Answers
Given the graph of an inequality, you can identify that the boundary has the form of a "V". Therefore, you can identify that it is an Absolute Value Inequality.
By definition, an Absolute Value Equation written in Vertex Form is:
[tex]y=a|x-h|+k[/tex]Where "h" is the x-coordinate of the Vertex, and "k" is the y-coordinate of the Vertex. If "a" is negative, the graph opens down and if it is positive, the graph opens up.
In this case, the graph opens up, and you can identify in the graph that the Vertex is:
[tex]\mleft(-1,0\mright)[/tex]You can also identify that the boundary is formed by solid lines and the shaded region is below the boundary. This indicates that the inequality has this form:
[tex]\begin{gathered} y\leq a|x-(-1)| \\ \\ y\leq a|x+1| \end{gathered}[/tex]Notice that this inequality is given in the Answer choices:
[tex]y\le\mleft|x+1\mright|[/tex]In order to check it, let's choose two points on the shaded region:
[tex]\mleft(-2,-1\mright),(2,-2)[/tex]Substitute the coordinates into the inequality and evaluate. If they satisfy the inequality, then the are solutions to it:
- For the first point:
[tex]\begin{gathered} -1\le|-2+1| \\ \\ -1\le1\text{ (True)} \end{gathered}[/tex]- For the second point:
[tex]\begin{gathered} -2\le|2+1| \\ \\ -2\le3\text{ (True)} \end{gathered}[/tex]Hence, the answer is: Second option.
Related Questions
In ∆JKL, j=7.9inches, k=2 inches and l =9.8. find the measure of
Answers
By cosine rule,
[tex]\cos K=\frac{j^2+l^2-k^2}{2jl}[/tex]Where j = 7.9 inch, k = 2 inch and l = 9.8
[tex]\cos K=\frac{7.9^2+9.8^2-2^2}{2\times7.9\times9.8}=\frac{154.45}{154.84}=0.99748[/tex][tex]\begin{gathered} \cos K=0.99748 \\ K=\cos ^{-1}0.99748=4.067\approx4^o \end{gathered}[/tex]Solution: The measure of angle K is 4 degrees
Find the perimeter of the figure below. Notice that one side length is not given.Assume that all intersecting sides meet at right angles.Be sure to include the correct unit in your answer.8 ftftft2ft9 ft151Х5?7 ft14 ftCheck2020 MCG Edus
Answers
We are asked to find the perimeter of the given figure.
Recall that the perimeter is basically the sum of all the sides in the figure.
But the length of one side is missing that can easily be found.
Let me draw the figure to illustrate the idea.
Step 1: Find the length of the missing side
As you can see in the above figure,
We found the length of the missing side by subtracting the length of 9 ft from the 14 ft, which will give us the length of the missing side drawn in red color.
Step 2: Find the parameter of the figure
Now we can proceed to find the perimeter of the figure.
Add up the lengths of each side
[tex]\begin{gathered} Perimeter=5ft+15ft+14ft+7ft+9ft+8ft \\ Perimeter=58ft \end{gathered}[/tex]Therefore,
The length of the missing side is 5 ft
The perimeter of the figure is 58 ft
Note:
The unit of the perimeter of the rectangle is ft
Whereas the unit of the area of the rectangle is ft^2
Rewrite all the equation using the inverse operation.I WILL SEND PICTURES OF PROBLEM
Answers
Explanation
Step 1
[tex]\begin{gathered} a+15=32 \\ \text{subtract 15 in both sides} \\ a+15-15=32-15 \\ a=17 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} b-12=75 \\ \text{add 12 in both sides} \\ b-12+12=75+12 \\ b=87 \end{gathered}[/tex]Step 3
[tex]\begin{gathered} 9x=90 \\ we\text{ n}eed\text{ isolate x, so divide both sides by 9} \\ \frac{9x}{9}=\frac{90}{9} \\ x=10 \end{gathered}[/tex]Step 4
[tex]\begin{gathered} \frac{x}{6}=7 \\ \text{Multiply both sides by 6} \\ \frac{x}{6}\cdot6=7\cdot6 \\ x=42 \end{gathered}[/tex]I hope this helps you
find a decimal that is equal to each fraction. round to the nearest thousandth if necessary 271/100
Answers
Here, we want to find the decimal equal to the given fraction
To do this, we look at the number which is the denominator
The number here is 100
What this mean is that we are going to shift the decimal point two times (due to 2 zeros; if 1000, 3 times)
The decimal point is not visible on the numerator which means it is at the back of the last number 1 but it is not necessary to write it
By virtue of the movement, the decimal point will be moved two times, which will make it land at the back of the first number 2
So, we have the expression as;
[tex]\frac{271}{100}\text{ = 2.71}[/tex]Options for the first box are: One valid solution, two valid solutions Options for the second box are: no extraneous solutions, one extraneous solution Options for the third box: 5, 0, 2, 4
Answers
ANSWER
The equation has one valid solution and one extraneous solution.
