One side of a triangles two centimeters shorter than the base. The other side is four centimeters longer than the base. What lengths of the base will allow the perimeter to be greater than 29 cm?
Answers
Answer:
x > 9 cm
Explanation:
Let the length of the base = x cm
One side of a triangle is 2 cm shorter than the base.
Length = (x-2)cm
The other side is 4 cm than the base, therefore:
Length of the other side = (x+4)cm
Perimeter = x+(x-2)+(x+4)
If the perimeter is greater than 29, then:
x+(x-2)+(x+4)>29
3x-2+4>29
3x+2>29
3x>29-2
3x>27
x>27/3
x>9
The length of the base greater than 9cm will allow the perimeter to be more than 29 cm.
Related Questions
S/14 = 14 a. -196 b. 196 C. 28 d. 0
Answers
In the given equation, the value of S is divided by 14, so to calculate the value of S you have to invert the operation, that is, multiply it by 14 so that both operations cancel each other.
And, for the equality to be valid, all operations made in one side of the = sign must be done on the other side as well. So, multiply both sides of the equation by 14:
[tex]\begin{gathered} \frac{14S}{14}=14\cdot14 \\ S=196 \end{gathered}[/tex]S=196 the correct choise is b.
• if the area of a square is 100cm ^2, what is the perimeter? • if the perimeter of a square is 116cm, what is it's area?
Answers
1) Given data:
Area of square = 100 cm square
[tex]A=a^2[/tex][tex]\begin{gathered} a^2=100 \\ a=10\operatorname{cm} \end{gathered}[/tex]The perimeter of square is,
[tex]\begin{gathered} P=4a \\ P=4\times10 \\ P=40\operatorname{cm} \end{gathered}[/tex]2) Given data:
Perimeter of square = 116 cm
[tex]P=4a[/tex][tex]\begin{gathered} 4a=116 \\ a=29 \end{gathered}[/tex]The area os square is,
[tex]\begin{gathered} A=a^2 \\ A=29\times29 \\ A=841\operatorname{cm}\text{ square} \end{gathered}[/tex]What is the equation of the line that passes through the point (4, 9) with a slope of - 5/8 Write the equation in point-slope form.
Answers
the slope of the line is -5/8 and it is passing through (4, 9)
the equation of a line is
[tex]y-9=m(x-4)[/tex]put m = -5/8
[tex]\begin{gathered} y-9=-\frac{5}{8}(x-4) \\ y-9=-\frac{5}{8}x+\frac{1}{2} \end{gathered}[/tex]so the equation of line is
y = -5/8 x + (1/2) + 9
y = -5/8 x + 19/2
question will be in picture
Answers
given:
[tex]-7\le x[/tex]so, the line that represents the given inequality will be: b
In an octagon, five of the angles are equal and each of the other three angles is 24° greater than each of the five other ones. Determine the angles of the octagon anto
Answers
Given:
5 angles are equal: x
Each of the other angles is 24 greater than the other 5 angles: x+24
An octagon has 8 angles; the sum of the interior angles of an octaogn is 1080º
[tex]5x+3(x+24)=1080º[/tex]Use the equation above to solve x:
[tex]\begin{gathered} 5x+3x+72=1080 \\ 8x+72=1080 \\ 8x=1080-72 \\ 8x=1008 \\ x=\frac{1008}{8} \\ \\ x=126 \end{gathered}[/tex]The 5 angles that are equal measure 126º
The other 3 angles measure:
[tex]x+24=126+24=150º[/tex]Then, the angles of the octagon are: 126º,126º,126º,126º,126º,150º,150º,150ºi forgot how i solved this, what im getting is 4x -24 which is wrong
Answers
Answer:
[tex](4x^2+22x-12)cm^2[/tex]Explanation:
From the given figure:
• The base of the triangle, b = (4x-2) cm
,• The perpendicular height, h = (2x+12) cm
The area of a triangle is calculated using the formula:
[tex]A=\frac{1}{2}bh[/tex]Substitute the given expressions:
[tex]\begin{gathered} A=\frac{1}{2}(4x-2)(2x+12) \\ Factor\text{ }4x-2\implies4x-2=2(2x-1) \\ A=\frac{1}{2}\times2(2x-1)(2x+12) \\ A=(2x-1)(2x+12) \end{gathered}[/tex]Next, open the brackets:
[tex]\begin{gathered} A=2x(2x+12)-1(2x+12) \\ =4x^2+24x-2x-12 \\ =(4x^2+22x-12)cm^2 \end{gathered}[/tex]The area of the triangle is:
[tex](4x^2+22x-12)cm^2[/tex]What is the relationship between the pair of angles ABC and LMN shownin the diagram below?
