I’m a parent and I’m not sure I’m understanding this question the practice test question says “How would you take apart 14 to solve 28 - 14? The choices are 7 and 710 and 4 12 and 220 and 8. I said 7 and 7
Answers
There are several ways of taking apart the number 14:
1 and 13
2 and 12
3 and 11
4 and 10
5 and 9
6 and 8
7 and 7
Nevertheless, as we can see by the note below that exercise,
"Have your child take apart 16 to make a ten to find 87 - 16",
we can conclude that the exercise is asking how to take apart 14 to make a ten. By doing so, the subtraction operation (28 - 14) gets simpler since you could subtract 4, and then subtract the ten:
14 = 10 + 4 (1 ten and 4 units)
So, when we do 28 - 14, we can do that in two steps:
• 28 - 4 = ,24
,• 24, - 10 = 14
Therefore, based on the note below exercise 6, the expected answer is
10 and 4
Related Questions
The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,where t is measured in seconds.(A)(i) Find the average velocity over the time interval [3,4].Average Velocity = ___ meters per second(ii) Find the average velocity over the time interval [3.5,4].Average Velocity=____meters per second(iii) Find the average velocity over the time interval [4,5].Average Velocity= ____meters per second(iv) Find the average velocity over the time interval (4,4.5] Average Velocity = ____meters per.(B) Find the instantaneous velocity when t=4.Instantaneous velocity= ____ meters per second.
Answers
Given
The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,
What is the slope of the line that passes through the points (6,-10) and (3,-13)? Write in simplist form
Answers
Use the slope formula to find the slope of a line that goes through two points:
[tex]\begin{gathered} \text{Coordinates of two points}\rightarrow\text{ }(x_1,y_1),(x_2,y_2) \\ \text{Slope of a line through those points}\rightarrow m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Substitute the coordinates (6,-10) and (3,-13) into the slope formula:
[tex]\begin{gathered} m=\frac{(-13)-(-10)}{(3)-(6)} \\ =\frac{-13+10}{3-6} \\ =\frac{-3}{-3} \\ =1 \end{gathered}[/tex]Therefore, the slope of a line that passes through those points, is 1.
A gift box is 12 inches long 8 inches wide and 2 inches high how much wrapping paper is needed to wrap the gift box
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Given that a box is 12 inches long 8 inches wide and 2 inches high, the area of wrapping paper needed to wrap the gift box is equal to the total surface area of the box.
[tex]\begin{gathered} \text{length l =12 inches} \\ \text{width w = 8 inches} \\ \text{ height h = 2 inches} \end{gathered}[/tex]The total surface area of the box can be calculated using the formula;
[tex]undefined[/tex]Which points are included in the solution Set of the systems of equations graphed below?
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Given:
Required:
We need to find the points are included in the solution
Explanation:
Recall that the solution of the system of inequalities is the intersection region of all the solutions in the system.
The points G and F lie inside the intersection.
The points in the solution are G and F.
Final answer:
Points F and G.
Exercise 2 Find a formula for Y in terms of X
Answers
Given:
y is inversely proportional to square of x.
The equation is written as,
[tex]\begin{gathered} y\propto\frac{1}{x^2} \\ y=\frac{c}{x^2}\ldots\ldots\ldots c\text{ is constant} \end{gathered}[/tex]Also y = 0.25 when x = 5.
[tex]\begin{gathered} y=\frac{c}{x^2} \\ 0.25=\frac{c}{5^2} \\ 25\times0.25=c \\ c=\frac{25}{4} \end{gathered}[/tex]So, the equation of y interms of x is,
[tex]y=\frac{25}{4x^2}[/tex]When x increases,
[tex]\begin{gathered} \lim _{x\to\infty}y=\lim _{x\to\infty}(\frac{25}{4x^2}) \\ =\frac{25}{4}\lim _{x\to\infty}(\frac{1}{x^2}) \\ =0 \end{gathered}[/tex]Hence, the value of x increases then y decreases.
