True or false? Based only on the given information, it is guaranteed thatAD EBDADGiven: ADI ACDBICBAC = BCBCDO A. TrueB. FalseSUBMIT
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According to the information given, we can assure:
For both triangles, two interior angles and the side between them have the same measure and length, respectively. This is consistent with the ALA triangle congruence criterion.
ANSWER:
True.
Related Questions
Graph the following equation:(y + 4) = 2(x - 2)Step 1 of 3: Find a point on the line and the slope of the line.
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Given:
The equation of line is,
[tex]y+4=2(x-2)[/tex]Find the slope of equation,
[tex]\begin{gathered} y+4=2(x-2) \\ y+4=2x-4 \\ y=2x-8 \\ \text{slope= 2} \end{gathered}[/tex]Find the points on line,
[tex]\begin{gathered} \text{For x=0,} \\ y=2x-8 \\ y=-8 \\ (x,y)=(0,-8) \\ \text{for x=4,} \\ y=2x-8 \\ y=2(4)-8 \\ y=0 \\ (x,y)=(4,0) \\ \text{For x=2} \\ y=2x-8 \\ y=2(2)-8=-4 \\ (x,y)=(2,-4) \\ \text{For }x=5 \\ y=2x-8 \\ y=2(5)-8=2 \\ (x,y)=(5,2) \end{gathered}[/tex]The graph of equation of line is,
What is the sum of the exterior angles of a polygon with 30 sides a) 180°b) 30°c) 90°d) 360°
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Note that:
The sum of the exterior angles of a polygon does not depend on the number of sides of the polygon
The sum of the exterior angles of a polygon is 360°
Therefore, the correct option is 360°
What’s the answer?? Just a part of a homework practice
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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.
3. Which of the following points would produce a negative slope? (A) (B) (C) (D) (-1,2) and (4,2) (-2,-2) and (0,4) (1,3) and (-1,4) (2,4) and (-2,-1)
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The sequation to calculate the slope is,
[tex]m=\frac{y2-y1}{x2-x1}[/tex]The solpe of line joining (-1,2) and (4,2) is,
[tex]\begin{gathered} m=\frac{2-2}{4+1} \\ m=0 \end{gathered}[/tex]The slope of the line joining (-2,-2) and (0,4) is,
[tex]\begin{gathered} m=\frac{4+2}{0+2} \\ m=3 \end{gathered}[/tex]The slope of the line joining (1,3) and (-1,4) is,
[tex]\begin{gathered} m=\frac{4-3}{-1-1} \\ m=-\frac{1}{2} \end{gathered}[/tex]Negative slope.
The slope of the line joining (2,4) and (-2,-1) is,
[tex]\begin{gathered} m=\frac{-1-4}{-2-2} \\ m=\frac{5}{4} \end{gathered}[/tex]Positive slope.
How come my answer is wrong? It says it’s equal to the correct answer but it’s not the right answer.
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A box contains six red pens, four blue pens, eight green pens, and some black pens. Leslie picks a pen and returns it to the box each time. The outcomes are recorded in the table.a. what is the experimental probability of drawing a green pen?b. if the theoretical probability of drawing a black pen is 1/10, how many black pens are in the box
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given the follwing parameters,
number of times a Red Pen is picked is 8
numbr o f times the Blue Pen is picked is 5
Number of times the Green Pen is picked is 14
Number of times the Black Pen is picked is 3
so,
(a) to get the experimental probability of drawing a Green Pen is,
P = favoured results/all obtained
then,
14/(8+5+14+3)
= 14/30 that is a
(
The length of the diagonal of a Rectangle is 14cm,and it forms a 30 degree angle in one corner of the rectangle.What is the area of the rectangle.(A=LxW)
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We can find W and L using the sine and the cosine functions:
[tex]\begin{gathered} \sin (30)=\frac{W}{14} \\ so\colon \\ W=14\cdot\sin (30) \\ --------- \\ \cos (30)=\frac{L}{14} \\ so\colon \\ L=14\cdot\cos (30) \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} A=L\cdot W \\ A=14\cdot\cos (30)\cdot14\cdot\sin (30) \\ A=49\sqrt[]{3} \\ A\approx84.87cm^2 \end{gathered}[/tex]Answer:
84.87 cm²
X) *11.4.14 Find the volume of the cylinder in terms of it and to the nearest tenth. 2 in 1 in The volume in terms of it is V= in3
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We can calculate the volume of the cylinder as the product of the area of the base and the height of the cylinder.
