If you add 10 and then subtract 1, you get the same result as if you just added 9.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have to add 24+9 by making 10s.
As per the given question, the required solution would be as:
24 + 10 - 1 = 33
Therefore, if you add 10 and then subtract 1, you get the same result as if you just added 9.
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Final answer:
To add 24 and 9 using tens, break 9 into 6 and 3, add 6 to 24 to get 30, and then add the remaining 3 to reach 33.
Explanation:
To add 24 and 9 by making 10s, you can first break down the number 9 into 6 and 3.
Add 6 to 24 to make a round number, which is 30.
Now you have made a '10' because 30 is a multiple of 10.
Next, add the remaining 3 to get 33.
So, 24 + 9 = 33.
A triangular prism has a base area or 20 square feet and a height of 4 feet. What’s the volume
Answer:
Just multiply four times twenty and youll get your answer
See picture for solution to your problem.
The length of a rectangle is 6 m longer than its width. If the perimeter of the rectangle is 48 m, find its area.
Answer:
135m^2
Step-by-step explanation:
length = l
width = w
l + l + w + w = 48
l = w+6
w+6 + w+6 + w + w = 48
4w + 12=48
4w=36
w=9
l=15
15*9=135
Answer:
A = 135m²
Step-by-step explanation:
Represent the problem with equationsRecall the formula for perimeterFind the dimensions of the rectangle (length and width)Recall the formula for areaUse the dimensions to find the areaWrite equations to represent the problem.
l = w + (6m) The length is 6m more than the width
P = (48m) Perimeter is 48m
***We put brackets around numbers with the "m" to avoid confusing the units with a variable.
The formula for perimeter of a rectangle is P = 2(l + w)
Substitute "l" and "P" into the perimeter formula with the equations above. Simplify, then isolate "w".
P = 2(l + w)
(48m) = 2(w + (6m) + w) Collect like terms (w + w = 2w)
(48m) = 2(2w + (6m)) Distribute over brackets
(48m) = 4w + (12m) Start isolating "w"
(48m) - (12m) = 4w + (12m) - (12m) Subtract 12m from both sides
(36m) = 4w
4w/4 = (36m)/4 Divide both sides by 4
w = 9m Width of rectangle
Find "l" using the formula for length. Substitute the width.
l = w + (6m)
l = (9m) + (6m) Add
l = 15m Length of rectangle
Use the formula for the area of a rectangle A = lw.
Substitute the values we found for length and width.
A = lw
A = (15m)(9m) Multiply
A = 135m² Area of rectangle
Therefore the area of the rectangle is 135m².
Factor the expression using the GCF: 15x - 25
To factor the expression 15x - 25 using the greatest common factor (GCF), divide each term by the GCF. The factored form is 5(3x - 5).
Explanation:To factor the expression 15x - 25 using the greatest common factor (GCF), we need to find the largest number that divides both terms evenly. In this case, the GCF is 5. We can then divide each term by 5 to factor out the GCF:
15x ÷ 5 = 3x
-25 ÷ 5 = -5
Therefore, the factored form of the expression 15x - 25 is 5(3x - 5).
The expression 15x - 25 is factored by finding the Greatest Common Factor, which is 5, and then dividing each term by 5 to get the factored expression 5(3x - 5).
To factor the expression using the Greatest Common Factor (GCF), we need to identify the highest number that divides both coefficients in the expression 15x - 25. In this case, both 15 and 25 are divisible by 5, so 5 is the GCF of the expression. Applying the distributive property, we factor out the GCF:
Determine the GCF: 5.Divide each term by the GCF: 15x/5 = 3x and 25/5 = 5.Write the factored expression: 5(3x - 5).Now, the expression 15x - 25 is fully factored as 5(3x - 5).
The profits for video game companies depend on what game platform the game runs on, which can either be a portable system (p) with a built in screen, or a standard system (s) that you have to hook up to a television. The profit off of a portable game system is $72, while the profit from a standard game system is $90. The store manager has to make at least $360 per day in order to keep the store open. Which graph represents this inequality? Write the inequality that represents the number of games that must be sold everyday to meet or beat the sales goal.
To meet or beat the sales goal, the inequality 72x + 90y ≥ 360 can be used to represent the number of games that must be sold every day. The graph of this inequality would show the region above or on the line 72x + 90y = 360.
