Answer:
[tex]360kg[/tex]Explanation:
Here, we want to get the maximum load supported
From the first part of the question, we have it that:
The maximum load g, varies jointly with the width w and the height h, and inversely as the length l between the supports
Mathematically, we have that as:
[tex]g\text{ = k }\times\frac{wh}{l}[/tex]where k is the proportionality constant
Now, let us get the value of k
We substitute the first set of values as follows:
[tex]\begin{gathered} 360\text{ = }\frac{k\times0.1\times0.06}{6} \\ \\ k\text{ = 360,000 }\frac{kg}{m} \end{gathered}[/tex]Now, using this value of k, we want to get the value of g
Mathematically, we have that as:
[tex]g\text{ = }\frac{360,000\times0.2\times0.08}{16}\text{ = 360 }kg[/tex]A 5000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $155,600?CARDThe number of tickets for sale at $28 should be
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
total seats = 5000
total revenue = $155600
Step 02:
system of equations:
x = # of $28 tickets
y = # of $40 tickets
equation 1:
x + y = 5000
equation 2:
28x + 40y = 155600
x + y = 5000 * (-28)
28x + 40y = 155600
-28x - 28y = - 140000
28x + 40y = 155600
-----------------------------------
12y = 15600
y = 15600 / 12
y = 1300
y in eq. 1:
x + y = 5000
x + 1300 = 5000
x = 5000 - 13000
x = 3700
The answer is:
x = 3700 of $28 tickets
y = 1300 of $40 tickets
Understanding of Multiplying by a Fraction Name: Draw a number line model to represent each multiplication problem. Then solve the problem.2/3×1/2=how do you do this
We have following:
1.
[tex]\frac{2}{3}\cdot\frac{1}{2}=\frac{2\cdot1}{3\cdot2}=\frac{2}{6}=\frac{1}{3}[/tex]2.
[tex]\frac{5}{6}\cdot\frac{3}{4}=\frac{5\cdot3}{6\cdot4}=\frac{15}{24}=\frac{5}{8}[/tex]Please answer all parts of the questions and show all work. Be sure to show all steps.
Answer:
• (a)See graph below
,• (b)The rock will be 258 feet high at t=2.39 seconds and at t=3.61 seconds.
Explanation:
Given the equation modeling the height, h(t) of the rock after t seconds:
[tex]h(t)=-16t^2+96t+120[/tex]Part A
To sketch the graph, we use the intercepts and the vertex.
When t=0:
[tex]\begin{gathered} h(0)=-16(0)^2+96(0)+120 \\ h(0)=120\text{ feet} \\ \implies(0,120) \end{gathered}[/tex]The y-intercept is (0,120)
When h(t)=0:
[tex]\begin{gathered} h(t)=-16t^2+96t+120=0 \\ \text{ We solve for t using the quadratic formula} \\ t=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\ t=\dfrac{-96\pm\sqrt{96^2-4(-16)(120)}}{2(-16)}=\dfrac{-96\pm\sqrt{16896}}{-32} \\ t=\dfrac{-96+\sqrt{16896}}{-32}\text{ or }t=\dfrac{-96-\sqrt{16896}}{-32} \\ t=-1.06\text{ or }t=7.06 \end{gathered}[/tex]The only possible x-intercept is (7.06, 0).
To find the vertex, we use the vertex formula below:
[tex]\begin{gathered} (h,k)=\left(-\frac{b}{2a},\frac{4ac-b^2}{4a}\right) \\ =\left(-\frac{96}{2(-16)},\frac{4(-16)(120)-96^2}{4(-16)}\right) \\ =(3,264) \end{gathered}[/tex]Use these points to sketch the graph as shown below:
Part B
When the rock is 258 feet high: h(t)=258
[tex]\begin{gathered} -16t^2+96t+120=258 \\ -16t^2+96t+120-258=0 \\ \implies-16t^2+96t-138=0 \end{gathered}[/tex]We solve the equation for t:
[tex]\begin{gathered} \text{ We solve for t using the quadratic formula} \\ t=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\ a=-16,b=96,c=-138 \\ t=\dfrac{-96\pm\sqrt{96^2-4(-16)(-138)}}{2(-16)}=\dfrac{-96\pm\sqrt{384}}{-32} \\ t=\dfrac{-96+\sqrt{384}}{-32}\text{ or }t=\dfrac{-96-\sqrt{384}}{-32} \\ t=2.39\text{ or }t=3.61 \end{gathered}[/tex]The rock will be 258 feet high at t=2.39 seconds and at t=3.61 seconds.
