A triangle has an area of 56 square units its height is 14 units what is the length of its base

Answers

Answer 1

the length of the base is 8
area=56
height= 14
A=1/2 bh
56=1/2 b(14)
56=b(14)/2
8=b

Related Questions

How do you change a ratio into a fraction baseballs to basketballs

Answers

[tex]\bf baseballs:basketballs\implies \cfrac{baseballs}{basketballs} \\\\\\ anything:whatever\implies\cfrac{anything}{whatever}[/tex]

if that's what you mean.

What are the orders of 3,7,9,11,13,17 and 19(mod20)?does 20 have primitive roots?

Answers

[tex]3\equiv3\mod{20}[/tex]
[tex]3^2\equiv9\mod{20}[/tex]
[tex]3^3\equiv27\equiv7\mod{20}[/tex]
[tex]3^4\equiv3\cdot3^3\equiv3\cdot7\equiv21\equiv1\mod{20}[/tex]

[tex]7\equiv7\mod{20}[/tex]
[tex]7^2\equiv49\equiv9\mod{20}[/tex]
[tex]7^3\equiv7\cdot7^2\equiv63\equiv3\mod{20}[/tex]
[tex]7^4\equiv7\cdot7^3\equiv21\equiv1\mod{20}[/tex]

[tex]9\equiv9\mod{20}[/tex]
[tex]9^2\equiv3^4\equiv1\mod{20}[/tex]

[tex]11\equiv11\mod{20}[/tex]
[tex]11^2\equiv121\equiv1\mod{20}[/tex]

[tex]13\equiv-7\equiv13\mod{20}[/tex]
[tex]13^2\equiv169\equiv9\mod{20}[/tex]
[tex]13^3\equiv13\cdot13^2\equiv(-7)9\equiv-63\equiv-3\mod{20}[/tex]
[tex]13^4\equiv13\cdot13^3\equiv(-7)(-3)\equiv21\equiv1\mod{20}[/tex]

[tex]17\equiv-3\equiv17\mod{20}[/tex]
[tex]17^2\equiv(-3)^2\equiv9\mod{20}[/tex]
[tex]17^3\equiv(-3)^3\equiv-27\equiv3\mod{20}[/tex]
[tex]17^4\equiv(-3)^4\equiv81\equiv1\mod{20}[/tex]

[tex]19\equiv-1\equiv19\mod{20}[/tex]
[tex]19^2\equiv19(-1)\equiv-19\equiv1\mod{20}[/tex]

Generally speaking, a number [tex]x[/tex] coprime to [tex]n[/tex] will be a primitive root of [tex]n[/tex] if we have [tex]x^n\equiv x\mod{n}[/tex], or [tex]x^{n-1}\equiv1\mod{n}[/tex]. In other words, if [tex]x[/tex] is of order [tex]n-1[/tex] modulo [tex]n[/tex], then [tex]x[/tex] is a primitive root of [tex]n[/tex].

Since none of these numbers has order 19, it follows that 20 does not have any primitive roots.

What does the value of the GCF
represent?

Answers

GCF its full form is Greatest Common Factor.
It is found when we have two or more numbers and the largest factor are common in both the numbers.

What is 35 divided by 768 plz I am really stuck on this one and need some improvement

Answers

35/ 768 = 0.04557

rounded up will be 0.05

hope this helps

jack is mowing a lawn that has a shed. needs to know area of lawn to mow. dimensions of yard are 5x by 13 x-4 . she'd are 2x by 2x+4. " find polynomial that describes area of lawn needed to mow. Polynomial in answer should have two terms.
please help.

Answers

The diagram of the lawn and the shed is shown below.

The area of the lawn needed to be mowed equals to the area of the yard minus the area of the shed

The area of the yard = [tex](5x)(13x-4) = 65 x^{2} -20x[/tex]
The area of the shed = [tex](2x)(2x+4)=4 x^{2} +8x[/tex]

The area of the lawn = [tex]65 x^{2} -20x-(4 x^{2} +8x)[/tex]
The area of the lawn = [tex]65 x^{2} -20x-4 x^{2} -8x[/tex]
The area of the lawn = [tex]61 x^{2} -28x[/tex]

Which expression is equivalent to the given expression? 100pts giveaway 3x(1.05) 3x + 3x + 3x 1.05x + 1.05x + 1.05x x + 3.15 1.05x + 3

Answers

17.2x+6.15
i am not sure but they may be right

I got, 17.35x+6.15

Btw you know it shows how many points your giving for the question

EASY 5 POINTS!!!!! You have a 1-gallon paint can in the shape of a cylinder. One gallon is 231 cubic inches. The radius of the can is 3 inches. What is the approximate height of the paint can? Use 3.14 for pi.

