The area of a triangle is given by:
[tex]A=\frac{bh}{2}[/tex]Where:
b = base = 18 m
h = height = 20 m
Then, substitute the values:
[tex]A=\frac{18\times20}{2}=\frac{360}{2}=180m^2[/tex]Answer: 180 m^2
What is the slope and y intercept of
-5-y=-3x
Answer:
Slope: 3
y-int: 5
Step-by-step explanation:
Isolate y:
-y = -3x + 5
y = 3x - 5
y = mx + b where x and y are variables, m is the slope and b is the y-int
Hope that helps
Answer:
slope is -3 and y-intercept is -5!
What is the value of the expression?
Enter your answer as a simplified mixed number
Expression is a combination of numbers, operators and variables.
-[-1 1/5 ÷ 0.6(1.3)}-5/6 is the expression and 4.234/6 is solution of the expression.
What is Expression?Expression is a combination of numbers, operators and variables.
-[-1 1/5 ÷ 0.6(1.3)}-5/6
The given expression has plus, minus , multiplication and divided symbols.
By using BODMAS rule we have to solve the expression.
-[-6/5 ÷ 0.78]-5/6
-[-1.2 ÷ 0.78]-5/6
-[-1.539]-5/6
1.539-5/6
(9.234-5)/6
4.234/6
Hence 4.234/6 is the value of expression -[-1 1/5 ÷ 0.6(1.3)}-5/6 after solving.
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what is the solution of 3+ x-2÷x-3<=4
3 + x - 2/x - 3 =< 4
Post the picture please of the problem
(3 + x - 2) / (x - 3) =< 4
3 + x - 2 =< 4(x - 3)
3 + x - 2 = < 4x - 12
x - 4x =< -12 - 3 + 2
- 3x = -15 + 2
-3x =< -13
x >= -13/-3
x >=13/3
I'm trying figure out how to solve this problem. I need to find the volume of the right trapezoidal prism.
In order to calculate the volume of this prism, first let's calculate the base area of the prism.
The bigger base of the trapezoid is 5, the smaller base is 3, and the height is 3, so the area of the trapezoid is:
[tex]\begin{gathered} A=\frac{(5+3)\cdot3}{2} \\ A=\frac{8\cdot3}{2}=12 \end{gathered}[/tex]Then, to find the volume of the prism, let's multiply the base area and the prism height (9 units):
[tex]\begin{gathered} V=12\cdot9 \\ V=108 \end{gathered}[/tex]So the volume is 108 cubic units.
Convert each percent to a fraction and a decimal. 22 2/9%
We will have the following:
First, we transform the percentage as a simple fraction:
[tex]22\frac{2}{9}=\frac{198}{9}+\frac{2}{9}=\frac{200}{9}\approx22.222222\ldots[/tex]So:
[tex]22\frac{2}{9}\approx22.222\ldots[/tex]So, the percentage is approximately 22.222.
***Explanation***
First, we are given a percentage:
[tex]22\frac{2}{9}\%[/tex]Now, in order to determine a fraction that represents this percentage we will have to bear in mind the following:
*A fraction represents a porcentage, so after solving for a simple fraction of the percentage given we obtain as solutions the simple fraction, that is:
[tex]22\frac{2}{9}=\frac{198}{9}+\frac{2}{9}=\frac{200}{9}[/tex]So, the fraction form of the porcentage given is 200 / 9.
And the decimal form is given by siply operating the fraction:
[tex]\frac{200}{9}=22.222222\ldots[/tex]So, it's decimal form is 22.222222... So, it is an infinitely long decimal, so we approximate its form, and it will be approiximately 22.2.
which of these points is the closest to the y-axis
A.(-6,0)
B.(-2,12)
C.(4,2)
D.(5,1)
Carlos has a box of coins that he uses when playing poker with friends. The box currently contains 39 coins, consisting of pennies, dimes, and quarters. The number of pennies is equal to the number of dimes, and the total value is $2.34. How many of each denomination of coin does he have?
Answer:
19 pennies 19 dimes,1 quarter
Step-by-step explanation: it calculate with calculator
Translate and then solve the inequality. “Ten subtracted from the quotient of a number and 7 is less than -6.”
