Given the equation:
[tex]3+\sqrt[\placeholder{⬚}]{3x-5}=x[/tex]Isolating the square root:
[tex][/tex]which of tje following proportion are true16/28=12/216/16=4/1430/40=24/3510/15=45/30
Notice that:
1)
[tex]\frac{16}{28}=\frac{4\cdot4}{7\cdot4}=\frac{4}{7}=\frac{4\cdot3}{7\cdot3}=\frac{12}{21}\text{.}[/tex]2)
[tex]\frac{6}{16}=\frac{2\cdot3}{2\cdot8}=\frac{3}{8}\ne\frac{2}{7}=\frac{2\cdot2}{2\cdot7}=\frac{4}{14}\text{.}[/tex]3)
[tex]\frac{30}{40}=\frac{10\cdot3}{10\cdot4}=\frac{3}{4}\ne\frac{2}{3}=\frac{12\cdot2}{12\cdot3}=\frac{24}{36}.[/tex]4)
[tex]\frac{10}{15}=\frac{5\cdot2}{5\cdot3}=\frac{2}{3}\ne\frac{9}{10}=\frac{5\cdot9}{5\cdot10}=\frac{45}{50}.[/tex]Answer: The only proportion that is true is the first one.
A regular plot of land is 70 meters wide by 79 meters long. Find the length of the diagonal and, if necessary, round to the nearest tenth meter
Given :
The length is given l=79 m and width is given w=70m.
Explanation :
Let the length of diagonal be x.
To find the length of diagonal , use the Pythagoras theorem.
[tex]x^2=l^2+w^2[/tex]Substitute the values in the formula,
[tex]\begin{gathered} x^2=79^2+70^2 \\ x^2=6241+4900 \\ x^2=11141 \\ x=\sqrt[]{11141} \\ x=105.55m \end{gathered}[/tex]Answer :
The length of the diagonal is 105.6 m.
The correct option is D.
1 + xThe function g is defined by g(x)=7+2xFind g(a+5).
The function is given as:
[tex]g(x)=\frac{1+x}{7+2x}[/tex]We need to find the expression g(a + 5).
This means that we are going to plug in "a + 5" into "x" of the function. So, substituting, it gives us,
[tex]\begin{gathered} g(x)=\frac{1+x}{7+2x} \\ g(a+5)=\frac{1+(a+5)}{7+2(a+5)} \end{gathered}[/tex]Now, we need to simplify the expression. Steps are shown below:
[tex]\begin{gathered} g(a+5)=\frac{1+(a+5)}{7+2(a+5)} \\ =\frac{1+a+5}{7+2a+10} \\ =\frac{6+a}{17+2a} \end{gathered}[/tex]Answer[tex]\frac{6+a}{17+2a}[/tex]If ST = x + 4, TU = 10, and SU = 9x + 6, what is ST?
Given:
[tex]\begin{gathered} ST=x+4 \\ \\ TU=10 \\ \\ SU=9x+6 \end{gathered}[/tex]Find-:
The value of "x."
Explanation-:
The line of property
[tex]SU=ST+TU[/tex]Put the value is:
[tex]9x+6=x+4+10[/tex][tex]\begin{gathered} 9x+6=x+14 \\ \\ 9x-x=14-6 \\ \\ 8x=8 \\ \\ x=\frac{8}{8} \\ \\ x=1 \end{gathered}[/tex]So, the value of "x" is 1.
Kevin went for a drive in his new car. He drove for 377.6 miles at a speed of 59 miles per hour. For how many hours did he drive ?
We know that the average speed (v) can be calculated as the quotient between the distance D and the time t.
As v = 59 mi/h and D = 377.6 mi., we can calculate the time as:
[tex]v=\frac{D}{t}\longrightarrow t=\frac{D}{v}=\frac{377.6\text{ mi}}{59\text{ mi/h}}=6.4\text{ h}[/tex]Answer: he drove for 6.4 hours.
7/8 = X/16 X=how do I solve it
x= 14
1) Let's solve this equation considering that we're dealing with two ratios.
