Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into thecorrect position in the answer box. Release your mouse button
Since we have a right isosceles triangle,we have the following:
using the pythagorean theorem, we have:
[tex]\begin{gathered} x^2+x^2=(12)^2 \\ \Rightarrow2x^2=144 \\ \Rightarrow x^2=\frac{144}{2}=72 \\ \Rightarrow x=\sqrt[]{72}=6\cdot\sqrt[]{2} \\ x=6\cdot\sqrt[]{2} \end{gathered}[/tex]therefore, the length of each leg of the isosceles right triangle is 6*sqrt(2)
what digit is in the
The absolute value of |3| is 3.
What is the area of the acute triangle given below? A. 36 sq. units O B. 26 sq. units O C. 18 sq. units D. 72 sq. units
Solution
From the info given we have this:
h= 6ft
b = 12ft
And we can use the following formula:
[tex]A=\frac{b\cdot h}{2}=\frac{12\cdot6}{2}=36ft^2[/tex]then the answer would be:
a ) 36 ft^2
evalute 2×[4×(2+1)×3]
Given the expression:
[tex]2\times\mleft[4\times\mleft(2+1\mright)\times3\mright][/tex]The answer will be as follows:
[tex]\begin{gathered} 2\times\mleft[4\times\mleft(2+1\mright)\times3\mright] \\ =2\times\mleft[4\times3\times3\mright] \\ =2\times36 \\ =72 \end{gathered}[/tex]so, the answer will be 72
-Quadratic Equations-The sum of two integers is 42 and their product is 432. Write and solve an equation to find the two integers.
numbersThe first thing to do is to write the exact relations from the question, as follows:
[tex]\begin{gathered} x+y=42 \\ x\times y=432 \end{gathered}[/tex]Where X and Y stand for the unknown integer numbers.
Now, we will isolate Y in the first equation and substitute in the second one. This way, we will be able to find the value of X. From this strategy, we perform the calculation that follows:
[tex]\begin{gathered} y=42-x\to x\times(42-x)=432 \\ 42x-x^2=432\to0=x^2-42x+432 \\ x^2-42x+432=0 \end{gathered}[/tex]Now, it is important to remember the Bhaskara relation. But first, let's remember that any quadratic equation attends to the following generic form:
[tex]y=ax^2+bx+c[/tex]And we use the Bhaskara relation to find the values of X where Y is 0. In the present question, the constants are the following:
[tex]\begin{gathered} a=1 \\ b=-42 \\ c=432 \end{gathered}[/tex]And the Bhaskara relation is:
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Now, we will substitute the values and perform the calculation.
[tex]\begin{gathered} x_{1,2}=\frac{-(-42)\pm\sqrt[]{(-42)^2-4\times1\times432}}{2\times1} \\ x_{1,2}=\frac{-(-42)\pm\sqrt[]{1,764-1,728}}{2}=\frac{42\pm\sqrt[]{36}}{2}=\frac{42\pm6}{2} \\ x_1=\frac{42+6}{2}=\frac{48}{2}=24_{} \\ x_2=\frac{42-6}{2}=\frac{36}{2}=18 \end{gathered}[/tex]As you can see, both numbers, 24 and 18, if summed will result in the number 42. For this reason, we found here, not only the value of X but also the value of Y. Because there is no distinction between X and Y, you say that:
The two number which are integers, their sum is 42 and their multiplication is 432 are the numbers 24 and 18.Drag a number next to the correct description in the chart. Not all answer choices will be used
a) The distance between 4 and -24 on a number line.
A distance in one dimension can be calculated as:
[tex]D=|x_1-x_2|=|4-(-24)|=|4+24|=|28|=28[/tex]b) The distance between -12 and 5 on a number line.
[tex]D=|-12-5|=|-17|=17[/tex]c) The distance between -14 and -6 on a number line.
[tex]D=|-14-(-6)|=|-14+6|=|-8|=8[/tex]Note: when calculating distances, it doesn't matter which of the two numbers we put first in the substracion. It will yield the same result.
