2 = 2, y2 = 4
slope = (4 - 0)/(2 - - 4) = 4/(2 + 4) = 4/6
Simplifying 4/6 to its lowest term
slope = 2/3
Solve the following system of equation using substitution4x + 2y = 10?/1x - y = 13What is the solution for x?
ANSWER
x = 6
EXPLANATION
The substitution method consists on taking one equation to solve for one variable as a function of the other. Then substitute that variable with the expression we find in the other equation and then solve for that other variable.
In this case, we want to solve for x, so we'll take one of the equations and find y as a function of x. For the second equation:
[tex]\begin{gathered} x-y=13 \\ y=x-13 \end{gathered}[/tex]Now we replace y by x - 13 in the first equation:
[tex]4x+2(x-13)=10[/tex]And solve for x:
[tex]\begin{gathered} 4x+2x-2\cdot13=10 \\ 6x-26=10 \\ 6x=10+26 \\ 6x=36 \\ x=\frac{36}{6} \\ x=6 \end{gathered}[/tex]picture with question
In order to determine if the given triangles are similar, it is necessary to find the values of the missing angles.
Take into account that the sum of the interior angles of a triangle is equal to 180°, the for the missing angles you have:
180° - 90° - 46° = 44°
180° - 38° - 46° = 96°
AS YOU CAN NOTICE THE THREE ANGLES ARE NOT EQUAL.
Then, the triangles are NOT similar because it is necessary that the three angles are equal.
What is the system of inequalities associated with the following graph?A) {y<−1x {+y>1 B) {y>−1 {x+y≥1 C) {y<−1 {x+y≥1 D) {y < -1 {x + y <1
SOLUTION:
Step 1:
In this question, we are given the following:
What is the system of inequalities associated with the following graph?
Step 2:
The details of the solution are as follows:
CONCLUSION:
The final answer is:
C) {y<−1
{x+y≥1
What function best represents the perimeter of the orange boxes? *
The formula used to calculate the perimeter of a rectangle is given to be:
[tex]P=2l+2h[/tex]FIRST BOX
For the first orange box, we have that:
[tex]\begin{gathered} l=x+x=2x \\ h=2 \end{gathered}[/tex]Note that the box is divided into 2 parts.
Therefore, this perimeter is:
[tex]P_1=2(2x)+2(2)=2(2x)+4[/tex]SECOND BOX
For the second orange box, we have that:
[tex]\begin{gathered} l=x+x+x=3x \\ h=2 \end{gathered}[/tex]Note that the box is divided into 3 parts.
Therefore, the perimeter is:
[tex]P_2=2(3x)+2(2)=2(3x)+4[/tex]Using the associative property of multiplication, we have that:
[tex]P_2=3(2x)+4[/tex]Since x = 5, we have:
[tex]\begin{gathered} P_1=2(10)+4 \\ P_2=3(10)+4 \end{gathered}[/tex]where 2 and 3 are the number of divisions of the boxes.
If we represent the number of divisions with x, we have the perimeter's function to be:
[tex]P=10x+4[/tex]ANSWER
The correct option is the THIRD OPTION.
Write an equivalent expression of 4(6x+12), and state the property you used to write it.
Solution
Using the distributive property
4(6x + 12)
[tex]4(6x+12)=4\times6x+4\times12=24x+48[/tex]a smmall rectangular tray measures 16 cm by 18 cm determine the length of the diagonal . round you're answer to the nearest tenth.m
Given the dimension of the rectangle:
16 cm by 18 cm
We have the image of the rectangle below:
To find the length of the diagonal AC, use pythagorean theorem since ACD form a right triangle.
Thus, we have:
[tex]\begin{gathered} AC^2=AD^2+DC^2 \\ \\ AC=\sqrt[]{AD^2+DC^2} \end{gathered}[/tex]Input values into the formula:
[tex]\begin{gathered} AC=\sqrt[]{18^2+16^2} \\ \\ AC=\sqrt[]{324+256} \\ \\ AC=\sqrt[]{580} \\ \\ AC=24.08\approx24.1\text{ cm} \end{gathered}[/tex]Therefore, the length of the diagonal is 24.1 cm
ANSWER:
24.1 cm
-3x + 5y = -155x - 2y = -101. Find the solution2. Write an equation to replace the second equation so that the system will have infinitely many solutions.