Then we can cross multiply and simplify them this way:
[tex]\begin{gathered} \frac{7}{8}=\frac{x}{16} \\ 8x=16\cdot7 \\ \frac{8}{8}x=\frac{16\cdot7}{8} \\ x=2\cdot7 \\ x=14 \end{gathered}[/tex]2) So the answer is x= 14
1 5/6 - (-2 4/5)[tex]1 \frac{5}{6} - ( - 2 \frac{4}{5} )[/tex]
We have the following:
[tex]1\frac{5}{6}-(-2\frac{4}{5})[/tex]solving:
[tex]\begin{gathered} 1\frac{5}{6}=\frac{11}{6} \\ 2\frac{4}{5}=\frac{14}{5} \\ \frac{11}{6}+\frac{14}{5}=\frac{11\cdot5+14\cdot6}{30}=\frac{55+84}{30}=\frac{139}{30} \\ \frac{139}{30}=4\frac{19}{30} \end{gathered}[/tex]The answer is 4 19/30
Convert Following expression in radical form into an exponential expression in rational form, multiply and simplify then divide you do not need to evaluate just put in simplest form
9.
[tex]\frac{\sqrt[]{5^7}\cdot\sqrt[]{5^6}}{\sqrt[5]{5^3}}[/tex]Using the following properties:
[tex]\begin{gathered} x^a\cdot x^b=x^{a+b} \\ a^{-x}=\frac{1}{a^x} \\ \sqrt[z]{x^y}=x^{\frac{y}{z}} \end{gathered}[/tex][tex]\frac{\sqrt[]{5^7}\cdot\sqrt[]{5^6}}{\sqrt[5]{5^3}}=5^{\frac{7}{2}}\cdot5^{\frac{6}{2}}\cdot5^{-\frac{3}{5}}=5^{\frac{7}{2}+\frac{6}{2}-\frac{3}{5}}=5^{\frac{59}{10}}[/tex]Answer:
5 7/5
Step-by-step explanation:
As you can see there is a divisions sign so you will start there.
The square root of 5^6 will turn into 5 6/2 divided by 5 3/5.
You want to find the LCD for the denominator. That will be 10, 6 divided by 3 equals 2 so you will have 5 7/2 times 5 2/10. You then change the two to a 10 and multiply the 7 and 2 which will become 5 14/10.
Once simplified the answer is 5 7/5.
Hope this helps :)
Hi I need help with this question please thank you!
To answer this question we will factorize each term.
Notice that:
[tex]20x^4y=5xy(4x^3),[/tex][tex]10x^3y^3=5xy(2x^2y^2),[/tex][tex]5xy^2=5xy(y).[/tex]Therefore, the greatest common factor of the terms is:
[tex]5xy\text{.}[/tex]Answer:
[tex]5xy\text{.}[/tex]
I need to find out which ones are true and which ones I have to change to get the answers correct please help me.
Solution
- In order to solve this question, we need to apply the following rules:
[tex]\begin{gathered} Given \\ f(x)=ax^2+bx+c \\ \\ |a|>1:\text{ } \\ \text{ The graph gets narrower the larger }|a|\text{ gets} \\ \\ 0<|a|<1: \\ \text{ The graph gets wider the closer }|a|\text{ is to zero} \\ \\ a<0: \\ \text{ The graph has a peak} \\ \\ a>0: \\ \text{ The graph has a valley} \end{gathered}[/tex]- Applying this rule, we can proceed to solve this question.
- Based on these rules above, we can select the correct options as follows:
PLESSS HELP I NEED HELP PLESS HELP I NEEED HELP
For this exercise you need to remember that the area of a triangle can be calculated with the following formula:
[tex]A=\frac{bh}{2}[/tex]Where "b" is the base of the triangle and "h" is the height of the triangle.
