Answer:
x=6
x=2
Step-by-step explanation:
Fortunately for us, the function is written in factorized terms, so it is easier to find its roots.
The roots are the values for the 'x' variables that makes the functions goes to zero.
They are x=6 and x=2, any of those value make the function equals zero, or in other words, they are the points of interception with the 'y' axis.
To obtain these value
lets study the following condition
(x-6) * (x-2)=0
The above is accomplish when (x-6)=0 or (x-2)=0
We have two independent equations from where we obtain that x=6 and x=2
I NEED HELP NOW!!!! I'LL MARK YOU BRAINLIEST IF YOU ANSWER!!!!!
Answer:
0, 5, 7, 11, ...
Step-by-step explanation:
1^2 = 1; 1 - 1 = 0; 0 is divisible by 6
5^2 = 25; 25 - 1 = 24; 24 is divisible by 6
7^2 = 49; 49 - 1 = 48; 48 is divisible by 6
11^2 = 121; 121 - 1 = 120; 120 is divisible by 6
(4x^2y^3+2xy^2-2y)-(-7x^2y^3+6xy^2-2y)
Answer:
x y^2 (11 x y - 4)
Step-by-step explanation:
Simplify the following:
4 x^2 y^3 + 2 x y^2 - 2 y - (-7 x^2 y^3 + 6 x y^2 - 2 y)
Factor y out of -7 x^2 y^3 + 6 x y^2 - 2 y:
4 x^2 y^3 + 2 x y^2 - 2 y - y (-7 x^2 y^2 + 6 x y - 2)
-y (-2 + 6 x y - 7 x^2 y^2) = 2 y - 6 x y^2 + 7 x^2 y^3:
4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3
Grouping like terms, 4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3 = (4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y):
(4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x^2 y^3 4 + x^2 y^3 7 = 11 x^2 y^3:
11 x^2 y^3 + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x y^2 2 + x y^2 (-6) = -4 x y^2:
11 x^2 y^3 + -4 x y^2 + (2 y - 2 y)
2 y - 2 y = 0:
11 x^2 y^3 - 4 x y^2
Factor x y^2 out of 11 x^2 y^3 - 4 x y^2:
Answer: x y^2 (11 x y - 4)
Answer: xy2 • (11xy - 4)
Step-by-step explanation:
4 x^2 y^3 + 2 x y^2 - 2 y - (-7 x^2 y^3 + 6 x y^2 - 2 y)
Factor y out of -7 x^2 y^3 + 6 x y^2 - 2 y:
4 x^2 y^3 + 2 x y^2 - 2 y - y (-7 x^2 y^2 + 6 x y - 2)
-y (-2 + 6 x y - 7 x^2 y^2) = 2 y - 6 x y^2 + 7 x^2 y^3:
4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3
Grouping like terms, 4 x^2 y^3 + 2 x y^2 - 2 y + 2 y - 6 x y^2 + 7 x^2 y^3 = (4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y):
(4 x^2 y^3 + 7 x^2 y^3) + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x^2 y^3 4 + x^2 y^3 7 = 11 x^2 y^3:
11 x^2 y^3 + (2 x y^2 - 6 x y^2) + (2 y - 2 y)
x y^2 2 + x y^2 (-6) = -4 x y^2:
11 x^2 y^3 + -4 x y^2 + (2 y - 2 y)
2 y - 2 y = 0:
11 x^2 y^3 - 4 x y^2
Factor x y^2 out of 11 x^2 y^3 - 4 x y^2:
Answer: x y^2 (11 x y - 4)
PLEASE HELP
solve for R
what is R equal to
A triangle in the coordinate plane has coordinates of (2,3), (-4,-5), and (-2, 4). It is translated 3 units down. What are its new coordinates?
A) (5,3), (-1,-5), (1,4)
B) (2,6), (-4,-2), (-2, 7)
C) (2,0), (-4,-8), (-2, 1)
D) (-1,3), (-7,-5), (-5,4)
Answer: C) (2,0), (-4,-8), (-2, 1)
Step-by-step explanation:
The translation rule for translating a point (x,y) by k units down :-
[tex](x,y)\rightarrow(x,y-h)[/tex]
Given : A triangle in the coordinate plane has coordinates of (2,3), (-4,-5), and (-2, 4). It is translated 3 units down.
