Answer:
(x + 5)^2 = (5 - 3)^2
Step-by-step explanation:
Given the equation;
x^2 + 10x + 22 = 13
We have;
x^2 + 10x = 13 - 22
x^2 + 10x = -9
Adding half of 10 to both sides and completing the square as usual, we have;
(x + 5)^2 = 5^2 + (-9)
(x + 5)^2 = (5 - 3)^2
The rewritten equation, after completing the square, is
(x - 3/2)² = -79/4.
To rewrite the equation x² + 10x + 22 = 13x as (x + c)² = d or (x - c)² = d, we need to complete the square on the left side of the equation.
Step 1: Move the constant term (22) to the right side of the equation:
x² + 10x = 13x - 22
Step 2: Move all terms involving x to the left side:
x² + 10x - 13x = -22
x² - 3x = -22
Step 3: Take half of the coefficient of x (-3) and square it.
To both sides of the equation, add the following value:
x² - 3x + (-3/2)² = -22 + (-3/2)²
Simplifying:
x² - 3x + 9/4 = -22 + 9/4
Step 4: Make the right side of the equation simpler:
-22 + 9/4 = -88/4 + 9/4 = -79/4
Step 5: The left side of the equation should now be written as a perfect square trinomial:
(x - 3/2)² = -79/4
Therefore, the rewritten equation, after completing the square, is
(x - 3/2)² = -79/4.
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What is the solution set for |x/2|=8?
Answer:
D) x=16 and x=-16
Step-by-step explanation:
D) x=16 and x=-16
If you replace x with either one of them and then take the absolute value, you would have 8.
i am in doubt in this task... Thanks
Answer:
the answer is a
Step-by-step explanation:
Identify the variable(s), set up your equation(s), and solve. Richard has an elder sister who is twice his age and a younger sister who is two years younger than him. If the product of his sisters' ages is 70, how old is Richard?
Answer:
7 years
Step-by-step explanation:
Given that:
Let Richard's age = x
Elder sister's age = 2x
Youngwr sister's age = x - 2
Product of sisters ages = 70
2x * (x - 2) = 70
2x² - 4x = 70
2x² - 4x - 70 = 0
x² - 2x - 35 = 0
x² - 7x + 5x - 35 = 0
x(x - 7) +5(x - 7) = 0
(x - 7) or (x + 5) = 0
x = 7 or x = - 5
X can't be negative
Hence, x = 7
Richard is 7 years
3 and 11
Find the midpoint
Answer:
7
Step-by-step explanation:
can u help me with my math
1b think
I am not sure
PLZ HELP ASAP 20 POINTS!! wrote an equation in slope-intercept (y=mx+b) form for each line.
Answer: I’m sorry I cannot explain this any other way because I can not see the answers but —> If you a point that a line passes through, and its slope, this page will show you how to find the equation of the line. ✨
Step-by-step explanation: hope it help you later on!
Answer:
Y= -4x + 3
Step-by-step explanation: because the x value goes with mx, and the y value goes with b. :)
Original price: $264.91
Markdown: 79%
The sale price is $
could i please get some help?
A dolphin was swimming 28 meters below the ocean's surface. It changed its depth to avoid a
predator and ended up 21 meters below the surface.
What was the change in the dolphin's depth?
what is the answer to this equation ... 3 + 2c + 5c + 2 ??
Answer:
solution:7c+5
f/13 = 6.2 what is the value of f
Answer:
The value of f is 80.6.
Step-by-step explanation:
We are given the equation and asked to solve for f.
If we are given a fraction with a variable in the numerator, we can multiply both sides of the equation by the denominator to isolate it.
For example, if you look at this equation:
[tex]\displaystyle\frac{a}{26}=17.9[/tex]
We can multiply both sides by 26 to get the a by itself so the equation can be solved.
[tex]\displaystyle26\times\frac{a}{26}=17.9\times26\\\\a = 465.4[/tex]
Therefore, we can apply this same technique to the equation [tex]\frac{f}{13}=6.2.[/tex]
[tex]\displaystyle\frac{f}{13}=6.2\\\\13\times\frac{f}{13}=6.2\times13\\\\f = 80.6\ \text{or} \ \frac{403}{5}[/tex]
Therefore, the value of f is 80.6.
Answer:
f = 80.6
Step-by-step explanation:
Multiply both sides by 13.
f /13 =6.2
( f /13 )*(13)=(6.2)*(13)
f = 80.6
Simplify the ratio 12:8 and write the ratio in all three forms.