Which equation has the solution x = 5?
2x 8 = -2
52 – 7 = 12
-
7x - 4 = 101
9x - 2 = 47
Answer:
I think your missing some signs
7. Brian is packing boxes that can contain two types of items, board games and remote control cars. Board games weigh 3 pounds and remote controlled cars weigh 1.5 pounds, and the box can hold no more than 24 pounds. Also, in each box, the amount of remote control cars must be at least 4 times the amount of board games. Let x represent the number of board games. Let y represent the number of remote controlled cars.A. Write the system of inequalities that represents this situation. You should have 2 different inequalities that you wrote. B. Graph the system of inequalities on the coordinate plane below.
A)
[tex]\begin{gathered} 3x+1.5y\leq24\Rightarrow inequality(1) \\ y\ge4x\rightarrow inequality(2) \end{gathered}[/tex]Explanation
Step 1
Let x represents the number of board games
Let y represent the number of remote controlled cars
i)
a)Board games weigh 3 pounds
b) remote-controlled cars weigh 1.5 pounds
The box can hold no more than 24 pounds( in other words it must be equal or less thant 24),so
[tex]3x+1.5y\leq24\Rightarrow inequality(1)[/tex]ii) in each box, the amount of remote control cars must be at least 4 times the amount of board games( in other words, the number of remote control cars must be equal or greater than 4 times the amount of board games, so,
hence
[tex]y\ge4x\rightarrow inequality(2)[/tex]so,
A)
[tex]\begin{gathered} 3x+1.5y\leq24\Rightarrow inequality(1) \\ y\ge4x\rightarrow inequality(2) \end{gathered}[/tex]Step 2
graph the inequalities
a) set the sign = to convert the inequality in a funcion, isolate for y
b) fnd 2 coordinates of the line
C) draw the line
[tex]\begin{gathered} \leq\rightarrow\text{ continuous line} \\ \ge\rightarrow\text{ cointinuous line} \end{gathered}[/tex]i)
[tex]\begin{gathered} 3x+1.5y=24 \\ 1.5y=24-3x \\ y\leq\frac{24-3x}{1.5} \\ y=16-2x \\ \text{when x= 0} \\ y=16-0 \\ so,P1(0,16) \\ \text{when =3} \\ y=16-2(3) \\ y=16-6=10 \\ so\text{, P2(3,10)} \end{gathered}[/tex]draw a line(continuosus) that passes trougth P1 and P2
ii)
[tex]\begin{gathered} y\ge4x\rightarrow y=4x \\ \text{when x=0} \\ y=4\cdot0=0 \\ so\text{ , P3(}0,0) \\ \text{and when x= 2} \\ y=4(2)=8 \\ so,\text{ P4}(2,8) \end{gathered}[/tex]draw a line(continuosus) that passes trougth P3 and P4
I hope this helps you
This figure has two intersecting lines and a ray. What is the value of x? What is the measure of the angles? I NEED FULL DETAIL
The value of x in the intersecting lines is 7 and the measure of the angles are 38 and 52 degrees respectively.
How to solve angles?The sum of angles on a straight line is 180 degrees.
Complementary angles are angles that sum up to 90 degrees.