Given:
Ten subtracted from the quotient of a number and 7 is less than -6.
Let x be a number.
The given statement is written as,
[tex]\begin{gathered} \frac{x}{7}-10<-6 \\ \text{Add 10 on both side} \\ \frac{x}{7}-10+10<-6+10 \\ \frac{x}{7}<4 \\ \text{Multiply by 7 on both sides} \\ 7(\frac{x}{7})<7(4) \\ x<28 \end{gathered}[/tex]Answer: the inequality is,
[tex]\frac{x}{7}-10<-6[/tex]The solution is,
[tex]x<28[/tex]One leg of a right triangle is 7cm longer than the shorter leg, the hypotenuse is 17cm, and the area is 60 cm2. Recall the two formulas related to triangles are a2+b2=c2 and Area=1/2(base)(height).a. Sketch the triangle using x for the length of the shorter side, be sure to include all the given information provided in your sketch.b. Give the equation you would use to solve for the missing sides using the length of the hypotenuse...DO NOT SOLVE.c. give the equation you would use to solve for the missing sides using the area...DO NOT SOLVE.
Let the shorter leg be x cm;
then the other side is (7+x)cm;
the hypotenuse side is 17cm;
and the area of the right-angled triangle is 60 square centimeters.
(a)
(b) Recall the pythagorean theorem that the square of the longest side (hypotenuse) is equal to the sum of the squares of the two remaining sides.
[tex]\begin{gathered} (7+x)^2+x^2=17^2 \\ 49+14x+x^2+x^2=289 \\ 2x^2+14x-240=0 \end{gathered}[/tex](c) The area of a triangle is given as;
[tex]\begin{gathered} A=\frac{1}{2}(\text{base)(height)} \\ \text{Where the base =x;} \\ \text{and the height = 7+x} \\ A=60\operatorname{cm}^2 \end{gathered}[/tex][tex]\begin{gathered} 60=\frac{1}{2}\times x\times(7+x) \\ x^2+7x=120 \\ x^2+7x-120=0 \end{gathered}[/tex]Which of the following rational functions is graphed below?O A F(x) = (x - 1)(x - 5)O B. F(X) a (x - 1)(x-6)
Given the graph of a rational function
As shown: the function has vertical asymptotes at:
[tex]x=1,x=5[/tex]So, the dominator will be:
[tex](x-1)(x-5)[/tex]So, the function will be:
[tex]f(x)=\frac{x}{(x-1)(x-5)}[/tex]so, the answer is option B
The equation that represents the graph will be f(x) = x / [(x - 1)(x - 5)]. Thus, the correct option is B.
A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
From the graph, the equation of the asymptotes will be at x = 5, 1. Then the equation is given as,
f(x) = x / [(x - 1)(x - 5)]
Thus, the correct option is B.
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What is the scale factor for AMNP ~ AQRSk=type your answer...
Given
Graph
Procedure
[tex]\begin{gathered} \frac{RS}{NP}=\frac{15}{10} \\ \frac{RS}{NP}=1.5 \end{gathered}[/tex]
T
Which statement must be true if ARST = AXYZ?
OA LT = LX
OB. RS=XY
OC. RT = XY
OD. ZS = LX
The correct option is (B) RS = XY.
What are congruence rules of triangles?
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "≅" is the congruence symbol. When two figures resemble one another in terms of size and shape, this is what mathematics refers to as congruence.
Given, the two congruent triangles are ΔRST and ΔXYZ.
Thus corresponding sides and angles must be equal.
Therefore, ∠R = ∠X, ∠S = ∠Y, ∠T = ∠Z and RS = XY, RT = XZ, TS = ZY
Comparing this to the options in question, only (B) RS = XY is correct.
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Help!! What would K be?
The value of k in the first relation is 5/3 and in the second relation the value of k is 36.5.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that
The relation between x and y:
y = (5/3)x
y = kx
The value k = 5/3
The second relation between x and y:
y = 36.5x
k = 36.5
Thus, the value of k in the first relation is 5/3 and in the second relation the value of k is 36.5.
