Pretest: Unit 2
Question 34 of 45
If WXWZ, which of the following statements CANNOT be true?

Answer:

135 ft^3

Step-by-step explanation:

The volume of a cone is [tex]\frac{1}{3} \pi r^{2}h[/tex]. The radius is 4 and the height is 8, so these values can be plugged in:

[tex]V = \frac{1}{3} \pi \times 4^{2} \times 8[/tex]

[tex]V = \frac{128\pi }{3}[/tex]

This is about 134.041286553 which rounds to 135 ft^3.

Answer:

-7/2 or 2 are inputs that give 19 as output.

Step-by-step explanation:

The problem gives us a quadratic function [tex]\displaystyle \large{f(x)=2x^2+3x+5}[/tex]. When its output is 19, we want to know the input value(s).

Since an output which is f(x) = 19. Therefore:

[tex]\displaystyle \large{19=2x^2+3x+5}[/tex]

Rearrange the expression in quadratic equation.

[tex]\displaystyle \large{0=2x^2+3x+5-19}\\\\\displaystyle \large{0=2x^2+3x-14}\\\\\displaystyle \large{2x^2+3x-14=0}[/tex]

Factor the expression.

[tex]\displaystyle \large{(2x+7)(x-2)=0}[/tex]

Solve like linear equation which we get:

[tex]\displaystyle \large{x=-\dfrac{7}{2}, 2}[/tex]

If you input these x-values in the function, you will get 19 as the output which satisfies the condition.

Hence, inputs are -7/2, 2

Answer:

[tex]x=2, \quad x=-\dfrac{7}{2}[/tex]

Step-by-step explanation:

Set the function to 19:

[tex]\implies 2x^2+3x+5=19[/tex]

Subtract 19 from both sides:

[tex]\implies 2x^2+3x-14=0[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex]

Find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:  7 and -4

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 2x^2-4x+7x-14=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 2x(x-2)+7(x-2)=0[/tex]

Factor out the common term (x - 2):

[tex]\implies (2x+7)(x-2)=0[/tex]

Therefore the function's input values that when evaluated give a value of 19 are:

[tex](2x+7)=0 \implies x=-\dfrac{7}{2}[/tex]

[tex](x-2)=0 \implies x=2[/tex]

Answer: (2,-2)

Step-by-step explanation:

Rotating 90 degrees counterclockwise (about the origin) maps (x,y) onto (-y,x), so the answer is N'(2,-2)

Answer:

Step-by-step explanation:

follow the formula in the picture

Area = b * h

Area = 15 * 8

Area = 120 in²

Answer: C) 2.4

Given one opposite angle, two known sides and one missing side.

Hence use cosine rule:

[tex]\sf c = \sqrt{a^2 + b^2- 2ab \ cos\theta}[/tex]

insert values

[tex]\sf c = \sqrt{1.2^2 + 1.4^2- 2(1.2)(1.4) \ cos(134)}[/tex]

simplify

[tex]\sf c = 2.3945 \quad \approx \quad 2.4[/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The name of the expression under the radical symbol in a radical function is called a radicand.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The radical is the symbol that is used to represent the root in the expression n√x. The name of the expression under the radical symbol in a radical function is called a radicand.

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Answer:

7a^3-7a+1

Step-by-step explanation:

(7a³-2a-2) + (-5a + 3) =

Combine like terms

7a^3-2a-5a-2+3

7a^3-7a+1

Answer: [tex]\frac{4}{15}[/tex] of the pizza was left

Step-by-step explanation:

lets first get the denominators the same..

[tex]\frac{1}{3} = \frac{5}{15}[/tex]

[tex]\frac{2}{5} = \frac{6}{15}[/tex]

To find the total pizza eaten we add these two fractions

[tex]\frac{5}{15} +\frac{6}{15} =\frac{11}{15}[/tex]

we can think of [tex]\frac{15}{15}[/tex] as 1 pizza because it simplifies to 1

[tex]\frac{15}{15} -\frac{11}{15} =\frac{4}{15}[/tex]

Therefore, [tex]\frac{4}{15}[/tex] of the pizza was left

Answer:Amount left=4/15

Step-by-step explanation:

The solution is in the image

Answer:

0+1

Step-by-step explanat

Any two consecutive number in which the greater number is positive and smaller number is negative will give the sum of 1.

The result we get after adding some quantity is called the sum of the data.

Given we need to find two numbers whose sum is 1,

So, we can consider in this case two consecutive numbers of opposite sign the greater number should have a positive sign and the smaller number should have negative sign,

For example =

-4+5 = 1

-3+4 = 1

-2+3 = 1

-9+10 = 1

So, any two consecutive number in which the greater number is positive and smaller number is negative will give the sum of 1.

Hence, there can be many numbers which can give sum of 1.

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The measure of BD and BC are 7 and 7√2 respectively

A triangle is a shape with 3 sides and angles.

According to the theorem

CD/BD = BD/DA

From the given figure

CD = DA  = 14/2

CD = DA = 7

Substitute

7/BD = BD/7

BD² = 7²

BD² = 49
BD = 7

Determine the measure of BC

sin 45 = BD/BC
sin45 = 7/BC
BC = 7/sin45

BC = 7√2

Hence the measure of BD and BC are 7 and 7√2 respectively

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Answer:

31.4 in

Step-by-step explanation:

The circumference of of a circle given the diameter is πd :

C = π×d = 10π = 31.4159....