Answers
Solution:
From the given figure
Where
[tex][/tex]The side walls of a regular quadrilateral pyramid are equilateral triangles with sides equal to 8 cm. Calculate the pyramid:1) the sum of the lengths of all the sides;2) the area of the base;3) the length of the height of the side wall;4) the area of the side wall.
Answers
a) 64cm
b) 64 square cm
c) 4√3 cm
d) 16√3 square cm
Explanations:A regular quadrilateral pyramid with equilateral triangles is as shown below;
1) The pyramid has 8 side lengths, hence the sum of the length of all the sides is given as:
[tex]\begin{gathered} Sum\text{ of side lengths}=8\times8cm \\ Sum\text{ of side lengths}=64cm \end{gathered}[/tex]2) Since the triangular sides are equilateral, the base of the pyramid will be a square with side length of 8cm. The area of the base is expressed as:
[tex]\begin{gathered} A=length\times length \\ A=8cm\times8cm \\ A=64cm^2 \end{gathered}[/tex]3) Since one side wall is an equilateral triangle, the height will be perpendicular to the base as shown:
In order to determine the height, we will use the Pythagorean theorem as shown:
[tex]\begin{gathered} 8^2=h^2+4^2 \\ h^2=8^2-4^2 \\ h^2=64-16 \\ h^2=48 \\ h=\sqrt{48}=4\sqrt{3}cm \\ \end{gathered}[/tex]4) The area of the side wall is equivalent to the area of the triangle expressed as:
[tex]\begin{gathered} Area\text{ of side wall}=\frac{1}{2}\times base\times height \\ Area\text{ of side wall}=\frac{1}{2}\times8cm\times4\sqrt{3} \\ Area\text{ of side wall}=16\sqrt{3}cm^2 \end{gathered}[/tex]hello can u help me please5.Admission to the Basketball Hall of Fame in Springfield is $5.00 per student. A group of students bought admission tickets. One student spent an extra $9.00 for a poster. The total amount they spent was $34.00. How many students were in the group?a.4b.5c.6d.7
Answers
Given:
The price per student for the admission, m=$5.
Extra amount spent by a student, c=$ 9.
Total amount spent, T=$34.
Let x be the number of students. Then, the expression for the total amount is,
[tex]T=mx+c[/tex]Substitute values and solve for x.
[tex]\begin{gathered} 34=5x+9 \\ 34-9=5x \\ 25=5x \\ x=\frac{25}{5} \\ x=5 \end{gathered}[/tex]Therefore, the number of students is 5.
Option (b) is correct.
4. The triangles below lie on the same line. Find thehorizontal distance of the smaller triangle.25DA10Distance:pe here to searchN
Answers
Thus the horizontal distance of the smaller triangle is 2.
