Answer:
y = -3/2 x + 3
Step-by-step explanation:
If two lines' slopes multiply to get -1, they are perpendicular to each other.
In -6x+9y-12=0, find the slope by converting to slope-intercept form.
Isolate y:
-6x+9y-12=0
-6x+9y = 12
9y = 6x + 12
y = 6/9 x + 12/9
y = 2/3 x + 4/3
The slope in this line is 2/3.
To find the slope of a perpendicular line, find its negative reciprocal. The negative reciprocal is when you switch the top and bottoms numbers and multiply it by -1.
2/3 => -3/2
The slope of the perpendicular line is -3/2.
In -8x+2y-6=0, find the y-intercept by converting to slope-intercept form.
Isolate y:
-8x+2y-6=0
-8x + 2y = 6
2y = 8x + 6
y = 8/4 x + 6/2
y = 2x + 3
Slope-intercept form is y = mx + b, which b is the y-intercept.
The y-intercept is 3.
Substitute the slope and y-intercept values into the equation of a line in slope-intercept form.
y = mx + b
y = -3/2 x + 3
2 Kaley estimates that 2 out of
every q cheerleaders will forget to
bring their bows for practice. If
there are 36 cheerleaders in the
school, how many should she expect
to forget their bows?
Answer:
[tex]\frac{72}{q}[/tex] number of cheerleaders, she would expect to forget their bows.
Step-by-step explanation:
Kaley estimates that 2 out of every q cheerleaders will forget to bring their bows for practice.
So, if there are q cheerleaders then 2 of them will forget to bring their bows.
Then if there are 1 cheerleader then [tex]\frac{2}{q}[/tex] of them will forget to bring their bows.
Finally, if there are 36 cheerleaders then [tex]\frac{2 \times 36}{q} = \frac{72}{q} [/tex] of them will forget to bring their bows.
Therefore, [tex]\frac{72}{q}[/tex] number of cheerleaders, she would expect to forget their bows. (Answer)
Answer this question please
Answer:
x = 7,y = 8
Step-by-step explanation:
(20 + x + y )/ 5 = x
4x = 20 + y
x ≥ 6
y ≥ 6
if x = 6, y = 4 No
if x = 7, y = 8 Yes!
Some fourth grade students are creating a book of poems.
Part A
Jamie wrote 18 poems, which is 3 times as many poems as Kayla wrote. How many poems did Kayla write? Show your work.
Respond in the space provided.
Answer:
6
Step-by-step explanation:
you take 18 and divide it by 3
Three cards are drawn from a deck without replacement what is the probability of selecting two black cards and a heart?
Answer:
A deck=52
Probability of selecting black cards 26/52
26/52*3/52
Step-by-step explanation:
Correct me if I am wrong.
Solve the equation for x showing your work
4x-5(x-2)=12x+4-x
Answer:
x=1/2
Step-by-step explanation:
4x-5(x-2)=12x+4-x
4x-5x+10=12x-x+4
-x+10=11x+4
-x-11x+10=4
-12x+10=4
-12x=4-10
-12x=-6
12x=6
x=6/12
simplify
x=1/2
Answer: x = 1/2
Explanation :
First write the equation as you see it:
4x-5(x-2)=12x+4-x
Next do the math in the parentheses:
4x-5x+10=12x-x+4
Combine the x’s:
-12x+10=4
Switch the 10 and put it on the other side:
-12x=4-10
Change to negative to positive:
12x=6
Divide:
x=6/12
Simplify
x=1/2
Thus, you answer is x = 1/2
Hope this helps! :)
X^2+3x+2=0 solve by factoring
Answer: x=-1,-2
Step-by-step explanation:
X^2+3x+2=0
(x+1)(x+2)=0
x=-1,-2
2. New appliances for the kitchen will include a new refrigerator ($1,449.99), dishwasher ($489.99), and electric range ($616.99) which will be purchased at the local appliance store. Estimate the cost of the appliances to the nearest hundred dollars. Then calculate the actual total cost of the appliances.
Answer:
about $2,557
Actual cost : $2556.97
Step-by-step explanation:
well since all of them are .99 if you round to the hundreths it make another dollar cause it will force the .9 to become 1.0
so it be 1450 for the refrigerator, 490 for the dishwasher, and 617 for the electric range.
add those numbers to get about $2,557
Simplify: 1(-3.86 + 6.82)| + |(4.02 - 12.45)||
Answer:
11.39
Step-by-step explanation:
-3.86+6.82=2.96
abs(2.96)=2.96
----------------------
4.02-12.45=-8.43
abs(-8.43)=8.43
-----------------------
1(2.96)+8.43=2.96+8.43=11.39
how could you convert 3 yards 2 feet to inches?
