The first step in solving an equation (isolating the variable ) = 10
First, Is to do common thing to the both sides either by adding , substracting or dividing
Example: 2a = 10
To isolate variable a
Divivde the both sides by the coefficient of a which is 2
2a / 2 = 10/2
a = 5
2. Which inverse operations would you use to solve the equation - 8 = -6?A. Add 8 to each side and then divide each side by 5.B. Add 8 to each side and then multiply each side by 5.C. Subtract 8 from each side and then multiply each side by 5.D. Multiply each side by 5 and then add 8 to each side.
Equation is m/5 - 8 = -67
Now find Inverse operation
theres an order of operations , first we must isolate variable
this means get a term in m
this is make adding 8 , because m/5 -8+8 = m/5, isolated m
now add 8 at right side , then -67 +8 = -59
Then equation becomes m/5 = -59
Now multiply by 5 , and get m = (-59)• 5 = -295
So then right option is B) Add and multiply
which of the following is the equation of the line that creates the x-axis?
The equation of the line that creates the x-ais is
y = 0
Option 1 is correct
Which of the following verifies that A COW is similar to APIG?Gw2115751Oс412PA. SAS theoremB. Similarity cannot be determined.C. SSS theoremD. AA postulateOkay
In the two triangles COW and PIG, take the ratio of sides as follows:
[tex]\begin{gathered} \frac{CW}{GP}=\frac{7}{21}=\frac{1}{3} \\ \frac{CO}{PI}=\frac{4}{12}=\frac{1}{3} \\ \frac{OW}{IG}=\frac{5}{15}=\frac{1}{3} \end{gathered}[/tex]From the ratio it follows that the ratio of sides of the two triangles is equal, hence the triangles are similar by SSS theorem.
Option C is correct.
Part A :Han's age increased by 21 is 64.Use the variable h to represent Han's age.Part B : The difference of Han's age and 17 is 54
Let the age of Han = h
Part A : Given : Han's age increased by 21 is 64.
So, the equation that represent the Han's age will be :
[tex]h+21=64[/tex]Solve for h :
[tex]\begin{gathered} h+21=64 \\ h=64-21 \\ \\ h=43 \end{gathered}[/tex]Part B : If The difference of Han's age and 17 is 54
So, the equation will be :
[tex]h-17=54[/tex]in this case h will be : h = 54 + 17 = 71
I need help ASAP PLEASE!!
The answer is option D becouse the order of the similar sides is not the same.
triangle UWV has the two small side and then the big side, and triangle JKL have the big side first and then the two smalls one
Answer:
what do you need help with
Step-by-step explanation:
If k = 7 cm and v = 14 cm, what is the area of the figure below?
[tex]\begin{gathered} \text{Area = }\frac{1}{2}\times d_1(AD)\times d_2(CD) \\ Area\text{ = }\frac{1}{2}\text{ x 22 x 14} \\ \text{ = 11 x 14 = 154cm}^2 \end{gathered}[/tex]
Which of the following is another way to describe the vector 5i - 12j? magnitude 13 and S67°W magnitude 13 and S23°W magnitude 13 and S67°E magnitude 13 and S23°E
Answer:
Magnitude 13 and S23°E
Explanation:
Given the vector:
[tex]5i-12j[/tex]We want to find its (a)magnitude (b)direction.
Given a vector ai+bj, its magnitude and direction are calculated using the formulas:
[tex]\begin{gathered} Magnitude:r=\sqrt{a^2+b^2} \\ Direction:\theta=\tan^{-1}(\frac{b}{a}) \end{gathered}[/tex]Therefore, for the given vector:
[tex]\begin{gathered} r=\sqrt{5^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}=13 \\ \theta=\tan^{-1}(-\frac{12}{5})=-67.4\degree\approx-67\degree \end{gathered}[/tex]However, from the diagram of the vector below:
Since the angle is in Quadrant IV:
[tex]-67.4\degree=360-67=293\degree=S23\degree E[/tex]The magnitude of the vector is 13, and its direction is S23°E.
The last option is correct.
Two triangles – triangle ABC and triangle ABD – sit inside a circle with a diameter, represented by the line AB, equal to 5. Which of the following statements regarding Angle 1 (angle CAB) and Angle 2 (angle ADB) is correct?Angle 1 is less than Angle 2Not enough information to solve the problemAngle 1 is equal to Angle 2
Given:
C = 90 °
D = 90 °
The sum of interior angles of a triangle = 180 °
m1 + 90 + m
1 + m
1 is less than 90
D = 90
Answer:
Angle 1 is less than Angle 2
which problem can be shown using the equation 2 x 8 equals 16 ?