Then, its new coordinates will be :
[tex](2,3)\rightarrow(2,3-3)=(2,0)[/tex]
[tex](-4,-5)\rightarrow(-4,-5-3)=(-4,-8)[/tex]
[tex](-2, 4)\rightarrow(-2,4-3)=(-2,1)[/tex]
Hence, the new coordinates = (2,0), (-4,-8), (-2, 1)
In parallelogram ABCD, AB=7cm and the perimeter of ABCD is 30cm. What is the length of AD?
Answer:
8cm
Step-by-step explanation:
Ab=7cm
Since opposite sides are equal
Cd=7cm
7cm + 7cm = 14cm
Perimeter equals 30cm
:.30cm - 14cm =16cm (bc+ad)
Since both bc and ad are equal,
16cm/2=8cm
:.ad=8cm
Final answer:
In a parallelogram, opposite sides are equal, so by using the given perimeter of 30 cm and one side of 7 cm, we find the length of the adjacent side AD to be 8 cm.
Explanation:
In the given problem with parallelogram ABCD, we know AB = 7 cm and the perimeter is 30 cm. In a parallelogram, opposite sides are equal in length, so if AB = 7 cm, then CD also equals 7 cm. The perimeter P of a parallelogram is the sum of all its sides:
P = AB + BC + CD + DA
Given P = 30 cm and AB = CD = 7 cm, we can find the length of AD (which is also equal to BC) using the formula:
P = 2(AB + AD)
30 = 2(7 + AD)
30 = 14 + 2(AD)
30 - 14 = 2(AD)
16 = 2(AD)
AD = 16 / 2 = 8 cm
Therefore, the length of AD is 8 cm.
Is 23/48 less than 1/2
Answer:
yes.
Step-by-step explanation:
24/48 is half. Anything less than 24 would be less than half.
Answer:
Yes.
Step-by-step explanation:
Half of 2 is 1, so 1/2 means half.
Half of 48 is 24, so 24/48 is also half.
23/48 is less than 24/48, so 23/48 is less than 1/2.
Consider the following equation
Select the equation that has the same solution as the given equation.
Answer:
Option C [tex](3/2)p-5+(9/4)p=7-(5/4)p[/tex]
Step-by-step explanation:
we have that
The given equation is
[tex]-16p+37=49-21p[/tex]
Solve for p
Group terms that contain the same variable
[tex]-16p+21p=49-37[/tex]
Combine like terms
[tex]5p=12[/tex]
[tex]p=12/5[/tex]
[tex]p=2.4[/tex]
we know that
If a equation has the same solution as the given equation, then the solution of the given equation must satisfy the equation
Verify each case
case A) we have
[tex]2+1.25p=-3.75p+10[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]2+1.25(2.4)=-3.75(2.4)+10[/tex]
[tex]5=1[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
case B) we have
[tex]-55+12p=5p+16[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]-55+12(2.4)=5(2.4)+16[/tex]
[tex]-26.2=28[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
case C) we have
[tex](3/2)p-5+(9/4)p=7-(5/4)p[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex](3/2)(2.4)-5+(9/4)(2.4)=7-(5/4)(2.4)[/tex]
[tex]4=4[/tex] ----> is true
therefore
The equation has the same solution as the given equation
case D) we have
[tex]-14+6p=-9-6p[/tex]
substitute the value of p=2.4 in the equation and then compare the results
[tex]-14+6(2.4)=-9-6(2.4)[/tex]
[tex]0.4=-5.4[/tex] ----> is not true
therefore
The equation does not have the same solution as the given equation
At a point on the ground 60 Ft
from the base of a tree, the distance
to the top of the tree is 4 ft more
than 2 times the height of the tree.
Find the height of the tree in ft.
The height of the tree is 32 feet.
Step-by-step explanation:
Let the height of the tree be x.
Connect the top of the tree, the point on the ground, and the bottom of the tree to form a right triangle.
Use Pythagorean theorem to solve for x.
(4+2x)^2 = x^2 + 60^2
x = 32
The height of the tree is 4 feet.
Explanation:To find the height of the tree, we can set up a right triangle with the tree height as one leg, the distance from the base of the tree as the other leg, and the distance to the top of the tree as the hypotenuse. Let's call the tree height x. From the given information, we can write the equation:
x = 2x + 4
Simplifying this equation, we get:
x = 4
Therefore, the height of the tree is 4 feet.
