Slope is
[tex]\text{slope}=\frac{y2-y1}{x2-x1}[/tex]Then:
[tex]\text{slope}=\frac{-1-(-2)}{4-3}=\frac{-1+2}{1}=\frac{1}{1}=1[/tex]Answer: slope = 1
A farm raises cows and chickens. The farm has total of 43 animals. One day he counts the legs of all his animals and realizes he has a total of 122. How many cows and chickens does he have?
Assume that there are x cows and y chickens in the form
Since there are 43 animals, then
Add x and y, then equate the sum by 43
[tex]x+y=43\rightarrow(1)[/tex]Since a cow has 4 legs and a chicken has 2 legs
Since there are 122 legs, then
Multiply x by 4 and y by 3, then add the products and equate the sum by 122
[tex]4x+2y=122\rightarrow(2)[/tex]Now, we have a system of equations to solve it
Multiply equation (1) by -2 to make the coefficients of y equal in values and opposite in signs
[tex]\begin{gathered} -2(x)+-2(y)=-2(43) \\ -2x-2y=-86\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3) to eliminate y
[tex]\begin{gathered} (4x-2x)+(2y-2y)=(122-86) \\ 2x+0=36 \\ 2x=36 \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}=\frac{36}{2} \\ x=18 \end{gathered}[/tex]Substitute x by 18 in equation (1)
[tex]18+y=43[/tex]Subtract 18 from each side
[tex]\begin{gathered} 18-18+y=43-18 \\ y=25 \end{gathered}[/tex]The answer is
There are 18 cows and 25 chickens on the farm
Thor is at the lowest point of Asgard whichis 280 feet below sea level (-280 ft.). He flies tothe highest point 520 feet above sea level(520 ft.). How far did he fly? Answer in acomplete sentence.
We have that:
We want to find how far did he fly. This means, we want to find the distance between -280 ft and 520 ft. (Which is 520 ft + 280 ft = 800 ft)
In order to find it out we substract them (we substract the first measure from the second):
520 - (-280)
Since - (-280) = +280, then
520 - (-280) = 520 + 280
= 800
Answer: he flied 800 ft
What is the product of 125 × 25
Answer:
Step-by-step explanation:
125 X 25
= 3,125
HELP ASAP MATH PRE CALC
The values for the dimensions of the open box are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.
The cube as a three dimensional shapes.A cube is 3- dimensional shape with 6 equal sides, 6 faces, and 6 vertices. Each face of a cube is a square. In there dimension, the cube's sides are; the L = length, W = width, and H = height.
From question, squares of equal sides x are cut out of each corner of the metal sheet, hence the dimension for the height of the box is equal to x.
So; H = (x) inches,
L = (30 - x)inches, and
W = (30 - x)inches.
Therefore, the dimensions of the box that can maximize the volume of the metal sheet of 30inches by 30inches are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.
Know more 3-dimensional shapes here: https://brainly.com/question/326906
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Can someone help me with this geometry question? First box has 3 options: 60,96,48Second box has two options: 480 and 552Third box: 180 and 216
Surface area of a square prism is:
[tex]\begin{gathered} \text{4\lparen ah\rparen= SA square prism} \\ 4(20)(6)\text{= SA square prism} \\ 80(6)\text{= SA square prism} \\ 480=\text{SA square prism} \\ \\ \end{gathered}[/tex]The surface area of the square prism 480.
The surface area for the cube is:
[tex]\begin{gathered} 5a^2=\text{ SA cube} \\ 5(6)^2=\text{ SA cube} \\ 5(36)=\text{ SA cube} \\ 180=\text{ Surface area of the cube} \end{gathered}[/tex]The surface area of the cube is: 180.
The surface area of the pyramid is:
[tex]\begin{gathered} SurfaceAreaPyramid=4bh \\ SAPyramid=\text{4\lparen6\rparen\lparen4\rparen} \\ SAPyramid=\text{ 96} \\ \end{gathered}[/tex]The surface area of the pyramid i 96.
In each geometric figure, we have to remove the inner square faces, since they are not on the surface.
The total surface area is:
[tex]\begin{gathered} SA\text{ cube + SA square prism + SA pyramid= Total SA} \\ 180\text{ + 480 + 96= Total SA} \\ 756=\text{ Total surface area. } \end{gathered}[/tex]The total surface area is 756.