Answer:
132 inches
Step-by-step explanation:
first convert yards(yd) to feet(ft)
3yd* (3ft / 1 yd) (yds cancel)
3 * 3ft = 9ft
9ft + 2ft = 11ft
11ft * (12in / 1ft) (ft cancel)
11 * 12in = 132in
Answer:
110 inches
Step-by-step explanation:
1 yard = 36 * 3 = 108 + 2 = 110
segment addition with variables
x equals 22
Explanation:____________________________________________
The Segment Postulate states the following:
Given two end points A and B, a third point C lines on the segment AB if and only if the distances between the points satisfy the equation:
[tex]\overline{AB}=\overline{AC}+\overline{CB}[/tex]
____________________________________________
From the figure:
[tex]\overline{AC}=8+x \\ \\ \overline{CB}=10 \\ \\ \overline{AB}=40[/tex]
Our goal is to find x:
[tex]\overline{AB}=\overline{AC}+\overline{CB} \\ \\ Substituting \ values: \\ \\ 40=(8+x)+10 \\ \\ 18+x=40 \\ \\ Subtracting \ 18 \ from \ both \ sides: \\ \\ 18-18+x=40-18 \\ \\ \boxed{x=22}[/tex]
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Solve. b=3/4 a+b=21.
Given expression is:
[tex]a+b = 21[/tex][tex]b = \frac{3}{4}[/tex]By substituting the value of "b" in the given expression, we get
→ [tex]a + \frac{3}{4} = 21[/tex]
→ [tex]a = 21 - \frac{3}{4}[/tex]
By taking L.C.M, we get
[tex]= \frac{84-3}{4}[/tex]
[tex]= \frac{81}{4}[/tex]
Thus the response above is correct.
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Louis bought a burger and soda for $8. Kate purchased a slice of pizza and soda for $9. Biff purchased a burger, a slice of pizza and a soda for $13.50 what is the equation for each purchase?
The equation for Louis's purchase is: [tex]x+y=8[/tex]
The equation for Kate's purchase is: [tex]y+z=9[/tex]
The equation for Biff's purchase is: [tex]x+y+z=13.50[/tex]
Step-by-step explanation:
First of all we have to define variables for each item involved in the purchase
Let x represent burger
y represent soda
z be the slice of pizza
Then
"Louis bought a burger and soda for $8"
[tex]x+y=8[/tex]
"Kate purchased a slice of pizza and soda for $9"
[tex]y+z=9[/tex]
"Biff purchased a burger, a slice of pizza and a soda for $13.50"
[tex]x+y+z=13.50[/tex]
The equation for Louis's purchase is: [tex]x+y=8[/tex]
The equation for Kate's purchase is: [tex]y+z=9[/tex]
The equation for Biff's purchase is: [tex]x+y+z=13.50[/tex]
Keywords: Linear Equations, Variables
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13 dollars to 15 percent
Answer:
$1.95 is 15% of 13 dollars
Answer:
13 - 15% (1.90) = 11.10
Step-by-step explanation:
13 - 15% (1.90) = 11.10
Jerri was using a recipe for a large cake that required one-third of a tablespoon of cinnamon. Instead of making one large cake, Jerri decided to use the recipe to make four small cakes. How much should she use for each of the four small cakes?
A) 1/12 of a tablespoon
B) 1/3 of a tablespoon
C) 4/3 of a tablespoon
D) 1/4 of a tablespoon
If Jerri decides to make four small cakes out of a large cake recipe, she should divide the quantity of the required ingredient (in this case, cinnamon) by 4. Hence, for each small cake, she should use 1/12 of a tablespoon of cinnamon.
Explanation:The recipe Jerri is working with requires one-third of a tablespoon of cinnamon for a large cake. If she decides to use the same recipe to make four small cakes, she should divide the quantity of the cinnamon by 4, as the four smaller cakes together will make up the same quantity/volume as the one large cake.
The calculation can be done as follows: (1/3) tablespoon of cinnamon divided by 4 equals 1/12 tablespoon. Therefore, for each smaller cake, Jerri should use 1/12 of a tablespoon of cinnamon.
The correct answer is (A) 1/12 of a tablespoon.
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3) Write an equation for the relationship between the number of rectangles (x) and the perimeter of
the figure (y)?
Let the number of rectangles = R
Perimeter is 2(L) + 2(W)
The length remains the same when you add more triangles ( 6).
The width changes by multiplying the width by the number of rectangles.
Since the width of the rectangles are 1, multiply the number of rectangles R by 1 to get R.