A valid solution for x is 5
[tex]\sqrt[]{x-1}-5=x-8[/tex]
Add 5 to both-side of the equation
[tex]\sqrt[]{x-1}-5+5=x-8+5[/tex][tex]\sqrt[]{x-1}=x-3[/tex]Take the square of both-side
[tex]x-1=(x-3)^2[/tex]x - 1=x²-6x + 9
Rearrange
x² - 6x + 9 - x + 1 =0
x² - 7x + 10 = 0
We can solve the above quadratic equation using factorization method
x² - 5x - 2x + 10 = 0
x(x-5) - 2(x - 5) = 0
(x-5)(x-2)=0
Either x -5 =0 OR x-2 =0
Either x =5 or x=2
To check whether the equation is valid or non-extraneous, let's plug the values into the equation and see if it gives a true statement
For x =5
[tex]\sqrt[]{5-1}-5=5-8[/tex][tex]\sqrt[]{4}-5=-3[/tex][tex]-3=-3[/tex]The above is a true statement
For x =2
[tex]\sqrt[]{2-1}-5=2-8[/tex][tex]1-5=2-8[/tex]The above is not a true statement
Therefore, the equation has one valid solution and one extraneous solution.
A valid solution for x is 5
Can someone help me with this
Answers
The surface area of trapezoidal is 125 cm² that is the popcorn box has a surface area 125 cm².
Given that,
In the picture we have a popcorn with dimensions of trapezoidal.
We have to find what is the surface area of the trapezoidal.
We know that,
The surface area of trapezoidal is 1/2(b₁+b₂)×h
Here,
b₁=5 cm
b₂= 5cm
h= 25 cm
The surface area of trapezoidal= 1/2(b₁+b₂)×h
The surface area of trapezoidal= 1/2(5+5)×25
The surface area of trapezoidal= 1/2(10)×25
The surface area of trapezoidal= 5×25
The surface area of trapezoidal= 125
Therefore, The surface area of trapezoidal is 125 cm² that is the popcorn box has a surface area 125 cm².
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Write the congruence statements represented by the markers in each diagram
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The congruence statements
PS= QR<PSQ= <QRP
<UTV= <VWX<TUV= <XWV
What is Congruence?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.
Given:
From the Figure
PS= QR
<PSQ= <QRP
and, from another figure
<UTV= <VWX
<TUV= <XWV
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Given that y varies directly with x, and y=28 when x=7 What is y when x=52
Answers
Answer:
y=208
Explanation:
If y varies directly with x, the equation of variation is:
[tex]y=kx[/tex]When y=28 and x=7
[tex]\begin{gathered} 28=7k \\ k=\frac{28}{7} \\ k=4 \end{gathered}[/tex]The equation connecting y and x is:
[tex]y=4x[/tex]Therefore, when x=52
[tex]\begin{gathered} y=4\times52 \\ y=208 \end{gathered}[/tex]If f(1) = 3, then what ordered pair is in f? (_,_)
Answers
Given:
if f(1) = 3
We are to find the ordered pair that is in f.
f(1) = 3 is a fuction.
f(1) = 3
Then,
f(x) = 3
f(x) = y
So,
f(1) = 3
Therefore,
x = 1, y = 3
So the ordered pair of f is (1, 3)
I sent the attachment cuz I rather not type :3
Answers
If two matrices are equal, then each of its elements must be equal.