Answer
Option C is correct.
A rabbit jumps 2 feet, A kangaroo jumps 16 feet. The kangaroo jumps 8 times as far as the rabbit.
2 × 8 = 16
Hope this Helps!!!
Given y = sin x - 5 the vertical shift is
Solution:
The equation is given below as
[tex]y=sinx-5[/tex]The parent function is given below as
[tex]y=sinx[/tex]The graph using a graphing calculator is given below as
The uncion in the question is given below as
[tex]y=sinx-5[/tex]A vertical shift is just a change in the y-value of each function. It is literally picking up the entire function or graph and moving the entire thing up or down. If it is moved up, we add to the y-value, if it is moved down, we subtract from the y-value.
Hence,
The vertical isshoift is 5 units DOWN
Graph each function using the techniques of shifting,compressing,, and or reflecting.Start with the graph of the basic function
we know that
The given zeros are
x=0
x=i
x=1+i
Remember that
the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P
so
the other zeros of the given polynomial f(x) are
x=-i
x=1-i
The polynomial in factored form is given by
[tex]f(x)=x(x-i)(x+i)(x-(1+i))(x-(1-i))[/tex]Simplify
[tex]\begin{gathered} f(x)=x(x^2-i^2)(x^2-x(1-i)-x(1+i)+(1-i^2)) \\ f(x)=x(x^2+1)(x^2-x+xi-x-xi+1+1) \\ f(x)=x(x^2+1)(x^2-2x+2) \end{gathered}[/tex]simplify
[tex]\begin{gathered} f(x)=(x^3+x)(x^2-2x+2) \\ f(x)=x^5-2x^4+2x^3+x^3-2x^2+2x \\ f(x)=x^5-2x^4+3x^3-2x^2+2x \end{gathered}[/tex]A local bank wanted to determine how much demand there was for the drive-upATM. The bank recorded the number of users of the drive-up ATM each day duringa particular week. The following numbers were recorded:What was the mean (average) number of drive-up ATM users per day? (Round youranswer to the nearest whole number, if necessary.)
ANSWER
[tex]\begin{equation*} \approx72\text{ users per day} \end{equation*}[/tex]EXPLANATION
To find the mean(average) number of drive-up ATM users per day, we have to find the sum of all the ATM users per day for that week and divide it by the number of days.
That is:
[tex]\begin{gathered} \frac{65+68+54+52+95+90+83}{7} \\ \\ \frac{507}{7} \\ \\ 72.43\approx72\text{ users per day} \end{gathered}[/tex]That is the answer.
Yolanda's penny bank is 3/4 full. After she removes 280 pennies, it is 1/2 full. How many pennies can Yolanda's bank hold?
We now that the bank is 3/4 full after she removes a part is 1/2 full, so the parte that she removes is
[tex]\frac{3}{4}-\frac{1}{2}=\frac{1}{4}[/tex]this means that 280 pennies is 1/4 of the bank. This means that the bank can hold for times this amount, this means 1120 pennies.
[tex]280\cdot4=1120[/tex]The answer is 1120 pennies.
Find the equation of the plane with normal (-5, -4, -1) which passes through (1, -4,-5).
Equation of the plane is
[tex]\begin{gathered} -5(x-1)-4(y+4)-(z+5)=0 \\ -5x-4y-z-16=0 \\ 5x+4y+z+16=0 \end{gathered}[/tex]33. Suppose that the scores on a statewide standardized test are normally distributed with a mean of 70 and a standard deviation of 5. Estimate the percentage of scores that were(a) between 65 and 75. %(b) above 80. %(c) below 55. %(d) between 65 and 80. %
ANSWER:
(a) 68.27%
(b) 2.28%
(c) 0.13%
(d) 81.85%
STEP-BY-STEP EXPLANATION:
We have the following information:
[tex]\begin{gathered} m=70 \\ sd=5 \end{gathered}[/tex]To calculate the probability we must calculate the z-value, which we do by means of the following formula:
[tex]Z=\frac{x-m}{sd}[/tex]Then, with the value of Z and the help of the normal distribution table, we can calculate the probability.
The table is as follows:
Now, we calculate the probability in each case using the information above.