Therefore,
3x + 17 + 6x + 10 = 90 (complementary angle)
combine like terms
3x + 17 + 6x + 10 = 90
3x + 6x + 17 + 10 = 90
9x + 27 = 90
subtract 27 from both sides of the equation
9x + 27 = 90
9x + 27 - 27 = 90 - 27
9x = 63
divide both sides by 9
9x / 9 = 63 / 9
x = 7
3(7) + 17 = 21 + 17 = 38°
6(7) + 10 = 52°
Therefore, the two angles are 38 degrees and 52 degrees respectively.
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Use f(x) = 5x − 4 and g(x) = 3 − x2 to evaluate the expression. (a) (f ∘ g)(−2) (b) (g ∘ f)(−2)
The composite functions are evaluated as:
a. (f ∘ g)(−2) = -9
b. (g ∘ f)(−2) = - 193
How to Solve Composite Functions?Given the functions,
f(x) = 5x − 4
g(x) = 3 − x²
a. To find the composite function, (f ∘ g)(−2), we will replace g(-2) instead of x in the function f(x).
Therefore, we would have:
(f ∘ g)(−2) = f(g(-2))
f(g(-2)) = 5(3 − (-2²)) − 4
f(g(-2)) = 5(3 − 4) − 4
f(g(-2)) = 5(-1) − 4
f(g(-2)) = -5 − 4
f(g(-2)) = -9
Therefore, (f ∘ g)(−2) = -9.
b. Also, the composite function (g ∘ f)(−2) would be evaluated by replacing f(-2) instead of x in g(x).
Therefore:
(g ∘ f)(−2) = g(f(-2))
g(f(-2)) = 3 − (5(-2) − 4)²
g(f(-2)) = 3 − (-10 − 4)²
g(f(-2)) = 3 − (-14)²
g(f(-2)) = 3 − 196
g(f(-2)) = -193
Therefore, (g ∘ f)(−2) = - 193
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A brand of frozen green beans lists a weight of 32 ounces on its bag. Because of variability in the manufacturing process, the bags often contain slightly more, or less, than 32 ounces of green beans. An inspector takes a random sample of 25 bags of green beans and records their weights. The weights and their relative frequencies are summarized in the histogram below.
A histogram titled Green Beans has actual weight (ounces) on the x-axis, and relative frequency on the y-axis. 31.8 to 31.9, 0.04; 31.9 to 32.0, 0.04; 32 to 32.1, 0.12; 32.1 to 32.2, 0.2; 32.2 to 32.3, 0.36; 32.3 to 32.4, 0.23.
Which interval contains the median bag weight?
31.9–32.0 ounces
32.0–32.1 ounces
32.1–32.2 ounces
32.2–32.3 ounces
The mode of the data lies at the end of the histogram, one can find that more values are concentrated at the ending of histogram, so the data is skewed data. Hence option 2: 32.0–32.1 ounces is the more appropriate.
As per the question statement, a brand of frozen green beans lists a weight of 32 ounces on its bag but because of variability in the manufacturing process, the bags often contain slightly more, or less, than 32 ounces of green beans then an inspector takes a random sample of 25 bags of green beans and records their weights and weights and their relative frequencies are summarized and an histogram was plotted.
A histogram titled Green Beans has been defined by actual weight (ounces) on the x-axis, and the relative frequency on the y-axis.
31.8 to 31.9, 0.04; 31.9 to 32.0, 0.04; 32 to 32.1, 0.12; 32.1 to 32.2, 0.2; 32.2 to 32.3, 0.36; 32.3 to 32.4, 0.23.
So, the mode of the data lies at the end of the histogram, one can find that more values are concentrated at the ending of histogram, so the data is skewed data. Hence option 2: 32.0–32.1 ounces is the more appropriate.