The pH of a fruit juice is 5.3 Find the hydronium ion concentration [H3O+] of the juice. Use the formula pH = -log[H30+]
Answers
Answer:
[tex]\lbrack H_3O^+\rbrack\text{ = }5.0\text{ }\times10^{-6\text{ }}moles\text{ per liter}[/tex]Explanation:
By definition, the pH of a solution is the negative logarithm to base 10 of the concentration of Hydroxonium or oxonium ion
Mathematically, we have this as:
[tex]pH=-log\lbrack H_3O^+\rbrack_{}[/tex]We can change the formula subject so we would have hydroxonium ion on the left
Mathematically, we have this as:
[tex]\lbrack H_3O^+\rbrack\text{ = ANTILOG (-pH)}[/tex]Finally, we have the calculation as follows:
[tex]\lbrack H_3O^+\rbrack\text{ = antilog(-5.3) = }0.000005011872[/tex]In the scientific form,we have this as:
[tex]5.0\text{ }\times10^{-6\text{ }}moles\text{ per liter}[/tex]
Instructions: Write the function in slope-intercept form that represents the given. The roasting guide for a turkey suggests cooking for 100 minutes plus an additional 8 minutes per pound (x). Write the equation for total cooking time in terms of pounds of turkey.
Answers
Answer:
y = 8x + 100
Explanation:
Let us call the total cooking time y and the x the number of pounds of turkey, then we know that the roasing guid
In circle C with m BCD= 48°, find the angle measure of minor arc BD.DB
Answers
Notice that angle BCD is a central angle, therefore, the measure of its arc will be the same as the measure of the angle, therefore, the measure of the minor arc BD is 48 degrees
Lucille wrote three numbers between 0.75 and 0.76 what numbers could she have written?
Answers
As an answer to this question, any decimal between 0.75 and 0.76 will do.
So let us choose the three numbers at random.
0.751 , 0.754, and 0.756 will do.
A club that has 20 members is selecting a 5 representatives to send to a national conference. How many different groups of 5 can there be?
Answers
There can be a total of 15504 groups of selection
How to determine the groups of selection?From the question, we have
Total number of persons, n = 20
Numbers to selection, r = 5 i.e. the committee members
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 20 and r = 5
Substitute the known values in the above equation
Total = ²⁰C₅
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 20!/15!5!
Evaluate
Total = 15504
Hence, the number of ways is 15504
Read more about combination at
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Answer:
There can be 4 groups of 5.
PLEASE HELP ME ASAP PLEASE PLEASE PLEASE
jaren is selling lampshades at a craft fair. for the price per lampshade in dollars is f (x) and it is a function of the
Number of lampshades bought as shown by the graph below. What is the total cost of buying 10 lampshades from Janet's stall
Answers
According to the graphic the total cost of buying 10 lampshades is 8 dollars
in pqr, what is the measurement of angle Q? 200 degrees871059010
Answers
In the triangle PQR we know that its angles have the following measures:
∠P=(6x+5)º
∠Q=(11x-5)º
∠R=xº
To determine the measures of ∠Q, you have to determine the value of x first. To do so you have to keep in mind that the measure of the inner angles of any triangle is 180º, so, for this triangle, the measure of the inner angles can be expressed as:
[tex]\begin{gathered} \angle P+\angle Q+\angle R=180º \\ (6x+5)+(11x-5)+x=180º \end{gathered}[/tex]From this expression, we can calculate the value of x.
-First, take the parentheses away, order the like terms together and simplify them:
[tex]\begin{gathered} 6x+11x+x+5-5=180º \\ 18x=180º \end{gathered}[/tex]-Second, divide both sides by 18 to determine the value of x:
[tex]\begin{gathered} \frac{18x}{18}=\frac{180}{18} \\ x=10 \end{gathered}[/tex]Now that we know that the value of x is 10º, we can determine the measure of ∠Q by replacing this value on the given expression for its measure:
[tex]\begin{gathered} \angle Q=11x-5 \\ \angle Q=11\cdot10-5 \\ \angle Q=110-5 \\ \angle Q=105º \end{gathered}[/tex]∠Q=105º, the correct option is the third one.
A 33-ft ladder leans against a building so that the angle between the ground and the ladder is 85°.how high does the ladder reach on the building ?