To meet or beat the sales goal of at least $360 per day, we can set up an inequality based on the profits from selling games. Let x be the number of portable game systems sold and y be the number of standard game systems sold. The inequality representing the number of games that must be sold every day is 72x + 90y ≥ 360.
To graph this inequality, we can plot the points on a graph where each point represents a combination of x and y. Then we shade the region that satisfies the inequality, which is the region above or on the line 72x + 90y = 360.
See the graph in the attached image for visual representation.
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find and sketch the level curves f(x,y)=c on the same set of coordinates axes for the given values of c. refer to these level curves as a contour map. z=5x-y; c=-2, -1, 0, 1, 2
Answer:
see below
Step-by-step explanation:
The five linear equations produce five parallel contour lines. The value of z increases as the lines shift to the right.
Final answer:
Level curves for the function f(x, y) = 5x - y for different values of c are straight lines with a slope of 5. They can be plotted on the same coordinate axes to form a contour map, with each line corresponding to one value of c.
Explanation:
Level Curves for the Function f(x, y) = 5x - y
To find the level curves of the function f(x, y) = 5x - y for the given values of c, we set f(x, y) equal to each constant and solve for y in terms of x:
For c = -2: -2 = 5x - y → y = 5x + 2
For c = -1: -1 = 5x - y → y = 5x + 1
For c = 0: 0 = 5x - y → y = 5x
For c = 1: 1 = 5x - y → y = 5x - 1
For c = 2: 2 = 5x - y → y = 5x - 2
These equations represent lines with a slope of 5 and various y-intercepts. The level curves can be drawn on a set of coordinate axes by plotting the lines according to their y-intercepts. Each line represents a different level curve and the set of these lines can be referred to as a contour map.
Enter the number
15.666666666667 rounded to the nearest hundredth (two decimal places):
Answer: 15.67
Step-by-step explanation:
Pot Santa
Answer:
15.67
Step-by-step explanation:
focus only on the underlined area
15.666666666667
round the last 6 underlined is what we are going to use to round the one before it
5 or more goes up so the six is now rounded to a seven on that part leaving you with 15.67
write a multiplication equation with one variable, and one fraction that has a solution of 8
Final answer:
To create an equation yielding a solution of 8, use a variable x and the fraction 1/4. By multiplying x by 32, the equation will result in 8.
Explanation:
To write a multiplication equation with one variable and one fraction yielding a solution of 8:
Start with the fraction 1/4.
Multiply that fraction by x = 32 to get a product of 8.
Triangle 2 and triangle 3 were created by drawing an altitude in triangle 1. What is the relationship between the green highlighted
segment in triangle 2 and the blue highlighted segment in triangle 1?
A. The highlighted segments are corresponding sides of triangles 1 and 3.
B. The highlighted segments are corresponding sides of triangles 2 and 3.
C. The highlighted segments have no corresponding relationship.
D. The highlighted segments are congruent.
Answer:
Triangle 1 line segment AB and triangle 2 line segment BA correspond to each other
Step-by-step explanation:
Point b and point a don't correspond to anything else
triangle 1 and 2 are congruent my answer would be a 50/50 guess between C and D If it were me id risk it and go D but it is up to you.
1. How many favorable outcomes are expressed in the
probability ?
7/9
Answer:
9
Step-by-step explanation:
Describe the vector as an ordered pair round the coordinates to the nearest tenth. The diagram is not drawn to scale.
A.)<-58.1, 50.5>
B.)<-102, 117.4>
C.)<-117.4, 102>
D.)<-50.5, 58.1>
Answer:
D.)<-50.5, 58.1>
Step-by-step explanation:
The vector can be decomposed into its x and y components using trigonometry.
The x and y components of the vector, together with the vector length forms a right triangle, as shown in the figure attached.
The x-component of the vector is given by
[tex]sin (-41^o)=\dfrac{x}{77}[/tex]
[tex]x=77*sin (-41^o)[/tex]
[tex]x=-50.5[/tex]
And the y-component of the vector is given by
[tex]cos(-41^o)=\dfrac{y}{77}[/tex]
[tex]y=77*cos(-41^o)[/tex]
[tex]y=58.1[/tex]
Thus, the vector as an ordered pair is represent by
[tex]\boxed{ (-50.5, 58.1)}[/tex]
which is choice D.
Can you show work to for y=4x-3?