(a)
between 65 and 75:
[tex]\begin{gathered} P(65\le x\le70)=\frac{65-70}{5}\le x\le\frac{75-70}{5} \\ P(65\le x\le70)=-1\le x\le1 \\ P=0.8413-0.1587=0.6827 \end{gathered}[/tex]68.27% between 65 and 75.
(b)
above 80:
[tex]\begin{gathered} P(x>80)=x>\frac{80-70}{5} \\ P(x>80)=x>2\rightarrow1-x<2 \\ P=1-0.9772=0.0228 \end{gathered}[/tex]2.28% above 80.
(c)
below 55:
[tex]\begin{gathered} P(x<55)=x<\frac{55-70}{5} \\ P(x<55)=x<-3 \\ P=0.0013 \end{gathered}[/tex]0.13% below 55.
(d)
between 65 and 80:
[tex]\begin{gathered} P(65\le x\le80)=\frac{65-70}{5}\le x\le\frac{80-70}{5} \\ P(65\le x\le80)=-1\le x\le2 \\ P=0.9772-0.1587=0.8185 \end{gathered}[/tex]81.85% between 65 and 80.
When Mason left his house in the morning, his cell phone battery was partially charged. Let BB represent the charge remaining in Mason's battery, as a percentage, tt hours since Mason left his house. The table below has select values showing the linear relationship between tt and B.B. Determine the charge of the battery when Mason left his house.
First, we will find the equation of the relationship between t and B.
A linear equation is of the form:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Where
(x1, y1) is a point the line goes through and (x2, y2) is another point the line goes through
Note: the independent variable here is t and the dependent is B. We will find the equation in the regular x and y variable, then change to t and B.
Let's take two points from the table:
[tex]\begin{gathered} (x_1,y_1)=(1,42) \\ \text{and} \\ (x_2,y_2)=(5,18) \end{gathered}[/tex]Now, we will substitute the points into the line equation and figure out the answer:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-42=\frac{18-42}{5-1}(x-1) \\ y-42=\frac{-24}{4}(x-1) \\ y-42=-6(x-1) \\ y-42=-6x+6 \\ y=-6x+6+42 \\ y=-6x+48 \end{gathered}[/tex]In terms of "t" and "B", we can write the equation as:
[tex]B=-6t+48[/tex]----------------------------------------------------------------------------------------------------------------
Now,
Plugging in t = 3 into the equation will give us the charge amount (B) after 3 hours:
[tex]\begin{gathered} B=-6t+48 \\ B=-6(3)+48 \\ B=-18+48 \\ B=30 \end{gathered}[/tex]Thus, Melanie's phone had 30% battery charge after 3 hours she left home.The solution for a(bx+7)=c is x=10. Give possible values for a,b and c
Given the equation;
[tex]\begin{gathered} a(bx+7)=c \\ Where; \\ x=10 \end{gathered}[/tex]We will begin by inserting the value of x into the left hand side of the equation as follows;
[tex]\begin{gathered} a(b(10)+7)=c \\ a(10b+7)=c \\ \text{If } \\ a=1,\text{ then;} \\ 10b+7=c \\ S\text{imilarly, if} \\ b=2,\text{ then} \\ 10(2)+7=c \\ 20+7=c \\ 27=c \end{gathered}[/tex]ANSWER:
Therefore, the possible values for a, b, and c are;
[tex]\begin{gathered} a=1 \\ b=2 \\ c=27 \end{gathered}[/tex]select all that applym
m∠c
m∠b + m∠d
Explanation:m∠a = 2m∠b
m∠a + m∠b = 90 degrees
2m∠b + m∠b = 90°
3m∠b = 90
m∠b = 90/3
m∠b= 30°
m∠a = 2m∠b
m∠a = 2(30°)
m∠a = 60°
m∠c + m∠b = 90°
m∠c + 30 = 90
m∠c = 90 - 30
m∠c = 60°
m∠c + m∠d = 90°
60 + m∠d = 90
m∠d = 90 - 60
m∠d = 30°
Acute angles are angles less than 90°.
m∠c is less than 90. Hence, it is an acute angle.
m∠a + m∠c = 60 + 60 = 120 > 90
m∠b + m∠d = 30 + 30 = 60 < 90. Hence, it is an acute angle
m∠a + m∠d = 60 + 30 = 90
m∠c + m∠d = 60 + 30 = 90
1.3.AP-3Find the midpoint of the line segment joining the points (6,4) and (-4,- 4).The midpoint is DI(Type an ordered pair. Use integers or simplified fractions for any numbers in the express
The mid point is caculated from the formula,
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Therefore the mid point is
[tex](\frac{6-4}{2},\frac{4-4}{2})=(1,0)[/tex]Suppose that the mean and standard deviation of the scores in a Statistics exam are 75 and 9.5 respectively. What minimum score should a student obtain to be a part of the top 2.5%? Round answers to 2 decimal places.