A.) 5 inches
B.) 25 inches
C.) 8 inches
D.) 26 inches

Answers

We know that the volume is: V = 1 gallon = 231 in³
Also : r = 3 in.
The volume of a cylinder: V = r² π h
231 = 3³ · 3.14 · h
231 = 9 · 3.14 · h
231 = 28.26 h
h = 231 : 28.26
h = 8.17 ≈ 8 in
Answer: C) 8 in.

Answer:

The height of the cylinder shaped can = 8.17 inches

Step-by-step explanation:

Volume of the cylinder shaped can = 1 gallon

1 gallon = 231 cubic inches

So, Volume of the cylinder shaped can = 231 cubic inches

Radius of the can = 3 inches

[tex]\text{Now, Volume of the cylinder = }\pi\times radius^2\times height\\\\\implies 231=3.14\times 3^2\times height\\\\\implies height=\frac{231}{3.14\times 9}\\\\\implies height\approx 8.17\text{ inchjes}[/tex]

Hence, The height of the cylinder shaped can = 8.17 inches

The sum of two consecutive even integers is 138. Write an equation and solve

Answers

x+(x+2)=138
2x+2=138
2x=136
x=68
Final answers: 68,70

Final answer:

The two consecutive even integers that sum to 138 are 68 and 70. The equation n + (n + 2) = 138 was used to determine these integers.

Explanation:

The problem is asking for two consecutive even integers whose sum is 138. Let's denote the first integer as n (where n is an even number). As the problem says the numbers are consecutive even integers, we know the next number must be n + 2.

We can form an equation based on the information given. The sum of these two integers is equal to 138, so:

n + (n + 2) = 138

If we simplify the equation, it becomes:

2n + 2 = 138By subtracting 2 from both sides, 2n = 136We then divide both sides by 2 to get n = 68

Therefore, the two consecutive numbers are 68 and 70 as they add up to 138.

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Under what circumstance are two non right triangles congruent

Answers

Only if three sides are equal.

Question 11(Multiple Choice Worth 5 points) (09.03 MC) A group of people were given a personality test to determine if they were Type A or Type B. The results are shown in the table below: Male Female Type A 55 75 Type B 48 22 Compare P(Male | Type A) with P(Male or Type A).

Answers

The solution would be like this for this specific problem:

[tex]\large P(F) \times P(B )= \frac {97} {200} \times \frac {70}{200} = \frac {97 \times 70} {200 \times 200} = 0.16975[/tex]

You need to compare the results of: P(female or type B) which is written in correct symbols as:

[tex]\large P (F\cup B) [/tex]

and P(female | given type B) which is written in correct symbols as:

[tex]\large P(FlB)

\large (F\cup B)=0.835 - 0.17 = 0.665

\large P (FlB) = 0.314

\large P (F \cup B) \ \textgreater \ P (F|B)[/tex]

So, the correct answer would be: P (Female or Type B) > P (Female | Type B).

Answer:

The answer is P(Female or Type B) > P(Female | Type B)

Step-by-step explanation:

Just took the test.

Also check if you want the answer for males or females before you choose because they are completely different questions

Can anyone please solve the attached file?

Answers

The given matrix is
[tex] A= \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] [/tex]

A given vector is of the form [a b c]'.
If a given vector {x} is an eigenvector of A, then
[tex]det \left[\begin{array}{ccc}1-a&2&3\\4&5-b&6\\7&8&9-c\end{array}\right] =0[/tex]

Test the vector x₁ = [1 -2 1]'
[tex]det \left[\begin{array}{ccc}0&2&3\\4&7&6\\7&8&8\end{array}\right] =-2(32-42)+3(32-49)=-31[/tex]
This is not an eigenvector because the determinant is not zero.

Test x₂ = [-1 0 1]'
[tex] det \left[\begin{array}{ccc}2&2&3\\4&5&6\\7&8&8\end{array}\right] =2(40-48)-2(32-42)+3(32-35)=-5[/tex]
This is not an eigenvector because the determinant is not ero.

Test x₃ = [0 0 0]'
[tex]det \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] =(45-48)-2(36-42)+3(32-35)=0[/tex]
This vector is an eigevector because the determinant is zero.