Problem
-3x + 5y = -15
5x - 2y = -10
Solution
For this case we can solve x from the first equation and we got:
3x = 5y +15
x= (5y+15)/3
Now we can replace this value into the second equation and we got:
5((5y+15)/3) -2y = -10
25/3y +25 -2y= -10
And solving for y we got:
(25/3 -2)y =-10-25
19/3 y = -35
y= -105/19
And then we can solve for x and we got:
x= (5*(-105/19) +15)/3 = -80/19
Find the radius of the circle with a circumference of 39 yards. Round your answer to the nearest hundredth of a yard.the radius of the circle is blank yards
Answer:
6.207
Explanation:
The circumference C of the circle is given by
[tex]C=2\pi r[/tex]where r is the radius.
Now we are given that C = 39 yd; therefore,
[tex]39=2\pi r[/tex]dividing both sides by 2pi gives
[tex]\frac{39}{2\pi}=\frac{2\pi r}{2\pi}[/tex][tex]r=\frac{39}{2\pi}[/tex][tex]r=6.207yd[/tex]Hence, the radius of the circle is 6.207 yards.
(5n+6)(5n-5) distribute property
We have the following:
[tex](5n+6)\cdot(5n-5)[/tex]we apply distribute property:
[tex]25n^2-25n+30n-30=25n^2+5n-30[/tex]Resultant of the distributive property is 25n² + 5n - 30 .
Given,
(5n+6)(5n-5)
Now,
Distributive property in multiplication : a x (b x c) = (axb) x c
Thus apply the property in the given expression,
(5n+6)(5n-5)
= 25n² - 25n + 30n - 30
Solve the terms with variable n,
= 25n² + 5n - 30
Final expression : 25n² + 5n - 30
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determine the degree of the polynomial[tex] - 65b + {53x}^{3}y[/tex]
Determine the degree of the polynomial
656+ 3x^3 y
Degree of the polynomial = 4 = (3 + 1)
3x^3 grade (3)
y grade (1)
________________
The degree of the polynomial is 4
A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?
The springs from the original pogo stick and the toddler's pogo stick length are equal after 1 second and 0.9994 second.
Explanation:The given functions are:
[tex]\begin{gathered} f(\theta)=2\cos \theta+\sqrt[]{3} \\ g(\theta)=1-\sin ^2\theta+\sqrt[]{3} \end{gathered}[/tex]The springs from the original pogo stick and the toddler's pogo stick length are equal when both functions coincide
That is;
[tex]\begin{gathered} f(\theta)=g(\theta) \\ \Rightarrow2\cos \theta+\sqrt[]{3}=1-\sin ^2\theta+\sqrt[]{3} \end{gathered}[/tex]Solving the equation, we have:
[tex]\begin{gathered} 2\cos \theta+\sqrt[]{3}=1-\sin ^2\theta+\sqrt[]{3} \\ Subtract\sqrt[]{3}\text{ from both sides} \\ 2\cos \theta=1-\sin ^2\theta \end{gathered}[/tex]Note the identity below:
[tex]\begin{gathered} \cos ^2\theta+\sin ^2\theta=1 \\ \cos ^2\theta=1-\sin ^2\theta \end{gathered}[/tex]This means
[tex]\begin{gathered} 2\cos \theta=\cos ^2\theta \\ \cos ^2\theta-2\cos \theta=0 \\ \cos \theta(\cos \theta-2)=0 \\ \cos \theta=0 \\ \Rightarrow\theta=\cos ^{-1}(0)=1 \\ \\ OR \\ \cos \theta-2=0 \\ \cos \theta=2 \\ \theta=\cos ^{-1}(2)=0.9994 \end{gathered}[/tex]The springs from the original pogo stick and the toddler's pogo stick length are equal after 1 second and 0.9994 second.
CheckWhich applies the power of a power rule properly to simplify this expression?(7-8)O (78)4 = 7-8) +(-4) = 7-12 =17121O (7-8)4 = 7(+8)+(-4) = 74 =741O (7-3) = 71-8)(-4) = 7-32 =732O 7-8,4 = 7(-8)(-4) = 72IntroDone
We are given the expression below
[tex](7^{-8})^{-4}[/tex]This expression can be solved by using one of the laws of indices which is denoted below:
[tex](a^m)^n=a^{m\times n}[/tex]Using the above the given expression beocmes
[tex]undefined[/tex]the ordered pair (2,16) is a solution for which equation(s) check all that apply
We have the following:
We must evaluate each equation (x = 2), if the result is 16 it will be a solution
A.