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You randomly observe purchases at a candy store and record the weight of each bag of candy with 100 different customers. You find the proportion of weights greater than 2 pounds. Is investigating this sample proportion the same as investigating the sampling distribution of the proportion?No, the sample comes from only one store. The sample needs to be expanded to multiple candy stores.Yes, the customers will most likely purchase different weights of candy, and the different amounts will be evenly distributed.No, the sampling distribution of the proportion is the distribution of the proportions from all samples, not just one.Yes, at least 100 customers were observed.
Solution
No, the sampling distribution of the proportion is the distribution of the proportions from all samples, not just one.
Ramiro got a job through the McGovern Employment Agency. The job pays $59400 per year, and the agency fee is equal to 25% of one month's pay How much must Ramir0 pay the agency? Round to the nearest cent. There are 12 months in a year. Input the numbers only -do not insert a dollar sign. Previous o new data to save astchegked at 2:0am Submit Q
He earns $59,400 per year and the agency fee is 25% of one month salary . His one month salary can be calculated as follows
[tex]\frac{59400}{12}=4950[/tex]25% of one month salary can be calculated as follows
[tex]\frac{25}{100}\times4950=\frac{123750}{100}=1237.5[/tex]Find the EQUATION OF THE TANGENT to g(x)=(x-4)^2 at it’s y-intercept. Please use an appropriate limit, much appreciated!
Answer: y = –8x + 16
Explanation
Given
[tex]g\mleft(x\mright)=\left(x-4\right)^2[/tex]First, we have to know the y-intercept, which is the point where x = 0:
[tex]g(0)=(0-4)^2[/tex][tex]g(0)=16[/tex]Thus, the y-intercept is (0, 16).
Next, we have to get the derivative of the function, as the tangent line is the derivative:
[tex]\frac{dg(x)}{dx}=2(x-4)[/tex]Then, we have to compute the slope:
[tex]m=-8[/tex]Finally, we find the line in the slope-intercept form (y = mx + b):
[tex]b=16[/tex]Thus:
[tex]y=-8x+16[/tex]A crate full of oranges weighs 28.4 lb. If the empty crate weighs 3.75 lb. what do oranges alone weigh?
Given,
The weight of crate with full of oranges is 28.4 lb.
The weight of empth crate is 3.75 lb.
So,
The weight of oranges is,
Weight of oranges= weight of caret with orange- weight of emplty crate
[tex]\begin{gathered} =28.4\text{ lb-3.75 lb} \\ =24.65\text{ lb} \end{gathered}[/tex]Hence, the weight of the oranges is 24.65 lb.
Two lines that have a point in common are calledlines.
When a line shares a common point with another line, they are callled intersection lines. In some cases, the lines may be on top of each other, thus describing as collinear or on the same line. Lines can also be parallel, coplane (located in the same plane), congruent, etc. Howerer, the best answer for your question is the intersection of the lines.
The answer is intersection lines
Which number sentence can be used to find the area of the rectangle?
A. 9x3= square centimeters
B. 8x2= square centimeters
C. 9+3= square centimeters
OD. 8+2=square centimeters
Two numbers that can be used to find the area of the rectangle are:
(A) 9×3 cm²(B) 8×2 cm²What are rectangles?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width. A quadrilateral with all of its angles equal, or right angles, is a rectangle. In addition to having all equal angles, a square also has all equal sides. Therefore, a special case of a square is a rectangle. To put it another way, a rectangle can also be a square (when all sides to are equal).So, we know that the formula for the area of the rectangle is:
l × bWhere l is length and b is breadth.
As the l and b are multiplied, then options (C) and (CD) are wrong as they are performing addition, and the correct options can be (A) and (B) and they are performing multiplication.One number can be the length and the second can be the breadth of the rectangle.Therefore, two numbers that can be used to find the area of the rectangle are:
(A) 9×3 cm²(B) 8×2 cm²Know more about rectangles here:
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Emily is standing 24 feet away from a light pole. The distance between Emily to a point of tangency on the pole is 12 feet. What is the radius of the light pole?Note : In the figure distance between Emily and the point of tangency is marked as 24 ft instead of 12.
