Answer:
[tex]125.9 ft^2[/tex]
Step-by-step explanation:
Missing question:
An artist is making a rectangular canvas for a custom painting. the canvas has a width of 9 1/2 feet and a length of 13 1/4 feet . what is the area of canvas in square feet?
The area of a rectangle is given by the formula
[tex]A=L\cdot w[/tex] (1)
where
A is the area
L is the length
w is the width
In this problem, we have a rectangular canvas, so we want to find its area.
We know that:
[tex]w=9\frac{1}{2}ft[/tex] is the width, converting into an improper fraction,
[tex]w=\frac{9\cdot 2+1}{2}=\frac{19}{2}[/tex] ft
[tex]L=13\frac{1}{4}ft[/tex] is the length, converting into improper fraction,
[tex]L=\frac{13\cdot 4+1}{4}=\frac{53}{4}[/tex] ft
Substituting into eq (1), we can find the area of the canvas:
[tex]A=\frac{19}{2}\cdot \frac{53}{4}=\frac{1007}{8}=125.9 ft^2[/tex]
The graph of y = -x 2 + 3x - 2 is shown. The ZERO(S) of this function is/are
Answer:
x=2 , 1
Step-by-step explanation:
the zeros are the value of X
-x+2x+x-2
-x(x-2)+x-2
(x-2)×(x+1)
x = 2 , 1
Estimate the quotient by rounding each number to the nearest whole number. 33.7/ 9.5
Answer: 34/10=3.4 The estimated quotient is 3.4
Step-by-step explanation: Basically, you are dividing 33.7 by 9.5, but first you will need to round to the nearest whole number. A whole number does not contain a decimal. 33.7 rounded to the nearest whole number is 34. 9.5 rounded to the nearest whole number is 10. So, you are dividing 34 by 10. 34 divided by 10 is 3.4.
The quotient of 33.7/9.5, rounded to the nearest whole number is: 4.
What is Quotient of Two Numbers?Quotient of a two numbers, "a" and "b" equals a/b.Quotient means division.Therefore, the quotient between 33.7 and 9.5 would be:
33.7/9.5 = 3.547 (division).
We are asked to round to the nearest whole number.
Therefore, the quotient of 33.7/9.5, rounded to the nearest whole number is: 4.
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31 workers are working on a construction site. 5 more workers work for company A than for company B. How many workers work for each company?
25pts
Answer:
18 work for company A and 13 for company B
Step-by-step explanation:
Company A = A
Company B = B
A = B + 5
A + B = 31
B + 5 + B = 31
2B + 5 = 31
2B = 26
B = 13 -->
A = 13 + 5
A = 18
I
If f(x) = 2x² - x -9 , find:
a. f(-2)
b. f(x-2)
c. r?
Answer:
[tex]f(x) = 2 {x}^{2} - x - 9 \\ \\ a) \: plug \: x = - 2 \\ f( - 2) = 2 \times {( - 2)}^{2} - ( - 2) - 9 \\ f( - 2) = 2 \times 4 + 2 - 9 \\ f( - 2) =8 + 2 - 9 \\ f( - 2) =10 - 9 \\ \huge \red{ \boxed{ f( - 2) =1}} \\ \\ b) \: \: plug \: x = x - 2 \\ f(x - 2) = 2 {(x - 2)}^{2} - (x - 2) - 9 \\ f(x - 2) = 2 {( {x}^{2} - 4x + 4 )} - x + 2- 9 \\ f(x - 2) = 2 {x}^{2} - 8x + 8 - x + 2- 9 \\ \purple{ \boxed{\bold{f(x - 2) = 2 {x}^{2} - 9x + 1}}} \\ \\ c) \: \: plug \: x = r \\ \orange{\boxed{\bold{f(r) = 2 {r}^{2} - r - 9}}}[/tex]
Find the value of the expression. Left-bracket (three-fifths) Superscript 0 Right-bracket Superscript negative 2 The value is .
Answer:
1
Step-by-step explanation:
Answer:
answer in picture as well
1
Step-by-step explanation:
Last quarter, 84 seventh grade students
made honor roll. If there are 400 students in
the seventh grade, what percent made
honor roll?
Answer:
21%
Step-by-step explanation:
okay so 400 is your denominator, and 84 is your numerator, so divide 400 by 4 so you get 100, because your percentage should be out of 100. because you divided 400 by 4, you also have to do that for 84, giving you 21 out of 100. converted to a decimal its .21, or 21%
Final answer:
To find the percentage of seventh grade students who made honor roll, a proportion is used, yielding a result of 21 percent.