Now replace W in the perimeter frmula with R:
Now the perimetr would be: P = 2L + 2R
8. Teo makes a necklace of x wooden beads at $0.50
each and 6 glass beads at $1.25 each. The average
cost of the beads in the necklace is $0.75. Write
an equation to model the situation.
Answer:
0.5x + 7.5 / (x + 6)
Step-by-step explanation:
Let x be the number of wooden beads
wooden bead = $0.50 each
glass bead = $1.25 each
since average cost of bead = (cost of wooden bead + cost of glass bead)/ total number of beads
equation is (0.5x + (6*1.25))/(x + 6)
The model equation is therefore 0.5x + 7.5 / (x + 6)
Given f(x) = x^2 – 3 and g(x) = x+2/x . Find (g ° f)(4).
A. 11/13
B. 6
C. 15/13
D. -6
Answer:
C
Step-by-step explanation:
Given the two functions, we need to find
(g ° f)(4)
This means, we need to put the function f(x) INTO the function g(x) and then evaluate that new function at x = 4.
We put the whole expression of f(x) into "x" of g(x). Shown below:
[tex]f(x)=x^2-3\\g(x)=\frac{x+2}{x}\\(gof)(x)=\frac{x^2-3+2}{x^2-3}\\(gof)(x)=\frac{x^2-1}{x^2-3}[/tex]
Now we plug in 4 into x and evaluate:
[tex](gof)(x)=\frac{x^2-1}{x^2-3}\\(gof)(4)=\frac{4^2-1}{4^2-3}\\(gof)(4)=\frac{15}{13}[/tex]
Thus,
correct answer is C
What is the slope of the line?
Answer Choices:
A.1
B.3
C.1/3
D.-3
Answer:
B
Step-by-step explanation:
You could plug in the point given with another point but for simplicity, you can count how far away you are from the vertex. (Since the y intercept is at 0,0)
Go up 3 spots from the vertex, and then go one spot to the right. Ay now you're at (1,3)
You went up 3 and right 1, which translates to simply 3
Determine the kinetic energy of 8000 Newton’s roller coaster car that is moving with a speed of 20.0 meters/seconds
Answer:
The kinetic energy of the roller coaster is 1600000 J.
Step-by-step explanation:
Given:
Mass of the roller coaster is 8000 Newton's and speed 20.0 meters/seconds.
Now, we need to find the kinetic energy [tex]E_{k}[/tex] of the roller coaster.
So, Mass of roller coaster (m) = 8000 N.
Velocity of roller coaster (v) = 20.0 m/s.
Now, putting the formula of kinetic energy:
[tex]E_{k} = \frac{1}{2}\times m\times v^{2}[/tex]
[tex]E_{k}=\frac{1}{2} \times 8000\times 20^{2}[/tex]
[tex]E_{k}=\frac{1}{2} \times 8000\times 400[/tex]
[tex]E_{k}=\frac{1}{2} \times 3200000[/tex]
[tex]E_{k}=1600000[/tex]
Therefore, the kinetic energy of the roller coaster is 1600000 J.
Choose the expression that represents a quadratic expression. 6x4 − 5x3 + 3x2 −7x − 8 5x3 + 3x2 −7x − 8 2x2 + 3x − 1 3x − 1
Correct option:
[tex]2x^2+3x-13x-1[/tex]
Explanation:A quadratic function is given by the form:
[tex]f(x)=ax^2+bx+c \\ \\ Being \ a,b,c \ any \ real \ constants[/tex]
On the other hand, a quadratic equation is given by the form:
[tex]ax^2+bx+c=0 \\ \\ Being \ a,b,c \ any \ real \ constants[/tex]
And a quadratic expression is given by the form:
[tex]ax^2+bx+c \\ \\ Being \ a,b,c \ any \ real \ constants[/tex]
As you can see, when talking about the term quadratic the higher degree of the polynomial is 2. The options are:
[tex]1. \ 6x^4-5x^3+3x^2-7x-8 \\ \\ 2. \ 5x^3+3x^2-7x-8 \\ \\ 3. \ 2x^2+3x-13x-1[/tex]
So the only option that meets our requirement is:
[tex]2x^2+3x-13x-1[/tex]
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Answer:
2x^2+3x-13x-1
Step-by-step explanation:
complete the table to determine if wavelength varies inversely with frequency...