[tex]V=A_b\cdot h[/tex]The area of the base is equal to:
[tex]A_b=\pi r^2=\pi\cdot2^2=4\pi[/tex]Then, the volume becomes:
[tex]V=A_b\cdot h=4\pi\cdot1=4\pi\approx12.6\text{ in}^3[/tex]Answer:
The volume in function of π is V = 4π in^3.
The volume rounded to the nearest tenth is 12.6 in^3.
For questions 5&6 find F -1(x), the inverse of F(x)
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To find the inverse function, we can follow the next steps:
First Function1. Replace x with y as follows:
[tex]y=3x+7\Rightarrow x=3y+7[/tex]2. Solve the resulting equation for y. Subtract 7 from both sides of the equation:
[tex]x-7=3y+7-7\Rightarrow x-7=3y[/tex]3. Divide both sides of the equation by 3:
[tex]\frac{(x-7)}{3}=\frac{3}{3}y\Rightarrow y=\frac{(x-7)}{3}=\frac{1}{3}(x-7)=\frac{x}{3}-\frac{7}{3}[/tex]Second FunctionWe need to repeat the process to obtain the inverse of this function:
1. Replace x with y:
[tex]y=8x\Rightarrow x=8y[/tex]2. Solve for y. Divide both sides by 8:
[tex]\frac{x}{8}=\frac{8}{8}y\Rightarrow y=\frac{x}{8}[/tex]In summary, we have that the inverse functions are:
For function
[tex]y=3x+7[/tex]The inverse function is:
[tex]y=F^{-1}^{}(x)=\frac{(x-7)}{3}[/tex]And, for the function
[tex]y=8x[/tex]The inverse function is:
[tex]y=f^{-1}(x)=\frac{1}{8}x[/tex]the length of a rectangle is 11 yd more than twice the width and the area of the rectangle is 63 yd squared. find the dimensions of the rectangle.
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the length of a rectangle is 11 yd more than twice the width and the area of the rectangle is 63 yd squared. find the dimensions of the rectangle.
Let
L ------> the lenght
W ----> the width
we know that
the area of rectangle is
A=L*W
A=63 yd2
63=L*W -------> equation 1
and
L=2W+11 ------> equation 2
substitute equation 2 in equation 1
63=(2W+11)*w
2W^2+11w-63=0
solve the quadratic equation using the formula
a=2
b=11
c=-63
substitute
[tex]w=\frac{-11\pm\sqrt[]{11^2-4(2)(-63)}}{2(2)}[/tex][tex]\begin{gathered} w=\frac{-11\pm\sqrt[]{625}}{4} \\ \\ w=\frac{-11\pm25}{4} \\ \end{gathered}[/tex]the solutions for W are
w=3.5 and w=-9 (is not a solution, because is negative)
so
Find the value of L
L=2W+11 -------> L=2(3.5)+11
L=18
therefore
the dimensions are
Length is 18 yardsWidth is 3.5 yardsAssume the random variablex is normally distributed with mean p=85 and standard deviation o=5. Find the indicated probabiliP73
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Remember that
z =(x - μ)/σ
we have
μ=85
σ=5
For x=73
Find out the value of Z1
z1=(73-85)/5
z1=-2.4
For x=76
Find out the value of Z2
z2=(76-85)/5
z2=-1.8
using a z-scores table values
we have that
P(73What are the solutions to the equation (x-3)(x+5)=-15
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Hence, the solutions of the equation is [tex]x = 0, -2[/tex].
What is the equation?
A mathematical statement that shows that two mathematical expressions are equal.
Here given expression is
[tex](x-3)(x+5)=-15\\\\x^2+5x-3x-15=-15\\\\x^2+5x-3x=0\\\\x^2+2x=0\\\\x(x+2)=0\\\\x=0,-2[/tex]
Hence, the solutions of the equation is [tex]x = 0, -2[/tex].