Answers
We have the next situation:
Now, we need to label the sides:
- The largest side is always the hypotenuse
- The adjacent side is between the right angle and the given angle.
- The opposite side is opposite to the given angle.
Hence,
Hypotenuse = 33 ftt
Opposite side = h
Then, we need to find h:
We need to use a trigonometric function that involves the side that we know and the missing side:
So,
sinθ = opposite side / hypotenuse
Replacing:
Sin85 = 33ft / h
Solve for h:
h= 33ft¨*sin 85
h= 32.87
The answer is 32.87
List the potential rational zeros of the polynomial function. Do not find the zeros.f(x) = -4x^4 + 2x^2 - 3x + 6A± , ± , ± , ± , ± 1, ± 2, ± 3, ± 4, ± 6B± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6C± , ± , ± , ± , ± , ± 1, ± 2, ± 4D± , ± , ± , ± , ± , ± 1, ± 2, ± 3, ± 6
Answers
Answer:
±1,±2,±3 and ±6
Explanation:
We make use of the Rational Zero theorem below:
If a polynomial has integer coefficients, then every rational zero of f(x) has the form p/q where p is a factor of the constant term and q is a factor of the leading coefficient.
Given the function:
[tex]f\mleft(x\mright)=-4x^4+2x^2-3x+6[/tex]The steps to follow are given below.
Step 1: Determine all factors of the constant term and all factors of the leading coefficient.
The constant term is 6: Factors are ±1,±2,±3 and ±6
The leading coefficient is -4: Factors are ±1,±2, and ±4.
Step 2: Determine all possible values of p/q.
[tex]\begin{gathered} \frac{p}{q}=\pm\frac{1}{1},\pm\frac{2}{1},\pm\frac{2}{2},\pm\frac{3}{1},\pm\frac{6}{1},\pm\frac{6}{2} \\ =\pm1,\pm2,\pm1,\pm3,\pm6,\pm3 \\ =\pm1,\pm2,\pm3,\pm6 \end{gathered}[/tex]Therefore, the potential zeros are: ±1,±2,±3 and ±6.
The bakery you choose cost $1000 per month to rent. The bakery that you almost rented was one fourth for the cost but was too small how much was the other bakery per month PLEASE HELPthis would be for a fifth grader and they have to show how they come up with the answer he would have to use the same scenario on multiple questions like this
Answers
The bakery you choose cost $1000 per month.
The bakery that you almost rented was one fourth for the cost: 1/4 of $1000.
When you have a fraction of a quantity you have to multiply the fraction by the value. Doing so, we have:
[tex]\begin{gathered} \frac{1}{4}\cdot1000 \\ \frac{1}{4}\cdot\frac{1000}{1}\text{ (Converting 1000 to a fraction)} \\ \frac{1000}{4}\text{ (Multiplying the numerators and then the denominators)} \\ 250\text{ (Dividing)} \\ \text{The answer is \$250} \end{gathered}[/tex]solve equation. -2(y-1)=9
Answers
y = -7/2
Explanation:-2(y-1)=9
expand the bracket:
-2 × y -2 × -1 = 9
-2y + 2 = 9
collect like terms:
-2y = 9 -2
-2y = 7
Divide both sides by -2:
-2y/-2 = 7/-2
y = -7/2
Help !!!! Please asap
Answers
Looking at the graph, the domain is:
[3, ♾️)
This is the case because the graph begins at 3, hence it is a defined starting point, and so brackets are used to indicate this.
Looking at the graph, the range is:
(-♾️, ♾️)
This is the case because the graph rises towards infinity as the x-coordinates become greater than 3. At the x-coordinate x=3, the graph extends infinitely downwards, and thus the graph extends upwards and downwards towards positive and negative infinity. Also note that infinity is a concept, not a defined point, so we use parentheses to indicate this.
2.) Your unusual boss decided to offer you a fourthoption to complicate your decision.Your payment would be described by the functionP(x) = 95,000x + 200,000, with x representingdays you work and P representing dollars you earn.Explain the meaning of the function based on thissituation and then decide if you would take this optionover the other three choices.On the next slide, you use a graph to support yourdecision.
