The equation is given as
14 + 35 = 7 (2 + _)
We shall represent the dash as letter y (the unknown variable)
14 + 35 = 7 (2 + y)
49 = 7 (2 + y)
Divide both sides of the equation by 7 (to eliminate it from the right side of the equation)
Find x if g(x + 2) = 6
Notation scientific ad and subtract2.4 *10^5 + 0.5*10^5 =
We will operate as follows:
[tex]2.4\cdot10^5+0.5\cdot10^5=2.9\cdot10^5[/tex]What form is the following number in standard form or scientific notation? 0.0000000008
I need help solving the linear system I need to create an ordered pair
To create the ordered pairs you need to pic any value of x and look what the corresponding value fo y is.
For the point where both linear dunctions cross each other the value in the x-axis is x= 2 and the value in the y-axis is y=7
in looking for 450% of 80 I am not sure what I am looking for
Given the expression 450% of 80, we are to evealuate it.
You must know that of means multiplication
Hence the expression becomes;
[tex]450\text{\%}\times\text{ 80}[/tex]Simplify:
[tex]\begin{gathered} =\frac{450}{100}\times80 \\ =\text{ }\frac{45}{10}\times80 \\ =45\times8\text{ } \\ =\text{ 360} \end{gathered}[/tex]Hence 450% of 80 will give 360
Solve the following system of equations by graphing and state whether the system is dependent, independent, or consistent. 1/2x + 3/4y = 12x - 3y = 4
We have to solve the following system of equations:
[tex]\begin{gathered} \frac{1}{2}x+\frac{3}{4}y=1 \\ 2x-3y=4 \end{gathered}[/tex]We have to graph the equations and, as they are written in standard form, we are going to calculate the intercepts for both.
We will write the equations in slope-intercept form.
For the first equation we have:
[tex]\begin{gathered} \frac{1}{2}x+\frac{3}{4}y=1 \\ \frac{3}{4}y=-\frac{1}{2}x+1 \\ y=\frac{4}{3}(-\frac{1}{2}x+1) \\ y=-\frac{2}{3}x+\frac{4}{3} \end{gathered}[/tex]For the second equation we have:
[tex]\begin{gathered} 2x-3y=4 \\ 2x-4=3y \\ y=\frac{1}{3}(2x-4) \\ y=\frac{2}{3}x-\frac{4}{3} \end{gathered}[/tex]Both slopes are different, what means that the lines are not parallel and will intersect, so we already know that the system is independent.
Using the slopes and the y-intercepts, we can graph the equations as:
The solution to the system is the intersection point which is (2,0).
Answer:
The system is independent and its solution is (x,y) = (2,0)
Represent the following expressions as a power of the number a (a≠0): (a^5*a/a^-3)^-1
PLS HELP
We can simplify the given expression:
((a⁵*a)/(a⁻³) )⁻¹
To get:
a⁻⁹
How to simplify the expression?There are some properties we need to use:
xᵃ*xᵇ = xᵃ⁺ᵇ(xᵃ)ᵇ = xᵃ*ᵇx⁻ᵃ = 1/xᵃOur expression is:
((a⁵*a)/(a⁻³) )⁻¹
First we can simplify the numerator:
a⁵*a = a⁵⁺¹ = a⁶
((a⁶)/(a⁻³) )⁻¹
Using the third property we can also rewrite the denominator:
(1/a⁻³) = a³
Replacing that we get:
((a⁶)/(a⁻³) )⁻¹ = ((a⁶)*a³ )⁻¹ = (a⁶⁺³)⁻¹ = a⁻⁹
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Add the rational expressions and type your answer in simplest form. When typing your answers, type your terms with variables in alphabetical order without any spaces between your characters. \frac{\left(c+2\right)}{3}-\frac{\left(c-4\right)}{4} The numerator is AnswerThe denominator is Answer
Solve the operation between rationals, proceed as if they were numerical fractions:
[tex]\begin{gathered} \frac{c+2}{3}-\frac{c-4}{4} \\ \frac{4(c+2)-3(c-4)}{12} \\ \frac{4c+8-3c+12}{12} \\ \frac{c+20}{12} \end{gathered}[/tex]According to this:
The numerator is c+20
The denominator is 12
The diameter of a circle is 20 kilometers. What is the angle measure of an arc bounding a sector with area 10pi square kilometers?Give the exact answer in simplest form. ____°. (pi, fraction,)
The area of a circular sector is given by:
[tex]A=\frac{1}{4}\cdot\pi\cdot d^2\cdot\frac{\theta}{360}[/tex]Where:
π ≈ 3.14159
d = diameter of the circle
θ = angle of the circular sector
In our problem we have that:
[tex]\begin{gathered} A=10\cdot\pi\cdot km^2 \\ d=20\operatorname{km} \end{gathered}[/tex]And we need to find the value of the angle θ. So in order to solve the problem, we replace the given data in the formula of above:
[tex]\begin{gathered} A=\frac{1}{4}\cdot\pi\cdot d^2\cdot\frac{\theta}{360^{\circ}} \\ 10\cdot\pi\cdot km^2=\frac{1}{4}\cdot\pi\cdot(20\operatorname{km})^2\cdot\frac{\theta}{360^{\circ}} \end{gathered}[/tex]And now we solve for θ:
[tex]\begin{gathered} 10\cdot\pi\cdot km^2=\frac{1}{4}\cdot\pi\cdot400\cdot km^2\cdot\frac{\theta}{360^{\circ}} \\ 10=100\cdot\frac{\theta}{360^{\circ}} \\ 360^{\circ}\cdot\frac{10}{100}=\theta \\ \theta=36^{\circ} \end{gathered}[/tex]So the answer is that the angle of the circular sector is: 36°
What is next in sequence 2 and 1/4, 2 and 3/4, 3 and 1/4 come in 3 and 3/4,
Given:
[tex]2\frac{1}{4},2\frac{3}{4},3\frac{1}{4},3\frac{3}{4},.......[/tex]Required:
To find the next term in the given sequence.