Analyzing the information given in the exercise, you can identify that, in this case:
[tex]\begin{gathered} b=x=11units \\ h=7units \end{gathered}[/tex]Then, knowing these values, you can substitute them into the formula and then evaluate, in order to find the area of the triangle. This is:
[tex]\begin{gathered} A=\frac{(11units)(7units)}{2} \\ \\ A=\frac{77units^2}{2} \\ \\ A=38.5units^2 \end{gathered}[/tex]The answer is: Option B.
Determine if each of the following relationships form a function.(1,1), (3,2), (5,4), (-9,6)
Determine if each of the following relationships form a function.
(1,1), (3,2), (5,4), (-9,6)
we know that
A relationship between x and y form a function, if for one value of x there is only one value of y
In this problem we have that
for one value of x there is only one value of y
therefore
Yes, form a function
HEL LE Maria has 36 episodes of Grey's Anatomy to watch with her friends. They watch 3 episodes each day. Which of the following equations represents the number days, d, it took for them to have 21 episodes left? 0210 - 3 = 36 O 21 - 3d = 36 36 - 3d = 21 36 + 3d = 21 LE
Total episodes: 36
Episodes watched per day: 3
Number of days: d
To represents the number of days, d, it will take for them to have 21 episodes left:
Subtract the episodes watched per day (3d) to the total episodes (36), and that expression must be equal to 21:
36-3d=21
What is the volume of this rectangular prism? 5/3 cm 1/4 cm 3/2 cm
The volume of the prism can be determined as,
[tex]\begin{gathered} V=\frac{5}{3}cm\times\frac{1}{4}cm\times\frac{3}{2}cm \\ V=\frac{5}{8}cm^3 \end{gathered}[/tex]Thus, the required volume is 5/8 cubic centimeters.
Write an equation for the line that contains (-32, -12) and is perpendicularto the graph -8x + 10y = 40Can anyone that KNOWS the answer help?
The first step is finding the slope of the equation -8x + 10y = 40.
To do so, let's put this equation in the slope-intercept form: y = mx + b, where m is the slope.
So we have:
[tex]\begin{gathered} -8x+10y=40 \\ -4x+5y=20 \\ 5y=4x+20 \\ y=\frac{4}{5}x+4 \end{gathered}[/tex]Then, since the line we want is perpendicular to this given line, their slopes have the following relation:
[tex]m_2=-\frac{1}{m_1}[/tex]So, calculating the slope of the line, we have:
[tex]m_2=-\frac{1}{\frac{4}{5}}=-\frac{5}{4}[/tex]Finally, our equation has the point (-32, -12) as a solution, so we have:
[tex]\begin{gathered} y=mx+b \\ y=-\frac{5}{4}x+b \\ -12=-\frac{5}{4}\cdot(-32)+b \\ -12=-5\cdot(-8)+b \\ -12=40+b \\ b=-12-40 \\ b=-52 \end{gathered}[/tex]So our equation is y = (-5/4)x - 52
Below is a model of the infield of a baseball stadium. How long is each side of the field Hurry pleaseee
We have the following:
[tex]\begin{gathered} A=s^2 \\ s=\sqrt{A} \end{gathered}[/tex]A = 81, replacing:
[tex]A=\sqrt{81}=9[/tex]therefore, each side measures 9 in
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
Third-degree, with zeros of -3,-1, and 2 and passes through the point (3,6)
Since the polynomial must have zeroes at x=-3, x=-1, x=2, then, we can write it as a combination of the factors (x+3), (x+1), (x-2):
[tex]p(x)=k(x+3)(x+1)(x-2)[/tex]The constant k will help us to adjust the value of the polynomial when x=3:
[tex]\begin{gathered} p(3)=k(3+3)(3+1)(3-2) \\ =k(6)(4)(1) \\ =24k \end{gathered}[/tex]Since p(3) must be equal to 6, then:
[tex]\begin{gathered} 24k=6 \\ \Rightarrow k=\frac{6}{24} \\ \Rightarrow k=\frac{1}{4} \end{gathered}[/tex]Therefore, the following polynomial function has zeroes at -3, -1 and 2, and passes through the point (3,6):
[tex]p(x)=\frac{1}{4}(x+3)(x+1)(x-2)[/tex]ubtract. - B the model to help
As you can see in the model
[tex]\frac{1}{2}=\frac{4}{8}[/tex]Then
[tex]\frac{5}{8}-\frac{1}{2}=\frac{5}{8}-\frac{4}{8}=\frac{5-4}{8}=\frac{1}{8}[/tex]This is the same as if you removed 4 pieces of 1/8 from the 5 pieces of 1/8, resulting in 1 piece of 1/8.