Histogram: A diagram with rectangles whose width is equal to the class interval and whose size is related to the frequency of a variable.Skewed data: When a collection of data deviates from the symmetrical bell curve, or normal distribution, it is said to have skew.To learn more about Histogram, click on the link given below:
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The telephone cable in the illustration currently runs from A to B to C to D.How much cable ( in yards) is required to run from A to D directly? yd
Given
[tex]\begin{gathered} A\text{ to B =106 yd} \\ B\text{ to C= 72yd} \\ C\text{ to D=48 yd} \end{gathered}[/tex]Solution
[tex]\begin{gathered} P\text{ to D = 106+48} \\ P\text{ to D =154} \end{gathered}[/tex]So to find A to D directly, We use pythagoras
[tex]\begin{gathered} AD^2=154^2+72^2 \\ AD^2=23716+5184 \\ AD^2=28900 \\ Take\text{ the square root of both sides} \\ AD=\sqrt[]{28900} \\ AD\text{ =170 } \end{gathered}[/tex]The final answer
170 yd is required to run from A to D directly
Instructions: For the following quadratic functions, write the function in factored form and then find the -intercepts, axis of symmetry, vertex, and domain and range.
Given the function:
[tex]y=x²-2x-8[/tex]we have that the factored form is:
[tex]y=(x-4)(x+2)[/tex]with this representation, we can see that the x-intercepts are:
[tex]\begin{gathered} x=4 \\ x=-2 \end{gathered}[/tex]Next, the axis of symmetry can be found with the following expression:
[tex]x=-\frac{b}{2a}[/tex]in this case, a = 1 and b = -2 (since a and b are the main coefficients on the equation), then, the axis of symmetry is:
[tex]x=-\frac{-(2)}{2(1)}=1\Rightarrow x=1[/tex]The vertex can be found by evaluating the axis of symmetry on the equation. then, if we make x = 1, we get:
[tex]y=(1)²-2(1)-8=1-2-8=-9[/tex]therefore, the vertex is the point (1,-9).
Finally, the domain of the function is the set of all real numbers (-inf,inf), since it is a polynomial function. The range is [-9,inf), since the vertex is located at the point (1,-9)
Your study partner says that the product of
-12m-3m is -15m. What mistake did your study partner make?
The product of -12m and -3m is -36 m² after applying the arithmetic operation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
Your study partner says that the product of -12m . -3m is -15m
As we know, the arithmetic operation is the operation in which we do the addition of numbers, subtraction, multiplication, and division.
Applying the arithmetic operation:
= (-12)(-3)
= -36 m²
Or
= -(12+12+12)(-1)
= -(36)(-1)
= +36
Thus, the product of -12m and -3m is -36 m² after applying the arithmetic operation.
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Rational Functions 16m^2———-24m^7(Simplify)
The given rational function is
[tex]\frac{16m^2}{24m^7}[/tex]To simplify it we will divide 16 and 24 by their greatest common factor and subtract the powers of m
[tex]16\rightarrow1\times16,2\times8,4\times4[/tex]Then the factors of 16 are 1, 2, 4, 8, 16
[tex]24\rightarrow1\times24,2\times12,3\times8,4\times6[/tex]The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The common factors of 16 and 24 are 1, 2, 4, 8
The greatest one is 8
Then we will divide 16 and 24 by 8 to simplify the fraction
[tex]\begin{gathered} \frac{16m^2}{24m^7}= \\ \\ \frac{\frac{16}{8}m^2}{\frac{24}{8}m^7}= \\ \\ \frac{2m^2}{3m^7} \end{gathered}[/tex]Now, we will subtract the powers of m
[tex]\frac{2m^2}{3m^7}=\frac{2}{3}m^{2-7}=\frac{2}{3}m^{-5}[/tex]To put the fraction in the simplest form we will write m^-5 by a positive power by changing its place from up to downing
[tex]\frac{2}{3}m^{-5}=\frac{2}{3m^5}[/tex]The answer is
[tex]\frac{16m^2}{24m^7}=\frac{2}{3m^5}[/tex]Urgent!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!A bicycle company produces y blcycles at a cost represented by the polynomial y ^ 2 + 10y + 400, 000 . The revenue for y represented by 3y^ 2 +10y+700. Find a polynomial that represents their profit. If the company only has enough materials to make 400 bicycles , should it make the bicycles ?