The completed table shows that the product of wavelength and frequency (k) is approximately constant for X-rays, radio waves, green light, and UV rays. Here are the final values for a, b, c, and d: [tex]a = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ b = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ c = \frac{1}{3} \times 10^{8} \, \text{m/s} , \ d = \frac{2}{15} \times 10^{-8} \, \text{m/s}.[/tex]
To determine if wavelength varies inversely with frequency, we can use the formula [tex]\(k = \text{wavelength} \times \text{frequency}\).[/tex]. Rearranging this formula to solve for k, we get [tex]\(k = \frac{1}{\text{frequency}} \times \text{wavelength}\)[/tex].
Now, we can calculate the values of k for each type of radiation:
[tex]\[a = \frac{1}{3 \times 10^{18}} \times (1 \times 10^{-10}) = \frac{1}{3} \times 10^{-28} \, \text{m/s}.\]\[b = \frac{1}{3 \times 10^9} \times (1 \times 10^{-1}) = \frac{1}{3} \times 10^{-10} \, \text{m/s}.\]\[c = \frac{1}{5 \times 10^{11}} \times (600 \times 10^{-6}) = \frac{1}{3} \times 10^{-8} \, \text{m/s}.\]\[d = \frac{1}{7.5 \times 10^{14}} \times (4 \times 10^{-7}) = \frac{4}{30} \times 10^{-21} \, \text{m/s}.\][/tex]
Now we express the values in terms of [tex]\(10^8\)[/tex]:
[tex]\[a = \frac{1}{3} \times 10^{-20} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[b = \frac{1}{3} \times 10^{-2} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[c = \frac{1}{3} \times 10^{0} \, \text{m/s} = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[d = \frac{4}{30} \times 10^{-13} \, \text{m/s} = \frac{2}{15} \times 10^{-8} \, \text{m/s}.\][/tex]
So, the completed table is as follows:
[tex]\[a = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[b = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[c = \frac{1}{3} \times 10^{8} \, \text{m/s}.\]\[d = \frac{2}{15} \times 10^{-8} \, \text{m/s}.\][/tex]
Mrs. Ruiz has 11/12 yard of string to hang 3 banners. She uses the same length of string to hang each banner. How much string does she use for each banner?
Answer:
[tex]\frac{11}{36}[/tex] yard
Step-by-step explanation:
Length of string Mrs. Ruiz has = [tex]\frac{11}{12}[/tex] yard
Mrs. Ruiz needs to hang 3 banners using the string.
Having known that each banner uses same length of string to be hung we can divide total length of sting into 3 equal parts.
So, we can divide [tex]\frac{11}{12}[/tex] yard by 3 as
⇒ [tex]\frac{11}{12}\div 3[/tex]
Changing the division sing to multiplication by taking reciprocal of divisor.
⇒ [tex]\frac{11}{12}\times \frac{1}{3}[/tex]
We can now multiply numerators and denominators.
⇒ [tex]\frac{11}{36}[/tex] yard
∴ Mrs. Ruiz must used [tex]\frac{11}{36}[/tex] yard of string for each banner.
If p + q = 36, and p -q = 20, then q = ?
Answer:
q = 8
Step-by-step explanation:
Given the 2 equations
p + q = 36 → (1)
p - q = 20 → (2)
Add the 2 equations term by term
2p = 56 ( divide both sides by 2 )
p = 28
Substitute p = 28 into (1)
28 + q = 36 ( subtract 28 from both sides )
q = 8
If p + q = 36, and p -q = 20, then q = B
The given question is an example of an algebraic equation that involves the use of BODMAS and the substitution method.
Let
p + q = 36 ---- (eqaution 1), and;p - q = 20 ---- (equation 2)From equation (1)
Let p = 36 - q.
Then we can substitute the value of p into equation (2)
p - q = 20
36 - q - q = 20
36 - 2q = 20
collecting the like terms
-2q = 20 - 36
- 2q = - 16
Divide both sides by (-2)
q = -16/-2
q = 8
Therefore, we can conclude that the value of q = 8
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Find the probability of rolling an even prime number on a simple dice
Answer:
3/6 or 1/2 or 50:50 there all right
Step-by-step explanation:
I am guessing that by simple dice you mean a 6 sided die and we know that 6 sided dice goes up to 6 and there are 3 prime number up to 6 which are 2 3 5 so if 3 out of 6 numbers are prime it is half of the dice so there is a 50/50 chance you role a prime number
How many liters of each of a 15% acid solution and a 65% acid solution must be used to produce 80 liter of 60% acid solution?
Answer:
8 liters of 15% solution and 72 liters of 65% solution
Step-by-step explanation:
If x is the liters of 15% solution, and y is the liters of 65% solution, then:
x + y = 80
0.15x + 0.65y = 0.60(80)
Solve the system of equations with substitution or elimination. Using substitution:
0.15x + 0.65(80 − x) = 0.60(80)
0.15x + 52 − 0.65x = 48
4 = 0.5x
x = 8
y = 72
You need 8 liters of 15% solution and 72 liters of 65% solution.