Answer:
Is the equation that you need answered
y = 4x - 3 ?
That is not a real equation, therefore you can not answer that/show work
Answer:
Step-by-step explanation:
Not sure what they are looking for here.
you can plug in different x and get a y
x = 0 y = -3
x = -3 y = -15
x = 4 y = 13
Ashley is taking out a loan in the amount of $12,000. Her choices for the loan are a 4-year loan at 7.00% annual simple interest and a 5-year loan at 8.00% annual simple interest. What is the difference in the amount of interest Ashley would have to pay for these two loans?
Simple interest formula: A= P(1+Ryan)
A = 12000(1+ 0.07x4) = 15,360.00
Amount of interest = 15360-12000= 3,360.00
A= 12000(1+0.08x5) = 16,800.00
Interest = 16,800-12,000 = 4,800.00
Difference in interest = 4800 - 3360 = $1,440.00
Answer:
1440
Step-by-step explanation:
What is the definition of unit?
Answer:
an individual thing or person regarded as single and complete but which can also form an individual component of a larger or more complex whole
Finding the length of NM?
Because the triangles are congruent we know that NM = ST = 50.
answer: 50
The length of NM line segment for the considered situation is given by: Option D: 50 mi
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF\\[/tex]
(|AB| denotes length of line segment AB, and so on for others).
For these cases, the two triangles in the image are congruent.
So their corresponding sides must be of same measures.
The three sides of triangle RST are of measures 75, 67 and 50 miles
The two sides of triangle NLM are 67 miles and 75 miles. So obviously third one can be nothing except 50 miles so that the triangle NLM also have sides of same measure as of the triangle RST.
Thus, the length of NM line segment for the considered situation is given by: Option D: 50 mi
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How can you write the expression with a rationalized denominator? square root of three minus six over square root of three plus six
Answer:
[tex]- (\frac{15 - 4\sqrt{3} }{11} )[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{3}-6}{\sqrt{3} +6} = \frac{(\sqrt{3}-6)(\sqrt{3}-6)}{(\sqrt{3} +6)(\sqrt{3} -6)}[/tex]
[tex]= \frac{(\sqrt{3})^2 - (2\times6\times\sqrt{3}) +6^{2} }{(\sqrt{3})^2 - 6^{2}} = \frac{9 - 12\sqrt{3} + 36}{3 - 36}[/tex]
[tex]\frac{45 -12\sqrt{3} }{-33} =- (\frac{15 - 4\sqrt{3} }{11} )[/tex]
3(x + 1) + 4x + 3 = 34
Answer:
Step-by-step explanation:
3(x + 1) + 4x + 3 = 34......distribute thru the parenthesis
3x + 3 + 4x + 3 = 34....combine like terms
7x + 6 = 34....subtract 6 from both sides
7x = 34 - 6
7x = 28....divide by 7
x = 28/7
x = 4 <====
Answer:
look at the picture shown
Expand.
If necessary, combine like terms.
(4x + 1)(4x + 1) =
Answer: 16x² + 8x + 1
Step-by-step explanation:
(4x + 1)(4x + 1)
This expansion can be done in two ways either by direct expansion or by indirect expansion
(1) Direct expansion
(4x + 1)(4x + 1 )
4x X 4x + 4x X 1 + 1 X 4x + 1 X 1
= 16x² + 4x + 4x + 1
= 16x² + 8x + 1
(2) Method
This can be written thus:
(4x + 1 )(4x + 1 ) = (4x + 1 )²
= (4x)² + 2( 4x X 1 ) + 1²
= 16x² + 2(4x) + 1
= 16x² + 8x + 1.
(4x + 1)(4x + 1)
4x · 4x = 16x²
4x · 1 = 4x
1 · 4x = 4x
1 · 1 = 1
16x² + 4x + 4x + 1
16x² + 8x + 1
help need an answer quick
Answer:
Step-by-step explanation:
the sum of twice a number and 4 times another number is 4. the first number decreased by the second number is 5. Find the numbers
The two numbers being asked in the question are 4 and -1.
Explanation:This question can be solved using a system of linear equations. Let's call the first number x and the second number y.
From the first statement, we can create one equation: 2x + 4y = 4
From the second statement, we can create another equation: x - y = 5
To solve this system, we can use substitution or elimination method. If we multiply the second equation by 2, we get 2x - 2y = 10. Now, we can subtract the second equation from the first: (2x + 4y) - (2x - 2y) = 4 - 10, which simplifies to 6y = -6. Dividing both sides by 6, we get y = -1.