Answer:
Step-by-step explanation:
1. Simplify
greatest common factor = 4
3:2
a. 3 to 2
b. 3:2
c. 3/2
solve for p2. p1v1 = p2v2
Answer:
P₂ = [tex]\frac{P_{1} V_{1} }{V_{2} }[/tex]
Step-by-step explanation:
Given expression:
Boyle's law:
P₁ V₁ = P₂ V₂
Problem is to find P₂;
Solution:
P₁ V₁ = P₂ V₂
To solve this problem, multiply both sides by [tex]\frac{1}{V_{2} }[/tex];
P₁ V₁ x [tex]\frac{1}{V_{2} }[/tex]; = P₂ V₂ x [tex]\frac{1}{V_{2} }[/tex];
[tex]\frac{1}{V_{2} }[/tex] cancels out V₂ on the right hand side;
P₂ = [tex]\frac{P_{1} V_{1} }{V_{2} }[/tex]
What is the image of the point (7,-5) after a rotation of 270° counterclockwise
about the origin?
Answer:
(-5, -7)
Step-by-step explanation:
if you rotate the point by 270 degrees counterclockwise, you get (5,-7) and I'm guessing image is another way to say reflection so after it is reflected then the point would be (-5,-7)
Pls show the work
2x - 3y = 12
Answer:
y= -2/3x - 4
x= 3/2y + 6
Step-by-step explanation:
2x - 3y = 12 (plus 3y)
2x = 3y +12 (divide by 2)
x = 3/2y + 6
2x - 3y = 12 (minus 2x)
-3y = 2x + 12 (divide by -3)
y = -2/3x - 4
Marisa made 60 mums for homecoming. These mums took 48 hours to make. Each mum takes the same amount of time to make. How many hours will it take Marisa to make 20 mums?
Answer: 25
Step-by-step explanation: 60/48=1.25, 1.25 x 20=25
The members of a crew team can weigh no more than 165 pounds each. Write an INEQUALITY for the acceptable weights. Graph the solutions.
Answer:
shut up b
sorry gad will elp you
Step-by-step explanation:
Mario tracks his heart rate after throwing warm-up pitches before a game. In 1/4 minutes, Mario's heart beats 28 times
Answer:112
Step-by-step explanation: 1/4 divided by 28/1 = 1/112
Answer:
112 and very light
Step-by-step explanation:
Select the correct locations on the graph. Select the lines that represent functions.
Answer:
SECOND QOURDANT
Step-by-step explanation:
The graph lying in first quadrant and graph of horizontal line lying in the fourth quadrant are representing functions.
A function is such type of mapping which strictly has one and only one value corresponding to each input given to the function.
The graph of first quadrant satisfies the condition of a mapping being a function.
The second quadrant contains a graph of parabola but as it is visible, the graph has two values for each input x it takes from -3 to -6. Example: At x = -6, the function outputs y = 2 and y = 5 two values. Thus it is NOT a function.
The third quadrant contains similar graph which also doesn't satisfy the single output constraint. Example, at x = -1, it outputs y = -2 and y = -6 both. Thus its NOT a function.
The fourth quadrant has a graph of two lines. First line is horizontal and has only one value to each x it allows as valid input. Thus it represents a function.
In the same fourth quadrant lies another line but that is vertical. For value x=4. it has several values of y. Thus its NOT a function either.
Thus the graph lying in first quadrant and graph of horizontal line lying in the fourth quadrant are representing functions.
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Educators in Michigan have been trying to raising math achievement scores for several years without success. Results from the state assessment test given in fourth grade show that 52% of all fourth graders cannot subtract when borrowing from zero (regrouping with zero in the subtrahend). Two new techniques for teaching this concept have been developed by teachers who belong to the Michigan Council of Teachers of Mathematics. It is decided that each technique be used in randomly selected classrooms throughout the state. Sixty third-grade classrooms are selected to try each of the techniques. Results from the state assessment test will then be monitored for each of the next two years to see whether either of the two techniques will be effective in teaching subtraction from zero. Sixty-three percent of the students who were taught with first technique passed the objective. Only 32% of students who were taught with the second technique passed the objective.
1. The population is:______.
A. All fourth graders in Michigan.
B. All third graders in Michigan.
C. The students who were in the 60 third-grade classrooms that used each technique.
D. All students in fourth grade who were taught with one of the techniques.
2. The sample is:______.
A. All fourth graders in Michigan.
B. All third graders in Michigan.
C. The students who were in the 60 third-grade classrooms that used each technique.
D. All students in fourth grade who were taught with one of the techniques.
3. An example of a parameter in the study is:______.
A. 63% of the students taught using technique 1 achieved the objective of subtracting from zero.
B. 32% of the students taught using technique 2 passed the state objective test.
C. 52% of all fourth graders in Michigan cannot subtract from zero.
D. 52% of all fourth graders in Michigan cannot pass the fourth-grade mathematics state assessment test.
4. An example of a statistic in the study is:_______.
a. 63% of the students taught using technique 1 achieved the objective of subtracting from zero.
b. 32% of the students taught using technique 2 passed the state objective test.
c. 52% of all fourth graders in Michigan cannot subtract from zero.
d. both a & b.
e. all of the above.