Answer:
The eigenvector is x₃

The directions for mixing an insect spray say to use 1 1/2 ounces of chemical in each gallon of water. How many ounces of chemical should be mixed with 3 4/5 gallons of water? First, estimate the answer to the application problem. Then find the exact answer.

Answers

1 1/2 oz to each gallon.
Total required for 3 4/5 gal is the product of 1 1/2 and 3 4/5, which is approximately 4*1 1/2 = 6 oz.

Exact answer
1 1/2 * 3 4/5
=3/2 * 19/5
=57/10
=5.7 oz

[tex]\bf \begin{array}{ccllll} chemical&water\ gallons\\ -----&-------\\ 1\frac{1}{2}&1\\\\ x&3\frac{4}{5} \end{array}\implies \cfrac{1\frac{1}{2}}{x}=\cfrac{1}{3\frac{4}{5}} \\\\\\ \cfrac{\frac{1\cdot 2+1}{2}}{x}=\cfrac{\frac{1}{1}}{\frac{3\cdot 5+4}{5}}\implies \cfrac{\frac{3}{2}}{\frac{x}{1}}=\cfrac{\frac{1}{1}}{\frac{19}{5}}\implies \cfrac{3}{2}\cdot \cfrac{1}{x}=\cfrac{1}{1}\cdot \cfrac{5}{19}\implies \cfrac{3}{2x}=\cfrac{5}{19}[/tex]

[tex]\bf 3\cdot 19=2x\cdot 5\implies 57=10x\implies \cfrac{57}{10}=x\implies \boxed{5\frac{7}{10}=x} \\\\\\ \cfrac{5\cdot 10+7}{10}\implies \cfrac{57}{10}[/tex]

The table below shows the number of marbles of different colors in a bag: Color of Marbles Number of Marbles Pink 5 Blue 2 Green 3 Ursula draws a marble from the bag randomly without looking. She then draws another marble from the bag without replacing the first one. Which expression shows the probability of drawing green marbles in both the trials? plz help!!!!

Answers

[tex] \frac{3}{10} [/tex] x [tex] \frac{2}{9} [/tex] = [tex] \frac{1}{15} [/tex]

[tex]|\Omega|=10\cdot9=90\\ |A|=3\cdot2=6\\\\ P(A)=\dfrac{6}{90}=\dfrac{1}{15}\approx6,7\%[/tex]

Simplify the expression by using a double-angle formula. 2 cos^2 4 theta -1

Answers

You are given 2cos² (4θ - 1). You are asked to simplify the expression by using a double-angle formula.

Apply the double angle of the cosine function
cos2θ = 2cos² θ - 1

Rearranging the expression and then substituting them
2cos² θ = cos2θ + 1
2cos² (4θ - 1) = cos 2(4θ - 1) + 1
cos2(4θ - 1) + 1

can someone explain to me multi step algebra equations? 15 points Thaaaanks~

Answers

so take 4x-2x=4 first combine like terms so now u have 2x=4. now you will isolate the x to find what it equals. divide 2 from both sides so u have x=2. did this help any?

Final answer:

Multi-step algebra equations involve operations like addition, subtraction, multiplication, or division to solve for an unknown. These equations require simplifying terms, solving for unknowns, and checking the answers. Money examples and practice statements are useful for understanding these concepts.

Explanation:

Multi-step algebra equations are problems that require more than one operation, such as addition, subtraction, multiplication, or division, to solve for the unknown variable. The following steps are typically involved in solving these equations:

Eliminate terms wherever possible to simplify the algebra. This might involve combining like terms or canceling out terms on both sides of the equation.Solve the simultaneous equations for the unknowns. This can be done through methods such as substitution or elimination when dealing with more than one equation.Check the answer to ensure it fits the original equation. Substituting the solution back into the original equation can verify its correctness.

An example of this process could be the following scenario: You are given two equations in a word problem involving motion, one equation for velocity and another for time. To find the distance traveled, you would identify the known variables and the unknown variable (in this case, distance), simplify both equations as much as possible, and then combine them to solve for distance.

Money examples are often used for educational purposes because they provide a familiar context for understanding mathematical principles, making them easier to grasp. Additionally, practicing with state-ments, such as covering up a number to solve for it with the remaining information, can help build problem-solving skills.

What is the largest possible value of y, if y = - | 3 - x | + 5

Answers

Given any expression A, absolute value of A, that is |A|, is always positive or 0.

So |3-x| is always positive or 0, thus -|3-x| is always negative or 0.

Since we want the largest value of - | 3 - x | + 5, we must keep - | 3 - x | as large as possible, that is, we must keep | 3 - x | as small as possible.