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The roots of the equation 2×^2 + 3x -4=0 are a and b.
find the values of
a^2ß^2
Answer:
hello : a²b² =4
Step-by-step explanation:
2ײ + 3x - 4=0
The roots of this equation exist because (2)(-4)<0
note : a'x²+b'x +c' =0.......The roots of this equation : a and b
a×b = c'/a' a' =2 and b'=3 and c' = - 4
in this exercice ; a²b² = (ab)² = (c'/a')² = (-4/2)² = (-2)² =4
Answer:
4
Step-by-step explanation:
given a quadratic equation in standard form
y = ax² + bx + c = 0 : a ≠ 0
with roots α and β, then
the sum of the roots α + β = - [tex]\frac{b}{a}[/tex] and
the product of the roots αβ = [tex]\frac{c}{a}[/tex]
2x² + 3x - 4 = 0 ← is in standard form
with a = 2, b = 3 and c = - 4
αβ = [tex]\frac{-4}{2}[/tex] = - 2, hence
α²β² = (αβ)² = (- 2)² = 4
a pair of shoes is on sale for 30% off . the original price is p. which expression can be used to find the price of shoes after the dicount?
Answer:
.30p
Step-by-step explanation:
What does it mean for data to be continuous?
Answer:
For data to be continuous, it can take on any value.
Step-by-step explanation:
For example, a line on a coordinate graph never stops at a certain point, if it does, it would be discrete.
he simultaneous equations
5x + y = 21
x - 3y = 9
With working out
Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
5x + y = 21 → (1)
x - 3y = 9 → (2)
Multiply (1) by 3 and add the result to (2) to eliminate y term
15x + 3y = 63 → (3)
Add (2) and (3) term by term
(x + 15x) + )- 3y + 3y) = (9 + 63)
16x = 72 ( divide both sides by 16 )
x = 4.5
Substitute x = 4.5 into (1) for corresponding value of y
22.5 + y = 21 ( subtract 22.5 from both sides )
y = - 1.5
Solution is (4.5, - 1.5 )
What is the volume of the pyramid?
A solid right pyramid has a square base. The length of the
base edge is 4 cm and the height of the pyramid is 3 cm.
Answer: 16 cm^2.
Step-by-step explanation: The volume of a pyramid is equal to one-third the product of the area of the base and the height:
[tex]V=\frac{1}{3}A*h[/tex]
In this case, the base is a square, so its area is:
A=L^2 where "L" is the lenght of the base edge
So the volume would be:
[tex]V=\frac{1}{3}L^{2} *h[/tex]
[tex]V=\frac{1}{3}4^{2} *3[/tex]
V=16*3/3
[tex]V=16cm^{2}[/tex]
Simplify the expression 3/2 (5/3) -1 1/4 + 1/2
Answer:
7/4, 1.25 or 1 3/4
Step-by-step explanation:
Answer:
Exact form 7/4
Decimal form 1.75
Mixed Number 1 3/4
Step-by-step explanation:
Translate into an equation: 5 times the sum of V and 48 is 290.
Answer:
5(V + 48) = 290
Step-by-step explanation:
5 times the sum of V and 48 is 290: V + 48
5 times the sum of V and 48 is 290: 5(V + 48)
5 times the sum of V and 48 is 290: 5(V + 48) = 290
What is the value of cos A?
Answer:
3/5
Step-by-step explanation:
cos A = [tex]\frac{AC}{AB}[/tex]=[tex]\frac{9}{15}[/tex]=[tex]\frac{3}{5}[/tex]
Answer:
Cos A = 3/5
Step-by-step explanation:
Points to remember
Trigonometric ratios
Sin θ = Opposite side/Hypotenuse
Cos θ = Adjacent side/Hypotenuse
Tan θ = Opposite side/Adjacent side
From the figure we can see a right angled triangle, ABC
AC = 9, CB = 12 and AB = 15
To find the value of Cos A
Cos A = Adjacent side/Hypotenuse
= AC/AB
= 9/15 = 3/5
Therefore the value of Cos A = 3/5
What is the value of x?
50°
100
А. 50°
Ов. 150°
Ос. 100°
Op. 30°
Answer:
The answer is 30
Step-by-step explanation:
BC the inside of a triangle equals 180
Northlake High School has two lunch periods. Students can eat their lunch in
the cafeteria or on an outside patio. About 42% of students who have first
lunch eat outside. Compare this with the percentage of second-lunch
students who eat outside.
First lunch
Second lunch
Total
Eat outside
0.19
0.21
0.40
Eat inside
0.26
0.34
0.60
Total
0.45
0.55
10
|
Select the true statement.
O
A. A greater percentage of second-lunch students (45%) eat outside.
O
B. A smaller percentage of second-lunch students (21%) eat outside.
O
C. A greater percentage of second-lunch students (55%) eat outside.
O
D. A smaller percentage of second-lunch students (38%) eat outside.
Answer: d
Step-by-step explanation:
The true statement is a smaller percentage of second-lunch students (38%) eat outside.