5. The dependent variable is the:______.
A. Results from the fourth-grade state assessment test in mathematics state assessment.
B. Instruction in math in third grade.
C. Two new techniques for teaching subtraction from zero.
D. Percentage of children who passed the objective subtraction from zero.
6. The independent variable is the:______.
A. Results from the fourth-grade state assessment test in mathematics state assessment.
B. Instruction in math in third grade.
C. Two new techniques for teaching subtraction from zero.
D. Percentage of children who passed the objective subtraction from zero.
Answer:
1. A. All fourth graders in Michigan.
2. C. The students who were in the 60 third-grade classrooms that used each technique.
3. C. 52% of all fourth graders in Michigan cannot subtract from zero.
4. d. both a & b.
5. D. Percentage of children who passed the objective subtraction from zero.
6. C. Two new techniques for teaching subtraction from zero.
Step-by-step explanation:
1. We can make this conclusion since an assessment test often comes after students undergo the required lessons (that is using taught the new techniques, so when they entered the fourth grade the assessment would be taken to determine their performance. Hence, the population of the study is the entire fourth-graders in Michigan.
2. The sample includes only students who made up the "60 third-grade classrooms that used each technique". In other words, they were the subject of the study.
3. Remember, a parameter often refers to numbers that summarize the entire data of a particular population. So we could say, that 52% of all fourth graders in Michigan that cannot subtract from zero make up the parameter.
4. A statistic is usually any resulting values gotten from a sample. Hence, both statements a and b are statistics from the sample.
5. Remember, the dependent variable is a variable that can be influenced by another variable; the independent variable. In other words, the percentage of children who passed the objective subtraction from zero could be affected by the independent variable.
6. The independent variable is the variable that could influence the dependent variable. In other words, the two new techniques for teaching subtraction from zero could influence "the percentage of children who passed the objective subtraction from zero."
Plz help...kinda confused.....only answer if ya know....:)
-3=-v+7
v=
Answer:
-3 = -v + 7
-3 - 7 = -v
3+7 = -v
-10 = -v
10 = v
Step-by-step explanation:
this is the answer i got, using basic algebra...
i hope this helps....
have a great day ahead :)
Answer:
v = 10
Step-by-step explanation:
[tex]-3=-v+7\\\\-v+7=-3\\\\-v+7-7=-3-7\\\\-v=-10\\\\\frac{-v=-10}{-1}\\\\ \boxed{v=10}[/tex]
Hope this helps.
entlying
A and B are forces acting on a falling object. Which
force, A or B, represents gravity in the diagram?
Force
is gravity because it attracts the ball
to the ground.
Answer:
B... Because indicates the direction of gravity because its direction is downward
Answer:b
Step-by-step explanation:
PLZ HELP ASAP 30 POINTS!!! write the equation of the line in standard form and slope-interpret form.
standard form:
slope-interpret form:
what is the slope of (-3,-5) (-2,-2)
Answer:
m=3
Step-by-step explanation:
What is 100000000000000x234500000020000030040040
Answer:
234500000020000000000000000
Step-by-step explanation:
if a dog can eat one thirds of a bag of food in 1/2 a week how many bags of food can the dog eat in one week
Answer:
Two thirds of a bag.
Step-by-step explanation:
1/2 * 2 = 1
1/3 * 2 = 2/3
Hope this helped!
After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests you start by jogging for 14 minutes each day. Each week after, he suggests that you increase your daily jogging time by 7 minutes.
PLEASE HELP!!Choose the slope and y-intercept that
correspond with the graph.
the answer is -1/3 y-incercept= -1
Answer:
The first one
Step-by-step explanation:
It’s y intercept is 1 and the slope is 1/3 because it goes up one and to the left 3 . I know it’s negative because it’s going down to the right.
Rectangle ABCD with coordinates A(1, 1), B(4, 1), C(4, 2), and D(1, 2) dilates with respect to the origin to give rectangle A'B'C'D'. If = 6, what is the scale factor of the dilation? A. 6 B. 3 C. 2 D. E. 4
Answer:
A.
Step-by-step explanation:
Answer:
Answer is C. (2)
for PLATO
Step-by-step explanation:
A'B' = 2 * AB
Therefore, the dilation factor is 2.
A plane flies at an altitude of 3.5 kilometers and then starts to descend when it is 60
kilometers from the runway. What is the angle of depression for the descent of the plane?
Round to the nearest degree.
Answer:
Angle of depression = 3.37°
Step-by-step explanation:
We are told that A plane flies at an altitude of 3.5 kilometers and then starts to descend when it is 60
kilometers from the runway.
I've attached an image of a triangle depicting this question.
From the triangle, we can find the angle of depression θ from trigonometric ratio since it's a right angle triangle.
Thus;
3.5/60 = tan θ
tan θ = 0.0583
θ = tan^(-1) 0.0583
θ = 3.37°