The smallest possible value of | 3 - x | is 0. This happens for x=3.

The largest possible value of y = - | 3 - x | + 5 = 0+5 =5

Answer: 5

In the diagram, PN is the perpendicular bisector of AB and is also the angle bisector of

Answers

The perpendicular bisector is a line segment that is drawn from a vertex of an angle to the midpoint of another line segment creating a right triangle or a 90° angle in the process. Suppose AB is the base segment of the triangle, therefore the perpendicular sector is also the angle bisector of the other angle of the triangle, supposedly angle C. Angle bisector is a line segment that divides the angle into two equal parts. Imagine a line drawn from the top vertex C extended down to the midpoint of line AB. That is the perpendicular and angle bisector.

if you were to load 225 boxes onto a truck and the boxes are created with each crate containing 9 boxes how many crates would you need to load

Answers

You would need 25 Crates because 225 divided by 9 is 25.

225 / 9 = 25 (Total number of boxes / the number of boxes per crate)

You would need to load 25 crates

The price of a calculator dropped from $32.88 to $25.95. What was the percent decrease in price

Answers

%change=100(final-initial)/initial

%change=100(25.95-32.88)/32.88

%change≈ -21.08%

So the percent decrease in price was about 21%

32.88 - 25.95 is 6.93

well, if we take the 32.88 to be the 100%, how much is 6.93 off of it in percentage?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 32.88&100\\ 6.93&x \end{array}\implies \cfrac{32.88}{6.93}=\cfrac{100}{x}[/tex]

solve for "x".

Perry has an opportunity to put $2291 into an investment with an APR of 7.6%. How long will it take his investment to double?

Answers

2×2291=2291 (1+0.076)^t==> 2=(1+0.076)^t
Solve for t
Log (2)=t×log (1.076)
T=log (2)÷log (1.076)
T=9.46 years round your answer to get 9 years

please help me!!!
The scale for the map of Missouri is 1 in = 30 mi. On the map, the distance from Springfield to Columbus is about 5.6 in. How far apart are the two cities? Round your answer to the nearest mile.

Answers

if 1 inch = 30 miles

thn multiply 30 x 5.6

30 x 5.6 = 168 miles apart

The actual distance between Springfield and Columbia is 168 miles.

Therefore, the correct answer is:

b. 168 mi

To find the actual distance between Springfield and Columbia, we can use the scale provided in the map.

Given that 1 inch on the map represents 30 miles in real life, and the distance on the map from Springfield to Columbia is 5.6 inches, we can use the following calculation to find the actual distance:

[tex]\[ \text{Actual distance} = \text{Map distance} \times \text{Scale factor} \][/tex]

[tex]\[ \text{Actual distance} = 5.6 \, \text{inches} \times 30 \, \text{miles/inch} \][/tex]

[tex]\[ \text{Actual distance} = 168 \, \text{miles} \][/tex]

So, the actual distance between Springfield and Columbia is 168 miles.

Therefore, the correct answer is:

b. 168 mi

Elixir of acetaminophen contains 160 my per 5 milliliters. How much acetaminophen is needed to prepare 2 ounces of elixir?

Answers

60 milliliters is equal to two ounces.

The primary goal of using correlational research is to

Answers

The Primary goal of using correlation research is to determine the nature and strength of the association between two measured variables.
Here you must know the terms correlation and variable. The term Correlation is simply defined as the relation between two variables. variables are factors that are liable to vary or change.

Final answer:

Correlational research is used to determine whether there's a relationship between two or more variables without establishing a cause-and-effect connection. It identifies how closely connected variables are by observing them as they naturally occur.

Explanation:

The primary goal of using correlational research is to determine whether a relationship exists between two or more variables, but without establishing a cause-and-effect connection. In this method, a researcher may observe variables as they naturally occur with no intervention or manipulation. By examining the degree to which these variables move together, the researcher can identify how closely connected they are. For example, in psychological studies, a correlational research might be used to investigate the relationship between study habits and academic performance. However, it's critical to note that correlation does not imply causation.

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is 70 thousand written in standard form or word form

Answers

70 thousand is written in word flrm

Standard form is using numbers for example 1,000 word form use words for example one thousand so since you already said the standard form the word form is seventy thousand and its a word form hope that helps.

Factor completely 2x3 + 14x2 + 4x + 28.

Answers

6 + 28 + 4x +28

34 +28 + 4x

62 + 4x?

Not quite sure if that was what you were looking for

Hi there!