Explanation:
Clearly the given sequence is in arithmetic.
Therefore,
[tex]a_5=a+(n-1)d[/tex]Here,
[tex]\begin{gathered} a=2\frac{1}{4} \\ =\frac{9}{4} \\ \\ n=5 \\ \\ d=2\frac{3}{4}-2\frac{1}{4} \\ =\frac{11}{4}-\frac{9}{4} \\ =\frac{2}{4} \end{gathered}[/tex][tex]\begin{gathered} a_5=\frac{9}{4}+(5-1)\frac{2}{4} \\ \\ =\frac{9}{4}+2 \\ \\ =\frac{17}{4} \\ \\ =4\frac{1}{4} \end{gathered}[/tex]Final Answer:
The next term in the sequence is 4 1/4.
Decide if the following biconditionalstatement is true or false:Two angles are congruent if and only ifthey are vertical angles.TrueFalse
Answer:
False
Explanation:
A biconditional statement is true if both conditionals are true.
• The statement: Two angles are congruent if they are vertical angles is ,True,.
,• The Statement: Two angles are congruent only if they are vertical angles is ,False,.
Therefore, the biconditional statement is false.
In the above graph of y = f( x ), find the slope of the secant line through the points ( -4, f( -4 ) ) and ( 1, f( 1 ) ).
Answer:
slope = 3 / 5
Explanation:
First, let us note from the graph that
[tex]f(-4)=1[/tex]and
[tex]f(1)=4[/tex]Therefore, the two points that lie on the secant line are
[tex]\begin{gathered} (-4,1) \\ (1,4) \end{gathered}[/tex]The slope of the line (the secant) passing through these two points is
[tex]slope=\frac{4-1}{1-(-4)}[/tex][tex]=\frac{3}{5}[/tex][tex]\boxed{slope=\frac{3}{5}\text{.}}[/tex]Hence, the slope of the secant is 3/5.
You must do this one by hand. No desmos!!! Find the solution to the following system of equations:
The equations are given
[tex]\begin{gathered} -5x+y=-5\ldots\ldots\ldots\ldots1 \\ -4x+2y=2\ldots\ldots\ldots\ldots\ldots\text{.}.2 \end{gathered}[/tex]ExplanationTo determine the coordinates of x and y by elimination method.
Divide equation 2 by 2.
[tex]\begin{gathered} -\frac{4x}{2}+\frac{2y}{2}=\frac{2}{2} \\ -2x+y=1\ldots\ldots\ldots\ldots..3 \end{gathered}[/tex]Now subtract equation 1 by 3,
[tex]\begin{gathered} (-5x+y+5)-(-2x+y-1)=0 \\ -5x+y+5+2x-y+1=0 \\ -3x+6=0 \\ x=2 \end{gathered}[/tex]Substitute the value of x in the equation 1.
[tex]\begin{gathered} -5\times2+y=-5 \\ -10+y=-5 \\ y=5 \end{gathered}[/tex]AnswerThe solution of the system of equations is [tex](2,5)[/tex]The correct option is A.
Find the value of r in the equation below.11 = = 12
A scientist uses the equation shown below to predict the future population of a species. In the equation, y represents the estimated population and t represents the number of years.
1200
Explanation:y represents the estimated population
t represents the number of years.