Answer: A) 28, B) 17 C) 8
need help asappppppp
Ok, so:
Let me draw the situation here below:
We're going to use the pythagorean theorem:
If 9² + 12² = 15², then, the triangle is a right triangle.
So, 81 + 144 = 225
So, the relation is good.
Then, the statement is true.
To find the solution when adding vectors, simply draw and label the given information. Answer here
the answer to the statement is
To find the __________solution when adding vectors simply draw and label the given information.
is
To find the resultant solution when adding vectors simply draw and label the given information.
then the answer is
resultant
You buy a square lot that is 330 ft. on each side. What is its size in acres?
Given in the question:
a.) A square lot is 330 ft. on each side.
To be able to determine the size of the lot in acres, let's first recall how many sq. ft. are there in 1 acre.
[tex]\text{ 1 acre = 43,560 ft.}^2[/tex]Step 1: Let's determine the area of the lot.
[tex]\text{ Area = s}^2\text{ ; Formula in getting the area of a square}[/tex]We get,
[tex]\text{ Area = 330}^2[/tex][tex]\text{ Area = }108,900ft.^2[/tex]Therefore, the area of the lot is 108,900 sq. ft.
Step 2: Let's convert the area in sq. ft. to an acre.
[tex]\text{ 1 acre = 43,560 ft}^2[/tex][tex]\text{ = 108,900 (ft}^2)\text{ x }\frac{1\text{ acre}}{43,560(ft^2)}[/tex][tex]\text{ = }\frac{108,900}{43,560}\text{ acre}[/tex][tex]\text{ = 2.5 acres}[/tex]Therefore, the size of the lot in acres is 2.5
There is a line that includes the point (0, 10) and has a slope of 7. What is its equation inslope-intercept form?
We have that the slope-intercept form is
[tex]y=mx+b[/tex]where
m is the slope
b is the y-intercept, the value of the y-coordinate when x=0
in this case, we have
m=7
b=10
we substitute the values and we find the slope-intercept form
[tex]y=7x+10[/tex]Solve for x? Round to the nearest whole number
The solution for x, considering the relations in a right triangle, is given as follows:
x = 924.
Solution for xFor the large triangle, we have that:
The base is of b.The height is of 500.The angle adjacent to the base is of 20º.The value of b is found applying the tangent of the angle, as follows:
tan(20º) = 500/b
0.36397023426 = 500/b
b = 500/0.36397023426
b = 1374.
For the smaller triangle, it is found that:
The base is of a.The height is of 500.The angle adjacent to the base is of 48º.Hence the value of the base is also found with the tangent as follows:
tan(48º) = 500/a
1.11061251483= 500/a
a = 500/1.11061251483
a = 450.
Hence the measure of x is calculated as follows:
x = 1374 - 450 = 924.
More can be learned about right triangles at https://brainly.com/question/2217700
#SPJ1
graph the system of inequalitiesy > -3x + 5y ≤ x - 2
Solution
The solution therefore, is (1.75, -0.25) and all points beyound the intersection of both lines
Janet solved the inequality and was asked to express her answer in set notation. Determine ifshe made a mistake, correct the mistake if she made one and create the correct expression inset notation.-X - 2 <-3-x < -1x < -1Set Notation: {x | x < -1}
It is given that:
[tex]\begin{gathered} -x-2<-3 \\ -x-2+2<-3+2 \\ -x<-1 \\ x>1 \end{gathered}[/tex]So she made a mistake in the last step.
The answer should be x>1
The set notation will be:
[tex]\mleft\lbrace x|x>1\mright\rbrace[/tex]x + 5y = 12Step 2 of 2: Determine the missing coordinate in the ordered pair (?, -2) so that it will satisfy the given equation.
given the equation:
x + 5y = 12
given the ordered pair (?, -2)
recall that,
A coordinate is (x, y)
that means from the ordered pairs given,
y = -2
x = ?
let's substitite y = -2 into the given equation
x + 5y = 12
x + 5(-2) = 12
x - 10 = 12
collecting like terms
x = 12 + 10
x = 22
therefore, the coordinate that will satisfy the given eq
Silvia manages a sub shop and needs to prepare smoked turkey sandwiches. She has 1- lb of turkey in the cooler, and each sandwich requires001Ib of turkey. How many sandwiches can she make?