A food safety guideline is that the mercury in fish should be below one part per million (ppm). listed below are the amounts of mercury found in tuna sushi sampled at different stores in a major city. construct a 98% confidence interval estimate of the mean amount of mercury in the population. does it appear that there’s too much mercury in tuna sushi?0.58 0.82 0.10 0.88 1.32 0.50 0.92
The amounts of mercury found in tuna sushi sampled at different stores are:
0.58, 0.82, 0.10, 0.88, 1.32, 0.50, 0.92
Number of samples, N = 7
[tex]\begin{gathered} \text{The mean, }\mu\text{ = }\frac{0.58+0.82+0.10+0.88+1.32+0.50+0.92}{7} \\ \mu\text{ = }\frac{5.12}{7} \\ \mu\text{ =}0.73 \end{gathered}[/tex]Standard deviation
[tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{\sum ^{}_{}{(x_1-\mu)^2}}{N}} \\ \sigma\text{ = }\sqrt[]{\frac{(0.58-0.73)^2+(0.82-0.73)^2+(0.10-0.73)^2+(0.88-0.73)^2+(1.32-0.73)^2+(0.50-0.73)^2+(0.92-0.73)^2}{7}} \\ \sigma\text{ =}\sqrt[]{\frac{0.9087}{7}} \\ \sigma\text{ =}\sqrt[]{0.1298} \\ \sigma\text{ = }0.36 \end{gathered}[/tex]The confidence interval is given by the equation:
[tex]\begin{gathered} CI\text{ = }\mu\pm z\frac{\sigma}{\sqrt[]{N}} \\ CI=0.73\pm2.33(\frac{0.36}{\sqrt[]{7}}) \\ CI\text{ = }0.73\pm0.32 \\ CI\text{ = (0.73-0.317})\text{ to (0.73+0.317)} \\ CI\text{ = }0.413\text{ < }\mu<1.047 \end{gathered}[/tex]Find percent change of 50 to 43
Answer:
-14.00%
Step-by-step explanation:
((43-50)/50)*100 = -14.00%
Help on math question precalculus Match the description with the correct base for the logarithm.-LOG without a subscript has a base of -Ln has a base of Choices =10,e
The formal way of writing a logarithm is the following:
[tex]\log _ab[/tex]Where "a" is the base of the logarithm and "b2 is the argument.
If "a = 10", then the base is not written, like this:
[tex]\log _{10}b=\log b[/tex]In the case that the base is the constant number "e" then the logarithm is called a "natural logarithm" and it is written as follows:
[tex]\log _eb=\ln b[/tex]A class has 21 children, 10 are girls and 11 are boys. what fraction of the class is made up of boys?
A class has 21 children, 10 are girls and 11 are boys. what fraction of the class is made up of boys?
Let
x -----> number of boys
y -----> total number of children
we have that
x=11 -----> given
y=21 ----> given
therefore
The fraction of the class that is made up of boys is equal to
x/y
substitute
11/21Find the solution of this system of linearequations. Separate the x- and y- values with acomma. Enclose them in a pair of parantheses. System of equations4x + 8y = 838x + 7y = 76- 8x - 16y = -1668x + 7y = 76
Given,
System of equation is,
[tex]\begin{gathered} 4x+8y=83\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i) \\ 8x+7y=76\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(ii) \end{gathered}[/tex]Taking the equation (i) as,
[tex]\begin{gathered} 4x+8y=83 \\ 4x=83-8y \\ x=\frac{83-8y}{4} \end{gathered}[/tex]Substituting the value of x in equation (ii) then,
[tex]\begin{gathered} 8x+7y=76 \\ 8(\frac{83-8y}{4})+7y=76 \\ 664-64y+28y=304 \\ 36y=360 \\ y=10 \end{gathered}[/tex]Substituting the value of y in above equation then,
[tex]\begin{gathered} x=\frac{83-8\times10}{4} \\ x=\frac{3}{4} \end{gathered}[/tex]Hence, the value of x is 3/4 and y is 10. (3/4, 10)
System of equation is,
[tex]\begin{gathered} -8x-16y=-166\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i) \\ 8x+7y=76\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(ii) \end{gathered}[/tex]Taking the equation (i) as,
[tex]\begin{gathered} -8x-16y=-166 \\ 8x+16y=166 \\ 4x+8y=83 \\ 4x=83-8y \\ x=\frac{83-8y}{4} \end{gathered}[/tex]Substituting the value of x in equation (ii) then,
[tex]\begin{gathered} 8x+7y=76 \\ 8(\frac{83-8y}{4})+7y=76 \\ 664-64y+28y=304 \\ 36y=360 \\ y=10 \end{gathered}[/tex]Substituting the value of y in above equation then,
[tex]\begin{gathered} x=\frac{83-8\times10}{4} \\ x=\frac{3}{4} \end{gathered}[/tex]Hence, the value of x is 3/4 and y is 10. (3/4, 10)
QuestionAreli invested a principal of $950 in her bank account with an interest rate of 3%. How much interest did she earn in 5years?