If:
[tex]\begin{bmatrix}{a+3} & {4} \\ {6} & {b-1}\end{bmatrix}=\begin{bmatrix}{-3} & {4} \\ {6} & {2}\end{bmatrix}[/tex]This means that:
[tex]\begin{gathered} a+3=-3 \\ 4=4 \\ 6=6 \\ b-1=2 \end{gathered}[/tex]Isolate a and b from their respective equations to find their value:
[tex]\begin{gathered} a+3=-3 \\ \Rightarrow a=-3-3 \\ \therefore a=-6 \end{gathered}[/tex][tex]\begin{gathered} b-1=2 \\ \Rightarrow b=2+1 \\ \therefore b=3 \end{gathered}[/tex]Therefore, the value of a is -6 and the value of b is 3.
5(1+s)=9s+6
----------------
Answers
Answer:
5(1+s) = -9s +6
Step-by-step explanation:
What is the area of the portion of the triangle that lies outside of the circle but within the triangle? Provide the answer along with an explanation of how to calculate the answer.
Answers
Answer:
Explanation:
Given:
To determine the area of the portion of the triangle that lies outside of the circle but within the triangle, we find the areas of triangle and circle first:
For the triangle, we use the formula:
A=1/2bh
where:
b=base
h=height
We plug in what we know:
[tex]\begin{gathered} A=\frac{1}{2}bh \\ =\frac{1}{2}(20ft)(20ft) \\ =\frac{1}{2}(400ft^2) \\ \text{Calculate} \\ A=200ft^2 \end{gathered}[/tex]Next, we solve for the area of the circle using the given formula:
A=πr^2
where:
r=radius
So,
[tex]\begin{gathered} A=\pi r^2 \\ =\pi(6ft)^2 \\ \text{Calculate} \\ A=113.1ft^2 \end{gathered}[/tex]Then, to find the area of the portion of the triangle that lies outside of the circle but within the triangle:
Area of the portion = Area of the Triangle - Area of the Circle
We plug in what we know:
[tex]\begin{gathered} \text{ }=200ft^2-113.1ft^2 \\ \text{Area of the portion = }86.9ft^2 \end{gathered}[/tex]Therefore, the answer is 86.9 ft^2.
sherry needs to borrow $6,200 to replace the air conditioner in her home. from her credit union, sherry obtains a 30 month loan with an annual simple interest rate of 5.75% use the formula I=Prt (time in years)
Answers
Simple Interest Equation (Principal + Interest)
A = P(1 + rt)
Where:
A = Total Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest per year in decimal; r = R/100
R = Rate of Interest per year as a percent; R = r * 100
t = Time Period involved in months or years
Calculation:
First, converting R percent to r a decimal
r = R/100 = 5.75%/100 = 0.0575 per year.
Putting time into years for simplicity,
30 months / 12 months/year = 2.5 years.
Solving our equation:
A = 6200(1 + (0.0575 × 2.5)) = 7091.25
A = $7,091.25
The total amount accrued, principal plus interest, from simple interest on a principal of $6,200.00 at a rate of 5.75% per year for 2.5 years (30 months) is $7,091.25.