The total amount of turkey available to make the sandwiches is 1 1/2lb. Each sandwich requires 1/2lb of turkey. To determine how many sandwiches can be made you have to divide the total amount by the amount needed per sandwich:
[tex]1\frac{1}{2}\div\frac{1}{2}[/tex]First, you have to express the mixed number as a fraction:
-Divide the whole number by 1 and add 1/2
[tex]\frac{1}{1}+\frac{1}{2}[/tex]-Multiply the first fraction by 2 to express it using the same denominator and add 1/2
[tex]\frac{1\cdot2}{1\cdot2}+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{2+1}{2}=\frac{3}{2}[/tex]Now you can write the division as follows:
[tex]1\frac{1}{2}\div\frac{1}{2}=\frac{3}{2}\div\frac{1}{2}[/tex]To divide two fractions, you have to multiply the dividend by the reciprocal (inverse) fraction of the dividend. So, switch 1/2 upside down and multiply both fractions:
[tex]\frac{3}{2}\div\frac{1}{2}=\frac{3}{2}\cdot\frac{2}{1}=\frac{3\cdot2}{2\cdot1}=\frac{6}{2}=3[/tex]Silvia can make 3 sandwiches with the smoked turkey available.
Write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it.
can u also do the which rule part in addition to the proofs? thanks !
and u get brainliest if you make a proof chart
For the given parallelogram;
ΔESN ≅ ΔSNA (By ASA congruence).
What is meant by the term ASA congruence?According to the ASA congruence rule, if two angles of one triangle and the side provided between these two angles are equal to two angles of another triangle as well as the side provided between them, therefore the two triangles are congruent.In parallelogram ESAN
Given: SA || NE
SE || NA
Thus, it form parallelogram ESAN (apposite pair of sides parallel)
So,
∠ESN = ∠SNA (alternate interior angle)
∠ENS = ∠NSA (alternate interior angle)
SN = SN common
Thus, ΔESN ≅ ΔSNA (By ASA congruence).
To know more about the ASA congruence, here
https://brainly.com/question/2398724
#SPJ1
This is a 30-60-90 triangle.What is the measure of x?Rationalize the denominator.x = [?]?12
The value of x is:
[tex]x=4\sqrt[]{3}[/tex]To solvbe this, we need to use the tan function. The 60º is at the top left of the triangle, and the 30º angle is on the bottom right.
Then we know, the angle bottom right = 30º, the opposite leg = x and the adjacent leg = 12
The trignometrical function that relates those 3 things is tangent:
[tex]\tan (\theta)=\frac{\text{opposite leg}}{\text{ adjacent leg}}[/tex]In this case:
[tex]\begin{gathered} \tan (30º)=\frac{x}{12} \\ x=12\cdot\tan (30º) \end{gathered}[/tex]Thus:
[tex]\tan (30º)=\frac{1}{\sqrt[]{3}}\Rightarrow x=12\cdot\tan (30º)=\frac{12}{\sqrt[]{3}}[/tex]Now we need to rationalize the answer. To do it, we multiply and divide by the denominator:
[tex]x=\frac{12}{\sqrt[]{3}}\times\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{12\sqrt[]{3}}{3}=4\sqrt[]{3}^{}[/tex]And that's the answer
Y=-10x-75How do I get the x-intercept of this linear equation
In order to find the x-intercept, we must make y equal to 0.
[tex]0=-10x-75[/tex]then, clear the equation for x
[tex]\begin{gathered} 10x=-75 \\ x=-\frac{75}{10} \\ x=-7.5 \end{gathered}[/tex]The x-intercept of the linear equation is (-7.5,0)
Ged test how do I determine the value of x?
D) 26"
1) Similar triangles have proportional sides and congruent angles.