In order to calculate the profit, let's subtract the revenue and the cost:
[tex]\begin{gathered} \text{profit}=\text{revenue-cost} \\ \text{profit}=3y^2+10y+700-(y^2+10y+400000) \\ \text{profit}=2y^2-399300 \end{gathered}[/tex]Now, for 400 bicycles, let's calculate the profit:
[tex]\begin{gathered} \text{profit}=2\cdot400^2-399300 \\ \text{profit}=320000-399300 \\ \text{profit}=-79300 \end{gathered}[/tex]Since the profit is negative, the company should not make the bicycles.
There are 2 sets of balls numbered 1 through 19 placed in a bowl. If 2 balls are randomly chosen without replacement, find the probability that the balls have the samenumber. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that the two chosen balls from each set have the same number is 0.027027.
We assume that both sets of balls are mixed together to make a single set. The two balls are drawn at random from the bowl since order is unimportant, and they are picked without replacement. We use the entire number of balls in the bowl to determine the total number of combinations made by randomly selecting two balls. The value of n is 2*19 = 38, along with the number of balls being chosen, r = 2.
N = 38C2 = 703
Divide the total number of outcomes where the two randomly picked balls have the same number by the total number of ways to choose two balls from the bowl to obtain the probability that the two randomly chosen balls have the same number.
P = 19/703 = 1/37 = 0.027027
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The approximate areas of Wisconsin and South Carolina are listed below:
Wisconsin: 1.7 x 105 square kilometers
South Carolina: 8.29 × 104 square kilometers
How much larger is Wisconsin? Express your answer using scientific notation.
Step-by-step explanation:
you mean
1.7 × 10⁵ square kilometers (km²) and
8.29 × 10⁴ km²
1.7 × 10⁵ = 17 × 10⁴
how much larger is this than
8.29 + 10⁴ ?
(17 - 8.29) × 10⁴ = 8.71 × 10⁴ km²
so, Wisconsin is 8.71 × 10⁴ km² larger than South Carolina.
what is 10-6+8/2x3 please help
Answer:
16
Step-by-step explanation:
For the equation, 2x+y=6, complete the following ordered pairs: (0,_), (_,0), (_,-6)
Answers in bold
(0, 6)
(3, 0)
(6, -6)
==============================================
Explanation:
The first point given is (0, _) where we don't know what goes in the blank just yet. Let's call this unknown y. The point is (0, y)
Plug in x = 0 to solve for y.
2x+y = 6
2*0+y = 6
0+y = 6
y = 6
Therefore, the point is (0,6) which is the y intercept. This is where the graph crosses the y axis.
------------------------
Next we move onto (_,0)
Plug in y = 0 to find x
2x+y = 6
2x+0 = 6
2x = 6
x = 6/2
x = 3
The point (_, 0) updates to (3,0) which is the x intercept. This is where the graph crosses the x axis.
------------------------
Lastly, we'll use y = -6 to find x.
2x+y = 6
2x-6 = 6
2x = 6+6
2x = 12
x = 12/2
x = 6
We go from (_, -6) to (6, -6)
------------------------
We can use a graphing tool like Desmos to visually confirm the answers. See below.
Help me math can you help me set 2Directions: Find the slope between each pair of points Show all work on a separate sheet ofpaper. After completing each set, find matching answers. One will have a letter and the other anumber. Write the letter in the matching numbered box at the bottom of the page.
(T) Given: pair of points (7,5) and (10,9)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(7,5) and (10,9)
Hence,
[tex]\begin{gathered} x_1=7 \\ y_1=5 \\ x_2=10 \\ y_2=9 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{9-5}{10-7} \\ \\ Slope=\frac{4}{3} \end{gathered}[/tex]Thus, slope = 4/3.