2x³ + 14x² + 4x + 28

2(x+7)(x² +2)

I hope that helps!

Find all values of c such that f is continuous on (-∞, ∞). $ f(x) = \left\{ \begin{array}{lcl} {\color{red}5} - x^{2}, & & x \le c \\ x, & & x > c \end{array}\right. $

Answers

[tex]f(x)=\begin{cases}5-x^2&\text{for }x\le c\\x&\text{for }x>c\end{cases}[/tex]

will be continuous as long as

[tex]\displaystyle\lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)=f(c)[/tex]

We have

[tex]\displaystyle\lim_{x\to c^-}f(x)=\lim_{x\to c}(5-x^2)=5-c^2[/tex]

[tex]\displaystyle\lim_{x\to c^+}f(x)=\lim_{x\to c}x=c[/tex]

so we must satisfy

[tex]5-c^2=c\implies c^2+c-5=0\implies c=\dfrac{-1\pm\sqrt{21}}2[/tex]

The values of c such that the function f is continuous are: c = -2.79 and c = 1.79

The function is given as:

[tex]f(x) = \left\{ \begin{array}{lcl} {5} - x^{2}, & & x \le c \\ x, & & x > c \end{array}\right.[/tex]

For the function to be continuous, then the following must be true

[tex]5 - x^2 = x[/tex]

Substitute c for x

[tex]5 - c^2 = c[/tex]

Express as a quadratic function

[tex]c^2 + c - 5 = 0[/tex]

Using a graphing calculator, the values of c are:

c = -2.79 and c = 1.79

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Simplifying expressions with exponents

Answers

When dividing two terms with the same base, subtract the exponent in the denominator from the exponent in the numerator: Power of a Power: To raise a power to a power, multiply theexponents.

[tex]\bf (2x^2y^3)^2(3y)\implies (2x^2y^3)^2(3y^1)\implies (2x^{2\cdot 2}y^{3\cdot 2})(3y^1) \\\\\\ 2x^4y^63y^1\implies 2\cdot 3x^4y^{6+1}\implies 6x^4y^7[/tex]

Answers

The distribution of the number of occurrences of the letter t on the pages of a book is found to be a normal distribution with a mean of 44 and a standard deviation of 18. If there are 500 pages in the book, which sentence most closely summarizes the data?

A. The letter t occurs less than 26 times on approximately 170 of these pages.

B. The letter t occurs less than 26 times on approximately 15 of these pages.

C. The letter t occurs more than 26 times on approximately 420 of these pages.

D. The letter t occurs more than 26 times on approximately 80 of these pages.

.Answer:
mean = 44
sd = 18
that means that "26" is 1 s.d. down, or at the 16th %ile

so, there is a .16 chance that "t" will occur less than 26 times on any single page.
consequently, there is a .84 chance that it will occur more than 26 times on any single page.

Using that information, and knowing that 16% of 500 is 80, and 84% of 500 is 420, can you see where "C" is correct?

Final answer:

The data represents a normal distribution where approximately 68 percent of the pages will have a number of occurrences of the letter t within one standard deviation of the mean, 95 percent within two standard deviations, and more than 99 percent within three standard deviations.

Explanation:

The sentence that most closely summarizes the data is: For data having a distribution that is bell-shaped and symmetric, the following are true:

Approximately 68 percent of the data is within one standard deviation of the mean.Approximately 95 percent of the data is within two standard deviations of the mean.More than 99 percent of the data is within three standard deviations of the mean. This is known as the Empirical Rule.

Using this information, we can conclude that approximately 68 percent of the pages in the book will have a number of occurrences of the letter t within one standard deviation of the mean, which is 44. Approximately 95 percent of the pages will have a number of occurrences within two standard deviations, and more than 99 percent will have a number of occurrences within three standard deviations.

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Ava wants to wash one load of laundry at a local laundromat. At laundromat A, it costs $6.35 to wash and $1.25 to dry one load of laundry. At laundromat B, it costs $5.95 to wash and $0.85 to dry one load of laundry. Which laundromat has the better price for doing one load of laundry, and by how much?

Answers

Laundromat A = 6.35 +1.25 = 7.60 for one load

Laundromat B = 5.95 +0.85 = 6.80 for one load

7.60-6.80 = 0.80

Laundromat B is has the better price by 0.80 cents

14. Simplify (4x^– 4)^– 3.

Answers

[tex](4x^{-4})^{-3}=4^{-3}\cdot x^{12}=\dfrac{x^{12}}{64}[/tex]

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