Substitute y = -1 into the equation x - y = 5, we get x - (-1) = 5. Therefore, x = 5 - 1 = 4.
So, the first number x is 4 and the second number y is -1.
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Ryan is trying to determine whether 2.7x – 5.9 is equivalent to 2.8x – 5.9. To test this, he substitutes 0 for x into both expressions. Explain why this will not give him the correct answer.
Answer:
read explanation
Step-by-step explanation:
This won't give him the correct answer because if he substitutes zero into anything he will get -5.9. 0 multiplied by anything is 0 and if you put that into bot equations you get the same answer so it won't help him. he should instead try 1 or something like that.
the nutritional label on a carton of soy milk says that one glass contains 7 grams of protein. How many miligrams of proten does one glass contain?
Answer:
700 milligrams of protein is contained in one glass.
Step-by-step explanation:
Given:
Protein present in on glass of soy milk = 7 grams
To Find:
How many milligrams of protein does one glass contain =?
Solution:
We have to convert grams to milligrams
We know that 1 gram = 100 milligram
then 7 grams will be = [tex]7 \times 100[/tex] milligrams
7 grams = 700 milligrams
Therefore in one glass of soy milk there will be 700 milligrams of proteins
Area of circumference of 50.24ft
Answer:
[tex]200.96sq.ft.[/tex]
Step-by-step explanation:
Given:
Circumference= 50.24 ft.
We have to find the area of the circle.
Finding the radius with the help of given circumference
Circumference of a circle= [tex]2\pi r[/tex]
[tex]50.24=2*\pi* r\\\\50.24=2*(3.14)*r\\\\50.24=6.28*r\\\\r=\frac{50.24}{6.28} \\\\r= 8ft.[/tex]
Area of a circle= [tex]\pi r2[/tex]
[tex]=\pi *8*8\\\\=64*\pi \\\\=64*3.14\\\\=200.96sq.ft.[/tex]
which percentage of weight was lost if a patient weighed 102 kg and is currently 96 kg?
Final answer:
To find the percentage of weight lost, calculate the difference in weight and then divide by the original weight, multiplying by 100%. The patient has lost approximately 5.88% of their original weight.
Explanation:
To determine the percentage of weight lost by a patient who weighed 102 kg and now weighs 96 kg, we use the following steps:
First, find the difference in weight: 102 kg - 96 kg = 6 kg.Next, calculate the percentage of the original weight that this difference represents: (6 kg / 102 kg) × 100%.Perform the calculation: (6 / 102) × 100% ≈ 5.88%.So, the patient has lost approximately 5.88% of their original weight.
Which of the following fractions is not equivalent to 6/21
Answer:
3/7 and 4/14
Step-by-step explanation:
a) 3/7 is not an equivalent of 6/21 because when you multiply the numerator and the denominator by 2 you get: 6/14
b) 4/14 is not an equivalent
Answer:
3/7
Step-by-step explanation:
6/21 = 6 ÷ 3 / 21 ÷ 3 = 2 / 7
6 / 21 = 4 ÷ 2 / 14 ÷ 2 = 2 / 7
6/21 = 12 ÷ 6 / 42 ÷ 6 = 2 / 7
When a number is decreased by 78%, the result is 16. What is the original
number to the nearest tenth?
Answer:
70
Step-by-step explanation:
16÷(100%-78%) = 16÷22% = 72.73 =70(correct to the nearest tenth)
PLEASE HELP PLEASE HELP
List four values that would be a solution to -2x > 10. Then, in 2 to 3 complete sentences, explain how you know your four values are solutions.
Answer:
-6, -7, -8, -9
Step-by-step explanation:
-2x > 10
x < -5
So x can be -6, -7, -8, -9
Any number less than -5 is a solution.