$ 142.5
Explanation
to solve this we can use the formula:
[tex]i=\text{Prt}[/tex]where i is the interest, P is the principal, r is the rate ( in decimals) and t is the time
then
Step 1
Let
[tex]\begin{gathered} i=i \\ P=950 \\ r=3\text{ \% =0.03} \\ \text{Time= 5 years} \end{gathered}[/tex]replace in the formula
[tex]\begin{gathered} i=950\cdot0.03\cdot5 \\ i=142.5 \end{gathered}[/tex]hence, the answer is
$ 142.5
I hope this helps you
in the figure shown MN is parallel to segment YZ what is the length of segment YZ
We will solve this question using the similar angle theorem
The shape consist of two triangles which i am going to draw out,
One is a big triangle while the other is a small triangle
Let NZ = a
To find NZ We will equate the ratio of the big triangle to that of the small triangle
[tex]\frac{7.5\operatorname{cm}}{3\operatorname{cm}}=\frac{(a+5)cm}{5\operatorname{cm}}[/tex]We then cross multiply to get,
[tex]\begin{gathered} 3(a+5)=7.5\times5 \\ 3a+15=37.5 \\ by\text{ collecting like terms we will have that} \\ 3a=37.5-15 \\ 3a=22.5 \\ \frac{3a}{3}=\frac{22.5}{3} \\ a=7.5\operatorname{cm} \end{gathered}[/tex]Therefore XZ=XN+NZ
[tex]XZ=5+7.5=12.5\operatorname{cm}[/tex]To calculate YZ ,
We will use the pythagorean theorem,
[tex]\begin{gathered} XZ^2=YZ^2+XY^2 \\ 12.5^2=YZ^2+7.5^2 \\ 156.25=YZ^2+56.25 \\ YZ^2=156.25-56.25 \\ YZ^2=100 \\ YZ=\sqrt[]{100} \\ \vec{YZ}=10.0cm \end{gathered}[/tex]Therefore ,
The value of YZ is
[tex]\vec{YZ}=10.0\operatorname{cm}[/tex]Hence ,
The correct answer is OPTION B
a) Jayla says that the equation y=2*3 matches the graph Substitute the ordered pairs (from part() into the equation to prove that jayla is correct. Make sure to show ALL steps
From the graph let's take the points as the ordered pairs:
(3, 3), (4, 5), and (5, 7)
Given the equation:
y = 2x - 3
Let's verify for all points, if the equation matches the graph:
a) (x, y) ==> (3, 3)
Substitute 3 for x and 3 for y in the equation
y = 2x - 3
3 = 3(3) - 3
3 = 6 - 3
3 = 3
b) (x, y) ==> (4, 5)
Substitute 4 for x and 5 for y:
y = 2x - 3
5 = 2(4) - 3
5 = 8 - 3
5 = 5
c) (x, y) ==> (5, 7)
Substitute 5 for x and 7 for y:
y = 2x - 3
7 = 5(2) - 3
7 = 10 - 3
7 = 7
Since the left side equals the right side of the equation, the equation
y=2x-3 matches the graph.
Therefore, Jayla is correct.
help meee pleaseeee pleasee
Answer:
f(x) = (-1/4)x - 5
Step-by-step explanation:
(-8, -3), (-12, -2)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -2 - (-3) -2 + 3 1 -1
m = ------------ = ------------- = ----------- = --------- = -------
x₂ - x₁ -12 - (-8) -12 + 8 -4 4
y - y₁ = m(x - x₁)
y - (-3) = (-1/4)(x - (-8)
y + 3 = (-1/4)(x + 8)
y + 3 = (-1/4)x - 2
-3 -3
-------------------------------
y = (-1/4)x - 5
I hope this helps!
What is the sum of -15 + 182A. 33B. 3c. -3 D-33Your answer
-15 + 18 is the same as 18 - 15, which is equal to 3.