Please help me with this problem:The data shows the number of grams of fat found in 9 different health bars.11, 11.5, 10.5, 17, 14.5, 14.5, 18, 17, 19What is the IQR (interquartile range) for the data? 6.25714.517.5
Answers
The interquartile range = 6.25
Explanation:The given dataset is:
11, 11.5, 10.5, 17, 14.5, 14.5, 18, 17, 19
Rearrange the data in ascending order
10.5, 11, 11.5, 14.5, 14.5, 17, 17, 18, 19
The number of terms in the data, N = 9
The lower quartile is calculated as:
[tex]\begin{gathered} Q_1=(\frac{N+1}{4})^{th}term \\ \\ Q_1=\frac{9+1}{4}^{th}term \\ \\ Q_1=2.5th\text{ term} \\ \\ Q_1=\frac{11+11.5}{2} \\ \\ Q_1=\frac{22.5}{2} \\ \\ Q_1=11.25 \end{gathered}[/tex]The upper quartile is calculated as:
[tex]\begin{gathered} Q_3=(\frac{3(N+1)}{4})^{th\text{ }}term \\ \\ Q_3=\frac{3(9+1)}{4}th\text{ terms} \\ \\ Q_3=7.5th\text{ term} \\ \\ Q_3=\frac{17+18}{2} \\ \\ Q_3=17.5 \end{gathered}[/tex]The interquartile range = Upper quartile - Lower quartile
The interquartile range = 17.5 - 11.25
The interquartile range = 6.25
Which set of polar coordinates names the same point as (-5.5) ? ZT O O A. (5, O B. (5:59) O 5 57 4 377 O c. -5 O D. 7T 5. )
Answers
Recall that the following points represent the same point as the point (x,θ)
[tex]\begin{gathered} (-x,\theta+\pi), \\ (-x,\theta-\pi), \\ (x,\theta+2n\pi)\text{.} \end{gathered}[/tex]Now, notice that:
[tex]\frac{5\pi}{4}=\frac{4\pi}{4}+\frac{\pi}{4}=\pi+\frac{\pi}{4}\text{.}[/tex]Therefore, the point:
[tex](5,\frac{5\pi}{4})[/tex]represent the same point as the point
[tex](-5,\frac{\pi}{4})\text{.}[/tex]Answer: Option B.
The number line represents -4 1/2 +3 1/4 What is the sum?
Answers
Answer
Option C is correct.
-4 ½ + 3 ¼ = -1 ¼
Explanation
We are asked to solve the expression
-4 ½ + 3 ¼
To solve this, we first convert the mixed fractions into improper fractions
-4 ½ = -(9/2)
3 ¼ = (13/4)
We can then take the LCM by expressing both fractions to have the same denominatorr
-4 ½ = -(9/2) = -(18/4)
3 ¼ = (13/4)
-4 ½ + 3 ¼
= -(18/4) + (13/4)
= (-18 + 13)/4
= (-5/4)
= -1 ¼
Hope this Helps!!!
Which sequence is generated by the function f(n+1)(n)-2for f(1)=10?
Answers
Given the following:
[tex]\begin{gathered} f(n+1)=f(n)-2 \\ \text{where f(1)=10} \end{gathered}[/tex]To generate the sequence, we have:
[tex]\begin{gathered} \text{when n=1} \\ f(1+1)=f(1)-2 \\ f(2)=10-2=8 \end{gathered}[/tex][tex]\begin{gathered} \text{when n=2} \\ f(2+1)=f(2)-2 \\ f(3)=8-2=6 \end{gathered}[/tex][tex]\begin{gathered} \text{when n=3} \\ f(3+1)=f(3)-2_{} \\ f(4)=6-2=4 \end{gathered}[/tex][tex]\begin{gathered} \text{when n=4} \\ f(4+1)=f(4)-2 \\ f(5)=4-2=2 \end{gathered}[/tex]Hence, the correct option is Option D
An object is thrown with an initial velocity of 10 m/s off a cliff that is 660 m high. Use the formula s=4.9t^2 + v0t.a.How long does it take for the object to hit the ground?b. How far will it fall in 3 seconds?