Therefore, the result of the subtraction is
[tex]\frac{1}{8}[/tex]Hi , i need help with this question: what is the anwser to the division problem. 9÷4590
Problem
what is the anwser to the division problem.
9÷4590
Solution
We have the following number given:
[tex]\frac{9}{4590}[/tex]The first step would be simplify the fraction and we can divide both numbers by 9 and we got:
[tex]\frac{9}{9}=1,\frac{4590}{9}=510[/tex]So then our fraction becomes:
[tex]\frac{1}{510}[/tex]And if we convert this into a decimal we got 0.00196.
What are the solutions to the following system?{-2x+y=-5y=-3x2 + 50 (0, 2)O (1, -2)o (12.-1) and (- 12.-1):o 15.-10) and (-75-10
Answer:
[tex](\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}[/tex]Explanation:
Here, we want to solve the system of equations
Since we have y in both equations, let us start by rewriting the second equation to look like the first
We have that as:
[tex]\begin{gathered} -2x^2+y\text{ = }-5 \\ y+3x^2\text{ = 5} \end{gathered}[/tex]Subtract equation ii from i
We have it that:
[tex]\begin{gathered} -5x^2=\text{ -10} \\ 5x^2=10 \\ x^2=\text{ 2} \\ \\ x\text{ = }\pm\sqrt[]{2} \end{gathered}[/tex]when x = positive root 2, we have it that:
[tex]\begin{gathered} -2x^2+y\text{ = -5} \\ -2(\sqrt[]{2\text{ }})^2+y\text{ = -5} \\ -4+y\text{ = -5} \\ y\text{ = -5+4} \\ y\text{ = -1} \end{gathered}[/tex]when x = negative root 2:
We will still get the same answer as the square of both returns the same value
Thus, we have the solution to the system of equations as:
[tex](\sqrt[]{2\text{ }},-1)\text{ and (-}\sqrt[]{2\text{ }}\text{ ,-1)}[/tex]Evaluate with no calculator sin(sin^-1(3/8))
Since the sine ratio is opposite side/hypotenuse
Then in
[tex]\sin (\sin ^{-1}\frac{3}{8})[/tex]This means the angle has opposite side 3 and hypotenuse 8 in a right triangle
Then use this rule to evaluate without a calculator
[tex]\sin (\sin ^{-1}\frac{a}{b})=\frac{a}{b}[/tex]Because sin will cancel sin^-1
[tex]\sin (\sin ^{-1}\frac{3}{8})=\frac{3}{8}[/tex]The answer is 3/8
Evaluate each expression using the graphs of y=f(x) and y = g(x) shown below.(a) (gof)(-1) (b) (gof)(0) (c) (fog) - 1) (d) (fog)(4)
Answer:
a) 5
b) 6
c) -2
d) -3
Explanation:
Given:
a) From the graph, we can see that f(-1) = 1 and g(1) = 5, so we'll have that;
[tex](g\circ f)(-1)=g(f(-1))=g(1)=5[/tex]b) From the graph, we can notice that f(0) = 0, g(0) = 6, so we'll have that;
[tex](g\circ f)(0)=g(f(0))=g(0)=6[/tex]c) From the graph, we can notice that g(-1) = 4 and f(4) = -2, so we'll have that;
[tex](f\circ g)(-1)=f(g(-1))=f(4)=-2[/tex]d) From the graph, we can see that g(4) = 3 and f(3) = -3, so we'll have that;
[tex](f\circ g)(4)=f(g(4))=f(4)=-3[/tex]General MathematicsProblem:What interest rate would yield ₱1,200 interest on ₱10,000 in 2 years?