From the given figure,
AB = Distance between Emily to a point of tangency.
BC = Radius of the pole
AC = Distance between Emily and the pole.
ABC is a right angled triangle at B.
Now,
[tex]\begin{gathered} In\text{ }\Delta ABC\text{ , By Using Pythagoras theorem } \\ AC^2=AB^2+BC^2 \end{gathered}[/tex]Substituting the given values in the statement,
[tex]\begin{gathered} 24^2=12^2+r^2 \\ r^2=24^2-12^2 \\ r^2\text{ = }432 \\ r\text{ = 20.78 ft} \end{gathered}[/tex]Thus the radius of the pole is 20.78 ft .
Quadrilateral ABCD is rotated 90 degrees about the orgin. What are the coordinates of the quadrilateral A'B'C'D?
The coordinates of the object image are;
A {5,5}
B{5,1}
C{2,1}
D{1,5}
The rule for rotation of a point {x,y} through 90 degrees about the orgin, is that the object coordinates {x,y} change to image coordinates { y,-x}. This means the coordinates shift positions and the y coordinate acquires a negative sign. So in this case;
A {5,5}------- A' { 5,-5}
B{5,1}----------B' {1,-5}
C{2,1} ---------C' {1,-2}
D{1,5} ---------D' { 5,-1}
Answer
A.
you put $939 into an investment at 8% annual interest for 6 years what will your balance be at the end of 6 years
The amount put into the investment which is 939 is the principal, P.
The annual interest is 8% (or 0.08) while the duration in years is 6, that is T.
The simple interest formula is given as;
[tex]\begin{gathered} I=\text{PRT} \\ I=939\times0.08\times6 \\ I=450.72 \\ \text{The balance at the end of 6 years will be;} \\ A=P+I \\ A=939+450.72 \\ A=1389.72 \end{gathered}[/tex]The balance at the end of 6 years will be $1,389.72
4x-1/2+2/3x very hard :]
The required polynomial (24x² - 3x + 4) / 6x is equivalent to the given expression 4x - 1/2 + 2/3x.
What is the expression?Expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression below which is given in the question.
⇒ 4x - 1/2 + 2/3x
Rearrange the terms likewise and apply the arithmetic operation
⇒ 4x + 2/3x - 1/2
Take the LCM in the above expression,
⇒ (6x × 4x + 2 × 2 - 3x ×1) / 6x
⇒ (24x² + 4 - 3x) / 6x
⇒ (24x² - 3x + 4) / 6x
The required polynomial (24x² - 3x + 4) / 6x is equivalent to the given expression.
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The question seems to be incomplete the correct question would be
Which polynomial is equivalent to the below expression?
4x - 1/2 + 2/3x
Mike wants to buy a new suit. The suit he likes is on sale for 30% off it’s original price. Her parents agree to pay for 50$ of the cost. If the original cost of the bike is 150$, how much of her own money will sierra have to pay? (No sales tax is charged.)
Percentage, a relative value indicating hundredth parts of any quantity.
Sierra needs to pay $55 of her own money to get the bike.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given that ,
Mike wants to buy a new suit. The suit he likes is on sale for 30% off it’s original price. Her parents agree to pay for 50$ of the cost.
the original cost of the bike is 150$.
We need to find how much has to pay her own.
Now firstly let us calculate what is the 30% of 150
We need to convert 30% to decimal by dividing with hundred
30/100=0.3
Now multiply 0.3 with 150
0.3×150=$45
Hence the off value is $45
Now subtract $45 from $150 we get
$150-$45=$105.
Siera parents will pay $50.
$105-$50
We get $55.
Hence Sierra has to pay $55 of her own money to get the bike.
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Need help with equation of a circle
It is important to know that the standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h, k) is the center.
According to the given image, the center is (-1,2). So, h = -1 and k = 2.
Also, the radius shown is 2 units. So, r = 2.