Answers
hello
to solve this question, we proceed to apply the formula given
initial velocity v0 =
[tex]\begin{gathered} v_0=10\text{ m/s} \\ s=660m \end{gathered}[/tex]next we proceed to substitute the values into the equation
[tex]\begin{gathered} s=4.9t^2+v_0t \\ 600=4.9t^2+10t \\ 4.9t^2+10t-600=0 \end{gathered}[/tex]we'll proceed to solve this quadratic equation to find the time it took the ball to hit the ground
there are several methods to solve a quadratic equation and for the purpose of this session, i'll make use of quadratic formula
[tex]t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]in our equation, we have
[tex]\begin{gathered} a=4.9 \\ b=10 \\ c=-600 \end{gathered}[/tex]let's substitute the values into the equation
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t=\frac{-10\pm\sqrt[]{10^2-4\times(4.9\times-600)}}{2\times4.9} \\ t=\frac{-10\pm\sqrt[]{100+11760}}{9} \\ t=\frac{-10\pm\sqrt[]{11860}}{9} \\ t=\frac{-10\pm108.9}{9} \\ t=\frac{98.9}{9}\text{ or t}=\frac{-118.9}{9} \\ t=10.99\text{ ot t}=-13.21 \end{gathered}[/tex]but since time can't have a negative value, the answer is approximately 10.99.
the time taken for the object to hit the ground is approximately 10.99s
b.
how far will it fall in 3s
to find the distance the object travelled in 3s, let's substitute the value of time in the original equation
[tex]\begin{gathered} s=4.9t^2+v_0t \\ t=3 \\ v_0=10\text{ m/s} \\ s=4.9(3)^2+10\times3 \\ s=4.9\times9+30 \\ s=44.1+30 \\ s=74.1m \end{gathered}[/tex]in 3s, the ball travelled a distance of 74.1m
Leah just accepted a job at a new company where she will make an annual salary of $65000. Leah was told that for each year she stays with the company, she will be given a salary raise of $2500. How much would Leah make as a salary after 6 years working for the company? What would be her salary after t years? Salary after 6 years: Salary after t years:
Answers
Explanation
Step 1
let s represents the salaray
let t represents the number of years she works.
she will make an annual salary of $65000. Leah was told that for each year she stays with the company, she will be given a salary raise of $2500
hence.
[tex]S=65000+2500t[/tex]and, we have the function for the salary:
for example, after 1 year
it means, t=1
replace
[tex]\begin{gathered} S=65000+2500t \\ S=65000+2500\cdot1 \\ S=65000+2500 \\ S=67500 \end{gathered}[/tex]so After 6 years
it is, when t= 6
[tex]\begin{gathered} S=65000+2500t \\ S=65000+2500\cdot6 \\ S=65000+15000 \\ S=80000 \end{gathered}[/tex]I hope this helps you
7. A right triangle has a hypotenuse of 13 and a leg of 8. What is the other leg? Show your work.
Answers
the other leg is √105
Explanation:Given:
Hypotenuse = 13
one of the legs of the triangle = 8
To find:
the other leg of the triangle
The triangle is right-angled. So, to get the third side, we will apply Pythagoras theorem:
Hypotenuse² = opposite² + adjacent²
let opposite = leg 1 = 8
adjacent = leg 2
Hypotenuse² = = leg1² + leg2²
[tex]\begin{gathered} 13^2=\text{ 8}^2\text{ + leg}_2^2 \\ \\ 169\text{ = 64 + leg}_2^2 \\ \\ 169\text{ - 64 = leg}_2^2 \\ \\ 105\text{ = leg}_2^2 \end{gathered}[/tex][tex]\begin{gathered} square\text{ root both sides:} \\ \sqrt{105}\text{ = leg}_2 \\ Can^{\prime}t\text{ be reduced an further inradical form} \\ \\ leg_2\text{ = }\sqrt{105}\text{ } \end{gathered}[/tex]Hence, the other leg is √105
An onion soup recipe calls for 3 2/3 cups of chopped onions Katrina has already chopped 1 1/3 cups of onions she wants to know how many more cups she needs to chop what X be the number of cups of onions Katrina still needs to chop write an equation to describe the situation
Answers
To determine the number of cups she still needs to chop we need to subtract the amount she already chopped to the amount she needs, then we have the equation:
[tex]x=3\frac{2}{3}-1\frac{1}{3}[/tex]This can be written as:
[tex]x+1\frac{1}{3}=3\frac{2}{3}[/tex]Now, we solve it:
[tex]\begin{gathered} x=3\frac{2}{3}-1\frac{1}{3} \\ x=\frac{11}{3}-\frac{4}{3} \\ x=\frac{7}{3} \end{gathered}[/tex]Therefore she needs to chop 7/3 more cups of onions.