2) As the picture state that these two triangles are similar, then we can write out the following ratios:
[tex]\frac{x}{8}=\frac{19\frac{1}{2}}{6}=\frac{32\frac{1}{2}}{10}[/tex]But notice that, since we have Mixed Numbers it is easier to convert them to Improper fractions:
[tex]\begin{gathered} 32\frac{1}{2}=\frac{2\times32+1}{2}=\frac{65}{2} \\ 19\frac{1}{2}=\frac{2\times19+1}{2}=\frac{39}{2} \\ \end{gathered}[/tex]To convert it keep the denominator and multiply that by the whole number and then add to the numerator.
2.2) Now we can plug them back, but we just need two ratios the one with the missing length and a ratio with known length:
[tex]\begin{gathered} \frac{x}{8}=\frac{19\frac{1}{2}}{6}\Rightarrow\frac{x}{8}=\frac{\frac{39}{2}}{6} \\ \frac{x}{8}=\frac{\frac{39}{2}}{6} \\ 6x=8\cdot\frac{39}{2} \\ 6x=156 \\ \frac{6x}{6}=\frac{156}{6} \\ x=26 \end{gathered}[/tex]Hence, the line segment AB is 26inches long
Complete the table below. Provide an answer for each integer division problem, and write a related equation using integer multiplication.
You need to remember the Sign Rules for Division:
[tex]\begin{gathered} \frac{-}{-}=+ \\ \\ \frac{+}{+}=+ \\ \\ \frac{-}{+}=- \\ \\ \frac{+}{-}=- \end{gathered}[/tex]And the Sign Rules for Multiplication:
[tex]\begin{gathered} -\cdot-=+ \\ +\cdot+=+ \\ -\cdot+=-_{} \\ +\cdot-=- \end{gathered}[/tex]Then, knowing those rules, you can solve the operations given in the exercise:
1. For the Integer Division:
[tex]-36\div(-9)=4[/tex]The result is positive because both numbers have the same sign.
Now, knowing that result, you can set up the following Related Equation using Integer Multiplication:
[tex](-9)(4)=-36[/tex]2. For the second Division, you get:
[tex]24\div(-8)=-3[/tex]Then, its corresponding Related Equation using Integer Multiplication can be:
[tex](-8)(-3)=24[/tex]3. For the next one, you get:
[tex]50\div10=5[/tex]So, its corresponding Related Equation using Integer Multiplication can be:
[tex]10\cdot5=50[/tex]4. For the last Division, you get:
[tex]42\div6=7[/tex]Hence, its corresponding Related Equation using Integer Multiplication can be:
[tex]7\cdot6=42[/tex]Therefore, the answer is:
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
13
Step-by-step explanation:
The value of x is 13. This can be shown thus:
(x - 7)² = 36
(x - 7)² = 6²
Therefore, x - 7 = 6
Collect like terms
x = 6 + 7
x = 13
a car's speedometer has a percent error of 5% the speedometer currently shows that the car is traveling at a speed of 60 miles per hour which statement describes the actual speed of a car would be
We know that the percent error is 5%, so, if the speed shown by the car is 60 miles per hour, then we have to subtract the percentage error to find the actual speed.
[tex]\begin{gathered} 0.05\cdot60=3 \\ 60-3=57 \\ 60+3=63 \end{gathered}[/tex]The actual speed is 57 miles per hour.
Hence, the right statement is C because the speed could be 57 or 63 miles per hour.what is a factor of the expression 250 x cubed - 16 y ^ 3
Consider the given expression as,
[tex]250x^3-16y^3[/tex]The equation can be written as,
[tex](\sqrt[3]{250}x)^3-(\sqrt[3]{16}y)^3[/tex]Use the algebraic identity,
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]Substitute the values and simplify,
[tex](\sqrt[3]{250}x)^3-(\sqrt[3]{16}y)^3=(\sqrt[3]{250}x-\sqrt[3]{16}y)\mleft\lbrace(\sqrt[3]{250}x)^2+(\sqrt[3]{250}x)(\sqrt[3]{16}y)+(\sqrt[3]{16}y)^2\mright\rbrace[/tex]Thus, the factors of the given expression are,
[tex](\sqrt[3]{250}x-\sqrt[3]{16}y)\text{ and }\lbrace(\sqrt[3]{250}x)^2\text{ and }(\sqrt[3]{250}x)(\sqrt[3]{16}y)+(\sqrt[3]{16}y)^2\rbrace[/tex]Kevin rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 95 cents for each mile driven, Kevin had to payS1850 when he returned the truck or how many miles did he drive the truck?