8 liters of the 15% solution and 72 liters of the 65% solution are required.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
If x is the liters of 15% solution, and y is the liters of 65% solution, then:
x + y = 80
0.15x + 0.65y = 0.60(80)
Use substitution or elimination to solve the mathematical model. Using a substitute
0.15x + 0.65(80 − x) = 0.60(80)
0.15x + 52 − 0.65x = 48
4 = 0.5x
x = 8
y = 72
8 liters of the 15% solution and 72 liters of the 65% solution are required.
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Billy plotted −3
4
and −1
4
on a number line to determine that −3
4
is smaller than −1
4
Is he corectt??
He is correct.
The further away ( to the left) from 0 a negative number is the smaller it is.
Billy correctly determined that −3/4 is smaller than −1/4 by plotting them on a number line. Numbers further to the left on the number line are smaller, and thus −3/4 is less because its absolute value is greater than that of −1/4 when both are negative.
Explanation:Billy is correct in determining that −3/4 is smaller than −1/4. On a number line, negative numbers to the left are smaller than those to the right. Since −3/4 is further to the left than −1/4, it is indeed the smaller number. Comparing fractions with negative signs can initially be challenging, but remembering that the further left a number is on the number line, the smaller it is, can help clarify comparisons.
When plotting fractions on a number line, it is helpful to consider the absolute value of those fractions. The absolute value of −3/4 is 3/4, and the absolute value of −1/4 is 1/4. Since 3/4 is greater than 1/4, the negative version, −3/4, will be further to the left than −1/4 and therefore less than −1/4.
NEED ASAP AND FULLY EXPLAINED!
A function is shown.
h(t) = -t^2+10t-16
For which interval of t-values is the function both positive and increasing?
a. t < 5
b.t >8
c. 2 <t<5
d. 5<t<8
Answer:
B
Step-by-step explanation:
A.) If you plug in 5 for t, you'd get -5 squared + 10(5) - 16
Which would equal 25 + 50 - 16 = 59
Answer a says t is less than 5, so for example let's plug in 4. You'd get a lower number, which means its decreasing. A is wrong
B.) Now let's plug in 8 for t.
-8 squared = 64.
64 + 10(8) - 16 = 144 - 16 = 128
Your answer here is positive, and B states is t > 8. Any number above 8 is going to give you a positive number and it is increasing
Answer:
B. t>8
Step-by-step explanation:
The polynomial 10x3 + 35x2 − 4x − 14 is factored by grouping.
10x3 + 35x2 − 4x − 14
5x2(____) − 2(____)
What is the common factor that is missing from both sets of parentheses?The polynomial 10x3 + 35x2 − 4x − 14 is factored by grouping.
10x3 + 35x2 − 4x − 14
5x2(____) − 2(____)
What is the common factor that is missing from both sets of parentheses?The polynomial 10x3 + 35x2 − 4x − 14 is factored by grouping.
10x3 + 35x2 − 4x − 14
5x2(____) − 2(____)
What is the common factor that is missing from both sets of parentheses?
Answer: B
Step-by-step explanation:
The common factor missing from both sets of parentheses in the polynomial 10x^3 + 35x^2 - 4x - 14 when factored by grouping is (2x + 7).
To factor the polynomial 10x3 + 35x2 - 4x - 14 by grouping, we must first split the polynomial into two pairs that have a common factor. We can pair the terms as follows: (10x3 + 35x2) and (-4x - 14).
Factoring out the greatest common factor from each pair, we get:
5x2(2x + 7)
-2(2x + 7)
Now, we can observe that both pairs contain the common factor (2x + 7). So, the polynomial can be re-written using this common factor:
5x2(2x + 7) - 2(2x + 7)
Drawn out completely, the factored form of the polynomial using the distributive property (also known as factoring by grouping) thus becomes:
(5x2 - 2)(2x + 7)
Pedro and Ivan races each other in a 24-mile bike race. After 20min, Pedro had traveled 5 miles. Ivan had spent the 20 minutes traveling at a rate of 16mph. Which person was in 1st place after 20min?
Answer:
ivan will
Step-by-step explanation:
16mph
16/3=5.333
60/3=20minutes
so instead of 5 miles in 20 minutes like pedro ivan did 5.333 repeating
66 * 20 equals 6 * 2 *
Answer:
x=110
Step-by-step explanation:
66*20=6*2*x
1320=12x
x=1320/12
x=110