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P(x) = 95,000x + 200,000
5 lb of apples cost $8.20. How much is it for 1 lb?
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Marked angle 3 different ways
Answers
Answer:
where are question I don't understand this question
Question 1 of 10 The graphs below have the same shape. What is the equation of the red graph? w GE? F%= 3 - 74 G(X)
Answers
The equation of the red graph (Parabola) is g(x) = 1 – x².
The given graph is the graph of the parabolas.
We are given;
The equation of the blue graph (Parabola) is f(x) = 4 – x².
We need to find the equation of the red graph g(x).
Let's observe the graph;
All of the lines in the blue graph pass through point 4 on the graph. The same is true for the red line, except that they all pass through 1. As a result, we should alter the 4 in the blue line equation to a 1 to represent the red line.
The equation of the blue graph is:
f(x) = 4 – x²
Substitute 4 by 1;
p(x) = 1 – x² = g(x)
This is our required equation.
Thus, the equation of the red graph (Parabola) is g(x) = 1 – x².
To learn more about parabolas visit:
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Miranda has $100.00 in a saving account that earns 10 percent interest, compounded annually. what wull the balance be after 1 year round to the nearest cent
Answers
Solve for y. d = 5x + 5y 0 y = 5x-d 5 d-5.2 O Y = y = 5(d - 5x) o y Y d-5x 5
Answers
Given the equation:
[tex]d=5x+5y[/tex]Solve for y , which mean make y alone on the left side.
So,
[tex]5y=d-5x[/tex]Divide the equation by 5
[tex]y=\frac{d-5x}{5}[/tex]The answer is the last option
A piece of wire 5/4 m long is to be cut into 20 pieces of the same length. What is the length of each piece?Each piece is ____ m long.(Simplify your answer. Type an integer or a fraction.)
Answers
When we divide a fraction by a number, that's equivalent to multiplying the first fraction by the inverse of that number.
In this problem, we need to divide the fraction 5/4 by 20. So we obtain:
[tex]\frac{5}{4}\colon20=\frac{5}{4}\cdot\frac{1}{20}[/tex]Now, we need to multiply the numerator of the first fraction by the numerator of the second one, and the denominator of the first fraction by the denominators of the second one:
[tex]\frac{5}{4}\cdot\frac{1}{20}=\frac{5\cdot1}{4\cdot20}=\frac{5}{80}[/tex]Now, we need to simplify the answer. To do so, we can divide both the numerator and the denominator by 5:
[tex]\frac{5\colon5}{80\colon5}=\frac{1}{16}[/tex]Therefore:
Each piece is 1/16 m long.
I don’t understand the question its asking for the depth at 4 weeks and 9 weeks
Answers
Answer
Lake depth after 4 weeks: 343.6 ft
Lake depth after 9 weeks: 340.6 ft
Step-by-step explanation
The relation between time and lake depth is linear. Using the x-variable to represent time and the y-variable to represent the lake depth, we can use the next equation to relate these variables:
[tex]y=mx+b[/tex]where m is the slope and (0, b) is the y-intercept of the line.
The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the table, this line passes through (0, 346) and (2, 344.8), then its slope is:
[tex]m=\frac{344.8-346}{2-0}=\frac{-1.2}{2}=-0.6[/tex]From the table, this line passes through (0, 346), then parameter b is 346.
Substituting m = -0.6 and b = 346, the equation of the line is:
[tex]y=-0.6x+346[/tex]Evaluating this line at x = 4, that is, when time = 4 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(4)+346 \\ y=-2.4+346 \\ y=343.6\text{ ft} \end{gathered}[/tex]Evaluating the equation of the line at x = 9, that is, when time = 9 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(9)+346 \\ y=-5.4+346 \\ y=340.6\text{ ft} \end{gathered}[/tex]