What is the true statement?Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentages is %.
Percentage of the second lunch students that eat outside = (0.21/0.55) x 100 = 38%
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Divide. Write the quotient in lowest terms.
Answer:
[tex] \frac{11}{12} [/tex]
The quotient in lowest terms is 2.
The quotient step by step for the given expression:
1. Given Expression:
[tex]\[ \frac{3}{\frac{2}{4}} : 3 \][/tex]
2. Step 1: Simplify the Complex Fraction:
- The complex fraction is [tex]\( \frac{3}{\frac{2}{4}} \).[/tex]
- To simplify, multiply the numerator by the reciprocal of the denominator:
[tex]\[ \frac{3}{\frac{2}{4}} = 3 \times \frac{4}{2} = 6 \][/tex]
3. Step 2: Divide by 3:
- Now divide the simplified fraction (6) by 3:
[tex]\[ 6 : 3 = 2 \][/tex]
Therefore, the quotient in lowest terms is 2.
-52 - x = 9(x+9) + 9x
Step-by-step explanation:
-52-1x= 9(x+9)+9x
-52-1x= 9x+81+9x (now combine like terms)
-52-1x= 18x+81
-1x= 18x+81
-52
-1x=18x+29
-1x=29
+18x
17x= 29
÷17
x=1.705
Hope this helps, I'm not good at explaining it with words, so I just showed the work...
Suppose an elevator is 400 feet above the ground. It descends at a steady rate.
After 15 seconds, it is 250 feet above the ground.
Write a linear function for the height of the elevator as a function of time.
Answer:
The answer is....
Step-by-step explanation:
y= -10x+400
Follow below steps:
The student's question involves writing a linear function for the height of an elevator as a function of time, given that the elevator descends from 400 feet to 250 feet in 15 seconds.
First, let's find the rate of descent by calculating the change in height over the change in time. This gives us (250 feet - 400 feet) / (15 seconds) = -10 feet per second. The negative sign indicates a downward movement.
Now, we can construct the linear function for height h(t), where t is the time in seconds. The initial height is 400 feet, so the y-intercept of our linear equation is 400. With a slope of -10, the function takes the form:
h(t) = -10t + 400
This function represents the height of the elevator after t seconds.
If an airplane flies at an average speed of 7.5 miles per minute, in 1 1/2 hours it will have flown?
Answer:
675 miles
Step-by-step explanation:
7.5*90 (for the 1 1/2 hour)
Answer:
1 1/2= 90 minutes
90 minutes/7.5 miles per minute
Multiply
90/7.5
= 675 miles in 1 1/2
Hope this helped :)
Given: -x > 4. Choose the solution set.
Final answer:
The solution to the inequality -x > 4 is all real numbers less than -4, which can be expressed as the interval (-∞, -4). This is found by dividing both sides by -1 and reversing the inequality to x < -4.
Explanation:
When considering the inequality -x > 4, we are trying to find the set of all values for the variable x that make the inequality true. The solution to such an inequality requires inverse operations and understanding the rules for inequalities, especially the rule that multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol.
Step by step, let's solve the given inequality:
Divide both sides of the inequality by -1 to isolate x. It is important to remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality, so our inequality becomes x < -4 after this step.Now that we have x isolated, we can interpret the solution set. The values of x that satisfy this inequality are all real numbers less than -4. Therefore, the solution set can be written in interval notation as (-∞, -4).This means that any number lower than -4 will be a valid solution for the inequality -x > 4. It's also valuable to visualize this set on a number line, where everything to the left of -4 (but not including -4 itself) is part of the solution set.
Isaac wants the equation below to have no solution when the missing number is placed in the box.
Which number should he place in the box?
Answer: 4
Step-by-step explanation: To have an equation with no solution you have to get something like 0=1 meaning you have to remove all the variables. In this equation you would distribute to get xy+2y+2x=2x+12+4x where y is the missing number. then combining like terms you get xy+2x+2y=6x+12. Subtracting 2x from both sides you get xy+2y=4x+12. Now to get the variables gone y has to be 4 so that the variables to cancel out. By plugging in 4 you can see this works; 4x+8=4x+12 and by subtracting 4x from both sides you get 8=12 which is not true meaning there is no solution.
ANSWER
[tex]^{\boxed {}} = 4.[/tex]
EXPLANATION.