The equation that predicts the population after t years is given as:
[tex]y=150\times4^t[/tex]Substitute t = 3/2 into the equation
[tex]\begin{gathered} y=150\times4^{\frac{3}{2}} \\ y=150\times2^{2(\frac{3}{2})} \\ y=150\times2^3 \\ y=150\times8 \\ y=1200 \end{gathered}[/tex]The closest valuie to the value of y is 1200
1) 3 = x + 13I need help
We have the following:
[tex]3=x+13[/tex]solving:
[tex]\begin{gathered} x=3-13 \\ x=-10 \end{gathered}[/tex]The answer is -10
Fill in missing terms. Simplify any fractions. 3(t+1)=3T+1= Divide both sides by 3T= Subtract 1 from both sides
Given:
The equation is given as,
[tex]3(t+1)=3[/tex]The objective is to complete the missing terms.
Explanation:
In the first step, dividing both sides by 3,
[tex]\begin{gathered} \frac{3(t+1)}{3}=\frac{3}{3} \\ t+1=1 \end{gathered}[/tex]In the next step, subtract 1 from both sides.
[tex]\begin{gathered} (t+1)-1=1-1 \\ t=0 \end{gathered}[/tex]Hence, the result of first box is 1 and the second box is 0.
what is the slope of the line below?Show your work.
To be able to determine the slope, let's identify at least two points that pass through the graph and use it in the following formula:
[tex]\text{ Slope (m) = }\frac{y_2-y_1}{x_2-x_1}[/tex]Let,
Point A: x1, y1 = -4, -4
Point B: x2, y2 = 4, -4
We get,
[tex]\text{ Slope (m) = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{-4\text{ - (-4)}}{4\text{ - (-4)}}[/tex][tex]\text{ = }\frac{-4\text{ + 4}}{4\text{ + 4}}[/tex][tex]\text{ = }\frac{0}{8}\text{ = 0}[/tex][tex]\text{ Slope (m) = 0}[/tex]Therefore, the slope of the line is 0.
what are the solutions of the equation 2x ^ 2 equals 18 use a group of related function whose group answers the question
The given expression is :
[tex]2x^2=18[/tex]Simplify the equation for x :
[tex]2x^2=18[/tex]Divide both side by 2 :
[tex]\begin{gathered} \frac{2x^2}{2}=\frac{18}{2} \\ x^2=9 \end{gathered}[/tex]taking square root on both side :
[tex]\begin{gathered} x^2=9 \\ \sqrt[]{x^2}=\sqrt[]{9} \\ x=\pm3 \end{gathered}[/tex]Answer :
how do I find a unit rate for graphs
Unit rate of graph can be calculated by finding the slope of the graph or by dividing it's change in 'y' to the change in 'x' .
Generally, for linear graph unit rate can be calculated by finding it's slope but for curve graph it can be done by dividing it's change in 'y' to the change in 'x'.
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I need help with this practice problem solving My attempted answer is in the pic, though I am not sure if I am correct or not
Solution
To convert from polar coordinate to rectangular coordinate,
[tex]\begin{gathered} (r,\theta)\to(r\cdot\cos \theta,r\cdot\sin \theta) \\ \\ \Rightarrow(3\sqrt[]{5},-\frac{\pi}{8})\to(3\sqrt[]{5}\cdot\cos (-\frac{\pi}{8}),3\sqrt[]{5}\cdot\sin (-\frac{\pi}{8})) \\ \\ \Rightarrow(3\sqrt[]{5}\cdot\cos (-\frac{\pi}{8}),3\sqrt[]{5}\cdot\sin (-\frac{\pi}{8}))=(6.20,-2.57) \end{gathered}[/tex]X^2+15x+24y+10 what is the constant expression
The constant term in the given expression is 10.
The given polynomial is x²+15x+24y+10.
What is the polynomial?A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.
Constants are considered as algebraic expressions which only involve numbers.
In the given algebraic expression x²+15x+24y+10, the constant term is 10.
Hence, the constant term in the given expression is 10.
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When solving the radical equation 2 + 20 + 11 = I, the values I =-1 and I = 7 are obtained. Determine if either of these values is a solution of the radical equation. Select the correct two answers. (1 point) Since substituting I = -1 into the original equation resulted in a true statement, I= -1 is a solution to this equation. Since substituting I = 7 into the original equation resulted in a false statement, I = 7 is a not solution to this equation. Since substituting I=-l into the original equation resulted in a false statement, r=-1 is not a solution to this equation. Since substituting I=7 into the original equation resulted in a true statement, I=7 is a solution to this equation.
timothy and freda were asked to solve 675÷5 who is correct and why I can send you a picture would you like that ??
Since both came to the same answer using a different method, I would say that both are correct.