Find the interval in which the following quadratic is decreasing.
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The quadratic is decreasing in the interval in which the y values decrease with the increase in x values.
In the interval, (-∞, 0), the y values decrease with increase in x values.
Hence, the quadratic is decreasing in the interval (-∞, 0),
3. An equation that crosses the y-axis at -5 and crosses the x-axis at 24. An equation that crosses the y-axis at -5 and crosses the x-axis at -65. An equation that crosses the y-axis at -5 and crosses the point (2,3)
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We need to find the equation of the line which:
• crosses the y-axis at -5
,• crosses the x-axis at 2
The y-axis cutting point is (0,-5)
The x-axis cutting point is (2,0)
The equation of line is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-axis cutting point
m is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
y_2 = 0
y_1 = -5
x_2 = 2
x_1 = 0
So, slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0--5}{2-0}=\frac{0+5}{2}=\frac{5}{2}[/tex]We got m, we also know b.
The y cutting point is -5, so b = -5
The equation is:
[tex]y=\frac{5}{2}x-5[/tex]The graph would look like:
More clear version:
Use the number line to video to find two other solutions to the inequality 7 + m < 20.
Answers
Answer:
m = 2 and m = 3
Explanation:
To find the solutions to the inequality, we need to isolate m. So, we can subtract 7 from both sides as:
7 + m < 20
7 + m - 7 < 20 - 7
m < 13
Therefore, any number that is less than 13, is a solution of the inequality.
For example: 2 and 3 are solutions of the inequality.
Find the minimum weight resistance possible for A 230 pound man
Answers
Hello there. To find this minimum weight resistance, we need to convert the percentage value to decimals and multiply it by the weight of the person.
8% converted to decimals is equal to 0.08.
Now, multiply it by the weight of the 230 pound man
0.08 * 230 = 18.4 pounds
This is the minimum weight resistance this U gym offers to the customers.
A website recorded the number y of referrals it received from social media websites over a 10-year period. The results can be modeled by y = 2500(1.50), where t is the year and 0 ≤ t ≤9.Interpret the values of a and b in this situation.O a represents the number of referrals after 9 years; b represents the growth factor of the number of referrals each year.a represents the number of referrals it received at the start of the model; b represents the decay factor of the number of referralseach year.O a represents the number of referrals after 9 years; b represents the decay factor of the number of referrals each year.a represents the number of referrals it received at the start of the model; b represents the growth factor of the number ofreferrals each year.What is the annual percent increase?The annual percent increase is%.
Answers
In this problem
we have an exponential growth function
[tex]y=2500(1.50)^t[/tex]where
a=2500 ----> initial value of the number of referrals at the start of the model
b=1.50 ---> the base of the exponential function (growth factor of the number of referrals each year
therefore
The answer Part 1 is the last option
Part 2
Find out the annual percent increase
we know that
b=1+r
b=1.50
1.50=1+r
r=1.50-1
r=0.50
therefore
r=50%
The annual percent increase is 50%Hey everybody! Can somebody help me solve this problem? I don't need a big explanation just the answer and a brief explanation on how you get it! Look at photo for problem.
Answers
Given the ordered pairs:
(-12, -16), (-3, -4), (0, 0), (9, 12)
Let's say that the first coordinate corresponds to x, and the second one corresponds to y. Then, the constant of variation k relates x and y as:
[tex]y=k\cdot x[/tex]Using the ordered pairs:
[tex]\begin{gathered} -16=-12k\Rightarrow k=\frac{4}{3} \\ -4=-3k\Rightarrow k=\frac{4}{3} \\ 0=0\cdot k\text{ (this means that it is correct)} \\ 12=9k\Rightarrow k=\frac{4}{3} \end{gathered}[/tex]We conclude that the constant of variation is:
[tex]k=\frac{4}{3}[/tex]solver for r: C=2(pie)r
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We have the following equation:
[tex]C=2\pi r[/tex]We want to rewrite it in a way 'C' is a function of 'r'. We can accomplish that, if we divide both sides by 2pi.