Perform the indicated operations and simplify the result so there are no quotients.
Answers
Given an expression:
[tex]\csc \theta(\sin \theta+\cos \theta)[/tex]We have to simplify the given expression.
[tex]\begin{gathered} \csc \theta(\sin \theta+\cos \theta)=\csc \theta\sin \theta+\csc \theta\cos \theta \\ =\frac{1}{\sin\theta}\cdot\sin \theta+\frac{1}{\sin\theta}\cdot\cos \theta \\ =1+\frac{\cos \theta}{\sin \theta} \\ =1+\cot \theta \end{gathered}[/tex]Thus, the answer is 1 + cot theta.
2. Which of the following statements istrue? (1 pt)a) The longest side in a right triangle iscalled the hypotenuse.b) Pythagorean Theorem works for alltriangles.c) The Pythagorean Theorem is used to findmissing angles.
Answers
Option A is correct
Explanation:Pythagorean Theorem only work for right angle triangles.
Hence, the option Pythagorean Theorem works for all triangles is wrong
The Pythagorean Theorem is used to find missing sides of right angle triangles.
The option The Pythagorean Theorem is used to find missing angles is wrong
The longest side in a right triangle is called the hypotenuse.
This is correct
Option A is correct
for each problem, identify the variables, write the equations, and solve
Answers
Let the 4-passenger cars be represented with F
Let the 6-passenger cars be represented with S
Rocket Coaster has 15 cars
So that F + S = 15 ----- Equation 1
Also, we were told that the total room for 72 passenger
so that 4F + 6S = 72 ----- Equation 2
Solving the two equations simultaneously using the substitution method,
Step 1
From equation 1:
Make F the subject of the formula
F = 15 - S ---- Equation 3
Step 2
substitute equation 3 into equation 2
4 (15 - S) + 6S = 72
Step 3
60 - 4S + 6S = 72
6S - 4S = 72 - 60
2S = 12
divide both sides by 2
S = 12/ 2
S= 6
Step 4
Substitute the value of S = 6 into equation 3
F = 15 - 6
F = 9
So the number of 4-passenger cars = 9
the number of 6-passenger cars = 6
Time 13.5 Time 16 Time 12.6 Time 15.2 Time 12.8 Time 11.8 Time 17.2 Time 12.1. what is the difference between Sarah's time and the mean time of the runners. I know that you divide eight by the sum when you add up all the numbers together from smallest to largest and could you answer this for me l really don't in a word problem when to multiply, add, divide,or, subtract could you ex plain or tell what the key words are that let a student know to add, multiply ,divide, subtract the key words please.
Answers
The mean of a data set is equal to the addition of the values of the data divided by the total number of values in the set.
In our problem:
[tex]\begin{gathered} \operatorname{mean}=\frac{13.5+16+12.6+15.2+12.8+11.8+17.2+12.1}{8}=\frac{111.2}{8} \\ \Rightarrow\operatorname{mean}=13.9 \end{gathered}[/tex]Although you already calculated that, as I understand from what you wrote in the question tab.
The median of a data set can be found by ordering the values in the data set from least to greatest and then taking the middle value. In our problem:
[tex]\begin{gathered} 11.8,12.1,12.6,12.8,13.5,15.2,16,17.2 \\ \Rightarrow\operatorname{median}=\frac{12.8+13.5}{2}=13.15 \\ \Rightarrow\operatorname{median}=13.15 \end{gathered}[/tex]How to divide 111.2 by 8:
The difference between Sarah's time and the mean time of the runners is:
[tex]\operatorname{mean}-\text{Sarah}=13.9-12.1=1.8[/tex]The answer we are looking for is 1.8
Consider the equation: x2 – 3x = 18A) First, use the "completing the square" process to write this equation in the form (x + D)² =or (2 – D)? = E. Enter the values of D and E as reduced fractions or integers.=z? - 3x = 18 is equivalent to:– 3rPreview left side of egn:B) Solve your equation and enter your answers below as a list of numbers, separated with a commawhere necessary.Answer(s):
Answers
Part A.