The mean and standard deviation of the scores are 75 and 9.5 respectively.
The z-score is a means to find the probability of getting a particular score. This is calculated to be:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the score, μ is the mean, and σ is the standard deviation.
To be a part of the top 2.5 percent, the probability is:
[tex]P=\frac{2.5}{100}=0.025[/tex]The z-score for this probability, that is, P
Find the mean, median, and mode of the following problem.The heights (in centimeters) of 7 students in a class are 152, 170, 165, 168, 159, 160, and 152. Find the mean, median, and mode of the heights.
Given
The heights of 7 students in a class are 152, 170, 165, 168, 159, 160, and 152.
Find
Mean , Median and Mode
Explanation
Mean = Sum of observations / Number of observation
so ,
[tex]\begin{gathered} Mean=\frac{152+170+165+168+159+160+152}{7} \\ \\ Mean=\frac{1126}{7} \\ \\ Mean=160.857\approx160.86 \end{gathered}[/tex]to find median , we need to arrange data in an increasing order
so ,
152 , 152 , 159 , 160 , 165 , 168 and 170
there are 7 students . so
median =
[tex]\begin{gathered} \frac{number\text{ of terms + 1}}{2} \\ \frac{7th+1}{2} \\ \\ 4th\text{ term} \end{gathered}[/tex]so, median = 160
now mode ,
mode is that number which occurs most times.
so , 152 occurs two times.
hence , mode = 152
Final Answer
Therefore , Mean = 160.86 , Median = 160 and Mode = 152
I need to convert 532 mm squared to cm square
5.32 cm²
Explanations:1 mm = 0.1 cm
1 mm² = 0.1² cm²
1 mm² = 0.01 cm²
532 mm² = 532 x 0.01 cm²
532 mm² = 5.32 cm²
Fill in the blanks to make the equation true. (x…)(x…)=x^2-4x-32
Given
[tex]x^2-4x-32[/tex]Factor the expression
[tex]\begin{gathered} (x^2+4x)+(-8x-32) \\ \text{Factor x and -8} \\ x(x+4)-8(x+4) \end{gathered}[/tex]Factor the common term x + 4
[tex](x+4)(x-8)[/tex]Answer:
[tex](x+4)(x-8)=x^2-4x-32[/tex]Consider the line 2x +5y = -2.(a) What is the slope of a line parallel to this line?(b) What is the slope of a line perpendicular to this line?
ANSWER:
(a) Parallel slope = -2/5
(b) Perpendicular slope = 5/2
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]2x+5y=-2[/tex]To determine the slope, we solve for y, like so:
[tex]\begin{gathered} 5y=-2-2x \\ y=-\frac{2}{5}-\frac{2}{5}x \end{gathered}[/tex]The slope is the quotient of x, so the slope of the line is -2/5
(a)
When two lines are parallel the slope is the same.
Therefore :
m = -2/5
(b)
Now, when the lines are perpendicular, the product of both slopes is equal to -1, just like this:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ -\frac{2}{5}\cdot m_2=-1 \\ m_2=\frac{5}{2} \end{gathered}[/tex](a) Parallel slope = -2/5
(b) Perpendicular slope = 5/2
complete the remainder for the table of the given function rule y equals x / 4 + 7
y = x/4 +7
To complete the y values, we have to replace the x values in the equation:
x=-4
y= (-4)/4 +7 = -1+7 =6
x=0
y= 0/4 +7 = 0+7= 7
x=4
y = 4/4 +7 = 1 +7 = 8
x= 8
y= 8/4+7 = 2+7 = 9
Go step by step to reduce the radical. V252 VIVO You must answer all questions above in order to submit. pe here to search
Given:
[tex]\sqrt[]{252}[/tex]Let's reduce the radical number.