The listed ones are the solutions because they satisfy the the inequality,
-2x > 10
x = -6, -2(-6) > 10 12 > 10
x = -7, -2(-7) > 10 14 > 10
x = -8, -2(-8) > 10 16 > 10
x = -9, -2(-9) > 10 18 > 10
On the coordinate grid, the graph of y = RootIndex 3 StartRoot x minus 1 EndRoot + 3 is shown. It is a translation of y = RootIndex 3 StartRoot x EndRoot. On a coordinate plane, a cube root function goes through (negative 7, 1), has an inflection point at (1, 3), and goes through (2, 4). What is the domain of the graphed function? {x | 1 < x < 5} {y | 1 < y < 5} {x | x is a real number} {y | y is a real number}
The domain of a graph is the set of input values the function can take
The domain of the graphed function is (c) {x | x is a real number}
The equation of the graph is given as:
[tex]y = \sqrt[3]{x -1} + 3[/tex]
The above function is a cubic function, and a cubic function can take any real number as its input
This means that, the input values of the function [tex]y = \sqrt[3]{x -1} + 3[/tex] is the set of real numbers
Hence, the domain of the graphed function is (c) {x | x is a real number}
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The domain of the translated cube root function y = ∛(x - 1) + 3 is {x | x is a real number}, since cube root functions accept all real numbers.
Explanation:The graph of the function y = ∛(x - 1) + 3, which is a cube root function, is a translated version of the parent function y = ∛x. The translation involves shifting the graph to the right by 1 unit and up by 3 units. Given that a cube root function, like y = ∛x, can accept any real number as an argument because there are real cube roots for all real numbers, the domain of the translated function would also be all real numbers. This remains true even after the function is translated. Hence, the domain of the graphed function is {x | x is a real number}.
kylee has a coin and a number cube. she flips the coin once and rolls the number cube once. what is the probability that the coin lands tails-up and the cube lands on a 4?
Final answer:
The combined probability of the coin landing tails-up and the number cube landing on a 4 is 8.33%.
Explanation:
The question involves calculating the probability of two independent events: the coin landing tails-up and the dice landing on a 4. The probability of a coin landing on tails is 0.5, and the probability of a dice landing on a particular number, say 4, is 1/6 since a dice has six faces. Since these two events are independent, their combined probability is found by multiplying the probabilities of each event.
The probability of the coin landing tails-up is 0.5, and the probability of the number cube (dice) landing on a 4 is 1/6. So, the combined probability of both events occurring is (0.5) × (1/6) = 0.0833, or 8.33% when expressed as a percentage.
Apply the multiplication property of equality to write an equation equivalent to 7n=28
The value of n from the equation 7n = 28 is n = 4
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
7n = 28 be equation (1)
On simplifying the equation , we get
Divide by 7 on both sides of the equation , we get
n = 28/7
n = 4
Another equation which satisfies the relation is 4n = 16
n = 4
Therefore, the value of n is 4
Hence , the value of the equation is 4
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What is the piecewise model of f(x)=.7|x-4|+2?
Answer:
The piecewise model of the function is
[tex]f(x)=-0.7x+4.8[/tex] -----> For [tex]x<4[/tex]
[tex]f(x)=0.7x-0.8[/tex] -------> For [tex]x\geq 4[/tex]
Step-by-step explanation:
we know that
The general form of absolute value equation is
[tex]f\left(x\right)=a\left|x-h\right|+k[/tex]
where
The variable a, tells us how far the graph stretches vertically, and whether the graph opens up or down
(h,k) is the vertex of the absolute value
In this problem we have
[tex]f\left(x\right)=0.7\left|x-4\right|+2[/tex]
we have
[tex]a=0.7[/tex]
The coefficient a is positive ----> the graphs open up
The vertex is the point (4,2)
Find the piecewise model
case 1) positive value
[tex]f(x)=0.7[(x-4)]+2[/tex]
[tex]f(x)=0.7x-2.8+2\\f(x)=0.7x-0.8[/tex]
Is a linear equation with positive slope
[tex](x-4)\geq 0\\x\geq 4[/tex]
The domain is the interval [4,∞)
case 2) negative value
[tex]f(x)=0.7[-(x-4)]+2[/tex]
[tex]f(x)=-0.7x+2.8+2\\f(x)=-0.7x+4.8[/tex]
Is a linear equation with negative slope
[tex](x-4)< 0\\x<4[/tex]
The domain is the interval (-∞,4)
[tex]x<4[/tex]
therefore
The piecewise model of the function is
[tex]f(x)=-0.7x+4.8[/tex] -----> For [tex]x<4[/tex]
[tex]f(x)=0.7x-0.8[/tex] -------> For [tex]x\geq 4[/tex]