C ≈ 31.4

The units will still be in as this is a length not an area .

Hope this helped and brainliest please

40

Step-by-step explanation:

[tex]{ \red{ \tt{given \: }}} \: :- \: { \green{ \tt{x = - 3}}}[/tex]

Then, Substitute the value of "x" in this below equation..

[tex]{ \orange{ \tt{ {x}^{2} - 7x + 10}}}[/tex]

[tex]{ \orange{ \tt{ {( - 3)}^{2} - 7( - 3) + 10}}}[/tex]

[tex]{ \orange{ \tt{9}}} \: + \: { \orange{ \tt{21}}} \: + \: { \orange{ \tt{10}}}[/tex]

[tex] = { \orange{ \tt{40}}}[/tex]

The ratio of the lengths of and is 1: 1

PQ parallel to RS

PR and PS; perpendicular to PQ and RS.

Perpendicular lines are lines that intersect at a 90 degrees angle. Parallel lines are lines that are always the same distance apart.

FOR parallel lines, the perpendicular line joining then is always the same; here the 4 angles formed are all 90°

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The equation which has the correct sign on the product is 27(-5) = -135

- × - = +

- × + = -

+ × - = -

+ × + = +

Given equations:

27(-5) = -135

(-4)(-4) = -16

(-61) (3) = 183

22 × 4 = -88

Correct equation:

27(-5) = -135

(-4)(-4) = 16

(-61) (3) = -183

22 × 4 = 88

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Answer:

2) d. 60°

3) a. AB

Step-by-step explanation:

Question 2

ΔABC and ΔCDA are congruent because:

This means the corresponding side lengths and angles are equal.

Therefore,

∠CDA = ∠ABC

⇒ x = 60°

Question 3

The hypotenuse is the longest side of a right triangle - the side opposite the right angle (the right angle is shown as a small square).

Therefore, the hypotenuse of ΔABC is the line AB.

Based on this construction, the value of m∠ABC is 64°.

From the point, E and D, two arcs are made which are intersecting each other at point P.

It means, that line BP is the bisector of angle ABC. ABC will be:

= 2 * 32=64

Therefore, based on this construction, the value of m∠ABC is 64°.

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Step-by-step explanation:

draw the graph then use the graph to answer the following questions

Answer:

dividing a company's yearly accounts receivable balance by its yearly total net sales

Answer:

the orange one

Step-by-step explanation:

(10 + 10) : (5-3) =

20 : 2 =

10

Answer:

2(19x - 1)

Step-by-step explanation:

The GCF of 38 and 8 is 2 :

Now we take a common factor of 2 :

2(19x - 1)

Hope this helped and have a good day

Answer:
2(19x-4)

The gcf of 38 and 8 is 2 so factor it out.

Answer:

4 8 1 4 0,683 the (783)-213=509

The equation which is used to find the value of c will be c = 5/Cos 35

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

We are given the following

m<ACB = 90degrees

m<ABC = 35degrees

The side opposite to m<ABC is AC

BA = hypotenuse

CB = adjacent = 5inches

Required

The equation to solve BA which is c

Using the Pythagoras theorem;

Cos Ф = Adjacent/Hypotenuse

Cos m<ABC = CB/BA

Cos m<ABC = 5/c

c = 5/cosm<ABC

c = 5/Cos 35

Hence the equation that can be used to solve for c is c = 5/Cos 35

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Mitra used 156 white tiles of 2x2 cm and 76 black tiles of 2x3 cm to form a pattern with an area of 1092 cm²

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of white tiles and y represent the number of black tiles.

Area of white tiles = 2 cm * 2 cm = 4 cm²

Area of black tiles = 2 cm * 3 cm = 6 cm²

She used twice as many white tiles as black tiles. Hence:

x = 2y   (1)

Also, the finished pattern was 1092 square centimeters in area. Hence:

4x + 6y = 1092   (2)

From both equations:

x = 156, y = 78

Mitra used 156 white tiles of 2x2 cm and 76 black tiles of 2x3 cm to form a pattern with an area of 1092 cm²

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Answer:

y=x^(2)+10x+11,y=x^(2)+x-7

Step-by-step explanation:

I think so bro

Step-by-step explanation:

I assume you mean

y = x² + 10x + 11

y = x² + x - 7

well, I subtract equation 2 from equation 1 :

0 = 9x + 18

9x = -18

x = -2

y = x² + x - 7 = (-2)² - 2 - 7 = 4 - 2 - 7 = -5

the solution (the intersection point of both graphs) is the point (-2, -5).

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$8000\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &2 \end{cases} \\\\\\ 8000=5000[1+(\frac{r}{100})(2)]\implies \cfrac{8000}{5000}=1+\cfrac{r}{50}\implies \cfrac{8}{5}=1+\cfrac{r}{50} \\\\\\ \cfrac{8}{5}-1=\cfrac{r}{50}\implies \cfrac{3}{5}=\cfrac{r}{50}\implies \cfrac{3(50)}{5}=r\implies 30=r[/tex]

Reason:

There are 4 outcomes we don't want (rolling 1,2,3 or 4) and 2 outcomes we do want (rolling 5 or 6)

This gives the odds against ratio of 4:2 or 2:1

This can be written out as "2 to 1" or "two to one".

Having 2 to 1 odds means that we're twice as likely to get something we don't want vs something we do want.

Side note: the odds in favor will have us flip the ratio.