The quadratic equation,
[tex]ax^2+bx+c=0[/tex]is equivalent to
[tex]a(x+\frac{b}{2a})^2=\frac{b^2}{4a}-c[/tex]In our case a=1, b=-3 and c=-18. Then, by substituting these value into the last result, we have
[tex](x+\frac{-3}{2(1)})^2=(\frac{-3}{2(1)})^2+18[/tex]which gives
[tex]\begin{gathered} (x-\frac{3}{2})^2=\frac{9}{4}+18 \\ (x-\frac{3}{2})^2=\frac{9}{4}+18 \\ (x-\frac{3}{2})^2=\frac{9+72}{4} \\ (x-\frac{3}{2})^2=\frac{81}{4} \end{gathered}[/tex]Therefore, the answer for part A is:
[tex](x-\frac{3}{2})^2=\frac{81}{4}[/tex]Part B.
Now, we need to solve the last result for x. Then, by applying square root to both sides, we have
[tex]x-\frac{3}{2}=\pm\sqrt[]{\frac{81}{4}}[/tex]which gives
[tex]x-\frac{3}{2}=\pm\frac{9}{2}[/tex]then, by adding 3/2 to both sides, we obtain
[tex]x=\frac{3}{2}\pm\frac{9}{2}[/tex]Then, we have 2 solutions,
[tex]\begin{gathered} x=\frac{3}{2}+\frac{9}{2}=\frac{12}{2}=6 \\ \text{and} \\ x=\frac{3}{2}-\frac{9}{2}=\frac{-6}{2}=-3 \end{gathered}[/tex]Therefore, the answer for part B is: -3, 6
Determine the equation of the line that goes through the following points. Write the final equation aslope-intercept form.(-2,6 ) and (4,-3)The equation is
Answers
The slope-intercept form is y = mx + b
Where m is the slope and b is constant represents y-intercept
given the points (-2, 6) and (4,-3)
So, the slope is = m
[tex]m=\frac{6-(-3)}{-2-4}=\frac{9}{-6}=-\frac{3}{2}=-1.5[/tex]So, y = -1.5 x + b
To find b substitute with one of the given points
So,
When x = -2 , y = 6
So,
6 = -1.5 * -2 + b
6 = 3 + b
b = 6 - 3 = 3
So, y = -1.5 x + 3
So, the equation of the line is y = -1.5 x + 3
c) blank + 48 minutes= 16:00
Answers
15:12
Explanation
to find the missing value we need to solve the equation
[tex]blank+48minutes=16\colon00[/tex]so, to isolate the blank subtract 48 minutes in both sides
[tex]\begin{gathered} blank+48minutes-48minutes=16\colon00-48minutes \\ blank=16\colon00-48minutes \end{gathered}[/tex]To subtract time,subtract minutes then subtract the hours, since we can not have negative minutes , add 60to minutes and subtract 1 from the hours , so
[tex]16\colon00\text{ =15 hours +60 minutes}[/tex]replace and do the subtraction
[tex]\begin{gathered} blank=16\colon00-48minutes \\ blank=15\colon00-48minutes+60\text{minutes} \\ blank=15\colon12 \end{gathered}[/tex]therefore, the answer is
15:12
I hope this helps you
In a survey, 221people said theyhave cable TV. Thisrepresents 65% of thepeople surveyed.How many peoplewere surveyed?
Answers
1) Gathering the data
221 people = 65%
2) To find the 100% people surveyed let's set a direct proportion. And then cross multiply to have an equation:
% people
65-----------221
100-------- y
65y = 22100 Dividing both sides by 65
y =340
So, 340 people were surveyed.
what's the value of x for the equation 2(x-4)=6x+4
Answers
we have the equation
2(x-4)=6x+4
solve for x
Apply distributive property left side
2x-2(4)=6x+4
2x-8=6x+4
Group terms
6x-2x=-8-4
combine like terms
4x=-12
divide by 4 both sides
x=-12/4
x=-3