To answer this, first subtract $ 18.99 from the total ( $ 1850 )
$1850 - $
Find the vertex and write the quadratic function in vertex form (which our OpenStax textbook also calls the standard form).f(x)=x2−12 x + 117
Given
[tex]f(x)=x^2-12x+117[/tex]To find:
The vertex and the equation in vertex form.
Explanation:
It is given that,
[tex]f(x)=x^2-12x+117[/tex]That implies,
[tex]\begin{gathered} f(x)=x^2-12x+117 \\ f(x)=[(x-6)^2-36]+117 \\ f(x)=(x-6)^2+81 \\ y-81=(x-6)^2 \end{gathered}[/tex]Hence, the vertex is (6,81) and the vertex form of the equation is
[tex]y=(x-6)^2+81[/tex]You planted 460 acres in soybeans You treated 2.4 pints per acre the herbicide sells for $101 per 2.5 container How many gallons of herbicide will you use ?
Since 2.4 pints per acre were used, multiply the total amount of acres (460) times 2.4 to find the total volume of herbicide to be used:
[tex]460\times2.4\text{ pints}=1104\text{ pints}[/tex]Since 1 gallon is equal to 8 pints, divide the number of pints over 8 to find the number of gallons that will be used:
[tex]\frac{1104}{8}=138[/tex]Therefore, 138 gallons will be used.
A road sign reads "Speed Limit 30." Which statement best represents the allowed driving speeds (x) on this road?
hello
this question involves a simple multiplication of numbers
Answer:
Step-by-step explanation:3xp23
x
a nurse has chlorpromazine for injection that contains 10 mg per 2 ml he must give a patient 0.025 grams. how many ml should he give the patient
Our data are the following
1. We have an injection that contains 10 mg/ 2ml.
We want to know how many ml should he give if the nurse must give a patient 0.015 gr.
for this purpose we proceed with the so-called rule of 3:
So, we resolve the above rule to x ml, that is:
x ml = (0.025 mg x 2ml ) ÷ 10 mg ,
the above is equivalent to say
x ml = ( 0.05 ml ) ÷ 10 = 0.005 ml
So, we can conclude that
the ml should he give the patient is 0.005 ml
If a coffee table was originally priced at $64 but was on sale for 75% off the original price. What is the sale price?
Answer:
$16
Explanation:
Original Price of the table =$64
There is a sale for 75% off the original price.
75% of the original price = 75% x 64
=0.75 x 64
=$48
Therefore, the sales price will be:
[tex]\begin{gathered} Original\; Price-Amount\text{ off} \\ =64-48 \\ =\$16 \end{gathered}[/tex]The sale price of the table is $16.
2. The distance-time graph shows two cars that are traveling at the same time. Which car has the greater speed, and by how much? DA Car B Car A Distance (km) 480 420 3601 300 2401 1801 120 60 0 2 3 4 5 6 7t Time (h) 12
The speed of the car = distance/time
Let us find the speed of each car
Car A starts from (0, 0) to (6, 360)
Its speed is
[tex]SA=\frac{360-0}{6-0}=\frac{360}{6}=60[/tex]The speed of car A is 60 km/h
car B starts at (1, 0) to (6, 480)
Its speed is
[tex]SB=\frac{480-0}{6-1}=\frac{480}{5}=96[/tex]The speed of car B is 96 km/h
Therefor car B is faster than car A
Since the difference between their speeds = 96 - 60 = 36 km/h
Car B is faster by 36 km/h