To know more about the equation
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!!PLEASE ANSWER FAST PLEASE!! Given f(x)=(1/4)(5-x)² what is the value of f(11)
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Answer:
f(11) = 9
Explanation:
The equation for f(x) is:
[tex]f(x)=\frac{1}{4}(5-x)^2[/tex]To know the value of f(11), we need to replace x by 11 and solve, so:
[tex]\begin{gathered} f(11)=\frac{1}{4}(5-11)^2 \\ f(11)=\frac{1}{4}(-6)^2 \\ f(11)=\frac{1}{4}(36) \\ f(11)=9 \end{gathered}[/tex]Therefore, the value of f(11) is 9.
From the diagram below, if side AB is 36 cm., side DE would be ______.
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Given
AB = 36 cm
Find
Side DE
Explanation
here we use mid segment theorem ,
this theorem states that the mid segment connecting the mid points of two sides of a triangle is parallel to the third side of the triangle and the length of the midsegment is half the length of the third side.
so , DE = 1/2 AC
DE = 36/2 = 18 cm
final Answer
therefore , the correct option is c
Need help !! Geometry unit 3 parallel and perpendicular lines
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ANSWER;
Converse; Exterior alternate angles are equal
[tex]x\text{ = 3}[/tex]EXPLANATION;
Here, we want to get the value of x given that the lines l and m are parallel
From the diagram given, we can see that;
[tex]15x\text{ +29 = 26x-4}[/tex]The reason for this is that they are a pair of exterior alternate angles
Mathematically, exterior alternate angles are equal
From here, we can proceed to solve for the value of x;
[tex]\begin{gathered} 26x-15x\text{ = 29+4} \\ 11x=33 \\ x\text{ = }\frac{33}{11} \\ x\text{ = 3} \end{gathered}[/tex]Okay so I’m doing this assignment and got stuck ont his question can someone help me out please
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ANSWER
[tex]B.\text{ }\frac{256}{3}[/tex]EXPLANATION
We want to find the value of the function for F(4):
[tex]F(x)=\frac{1}{3}*4^x[/tex]To do this, substitute the value of x for 4 in the function and simplify:
[tex]\begin{gathered} F(4)=\frac{1}{3}*4^4 \\ F(4)=\frac{1}{3}*256 \\ F(4)=\frac{256}{3} \end{gathered}[/tex]Therefore, the answer is option B.
Teresa surveyed 100 students about whether they like pop music or country music. Outof the 100 students surveyed, 42 like only pop, 34 like only country, 15 like both popandcountry, and 9 do not like either pop or country. Complete the two-way frequency table.
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SOLUTION
Write out the given information
[tex]\begin{gathered} \text{Total number of student surveyed=100} \\ \text{like pop only=42} \\ \text{like country only=34} \end{gathered}[/tex][tex]\begin{gathered} \text{like both pop and country=15} \\ Do\text{ not like any =9} \end{gathered}[/tex]Construct the two- way frequency table
Helen has a box of marbles. 1/2 of the marbles are yellow. 1/8 of the
marbles are red. The rest of the marbles are blue. Helen pulls one marble
out of the box at random, records its color, replaces it, and mixes up the
marbles again. If she does this 400 times, how many blue marbles should
she expect to pull out?
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Answer:
150 blue marbles
Step-by-step explanation:
Hello!
If 1/2 of the marbles are yellow, and 1/8 of the marbles are red, then 3/8 of the marbles should be blue.
The percentages are as given:
Yellow = 50%Red = 12.5%Blue = 37.5%To calculate the possible number of blue marbles out of the 400 marbles, we can find 37.5% of 400, as there is a 37.5% chance of getting blue for each turn.
Calculate37.5% of 4000.375 * 400150Helen should expect to pick out 150 blue marbles.
Question60 is 40% of what number?
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let the required number be x then
[tex]\begin{gathered} \frac{60}{x}\times100=40 \\ x=\frac{60}{40}\times100 \\ x=150 \end{gathered}[/tex]So 60 is 40% of 150.
Sales tax in South Carolina is 5%. Mr. Smith bought a new car there for $18,700. What did he pay in sales tax?
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Answer: $935
Step-by-step explanation:
Mr. Smith paid $935 in sales tax
keith lives 5/6 mile north of the school Karen lives 2/3 Mile North of the school what is the distance from Keith's house to Karen's house?