We have:
Factor 36 out of 252:
[tex]\begin{gathered} \sqrt[]{36(7)} \\ \\ =\sqrt[]{36}\text{ }\sqrt[]{7} \end{gathered}[/tex]Rewrite 36 as 6²:
[tex]\begin{gathered} \sqrt[]{6^2}\text{ }\sqrt[]{7} \\ \\ =6\sqrt[]{7} \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} =\sqrt[]{36\text{ }}\text{ }\sqrt[]{7} \\ \\ =6\text{ }\sqrt[]{7} \end{gathered}[/tex]Are y=7/3x+6 and y=-3/7x+4 lines parallel perpendicular or neither?I just need a brief explanation with the answer
Step 1: Theorem
Two lines are perpendicular if the product of their slope is equal to -1.
Two lines are parallel if their slope is equal.
Step 2:
[tex]\begin{gathered} \text{Write the general equation of a line in slope-intercept form} \\ y\text{ = mx + c} \\ \text{m = slope} \end{gathered}[/tex]Step 3:
Determine the slope from each equation
[tex]\begin{gathered} y\text{ = }\frac{7}{3}\text{ x + 6} \\ m_1\text{ = }\frac{7}{3} \\ y\text{ = }\frac{-3}{7}x\text{ + 4} \\ m_2\text{ = }\frac{-3}{7} \end{gathered}[/tex]Step 4: Determine if the two lines are parallel or perpendicular.
[tex]\begin{gathered} m_1\text{ }\ne m_2\text{ hence the lines are not parallel} \\ m_1\text{ }\times m_2\text{ = }\frac{7}{3}\text{ }\times\text{ }\frac{-3}{7}\text{ = }\frac{-27}{27}\text{ = -1} \end{gathered}[/tex]Final answer
Since the product of the two lines is equal to -1, hence, the two lines are perpendicular.
Perpendicular
Your answer Write an equation PERPENDICULAR to y =-5/2x + 15 that passes through the point (-5, 4).* +++
Two lines are perpendicular if the multiplication of their slopes is equal to -1.
In y =-5/2x + 15 the slope is -5/2, then the slope (m) of the new line is:
-5/2*m = -1
m = -1*2/(-5)
m = 2/5
The slope-intercept form of a line is:
y =mx + b
where m is the slope and b is the y-intercept. Replacing with m = 2/5 and the point (-5,4) into the equation, we get:
4 = 2/5*(-5) + b
4 = -2 + b
4+2 = b
6 = b
Then, the equation is: y = 2/5x + 6
2 The temperature in Anchorage, Alaska, at6:00 A.M. was 2°C. If the temperature drops2 degrees each hour, what is the temperaturein degrees Celsius at 2:00 P.M.?
In order to solve this problem, we need to use proportions.
First, let's find the number of hours from 6:00 A.M. to 2:00 P.M.:
from 6 am to 12 pm, there are 6 hours (12 - 6 = 6)
from 12 pm to 2 pm, there are 2 hours more, since after 12 pm comes 1 pm, then 2 pm.
Thus, from 6:00 A.M. to 2:00 P.M. there are 8 hours (6 + 2 = 8).
Now, since the temperature drops 2 degrees Celsius each hour, after 8 hours it will drop:
(2ºC) * 8 = 16ºC
Finally, to find the final temperature, we subtract 16ºC from the initial temperature (2ºC):
2ºC - 16ºC = -14ºC
Therefore, at 2:00 P.M., the temperature is -14ºC.
Which trig function would you use to solve each 1?
Step 1. The first step is to remember the definitions for the sine, cosine, and tangent for right triangles:
[tex]\begin{gathered} \cos A=\frac{\text{adjacent side}}{\text{hypotenuse}} \\ \sin A=\frac{\text{opposite side}}{\text{hypotenuse}} \\ \tan A=\frac{\text{opposite side}}{\text{adjacent side}} \end{gathered}[/tex]Where A is the angle, the opposite side is the opposite side to this angle, the adjacent side is the side adjacent to this angle, and the hypotenuse is the side opposite to the 90° angle.
This is all summarized in the following diagram:
Step 2. For the first triangle, we know one angle, we are looking for the opposite side, and we also know the adjacent side.
The trigonometric function that relates all of these three: Angle, opposite side, and the adjacent side, is the tangent:
[tex]\tan 32=\frac{x}{13}[/tex]Step 3. For the second triangle, we know the angle, the hypotenuse of 11, and we are looking for the adjacent side x.
The trigonometric function that relates these three: angle, hypotenuse and the adjacent side is the cosine:
[tex]\cos 60=\frac{x}{11}[/tex]Step 4. For the third
Answer:
First triangle: Tangent
Second triangle: Cosine