The given equation is
[tex] \boxed {}(x + 2) + 2x = 2(x + 6) + 4x[/tex]
Let us expand the right hand side to obtain:
[tex]\boxed {}(x + 2) + 2x = 2x + 12+ 4x[/tex]
We group similar terms and keep the expression with the box on the left.
[tex]\boxed {}(x + 2) = 2x - 2x+ 12+ 4x[/tex]
Simplify
[tex]\boxed {}(x + 2) = 4x + 12[/tex]
We can see that the value of box the will be the equation to have no solution is 4.
Let us substitute 4 for box.
[tex]4(x + 2) = 4x + 12[/tex]
[tex]4x + 8 = 4x + 12[/tex]
[tex]4x - 4x = 12 - 8[/tex]
[tex]0 = 4[/tex]
This is not true. Hence the equation has no solution when
[tex]\boxed {} = 4[/tex]
Hamid ha gained weight, he now weighs 88kg which is 10% higher than the normal, what i Hamid normal weight?
Answer:
80 kg is Hamid's normal weight
Step-by-step explanation:
The following equation will help you to find the answer:
(1.10)x = 88
Answer:79.2kg
Step-by-step explanation:
10%of 88kg is 8.8. Subtract 8.8 from 88 and the answer is 79.2.
Select the correct answer and then click Done
What is the median of the set of values?
307 309 323 304 390 398
Answer : The median of the given set of data of values is, 323
Step-by-step explanation :
Median : It is the middle term that is sorted by the list of numbers. It is determine by placing the numbers in increasing order.
For odd observations the formula will be: [tex]\frac{n+1}{2}[/tex]
For even observations the formula will be: [tex]\frac{n}{2}+1^{th}\text{ term}[/tex]
As we are given that the set of data:
307, 309, 323, 304, 390, 398
First we have to placing the numbers in increasing order.
304, 307, 309, 323, 390, 398
Now we have to determine the median.
For even data:
[tex]\frac{n}{2}+1^{th}\text{ term}[/tex]
n = 6
[tex]\frac{6}{2}+1^{th}\text{ term}[/tex]
[tex]4^{th}\text{ term}[/tex]
The number at 4th position is, 323
Thus, the median of the given set of data of values is, 323
how much is 2/3 × 5
Answer:
Answer:3.33
Answer:3.33 Step-by-step explanation:
The answer is 3.33
2/3 × 5 = 3.33
Answer:
Step-by-step explanation:
2/3 × 5 = 10/3
Interest rate is 4.25%, the time is 3 1/4 years, simple interest is $330. What is the principal?
Answer:
$2389.14
Step-by-step explanation:
The equation is I = PRT
330= (0.0425)(3.25)P
P=2389.14
Answer:
$2389.14.
Step-by-step explanation:
Use the formula
I = PRT/100 where I = interest , P is the principle, t = time and R = the rate.
330 = P * 4.25 * 3.25 / 100
33000 = P * 13.8125
P = 33,000 / 13.8125
P = $2389.14.
Which is the definition of a line sediment
Answer:
If it is sediment: A sediment trap is a T-shaped pipe configuration designed to catch any debris in a gas line before it goes into the appliance.
Or if it was a typo and its supposed to say segment:line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
Step-by-step explanation:
I know this because of the help of google.
Which expression is equivalent to (x^4/3 x^2/3)^1/3?
Answer: [tex]x^{\frac{2}{3} }[/tex]
Step-by-step explanation:
We have several properties of exponents in use here. The two that are used are:
[tex](x^{a})(x^{b}) = x^{a + b}[/tex] (Exponents with the same base that are being multiplied together can have the exponents added)
[tex](x^{a})^{b} = x^{(a)(b)}[/tex] (A base raised to a power, and then raised to another power means that you can multiply the exponents to get the same result as doing inside operations and then outside operations)
Let's apply it!
First, let's simplify what's inside the parenthesis.
[tex]x^{\frac{4}{3} } x^{\frac{2}{3} }[/tex] (Remember, they have the same base of "x", so we can add the exponents)
[tex]x^{\frac{4}{3} + \frac{2}{3} }[/tex] = [tex]x^{\frac{6}{3} }[/tex] = [tex]x^{2}[/tex]
Now we have [tex](x^{2})^{\frac{1}{3} }[/tex]. Let's use the second rule.
[tex](x^{2})^{\frac{1}{3} }[/tex] = [tex]x^{\frac{2}{3} }[/tex]
Hope this helps! :^)
Answer:
B
Step-by-step explanation:
Just took the test