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The distance from Keith's house to Karen's house is
= 5/6 - 2/3
= 5/6 - 4/6
= 1/6 miles
A hot air balloon was descending at a rate of 25 feet per minute and was known to be at an altitude of 425 feet above the ground 21 minutes after it began its descenta) determine the slope-intercept form of the equationb) How high was the balloon when it began its descent (0 minutes)c) How many minutes did it take to land?
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We can model the problem as a linear equation of the form:
[tex]y=mx+b[/tex]Where:
m = Slope (Rate of change)
b = y-intercept (Initial value)
a)
Since it is descending at a rate of 25ft per minute, the slope is:
[tex]m=-25[/tex]So, the equation is:
[tex]y=-25x+b[/tex]b) We know that the ballon was 425ft above the ground 21 minutes after it began its descent, so:
[tex]\begin{gathered} y=425,x=21 \\ so\colon \\ 425=-25(21)+b \\ 425=-525+b \\ b=950 \end{gathered}[/tex]Therefore, the balloon was 950ft when it began its descent, so, we can conclude that the y-intercept is 950, now the equation is complete
[tex]y=-25x+950[/tex]c) We need to know for which value of x, y is equal to 0, so:
[tex]\begin{gathered} y=0 \\ 0=-25x+950 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 25x=950 \\ x=\frac{950}{25} \\ x=38 \end{gathered}[/tex]The balloon will land after 38 minutes
1+1=? Need Help! Asap
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By definition, Addition is a mathematical operation.
In this case, you have the following Addition given in the exercise:
[tex]1+1[/tex]A tornado siren begins blaring from the center of town 9.5 seconds after a tornado was spotted. The siren is located 490 meters north of a school. If the siren’s sound wave travels at a constant velocity of 350 meters per second south, how long will it take the sound wave to travel from the siren to the school?
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The relationship between distance, time and velocity is:
[tex]v=\frac{d}{t}[/tex]The question ask us for the time, we can solve for t:
[tex]v=\frac{d}{t}\Rightarrow t=\frac{d}{v}[/tex]To find the time that it will take the sound wave travelling at 350 m/s to reach the school at 490m is the distance divided the velocity:
[tex]\begin{gathered} t=\frac{490m}{350\frac{m}{s}} \\ \end{gathered}[/tex][tex]t=1.4s[/tex]The answer is 1.4s
Suppose that $2000 is invested at a rate of 3.9%, compounded monthly. Assuming that no withdrawals are made, find the total amount after six years.Round your answer to the nearest cent.
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Compound interest formula:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A\colon\text{Amount} \\ P\colon\text{ Principal} \\ r\colon\text{ interest rate (in decimals)} \\ n\colon\text{ number of times interest is compounded in a year} \\ t\colon\text{ time (in years} \end{gathered}[/tex]Given data:
P= $2,000
r= 3,9% =0.039
n=monthly= 12
t= 6 years
[tex]\begin{gathered} A=2000(1+\frac{0.039}{12})^{12(6)} \\ \\ A=2000(1.00325)^{72} \\ \\ A\approx2526.33 \end{gathered}[/tex]Then, the total amount after six years is $
How do you find the range in a graph like this?
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Answer
y can take on any real number value except around 1 < y < 3 where none of the graphs have values around this region.
Hence, this is the range of the graph.
Explanation
The range of a function refers to the region of values where the fumction can exist. It refers to the values that the dependent variable [y or f(x)] can take on.
From the graph attached to this question, we can see that the function has different forms at different values of x.
But it is also evident that y can take on any real number value except around
1 < y < 3 where none of the graphs have values around this region.
Hence, this is the range of the graph.
Hope this Helps!!!
The following relation defines y as a one-to-one function of x x y3.0 7.45-8.4 -8.072.4 -9.16-1.5 7.45TrueFalse
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One-to-one functions are the ones that each value of "y" is related to only one value of "x". So we need to check in the provided values if that applies.
We have a group of 4 different values of "y". For these the value y = 7.45 is related to the x values of 3 and -1.5, therefore it is not a one-to-one function.
The fraction models below represent two fractions of the same whole: How much of the8음을16
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So 4/5 times 5/8 is 1/2.
What’s 1/5 + 1/2 ? Pls help me
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We need to calculate 1/5 + 1/2:
H = 1/5 + 1/2
Then: H = 7/10
estimate 2,829 divided by 33=?
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Answer: 100
Step-by-step explanation:
Calculate it and 85.7272727273 is closer to 100 so its 100