[tex]2\pi r=C\Rightarrow r=\frac{C}{2\pi}[/tex]From this, we have our result.
[tex]r=\frac{C}{2\pi}[/tex]Graph the line with the given slope m and y-intercept b.
m = 4, b = -5
Answers
Answer:
Step-by-step explanation:
What we know:
m = 4, b = -5
y = mx + b where m is the gradient/slope and b is the y-intercept
Substitute m and b values:
y = 4x + -5 which is the same as y = 4x - 5
Substitute all x values to find y coordinate:
When x = -7, y = (4 x -7) - 5 = -33
When x = -6, y = (4 x -6) - 5 = -29
When x = -5, y = …
Continue for all x values
what is the area if one of the triangular side of the figure?
Answers
Compound Shape
The shape of the figure attached consists on four triangles and one square.
The base of each triangle is B=12 cm and the height is H=10 cm, thus the area is:
[tex]A_t=\frac{BH}{2}[/tex]Calculating:
[tex]A_t=\frac{12\cdot10}{2}=60[/tex]The area of each triangle is 60 square cm.
Now for the square of a side length of L=12.
The area of a square of side length a, is:
[tex]A_s=a^2[/tex]Calculate the area of the square:
[tex]A_s=12^2=144[/tex]The total surface area is:
A = 60*4 + 144
A= 240 + 144
A = 384 square cm
$(20) = 4x^2+ 5x – 3 g(x) = 4x^3 – 3x^2 + 5 Find (f + g)(x)
Answers
The value of (f+g)(x) from the given functions is 4x³+x²+5x+2.
The given functions are f(x)=4x²+ 5x - 3 and g(x)=4x³ - 3x² + 5.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Now, (f+g)(x)=f(x)+g(x)
= 4x²+ 5x - 3+4x³ - 3x² + 5
= 4x³+4x²- 3x²+5x+5-3
= 4x³+x²+5x+2
Therefore, the value of (f+g)(x) from the given functions is 4x³+x²+5x+2.
To learn more about the function visit:
https://brainly.com/question/28303908.
#SPJ1
!!PLEASE HELP IMMEDIATELY!!
Solve the inequality
-1/3x - 12 > 21 or -6x + 10 < -2
x < ? or x > ?
solve for both
Answers
Answer:
x < 2 or x > -11
Step-by-step explanation:
b. 1. add 12 to both sides to get -1/3x > 33
2. multiply by -3/1 to both sides to get x > -11
a. 1) subtract 10 to both sides
2) divide by -6 to both sides
Convert the function p(x) = 2(x – 4)(x + 3)
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Expanding the expression,
[tex]\begin{gathered} p(x)=2(x-4)(x+3) \\ \rightarrow p(x)=2(x^2+3x-4x-12) \\ \rightarrow p(x)=2(x^2-x-12) \\ \rightarrow p(x)=2x^2-2x-24 \end{gathered}[/tex]We get that:
[tex]p(x)=2x^2-2x-24[/tex]An 80% confidence interval for a proportion is found to be (0.27, 0.33). Whatis the sample proportion?
Answers
Step 1
Given;
Step 2
When repeated random samples of a certain size n are taken from a population of values for a categorical variable, the mean of all sample proportions equals the population percentage (p).
[tex]\begin{gathered} Sample\text{ proportion=}\hat{p} \\ \hat{p}\pm margin\text{ error=cofidence interval} \end{gathered}[/tex]Thus;
[tex]\begin{gathered} Let\text{ }\hat{p}=x \\ Margin\text{ of error=y} \\ x-y=0.27 \\ x+y=0.33 \end{gathered}[/tex]checking properly, the sample proportion =0.30, because
[tex]\begin{gathered} 0.30-0.03=0.27 \\ 0.30+0.03=0.33 \end{gathered}[/tex]Answer; Option D
[tex]0.30[/tex]the diagonal of a rectangular swimming pool measures 19 yd if the length of the pool is 15 yd which measurement is closest to the width of the pool?