(B) Given: pair of points (-8,2) and (-5,-4)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-8,2) and (-5,-4)
Hence,
[tex]\begin{gathered} x_1=-8 \\ y_1=2 \\ x_2=-5 \\ y_2=-4 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{-4-2}{-5-(-8_)} \\ \\ Slope=\frac{-6}{3} \\ \\ Slope=-2 \end{gathered}[/tex]Thus, slope =-2.
(H) Given: pair of points (2,-2) and (-4,-1)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(2,-2) and (-4,-1)
Hence,
[tex]\begin{gathered} x_1=2 \\ y_1=-2 \\ x_2=-4 \\ y_2=-1 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{-1-(-2)}{-4-2} \\ \\ Slope=\frac{1}{-6} \\ \\ Slope=-\frac{1}{6} \end{gathered}[/tex]Thus, slope =-1/6.
(S) Given: pair of points (-4,9) and (-11,7)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-4,9) and (-11,7)
Hence,
[tex]\begin{gathered} x_1=-4 \\ y_1=9 \\ x_2=-11 \\ y_2=7 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{7-9}{-11-(-4)} \\ \\ Slope=\frac{-2}{-11+4}=\frac{-2}{-7} \\ \\ Slope=\frac{2}{7} \end{gathered}[/tex]Thus, slope = 2/7.
(O) Given: pair of points (5,-1) and (4,-6)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(5,-1) and (4,-6)
Hence,
[tex]\begin{gathered} x_1=5 \\ y_1=-1 \\ x_2=4 \\ y_2=-6 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{-6-(-1)}{4-5} \\ \\ Slope=\frac{-6+1}{-1}=\frac{-5}{-1} \\ \\ Slope=5 \end{gathered}[/tex]Thus, slope = 5.
(16) Given: pair of points (-5,-2) and (9,2)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-5,-2) and (9,2)
Hence,
[tex]\begin{gathered} x_1=-5 \\ y_1=-2 \\ x_2=9 \\ y_2=2 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{2-(-2)}{9-(-5)} \\ \\ Slope=\frac{2+2}{9+5}=\frac{4}{14} \\ \\ Slope=\frac{2}{7} \end{gathered}[/tex]Thus, slope =2/7.
(8) Given: pair of points (-10,-6) and (2,-8)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-10,-6) and (2,-8)
Hence,
[tex]\begin{gathered} x_1=-10 \\ y_1=-6 \\ x_2=2 \\ y_2=-8 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{-8-(-6)}{2-(-10)} \\ \\ Slope=\frac{-8+6}{2+10}=\frac{-2}{12} \\ \\ Slope=-\frac{1}{6} \end{gathered}[/tex]Thus, slope = -1/6.
(3) Given: pair of points (-2,1) and (-8,-7)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-2,1) and (-8,-7)
Hence,
[tex]\begin{gathered} x_1=-2 \\ y_1=1 \\ x_2=-8 \\ y_2=-7 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{-7-1}{-8-(-2)} \\ \\ Slope=\frac{-8}{-8+2}=\frac{-8}{-6} \\ \\ Slope=\frac{4}{3} \end{gathered}[/tex]Thus, slope = 4/3.
(5) Given: pair of points (-4,-2) and (-3,3)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-4,-2) and (-3,3)
Hence,
[tex]\begin{gathered} x_1=-4 \\ y_1=-2 \\ x_2=-3 \\ y_2=3 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{3-(-2)}{-3-(-4)} \\ \\ Slope=\frac{3+2}{-3+4}=\frac{5}{1} \\ \\ Slope=5 \end{gathered}[/tex]Thus, slope = 5.
(14) Given: pair of points (-2,-4) and (-7,6)
To find: The Slope?
Explanation:
We can find the slope by using the formula
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]We have given the points
(-2,-4) and (-7,6)
Hence,
[tex]\begin{gathered} x_1=-2 \\ y_1=-4 \\ x_2=-7 \\ y_2=6 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} Slope=\frac{6-(-4)}{-7-(-2)} \\ \\ Slope=\frac{6+4}{-7+2}=\frac{10}{-5} \\ \\ Slope=-2 \end{gathered}[/tex]Thus, slope = -2.