Answer
Interest rate = 6%
Explanation
From the information given in the question,
Interest, I = ₱1,200
Principal, P = ₱10,000
Time, T = 2 years
Interest rate, R = ?
Using Simple Interest formula:
[tex]I=\frac{PRT}{100}[/tex]Since I, P and T are know, we shall substitute these values into the formula to get R.
[tex]\begin{gathered} 1200=\frac{10000\times R\times2}{100} \\ 1200=200R \\ \text{Divide both sides by 200} \\ \frac{1200}{200}=\frac{200R}{200} \\ R=6 \end{gathered}[/tex]Therefore, the interest rate is 6%
y = 3x ÷ 9 and x = -6 what is the output?
y = 3x ÷ 9 and x = -6
y = 3(-6) ÷ 9 = -18 ÷ 9 = -2
y = -2
Answer:
y = -2
Which of the following statements about the Real Number System is always true?A Rational numbers include irrational numbers.B A number that is an integer is also a whole number and a natural number.C A number that is a whole number is also an integer and a rational Fimber.Tmber.D A number that is a whole numbers is also a natural number.
C
1) Let's draw a sketch to better understand this:
2) So, based on that we can say that
A number that is a Whole number is also an integer and a Rational Number.
Whole numbers are counting number with the 0 included
Integers numbers are whole numbers and the negative numbers
Rational numbers are any number that can be written as a ratio like 2, (2/1), 3/2, 5, 6/7, etc.
So whole numbers are integer numbers and rational ones simultaneously.
For example 2, 3, etc.
Drag and drop numbers into the equation to complete the equation of the line in slope-intercept form.The line passes through (8, 19) and (5, 1).
we are given two points
(8,19) and (5,1)
firstly, we need to calculate the slope
slope = y2 - y1 / x2 - x1
from the points
x1 = 8, y1 = 19, x2 = 5, y2 = 1
slope = 1 -19 / 5 - 8
slope = -18/-3
negative will cancel each other
slope = 18/3
slope = 6
slope intercept equation is
y - y1 = m(x - x1)
m = slope = 6
y1 = 19 and x1 = 8
y - 19 = 6(x - 8)
open the parentheses
y - 19 = 6*x - 6*8
y - 19 = 6x - 48
make y the subject of the formula
y = 6x - 48 + 19
y = 6x - 29
Graph the following:X>y^2 + 4y
Solution:
Given the inequality;
[tex]x>y^2+4y[/tex]The graph of inequality without an equal sign is done with broken lines,
The y-intercept is;
[tex]\begin{gathered} 0>y^2+4y \\ \\ 0>y(y+4) \end{gathered}[/tex]Thus, the graph is;
Part A: Show all work to solve the quadratic equation x2 − 12x + 35 = 0 by factoring.Part B: Using complete sentences, explain what the solutions from Part A represent on the graph.
Answer:
A) Notice that:
[tex]\begin{gathered} x^2-12x+35=x^2+(-5-7)x+(-5)(-7) \\ =x^2-5x-7x+(-5)(-7)=x(x-5)-7(x-5) \\ =(x-7)(x-5)\text{.} \end{gathered}[/tex]Therefore:
[tex]x^2-12x+35=0\text{ if and only if x=7 or x=5.}[/tex]B) The solutions from part A represent the x-coordinates of the x-intercepts of the graph of the function
[tex]f(x)=x^2-12x+35.[/tex]The hallway of an apartment building is 44 feet long
and 6 feet wide. A landlord has 300 square feet of carpet. Does she have
enough carpet to cover the hallway? Explain.
Answer:
Yes, there is enough carpet to cover the hallway. We know this because the area of the floor is shown as 44 times 6, which equals 264 feet. With 300>264, there is enough feet of carpet to cover
Step-by-step explanation:
44 times 6 = 264