Hence, the equation would be
[tex]\begin{gathered} (x-(-1))^2+(y-2)^2=2^2 \\ (x-(-1))^2+(y-2)^2=4 \end{gathered}[/tex]Hence, the answer is C.9. Alice bought a round-trip ticket to fly
from Baltimore to Chicago on
SuperAir for $250. That was $16
more than she would have paid on Jet
Airlines, which only offered a one-way
fair. How much did Jet Airlines charge
to fly from Baltimore to Chicago?
Jet Airlines charging $ 234 to fly from Baltimore to Chicago.
Given :
Tickets from Baltimore to Chicago on Super Air is $250
Which is $16 more than Jet Airlines.
Therefore she was going to pay $250 - $16 at the Jet Airlines.
= $ 234
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Rita has a circular hot tub . The hot tub has a circumference of 25.12 feet . It is 3.5 feet deep. c. The hot tub manual recommends filling the hot tub to 80% of its full capacity. Howmuch water should Rita put in the hot tub in order to follow the recommendation?
Step 1
The circular hot tube is in the shape of a cylinder. Therefore its volume will be;
[tex]v=\pi\times r^2\times h[/tex]where;
[tex]\begin{gathered} circumference=2\times\pi\times r=25.12ft \\ h=3.5feet \end{gathered}[/tex]Find r, using the circumference
[tex]\begin{gathered} 2\times\pi\times r=25.12 \\ \pi r=\frac{25.12}{2} \\ r=\frac{25.12}{2\pi} \\ \end{gathered}[/tex]Step 2
Find the volume of the hot tube at 100%
[tex]\begin{gathered} v=\pi\times(\frac{25.12}{2\pi})^2\times3.5 \\ v=3.5\pi\frac{25.12^2}{2^2\pi^2} \\ v=3.5\times\:50.21453046 \\ v=175.7508566ft^3 \end{gathered}[/tex]Step 3
Find the recommended capacity which is 80% full
[tex]\begin{gathered} \frac{175.7508566}{x}=\frac{100}{80} \\ x=140.6006853ft^3 \\ \end{gathered}[/tex]Note; 1 Cubic foot=7.48052 gallons of water. Therefore, the water Rita should put in the hot tub will be;
[tex]\begin{gathered} \frac{140.6006853ft^3}{1ft^3}=\frac{y}{7.48052} \\ y=1051.766238\text{ gallons of water} \\ \approx1051.77\text{ gallons of water} \end{gathered}[/tex]Answer;
[tex]1051.77\text{ gallons of water}[/tex]If ST = 11 and RT = 41, find RS. Use the number line below.RRS =(Type an integer or a decimal.)
1) Let's draw the line to better understand this
2) In this case, let's use the Segment Addition Postulate.
Since RT = 41 and ST=11
41 -11=30
So RS = 30
the graph shows the profit, y, of a community fundraiser, with respect to the number of tickets sold, x.use the graph to determine the y-intercept and what it represents A) the y-intercept = 35 and represents the number of tickets sold B) the y-intercept = -700 and represents the number of tickets sold C) the y-intercept = -700 and represents the initial amount of expensesD) the y-intercept = 35 and represents the initial amount of expenses
we have that
x -----> number of tickets sold
y ----> profit
Remember that
the y-intercept is the value of y, when the value of x is zero
in this context
the y-intercept is the profit when the number of tickets sold is zero (initial value of profit)
Looking at the graph
the y-intercept is $-700
therefore
the answer is option CKE= 1/2 mv^2 solve for v
Step-by-step explanation:
[tex]KE = \frac{1}{2} mv^{2}[/tex] solve for v
multiply both sides by 2:
[tex]2(KE) = 2(\frac{1}{2} mv^{2})\\2KE = mv^{2}[/tex]
divide both sides by m:
[tex]2KE = mv^{2}\\\frac{2KE}{m} = \frac{mv^{2}}{m} \\[/tex]
[tex]v^{2} = \frac{2KE}{m}[/tex]
take the sqrt of both sides:
[tex]\sqrt{v^{2}} = \sqrt{\frac{2KE}{m}}\\[/tex]
so:
[tex]v = \sqrt{\frac{2KE}{m}}\\ OR\\ v = -\sqrt{\frac{2KE}{m}}\\[/tex]