Answers
Answer:
11.67 yards
Explanation:
From the above figure, we can use the Pythagorean theorem to find the width of the pool as shown below;
[tex]\begin{gathered} 19^2=15^2+w^2 \\ 361=225+w^2 \\ 361-225=w^2 \\ 136=w^2 \\ \sqrt[]{136}=w \\ \therefore w=11.67\text{ yards} \end{gathered}[/tex]m(25+2)(x-7)(4%-8)"y =
Answers
From the figure we can obtain 2 equations:
[tex](2y+2)+(4x-8)=180[/tex]and
[tex](9x-7)+(4x-8)=180[/tex]first lets simplify both equations:
for the first;
[tex]2y+4x=186[/tex]and for the second one:
[tex]9x+4x=195\Rightarrow13x=195\Rightarrow x=\frac{195}{13}=15[/tex]Now we have that x=15 and we can substitute x for 15 in the first equation to find y:
[tex]2y+4(15)=186\Rightarrow2y=126\Rightarrow y=63[/tex]so the final answe is: x=15 and y=63
The graph models the heights, in feet, of two objectsdropped from different heights after x seconds.Which equation represents g(x) as a transformation off(x)?y45+O g(x) = f(x) -5O g(x) = f(x-5)O g(x) = f(x) + 5O g(x) = f(x + 5)40+35y = f(x)30-25+20-15+10+5+ly = g(x)0.5 1.0 1.5 20
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For this problem we know that y=f(x) at x=0 is 5 units above y=g(x). So then the best solution for this case it seems to be:
[tex]f(x)=g(x)+5[/tex]And solving for g(x) we got:
[tex]g(x)=f(x)-5[/tex]5 Which equations have the same value of x as 6 2 3 -9? Select three options. -9(6) 5x+4=-54 5x+4=-9 5x=-13 5X=-58
Answers
The given equation is-
[tex]\frac{5}{6}x+\frac{2}{3}=-9[/tex]If we multiply the equation by 6, we would have the same value for the variable x since we are multiplying the same number on each side. So, the second choice is an equivalent equation to the given one.
Let's multiply by 6.
[tex]\begin{gathered} 6\cdot\frac{5}{6}x+6\cdot\frac{2}{3}=-9\cdot6 \\ 5x+4=-54 \end{gathered}[/tex]So, the third expression is also an equivalent expression.
Then, let's subtract 4 on each side.
[tex]\begin{gathered} 5x+4-4=-54-4 \\ 5x=-58 \end{gathered}[/tex]The last choice is also an equivalent expression.
Therefore, the right choices are 2, 3, and 6.suppose that you have two square garden plots: One is 10’ x 10’ and the other is 15 x 15’. You want to cover both gardens with a 1 inch layer of mulch. If the 10 x 10 garden took 3 1/2 bags of mulch, could you calculate how many bags of mulch you need for the 15 x 15 garden by setting up the following proportion 3.5/10 = X/15. explain clearly why or why not. If the answer is no is there another proportion that you could set up? it may help you to make drawings of the Gardens
Answers
Answer:
Step-by-step explanation:
This question can be solved using a rule of three.
For each configuration, we need the perimeter and the amount of bags of mulch.
For a square of side s, the perimeter is P = 4s
If the 10 x 10 garden took 3 1/2 bags of mulch:
10x10 means that s = 10.
So the perimeter is:
P = 4*10 = 40
The number of bags of mulch is:
3 1/2 = 3 + (1/2) = 3 + 0.5 = 3.5
15 x 15 garden
15x15 means that s = 15.