Explanation:
To calculate the percentage of seventh grade students who made honor roll, we can set up a proportion where 84 students is to 400 students as x percent is to 100 percent. The proportion can be written as 84/400 = x/100. To find x, we cross-multiply and solve for x.
First, cross-multiply: 84 * 100 = 400x. This gives us 8400 = 400x. Next, divide both sides of the equation by 400 to solve for x: 8400 / 400 = x. This results in x being equal to 21. Therefore, 21 percent of the seventh grade students made honor roll.
Vanessa draws one side of an equilateral triangle ABC on the coordinate plane at points A(-2, 1) and B (4, 1). What are the two possible coordinates of vertex C? Round to the nearest tenth.
Answer:
two vertex are: (1 , 6.2) , (1 , - 4.2)
Step-by-step explanation:
A(-2, 1) and B (4, 1) AB is a parallel segment with x axis
The 3rd vertex P (x , y) will locate at the mid point of AB
x = (-2) + (4 - (-2)) /2 = 1 P (1 , y)
length AB = 4 - (-2) = 6
AP = AB (equilateral)
BP² = (4 - 1)² + (1 - y)² = 6²
1 - 2y + y² = 36 - 9 = 27
y² - 2y -26 = 0
y = ((-(-2)) ± √(-2)² - 4 x (-26)) / 2 = (2 ± √108) / 2 = 1 ± 5.2
y = 6.2 or y = -4.2
P (1 , 6.2) or P ( 1 , -4.2)
To find the possible coordinates of vertex C of an equilateral triangle with side AB on the coordinate plane, we calculate the midpoint of AB and use the length of the altitude to find two possible positions for C, approximated as (1, 6.2) and (1, -4.2).
Vanessa draws one side of an equilateral triangle on the coordinate plane at points A(-2, 1) and B (4, 1). To find the possible coordinates of vertex C, we first recognize that in an equilateral triangle, all sides are of equal length, and the altitude forms a 60-degree angle with the base.
Given points A(-2, 1) and B(4, 1), the distance AB is 6 units. Using the Pythagorean theorem in a 30-60-90 right triangle, the length of the altitude (half of the triangle height) from the midpoint of AB to C is 3√3. To find coordinate C, we add and subtract this distance from the midpoint of AB, which we calculate as ((-2 + 4)/2, (1 + 1)/2) = (1, 1).
Thus, the two possible coordinates for C are (1, 1 + 3√3) and (1, 1 - 3√3), which approximately are (1, 6.2) and (1, -4.2), rounding to the nearest tenth.
Find the length of side A on a triangle where side B is 4 and side C (the hypotenuse) is 5.
A) 4
B) 5
C) 3
D) 2
Answer:
Your answer is: C) 3
Step-by-step explanation:
The formula used to find side A in this problem is called the Pythagorean Theorum. The formula is as follows: a = the square root of c squared minus b squared. Or, you can say that the hypotenuse is equal to: c = the square root of a squared and b squared added together. This might sound confusing in the start, but here's all you have to do. c^2 = 25. 4^2 = 16. 25 - 16 = 9. The square root of 9 = 3. C) 3 is your answer.
If 2(x+5)=7x-5, then what is the value of 2X squared +10
Answer:
28
Step-by-step explanation:
in order to evaluate for the value of x from this 2(x+5)=7x-5 , we will open the bracket and the evaluate for x.
solution
2(x+5)=7x-5
2x + 10 = 7x - 5
collect the like terms together
2x + 10 +5 = 7x
15 = 7x - 2x
15 = 5x
divide both sides by 5
15/5 = 5x/5
3 = x
x =3
so, to evaluate for 2x² + 10
will be
2x² + 10
2 (3)² + 10
2 x 9 + 10
18 + 10
28
Convert:
? kilometers = 10,000 meters
Step-by-step explanation:
[tex]1km = 1000m \\ x = \frac{10000}{1000} \\ x = 10km[/tex]
Answer:
1
Step-by-step explanation:
IT means that that 1km is =10000m
PLS HELP ASAP LIKE PLSSSSS
.............................
Estimate the solution to the system of equations 2x+3y=6 -4x+3y=12
The solution of the system is x = - 1 and y = 8/3.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
We have a system of equations,
2x+3y=6 {equation 1}
-4x+3y=12 {equation 2}
Subtracting equation 2 to equation 1,
2x - (-4x) = 6 - 12
6x = - 6
x = - 1.
And y = 8/3
Therefore, the solution is x = - 1 and y = 8/3.
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What do you know about the scale factor for the dilation shown? Explain.