Mrs. algebra ordered some small and medium pizzas for her daughter‘s birthday party. The small pizzas cost $5.75 each and the medium pizzas cost $8.00 each. She bought three more medium pizzas than small pizzas and her total order came to $51.50 How many pizzas of each did Mrs. Algebra order? Write an equation and solve.
we have the following:
x is small pizzas
y is medium pizzas
[tex]\begin{gathered} 5.75\cdot x+8\cdot y=51.5 \\ y=x+3 \\ 5.75\cdot x+8\cdot(x+3)=51.5 \\ 5.75x+8x+24=51.5 \\ 13.75x=51.5-24 \\ x=\frac{27.5}{13.75} \\ x=2 \end{gathered}[/tex]therefore, the answer is:
2 small pizzas and 5 (2+3) medium pizzas
An Integer is a number with a fractional part. True or False
An integer is a number with a fractional part is true statement.
4. At a shelter, 15% of the dogs are puppies. If there are 60 dogs at the shelter, how many are puppies? * O 400 O 25 O 9 O 42
4. At a shelter, 15% of the dogs are puppies. If there are 60 dogs at the shelter, how many are puppies? * O 400 O 25 O 9 O 42
_____________________________________________________
60* (0.15) = 9
_______________________________
Answer
There are 9 puppies
Please provide a deep explanation with examples so I can understand and learn, thank you
Since the package of 500 sheets has dimensions of
[tex]216\times279\times45[/tex]Since 7000 sheets will need to be put in
[tex]\frac{7000}{500}=14[/tex]14 similar package
Since the dimensions of the case are
[tex]216\times279\times270[/tex]The length and the width of the package are the same as the length and the width of the case
Then we will use the heights of them to find how many package we can put in the case
[tex]\frac{270}{45}=6[/tex]That means we can fill the case with 6 packages
Since we have 14 packages, then we will need 6 + 6 + 2
3 cases 2 full and one has 2 packages only
a line passes through the points (2,5) and (-6,4). What is it's equation in point-slope form?
Answer:
y-5=⅛(x-2)
Explanation:
Given the points (2,5) and (-6,4).
To find the equation of the line joining these points in point-slope form, we begin by finding its slope.
[tex]\begin{gathered} \text{Slope,m}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{5-4}{2-(-6)} \\ =\frac{1}{2+6} \\ m=\frac{1}{8} \end{gathered}[/tex]Next, we substitute the slope and any of the given points into the point-slope form below:
[tex]y-y_1=m(x-x_1)[/tex]We use the point (2,5).
• x1=2, y1=5
[tex]y-5=\frac{1}{8}(x-2)[/tex]The equation in point-slope form is y-5=⅛(x-2).
H.O.T. FOCUS ON HIGHER ORDER THINKING 20. Communicate Mathematical Ideas Explain how to graph the inequality 8≥ y.
Given the inequality:
8 ≥ y
Let's graph the inequality.
To graph the inequality, take the following steps:
Step 1.
Rewrite the inequality for y and slip the inequality.
[tex]y\le8[/tex]Step 2.
Draw a solid horizontal line at y = 8.
Since the y is less than or equal to 8, shade the region below the boundary line.
Thus, we have the graph of the inequality below:
the stock market lost 231 points on Tuesday then walks 128 more points on Wednesday find a change of points over the two days
the change of the points is:
[tex]-231-128=-359[/tex]so in the 2 days the stock market lost 359 points
1-Findes the length indicated.2- Find the angle indicated.3-Find the distance between each pair of points.
1.
LM = LN - MN
LM = 22 - 5 (Replacing)
LM= 17 (Subtracting)
2.
m∠EDW= m∠EDC - m∠WDC
m∠EDW= 106° - 40° (Replacing)
m∠EDW= 66° (Subtracting)
3.