The perimeter is: P = 4*s = 4*15 = 60.
The number of bags is X.
Now applying the rule of three:
With the number of bags and the perimeter.
3.5 bags - 40'
X bags - 60'
Now we apply cross multiplication:
[tex]undefined[/tex]2x^3+ 15^2+ 27x + 5= x^2+ 5x + 12x + 5
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To determine if the equation is true we multiply the expression on the right side by the denominator on the left; if the result is the numerator on the left then the equation is true:
[tex]\begin{gathered} (2x+5)(x^2+5x+1)=2x^3+10x^2+2x+5x^2+25x+5 \\ =2x^3+15x^2+27x+5 \end{gathered}[/tex]Since the result is the numerator on the left side we conclude that the equation is true.
Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this section to solve the following exercise.The number of ducks and pigs in a field totals 37. The total number of legs among them is 98. Assuming each duck has exactly two legs and each plg has exactly fourlegs, determine how many ducks and how many pigs are in the field.ducks?pigs?
Answers
Lets call x to the number of ducks
and y the number of pigs.
Then:
[tex]2x+4y=98[/tex]Because there are 2 legs per duck and 4 legs per pig.
If the total of animals is 37, then:
[tex]x+y=37[/tex]Then:
[tex]x=37-y[/tex]And replacing on the first equation we get:
[tex]2(37-y)+4y=98[/tex][tex]74-2y+4y=98[/tex][tex]2y=98-74[/tex][tex]2y=24[/tex][tex]y=\frac{24}{2}[/tex][tex]y=12[/tex]There are 12 pigs and therefore 25 ducks.
15 points?Solve for A 5/A = P A = ???? That’s all it saysPlease state what A is.
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2. The product of two consecutive odd numbers is 143. Find the numbers. (Hint: If the first odd number is x, what is the next odd number?)
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Step-by-step explanation:
we have the 2 numbers x and (x+2).
x × (x + 2) = 143
x² + 2x = 143
x² + 2x - 143 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case this is
x = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =
= (-2 ± sqrt(4 + 572))/2 = (-2 ± sqrt(576))/2 =
= (-2 ± 24)/2 = (-1 ± 12)
x1 = -1 + 12 = 11
x2 = -1 - 12 = -13
so, we have 2 solutions : 11 and 13, -13 and -11
11× 13 = 143
-11×-13 = 143
What is the amplitude of the graph g(x)=f(x)+2 Where f(x)=cos x
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In the cosine equation
[tex]y=AcosB(x-C)+D[/tex]A is the amplitude
B is using it to find the period
C is the phase shift
D is the vertical shift
Since the given function is
[tex]g(x)=cos(x)+2[/tex]A = 1
B = 1
C = 0
D = 2
The amplitude is 1
The answer is 1
Suppose you are completely locked out outside of your house. You remember that you left your bedroom window, which is 12 feet above the ground, unlocked from the inside (meaning you can climb up the window if you have a ladder, which you do!). You go to your garage, grab the 20 ft ladder and place it so that it reaches exactly to your bedroom window. What is the angle of elevation needed to reach your window? How far away will the bottom of the ladder be from your house?
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A diagram of the situation is shown below:
In order to determine the angle of elevation x, use the sine function, as follow:
sin x = opposite side/hypotenuse
the opposite side is the distance from the ground to the wi
Find the sum of the arithmetic series 31+37 +43 +49 +... where n=8,OA. 416B. 1668OC. 832D. 834Reset Selection
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
[tex]\begin{gathered} a_1=31 \\ n=8 \\ d=37-31=6 \end{gathered}[/tex]STEP 2: Write the formula for finding sum of arithmetic series
STEP 3: Find the sum of the series
By substitution,
[tex]\begin{gathered} S_8=\frac{8}{2}[2(31)+(8-1)6] \\ S_8=4(62+42) \\ S_8=4(104)=416 \end{gathered}[/tex]Hence, the sum is 416