The scale factor is some number between 0 and 1 (not including either endpoint) because the image is smaller than the preimage.
Triangle ABC is the preimage, or the "before"; while triangle A'B'C' is the image, which is the "after".
preimage ----> image
before ----> after
Answer:
he scale factor is some number between 0 and 1 (not including either endpoint) because the image is smaller than the preimage.
Triangle ABC is the preimage, or the "before"; while triangle A'B'C' is the image, which is the "after".
Step-by-step explanation:
sixty-three less than 15 times a number is 72. what is the number?
Answer:
-3/5
Step-by-step explanation:
First represent this with numbers. Less means subtraction -, times means multiplication *, is means equals =.
And let's represent "a number" with x.
63 - 15x = 72
Solve for x. First subtract 63 from both sides.
-15x = 72-63
-15x = 9
x = -9/15 = -3/5
Answer:
-3/5
Step-by-step explanation:
The equation would be represented as 63 - 15 x X = 72
To further simplify the problem : 63 - 15x = 72
Then you subtract
- 15x = 9
- 3/5
Solve and check. Identify any extraneous solutions.
Answer:
w=1 There are no extraneous solutions
Step-by-step explanation:
Multiply each side by 10w
10w ( 5/2w - 3/5w ) = 19/10 * 10w
Distribute
5*5 - 3*2 = 19w
25-6 = 19w
19 = 19w
Divide each side by 19
19/19 = 19w/19
1= w
A concession stand sells hamburgers (h) for $2 and hotdogs (d) for $1. On Friday night they sold a total of 300 hamburgers and hotdogs and made $420. How many of each did they sell?
Which system of equations matches the situation?
Answer:
the correct system of equations is the first one.
Step-by-step explanation:
h+d=300
2h+d=420
Which type of triangle can have only acute angles?
equilateral
isosceles
scalene
Answer:
Equilateral triangles can have only acute angles because acute angles means less than 90° so every angles in equilateral triangle have 60°
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Gabriel is investigating the forces that result from contact. All of the following are types of contact forces, except which of the following? Electrostatic force, Air resistance, Spring compression, Friction force
Answer:
Electrostatic force
Step-by-step explanation:
The answer is Electrostatic force because physical contact isn't required here.
At a back to school sale, backpacks are marked down 15%. If the original price was $34, then what is the sale price?
Answer:
$28.90
Step-by-step explanation:
If it is marked down 15% then that means it is sold at 85% of the original price
x/34=85/100
cross multiply both fractions
100x=2890
x=28.90
Answer:
$28.90
Step-by-step explanation:
take 34 and multiply that by .15, that would get you 5.1
take 34 and subtract 5.1 and that should get you your new price
Which equation in point-slope form describes the line through points (4, –4) and (1, 2)?
Step-by-step explanation:
Given points (4 , -4) and ( 1, 2)
First calculating slope (m)
=( y2 - y1) /( x2 -x1)
= ( 2 + 4) / (1-4)
= 6/ -3
= -2
Now
The equation in point slope form
y - y1 = m ( x - x1)
y + 4 = -2 ( x - 4)
y + 4 = -2x + 8
2x + y - 8 + 4 = 0
2x + y -4 = 0 which is the required equation
The associative property states that you can
A
multiply or add terms in any order.
distribute the multiplier over the addends.
C
break down large numbers into smaller numbers.
group terms using parentheses to add or multiply
Answer:
add or multiply regardless of how the numbers are grouped.
Step-by-step explanation:
A basketball player has 45 steals, 72 assists, 90 rebounds, and 432 points. What is
the ratio of rebounds to steals?
оооо
Answer:
5:24
Step-by-step explanation:
We're provided with the number of rebounds as 90 while the points are 432. Expressing them into ratio of rebounds to steals we have
90:432
Simplification:
Dividing both sides by 2 we obtain
45:216
Dividing both sides of the above ratio by 3 we obtain
15:72
Dividing both sides of the above ratio further by 3 we obtain
5:24
Therefore, rhe simplified ratio of rebounds ro steals is 5:24
2) The triangles are similar. Find the similarity ratio of the first triangle to the 1 point
second triangle. Show Work. *
F 4 RD 6 A
105
Given:
Triangles FRI and DAY are similar.
To find:
Similarity ratio
Solution:
If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.
Here, FR and DA are corresponding sides.