Using the formula for the distance between two points we have:
[tex]\begin{gathered} d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ x1=8,x2=-6,y1=3,y2=3 \\ d=\sqrt[]{(8-(-6))^2+(3-3)^2}\text{ (Replacing)} \\ d=\sqrt[]{(8+6)^2+(0)^2}\text{ (Subtracting)} \\ d=\sqrt[]{(14)^2^{}}\text{ (Adding)} \\ d=14\text{ (Raising 14 to the power of 2 and taking the square root)} \\ d=14 \\ \text{ The distance between these points is 14} \end{gathered}[/tex]Using the formula for the midpoint we have:
[tex]\begin{gathered} (\frac{x1+x2}{2},\frac{y1+y2}{2}) \\ x1=8,x2=-6,y1=3,y2=3 \\ (\frac{8+(-6)}{2},\frac{3+3}{2}) \\ (\frac{2}{2},\frac{6}{2})\text{ (Subtracting and adding)} \\ (1,\text{ 3) (Dividing)} \\ \text{The midpoint is (1,3)} \end{gathered}[/tex]What’s the answer?? Just a part of a homework practice
The functions are
[tex]h(x)=0.42x^2+0.3x+4\text{ and }r(x)=-0.005x^2-0.2x+7[/tex]Multiply both functions s follows.
[tex]h(x)\times r(x)=(0.42x^2+0.3x+4)\times(-0.005x^2-0.2x+7)[/tex][tex]=0.42x^2\times(-0.005x^2-0.2x+7)+0.3x\times(-0.005x^2-0.2x+7)+4\times(-0.005x^2-0.2x+7)[/tex][tex]=0.42x^2\times(-0.005x^2)+0.42x^2\times(-0.2x)+0.42x^2\times7+0.3x\times(-0.005x^2)+0.3x\times(-0.2x)+0.3x\times7+4\times(-0.005x^2)+4\times(-0.2x)+4\times7)[/tex][tex]=-0.0021x^4-0.084x^3+2.94x^2-0.0015x^3-0.06x^2+2.1x-0.02x^2-0.8x+28[/tex][tex]=-0.0021x^4-0.084x^3-0.0015x^3+2.94x^2-0.06x^2-0.02x^2+2.1x-0.8x+28[/tex][tex]=-0.0021x^4-0.0855x^3+2.86x^2+1.3x+28[/tex]Hence the required product is
[tex]q(x)=-0.0021x^4-0.0855x^3+2.86x^2+1.3x+28[/tex]Hence the first option is correct.
translate the inequality into a sentence. ten subtracted from the product of 9 and a number is at most -17. use x for unknown number
I need a tutor for algebra
Answer:
0.40
Explanation:
From the question, we're given that;
* 8% of the members run only long-distance, so the probability that a member of the team will run only long-distance, P(A) = 8/100 = 0.08
* 12% compete only in non-running events, so the probability that a member will compete only in non-running events, P(B) = 12/100 = 0.12
* 32% are sprinters only, so the probability that a member is a sprinter only P(C) = 32/100 = 0.32
We're asked in the question to determine the probability that a randomly chosen team member runs only long-distance or competes only in sprint events, since these events cannot occur at the same time, we can use the below formula to solve as shown below;
[tex]P(\text{A or C) = P(A) + P(C)}[/tex]P(A or C) = 0.08 + 0.32 = 0.40
identify all pairs of alternate interior angles. Are the pairs of alternate interior angles equal in measure?
have two parallel lines L1 and L2 crosses by a secant line m.
It means that the measure of alternate interior angles is equal.
The alternate interior angles are:
∠3 and ∠6
∠4 and ∠5
pls help me i’ll give ty brainlist
[tex]\sqrt{25*7x^{4}*x^{1} } \\=\sqrt{25*x^{4}*7 *x^{1} } \\=\sqrt{25x^{4} } *\sqrt{7x}\\=5x^{2} \sqrt{7x}[/tex]
Option B is the answer.
Answer: C
i hope you can see my handwriting
Which equation could be represented by the number line? O A. -5 + 7 = 2 O.B. -3+(-4)= -7 O C. 4+ (-7)=-3 O D.7+(-6) = 1 SURAT E PREVIOUS
C. 4 + (-7) = -3
C. 4 + (-7) = -3 could represent by the number line because no other equation has reflected the lines' displacement of 7 grid from a certain point going to the left which is equivalent to -7.
The rest of the choices is not a possible equation to the line.
A. -5 + 7 = Displacement of 7 Grid to the Right from Point -5
B. -3 - 4 = Displacement of 4 Grid to the Left from Point -3
D. 7 - 6 = Displacement of 6 Grid to the Left from Point 7
8in 8in 8in area of irregular figures
Given data:
The given figure.
The expression for the area is,
[tex]\begin{gathered} A=(8\text{ in)(8 in)+}\frac{1}{2}(8\text{ in)( 8 in)} \\ =96in^2 \end{gathered}[/tex]Thus, the area of the given ffigure is 96 square-inches.