Answer:
(T ) = (3)
(B) = (14)
(H) = (8)
(S) = (16)
(O) = (5)
which of the following is equivalent to the fractions below after rationalizing the denominator and simplifying? 12/√2
SOLUTION
[tex]\frac{12}{\sqrt{2}}[/tex][tex]\frac{12}{\sqrt{2}}=\frac{12}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{12\sqrt{2}}{\sqrt{2}\times\sqrt{2}}[/tex][tex]\frac{12\sqrt{2}}{2}=6\sqrt{2}[/tex]Final answer:
If m angle JMK =67, find the m angle JKM
SOLUTION:
Step 1:
In this question, we are given the following:
If m angle JMK =67, find the m angle JKM
Step 2:
From step 1, we can see that:
[tex]\begin{gathered} \angle JMK=67^0 \\ \text{and } \\ \angle MJK=90^0 \\ \text{Then , we have that:} \end{gathered}[/tex][tex]\angle JKM=90^0-67^{0\text{ }}=23^0[/tex]CONCLUSION:
From the above solution, we can see clearly that the final answer is:
[tex]\angle JKM=23^0[/tex]
Wendy plotted points J and K on a coordinate plane, as shown
c(2,4)
ExplanationA right triangle is a type of triangle that has one of its angles equal to 90 degrees.
due to the line Jk is vertical , the line KL or JL must be horizontal to make a 90° angle
Step 1
so, the point we are looking for must have lie on the y-coordinate
[tex]\begin{gathered} y-component=-3 \\ y-component=4 \end{gathered}[/tex]therefore, the only possible option with y-coordinate equals 4 is
[tex](2,4)[/tex]therefore, the answer is
c(2,4)
I hope this helps you
rrange the equations in increasing order of the value of their solutions.-2=4–1793+4 = -1.11-163.20 +5.7 = -2.50110.10-1.60+44 = -7!ResetNea
-6, -2, 1, 2
Explanation:
We need to solve each expression individually:
1) 1/4 x + 5/2 x - 2 = 4 - 1/4 x
Collecting like terms:
1/4 x + 5/2 x + 1/4 x = 4 + 2
[tex]\begin{gathered} \frac{x\text{ + 5x(2) + x}}{4}=\text{ 6} \\ \frac{12x}{4}=\text{ 6} \\ 3x\text{ = 6} \\ x\text{ =2} \end{gathered}[/tex]2) 7.9x + x + 4 = -1.1x - 16
Collecting like terms:
7.9x + x + 1.1x = -16 -4
10x = -20
x = -20/10
x = -2
3) 3.2x + 5.7 = -2.5x
Collecting like terms:
3.2x + 2.5x = 5.7
5.7x = 5.7
x = 5.7/5.7
x = 1
4) 10.1x - 1.6x + 44 = -7
Collecting like terms:
8.5x = -7-44
8.5x = -51
x = -51/8.5
x = -6
The solutions: 2, -2, 1, -6
Arranging in increasing order of their solution (smallest to the highest):
-6, -2, 1, 2
What is the solution to -3/7m<21?
m < 49
m > 49
m > -49
m < -49
Answer:
[tex]m>-49[/tex]
Step-by-step explanation:
[tex]m>21(-7/3)=-49[/tex]
The earliest known unit of length to be used in a major construction project is the “megalithic yard” used by. Builders of stone-henge in southwestern Britiian about 2600 b.c. If 1 megalithic yard= 2.72 plus minus 0.05 ft, convert this length to inches. (Round to the nearest tenth of an inch.)