[tex]$\Rightarrow \frac{FR}{DA} =\frac{4}{6}[/tex]
Cancel the common factors of 4 and 6, we get
[tex]$\Rightarrow \frac{FR}{DA} =\frac{2}{3}[/tex]
⇒ FR : DA = 2 : 3
⇒ ΔFRI : ΔDAY = 2 : 3
Similarity ratio of the first triangle to the second triangle is 2 : 3.
The similarity ratio should be 2:3
Calculation of the similarity ratio;In the case when two triangles are same so the corresponding angles are congruent and the corresponding sides should be in proportion.
So,
[tex]FR \div DA = 4\div 6[/tex]
FR:DA = 2:3
Based on the above calculations, we can say that the ratio of first triangle to the second triangle should be 2:3
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what is the distance between the points
(1, -6) and (-5,2)?
10 units
9 units
5.6 units
7.2 units
Answer:
10 units
Step-by-step explanation:
Use distance formula
distance D = root ( (1 - -5)^2 + (-6 - 2)^2 )
D = root (6^2 + 8^2) = root (100) = 10
Which is more, 5 meters or 500 centimeters
Answer:
They are the same
Step-by-step explanation:
1 meter = 100 cm,
5 meters = 500 cm.
Answer:
5 m = 500 cm
Step-by-step explanation:
1 m = 100 cm
5m = 5 x 100 cm = 500 cm
Use the graph to identify the independent and the dependent variable. Check all that apply. The two variables are Eli and 5. The two variables are meters and seconds. Meters are graphed on the x-axis. Meters are graphed on the y-axis. Seconds is the independent variable. Seconds is the dependent variable.
Answer: B D E
Step-by-step explanation:
Answer:
bde
Step-by-step explanation:
Evaluate the expression.26
A.26
B.12
C.26
D.36
C.64
The expression [tex]\(2^6\)[/tex] means 2 raised to the power of 6. It indicates multiplying 2 by itself six times. So, [tex]\(2^6\)[/tex] is equal to 64. The correct answer is C. 64.
It seems like the expression you've written is [tex]2^{6}[/tex], which means 2 raised to the power of 6. Let's evaluate this expression:
[tex]\[ 2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64 \][/tex]
So, the correct answer is:
[tex]\[ \text{C. 64} \][/tex]
Q- Evaluate the expression [tex]2^{6}[/tex].
A. 26
B. 12
C. 64
D. 36
Which expression is equal to 7/8
A. 7 divided by 8
B. 8 x 7
C. 8 divided by 7
D. 7 x 8
Answer: A. 7 divided by 8.
Step-by-step explanation:
7/8 is the same as saying seven divided by 8.
The correct answer to the question: 'Which expression is equal to 7/8?' is A. 7 divided by 8. This is because the '/' in the fraction 7/8 represents division, so 7/8 is the same as '7 divided by 8'.
Explanation:In Mathematics, when dealing with fractions, division, and multiplication, it's crucial to understand their relationships. The symbol '/' in a fraction actually represents division. So, the fraction 7/8 can be interpreted as '7 divided by 8'. Therefore, the correct answer to your question is: 'Which expression is equal to 7/8?' is A. 7 divided by 8.
On the other hand, options B and D (8 x 7, 7 x 8) represent multiplication and C (8 divided by 7) is a different division operation where 8 is divided by 7, not 7 by 8.
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3/5 * (t + 41) = −3(3 − t)
t =
Answer:
T=14
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
HELP QUICK PLS, For each of the figures, write Absolute Value equation in the form
x−c=d, where c and d are some numbers, to satisfy the given solution set.
x= -8, and x= -4
a) The absolute value equation is |x - 11| = 6.
b) The absolute value equation is |x - 0| = 1/2, which simplifies to |x| = 1/2.
To write the absolute value equation in the form |x - c| = d for the given solution sets, we need to find the midpoint (c) between the two values and the distance (d) from the midpoint to either of the values.
b) For the solution set x = 5, x = 17:
Midpoint (c) = (5 + 17) / 2 = 22 / 2 = 11
Distance (d) from the midpoint to either value (e.g., 5) = |5 - 11| = 6
So, the absolute value equation is |x - 11| = 6.
d) For the solution set x = -1/2, x = 1/2:
Midpoint (c) = (-1/2 + 1/2) / 2 = 0 / 2 = 0
Distance (d) from the midpoint to either value (e.g., 1/2) = |-1/2 - 0| = 1/2
So, the absolute value equation is |x - 0| = 1/2, which simplifies to |x| = 1/2.
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Question
HELP QUICK PLS, For each of the figures, write Absolute Value equation in the form
|x−c=d|, where c and d are some numbers, to satisfy the given solution set.
a) x=5, x=17
b) x=-1/2, x=1/2