[tex]y=(2\cdot2)^2=4^2=16[/tex]B.
[tex]y=(2+2)^2=(4)^2=16[/tex]C.
[tex]y=2\cdot2^2=2\cdot4=8[/tex]D.
[tex]y=2\cdot2+2=4+2=6[/tex]Therefore, the correct answer is A and B
collin noticed that various combinations of the nickels and dimes could add uo to $0.75 let x equal the numver of nickles let y equal the number of dimes what is the domain where y is a function of x and the total value is $0.75
Input data
nickles = 5 cents
dimes = 10 cents
x = number of nickles
y = number of dimes
What is the component form of resultant of 4b⃗ −2aa = (7 , -5)b = ( -4 , 4)
1) Since we have this expression, let's do it in parts.
[tex]\begin{gathered} 4\langle-4,4\rangle-2\langle7,-5\rangle \\ x-component=4(-4)-2(7)=-16-14=-30 \\ y-component=4(4)-2(-5)=16+10=26 \\ \end{gathered}[/tex]Note that since each vector has two components x, and y. The resultant will be the vector:
[tex]\langle-30,26\rangle[/tex]On (07.03) Choose the correct simplification of the expression b5.54. (1 point)
explanation/ Working:
[tex]c^2.c^9=c^2\times c^9=c^{2+9}=c^{11}[/tex]Rule on iindex says when the base is same, you should add the powers
[tex]c^2.c^9=\text{ (c}\times c)\times(c\times c\times c\times c\times c\times c\times c\times c\times c)=c^{11}[/tex]From a point x = 80 feet in front of a public library, the angles of elevation to the base of the flagpole and the top of the flagpole are = 29.5° and 39° 45', respectively. The flagpole is mounted on the front of the library's roof. Find the height of the flagpole.
Let's draw the scenario to better understand the details.
To be able to determine the height of the flagpole, let's create two different triangles with 29.5° and 39° 45' angle. The two triangles have one common base at 80 Feet, yet have different heights at H+h and H respectively.
Where,
H = Height of the library
h = Height of the flag
The two triangles are proportional at a common base, thus, let's generate this expression using the Law of Sines:
[tex]\frac{H+h}{\sin(39\degree45^{\prime})}\text{ = }\frac{H}{\sin(29.5^{\circ})}[/tex]Let's simplify,
[tex]\frac{H+h}{\sin(39\degree45^{\prime})}\text{ = }\frac{H}{\sin(29.5^{\circ})}\text{ }\rightarrow\text{ (}H+h)(\sin (29.5^{\circ}))\text{ = (H)(}\sin (39\degree45^{\prime}))[/tex][tex]H\sin (29.5^{\circ})\text{ + h}\sin (29.5^{\circ})\text{ = H}\sin (39\degree45^{\prime})\text{ ; but }29.5^{\circ}=29^{\circ}30^{\prime}[/tex][tex]H\sin (29^{\circ}30^{\prime})\text{ + h}\sin (29^{\circ}30^{\prime})\text{ = H}\sin (39\degree45^{\prime})[/tex][tex]\text{h}\sin (29^{\circ}30^{\prime})\text{ = H}\sin (39\degree45^{\prime})\text{ - }H\sin (29^{\circ}30^{\prime})[/tex][tex]\text{ h(}0.4924235601)\text{ = H(0.63943900198) -H}(0.4924235601)[/tex][tex]\text{ h(}0.4924235601)\text{ = H(0.14701544188)}[/tex][tex]undefined[/tex]
An investment of R2000 is made at 10 %per year simple interest for 3 years. The amount earned is there invested for 5 years at 16 %simple interest calculator the value of the investment at the end of 8 year
Explanation
We are asked to calculate the value of the investment at the end of 8 years
For the first part, we will find how much R2000 will yield after 3 years
[tex]\begin{gathered} A=P(1+rt) \\ P=2000 \\ r=10\text{ \% =0.1} \\ t=3 \\ \\ A=2000(1+0.1\times3) \\ A=2000(1+0.3) \\ A=2000(1.3) \\ \\ A=R2600 \end{gathered}[/tex]For the second part, we will have to know how much R2600 will yield after 5 years
[tex]\begin{gathered} P=2600 \\ t=5\text{ years} \\ r=16\text{ \%=0.16} \\ \\ A=2600(1+0.16(5)) \\ A=2600(1+0.8) \\ A=R4680 \\ \end{gathered}[/tex]At the end of the 8 years, the value of the investment will be R4680