1 megalthic yard = 2.722 feet ( this means they multiplied with 2.722 to get to feet)
now we need to convert feet to inches :
1 ft = 12 inches
2.722 ft = x
cross multiply
2.722 x 12 = 1 X
therefore x = 32,664
rounding off to the nearest tenth of an inch is equivalent to 32.6 inches
Find the slope of the line that passesthrough these two points.Point 1Point 2(-4,6) (-1,3)YıX2 Y2y2-yimX2-X1m = [?]X1
The slope m of a line passing through two points A (x₁, y₁) and B (x₂, y₂) is expressed as
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1}\text{ ----- equation 1} \\ \text{where} \\ (x_1,y_1)\Rightarrow coordinate\text{ of point A} \\ (x_2,y_2)\Rightarrow coordinate\text{ of point B} \end{gathered}[/tex]Given the points: (-4, 6), (-1, 3).
This implies that
[tex]\begin{gathered} x_1=-4, \\ y_1=6, \\ x_2=-1, \\ y_2=3 \end{gathered}[/tex]Thus, substitute the above values into equation 1.
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \text{thus,} \\ m=\frac{3-6}{-1-(-4)} \\ =\frac{-3}{-3} \\ \Rightarrow m=-1 \end{gathered}[/tex]Hence, the
Complete the following statement.
The area under the curve associated with a z score of 3 is ____.
1: 0.4897
2: 0.4987
3: 0.6782
4: 0.5467
Answer:
the answer is 2
Step-by-step explanation:
check and see
There is a field trip to the zoo. tickets are $7 each adult, children tickets are $5 each. The total amount collected was $566. How many tickets were sold per adults and how many were sold per child
Answer:48 adult tickets, 46 child tickets
Step-by-step explanation: 7+5=12 12*47=564 566-564=2
Ok, so now we have to back up a little and do 12*46=552 566-552=14
14/7=2 Sooooooooooooooo. ((7+5)*46)+(7+7)=566
At batting practice Alexis hit 8 balls out of 15 into the outfield. Which equation below can be used to determine the percentage of balls it into the outfield?A. 15/8 = x/100B. 15/100 = x/8C. 8x = (100)(15)D. 15/8 = 100/x
EXPLANATION
Since Alexis hit, the appropriate relationship should consider a division between the number of balls Alexis hit and the total.
Dividing them gives the following expression:
[tex]\frac{8}{15}[/tex]Now, in order to represent as a percentage, we must multiply this fraction by 100:
[tex]\frac{8}{15}*100[/tex]Equaling the fraction to x, assuming that x represents the computed percentage:
[tex]\frac{8}{15}*100=x[/tex]Dividing both sides by 100:
[tex]\frac{8}{15}=\frac{x}{100}[/tex]Reversing the fractions:
[tex]\frac{15}{8}=\frac{100}{x}[/tex]In conclusion, the equation that gives the appropriate relationship is OPTION D
Find the absolute maximum and minimum for the given graph. Give your answer as an ordered pair. 5 3 2. 1 2 3 4 5 Absolute maximum: Absolute minimum:
The highest point as well as coordinates on the graph is the absolute maximum and it's coordinates. From the graph, the highest point is where = 0 and y = 4
The coordinate is (0, 4)
The lowest point as well as coordinates on the graph is the absolute minimum and it's coordinates. From the graph, the highest point is where = - 3 and y = - 5
The coordinate is (- 3, - 5)
Jaime want so make a square patio in his yard. He has enough concrete to pave an area of 193 square feet. If A represents the area of the patio, and s represents the side length of the patio, use the formula s=√A to find the length of each side of his patio. Round your answer to the nearest tenth of a foot.
Jaime wants to make a square patio in his yard.
Now, a square has all four sides equal.
We need to use the next equation given:
[tex]s=\sqrt{A}[/tex]Where s represents the side length and A represens the area of his patio.
Replace using A=193 ft², therefore:
[tex]\begin{gathered} s=\sqrt{193ft^2} \\ s=13.9ft \end{gathered}[/tex]Hence, the length of each side of his patio is 13.9 ft ( the value is rounded to the nearest tenth)