Find the midpoint for G(9, 7) , H(10, -7)
we have G(9, 7) , H(10, -7)
The formula to calculate the midpoint between two points is equal to
[tex]m(\frac{x1+x2}{2},\frac{y1+y2}{2}_{})[/tex]substitute the given coordinates
[tex]m(\frac{9+10}{2},\frac{7-7}{2}_{})[/tex][tex]m(9.5,0_{})[/tex]Suppose ABC is a right triangle of lengths a, b and c and right angle at c. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable.Find tan B when a=96 and c=100
To begin with, we will have to sketch the image of the question
To find the value of tan B
we will make use of the trigonometric identity
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]From the diagram given
[tex]\tan B=\frac{\text{opposite}}{\text{adjacent}}=\frac{b}{96}[/tex]Since the value of b is unknown, we will have to get the value of b
To do so, we will use the Pythagorean theorem
[tex]\begin{gathered} \text{hypoteuse}^2=\text{opposite}^2+\text{adjacent}^2 \\ b^2=100^2-96^2 \\ b=\sqrt[]{784} \\ b=28 \end{gathered}[/tex]Since we now know the value of b, we will then substitute this value into the tan B function
so that we will have
[tex]\tan \text{ B=}\frac{opposite}{adjecent}=\frac{b}{a}=\frac{28}{96}=\frac{7}{24}[/tex]Therefore
[tex]\tan \text{ B=}\frac{7}{24}[/tex]I’m trying to find out where the second point can be marked
ANSWER
First point = (0, 3)
Second point = (1, -1)
Third point = (2, -5)
Graph:
EXPLANATION
To plot a graph using the slope and the y-intercept, simply apply the following rules:
1. Evaluate the function at x = 0, to determine the y-intercept which was (0,3) from the question
2. Determine the slope by finding the change in y divided by change in x. This was -4 according to the question. Which could also be written as -4/1; that is, rise divided by run
3. Now, from the value (0, 3) we got in step 1, we move down by 4 units and then to the right by 1 unit. This will lead us to the Second point of (1, -1). Also from this point, we move down by 4 units and then to the right by 1 unit to get to the Third point of (2, -5). You may decide to continue this pattern if you want more points.
4. Draw a straight line joining the 3 points together.
Erika needs a test average of 85 or higher to make the honor roll. • There are four tests in the term. • Her first three test grades were 78, 80, and 88. Which inequality could be used to find what she needs to score on her fourth test, x, in order to make the honor roll?
Answer:
[tex]x\ge94[/tex]Explanation:
Average test score is expressed using the formula;
Average = Sum of the grades/Total number of test
Let x be the grade of the fourth test.
If Erika needs a test average of 85 or higher to make the honor roll, this can be expressed as;
[tex]\frac{78+80+88+x}{4}\ge85[/tex]Cross multiply
[tex]\begin{gathered} 78\text{ + 80 + 88 +x }\ge4\cdot85 \\ 246\text{ + x}\ge340 \end{gathered}[/tex]Subtract 246 from both sides
[tex]\begin{gathered} 246\text{ + x-246}\ge340-246 \\ x\ge94 \end{gathered}[/tex]Hence the inequality that could be used to find what she needs to score on her fourth test, in order to make the honor roll is
[tex]x\ge94[/tex]Let's Practice!1.Consider the following functions.f(x) = 3x2 + x + 2g(x) = 4x2 + 2(3x – 4)h(x) = 5(x2 - 1)a.lFind f(x) - g(x).b. Find g(x) - h(x).
To find the functions we need to remember that
[tex](f-g)(x)=f(x)-g(x)[/tex]Then
[tex]\begin{gathered} (f-g)(x)=(3x^2+x+2)-(4x^2+2(3x-4)) \\ =3x^2+x+2-(4x^2+6x-8) \\ =3x^2+x+2-4x^2-6x+8 \\ =-x^2-5x+10 \end{gathered}[/tex]Therefore
[tex]f(x)-g(x)=-x^2-5x+10[/tex]Similarly
[tex]\begin{gathered} (g-h)(x)=g(x)-h(x) \\ =4x^2+2(3x-4)-(5(x^2-1)) \\ =4x^2+6x-8-(5x^2-5) \\ =4x^2+6x-8-5x^2+5 \\ =-x^2+6x-3 \end{gathered}[/tex]therefore
[tex]g(x)-h(x)=-x^2+6x-3[/tex]TyR Match the name of each figure on the left with the best description on the right. a quadrilateral with rectangle one set of parallel sides a quadrilateral with four congruent sides trapezoid a quadrilateral with two pairs of parallel sides square a quadrilateral with four right angles rhombus a quadrilateral with four right angles and four congruent sides parallelogram
Parallelogram---->a quadrilateral with two pairs of parallel sides
Square----> a quadrilateral with four right angles and four congruent sides
Rectangle----> a quadrilateral with four right angles
Trapezoid----> . a quadrilateral with one set of parallel sides
Rhombus-----> a quadrilateral with four congruent sides
Answer: here
Step-by-step explanation:
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